a mathematical model for the starting process of a
TRANSCRIPT
AEDC-TR-76-39
A MATHEMATICAL MODEL FOR THE STARTING PROCESS
OF A TRANSONIC LUDWlEG TUBE WIND TUNNEL
t I
VON KARMAN GAS DYNAMICS FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER
AIR FORCE SYSTEMS COMMAND ARNOLD AIR FORCE STATION, TENNESSEE 37389
June 1976
Final Report for Period July 1974 - April 1975
I Approved for public release; distribution uniimited, l
Prepared for
DIRECTORATE OF TECHNOLOGY (DY) ARNOLD ENGINEERING DEVELOPMENT CENTER ARNOLD AIR FORCE STATION, TENNESSEE 37389
NOTICES
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This report has been reviewed by the Information Office (OI) and is releasable to the National Technical Information Service (NTIS). I t NTIS, it will be available to the general public, including foreign nations.
APPROVAL STATEMENT
This technical report has been reviewed and is approved for publication.
FOR THE COMMANDER
MARION L. LISTER Research & Development
Division Directorate of Technology
o
ROBERT O. DIETZ Director of Technology
UNCLASSIFIED REPORT DOCUMENTATION PAGE READ INSTRUCTIONS
BEFORE COMPLETING FORM I. REPORT NUMBER 12. GOVT ACCESSION NO. 3. RECIPIEN'''S CATALOG NUMBER
AEDC-TR-76-39
4. TITLE (and Subtitle) 5. TYPE OF REPORT /I PERIOD COVERED
STARTING Final Report - July 1974 A MATHEMATICAL MODEL FOR THE April 1975 PROCESS OF A TRANSONIC LUDWIEG TUBE WIND TUNNEL 6. PERFORMING ORG. REPORT NUMBER
7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(s)
Frederick L. Shope - ARO, Inc.
9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK
Arnold Engineering Development Center (DY) AREA II WORK UNIT NUMBERS
Air Force Systems Command Program Element 65807F Arnold Air Force Station, Tennessee 37389 II. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
Arnold Engineering Development Center (DYFS) June 1976 Air Force Systems Command 13. NUMBER OF PAGES
Arnold Air Force Station, Tennessee 37389 134 14. MONITORING AGENCY NAME II ADDRESS(iI dillerent Irom ControlllnS Olliee) 15. SECURITY CLASS. (01 thl. report)
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Approved for public release; distribution unlimited.
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lB. SUPPLEMENTARY NOTES
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19. KEY WORDS (Continue on reverse side if necessary and JdentJ/y by block number)
mathematical models test facilities transonic flow Reynolds number wind tunnels aerodynamics
20. ABSTRACT (Continue on reverse side If necessary and Identify by block number)
A simplified mathematical model is presented for the unsteady flow process of starting a transonic Ludwieg tube wind tunnel. The hardware modeled consists of a porous-walled test section surrounded by a plenum chamber with an exhaust system independent of the tun-nel's main starting valves, which are located downstream of the diffuser-test section. In the present method, the hardware is modeled as three control volumes: the plenum, the test section,
DD FORM I JAN 73 1473 EDITION OF I NOV 65 IS OBSOLETE
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20. ABSTRACT (Continued)
and the diffuser. The plenum is treated with the unsteady integral continuity equation with one-dimensional influx or outflux through the porous wall, through the plenum exhaust system, and through the flaps, which exhaust into the diffuser. The other two control volumes are treated with the steady integral continuity equation and a steady, adiabatic, one-dimensional energy equation whose stagnation conditions vary in time according to the classical solution for an unsteady expansion wave. Numerical solutions are compared with experimental pressure-time histories of a small, transonic, high Reynolds number tunnel referred to as HIRT. Agreement between the model and experiment is good.
AFSC Arnold AFS Tenn
UNCLASSIFIED
AEDC-TR-76-39
PREFACE
The work reported herein was conducted by the Arnold Engineering Development Center (AEDC), Air Force Systems Command (AFSC), under Program Element 65807F. The results were obtained by ARO, Inc. (a subsidiary of Sverdrup & Parcel and Associates, Inc.), contract operator of AEDC, AFSC, Arnold Air Force Station, Tennessee. The research was done under ARO Project No. V37 A-32A in support of the High Reynolds Number
Wind Tunnel (HIRT) project. The author of this report was Frederick L. Shope, ARO, Inc. The manuscript (ARO Control No. ARO-VKF-TR-75-147) was submitted for publication on September 26, 1975.
The author wishes to acknowledge R. F. Starr and M. 0. Varner for their many helpful discussions and the fruitful suggestions they made during the course of this effort.
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CONTENTS
1.0 INTRODUCTION ............................. .. 2.0 THE MATHEMATICAL MODEL
2.l Description of the Physical Situation to be Modeled
2.2 Goal of the Modeling
2.3 Formal Assumptions
2.4 Mathematical Formulation
2.5 Solution Procedure
3.0 RESULTS 3.l Description of Pilot Hardware ...... .
3.2 Comparison of Math Model and Experiment
3.3 Other Results from the Math Model
3.4 Application of the Math Model 4.0 SUMMARY AND CONCLUSIONS
REFERENCES
ILLUSTRATIONS
Figure
1. Major Components of the High Reynolds Number Wind Tunnel 2. Schema tic Illustration of the Flow Process during Start
3. Qualitative Plot of the Energy Equation
4. Energy Dome versus Position in Test Section for
7
8
14
16
17 25
31
35 43
47
50
51
9 10
11
Normal Subsonic Flow .............................. 12
5. Energy Dome versus Position in Test Section for
Normal Supersonic Flow ........... . . ........... 12
6. Energy Dome versus Position in Test Section for Subsonic
Flow with Choked Nozzle ....... . . . . . . .. ............ 13
7. Porous Wall and Flap Flow Coefficients
a. Porous Wall Flow Coefficient versus Porosity (7) .............. 19
b. Ejector Flap Flow Coefficient versus Area
Ratio (Ad Ats) ....... 19 8. Wall Porosity in Pilot HIRT .......... 20
9. Flow Chart of Solution Procedure ...... 26
10. Logic for Numerical Solution of an Algebraic Equation Y = F(X) for X,
Given Y when X = F-l (Y) is not a Closed Form Function . . . . . . . . . . . . 27
3
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Figure
11. Plenum Pressure versus Iteration Number for Convergent
and Divergent Cases .................. .
12. Pilot HIRT Elevation Line Drawing .......... .
13. Cross-Sectional View of Nozzle, Test Section, Diffuser, and
Main Valve System .................... . 14. Plenum Exhaust System 15. Plenum Pressure versus Time for Subsonic Run with Medium
29
32
33
34
Plenum Volume ...................... ........... 37 16. Plenum Pressure versus Time for Subsonic Run with Small
Plenum Volume ............ 38 17. Plenum Pressure versus Time for Subsonic Run with Large
Plenum Volume ..................... . 18. Plenum Exhaust Area-Time Curve for Mach 1.039 Run 19. Plenum Pressure versus Time for Supersonic Run (Mach 1.039)
with Plenum Exhaust 20. Plenum Pressure versus Time for Supersonic Run (Mach 1.228)
with Plenum Exhaust . . . . . . . . ~ . . . . . . . . . . . . 21. Plenum Pressure versus Time for Supersonic Run with Sliding
38 39
......... 39
......... 40
Sleeve Valve and Plenum Exhaust . . . . . . . . . . . . . . . . ...... 41 22. Plenum Pressure versus Time for Supersonic Run with I-I/2-percent
Porosity and No Plenum Exhaust ......................... 41 23. Plenum Pressure versus Time for Subsonic Run with Small
Flap Setting .................................... 42 24. Plenum Pressure versus Time for Subsonic Run with Large
Flap Setting ...................... 42 25. Various Pressures versus Time for Nominal Conditions 44 26. Various Pressures versus Time for Supersonic Run with
Plenum Exhaust .....,.............. ....... 44 27. Steady-State Values of Correction Coefficients, A15 and Al6
a. Momentum Correction Coefficient (AI 5) and Flap Correction
Coefficient (AI 6 ) versus Steady Test Section Mach Number ....... 45 b. Assumed Variation with Test Section Mach Number (Md) of
Momentum (AI 5) and Flap (AI6) Correction Coefficients during Starting Process .................
28. Relative Theoretical Mass Flow Rate for Nominal Conditions ......... 45
(Run 2258) of Subsonic Flow with No Plenum Exhaust . . . . . . . . . . 46 29. Relative Mass Flow Rates for a Supersonic Run (Mach 1.228)
with Plenum Exhaust (Run 2255) ........................ 47
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Figure
30. Nondimensional Equal Area Plenum Exhaust Area-Time Curves 48 31. Plenum Pressures versus Time for Three Plenum Exhaust Area-Time
Curves with Same Integrated Area ............ . ....... 49
32. Transient Loading of Test Section Wall at Exit for Nominal
Conditions and Selected Deviations ........... 50
TABLES
1. List of Exact Simultaneous Equations . . . . . . . . . . . . . . . . . . . 23 2. Geometric Data for Pilot HIRT Required by
Mathematical Model ............... 34 3. Summary of Run Conditions for Experimental Data
to be Compared with Theory ......... . .............. 36
APPENDIXES
A. SMALL PERTURBATION SOLUTION 53
B. APPROXIMATED EQUATIONS 56
C. DESCRIPTION OF THE COMPUTER PROGRAM HIRTSMl 57
NOMENCLATURE 133
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1.0 INTRODUCTION
This report documents an effort to mathematically model the aerodynamics involved in the unsteady process of starting a Ludwieg Tube wind tunnel. In essence, the model represents the end product of many people assimilating a large amount of experimental data obtained from a transonic Ludwieg tube facility and, thus, depends on several experimentally derived parameters and assumptions. The wind tunnel configuratibn studied here consists of a very long, circular supply tube which contracts to a rectangular, porous-walled test section. The test section expands through a diffuser into a valve manifold. Surrounding the test section is a plenum chamber with exhaust valves which can be controlled independently of the main valves. In addition, the plenum contains a set of ejector flaps which allow the plenum to exhaust itself into the diffuser.
When one considers that larger scale transonic Ludwieg tube facilities would have a price of order $10,000,000 and would produce a usable run time of only a few seconds per run, it is clear that considerable effort must be concentrated to ensure that the tunnel can be started rapidly under a wide range of operating conditions. A laboratory scale pilot facility (Ref. 1) (known as "Pilot HIRT") at Arnold Engineering Development Center provides an experimental vehicle to measure the effects of many of the important parameters in the tunnel starting process and to provide basic experimental data for verification of math models.
To clarify the need for a mathematical model of starting such a device, a brief explanation of the tunnel operation is required. Prior to a run, the tunnel is pumped to the desired charge pressure and temperature. A tunnel run is initiated by first opening the main valves downstream of the diffuser. This opening process sends unsteady expansion waves up the tunnel to the supply tube. Were it not for the plenum, the flow in the test section would become steady soon after the trailing edge of the unsteady wave from the valve, initiated by the valve area becoming steady, passed the test section into the supply tube. The test section flow cannot become steady until the plenum volume has been exhausted to the point where the summation of mass flow across the porous wall, through the flaps, and out the plenum exhaust (dumped to atmosphere) becomes zero and allows the plenum pressure to become steady. Since current state-of-the-art fast-opening valves easily reach the required flow area in advance of the plenum becomin~ steady, the plenum is the primary limitation upon how quickly the tunnel can be started and steady flow established in the test section.
The present model assumes that the unsteady expansion wave emanating from the main valves propagates instantaneously to all parts of the wind tunnel and that property variation within the wave at any location in the diffuser, test section, nozzle, or supply tube is totally controlled by the area-time curve of the main valve. While partially retaining
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the effect of the unsteady wave, this assumption allows use of the steady continuity equation in the test section coupled with the well-known exact solution for one-dimensional, variable area, isentropic flow (Ref. 2). Use of these equations at any instant requires a knowledge of stagnation conditions driving the flow, which vary through the nonisentropic expansion wave. Variation of the stagnation properties is computed via the exact solution for a one-dimensional unsteady wave in a variable area duct (Ref. 3). The unsteadiness of the plenum is handled via the unsteady continuity equation by equating the rate of mass accumulation in the plenum to the summation of all the flow rates entering and leaving the plenum. The air in the plenum is assumed to be a calorically perfect gas and its temperature is assumed either isentropic or equal to the stagnation temperature of the flow in the test section (whichever is greater), an experimentally based assumption. The main valves are treated as one-dimensional sonic orifices driven by the stagnation pressure and temperature of the unsteady wave. The plenum exhaust valves are handled similarly by assuming that the flow in the plenum is stagnant. Flow through the ejector flaps and across the porous wall is computed via an adaptation of the work of Ref. 4, which empirically corrected the flow rates with the pressure drops across these
devices.
In the discussion which follows, the mathematical model will first be presented, including a more detailed description of the physical situation, the assumptions underlying the model, the mathematical formulation, and the solution procedure. Next, the model will be compared with a sample of experimental data from the Pilot HIRT facility. The appendixes contain some of the mathematical details and a brief user's manual for the computer program.
2.0 THE MATHEMATICAL MODEL
2.1 DESCRIPTION OF THE PHYSICAL SITUATION TO BE MODELED
A11 of the essential features of the proposed HIR T facility which are to be modeled are given in Fig. 1. The overall length of the facility is 1,880 ft, and the supply tube has an inside diameter of 15 ft. The main valve system consists of a number of fast-acting valves, and the plenum exhaust also requires a multiple valve system. The pilot facility provides a precisely scaled (1/13) flow envelope but has a single sliding sleeve valve in place of the valve manifold of the full-scale tunnel and a single plenum exhaust valve fed by multiple tubes from the plenum.
A tunnel run is initiated by opening the main valves and possibly the plenum valves, not necessarily together or in the same length of time. Both sets of valves send nonisentropic expansion waves throughout the tunnel and primarily up the charge tube. The main valve system produces the steepest (or strongest) wave because it handles a much greater portion
8
Main Valves
Valve Manifold Diffuser
AEDC-TR-76-39
II Plenum Exhaust Valves
Test Section
~ppDY Tube
~------'l
Nozzle
Porous Test Section Walls
Figure 1. Major components of the High Reynolds Number Wind Tunnel.
of the flow rate than the plenum exhaust. At any point in the supply tube, the gas remains totally stagnant until the first expansion wave reaches that point; and the flow at that point does not become steady until the last expansion wave passes the point. The main valve system sends out its last expansion wave when the flow area becomes constant. The' plenum also continues to send out expansion (and sometimes compression) waves until the plenum pressure becomes steady. But the plenum does not become steady until the sum of all the flows into and out of it are zero (Fig. 2), and it invariably controls the start time of the tunnel. Since the main valves are much faster than the plenum response, the pressure in the test section drops rapidly below the plenum pressure, causing mass flow to enter the test section from the plenum. As the plenum gradually catches up to the test section, the wall crossflow (across the porous test section wall) gradually decreases and, in some cases, reverses. This process, coupled with the increasing main valve area, gradually increases the flow rate drawn from the supply tube. However, the flow rate from the tube may continue to increase only until the nozzle exit becomes choked, after which the supply tube flow becomes steady since the choke point will no longer pass additional expansion or compression waves (unless the compression wave is strong enough to unchoke the nozzle). Whether the nozzle eventually chokes and whether the test section eventually steadies out to supersonic or subsonic flow depends on the relative flow areas of the main valves, the plenum exhaust valves, and the test section, the direction of the flap and wall crossflows, and how the various steady conditions are approached in time relative to each other. Subsonic and very slightly supersonic test section Mach numbers can be obtained without steady-state plenum exhaust, though the plenum exhaust may be opened temporarily and then closed in order to reduce the starting time. For subsonic flows, the steady main valve area - in terms of the ideal, one-dimensional area
9
AEDC-TR-76-39
at the choke point - must be as much less than the nozzle area (where the nozzle meets the entrance to the test section) as is dictated by the steady test section Mach number to be attained (neglecting diffuser losses). A slightly supersonic test section can be obtained with a steady main valve area greater than or equal to the nozzle area if the flaps and porosity are set properly, giving a flow situation as follows: with the nozzle choked and the plenum steadied at a pressure very near the static test section pressure such that the static pressure and dynamic heads of the main flow force a small crossflow into the plenum, the net test section flow decreases from the choked flow rate at the nozzle. The slightly sub critical flow rate leaving the test section thus produces a slightly supersonic condition, resulting in a favorable pressure gradient for the plenum to exhaust its incoming crossflow out the flaps and hence become steady. Normally, however, supersonic conditions (up to Mach 1.3 in the pilot) are obtained by having the plenum exhaust area become steady at a flow area sufficient to pass all of the mass flow rate entering the plenum via wall crossflow and sometimes via reverse flap flow.
Plenum Control Volume
Test Section Control Vol u me
Pet ' Tet ' Pet o 0 0
(Stagnation Conditions)
P e ' Te ' P e (Stag nation Conditions) o 0 0
Figure 2. Schematic illustration of the flow process during start.
To understand the flow in terms of the mathematical model, the various flow configurations might be best thought of in terms of the steady energy equation relating the local pressure to the mass flux (Fig. 3). Subsonic flows fall on the branch to the
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right of the choke point, supersonic flows to the left. In general, all points in the tunnel
are initially at point A, which corresponds to no flow. Higher flow rates with correspondingly lower static pressures are illustrated by movement from point A to B
Choke Point
1.0 ---------* 'E --'E x· :J rr:: VI VI ro :z: c:: 0 VI c:: Supersonic Subsonic CI.> E "0 c:: 0 Z
0 0 1.0 P IPr>
P/P* 0
Nondi me ns ional Press ure,
Figure 3. Qualitative plot of the energy equation.
on the energy equation. Flows which become subsonically steady would halt to the right of C; while for supersonic flows, some portions of the tunnel would proceed beyond C to D. If the energy dome is then plotted versus axial position in the test section as shown in Figs. 4, 5, and 6, the importance of the wall crossflow and the relative timewise approach of various components to their steady conditions may be made clearer. For a normal subsonic run, Fig. 4 shows the energy dome at the entrance and exit of the test section. The constant time contours are shown as straight lines for purposes of illustration, though in reality they would have to be nonlinear to some degree in order for all points on the contour to fall on the surface of the dome cylinder and because the wall crossflow does not necessarily vary linearly along the test section. As the flow begins, the constant time contours do not remain parallel because the flow rate leaving the test section will not balance that at the entrance, the difference being the wall crossflow. For the most probable case of the plenum lagging the test section pressure, the crossflow will be into the test section, giving a greater flow rate at the exit than at the entrance. As time proceeds, however, the plenum pressure eventually catches up to the test section
so that the contours do become nearly straight and parallel as the crossflow becomes insignificant. This process assumes that the plenum exhaust, if opened, is eventually closed.
11
A E DC-T R -76-39
* 'E -'E x' 1.0 ::J u:: en en m ::E ro c: .!2 en c: Q)
E :a c: 0 Z
0
" ·E 'E x' ::J 1.0 u:: en en C1:I
::E m c: .!2 en c: Q)
E :a c: 0 z
0
Steady, Uniform Subsonic Flow
1.0 Nondimensional Pressure, P/P*
t = 0
Figure 4. Energy dome versus position in test section for normal subsonic flow.
Steady, Supersonic Flow
Real Nonli near Steady contOUl
t = 0
1.0 Nondimensional Pressure, P/P*
Figure 5. Energy dome versus position in test section for normal supersonic flow.
12
tl
Exit
XIL
tl
Exit
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If the plenum exhaust is not closed and the steady main valve area is sufficiently large,
the supersonic case of Fig. 5 may result. The initial constant time contours are similar to the subsonic case. However, the odgins of the contours at the entrance eventually stop at the peak of the dome while at the exit they proceed over the choke point downward on the supersonic branch as the crossflow reverses from entering to leaving the test section. The contours, however well approximated by straight lines in the subsonic case, become significantly nonlinear for the higher supersonic Mach numbers, as illustrated by the dotted "real nonlinear steady contour'! in Fig. 5. This results from a combination of the nonlinear
vadation of the wall crossflow and boundary layer growth. These nonlinear effects, though certainly present in the subsonic case, are more pronounced in the supersonic case because the pressure at the nozzle must remain unchanged at the choke value while the pressure at the exit varies significantly with the exit Mach number.
* 'E --'E x-
1.0 ;;;:J
u:: III VI ro ::2: ro c:::: 0 III c:::: Q)
E :c
c:::: 0
Z
Actual Condition
Desired Condition
steady, Subsonic Flow
t = 0
Entrance
o 1.0 Nondimensional Pressure, P/P*
Figure 6. Energy dome versus position in test section for subsonic flow with choked nozzle.
The slopes of the constant time contours in Figs. 4 and 5 depend on the magnitude of the wall crossflow, which in turn depends partially on the pressure difference between the plenum and the test section. Since the timewise variation of the plenum pressure can be controlled by controlling the flow area-time curve of the plenum exhaust valves,
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it appears that the shortest starting time for the tunnel would be obtained by controlling
the plenum pressure to precisely follow the test section pressure so that the plenum would
reach its steady conditions simultaneously with the main valve system. This would result in the constant time contours remaining parallel right up to their final position, or up
to the choke point for a supersonic run. In Fig. 6, the plenum is exhausted fast enough
so that the wall cross flow is always out of the test section, resulting in less flow rate
leaving the exit of the test section than entering. Thus, the constant time contour at
the entrance dome reaches its peak while the point on the exit dome is forced by the
plenum exhaust to become steady before reaching the peak though the desired steady
condition lies on the other side of the dome and cannot be reached. Hence, it appears
that the manner in which the various portions of the tunnel approach their steady
conditions in time relative to each other can affect the final outcome of a run.
The foregoing discussion of the test section flow in terms of the energy domes serves as an introduction to one of the key elements of the mathematical model, namely, the
steady energy equation in an unsteady environment. The domes also provide graphic
visualization for the flow process.
2.2 GOAL OF THE MODELING
The purpose of this mathematical model is to study the starting process, controlled by the plenum, in order to size the plenum exhaust system; determine the effect upon start time of the interaction of the area-time curves of the main valves, flaps, and plenum exhaust; and, in general, to provide the essential information necessary for trading off
facility cost and start time. To provide this information, the model must accept the following input data. The gross level mass flow rate depends upon the cross-sectional
area of the supply tube and nozzle exit. The geometric factor, on which the wall crossflow primarily depends, is the porosity, the fraction of the total surface area of the test section
walls drilled out to allow flow between the test section and plenum. Thus, the dimensions
of the test sections and porosity must be provided along with the experimentally derived
coefficients for the flow model. A key design parameter having first-order impact on the start time is the plenum volume ratioed to the test section volume. The area-time curves
of the main valves, plenum exhaust valves, and the flaps are required along with the experimental coefficients for the flap flow model. Finally, the characteristics of the gas
must be provided in terms of the ideal gas constant and the specific heat ratio.
This input to the model is then used to compute the following data concerning the flow. As functions of time the static and stagnation properities - pressure, density, and temperature - along with mass flow rate and Mach number are computed for three stations
along the tunnel circuit: the supply tube at the nozzle entrance, the test section entrance,
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and the test section exit. The plenum properties along with the mass flux through the
porous wall, flaps, plenum exhaust, and main valves are computed as functions of time.
There are many other considerations, neglected herein, which might be of interest
for other applications. One of the most important is the boundary layer, whose growth on the walls of the supply tube and test section varies with time. This unsteadiness occurs because at any given station along the tunnel, the particles of air passing that station at succeeding times into the run have travelled over successively longer lengths of tube from their starting points. If the effect of the boundary-layer growth on the local mass flow rate is thought of in terms changing the effective flow area, one might suspect that
the test section would never become steady. In reality, however, the boundary-layer growth, sufficiently late in the starting process, varies with approximately the same proportion in the nozzle and test section so that, though the effective flow areas may be varying, the area ratios (AI A *) are not. As experimentally documented in Refs. I and 5, this results in essentially constant Mach number once the plenum has become steady, thus
justifying the neglect of the boundary layer herein.
Neglect of the boundary layer means that no prediction is made of property variation
over the cross section of the flow area. Similarly, detailed variation of properties along the length of the test section is not predicted. Such information would be useful for
studying wall loading or flow uniformity but is of secondary importance for present purposes. Very severe non uniformity occurs in the diffuser section (connecting the test
section and main valve manifold), which has been subjected to a detailed experimental
study in Ref. 4. The complexity of the diffuser flow results from a combination of effects: shock waves, flow separation, flap exhaust, and the presence of the model or probe support sector. The performance of the diffuser is important because of its effect on the noise environment in subsonic flow in the test section and because its stagnation losses significantly impact the sizing of the real flow area of the main valve system. However, for purposes of the starting model, diffuser losses may be neglected if the main valve area is assumed to be the ideal, one-dimensional flow area needed to pass a given mass flow rate for a given set of driving stagnation conditions as determined from wave mechanics.
Three additional effects neglected herein deserve mention. First, wave spreading is neglected. This phenomenon is due to the difference in propagation speed between the leading and trailing edges of the unsteady wave. Since the wave propagation speed (equal to the local speed of sound minus the local velocity) is less for the trailing edge than the leading edge, the time delay between a change in main valve area and the sensing of this change in the supply tube is greater for the last area change than the first. In
fact, this delay is different for each position along the tunnel. However, over the greatest
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distance of importance in the pilot facility, this difference in delay is less than 0.5 msec
and is neglected in the model. Besides wave spreading, the model also neglects the finite time required for a disturbance to travel from one point to another. Such a consideration is important for determining the relative times for first motion of main valves and plenum exhaust valves; but for purposes of the starting model, the tunnel components determining start time - plenum, test section, and supply tube exit - are sufficiently close together that the propagation times (on the order of one millisecond in the pilot) are small compared with the starting time under study. However, neglect of the propagation time and wave spreading should not be construed to mean that the finite wave width is neglected. This width, or time difference between passage of a given point of the leading and trailing edges of the wave, depends primarily on the opening time of the valve but is also increased by the nonideal flow processes in the diffuser. Such effects are a ccounted for herein by correction of the area-time curve of the main valve. A final additional effect, accounted for empirically but not modeled in detail, is the nonisentropicity of the thermodynamics of the plenum. It has been experimentally observed that the temperature in the plenum approximates an isentropic process only during the initial portion of the starting process, but over the entire start time for the tunnel, the asymptotic plenum temperature is much closer to the stagnation temperature in the test section than that for a completely isentropic expansion. A good model of this process would have to include the mixing of the virgin plenum air with that entering from the test section as well as account for the heat transfer from the walls of the plenum. This possible refinement to the present model is not yet
included.
2.3 FORMAL ASSUMPT!ONS
Before proceeding to the equations comprising the mathematical model, the following list of assumptions should be reviewed:
a. Flow across all control volume surfaces is one dimensional.
b. The fluid is assumed to be a calorically perfect gas (constant specific heats).
c. Flow within the envelope comprised of the supply tube, test section, and main valves is inviscid, adiabatic, and irrotational except as accounted for by the unsteady wave equations.
d. Within this envelope and at a constant time, property variation from point to point is isentropic. Entropy variation with time is governed by the wave equations. Thus, at any given instant, the one-dimensional, variable area, isentropic equations of gas dynamics (Ref. 2) are applicable.
16
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e. Wave propagation time and wave spreading are zero. This justifies the steady
assumption needed to invoke the equations of Ref. 2.
2.4 MATHEMATICAL FORMULATION
The set of equations comprising the model naturally divides into two groups, one for subsonic flow and one for supersonic flow. Since the set of equations for supersonic flow is nearly an exact subset of the subsonic case, the latter will be presented first, followed by a discussion of the changes needed for supersonic flow. The subsonic model is in the form of 19 algebraic equations, not necessarily linear, involving 19 unknowns. This system of equations must be solved numerically at successive points in time until all properties have approached their asymptotic values. The solution at any time t depends entirely on the property values obtained for the solution at t - ..1.t, a short time earlier, as well as the given valve area-time curves, which may be thought of as forcing functions. Quantities which vary between t - ..1.t and t are usually evaluated at an intermediate time
t* such that (t - ..1.t) < t* < t. The time t* is usually taken as the midpoint of the time interval.
The model is based on mass conservation for three control volumes as illustrated in Fig. 2. Conservation of mass for the plenum is derived from the unsteady integral continuity equation for a control volume to give
pp(t) = pp(t - tu) + [mp/t*) + mpe(t*) + mlt*)] ~t p
(1)
Here Pp is the mass density in the plenum, assumed uniform throughout, and Vp is the volume of the plenum. The quantities mpt(t*), mpe(t*), and mf(t*) represent, respectively, the mass flow rates between the plenum and test section (pt), out the plenum exhaust (pe), and through the flaps (f). The formal continuity equation can not be precisely integrated because the dependence of the mass flow rates on t or Pp can not be written in simple closed form. However, the law of the mean provides that pp(t) may still be precisely computed if the flow rates are treated as constant but evaluated at a suitable intermediate point t*. If ..1.t is now chosen sufficiently small so that the flow rates may be suitably approximated by linear functions of time, t* can obviously be chosen as t - 1/2..1.t, the midpoint. For the other two control volumes in Fig. 2, the steady continuity equation is used, having been justified by assumption (e) of the last section. By noting that Eq. (1) assumes the flap and wall crossflows are positive when flow is into the plenum, continuity for the test section becomes
(2)
17
AEDC-TR-76-39
and for the diffuser-valve manifold control volume
(3)
The three new mass flow rates introduced here are, in terms of the subscripts, that leaving the supply tube (ct, for charge tube, as it is often called), the primary tunnel exit (e) provided by the main valves, and the diffuser-end (d) of the test section. It should be noted from Fig. 2 that md corresponds to a point upstream of where the flap flow enters the main stream.
Proceeding next to model each of these six mass flow rates, consider first the flow through the plenum exhaust and the main valves, which are both treated as single one-dimensional sonic orifices driven by the stagnation conditions.
(4)
(5)
In Eq. (4), Peo and Teo are the stagnation pressure and temperature in the valve manifold; and in Eq. (5), Pp and Tp are the pressure and temperature in the plenum, approximated as stagnant. The quantities Ae and Ape are the total flow areas of the main valves and plenum exhaust valves. These areas are assumed to be the ideal, one-dimensional flow areas of a sonic orifice. If the real valve areas are used, discharge coefficients must be included in Eqs. (4) and (5). The constant a is given by
y+l
(_2 )y_l ~ Y + 1 R
(6) a
where R is the ideal gas constant and 'Y is the ratio of the specific heats.
Consider next the flap and wall crossflows, which have been neatly modeled by Varner (Ref. 2) as simply proportional to the pressure drop across the devices. With a second order adaptation added here, Varner's model takes the following form
A _ m (t*) = - ~ [p (t*) - A15 Pt(t*)]
pt kw p (7)
mft*) (8)
18
AEDC·TR·76·39
Here Aw and Af are the effective flow areas through the porous wall and through the
flaps. While Af is the actual geometric area, Aw depends on the total surface area of
the test section walls (Atsw ), the porosity (7), and a flow coefficient. Varner gives this
relationship as
(9)
The flow coefficients kw and kf were determined by Varner from experimental data from
Pilot HIRT and are given in Fig. 7. The values of kw in Fig. 7 are for the porosity shown in Fig. 8. The coefficientsl A 15 and Al6 multiplying, respectively, the mean test
section pressure P t and the diffuser end test section pressure P d were added in an effort
to improve the accuracy of the asymptotic values of the numerical solution. The rationale
for each of these constants is different. Rigorous modeling of the crossflow must include not only the effect of pressure forces but also the momentum of the fluid as it moves along the test section wall. The coefficient Al5 thus represents an attempt to include momentum effects as a small correction to the existing crossflow model. Experimental evidence from the pilot facility indicates that this small momentum effect can make the
difference between choking and not choking when the desired steady conditions are very near sonic flow. In particular, it has been observed that during supersonic flow, where the net crossflow must be from the test section to the plenum, the test section pressure is actually slightly less than the plenum pressure.
500 500
400 400 u 0 O--~ u Q,) 300 300 ..!!!
Q,)
..!!! ¢:: ¢::
J! 200 (Ref. 4) .;:.. 200 ..:.<:
100 100 (Ref. 4)
0 0 2 4 6 8 10
0 0 O. 1 0.2 0.3 0.4 0.5
T Af/Ats a. Porous wall flow coefficient b. Ejector flap flow coefficient
versus porosity (7) versus area ratio (AdAts)
Figure 7. Porous wall and flap flow coefficients.
IThe subscripts 15, 16, and 17 have no significance beyond consistency with variable names in the computer program.
19
AEDC-TR-76-39
Flow Direction
118 Diameter
30de~" Test Section Side
Note: Not to Scale All Dimensions in Inches
Figure 8. Wall porosity in Pilot HIRT.
0.078
O. 063
This has been attributed to the fluid momentum in the test section overcoming the slightly adverse pressure gradient. The other constant, AI 6 in the flap model, was added to account for'some of the losses in the upstream portion of the diffuser. Unfortunately, both of these constants were found to be functions of the test section Mach number, thus indicating the need for more accurate modeling,
The mean test section pressure Pt in Eq. (7) is computed from a weighted average of the pressure at the nozzle-end of the test section P n and at the diffuser end Pd' That is,
(10)
where 0 ~ Al 7 ~ 1. Since a detailed model of axial property variation in the test section has not yet been included in the start model, properties are computed only at the nozzle and diffuser ends of the test section. For subsonic flows, the value of AI7 was not found critical to the accuracy of the solution and was thus taken as 0.5, assuming a linear variation. For supersonic flow, a value of 0.9 was used to account for the more pronounced axial gradients.
The remaining two mass flow rates (met and md) may be related to pressures already introduced above using the steady energy equation discussed earlier and shown in Fig. 3. At the diffuser end of the test section, the energy equation is
2
[md(t*) 12 = _2_ ~ P d(*) J Y m (t*U y - 1 Pet (t*)
o 0
20
_ [ P it*)lY;ll Pet (t*)J
o
(1)
AEDC-TR-76-39
where as before the subscript "ct" refers to the charge tube and the subscript" 0" indicates
stagnation properties. The quantiy rno is defined as
P ct (t*)
m (t*) == Ir a A a \,fRVT (t*) ts
cta
(12)
where Ats is the cross-sectional area of the test section. The stagnation properties (Peto and Tct o) are thought of as originating from the unsteady wave when it reaches the charge tube and are assumed the same, for any given time, throughout all of the flow envelope except the plenum. At the nozzle end of the test section, the flow rate is equal to that in the charge tube, since its value has not yet been modified by any wall crossflow. At this station, the energy equation is, therefore,
fPn(t*)] ~ _ [Pn(t*)lY;1 \
l!' ct (t*) P ct (t*~ a a .
2
Y - I (13)
To complete the portion of the model not ansmg from the unsteady wave, the thermodynamic equations of state for the plenum are needed. To compute the properties at t* for use in Eqs. (5), (7), and (8) while Eq. (1) gives the density at t, the density at t* is computed from
p (t*) = li2[p (t) + p (t - ~t)] P P P
(14)
The plenum temperature is assumed equal to the greater of the isentropic temperature and the stagnation temperature in the test section.
That is,
{ ~ p (t*) ~ y-l } T (t*) = max Tp(t* - ~t) P ,T (t*)
P P (t*-.0.t) cta P
(15)
In either event, the pressure may then be obtained from the perfect gas law:
(16)
Closing the system of equations presented so far requires relationships for how the stagnation properties vary in time. A careful accounting of the number of equations and the number of unknowns to this point would reveal that, given values of Pet and Tet
o 0
and assuming Peo = Peto and Teo = Tct o (which is what is done for the subsonic case),
21
AEDC-TR-76-39
it is possible to compute the value of met. This value of the flow rate from the charge tube represents that required by the sum total of all the expansion waves which at a given time have reached the charge tube from all parts of the tunnel. That is, met identifies an intermediate point within the entire unsteady wave, which begins with the first motion of a valve somewhere in the tunnel and ends when the plenum reaches its asymptotic pressure. Thus, met may be used to compute all other stagnation properties for that point in the unsteady wave. By using the equations of Ref. 3 and after some algebra, the charge tube Mach number at the desired point in the wave may be related to met by the equation:
_ y+l
mct(t*) = MCt(,t*) [1 + Y ~ 1 Mct(t*1 y-l mc (17)
where me is defined from
(18)
Here Aet is the cross-sectional area of the charge tube, and P e and Teare the charge conditions, that is, the air pressure and temperature after the tunnel has been pumped up but before any valves are opened. These charge conditions are assumed to apply uniformly throughout the envelope, including the plenum. After obtaining the charge tube Mach number, the stagnation pressure and temperature are readily computed from the following equations from Ref. 3:
P ct (t*) o {
I + I-=--!:. M2 (t*) }y~l 2 ct ----------------- Pc fl + Y - 1 M ( t* )12 L 2 ct 'J
(19)
(20)
Equations (1) through (20) thus comprise the subsonic portion of the starting model and are summarized in Table 1. The supersonic case is physically different from the subsonic case and requires solution of a different set of equations as noted in Table 1. The distinguishing factor of the supersonic case is that the nozzle exit is choked, making the
flow rate and stagnation conditions steady there. Once the nozzle chokes, the charge tube Mach number is a constant depending only on the area ratio between the charge tube and nozzle exit. From Ref. 2, the steady Mach number can be obtained by reverting the equation:
22
Table 1. list of Exact Simultaneous Equations
Equation
() ( ') [' () . () . '*)l~ Pp t = Pp t - Lll + mpt t* + mpe t* + mf\t V
"',(t*)
Peo(tt)Ae(t*)
VTeo (tt)
_l':':!. "'e/t*) ~ 'Ie/ t*) ~ + y Me"t*~ y-l"'e
laRequlre Numerical Reversion
p
23
Independent Variable
to be Computed
"'ct' M < 1
p a n
Pp (t*)
Yes
Yes
No
No
Yes
Yes
Yes
Yes
No
No
Yea
Yes
Yes
No
No
No
No
Text Equation Number
2
3
4
5
7
8
10
11
13
12
14
15
16
17
19
.20
AE DC-TR-76-39
Program Equation Number
5
6
7
2
4
3
11
12
13
14
18
17
19
8
9
10
AEDC-TR-76-39
~ Act 1 {2 [1 y - 1 ------- +--A
ts - Mct(t*) y+l 2 ~}
2(y-l) M2 (t*) ct (21)
With this final Mach number, the steady stagnation conditions (Peto ' Teto ' and mo) along with the steady charge tube flow rate (met) can be computed one final time from Eqs. (19), (20), (13), and (17), after which these equations and variables may be dropped from the simultaneous solution. Since met is now constant, the flow rate leaving the test section (rud) is solely dependent on the wall crossflow (rupt) according to Eq. (2) and is independent of the flow rate out the main valves (me), assuming the valve area Ae is sufficient to pass all the charge tube flow not removed by the plenum exhaust. Thus, Eqs. (3) and (4) may also be dropped from the system of equations. This is fortunate since it is no longer true that Peo = Peto ' which results from the nonisentropic recompression of the supersonic flow entering the diffuser. Thus, the original system of 19 equations and 19 unknowns reduces to 10 equations and 10 unknowns for the
supersonic case.
These two sets of equations were solved using an iterational technique which unfortunately failed to converge in the vicinity of the choke point in time. To provide an alternate solution procedure when the iterational technique failed to converge, a small perturbation solution was developed for the original exact equations. The small perturbation solution was then used as an initial guess for the iterational procedure when it converged and as the complete solution when it did not. The results of this lengthy derivation are recorded in Appendix A, but the essential ideas are discussed below.
The exact solution already assumes that ~t is a small quantity. For the small perturbation solution, therefore, any of the 19 variables at time t* may be assumed to be related to their values at t* - ~t by the general form
v.(t*) = v. (t* - ~t) + ,dt*) 1 1 1 (22)
where €i is the small increment in the variable and i = 1, 2, ... , 19. If these small perturbation equations are used to expand the original exact equations,a new system of equations involving the increments rather than the variables themselves is obtained. For all exact equations, except the energy equations relating the pressure and mass flux at the entrance and exit of the test section (Eqs. (11) and (13)), only terms of order €i need be retained in the small perturbation equations. Such is not the case for the energy equations because in the region of the peak (or choke point) in Fig. 3, there is no linear approximation to the function. In the expanded equation, the coefficient of €i approaches zero as the Mach number approaches one. Thus, the term of order €i 2 , whose coefficient is nonzero
at Mach number one, governs the form of the expansion. The resulting subsonic system
24
AEDC-TR-76-39
of equations is thus comprised of 17 linear equations and 2 second-degree equations, which can be solved analytically. The supersonic case is composed of 9 linear equations and
1 of second degree.
2.5 SOLUTION PROCEDURE
The procedure used to solve these two systems of equations is discussed in the following section. Included is a discussion of the overall logical procedure, the order in which the equations of the exact solutions are used, convergence considerations, and a general description of the computer program used to accomplish the calculation. The general solution procedure is illustrated by the flow chart in Fig. 9. The decision whether to use the supersonic or subsonic branch is decided by whether P d (t* - ..6.t) < P* or Pd(t* - ..6.t) > P*, that is whether the diffuser end of the test section was supersonic or subsonic at the midpoint of the previous time interval. If the previous interval was supersonic, the current one is also assumed to be supersonic. If the previous interval was subsonic but 1 - M(t* - ..6.t) ,;:;;;; M(t* - ..6.t) - M(t* - 2..6.t) , then the supersonic branch is used for the current time interval; otherwise the solution is assumed to remain subsonic. This cliterion is checked for both ends of the test section, and the switch to the supersonic branch is contingent upon either or both positions satisfying the inequality. In either event, the small perturbation solution is computed to provide a good starting point for the exact iterational procedure. If convergence does not occur before a given number of iterations, the small perturbation solution is used as the final solution, and the next time interval is begun.
The II exact iterational procedure" referred to above is accomplished by taking an initial guess for one of the 19 variables and then proceeding from equation to equation, determining new values for each of the 19 variables until a complete circuit is made and a second value of the variable initially guessed at is obtained. This process is repeated until the difference between two successive values of certain of the variables is within a preset limit. For the subsonic case, the equation order is as follows:
4,3,11,10,7,2,17,19,20,12,13,10,7,8,1,14,15,16,
5, ...
The supersonic equation order is
10, 7, 2, 11, 10, 7, 8, 1, 14, 15, 16, 5, ...
Some of these equations (Eqs. (11), (13), and (17)) require reversion from the form given but cannot be reverted analytically in closed form and must be solved numerically. The variable to be solved for in each equation is indicated in Table 1, and the three requiring numerical reversion are marked with an asterisk:
25
AEDC-TR-76-39
Defi ne Charge Conditions, Tunnel
Geometry, Fluid, Area Time Curves
compute Supersonic Small Perturbation
Solution
Compute Exact Supersonic
Solution
Yes
Redo Small L------------l Perturbation
Solution
Compute Subsonic S mall Perturbation
Solution
Compute Exact Subsonic Solution
Figure 9. Flow chart of solution procedure.
No
The complete solution thus requires numerical iteration at three distinct levels, which necessitates careful consideration of convergence criteria as well as what to do when the criteria can not be met because of stability problems. The most basic level of numerical iteration involves reversion of the two energy equations and the mass flux - Mach number
26
AEDC-TR-76-39
wave equation. Considering the general case where the function Y = F(X) must be solved for X given a value of Y and a guess Xl, the procedure is simply to adjust Xl in the direction which reduces the error criterion
El = y - ;(X) (23)
until IEll ~ IEmax I, Emax being the present, maximum allowable error. The precise logic of the procedure is illustrated in the flow chart in Fig. 10. Since this procedure must
Subroutine SOLVER Compute y
Estimate Xl
Choose I::.X Choose Emax
Figure 10. logic for numerical solution of an algebraic equation Y = F(X) for X, given Y when X = F-1 (Y) is not a closed form function.
27
AEDC-TR-76-39
be repeated many times at each time interval, it is of considerable importance (because
of impact on computer time) to achieve a solution with as few iterations as possible.
Since the number of iterations depends to a large extent on the accuracy of the guess
Xl, considerable effort was expended in obtaining approximate reversions of the three
equations. It was inadvertently discovered that the energy equation may be approximated
with surprising accuracy over the entire range of present interest with a single ellipse,
the reversion of which is trivial. The wave equation presented more of a problem. Since
an easily revertable second-degree expansion around Met = 0 failed to match the accuracy
of the elliptic energy equation, the expansion was carried to the seventh degree and then
formally reverted according to the procedure of Ref. 6. These expansions are summarized
in Appendix B.
The next higher level of iteration is, of course, the simultaneous solution of the
exact model equations, during which stability problems were encountered in the vicinity
of the choke point. The error criterion for halting the iteration may be generally expressed as
(nl (n+l) v· - V. I I
.:::; P err (24)
where test variables (Vi) are the pressures Pn , Pp(t), Pp(t*), Pd, Pt , and Peto ; Perr is
the maximum allowable error; and n is the iteration number. Figure 11 illustrates the stability problem encountered in striving to meet this error limit. Shown is how the plenum
pressure Pp (t*) varied with iteration number at two succeeding time points, one converging
and one not. Such stability problems are known to occur in applying the iterational technique to locating the intersection of two curves on a plane when the curves have
the same slope (same or opposite sign) at the point of intersection. Whether this simple
explanation in 2-space is applicable to 19-space where no two of the 19 functions lie
in the same plane is unclear. In any event, improvement in convergence rate was sought via the following procedures, most of which improved the situation:
a. Relative Errors. It was found that if Emax was much greater than 1/10
Perr , the numerical reversions could oscillate enough themselves from one iteration to the next to slow convergence.
b. Computational Precision. Single precision arithmetic (-~8 digits on an IBM
370) was found inadequate to achieve errors of Emax = 10- 5 (Perr = 10-4), and double precision (~16 digits) was, therefore, adopted.
28
AE DC·TR·76·39
36
.~ 35 VI c.. (J,) .... ::l VI VI (J,)
ct 34
33
36
co 'iii Co.
(J,)-
35 ... ::l VI VI Q) .... c...
34
Y
r- -
I
o 10
21 msec /-----1---
1-----
----1-----1-------SlIghlly Tergenl
20 msec
AAA " V v ~O~I~~e nl
20 30 40 50 60 Iteration Number, n
Figure 11. Plenum pressure versus iteration number for convergent and divergent cases.
c. Solution Weighting. The clearly periodic oscillation of Fig. 11 suggests that
the average of any two successive values should be closer to the final asymptote than either value. Accordingly, solution weighting,
(nl A (nl (1 _ Ajj)V(in+ U vi = jjVi + (25)
was employed on a regular basis;
d. Weight Cutting. It was further discovered that convergence rate could be greatly improved after the number of iterations reached a certain point if a lesser weight was applied to the current value Vi(n).
e. Error Cutting. It was found that, later in a computation when some of the pressures were very near their asymptotes, the amount of variation from one time point to the next eventually approached the error limit. This in effect allowed these values to vary at random within the error limits and deteriorate the convergence rate. It was thus found prudent to reduce the
error limits as necessary so as to maintain
29
AEDC-TR-76-39
\
v.(t*) - v.(t* - L'1t) I Perr ~ Y,[~Jt*) + ~j(t* - L'1t)]
and Emax ~ 1/10 Perro
f. Extrapolation. A second-order extrapolation function
vj(t*) = 2v j (t* - L'1t) - Vj(t* - 2L'1t)
(26)
(27)
was tested in an effort to improve the starting values for iteration through the 19 equations, but this generally produced no improvement in
convergence rate. A third-order function
was found not much better. Ultimately, of course, it is illogical to expect any finite order extrapolation scheme to predict the effect of changes in the forcing functions (area-time curves) if those coming changes had not been anticipated by the derivatives of less than that order.
g. Small Perturbation Solution. In place of an extrapolation function, there was used the more logical small perturbation solution. This considerably improved the convergence rate and provided sufficiently accurate results in lieu of the exact solution when it failed to converge in a reasonable length of time.
The complete mathematical model along with the above described convergence enhancement logic have been programmed in Fortran IV for solution on an IBM 370/165. The computer program HIRTSMI (for HIRT Starting Model) is composed of the normally expected components: the main program (MAIN) containing the exact equations, the convergence control logic, and the overall solution control logic; subroutines to control input (INPUT), output (PRINT and DUMP), and variable definition and initialization (CONST and INIT): and a subroutine which performs the calculation for the analytical solution to the simultaneous small perturbation equations (SMPERT). In addition, the program contains a package of utility subroutines : one routine contains the logic o(Fig. 10 to numerically revert any given function (SOLVER); a second expands out the binominal coefficients (BINOM) to give a series which is reverted by a third subroutine (REVERT) to the seventh-degree term; a fourth subroutine (QSIMUL) determines the points of intersection of two conics (the two final energy equations resulting from SMPERT) by converting them to a single fourth-degree polynominal, which has an exact analytical solution for the four roots (QANDC). Use of this program is described in Appendix C.
30
AE DC-TR-76-39
The program can be run in a partition of 11 OK bytes and easily completes about 200
time increments in less than a minute of central processor time, though occasionally a run may require up to three minutes. Peripheral storage is not essential, though provisions are made to dump the entire solution on to a direct (random) access data set (such as a disk file) so that the solution may be picked up at any point and continued. The results of calculations with HIRTSMI are compared in the next section with experimental results
from the Pilot HIRT facility.
3.0 RESULTS
Presented below is a comparison between the mathematical model and experimental pressure-time histories from Pilot HIRT. Included is a brief description of those characteristics of the tunnel important to the model. After a comparison of the model and data, some other results of the calculations are shown. The section concludes with a discussion of how the model can be applied in the design of certain portions of the
tunnel.
3.1 DESCRIPTION OF PILOT HARDWARE
Figure 12 shows an elevation line drawing of the Pilot HIRT facility, to which the present mathematical model was applied. Figure 13 shows most of the geometric data required by the model and also accurately illustrates the real life hardware, which is simplified in the model. The geometric parameters in the precise form used in the model are summarized in Table 2. The tunnel uses two alternate types of starting devices, the sliding sleeve valve shown in Fig. 13 and, for quicker starts, a Mylar@ diaphragm and cutter
located at the interface of the diffuser and the valve assembly. The plenum exhaust system, shown schematically in Fig. 14, also uses a diaphragm in addition to two valves to control the exhaust flow. The diaphragm initiates the flow, and the ball valve, whose setting cannot be changed during a run, determines the amount of plenum exhaust during the steady portion of the run. The quick-acting valve, however, may be rapidly closed during the run to provide a temporarily elevated plenum exhaust in excess of what the ball valve will pass. The complete system in Fig. 14 is modeled as the area-time curve of a one-dimensional sonic orifice, as is the multiple port system on the main valve.
The portion of the tunnel shown in Fig. 13 was heavily instrumented with pressure
taps to measure pressure-time histories at various locations in the nozzle test section , , diffuser, and plenum. Output from the pressure transducers was sampled every 2 msec by a data acquisition system based on a PDP 11/10 digital computer with certain of the signals also displayed on a recording oscillograph. Of primary interest here are the plenum
pressure-time histories, which comprise the primary basis for comparison of the theory and experiment.
31
W N
111 ft -+- 7 ft -I" 7 It .1
Transition Section (Nozzle)
High Pressure Air Charge System
Thrust Collar
Charge Tube
Thrust Stand
Test Section Liner
Plenum Chamber Ejector Flap Cylinder
Model Support Section
Diffuser
Plenum Exhaust
Figure 12. IPilot HI RT elevation line drawing.
Building Wall
Main Sliding Sleeve Valve Starting Device
45 in.
Exhaust System
» m CI (")
~ :D .!..I OJ tv c.o
w w
13.94 INom.
130.4* • 1
Model Support Strut Diffuser 12-in. Sliding Sleeve
Start Valve IShown Closed)
-/--m+.h 30.3 \ 29.0 '1
Ejector and Pressure Tube Bu ndle
"NOTE: All Dimensions in Inches
L r-
Figure 13. Cross-sectional view of nozzle, test section, diffuser, and main valve system.
52.0 -------~
» m o (")
.:., :Il .:.n m W to
AEDC-TR-76-39
Table 2. Geometric Data for Pilot HIRT Required by Mathematical Model
Charge Tube Diameter
Charge Tube Flow Area
Ratio of Charge Tube Area to Test Section Area
Test Section Length
Test Section Width
Test Section Height
Test Section Flow Area
Test Section Wall Surface Area
Test Section Porosity
Test Section Volume
Flap Flow Area
Ratio of Plenum Volume to Test Section Volume Nominally
Plenum Chamber
Section
Ej ec tor Flaps
1.162 ft
1.060 ft2
2.271
2.114 ft
0.7633 ft
0.6117 ft
0.4669 ft2
5.813 ft2
3.5 to 10%
0.9870 ft3
o to 0.2062 ft2
1.75 to 4.0 2.8
A-----c ...... To Main Exhaust (Valve or Diaphragm)
Plenum Exhaust Line (Ten 2-in.-ID Lines Manifolded Ahead of Diaphragm)
~~~-----Diaphragm (Ruptured to Initiate Flow)
To Atmosphere
--~ ... ~ To Atmosphere
6-in. Ball Valve (Orifice Variable)
Quick Acting Valve (Open or Closed)
Figure 14. Plenum exhaust system.
34
AEDC-TR-76-39
3.2 COMPARISON OF MATH MODEL AND EXPERIMENT
Data for nine different tunnel settings were studied with the mathematical model. Some basic data for runs typical of these nine conditions are summarized in Table 3. The data of primary interest in this table include the plenum-to-test section volume ratio,
porosity, the opening times of the main valve and plenum exhaust valve, the maximum plenum exhaust area, and the experimental test section Mach number. The conditions listed for Run 2258 may be considered nominal values from which variations in plenum volume, porosity, flap setting, and test section Mach number were examined.
Figure 15 compares the experimental plenum pressure as a function of time with the present mathematical model for the nominal conditions (Run 2258). The data illustrated is for a plenum volume 2.8 times the test section volume, a porosity of 4-1/2 percent, and a flap setting of 0.4 in. (the gap between the flap and the test section wall where the flap flow empties into the diffuser). The main starting device was a Mylar diaphragm; and the exit flow area, the primary factor determining the asymptotic test section Mach number (0.921), was obtained by capping off the proper number of exit ports on the main exhaust manifold (Fig. 13, 16-in. valve). Since the desired Mach number was subsonic, the plenum exhaust system was not used. The resulting data for these tunnel settings are plotted in Fig. 15 as circles, and the solid line represents the output of the computer program. The program was run for the indicated tunnel settings (Table 3), but several not readily apparent inputs were assumed. The starting device (diaphragm) was treated as a linear area-time curve reaching its maximum area in 2 msec. The maximum area shown in Table 3 is approximately 99.46 percent of the test section flow area, which is based on the ideal, one-dimensional flow area ratio needed to produce a test section Mach number of 0.921. The resulting theoretical plenum pressure-time history shown in Fig. 15 agrees well with the experimental data. The greatest discrepancy occurs at 25 msec and reaches a peak there of 6.5 percent. This difference, due to a temporary leveling of the experimental data between 10 and 25 msec, results from the finite time required for the initial expansion wave to traverse the plenum volume, which includes the plenum exhaust lines shown in Fig. 14. These lines extend to a distance of about 4 ft from the major portion of the plenum. Since the model assumes a uniform plenum, it cannot account for this factor. Figure 15 also illustrates another deficiency of the model, which in this case produces the 3.I-percent error at a time of about 100 msec. Part of this error is due to error accumulation in the small perturbation solution, to which the program reverted entirely beyond 45 msec because of non convergence of the exact iterational solution. Another part of the error, in this case the smaller part, is due to neglect of the axial momentum of the test section flow by the crossflow model, which results in the smaller slope of the theoretical curve in the region of 60 to 90 msec. Since this discrepancy has been found to be generally small for subsonic runs, the coefficient in the crossflow model (AI 5) has been left equal to one.
35
W 0\
I
I I
Run Number
2226
2236
2241
2251
2255
2258
2260
2263
2742
(a) -
(b)f
Charge Pressure, PC' psia
60.11
62.37
61.84
81.47
81.27
70.51
70.90
74.10
152.15 -
0.2 in. 2
0.9 in. 2
Plenum Volume (-) ,
Vp/Vts
2.8
2.8
2.8
2.5
2.5
2.8
4.0
1. 75
2.5
(C)"'f Co 0.4 in.
(d)Nominal Conditions
Table 3. Summary of Run Conditions for Experimental Data to be
Compared with Theory
Maximum Flow Area Total Opening Times
Porosity, Main Valve, Plenum Ex, Flaps'2 Main Valve, Plenum Ex, Flaps, Plenum
Ae , ft2 Ape, ft2 Delay, " 1,. Af , ft sec sec sec , sec
4.5 0.466886 0 0.045835a 0.002 --- --- ----
4.5 0.466331 0 0.2062 b 0.002 --- --- ---1.5 0.465911 0 0.09167 c 0.002 --- --- ---4.5 0.465911 0.1090 0.09167 0.002 0.040 --- 0.005
4.5 0.465911 0.1090 0.091G7 0.002 0.040 --- 0.004
4.5 0.464351 0 0.09167 0.002 --- --- ---4.5 0.466290 0 0.09167 0.002 --- --- ---4.5 0.466662 0 0.09167 0.002 --- --- ---4.0 0.465911 0.1090 0.09167 0.030 0.040 --- 0.005
Asymptotic Plenum
Pressure, psia
25.00
2;'.55
23.83
30.56
24.04
30.47
29.36
29.64
53.25
Test Sect ion Mach Number
(-) , M,.
0.992
0.962
1.013
1.039
1.228
0.921 d
0.960
0.975
1.100
~ m CJ (')
~ :0 ~ O'l
W to
AEDC-TR-76-39
1.0 0------------------------,
Conditions
VplVts = 2.8 Q)
T = 4. 5 percent 5 Theory VI VI 0.8 Mm = 0.921 ~ CL
'" Ii f = 0.4 in. E' ro
Ape = 0 .c u .s Run No. 2258 Q) .... 0.6 :::l Starti ng Device: Diaptmgm VI VI
~ 0 CL
E :::l c: .!!!
00000000 CL
'0 0.4 0
~ 0::
0.2 o 40 80 120 160 200
Time, msec
Figure 15. Plenum pressure versus time for subsonic run with medium plenum volume.
Since the amount of plenum volume which must be drawn down to the asymptotic
pressure may logically be expected to have a first-order impact on the starting time, the
plenum volume was the first parameter varied from the nominal conditions for Run 2258
(Fig. 15). Figures 16 and 17 show the plenum pressure for a smaller plenum volume ratio 0.75) and a larger ratio (4.0), respectively. As expected, the smaller volume case flattens more quickly than the medium volume case, and the larger volume more slowly. As in Fig. 15, the accuracy of the model is generally good for both the smaller and larger plenum volumes, though the effect of the wave propagation time in the plenum is much more pronounced for the larger volume.
Now return to a medium plenum volume case but vary another parameter - plenum exhaust - for a slightly supersonic run. The theoretical analysis depends on an
experimentally derived plenum exhaust area-time curve, shown in Fig. 18, in the nondimensional form used by the computer program. Unfortunately, the uncertainty in
the shape of this curve is quite large, and only the steady area is known accurately. Illustrated in Figs. 19 and 20 are the data for, two supersonic cases, Mach 1.039 and 1.228. Both the theory and experiment of Fig. 18 show a slight over-shoot bottoming out at 30 msec and then approaching the asymptote from below. In addition, the experimental data show a slight rebound peaking at 60 msec, a result not predicted by
the model. The rebound probably results from the overshoot, which would tend to draw
the test section below its asymptotic pressure while the plenum exhaust area was decreasing
37
AEDC-TR-76-39
1.0
Conditions
VplVts = 1. 75 Q)
T = 4.5 percent .... ::J on
Moo = O. 975 on 0.8 Q) .... "- Theory Q) lif = 0.4 in. 0> .... '" Ape = 0 .c:
<..)
oS Run No. 2263 Q) .... 0.6 ::J Starti ng Device: Diaphragm on on Q) .... "-E 0 ::J 0 c: ~ 0 "-
LOOOOOOOOO '0 0.4 0 0 0 0 0
~ 0:: Data
Time, msec
Figure 16. Plenum pressure versus time for subsonic run with small plenum volume.
1.0 Conditions
VplVts = 4. 0
'" T = 4. 5 percent .... ::J on Moo = 0.960 V> 0.8 ~ "- lif = 0.4 in. Q) 0> Theory ....
Ape = 0 '" .c: U 0 oS Run No. 2260 Q) .... 0.6 Starti ng Device: Diaphragm ::J on V>
E <>-E ::J c: Q)
0 a:: 0 '0 0.4 ~ '" 0::
O. 2 01..--..l.--....J401...--.J..---I80--.l----'---'---:-':"::----''---~200
Time, msec
Figure 17. Plenum pressure versus time for subsonic run with large plenum volume.
38
AEDC·TR·76·39
1.0
>< 0.8 '" E Ol> 0.
~ '" 0.
« 0.6 ",'
~ « ro Conditions c
0.4 0 'Vi
Moo = 1. 039 c
'" E Ape max = O. 1090 It2 :0
c 0 0.2 z tF = 40 msec
Run No. 2251
0 0 0.2 0.4 0.6 0.8 1.0
Nondimensional Time, t!lF
Figure 18. Plenum exhaust area-time curve for Mach 1.039 run.
1.0o-------------------------------------------~
Conditions
Vp/Vts = 2.5
'" ... T = 4.5 percent '" V>
VI 0.8 Moo = 1. 039 ~ c..
'" 01= 0.4 in. E' '" = O. 1090 ft2 .c A u pe max .s E 0.6
Run No. 2251 '" V> Starti ng Device: Diaphragm V>
'" ... c.. E
'" c Data '" c..
'0 0.4 :8 '" 0::
Time, msec
Figure 19. Plenum pressure versus time for supersonic run (Mach 1.039) with plenum exhaust.
to its steady value at 40 to 50 msec, This combination of occurrences would then produce
a slight refilling of the plenum, manifesting itself in the observed rebound. For the higher Mach number 0.288) of Fig. 20, the plenum exhaust curve of the previous case was retained intact up to its peak but was linearly stretched beyond the peak to make it approach the steady area needed for the tunnel to reach the desired asymptotic Mach
39
AEDC-TR-76-39
number. The peak area and closing time were unchanged. The disagreement between theory and data at the knee of the curve may be charged to the uncertainty in the plenum exhaust area-time curve, which is known to vary somewhat from run to run since the plenum diaphragm rupture is not precisely repeatable.
1.00-------------------------------------------,
Cl> L. :::J VI
~ 0.8 L. c... C1>
E' '" .c U
.s '" ~ 0.6 ~ ~
c... E :::J C
'" 0::: '0 0.4 o
:;::;
'" e>::
Theory
Conditions
VplVts = 2.5
t = 4.5 percent
Men = l. 228
6f = 0.4 in.
Ape = O. 1090 ft2
Run No. 2255
Starti ng DevIce: Diaphragm
0.2 '----'-----'-----'-----'---"'----'----'----'-----''------1 o 40 80 120 160 200
Tim:.- msec
Figure 20. Plenum pressure versus time for supersonic run (Mach 1.228) with plenum exhaust.
The next parameter variation for which the model was tested was the opening time of the main starting device. Figure 21 shows the data and theory for a supersonic run made with a relatively slow opening 12-in. sliding sleeve valve instead of the diaphragm. Though not apparent from the excellent agreement for this case, there is also some uncertainty in the effective opening time of the main valve, assumed to be 30 msec for the theoretical calculation. This uncertainty results because the choke point of the tunnel changes position as the valve area increases, moving from the valve to the nozzle exit. Since the time at which this change occurs is not easily determined experimentally, the exact effective opening time is not known. In addition, the area-time curves are not precisely repeated from run to run.
To continue with the testing of the model for variations in other parameters, the program was run for a case of reduced porosity 0.5 percent), maintaining the nominal conditions of medium plenum volume and flap setting. Figure 22 shows that the model agrees well with the data. Cases were also run for which the flap flow area was halved
40
E ::l VI VI Q) .....
0..
'" en ..... '" ~ u .s '" .... ::l Vl VI OJ ....
0..
E ::l c: '" c:: '0 ~ '" De
1. 0 0.-------------------------,
0.8
0.6
0.4
Theory
Conditions
VplV ts = 2.5
T = 4. 0 percent
Mco = 1. 100
of = 0.4 in .
Ape = O. 1090 ft2
Run No. 2742
Data Starting Device: 12-in. Sliding Sleeve Valve
Time, msec
AEDC-TR-76-39
Figure 21. Plenum pressure versus time for supersonic run with sliding sleeve valve and plenum exhaust.
1.0
Conditions
'" Vp/Vts = 2.8 .... ::l
'" T = 1. 5 percent V> Theory E c...
Mco = 1. 013 '" E' '" Ii f = 0.4 in. ~ u .s Ape = 0 E ::l 0.6 Run No. 2241 VI V>
E Starti ng Oevice: Diaphragm c... E ::l c: '" c:: '0 0.4 :8 '" De
0.20L---~--4LO-~L---~80----L---J12-0-~--~16~0-~-~200
Time, msec
Figure 22. Plenum pressure versus time for supersonic run with 1-1/2-percent porosity and no plenum exhaust.
41
AEDC-TR-76-39
Q) ..... :::J
~ E 0.. Q)
1:' '" r; u .s Q) ..... :::J
'" '" E 0..
E :::J c: ~ 0..
'0
~ '" ""
1.0 0---------------------------------------------,
0.8 Theory
0.6
0.4
0.2 o 40 80
Time, msec
Conditions
VplVts = 2.8
T = 4.5 percent
Moo = 0.992
6f=0.2in.
Ape' 0
Run No. 2226 Starti ng Device: Diaphragm
120 160 200
Figure 23. Plenum pressure versus time for subsonic run with small flap setting.
E :::J
'" '" a.> ..... 0.. Q) C'> ..... '" r; u .s E :::J
'" '" E 0..
E :::J c: Q)
0:: '0 0
'" ""
1.0 0---------------------------------------------,
0.8 Theory
0.6
0 0 0 0.4
0.2 o 40 80
0
Time, msec
Conditions
VplVts = 2,8
T = 4.5 percent
Moo = 0.962
Ii f = 0.9 in.
Ape = 0
Run No. 2236
Starting Device: Diaphragm
120 160 200
Figure 24. Plenum pressure versus time for subsonic run with large flap setting.
42
AEDC-TR-76-39
and doubled from the nominal settings. Illustrated in Figs. 23 and 24, both theoretical
calculations are in acceptable agreement with experiment. As in previous cases, the
disagreement just above the knees is due to the neglect of the finite wave propagation
time across the plenum. The disagreement very early in the run (10 msec) is due to uncertainty in the rupture time of the diaphragm, and the slowness of the model in approaching the asymptote may be charged to inadequate handling of the momentum
terms in the crossflow model.
3.3 OTHER RESULTS FROM THE MATH MODEL
To predict the data of primary interest, plenum pressure, the model must also calculate many other quantities including pressures and mass flow rates at various locations in the tunnel. Figure 25 shows the pressure-time histories for the case of nominal plenum volume (2.8) for a subsonic run with a diaphragm starting device. Besides plenum pressure, the stagnation pressure and static pressures at opposite ends of the test section are shown. This graph illustrates that the test section pressure initially drops much faster than the
plenum, as expected since the rate of plenum depletion is limited by the porosity and
flap area. Early in the run, the pressure at the exit of the test section leads the pressure at the entrance because the wall crossflow leaving the plenum increases the flow rate
from the entrance to the exit. Eventually, of course, the test section and plenum pressures approach each other as the flap and wall crossflows become negligible and the steady
conditions are reached. The stagnation pressure becomes nearly flat long before the static pressures in the test section and changes very slowly beyond 20 msec.
The subsonic case in Fig. 25 may be contrasted to the supersonic case in Fig. 26, which shows the same set of pressure curves. Besides the more rapid drop of all curves prior to 40 msec, due to the plenum exhaust, the most striking difference from the subsonic case is the approach of opposite ends of the test section to distinctly different asymptotes. The entrance to the test section levels rather suddenly at the choking pressure ratio, while the exit continues to drop to the lower pressure ratio corresponding to the supersonic Mach number. Another interesting feature is that the asymptotic pressure at the test section exit is lower than for the plenum even though the net wall crossflow must be into the plenum (to reduce the flow rate along the test section as needed for supercritical flow). Crossflow against the pressure gradient occurs because of the increasing momentum retained by the crossflow while separating off from the high-~peed test section flow. Another feature
of Fig. 26 due to this momentum is the crossing of the test section pressure curves at 12 msec, which signifies the reversing of the wall crossflow. To improve the cross flow model's representation of the effect of this momentum (which is neglected in modeling
the crossflow rate as a function of pressure difference only), the momentum correction
coefficient A15 in Eq. (7) was introduced. This quantity expediently models the small
43
AEDC·TR·76·39
'" ... i;l '"
1.0
~ 0.8 a..
E> 10 .c (.)
.s !Q ::I 0.6 :a 'a.. !9 o ;: ;! ~ 0.4 o
~
0.2 0
stagnation Pressure, PctolP c
Conditions
VpIVts = 2.8
T = 4.5 percent
Moo = 0.921
6f·0.4in.
Ape = 0
Run No. 2258 Starti ng Device: Diaphragm
Plenum Pressure, P piP c
Test Section Pressure, Nozzle End (Entrance), PnlPc
Test Section Pressure, Diffuser End (Exit), PdlPc
40 80 120 160 Time, msec
200
Figure 25. Various pressures versus time for nominal conditions.
1.0
(1)
'-::J III VI
'" 0.8 I-a..
'" C> I-m .c: u .s '" ~
0.6 ::J
'" '" Q.) .... a..
'" ::J 0 ·c '" > ~ 0.4 0
~ er::
0.2 0
Figure 26.
40
Conditions VpIVt = 2.5
T = 4.5 percent
Moo" 1. 228
6 f • 0. 4 in.
Ape = O. 1090 tt2
Run No. 2255 Starti ng Device: Diaphragm
Test Section Pressure, Nozzle End (Entrance), P niP c
Test Section Pressure, Diffuser End (Exit), P diP c
Pie nu m Press ure, P piP c
Choke Pressure
80 120 160 Time, msec
200
Various pressures versus time for supersonic run with plenum exhaust.
44
AEDC-TR-76-39
additional crossflow due to momentum in terms of a slightly elevated driving pressure.
The steady-state value of Ai 5 at a given steady test section Mach number was derived empirically for a given steady plenum pressure. These steady-state values of Al 5 are shown
in Fig. 27a. During a run, however, AI5 was assumed to vary according to the ramp
function of Fig. 27b to simulate the increasing momentum.
~ « ~ ~ Q)
'" ;:;:: Q> ... ::I VI
'" E <>..
1.4
1.3
1.2
1.1
1.0 1.0
Normal Shock
1.1 1. 2 1.3 1. 4 Steady Test Section Mach Number, Moo
a. Momentum correction coefficient (Al 5) and flap correction coefficient (A16 ) versus steady test section Mach number
~Iateaus Correspond
to the Asymptotic Test Section Mach Number
I A15 I
......+_->-__ -;1 A16
I I I
b. Assumed variation with test section Mach number (Md ) of momentum (Al 5)
and flap (A1 6) correction coefficients during starting process
Figure 27. Steady-state values of correction coefficients, A1 5 and A1 6·
Looking at the mass flow rate-time curves corresponding to Figs. 25 and 26 provides further insight into the behavior of the mathematical model. Figure 28 shows the flow rate entering (from the charge tube) and leaving the test section, the flow rate through the flaps, and across the porous wall for the nominal conditions and subsonic flow. The flap and wall crossflows, though leaving the plenum in this run, are shown on the positive
45
AEDC-TR-76-39
axis for convenience. All data are expressed as ratios of the steady, asymptotic flow rate through the main valves. The flow in the test section is seen to rise very rapidly, in concert with the breaking diaphragm, and to approach the final flow rate only as the flap and cross flows approach zero. Both flows from the plenum reach peaks at about 3 msec, which results from the pressure differences between the plenum and test section reaching a maximum. The crossflow further manifests itself in the disparity between the flow entering and leaving the test section. Various experimentally derived flow rates are given in Ref. 4 for the pilot tunnel. These relatively well behaved results for the subsonic case may be contrasted to the tangle of curves resulting from a supersonic case with plenum exhaust (Fig. 29), which is based on the same conditions as Fig. 26. Initially similar to the subsonic case with peak flap and crossflows at 3 msec, the curves are considerably modified by the opening of the plenum exhaust at 4 msec (a programmed delay). The leveling of the flap and crossflow curves at 22 msec is associated with choking in the test section. Eventually, the plenum exhaust forces both the crossflow and flap flow to reverse and eventually to exactly balance the plenum exhaust flow rate when steady flow is reached. Reversal of the flap flow requires, in terms of the flow model (Eq. (8)), a driving pressure at the flap exit greater than the plenum pressure and in general greater than the computed pressure at the exit of the test section. Though the flap correction coefficient (A16) is applied much like the wall crossflow coefficient, the physical explanation cannot be the same since the free-stream momentum is in the opposite direction of the reversed
0.8
.lB ro ~
!'5 0.6 u:: III III
~ '" 0.4 ~ '" <ii ~
0.2
10 20 30 40 50 Time, msec
Figure 28. Relative theoretical mass flow rates for nominal conditions (Run 2258) of subsonic flow with no plenum exhaust.
46
AEDC-TR-76-39
1.2 Charge Tube, mct/me(t -co)
----l.0
0.8 Test Section Exit md/me(t -+co)
In
~ '" a:::
~ 0.6 u: Flaps, mf/me(t-+co) Vl In
'" :2:
'" 0.4 :5 '" Q; Porous Wall, a:::
0.2 mpt/me(t -+co)
-0.2 '--__ "--__ "--__ ..1..-__ ..1..-_---1
o 10 20 30 40 50 Time, msec
Figure 29. Relative mass flow rates for a supersonic run (Mach 1.228) with plenum exhaust (Run 2255).
flap flow. A more likely explanation is the shock structure and flow separation at the diffuser entrance. Since precise modeling of this complex flow is beyond the scope of the present work, the flap flow correction coefficient (A16) was added to Eq. (8). Experimentally derived values of A16 as a function of steady test section Mach number are plotted in Fig. 27a along with the static pressure jump across a normal shock. The pressure rise during the reversed flap flow must be due to a flow more complex than a normal shock, since the pressure jump across the shock rises much more rapidly than experiment indicates. The lines through the circled points are cubic fits and are probably not accurate beyond Mach 1.25. As with the momentum correction, the flap correction was assumed to vary in time according to the ramp function in Fig. 27b.
3.4 APPLICATION OF THE MATH MODEL
Besides prediction of tunnel start time, there are several other ways the model can be applied in the design of a wind tunnel. Since the plenum exhaust area-time curves
can be varied arbitrarily in the model, the number of plenum valves (or total valve area)
47
AE DC-TR-76-39
to achieve various start times can be determined. In addition, the sensitivity of the start time to the shape of the area-time curves can be predicted. This is important because it indicates how finely controllable and repeatable (and expensive) the valves must be. Another potential application is estimation of the structural loading of the test section wall due to transient pressure differences between the plenum and test section.
To illustrate some of these possibilities, the program was run for the three different plenum exhaust area time curves shown in Fig. 30. The solid line is a typical area-time curve from Pilot HIRT, and the two broken lines are variations having the same average open area. Processing the model with the triangular curve should indicate whether a curve with the same peak as the basic curve but having a different shape would significantly affect starting time. The trapezoidal curve should indicate whether a smaller number of valves kept at full open for a longer time could achieve the same start time as the more peaked curves. The plenum pressure-time histories for these three curves are shown in Fig. 31. It is clear that the triangular curve has little effect on the shape of the pressure curve and does not affect starting time. On the other hand, the trapezoidal curve has a larger effect but still does not lengthen the starting time. The logical conclusions for the tunnel configuration studied here is that very accurate controllability is not required of the plenum valves and that the tunnel could be started just as quickly with about
1. 0 ..-------.:---~-.;:----------,
~ O. 8 E
Q) c.
!'f <l> 0.
« 0.6 ro Q)
'-« ~ o 0.4 VI c Q)
E :.c c ~ 0.2
I
I I
Area Is Same under All Curves
I "'-, I '" I r--------~ ------, I, \: \ I '\ I '" \ I , \
I '" \ I '" \ I " \ I '
-- Basic Curve --- Trapezoidal Curve --- Triangular Curve
o L-~ __ ~~ __ ~ __ ~~ __ ~~ __ ~~
o Q2 Q4 Q6 Q8 1.0 Nondi mensional Ti me, tltF
Figure 30. Nondimensional equal area plenum exhaust area-time curves.
48
AEDC-TR-76-39
2/3 of the available valve area if the valves were kept fully open for a longer duration. If these results were found to apply to a large scale facility, a considerable cost reduction could be realized.
'" .... :::J VI In
'" .... CL Q)
C"l .... '" .c: u .£ VI
'" boo :::J In In
'" '-CL VI :::J 0 '': co > '0
~ co a:::
1.0
Conditions
V plV ts = 2.5
0.8 Moo = 1. 04
T = 4.5 percent
0.6
-- Basic Plenum Exhaust Curve (Fig. 30) --- Trapezoidal Curve, Same Area --- Triangular Curve, Same Area
0.4
0.2 ~ __ ~ ____ ~ __ ~ __ ~ ____ ~ __ ~ ____ ~ __ ~ __ ~ _____ d
o 40 80 120 160 Time, msec
Figure 31. Plenum pressures versus time for three plenum exhaust area-time curves with same integrated area.
200
A second example of application of the model is illustrated by Fig. 32, which shows
the pressure differential across the wall at the test section exit as a function of time for several conditions. From these results, it can be seen that reducing the porosity has little impact on wall loading, but raising the Mach number from 0.921 to 1.228 or reducing the flap gap by 1/2 significantly increases the loading by 25 and 50 percent, respectively. In contrast, lengthening the effective valve opening time from 2 to 30 msec reduces the peak load to about 1/3 of the nominal case. The peaks of the curves for the diaphragm runs occur just as the diaphragm reaches its full open area. The curve for the valve run, however, peaks first when the plenum exhaust area peaks and later when the valve reaches its steady area around 30 msec. Two data points for the peak pressure differential from Ref. 4 are shown in Fig. 32 and agree with the model.
49
AEDC-TR-76-39
0.3
u a... ~ 0.2 a...
I 0-
.e::
'" ~ Q) .... Q.)
!E Cl Q) .... ~ VI VI Q) L-
a... 0.1
Sym
o Experiment (Ref. 4)
Reduced Flap Setti ng, /) f = 0.2 in. (Run No. 2226)
High Mach Number, Mro = 1. 228 (Run No. 2255)
(
Nominal conditi~ns (Run No. 2258);
VplVts - 2.8
T = 4.5 percent
/ Mro = O. 9~1 Ii f = 0.41 n. Diaphragm
rLOW Porosity, T = 1. 5 percent / (Run No. 2241)
(
Valve (Run No. 2742)
Notes Indicate Deviations from
Nomi nal Conditions
O~---d----~----~----~----~--~ o 10 20 30
Time, msec 40 50 60
Figure 32. Transient loading of test section wall at exit for nominal conditions and selected deviations.
4.0 SUMMARY AND CONCLUSIONS
A mathematical flow model for the process of starting a transonic Ludwieg tube wind tunnel has been developed. The present model uses the integral continuity equation for three specific control volumes, the steady form for the diffuser and test section control volumes, and the unsteady form for the plenum. The solution in the two former control volumes also uses the steady, isentropic energy equation, assumed applicable throughout the diffuser and test section control volumes for a given set of stagnation conditions. However, the stagnation conditions are allowed to vary in time according to the well-known exact solution for an unsteady, one-dimensional expansion wave. Application of this model
takes the form of a numerical solution of 19 simultaneous algebraic equations to be solved at successive time points until the flow becomes steady. The iterational solution procedure
50
AEDC-TR-76-39
for these exact equations becomes nonconvergent in the vicinity of choking and is replaced
with an analytical solution to a set of small perturbation equations until the choke point is passed. The numerical procedure is programmed for computer solution.
The mathematical model was evaluated by comparison with experimental plenum pressure-time histories from a small Ludwieg tube wind tunnel. Agreement between the
model and experiment was found to be good. Other numerical results from the computer model were also presented to illustrate application of the model to design of a large facility. Specific conclusions drawn from the present study include (1) verification of the model's ability to predict accurately plenum pressure-time histories and, therefore, tunnel starting time; (2) prediction that starting time is insensitive to the precise shape of area-time curve
of the plenum exhaust and, therefore, that very precise controllability is not required of the plenum valves; (3) prediction that starting time is not significantly lengthened by
even large changes in the shape of the plenum exhaust area-time curve if the area under the curve and open time are maintained, thus permitting considerable reduction in the number of start valves suggested by data from the pilot facility; and (4) verficiation that
aerodynamic loading of the test section walls (and, therefore, the support structure) can
be reduced by lengthening the opening time of the main starting valves, within limitations of the required starting time.
REFERENCES
l. Starr, R. F. and Schueler, C. J. "Experimental Studies of a Ludwieg Tube High
Reynolds Number Transonic Tunnel." AIAA Paper No. 73-212, January 1973.
2. Ames Research Staff. "Equations, Tables, and Charts for Compressible Flow." NACA Report 1135, 1953.
3. Hottner, T. H. "Investigations at the Model Tube Wind Tunnel." AVA Report No. 64 A 04 (Technical Translation), 1964.
4. Varner, M. 0., Stallings, D. W., and Starr, R. F. "Experimental Evaluation of the Aerodynamic Design Criteria and Performance of a Transonic Ludwieg Tube Wind Tunnel." AEDC-TR-75-132 (AD ), October 1975.
5. Porter, J. H., Mayne, A. W., and Starr, R. F. "Boundary-Layer Development in the
Nozzle and Test Section of a Transonic Ludwieg Tube." AEDC-TR-76-35.
6. Hodgman, Charles D. (ed.). Handbook of Chemistry and Physics. The Chemical Rubber Co., 1961 (42nd Edition).
51
AEDC-TR-76-39
APPENDIX A
SMALL PERTURBATION SOLUTION
This section presents the essential details of the small perturbation solution, the knowledge of which may be important to a user of the computer program HIRTSMI. Table A-I shows the small perturbation variables and the exact variables they represent. Use of the expansions (Eq. (22)) in the exact equations listed in Table I produces the
approximate small perturbation equations listed in Table A-2. Definitions of the coefficients
AI, Bl, Cl ... , if needed, should be extracted directly from the computer program (subroutine SMPERT) where they are coded as CAl, CBI, CCI, ... , respectively. The equations of Table A-2 can be solved analytically without recourse to numerical iterative procedures. To accomplish this task, the linear equations were solved algebraically to eliminate all variables except those contained in the quadratic equations, Eqs. (12) and
(13). After eliminating all variables but E12 and E13 from the two quadratics, Eqs. (12) and (13) were converted to a single quartic (subroutine QSIMUL), which was solved
analytically for its four roots. If necessary, the reader can extract the algebraic details of this procedure from the computer program. The correctness of the algebra has been infened from computation of residuals from the equations of Table A-2 (replacing the
zeros on the right-hand side with residuals). For all cases tested, the residuals were found to be on the order of the computer's accuracy (~l 0-16 ). Similarly, the accuracy of the
expansions in representing the exact equations was tested by computing residuals from the exact equations using perturbed values for the variables. The largest residuals (percentage basis) were generally less than 10-4 .
53
AEDC·TR·76·39
Table A-1. Perturbation Variables
Original Variable Perturbation Variable
· me (t*) El
· mpe (t*) E2
· mf (t*) E3
· mpt (t*) E4
Pp (t) E5
· (t*) md E6
· met (t*) €7
Met (t*) E8
Peo (t*) E9
Teo (t*) ElO
Pt (t*) Ell
Pd (t*) E12 -""'
Pn (t*) E13
· m 0
(t*) E14
P (t*) E17 a p
Pp (t*) E18
Tp (t*) E19
Ae (t*) EAe
Ape (t*) EApe
I Af (t*) EAf
(a)Variables 15 and 16 were eliminated.
S4
Program Equation
Numbera
1 AIEl
2 A2E2
'" ASES ,y
Table A-2. Perturbation Equations
+ B1 E9
+ B2E17
+ BSEAf
Perturbation Equationb
+ CIEAe + D1 EIO = 0
+ C2 EApe + D2 E19 = 0
+ C3 E17 + D3E12 = 0
4 A4E4 + B4E17 + C4 E11 - 0
S ASES + BSE2 + CS€3 + DS€4 + ES = 0
6 AG E6 + B6€4 + C6 €7 = 0
7 A7€S + B7€3 + C7 €1 '" 0
8 Ag€7 + Bg €8 = 0
9 A9 E9 + Bg€g '" 0
10 AIO €10 + BlO€S = 0
11 AII€ll + Bll €13 + C1I €12 = 0
AEDC-TR-76-39
12 A12€6 + B12 €14 + C12(PctoE12 - Pd €9) + D12 (Pc t o €12 2
- Pd€g) = 0
IS
14
17d
18
19
A13€7 + Bl3 E14 + C13 (Pc t o €13 - Pn€g) + D13 (Pc t o €13 - Pn €g)2 = OC
A14 €14 + B14 €9 + C14 €10 - 0
Al7E17 + B17E18 = 0
AlSE lS + Bla E5 + CIS = 0
A1g €19 + B19 E18 + C19E17 = 0
(a) See Table 1 for Corresponding Exact Equations
(b)Refer to Listing of Computer Program, Subroutine SMPERT, for Definitions of Ai' Bi' ...
(C)Variables PCto ' Pd , and Pn Are Evaluated at t* - 6t As Are All the Coefficients Ai, Bi, ...
(d)Equations 15 and 16 Were Eliminated
55
AEDC-TR-76-39
APPENDIX B APPROXIMATED EQUATIONS
Reversion of Eqs. (11), (13), and (7) requires a time-consuming numerical procedure which has a major impact on the run time of HIRTSM 1. To reduce the number of iterations needed for the reversions, approximations to the original equations were used to provide accurate initial guesses to the numerical procedure. Since these approximations may be of general interest, they are listed below. A good approximation to the mass flux-Mach number wave equation was obtained by expanding
(B-1)
in a series of powers of M using the binomina1 expansion. Reversion of this series for 'Y = 1.4 then produced
M = A
m - 1.200 ~2 + 2.0400 ~3 + 4.0480;ti4 + 8.7965 iiJ.5
+ 20.106 iiJ.6 + 47 .960 ~7 + ... (B-2)
where Iri == mime. The approximation used for the energy equation is much simpler and was discovered quite by accident. It was found that the equation
y+l
~2 = p2/y _ pY (B-3)
could be very reasonably approximated over the interval 0 ~ M ~ 1.4 by the ellipse
where
and
p
~ + p-;: = 1 ("'-')2 (- ,.....,*) 2 ffi* 1 - p*
,.....,=Jy-l~ m 2'
m o
p -
]"5* m ,
P
Po
56
m* for M
(B-4)
1
AEDC-TR-76-39
APPENDIX C DESCRIPTION OF THE COMPUTER PROGRAM HIRTSM1
Because of the complexity of the numerical calculations, potential users of the model must have access to the computer program (a manual calculation on a scientific calculator took about six hours to step through five time increments). For this reason, a listing of the source deck is given in this section along with a brief description of its content and use. Table C-l lists the 15 subroutines comprising HIRTSMI. Of primary interest are the routines MAIN and SMPERT, which house the exact model equations and the small perturbation equations, respectively. Table C-2 defines some of the more important variables used in the program, information which is potentially useful if a program modification is necessary.
Of primary interest to the potential user, however, is the input, instructions for which are listed in Table C-3. The first card (NCTL) allows the user to retain manual control over some of the superficial program logic. While intended primarily for debugging purposes, the NCTL variable may be used to restart a run previously written onto a data file. To make a normal run and relinquish all control to the program, a blank card may be used. The second card (lNSTR) provides the means to invoke certain program options via integer instructions. Table C-4 gives a set of values which have been used successfully to date, though occasional adjustments are necessary for some cases. Of particular importance for supersonic cases is INSTR(26). As the program approaches the choke point in the calculation (timewise, speaking), the number of iterations (ITER) for convergence always becomes inordinately large (~IOO); and the program must switch to the small pertubation solution entirely by automatically setting INSTR(23) = 2 when ITER;;:' INSTR(22). However, for supersonic cases, the solution is often not close to its asymptote, and significant error can accumulate from the small perturbation solution. To reduce this error, INSTR(26) may be used to direct the program to attempt to revert back to the exact solution a certain number of time increments (the input value of INSTR(26)) beyond the choke point. Sometimes the attempted reversion will be unsuccessful because the solution is either still too close to the choke point or is already too close to its asymptote; in which case ITER;;:' INSTR(22) will occur, and the program will continue with the small perturbation solution. When this situation occurs, the exact solution is not given a chance to correct the accumulated error, which may affect the asymptote by as much as 10 percent. If this result is encountered, different values of INSTR(26) should be tried, since even a temporary successful reversion to the exact solution can improve the accuracy of the solution considerably.
The remaining data cards constitute primarily a description of the tunnel and its
geometry. While most of the table entries are self explanatory, some of them deserve
more emphasis; On card number 4, the values of Al5 and A16, if used, should be entered
57
AEDC-TR-76-39
as negative to invoke the use of ramps. On card number 5, the weight used in computation of the test section pressure for subsonic flow is programmed as 0.5. The input value is used only in supersonic flow. On card number 6, the variable A14 is used to sort the roots from the quartic. A value of -0.2 has been found more effective than -0.1. If the root sorting logic finds more than one value of E13 acceptable, the program will halt in bewilderment, requiring some trial and error adjustment of A14 by the user. On card number 7, it has been found best to keep $EMAX ~ PERR/IO. The quantity AlO is used to obtain debugging information when T > AlO. Following card number 10, three separate decks for the nondimensional area-time curves for the main valves, plenum exhaust valves, and flaps must be provided. Each deck must contain the number of cards entered on card number one. The times and areas must be nondimensionalized by the values entered on card numbers 9 and 8, respectively, and, therefore, will vary only between zero and one. The times must proceed in ascending order. Table C-5 gives recommended values for some of these entries. The remaining input instructions (11, 12, ... ) may be ignored unless NCTL has been entered as other than zero, in which case the user is invited to decipher the program logic in order to determine the endless uses to which this option may be put.
Table C-6 presents a sample job stream and data deck. The first four cards are peculiar to the computer facility. The first "GO II card designates data set 03 a dummy in order to suppress debugging printouts sent to DSRN* IDEBUG. The remaining data cards may be understood via Table A-3.
A portion of the output from this run is shown in Table A-7. The first four pages show the input data along with the initial values of most program variables. In addition, an interpretation of the INSTR(I) options selected is printed. The flow area-time curves are the redimensionalized form in units of seconds and square feet (or whatever units are used in the input data). The form of the remaining output is that due to the selection of INSTR(5) = 2 and generally displays all computed properties at the midpoint or end of each time interval. Each five lines of data separated by a space corresponds to a single time interval, and each block of five numbers corresponds to the similarly positioned block of five variable names in the page heading. Interpretation of these names may be accomplished via Table C-2. The illustrated run went to 180 msec, generated about 1,700 records (lines of print), and required 42.6 sec of central processor (CPU) time on an IBM 370/165. This run may be used as a check case by potential users.
Table C-8 presents a machine listing of the final source deck. All necessary subprograms are included except those available from the IBM subroutine library, from which HIRTSMI uses DABS, DSQRT, DSIN, DCOS, DATAN2, CDSQRT, and CDABS.
*Data Set Reference Number
58
AEDC-TR-76-39
Table C-1. Description of Subroutines
PRIMARY MODEL SUBROUTINES
Subroutine Name
MAIN
SMPERT
Function
1. Overall program control
2. Exact model equations
3. Convergence control
Small perturbation equations
SPECIALIZED UTILITY SUBROUTINES
INPUT
CONST
INIT
DUMP
Obtains initial data from DSRN lIN
Defines certain program constants
Initializes certain program variables
Prints out all program variables at beginning and end of run and as needed for depugging
Prints numerical solution and controls paging
GENERAL UTILITY SUBROUTINES
SOLVER
BINOM
REVERT
QSIMUL
QANDC
CVBRT
DREAL
DIMAG
Provides logic for numerical reversion of a function (see Fig. 10)
Expands a binomial to seven terms
Reverts a series to seven terms
Converts two conics to a quartic
Computes the exact roots of a quartic
Computes the exact roots of a cubic
Returns the real part of a double precision complex number
Returns the imaginary part of a double precision complex number
59
AEDC-TR-76-39
REAL ARRAYS
Variable Name
AREA
AREATS
AREAM
TV
E
TVF
TDELAY
RW
V
RSTR
ISTR
REAL SCALARS
Pxi
MDxi
Txi
Rxi
Mxi
Axi
Table C-2. Definition of Major Program Variables
Definition
Input nondimensional area-time curves for main valves, flaps, and plenum exhaust valves
Interpolated areas for time t*
Peak of area-time curves (dimensional)
Nondimensional times for area-time curves
Convergence criteria errors
Total time for main valves, flaps, and plenum exhaust valves (dimensional)
Delays times for first motion of valves and flaps
Coefficients for the reverted expansion of the mass Flux-Mach number wave equation
Array equivalenced to major property values
Array equivalenced to certain real commoned variables to simplify writing of solution onto a storage device for restarting a run
Array equivalenced to certain integer variables for storage and restarting
Pressure
Mass flow rate
Temperature
Density
Mach number
Flow areas
60
x-codes:
x N
P
PT
D
= T
= CTO
CT
E
= F
PE
C
i - codes:
i blank
i 1
i 2
i "" 3
G
R
PERR
KF
KW
TSL
TSH
AEDC-TR-76-39
Table C-2. Continued.
Nozzle exit (test section entrance)
Plenum
Plenum at time t (PPT) or wall crossflow (MDPT)
Diffuser entrance (test section exit)
Test section midpoint (PT)
Stagnation condition, charge tube
Charge tube
Main valve exit
Flaps
Plenum exhaust
Charge conditions
Values at current time interval and current iteration
Converged values from last time interval
Values from last iteration, current interval
Scratch area
Specific heat ratio (~)
Ideal gas constant
Error limit on pressures
Flap flow coefficient
Wall crossflow coefficient
Test section length
Height
61
AE DC-TR-76-39
TSW
TSP
TSA
TSWA
TSV
CTD
CTA
PV
PVOTSV
TAUW
T
TI
DT
TSTR
TSTOP
Ai
INTEGER ARRAYS
INSTR
NVT
INTEGER SCALARS
I DEBUG
lIN
lOUT
ITER
Table C-2. Continued.
Width
Perimeter
Flow area
Wall surface area
Volume
Charge tube diameter
Charge tube flow area
Plenum volume
Plenum: test section volume ratio
Porosity
Time at end of current interval (t)
Time at end of last interval (t - ~t)
Time increment
Midpoint of current interval (t*)
Time for termination of run
Miscellaneous program constants
Program control instructions (see input)
Number of time pOints in each of three input area-time curves
Data set reference number (DSRN) for debugging output, normally dummied
DSRN of input data (usually 05 for card reader)
DSRN of primary output data (usually 06 for line printer)
Number of iterations
62
NP
IFLGi
Variable Index Value
NCTL 0
1
2
3
4
5
6
7
8
9
10
11
12
13
INSTR 1 06
03
2 05
3 06
4
5 1
2
6 ,<0
0
7 1
2
8 1
2
9 1
2
10 1
2
0
AEDC-TR-76-39
Table C-2. Concluded.
Printing time interval
Miscellaneous program control flags
Table C-3. Description of Program Input a. Main Program
Action
Proceed through normal programmed solu tion procedure
Read INSTR(*)
Write heading
Read data file and print reaul til
Proceed to normal calculation
Call INPUT
Call INIT
Call CONST
Call DUMP
Call SOLVER
Call PRINT
Call BINOM
Call REVERT
Stop
Print debugging data
Skip debugging prints (DSRN 03 Is Dummy)
Input DSRN
Output DSRN
Printing time interval
Pressures in psf
Pressures in psi
Call PRINT on every i tara tion f Call PRINT on ON convergence set to zero when IDEBUG
Extrapola te to next time interval as an inl tial guesB
Do not extrapolate
= lOUT
Use reverted series from mass flux - Mach number wave equation Use second-degree approximation
Use iterative solution to energy and wave equations
Use approx1ma te expansions for energy and wave equations
Average current value with previous average value
Average current value with previous unaveraged value
Do not invoke option
63
Defaul t Format Value
0 13
2613
03 (One Card)
05
06
1
2
0
2
1
1
0
AE DC-TR-76-39
Variable Index Value
INSTR 11 >0
12 1
>1
13 ,,0
0
14 >1
1
15 ~03
03
16 [1,1000 )a
17 [1,1000)
18 ~03
03
19 [1,1000)
20 0
>0
21 0
~O
22 0
>0
23 0
1
2
24 "0 0
25 1
2
26 0
>0
Table 3. Continued a. Concluded
Action
Iteration limit beyond which current weight is
Do not invoke option
Divide error limits PERR and $EMAX by INSTR(12) difference between successive time intervals (errors) x (INSTR(12) )
Print only time and pressure data
Print everything
halved
if the fractional is less than
Set DT ~ DT*INSTR(14) based on INSTR(12) ceiteria, do not cut error limi ts
Do not invoke option
Read solution from DSRN ... INSTR(15) , skip other input
Do not read solution
First record number to be read
Last record number to be read
Write solution on DSRN ~ INSTR(18)
Do not write solution
First record number to be written
Do not invoke option
When weight is halved, increment INSTR(l1) by INSTR(20)
Do not invoke option
Set INSTR(7) ~ 2 to extrapolate next time interval when weight is halved
Do not invoke option, set INSTR(22) ~ 23 1-1
Set INSTR(23) ~ 2 when number of iterations , INSTR(22)
Do not use small perturbation expansion
Use small perturbation initial guess for next time interval
Use small perturbation expansions as solution
SMPERT prints small perturbation results
Does not print without error
Use isentropic solution in plenum
Use anisentropic solution in plenum
Do not invoke option
Revert to exact equation after the input number of time increments beyond choking
aSquare brackets [] indicate the range of the variable.
64
Defaul t Format Value
0
1
1
03
0
0
03
0
0
0
9999999
0
0
2
9999999
Variable, Card Value units Numbera
NVT(I) 1 [2, so] NVT(2) [2, so] NVT(3) [2, so]
PC, psia 2
Te, OR
TSL, ft 3
TSH, ft
TSW, ft
CTD, ft
PVOTSV
TAUW 4
!{W, ft/sec
Table 3. Concluded INPUT b. Subroutine
Meaning
Number of area-time points for main valve Number of area-time points for plenum exhaust Number of area-time points for flaps
Charge pressure
Charge temperature
Test section length
Test section height
Test section width
Charge tube diameter
Ratio of plenum volume to test section volume Porosi ty (fraction, not percent)
valve
KF, ft/sec Wall crossflow coefficient ~
Flap flow coefficient from Dr. Varner's flow model
AlSb Crossflow constant MDPT = -AWOKW x (PP - AIS x PT)
Al6 b Flap flow constant MDF = -AF/KF x (PP - AI6 x PO)
A17 S >0 Tes t sec tion pressure weight, PT AI7 x PO + (1.00
R, ft2/sec2_oR 6 Perfect gas constant
G Ratio of specific heats (1')
All (O,1)c Fraction of new values to be accepted
A13, sec Set INSTR(23) ~ 2 When T > AI3
A14 e:12 and e:13 limi ts
DT, sec 7 Time increment for numerical calculation
TSTOP, sec Time to halt calculation
$EMAX (0,1) Maximum allowable error - used in SOLVER! PERR (0,1) Maximum allowable error - used in MAIN fractions,
AID, sec Time at which 1NSTR(6) is set different from zero
AREAM(I) , ft2 8 Maximum main valve flow area
AREAM(2) , ft2 Maximum plenum exhaust flow area
AREAM(3) , ft2 Maximum flap flow area
TVF(I) , sec 9 Final time in main valve area-time curve
TVF(2) , sec Final time in plenum exhaust area-time curve
TVF(3) , sec Final time in flap area-time curve
TOELAY(I) , sec 10 Time delay for main valve TOELAY(2) , sec Time delay for plenum exhaust
TOELAY(3) , sec Time delay for flaps
TV(I,1)
! ! l 1
AREA(l,1)
TV(2,1) [0. ,I.] Nondimensional time (final = 1.0) and for AREA(2,1) nondimensional area (maximum = 1.0)
TV(3,1) AREA (3,1)
nd 1 0 Return 1
l 1 Read ISTR(I2)
2 Read RSTR (I2) one card
3 Read V(I2,13)
12 Indices of array elements to be read I3
1STR >1 } Enter one per card each preceded by a RSTR >1 no. I card above - see common and
V >1 equivalence statements to determine indices
acar4 order in Input Deck
bIf l4't!1!6 than Zero, P..ampe of Fig. 27b Will Be Used
cRound Brackets Exclude End Points
QTbeae carda Omitted Unless NCTL F 0
- AI7) x PN
not percent
{ main valve }
{ plenum exhaust }
{ flaps }
Note: Xf INSTR(3) - I, any .et of units for which gc - 1 1n F - l/Ro ma w111 work properly.
65
AEDC-TR-76-39
Default Fo:rmat Value
2613
SEI6. B
SEI6. B
SEI6. B
1.0
1.0
1.0 SEI6. B
SEI6. B
O.S
1.070
-0.1
SEI6. B
1.070
SEI6.8
SEI6.8
SEI6. B
2EI6.8
2613
13 EI6.B E16.B
AE DC-TR-76-39
Table C-4. Suggested Values for INSTR(I)
I Suggested Value of
INSTR (I)
1 03
2 05
3 06
4 01
5 02
6 00
7 02
8 01
9 01
10 01
11 40 a
12 10
13 0 or 1
14 01
15 03
16 00
17 00
18 03
19 00
20 lOa
21 00
22 01
23 01
24 00
25 02
26 Oga
(a) Adjustment May Be Necessary for Specific Cases
66
AEDC-TR-76-39
Table CoS. Recommended Values for Certain Variables
Variable Names
KW, KF
A15, Al6
All
Al3
Al4
Al7
PERR
$EMAX
Recommended Value
See Fig. 7
See Fig. 27a, Enter Negative
0.5 or Leave Blank
Leave Blank
-0.2
0.9
0.49999999E-04
0.49999999E-05
Table CoG. Sample Jobstream and Input Data Deck
1.~~iORITY 2 livKF05145 JOB (iRQ, Ii VRV00090901'VJ7A~J1AI~094S2S~O~E.MSGlEVElm(2901,ClASSmA,TIMEa3 ii EKEC FO~TEPDS,PGMNO=V~~00090 liGO.FTOJF~Ol DO DUMMY I(GO.FT05FOOl DD ® (lOO
02 01 20 10 10 00 20 01 00 09 02 10 02
O.iSt!150iioE+O) 2.11 4000nOE 00 O.04000000E 00 0.90000000E 00 0.111760~OE+04 O.OOlOOOOOE 00 0.4659ili6E 00 O.030tH)oiiOE 00 O.OOOOOOiiOE 00 o.oooooonOE 00 1.00000000E 00 O.OOOI)OOOOE 00 0.16400000E GO 0.20GOOOOOE 00 O.JOOOOOOOE 00 0.450000fJ!IE 00 O.SOOOOOOOE 00 0.660000(;0£ 00 0.8000oo00E 00 0.900000nOE 00 1.00GOOOnOE GO O.OOOOOflQOE 00 1.000noono!!: 00
005JOOOOOOI::+O) O.61HoOOOE 00 0.31000000E$03
O.16330000E 00 1.!6200000e: 00 2.S0000000E 00 O.20000000e:+OJ ~1.049B8410E 00 ~1.08312800E 00
1*
1.40(HIOOOOE 00 o. H~OOOOOOE 00 0.90311 fl4E 01 O.04000iHIOE 00 0.005000001:: 00 Q.ooooooooe: 00 1.000000001:: 00 O.OOOOOOOOE 00 0.9t!JOOOOOE 00 0.9S000000e: 00 1.OOOOOOOOE 00 O.M298055E 00 0.97332608£ Oil O.64902737E 00 0.52418305£ 00 0.49810913E 00 o.48687801e: 00 1.OOOOOOOOE 00 1.0!)(1(')0000E 00
O.49999999E-05 0.49999999[-04 0.09167000E 00 0.00000000£ 00 o.ooooooooe: 00
67
,,0.20000000E 00
AEDC-TR-76-39
TABLE C-7 SAMPLE OUTPUT FROM HIRTSM1 FOR RUN 2742
69
'" ... c< .... VI :2
• ... '" ... <II Z .. . .., '" ... c< ... .~
"I '" ~' ~ ... til Z
.... <>
... "I c< ... til Z ... Q ..o: .... ~ .... N, O!:c< ....... ' <II VI ~;f!
..oNOO
'" N :x:>: ..... n'" zz ... -
-$'0-'10 ru ...
"'''' ....... VI VI Zz .......
:'\I~!J'I"'I
XX ....... .,,,Il ZZ --
"' .. <!I J to. ... ... <!I J ... 1"1'" <!I J ... ... "I'" <!I J ... ...... '" .... ... ....
"'" J ... ...
"I'" ...
"'0 tAl ... ... Q.o ....
30 ... Z
W'" <!I./'I .. <L Z
Wc> <!I .. 30
Z./'I
JO ... U Z
....
, .... , ..
·.,nOt
4-0 ...
-"I .., ... ,. Z
- ... -:'\1-
:> Z
-"I .... .... '" Z
"'0 lit .... ....
>-0 U Z·
7:0 Z
00 z
0<0 <!I J ... :xl:> <!I J I.L
-0 <!I J LL
1"1 CO
o <> <>
10.<> ,",0 .. .. ..
N · '" 1"1 ."
o
'" <> lIo "',.
'" '" ... '" · .. ... '" I o
'" lB-:> :>0 CO .... '" <>
o • · '" ... .. '" >",
til'" >-'0 00 >" Q.O
./'I. "I · <:>
'" '" o :>
'" 1!1'" Vlo ... .., ... D .... · ::>
'" Q
... :>
'" <> <>
";0
"'0 .... ... .... N · <>
<>
'" o 1"1
'" '> (JI
"'4 ... '" ... '" (JI · o
· <:>
o <>
'C~
"'''' til 1"1 ' ......
'" VI · <>
... Q
o
'" '" "'" VlO "'0
'" .... N · ""
.... '" , '" :>
'" lito 10.0 ......
", .... (JI · <>
... '" , '" 4 ...
lit ... n._ .....
M <> 0< · ::>
'" :>
o ", ... ,. .....
W.. '" Jl .0 .. · '"
1"1 '" , o ..
" '" ", ... 0'" ,.'" .. -
'" ... . '"
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AEDC-TR-76-39
TABLE 8 LISTING OF THE COMPUTER PROGRAM HIRTSM1
83
AEDC-TR-76-39
DATE " 75157 11/58/40 -- _._----------
r. HIRTS~l - ~JRT STnRTING MODEL _______ 1~IC.n~4L"_lLJA;:"fuM;O-Lt.ll ___ _=_-------------
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--R EAL;;-8T-N~I N • K F • K W DAT~ IFXTpVl.~.6.7.l0.14.161
DATA C/-.14895381DZ •• 453475010Z.-.43530673D2 •• 1406ASS4D2. -L-~5§23QO~702 •• 14939843D3.-.13208110D3 •• 38913333021
DEFINE FILE Ol(300.1200.U.J16) ~OP.QJDil?~~!~~~M~G~O~G~M~l ________________________________ __ MOOTPT(Dl.DZ)=-AWOKW*(Dl-D2*AlS)*A2
------.llJ "1E=O IFl!)l"l IFLG2=+1 IFlG6=1 IFL59=1
~-fFl510=1 YFLGll=~O~ __________________________________________________ __ IFlG12=1 IDEeUG=03
85
AEDC-TR-76-39
DATE", 15151 11/5B/40
. IIN,;05--.----------------------------IOUT=O/\ ;Ijf';i J5=Q ____________ _
10 REA)(IT~.120)~CTL
r.-----------------------C M-tlNUAL ~ROr,QAi1 -CO'lTROL . C_~--_~_~.::=_==_:__:_::!":_~_':'_~----_:___=_=_-----------__ - __ --
IF('1CTL.E~.O)GO TO 100 \(RllfjJJ)UTli5) N"'-C-=-T~L,---._-------------------
15 FOR~AT(.0~CTL= •• I3) C__ . __ ._ .. _L ___ 1! .. ___ .J_. ____ 4 5 6 1 R 9 10 11 12 13 14
r,o TO(100.125.129.1116,20.30,40.50.60,10.BO.90,151.9S),NCTL ~_'Ab~~lNP~_111J~OL) ______________________________________ ___
30 CALL' HITT(~10) ~O CALL' Cn."lSHU.O_L ______________________ _ 50 CALLI DU~P(&oIO)
_ 50 CALl-' _501.. VC'R (UQ.L ___________________________ _ 70 CALL' PRINT(~10)
.. ____ 'liL .. CALL' !'IT NO'!1li~O~) -:--______________________ _ 90 CALLI RFVE~T (&010)
_95. CA.L\,.I_?MPEQ'TJ~10)
c---------------------------------------------------C REAl) AN,) I)ffI.'1~_ 6~FA..ll1.._H:n RUN CON-'-TR'-'-O:<.L"-""IN"-S::.T"-'R-"'U"-'C'<,.T:.cI..,O""N-'-'S"--_______ _
C---------------------------------------------------_ Jj)(l_ ~E"A'2_nl~.!J.2QJ 1 NSTR'-___ -'-_________________ _ 120 FOQI1ATt('6J3)
J F t J NS T R ( 1 ) • NJ;:. 0 t 'UltRl,JG_"i_"i!ilBU:~) ______________ _ IF(INSTR(I).EQ.O)JNSTR(l;=JOEBUG IF' (lNSTR(2) .N~.f)illN:::_ltiS.I_Rll_) ___________________ _ IC'(JNSTR(2).EQ.oiINSTR(2i=IIN
_____ JF.<I f'jS.T ~ Lll • ~£ IL. Q=+-) ~I O,,-,U~T=-:=?I~N~.S,L.IL!Rc-:(~37:):-_______________ _ IF(TNSTR(3).EQ.0)TNSTR(1):IOUT IF' ( T NS rr~ ( ~) • ~~. QJ ~p-" l."!.S~R,,--,-,t 4LIL-__ I~(INSTR(4).EQ.0)INSTR(4;=1 I~ (INSTR( 5) .EQ.OLWSJ_RJ_5j __ =l. ___ . ____ . _____________ _ IF(JDEPUG.EQ.IOUT)INSTR(6)=0
_ 1£ (JNSI~1.L ... EJh_~TR ( 7 i:2 . ~ Y~(INSTR(~).EQ.O)IN~TR(8)=1 Y' (YNSTQ(9) .EQ._Q) .TNs:rgJ'~i-=-L ____________________ _ I~(lNSTR(12).EQ.O)TN~TR(12)=1 I~(lNSTR(14) .~(l_.ILLTfIIS_18.1H)=1 ______________ _ I. (I NSTR ( 15) • t;:Q. 0) PJSTR (15) =03 Jt=:J T N,SJRJllU .LMHNS TR'-"~1_':'8CL)-="''::0_::3_=_=-=-_---_------_--_ IF'(TNSTR(22).EQ.O)TNSTR(?2):9999999 IF (T N5TR(?5) • t;:Q. 0LI.tI!STR_.l2Sl.= .. 2._._. _________ . _______ _ t~(TNSTQ(26).~Q.O)tNSTR(?61=9999999
DO 12.1 1.=1,26 _______ . ___ . 121 JV(l)=TNSTR(I)
I F . .l 'LC.IL.H::.ill.G0 TO -'1..,0'--____________________ _
C--------------r. PRINT HEIIDJNG
C--------------__ 125 IotRJ1':E (YOUT •. 13H ______ . _____ ,, __ _ 130 FORI1AT('1',29X.74('$')/30X •• ,o.1?X,'$'/30X"$ HIRTSMl = MATHEMATI _.--l'c'!.L ST.~_!D_l~fi. \100El FOR .A...LV.flIHEG TUPE WyND TUNNEL ~. 130X, ". ,
86
AEDC-TR-76-39
DATE .. 75157 11/58/40
272X.'$'/30X.I$ AQNOLn R~SEARCH ORGANIZATION. ARNOLD UR FORCE STA _ ._JTHl.~LJ~' .. o...l.2)l...L!...i.!.IJOX. 1$ •• 72)(. "'130)('741 .'1 1~. ________ _
IF(~CTL.N!~O)GO Tn 10 129 _ILt J15aEQ. 03lJiQ_I0.--.lJ~ _____ .. _.
c---------------------------------------1:. RHD .. _Sl1UH J' ON _ EeO_'LD1\.J !LULE.......A...ND._fRl."I1_. ___ .
C---------------------------------------_ ... ___ . K.1~O __ ._. ___ . _._ 131 I~(J15.~E.07)GO Tn 1?8
REA r:> tJ 1.5~. £N.!L"'.lJ.2l.R]ilRllSI!L. Jl"'=Jl"'+l
.GO J.o_ 127 .. ___________ .. ____ ._. 12A READtJlS'JI6)RSTR.JSTR
___ ..cFIND (J15' J1.6"U-1 _--------------------127 I~(~l.FQ.O)CAlL DUMP
... _____ ~.Kl __ _ CALL' PRINT Kl=IPAGE._. ____________ . __ . _____ .. ____ _ I~(J16-1.~a.J17)GO TO 132
.. __ . .GlL.lJl..~ ___ . ______________ _ 132 IF(INSTRt~).EQ.o)r,n TO 1~4
.. WR nEJ lOUT .lJ3L_. ___________________ . __ ._ 133 FDR'1/1TPlQ
._.CII.LL.<...nU~P IPA3E=O CALL' PRINT
134 J16;:;Jlq . .!'I~IlE.il.0I,lJ.136J ____________ _
136 FOR'1AT( ..... ., o"'ru :::~O-M) 1 D'1Nl"MN-M~l
.. _ .... __ ~F.0!crL.N::'''-CWlll. TO 1 n GO TO 1116
.C------~~-----------~~~---~-~-----~~~~-_~----------C R~ary INPUT,lNTTIAL~lE V~RIARI.FS.ANn PRINT RFSULTS C-;;~-~;~:~;~-:'"-------------.~--=~---~=~~~~~~~
13q
140
141
II'"L'J4=O CALL INPUT CIILL' CO'lST CIILl' l~'TT CIILl' m,..,p I~(al~.GT.o.no)r,o TO 140 I~L:;lI"l TI'"(1I16.(';(. (-1.:)0) )(;0 TO 13q I\I..,a"f)A~S(A15)
AI6a=DM~S(Al"') I~l:;11=? 1115=1.'10 Al"'=l.no CAll PqyNT J~(JIB.EQ.01)r,0 Tn l~o
II'"(JIR.NE.07)SO Tn 145 W~ITE (JI8.!41) FOP"'AT(32(1"')"S~OPF - VK~/Af)P'.13('~'» W~LTE (JI8) PSf::ltlSTJL .. ~~_~ _________ ~ __
87
AEDC-TR-76-39
DATE" 75157 - -----~
JI6=Jll'o.1 ... _!30JO_ 15_L ___ . ______________ _ 145 WQITEIJ18'JI6)QSTR,ISTR
c.~----~~-..,-..,---..,_=..,~.:':~~ __ C SURT N~W TIM::, INTERVAL .c -~ - -~ -.-- --.-. .., . ..,_-.~..,..,_ ~ ~~.-c...--=-:.::-__
150 Tl=T ... _ .... ___ T=I·DL __ . _________ .
Y-(TFLG11.EQ.0)GO TO 280
11/5A/40
J3(LTOL2b9J.2..B1J(?_16) tIFLGCA1.J.l ____________________ _ 269 I-I~Dl.r,E.l.00)GO TO 270
.. Al!2"L.DO _________________ _ 616=1.00 GO TO ?76
-T70-All) =0.00 _A!2L~.LDO ____ _ 00 274 1=1.4 ll!:') =.MD.lu U..,ll DO 272 J=I.2
__ 21.2_HJ1::Jd.J.Lti:J.l..l_J.lL*:JA'-'I ... 3u) ____________________ ---
274 CONTINUE .. 1I15=,tI III
1116=11(2) _.l30 TO. 27.6 __ . . _______ _
2q2 I-I~Dl.GE.l.00)GO TO 284 ___ ._. __ --Al ~=..1Al5A_-.1..JlilL) *~MC!!DCLl"_'+!..I"_'.o.JDJJO"-____________________ _
1116::(AI6A-l.DO)*MDl+l.DO GO TO_.27t? _____ . ____________________ _
2B4 1115=Alo;/I _Ill':> :: A.l M II'"LGll=3
____ ll~If,Jllllilt(i'_2}LJ8::7') M:!JQLl~.L.!A""IL5'-'.uA":!I~6'7__=_:c_:__=_c_:___:_:_;__:__=_:_;__=_:__-----__ _ 276 FOR~ATI' ~Dl= •• r.16.8.' 615='.EI6.8.' AI6:'.EI6.8) .2.9Jl.lE"1 IFLr,2. __ I.IT .Q.U5 .. 1.5.~._._=__:_=_------------------
YFIY5.NE.YNSTQ(26»GO TO 143 _I ~ST!U2.:iL"1 ... ___________________________ _ WRITEITQUTol42)
_~~~}\Ji~~QTINr, TO EXAcT SUPERSONIC SOLUTION'I 143 I_IIINSTRIIO).EQ.O).OR.ITTF.R~LT.YNSTRIll»IGO TO 152
C W::YGHT CUTTTNG' _____________ _ 1111=.5*1111 A12=.l...-AU_ . ____ . ___ ~ ____ ~ _____________ _ I~STRIII)=I~STRIll).tNSTRI20f
____ lffi.UU1D!J.Ld.2.051 IIER.UI. TNSTR 1111 120~ FDR~IITI'O'.~X.'ITER='.Y].' WT ~ALVF.D TO ',F5.3.' INSTR(II) RAYSEn
10 TO '.171 . ______ . ____ ._. __ . _____ . ______ .. ____ . ___ . _____ _ IPIIGE=TPAGE+2
..l5Li-j T • (iE. f;.lQJ I OE.fiU~..I.I1!lI __ TSn=Tl+DT02
._---'lL!T .... l '1E_:;'lll=-~E~+ ~l :-:-::::0-::-:--:---------------------TFIIFLGl.!Q.2)YFLA4=1
_C.... S.EJ" j)RFSSUR!':S OF \".~'E--.l!E~J'_LQN __ l.:L~£'1NITY FOR I':RROR COMPUT",II-'..T ..... Y.o<.O,-,-N __ _ DO 153 Y=I.7
._...i53..'IIJ I.~) :TN!",r", __________________ _ ITf':'l::O
___ -.-lL.LT ..... .L..f..JSTnPI GO TO !l55.240) tYFLGl
88
AEDC-TR-76-39
DATE .. 75157 11/58/40 ---~----- --~------~ --=--'-----------------------
rFI~CTL.NE~O)GO TO 10 ___ ~15:LJtJilrE (lOUT • .L.S..!LL. ________________________ _
154 F'OR~AT (9 1 , ) _____ _ _J:ALLLD~
IFIJ18.EQ.07)WRIT'IJI8,1~6) __ .l.5I'LEllE!'1AI (2 (/60 ( , .. , II I 9999 STO~
_C!'_~~_==--------&_----------------C COMPUTE ARrAS OF VALVFS AT TSTR C--_-~~~~_!'~~~~=~~_~,---=-:.=-:.=-c::-c::-c::-.::.-=---=--:::.-__________________ _
155 DO 220 ,J" 1. 3 __ li=_IlY.I (.JI _____ '--__________________ _
IF(TSTP.GT.TVIJ.II»GO TO 200 T2gIT (.!!
DO 160 1=12.11 _ ~_~L""D!~L
IrIITSTR.LE.TVIJ.JMl».OR.ITSTR.GT.TVIJ.I»)GO TO 160 lliJl:;Y ____ _ IFL51=3
___ m_~ __ All.L;;_J5IR-TV ( J. 1M]1 A(2)=1./ITVIJ.I)-TV(J,I~1»
______ A5to.LS l.Jl:;.iAREA (J.x) -ARFA (J. I~lt ) <lA I U<lA (2) .AREA (JtI 'Ill GO TO 220
_ 1 ~o C.O}J..IViUL __ _ W!:lYTEIIOUT.190)
__ l.9JLf. OR 11H (i OS T oe AT ] 90 9) STO"
200 A!:lfATSIJ)=A~Lil~~~V~T~(J~)IL-____________________ _ GO TO/?lO.220.220) oIF'LGl
210 IFLG1=2 no CONTINIIE
_______ I.EJ.IrL(j].:-Q.31 TELGI::l
e-------------------------------------------C BEGIN ,IItEXLI1ERlLTlilN AI SAME TIME' INTERVAL
c-------------------------------------------(.'40 !TE~:::lI£R~L. __ . _________________________ _ 244 IF(YTEP.LT.INSTR/?2»GO TO 242
L'1518_L2.3_L::i:! ___ _ JF(TFLr.)2.FQ.)WRITEITOUT.245)
245 FOR'1AT (I 0SW!TCl-llNr, _t()-2'1.4~EBJJJRRAlrON SOLUTION ENTIREL V'l IFL312=;?
?4] ITE=l=l 242 ND=O
_. ___ !I!.'!=!L _______________ _ NCT"O I I" I I TEP .. G::.l !I! SIR J22.1. UN5.T.R..t2~ t~ ________ _
243 IF/!FLr,?~Q.l)GO Tn 250 c----~----"".:"-~~---""~"".""-_~~~~------------------=----------------r SFT CI-\ARr.F 'U~F AND NOZZLE VARYARLFS TO STEADY CI-IOKED VALUES c.,.- - -.,. -.,.- ~ - '::."".!'~ ~.,. -_.,._ =:-------. ---------.----------.-------------
IF(iFLr,~.~Q.2)GO TO 250 I ~L ;,6=2 ""Y"'CTAITSA IFLG=3 IFLG2".1 C~U.' snLV~R
- .. _---_._-----_.
89
AEDC-TR-76-39
MCT=$Xl _-.liCl",.$t-[ .....
O/ITE " 75157
A(1)"(1.+~MI02*MCT**~)/(1.+r,MI02*MCT)**2 . _ .. _._ T C. TO:: T C. *.A 11.1... ______ ._
TEO=TCTO J' CJO : P L * A j l1. ..... ".G.OJi!1l. RCTO=PCTO*o.OR/TCTO*A?
__ ."A~C-=-T(!;;.DSQRT (GRIITCIO) MDTSO=RCTO*ACTOIITSA
11/58/40
___ Mf2rlQ.:=RCI!l.!.~rn,,,:*,,,Cc.lT-,,/lL-. _____________________ _ M!\I=l.
____ .. Y ~::?SOf:> 0" °C.UL MDCT=R50RO*~CTO*OSQRT(TSOTO)*ACTO*TSA IrLG2~~~ ____________________________________________ _ WRTTE(To.UT.749)
__ l.liJ':JJR'1AI1! 0 !\IOZ Z LE JiA5....,.,Cc!]H""O",KLEuD..:.·.L) _________________ _ MCTl =Mr:T
. ___ .... TCIO l:::1.c..ll PCTOl=PCIO RCTOl=RcTO ACTOl=/lCIO M"Il=MN PNl::PN
____ t-!J)C T 1 :':-ID.C.,!. MI')TSOl=MOTSO
-----~ClQ1~~~-~~~----~-----------------------------PT=A17*PD+(I.DO-A17)*PN PTl =1"1
·-25·0 I"i'TYNSTRC231:-EQ·.OIGo. TO. 7'5<; _. ___ .. 1 F:.J I._f? T • A tJl ~S.J.R ( ?3) :: 2
ir«jNSTR(23).EQ.3).AND.(iTER.GE.YNSTRCll»)r,o. TO. 253
r._:~~_~~~~~:~:~:~!L~_L)~~~~_-~~~~_~:~~~:~_-_-_-.-_------------------------C C.ALi. .. 5MtlI..LP.ER"'tllH .. ~A.~
C--------------------------------..... ?5.1..PO .. i'.flLl ,,1,3.. ___ _ 11=1+25
____ ._Y~Jill=AR~E~AlT~Sl(IL)L_.~~--------__ ----__ ---__ __ EA(II= V(II.i)-V(II,2)
_ 2.60 CONUNJlL Ir«ARFATSr3).EQ.O.DO).AND.(EA(31.EQ.O~OO»MOFl=0.OO
__ ~~J2)Jffi.Jhilll) ./IND. (Et!!2) .EQ.O.OO) )MDPEl"O.DO CALli SMPE'lT
_____ ~~tG..~ 5.Dl)",. P"-T.L.~::JP,-,C,,-T!.CO,,,-*=-,P::..S;uoJ.!.P,-,OLJT,--_______________ _ IF(~1.FQ.JFLG2)GO TO 256
._. ___ If 1 TFl,GJ. () .. £Q ~.2.I.GQ..I.!l.~6. IPLGIO=2 IF(IFLr,2.~Q.l)IFLG2=Kl
··----1 mFLr.2. EQ. (:'~l '-') )"'G"'0:-=:::T~0"--::2-4-:-1------------------GO TO 756
258 rrLGIO=l _.2.S~ ..l.E.iCJ.III51BJ~3) • EQ. 3) • AND. (JTER. GE. YNSTR (11) ) ) r,o TO 254
IF(INSTR(23).EQ.2)GO TO 254 GO TO 755
254 Ir(JIB.EQ.03)GO'To. 1190 W3ITE(J18·J16IRSTR.ISTR
90
-- -- --~.-~~-----------
F'jN')(JiA~Jl"') ___ .. _f.HLIO __ U911 _______ _ 2~S IF'(JFLr,2)500.9999.251
CG-----.~-------____ ._ . ___ .... __ . ___ ~ ____ . C SUASO~IC RoaNCH C.,--_-"'_---.~.----.. -.--_ .. _._ ...
251 ~DE=Al*PEO*AR~ATS(l)/nSQRT(TFO)*A? ______ .-ULG..2E.~.L_.
1 F'L 1';6= I __ HLG12 ... 1. __________ ._. ___ _
~Dn=MDF'+M'F
I)ATE " 75157
C DIFFUSE'! MACH NUMI:iER_..AI'IO .. E'BESSUR~ ___ - __ ~ ______ _ $Y='4Df)/~DTSO
____ IF"LG=2 CtlLli Sf'L IJ~R MO".~>!.L __ IIID",~N
PD::::::>CTO*POP01'tD.l PT".5*(PD+P~)
__ . ___ f1!1eI~l!lfllE.1lPP....t.tlL ____ . _________ _ MDCT=Mnf)+I.4DPT
C C'1ARGE, TUBE MACI-! 'l.UJotAER _________ _ $Y="IDCT/MDCTC Il'"lG=4 CALL' S()L VFR
._ ~C.L",$l\L ___ _ NCT=$N II ( 1 ) '" ( 1 •• G M 1 Q 2 II ,~C 111-" 21.1'..1 Ld_G111.Q2.II.M_ClLII~ rr.TO=Trt>tI(l) PCTO=Pc"/U 1) "IIGOG"Il ______ ._. ____ _ RCTO=PrTOt>nnR/TcTot>o? PE!J=PCTO . __ . ____ .. TEO"TCTO REO=RcrO ACTn=f)~QRT(r,R!lTrTn)
1\ () ::::RCTO!}ACTO MXTO=A (1) "CH ~IJlS()=A (1 L".15.!!. ___________________ _
C N:l77LE "IAC>4 IIIJMAF'! ANn PRESSURF $Y:I.1DCT /WlTSO I I'"L G:::2 CALL SOLV":R M"J::::'!;)(l
!II'IJ=$N -_._._._---------p~"'lJcro .. poPO("I'IJ) II'"(IJT.LE.ocrOIiPSOPO)GO To 241 GO TO 1000
C------------------C SJPERSO'IJIC RA~NCH
C------------------<i()O PT=A 1711PO+ (1. ')O-A 1 i,.ipiT . --------.. ---11'"I.S2=-) 11'"[ 512=) ~OPT=~"OTIJT(PO,PT)
~f)n=MDrT-\mpT
'iClf=-'if)F.IiD'l
91
AEDC-TR-76-39
11/5A/40
AEDC-TR-76-39
TEO=TCTO _ ._f:>EJt=tiDE"J:tSQ8.lJJE!!.L!!Q.o1'I V.I'lHEAI!i.{ll.~
REO=PEO"OOR/T~O "A2
DATE = 75157 11/58/40
.C.DII"FUSF,::l P8E:55URE_ AN.I;LM.A~I:U!'U}1.f1.E.B._~ .. l>Y='1DD/MDTSO I 1l".LS=2 .. ____ .. ____ .... ____ ._ .. _ .. ____________ _
CALL' SOL VER .. ___ .. MD='tXl.
Nfl='tN PD=PCTI)"f>OPOL~.L .. __ ~ ___ ~.
C-------------------------C UOf)~ TE PLENUM CONDIT I Qt-l.'i .. _ .. __ ._._. __ _
C-------------------------.1000 1.1" (1F.J.Ji~J.LQQh99q9. 1002 1001 PT=(I.nO-AI71*PN+AI7"PD
GO TO 1003 __ . ___ .~_._. 100? PT=O.5nO"(PN+PDl 1003 Mr)PT='1nOToT (f>l>tPIL. _ ._
MDF=-APF~TS(31"OOKf"(PP-Pf)"AI6)*A? 8PT=RpJl~(MD£I~~~.~~eEL!~DuI~D~P~V __________________________________ __ RP=.S"fRPT)+RPT) I F ( I I" L r, 9. E Q. 2) G.Q_tQ_I Q I 0 ~---c-~----:-:-:;----:.,--~~ __ ~ __ ----PPT~PPIl"(RPT/RPTl)""r, TPT =PPT"OOR IRPI"A..2 ___ . __ ... PP=PPTI"(~P/RPTI)""r,
_.1 P= P~OOR/RP .. <I.AL_~_:::::-__ ::-::c::-___________________________ _
II"fTNSIR(25).EQ.l)GO TO 1020 I I" (TPT .GE. TCTO) GQ._IO-.l1!.2D ___ ... IFLG9=;:>
1010 tP=TCTO . TPT=TCTO
.. _ .... _.P2~?,E. ... P.~.I~:D'I2... PPT=RPT"RIIIPT/A2
1 020 MDPE"'-~ 1"PP*t...REAT.5.121 IDSQRT / TP l!AL.
C------------------C CONVERGENCEc.."iEC~.. __ ._ .... ___ ... _. _____ . ______ .. ____________ _
C------------------. _ ... 1£LGJ..=.L_ ..... _.~ .. DO 1050 1=1,7
1050 E (1) =2. "Da8S (V (I tll~.VJ1 .• JJJ./ty( I 'l)~\/j.J.!.lll._ .. ______ . ___ __ DO 1100 1';1.7
.I.f ( E ( I 1 ... (;1.. 'PrggJ !;rL.J_Q....U.J)J1. _ .... _____ ~ __________ _ 1100 CONiiNtJE
c ... W~LJLD.I\ TA .. .olLf.I.LE .. AN.D PR LeI NC!..T'--'C...,.()!C.N'-'VCl.E.!CR"'G""E.l.LQ-1l.DAfl.T"-'A"--____ . _______ ~ IFUi3=? IF (JIB.EQ.03) GO TO 1115 .. _. . .... _~ .. _ ........ _ .. __ .. ~. ____ ~_ ... _ .. ~ ___ _ WRTTE(JIBIJ16)RSTR.ISTR F I N')/ Jl R, , JI (»
1115 CALL' PRyNT .-~-.--.--.------------------
. ...ll.l6 .. 1£..( LNS.1.P_I.IJ""£.P....llM TO 11 AD II"(TNSIR(61.NE.0)WRJIE(YOUT.1120)V
1120 FOR'1AT/1S(I' 19AEl,,-.A)... ___ . ____ .
r.---------------------------------------------c. PERFORM E>nq~POLA.I.lQNIO._NH.J._lD1U '-1T..,E".,R"-'V..,A"'l ________________ _
e---------------------------------------------DJL1l70 1=}.7
92
AEDC-TR-76-39
MAIN DATE .. 75157 11/58/40
J:::I~XTPIIl .r SAVE DATA FOR ClIRRENT TNTERVill
AIII:::VIJtll TEITrIME.~Q.IIGO 10 ))6~ ____________________________ ~ ______ __
IEITELr;4.EQ.IIGO TO 1160 C OIRAPOIIAT!;'
V(J.ll=2.*VIJ.ll~VIJ.?1 __ ._. ___ lEJ..l.NSIR!61.NE e Ole,,11 PRINT C RESET ~4TA TO 8EGTNNINr, OF TIME TNTERVAL _-L15~Y~u(~JLI ________ ~ ________________________________________ __
IEITELr,4.EQ.IIIFLG4=2 _.11 rQ .CilJil.lNUE. .__ _._.
C-----------------------------------------------------. .c...JlE.Tnt~TE ~RROg CUTTING OR Dr DOUBlING IS REQUIRED
C-----------------------------------------------------_...l1.B1l .. LE.L1.liISIR II? i . EQ. I I • AND. (JN5TR 114 I • EQ.) I ) GO TO 1190 DO I1Bo; 1=1.7
.... __ . ___ U·.Ll.lll.G2. NL..U .• AND. I (T....e:.aJt .OR. II. rQ.M I I GO TO 1 185 EIYI=2.*D&AS(V(I.ll-V(I.211/fV(I.l,.V(I.2)I/INSTR(12)
_____ . ..u:.t.E.lli...aL...EERRu.I..IlGJlO--LTI.LO....J...lli..lB~S:>-__________________ _ IF(INSTR(141.GT.l'GO TO 11B4
. C.LQR OELC.UU .UJG ___ .... _. __ PERQ:PFRR/INSTR(12'
__ ... _ .. _ $£'''III}< =$EMAXLI.~IIHl21. ___ _ WRITE(iOUT.J183,PfRR.SEMaX
....llB3 EOR'IU.1..!O PERR ellI rol.Elb.f\ •• AND $FMAX CUT IQIoF'l(,.BI IPa3E=TPAGE+2
___ ... _.GO lJLU.2Jl .. C OT DOURL,IN!;
_lLB4. D.1!!:.tll!W£IuR-LI ... 1 ,..4 LeI ______ .
DTO>'V=n'fl>'v OODhl./OI DT02"OT*.5 wRTTElyour.11871DT
1187 FOR~ATI'O DT RAISE~ TOI.fI6.8) rpA'3E=YPAr,Et2 GO TO 1190
1195 CONTI NIIE.....-__________________________ .,--1190 IFIYTIMF.LE.2)GO TO 1191
.c,.",,.-----------------------------------------------C DEfERMI~f IE ~EXT INTERVAL ~s FREDYCTED TO CHOKE
L-------------------------------------------------D"tn=MD-MDl D'1N:::MN-MNI IEIDMD.LT.D'IDIIDMD=DMOI
. 1l'.1.!lM.l'l .. D.allMMl ... 1 ,.,.O"".M=N -=-D""M.llN"'l'-::c ___ ----, __ _ IELG2=n5IGN(!.SOO.FT-PCTooFSOPO' IEI!MD.nE.Il.DO-DMOII.OR.IMN~Gr.11.DO-DMNII)TELG2=-1
1191 DMDl=Mn-MDl O"1Nl "'MN-M"'I IE(IELG2.L~.0IIFLGIO=2 WRITEITOE3UG.2000IIELG2.DMO,DMN.MD.MN.MOl.MNl
2000 EOR'IATI'OJELG2=,.I3., DMQ.OMNm'.2E13.5.' Mn.MN:,.2E13.5, ._ .. _.....L. M01.M'I'1=' .203.51 C RESET DATA TO BEGTN~ING OF TIME tNTERVAL
IEIYNSTRI231.EQ.OIGO TO 1189
93
AEDC-TR-76-39
00 llSA 1",1.30 11Be VIJ.Z':YIT.I'
c;o TO 150
DATE .. 75157 11/58/40
~_RP~T~l~=RruP~TL-__________________________________________________ __ PPT1=PPT
__ ~£(JNSTRI71.EQ.lIGO yo ISO 00 11B(I. 1=1.7 J=II"XTPIII
I1B~ VeJ,2'=VeJ.l' . __ .JiQ -<Y .... Q'--L1 a5,,"0 ______________________________________________ _
C-------------------------------CR!1i£1_CllI'iIl£RGI"NCE CONTROL DATA
C-------------------------------1200 IfIIDEBUG.EG.IOUT,CALl PRINT IfeJNSTRe~'.NE.OICALL PRTNT Il"XNSTR (l 01
1210 00 1260 1-1,30 ____ ~1220.1240) .ll
VCI,31 .. VCX,11 GO TO 1260
1220 Ife'TER.NE~ll VeI.II-All*VeI.l'+A12 *VCI.31 ______ ~l~LI ________________________________ ~ __ ___
GO TO 1260 _.~JL_Y.1JJ41."!~
V(T,3'=VeT.1I ___ --1f..1HER.NI"'.J.l Y I I ,II ::AIl*Y (I el, +U2*Y e I ,It I
1260 CONTI"JUf tiel. . .TO 21t0 _. ~ ________ . ___________ _ E"IO
94
AE DC-TR-76-39
INPUT DATE '" 75157 . 11/58/40
SUB =lOUT! NEI r NPUT (*) IMPL~CTT REAL*B (A-H.M.O-Z,ST ·COM~ON ARE~(3.50).AREATS(3).AREAM(3).TV(3.501.A(lO),E(1),B(30I, I TVI'"I(3; .TDEI AY(3) .RW(7)
COMMON PC.RC.TC.AC.MOCTC.EAE'EAPE.EAF.MOTSTR.INFIN.TMGOGS.GPO2GS. 1 SGOR
COMMON G.GM1.GPl.OOG,GPl02.GMl02.GPlOG.GMlOG.GOGP1.GOGMl. 1 OOGM1.OOGpl.GpOGMl.SGMlO?TOGM1.TOG.MGpGM2.IQGpl.GpGMIZ. 2 MGPOGM.MGOGMl.R.GR.OOR.PI.PERR.AWOKW.OOA1,OOKF.KF.KW
COMMON TS~~TS~.TSW.TSP.TSA.TSWA.TSV.C'D.CTA.PV.PVOT5V,TAUW COMMON T.Tl.OT.TSTR.OT02.TSTOP,OOOT.OTOPV COMMON Al.A2.A3.A4.~5.A6 •• 7.A8.A9.AlO'All'A12.AI3.A14.A15.A16.i17 COMMON PN. PP ~ P~T. PO. PT. peTO. PEO. MOE. M~D; ~Dp, MOPT • MDCT. MOPE .MDTSO ,MPCTO -. lEO. IP. TPT • TcIO. RP, RPT. REO. RCTO • ACTO. MCT. AE. APE. Ap. MN. MD
COM~ON PN1. PPI. PpTl. POI. PTI. PCTOI. PEOI. MOE1. MDDl. ~nE~~D~p~I~l~.~M~n~C~I~l~'-DM~n~p~E~l~'DM~D~T~S~O~lL'rrMD~C~T~O~lL.~Iuf~O~l~'L-__ T~P~lu.~ __ _ TPTl; .TCTOl. RPl,RPT1. REOI. RCTOI. A~TOI. MCTI, AEI. aPEl. AEl. MNI. MOl
COM~ON PN2. PP2. PPT2. POZ. PT2. PCTOZ. MDD2. ~Df2. MOPIZ. MDCTZ. MDPE2.MOTSOZ,MDCTOZ. TPT2. TCT02. RPZ. RPT2. AI!)EZ. Af"2. MN2. MD2
COM~ON PN3. PP3. PPT3. P03. PT3. p~T03. WID3, ~O~MDPT3. MOen. MDPE3.MOTS03,MOr;T03. TP13, JCT03. RP3. RPT3. R~03. RCT03. ACT03.
PEO? IE02.
PE03. IE03. Men.
MOE3. . IP3.
AE3. __ .""_-APEJ-'. __ .A.E1.L MN",,3~''-c:-::~M!LD,,:3~:-:-__________________ _
COM~ON PSOPO.TSOTO,RSORO.MSOMO ___ ~PM~9~.~r!~~1.$Y2.$Xl.$XZ.$DX.$El.$E2.$fMAX.$fP.$DE
COM~ON rNSTR(26).JDEAUG.TYN.IOUT.NP.IP.JTER.NVT(3).I.~T.IP~GE. _~l "'",P,=!A 3E. $N. IT .LlL!_,,/ .. YMI • IT P;:IE ,NO. NN. NCT. iEt G tif'LGl • lELa? olEI G3 tiEl G4.
2IpLG§.JELG6,Y'LG7.IFLG8.TpLG9.II.r2.13.I4.IS ___ ~"'-~QflL.Jl.o..Ju.J3 .J4 .J5 .J!'> .,17 .,,/8. J9. Jl O •. Jli • J12. J13 .. Jl4 .J15.J 16. ,liT.
I J1S.J)9.J20.J21.J22.J23.J24.J25.J26 .. __ .Cl!.M.~ON_.NrrL. ----~-=-=c:----,--=-=.=-=---=-:=----------------
DIMENSiON V(30.4,.RSTR(S79,.ISTR(3S) ______ E.Q.U1I/AI [NeE (VCl/.PNI. (RSTRCl! .ARfACll). (ISTRO) .NP)
TNTEGEP $\1,
REAl"9 IN"IN.~p.J!~W .. ______ _ Ip(\lCTL.N'~O)GO Tn 200
___ . ~EAr:)( IT ~ .SO) NjLI_~ _____________ ----, _________ _ 50 rOR~AT (2613)
_.RLI! ') (I I N.110ll) ~-"'c~ _____________________ _ 100 rOR~AT(:;E16.BI
R E:A') ( 1I N , 1 00) T 51...1_ IS H..J"21UJ:ID ~ P v 0 T 5 V • TIl UW • I< W !Kf..!A"-'15L .!.1A"'1...,,6'----______ _ 1.A17.AIA.A19.A20.A21
REA') ( J IN .JJHU q!:" G"'-::c' A::cl~1~.=~A,,-,1~32C.!-'A,,-,1,-,4,==-=:----,..,--::,---______________ _ REA')(ri~,lOO)')T.TSTOP,$EMAX.PERR.AIO
___ .RE:.~ '1 (J T Nol 00 I A~EAM REA~(JTN.IOO)TVp
8EA')(YTN.IOO)TOELaY DO 110 J=1.3 ---------
__ DO __ l(lS 1=1.50 TVeJoII:O •
.. 1 ~ ~_3£.~L..L.t..LI.!..1 ~=,,-OJL' _________________ _
95
AE DC-T R-76-39
iNPUT DATE .. 75157 11/58/40
----IOl-:-\j-VTCO
·-:-J:--l -------------------------
-110 READIITN.1201 l~lL.~.aA~RLE~A~L~J.Llulu.uI~=ul~.dI~l~I ________________________ ___ 120 FOR~ATI2EI6.81
o __ ~UJBH-__________________________ __ 200 READIITN.SOII1.J2.I3
TEIIl.Eb.0IRE1URN I GO TOI220.240.2601.ll
.2.2.!L REA!') I TTN.501 151RI 121 GO TO 200
... ..2AlL REA' I T TN. I 00; R5rR (121 GO TO 200
_2.51L READITYN.1001 V/J2.Y31 GO TO 200 END
96
AEDC-TR-76-39
CON';T nATE::: 7'>157 11/'>'1/40
SUR~OUTJN. CO~ST(n)
I~PL1C'T qEAL~~ (A-H.M,D-Z,I) (,OM\10"l 1\ R. A ( 3. 'i n) • M~F II T 5 ( 3) ,liRE II M (3) , T V ( 3.50) • II ( 10) • F (7) • R ( 30) •
1 TV. (3) • DELAY (·n .r~I' (7) COM'10"l PC.PC.TC.AC.M~C'C.FhF.FI\~F.F.F.MnTSTR.1NFJN,TM~OAS.GPO2A5.
1 S(;::)l-1 COMMO"l R.3MI.3 P\.nnG.GP\n?AMln?AP\(IA.AMlOG.GnAPI,A03MI.
I nnSMl.n03PI.3DOAMI,5GMI02.TnGMl,TO~.MGPGM?TOGP1.GPG\112. 2 MGgOGM.M30AMl.R.GR.OnR.PT.PERP,IWnK~.nolll.0nKF.KF,KW
COM\10N TSL~TS~.TSw.rSP.TSI\.T5wA.T5V.CTn,('TA,pV,PVOTSV,TAUW COM\10N T.Tl.nT,rSTR,nTn2.TSTOP.onnT,OTOPV COM~O"l DI.A2.A3.A4,A'i,A6.A7.A8.AQ,~ln.All.AI?ft13,~14.Al'i'A16'A17 COM'~O'll P"l, PP. PPT. PO. PT, prTO, PFO, MOF.
M')f). '10", MDPT , t1DCT • MOgE: .'11)150 .!~DCTO, TfO.t.. TI:' .•. TDT • TeTO. QP. qPT, RFO. RCTO • ACTO. MCT. AE. A~E. AF. MN. MO
CDM'1I)"l PNI. PP1. ppn. M~Dl, ~D~I. MDPTI. M~CTI. T:>f1. TCrOl. ~P·l. 'lPTI. agEl. A~l. .~Nl, Mnl
rOH~ON P~? PPl. oPT? M)02. '10F2. MooT2. M~CT?, T"TZ. T~T02, RP? RPT? A"E2, AF2, MN2, M02
r.OM~O"l P'II3. PP1. PPTl. M~nJ, ~O~3, MnOT], MOCT1, T:>Tl. TeT01, RP1. RPT1. ADE3. AF1, ~N1. Mol
PO). PTI. PrTOI. MDPEI.MDTSOl,MDCTOl,
REOI. h'CTOI. ACTOI.
PEOI. TEO 1, MCTI.
pn? I->T? PCT02. PE02, MDPE2,·II1[HS02,MDCT02 •.. Tf02·,
REO? i->CT02. ACTOe. MCT2.
MOFI. TP 1 •. IIf I.
MflF? - TP?..L
AF;>,
1->01. PT3. PCT03. PE03. Mr)F3. MIlDJ:"3.Mf)TS01.MnCTQ3. T E 03.1 ._._lElt. __
RE01. ~CTn3. ACTOl. MCT3, flF3.
COM~ON pSlpn,lsnTn.PS"HO,~SOMO
CO~~O"l ~Y'%YI.~Y2.~XI.~X?%DX.$EI,~F?,$FMAX,~FP.~nF
C Nl '10'1 l NS T P ( ?h) • T DFfiIIG. T TN, 'OUT ,~JP. J 1->, T TER. ~!V T ( 1) • T • ~T • ! PAGE. INDA3t::,'P~. T T (1) •. J. TMI, I TlMf,ND,NN.~ICT. lFU;, IFl!ll ojF.LB?"df.!'Jl.3_1J.E.l.M.L. ?lFL,,5, TFL3f-..!r:L!;7, TFI r,8, TFl..A'h T I, T? 13, T4, I.'>
CDMMO'II JI .J2.Jl,J4 .J'i,Jhhl7,Jt\,Jq.Jll~.JII.JI?,Jl3,JI4,JI'i .•. Jlf> .• ,1l1 . .!.._
1 JIQ.Jlo,J2n.J21.J2?J21.J?4,J2'i.J?h COM \ION NCTL I~T::GEP :!i1J QEbl~8 IN~I'II.~F.KW
PI=3.1415926Sj5A9793 G~I:::G-J GOl=G+l r,lAl~?::.5nSMl
GPI02=GPI".5 OO<"=I./G r,,,, I :JG=r:'ll "OOr, r,"'lJG=r:p!"OOG AP n?GS:0.;"A PIJA"nOG r.nA\H=I;/G~l
GOG:>l=I;/G:>1 58MIO?=nS~RT(3~IO?)
TOG:;>. "'"'0:; T)r,gl=?/:;PI Del!;-Il:::) .1';"11 r,,,nSM1=GPl"003 1A 1 G:>G"'12=.~"APOG~1 r)')G"l=I./:1P)
97
AEDC-TR-76-39
OOR=l./R G~=" .. q 43P:lGM=-GPOGMI 4(;P"M2:-GPG412 MGO"Ml=-Ge»r;-"1 T~r,1GS=C?-G)~OOG""? TOr;-"I=;:>.I"Ml
CONC:;T
II'" C INST~ (5) .E~.l) GO_l'CL10IL ____________ _ ~<'=144.
A3=1./~2 r;(') TO ;:>00
Ion 4?=1. A3=~2
2!l1l. CO~IT l"'lIF
nATE'" 7!'1<;7
r S:-~TF'S i'"OQ \JNSTi'"A')Y M~C;S FLIJX F'R(lM MAOl NlJMqFR A (A)='1r,P()3M A(I~)=GMIO:> CALL qY'40"l· CALL ~I'"VF.:H
00 <>20 1=).7 no RWCIl=ACl)
sr;0~=Ds~~T(r, .. 004) Ii'" ('JCTI .E~. 7) ~FTURN
Rn JR'" F'Jn
98
11/'5"/40
AEDC-TR-76-39
T"l1T DATE = 75157 11l5A/ltO
--.~----.---- --_. __ ._------------SUR~OUTIN" rNtT(~) I~PLICTT '1EIILtlA (A-H,M,O-Z.~) ._ . _. _____ .. ___________ . __________ . COM'10N II A ~ II (3. 'i n) • ARE.'IT S (3) • AAF II M (3) • TV (3.50) • fl ( 10) • E (7) ,R (30) ,
1 TV"! 3) • T lELA Y (1) • 'IVI (7) _ .. __ .__ _______ . ____ _
C~M~ON PC,Rr.TC.AC,MOCTC.FAF.FAPF.FAF,MOTSTR,TNFIN,TM30GS.GPO2r,S. I Sr.1A _____ .. ____ _ CnM~ON G.3M).~PI'nhG.GPln?AMl02,APIOG.AM10G.AOGPI,G03Ml.
I onSM I. OOSP I. SPOGN) • SGM 10.20 TOGMI • TO[., MGPGM.2. TQAP I, GP.G_~1?9 _______ _ 2 ~r,OOGM.M30GMI.P.GP.OOR.PT.PFRR.AWnKW,OOAl.onKF,KF.KW
COM'10N TSU. 1S .... TSW, TSP. TSh. TSw~. TSV. eTo .CT 1\ ,PV. PVOTSV •. T t\UJ1!_ .. ____ _ COM~ON T,TI,DT.TSTR.OTO?TSTOP,oonT,oroPV cnM~ON A 1,112. A3.AI;. A5,A6.lIr,AA, A9,A 1 0 ./111. AI~.A13,A Ilt,AI2-'A.l6~.L7 __ COM~ON PN, pp, PPT, PO. PT. pcTO. PFO, MOF.
M')D. "ot:. MOPT • MneT , MOP. ,MDTSO .• MQGIIL._!. __ !fJ!_L __ .Ir:_! __ TOT. TeTO. RP, RPT. REO.- ACTO- • ACTO. MCT. AE, ~oE. lIF, MN. Mf) . __ ._. __ . ______ . ____ _
COM'10N PNI. PPI. PPTI. POI. PTI. PCTOI. PEOI. MDEl. "1')01, "Dq, MOPTl. Mocn. MI)PFl.MorSOl''''DCTOl, .TEOl, __ TPJ_L __ ToTI. TCTOI. qpI. ~PTI. REOl. RCTOI. ACTOl. Mcrl, AFI. ~oEI. AF'l. "till. MOl ___________ . ______________ _
CO~~ON PN? PP2. PPT2. pn? PT2. PCT02. PF02. MDE2. ~)D2. '1Dr:? MOPT? MOCT? MDPE2.MOTS02.MOCTOcL_Tf..o~.L __ J.J>c.,-__ T~T2. T~Tn?. RP2. RPT? ~E02. RCT02. ArT02, MCT2. AE2. h OE2. AF"2. I.1N2. "102 . _______ _
COM~O~ PN3. PP3. PPT3, 003. pr3. PCT03. PE03. MDE3, M)03. '101'"3. MDPTJ. _Moen. MnpD.MDT$.03.M('lCT03L_TFQ)_~ ___ T~_ TOT3, TeT03, ~P3. ~PT3. RE01. RCT03. ACT03. MCT3. AE3. AOf3. AF3, "N3. MOl
COM"O~ pSOPO.TSOTo.RSORO.MSOMO cn~"o~ ,Y,IY1,IY2,IXt.IX?,'OX.IEl.IE2.'EMAX.IEP.$OE COM'10'" T N5 Tq (?6) ,TOFRlJG. T yllJ. Y OllT ,NP. IP. ITFR .NVT (3) '-1 -;iif-;JPAGE ;-_.
l"'P~:;E ,'>N. TT (3) •• J. fMI. IT1MF,ND.NN,NCT. rFLG. IFL!?1.!lfJ..G_~!I[!,,_~~.!.I.f.l..t.4. 21.1. S5, TFL';"', rr:LG7, TFI_GS. Tr:LA9. r), P. 13, T4, I~ CO~"ON Jl. J? J3 .J". J<;, J6 .J7 •. J8. J9 "JI 0 .JII. Jl ?.H3.JI4 • .,J_.t5~Jl6.~11, __
I JI9,J19.J20,J21.J?2,J~3,J?4.J25.J?6 COM'ION ~CTL
nIM~NSTON V(30.4) f:lIITVAL FNeE (o'J.V ().t)) TNTt:GEP !Ii\) R~ftL~R TN~1N.(F.KW
nD :; I=lo~ ITCT)=?
t:; II'1FATSCT)=O. TSII=TSIJ"T5H TSP=?"cT<;w+TS>i) TC;W6=T<;L~TSP
CTA=PT*rTI~"?*.?~ TSV=TS,<llSL PV:;TSV"PV~)TSV
OTnov:::nT/':JV QC=oc"nORlTr"A2 "C=IS:-JnT(~Il"TC) ~)rTC=j;lr."aC"CTI\
WlTso=nr"lIc"TSIl I)J 50 ,J=I.4 f):} 10 1=1.7
99
AEDC·TR·76·39
10 V(t.J)=PC flO 20 T=Atl"3
i.'O V(I,J)=I). V (14~J) :M)T50 V(15.JI=M)CTC DO 30 I"'1~'19
;0 V(T,J)=TC OC) 40 T=20,23
4(\ V(T.J)"qC V(;:>4.JI=AC [Ii) 4'> T=2,,30 4" V(I,J)={).
50 CC)NTI'JII, T=O. Tl",O. "1')=0. TSn=O nH)2=.c;~DT
OOnT=l./[lT MIJ=O. "1Cl=O. 00 160 J=1.1 11=IJVT (J)
INIT
OC) 140 T=ldl TV(J9J)=TV(J,T)~TVF(J)
)40 ftRFI(J.I)=AqEA(J,I)~ARElMJJ) T.<TOE"'Y(J).~Q.O.IGO TO 160 f)') I!>O Tl=1.4'1 1=<;1*I1 A=!E~ (J, I) =/IREA (J. 1-\)
150 TV(),II=TV(J.T-I).TOFLAV(J) NV T (J) =NVT (J) -I _____ . ________ _
1"0 CONTINI). 00 170 1=1,3
170 V(J+25.?)=IIREA(T.1I PSoPO=TOG~l~~"Or,MI T50TO=TOG~1 _ RSO=!O.Tf)G~l~~OOGMI
Msn~o=PSO~O~D5QR1(TSOTO;"1)T5TR=MDTSo*~snMO
TIJFTN=I.E+70 A I =')S~PT (TOr-PI III1(;P0(1"11 IIGIIOORI. OO~I=I./AI A4=TOGPjIlIlGPG"112 1\5=1./"150"10 .1<,=) ,-P50:>O A7:::2."r,Pl/Mr')r.rr. ./1'I=-G"1\OG A9=?"r,Pl 1'(Al0.'Q.O.IAln=TNFTN 1·(I\I.FO.0.)1I11=.0; 1 F ( A 13. ,Q • I) • ) A 1 :1 = T NF I N IF(AI4.FQ.O.)~14=-O.1 IF(014.GT.0.)A14~-~14
A12=1.-All I'(nI5.fQ.O.DO)Al~=1.nO
OlifF. = 7">1'57 ll/r:;A/40
100
TI'..J IT
J-(h!6.FQ.O.OO)Al~~1.~O T.(~17.FQ.O.OO)A17=I.OQ IPII"F:=O NPII3E=,,>O JP:O nOI<-=l./KAwn<W=.)7·'AUW·T~WA/KW
JTE~=O T Fl (;=0 IrL52=) I rL 53=0 n"U,4::0 r-1.85=0 r-l.:;6=0 H"L,,7=0 TrLG8=n J rL ,,9=n ND=O N'J=O NCT::Q JI::O 12=0 13=0 14=0 '''>=0 00 ?OO r=),7
20f) E (TI =0. JF('JCTL.E~.~)~ETURN RETJR"J E'JD
AEDC-TR-76-39
nATE ::: 7~)c;7 11/'511/40
101
AEDC-TR-76-39
~JR~OUTTN~ nu~p (~)
I'1f.>L1CTT =I-AL"'I !n,:"H.M'(')~l'_~! __ _________ _ r ~W \40\l II R .. II ( :4.0; 0) ,Mew II T S ( 3) • tU~f. 11'1 ( 3) ,TV ( 3,0;0) • A ( 10) • F ( 7) .8 ( 30 ) •
1 TVC"(J) ,T"lr:LAY(3) .RW(7) C3M\40N PC.Rr..TC,Ar.MnrTr.._II_.~IIP_._IIF.MnTSTp.TNFIN.TM~O"S.GPO2,,5,
I SG:lR __________________ _ cnM'10~ r,.~~I.GP1.nOG.r,PI~?r.M10?r,PIOG.r,MIOr,.GOGPl.GOGM\.
1 00SM1.003p1. 3 0 0<;;'11 ,Sr,;MIQ21- LOGMlt TnG,MGPGJ":12t 'Ul!.itl~.GE'Ji'il.2. _____ _ ? '1r, P OGM,M50r,Ml,P."R,OOH,PT.pFRR.AWOKW.OOA1.OOKF,KF.KW
CO M\40'l TSL.'. TS'1. T~\J, TSf.>. TSI\. TSWI\, Tc;v ,CTI), CT II ,?V~PVOT5V ,TA!J~ ______ . rOM\40'l T,TI,nT.TSTR,nTo2,TSTOf.>.OOnT,(\TOPV COMI40~ ~I, A2. ft). 114. AC:;. 111';. ~7 ,IIA. ACI.lll 0 ,A11.A 17./113, A14. 1115./1 16 tAl.J ___ _ COM\40'l p~. pp, pOT, PO. PT. PCTo. PFO. MnF.
M"ln, '11')_, MnpT • MOcr _. MnpF,M(lTSQ _?MIlCJ'!l __ L TFO • ___ IP.--",-__ TOT • TCTO. =lP. PPT, P~o. RCTO • ArTO, MCT. liE. A ~F . AF • 'IN. MI')
C)M -'O'l 1"'11. oPI. pPTI. P[lI. PTI; PeTOI.- pFOl, -"'00;----~"n I, ~nFI, MnpTI. MnrTI. MnoFI,MOTSOI,MnrTOI. TFOI, _ TPJ_t ____ _ T" I I. Tr. 1 n I. RPI. PPTI. RFOI. RrTOI. ArTOI, MCTI. AFI. A;:IF I. An. o.4NI, MDI ______________ _
r.n'-'''o'l P'l2. oP2. PpT? 1"(')2. PT? prT02. PE02. MOE2, "'02. '1nC"2. MOpT? MI)CT;>. Mf)PC"?~IDTSO?MnCT02. _ TF::02.L _T.P£J __ _ T~T? TeTO;>. ~P? PPT?, Q~O?, RCTO?. ACTO?, MeT?, AE2, n~E;>. A!"2. t.4N;>. IAD2 _______ _
r~M~O'l p~3. PP1. PPT1. pnl, pr3. PCTU3. PF03. MnF3, "jOJ, \4n'), MOpn. '0\[')(11. MOOF1,MOT503,"1I)_CTQ], __ Jf..QJJ_._....le-"3u.'--__
TPT3, T~Tn:4. ~Pl. QPT1, PF01. RCT03. hr.'O]. MCT3, AE3. ft~F3. ~~:4. ~N3. Mnl
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Ion F~~\4~T(lO'ol6(' I'JSTP'tl?)/' '0\0(' 1"'5TR"I?)o2(/' ',l"l~)l. __ \0' Q 1 TF: ( T OU T • 1 ;:> 0) T DE SUC;' I TN. 1011 T , 1 I • T P 1\(," • f\Jp A r,F • ~IP • I P • T T E P • 12. J •
llC"I_~.IFlG).TFlG;:>.TFLA1'TFLr,"IFlr,C,.TFlr,".TFlr,1.TFlGA.1FLr,Q.ND,Nf\J. ? 'IrT.TTTMo.'IVT.T3.T4.15.1T,~lrTi.
I?I\ F"~\4AT(lO J1F~dr, TIN TOUT Tl I.' JT~R T? 1 'C"l~ IFLG) ?' IFI(;6'1' 'olRT7/'O TFLr,7 TFlr.R 1.' IT1"1[ ~IVT(]) 'JVT(?) '.lvT(l) ,~
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102
AEDC·TR·76·39
-------------------------~~-----------------DUMP DATE; 75157 11/5R/40
lIX.'TbU~ •• 13x.'~W'.14X •• KF.I. '.8FI6.~/.0 •• 7X.'AEM'.13X •• APM', 213X~ '_L\F'l' t.13X 9'IS~.!1J.~.1 '.l.~h'...I..S.1'l.A. .In.' eTA' .13)(. qsy' I 3' 1.8FI6.B/'O •• 7X.'PV'o.!1X.IAWOKW'dOX.. '.lOX.' I,
4 lOX., _'~lOX, •. __ ._....!-'10~~ ',IOX • ., I' I.RElb.R) W~l TI::.( lOUT, 160J.PC~BC!. 'Lc .. l'E' .. tlW. TP. PP 1. RPI. TP 1. PPT .RPT. TPT. PCTO.
1 ~CTO,TCTO.PEO.REO.TFO.Ar.ACTO.~DPF.MDCT.MDE.MOF.T.TI.MN,TSTR, 2"1D~ t. '4DD,-PD IP 'il1'.I-L'1Il..t1:I.cr . ...E.!?Z1.':!DF2. MOpEZ. MDE2. MDC TZ. SF ~A X. 3TST~P. DT ,PSDPO,TSOTO.RSORO'MS0'40.MDTSTR.MDTSO.MDCTC,MOCTO.PERR 4.PN3.PP3.'10F'3tPEJ) .. 1.t.IE03.!1ID15.Q.J..!.~u-"O[J;;EJ.L"-"A,-,Y,--_____________ _
l'lfl FOR'1AT C' O •• 7X, 'PC' ,14)(. 'R.C' .14X,'TC 1 .14)(. 'PP' .14)(. 'RP' .14)(. 1 tTP1914l1' 'PPI' ol.3XJ ,qp.L'L!_.! '8El6.R/'.Jt!.l..7X. tIPl' .13X. 'PPT!..ll.3,.!>)(~, __ _ Z.qPT'.13X"TPT'.1~x.'PCTO •• 12X"~CTO'.12X.ITCTO •• 13X.'PEO'I' I •
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WRITE(rOUT.?OO)Al.A2.A3.A4.A5,A6.A7.AS.A9.AlO.All.A12.A13.AI4.AI5. _. ___ ,Ltll'H.AtJ.ill.A.A19.!\?0.A21.A22.A23.A24
700 FOR'1ATC'0,.7X.·Al,.14X"A2'.14X~'A3 •• 14X"A4',14X"A5',14X. l' M,' ,14 x. '.1\ 7' .t.H)(.!..'-AB.!L~--'-.!Bli6. AI' fl' • 7X..t..!.A9L.:...~1 =-4!).X ..... .: •. 1!f\LoIlc'O'-'.'-'.'-:-c-:-~ ___ __ 113X,'AIl',13X.'Al?'.13X.'A13'.13X.'A14'.13X.'A15'.13X .'AI6'1' '. 4 8E16. BI' 0' • ,.I'!, • . '.Al1,! ... l..1X....!A.l8' .13X. • A I '1.!..t 13)(, 'liZ!)! .13)(. 'A21 I • ~ 13X,'A22·.13X.'A23'.13X,'A24t -II 1.6El.6 .. 1iL w~rTECTOUT.220)G.GM1,GPl.GMl02.r,PI02.00G,r,MlOG.r,P10G.GOGMl.
1 GOGo 1. SGM 1 02. T DB t.TO.BE'I • Oom·o .. GPDGMl.J.G.P..G.M.l.2..Uillit-!l. MGPGI12. MGPQr,M. 200r.0l.p.O~R.G~.DT02.nTopv.O()KE.INFIN.OOA1.OOnT.MGOGMI.TMGOGS. 3 GP)2GS.S50~ ... _._ .. _. , .. _., __ ,. __ .. ____ ..... _. __ .. _ ... _._'--____ __
??O FOP'1ATC'l •• RX.'G'.)4X.'GMl'.13x"GPl'.12X.IGMI02'.11X.'GPI02'. 1 l?X., f10G' ,12x.'-.' G'!lQf?-'..tl.lX!...! G~l.JlG II '-_.!...tlIll€?o..!U..!.~flll..!.'_G,zc0~GI.UM ... l.:.'~' ___ _ ?1Ix.·Gf1GPi·.lOX.·SGM1()2'.12x"TOG'.I~X.'iOGPl,.llX.,O~GMI'. 31 ox. 'GPOG'11 • .1 OX. I GP<1MJ.2'I..' 1 -/:lEI!>. t\,1'P' .Lt?x,L'If'lQ!:!J '.J lJ)!.!.!MG~:,-,2_, ';",;''--_ 4 jOX. 1 Mr,PJGI1'.11X.'0f1GPl',13X. 1~1.14X"OORI.ljX"GR'.13X.IDT02'1 .,. '. HE Iii. 'II' O •• 6X •• nTOPI/.' -' 11X. 'QQ.~F '.'.l.?J(.,! 1J'!£1.~.-'-!.U.X_L'.ililAJ.!.! _____ _ ~ 1?x,·nf1DT'.1IX.'4GOGMl'.10X,'TMGOGS'. lOX"GP02GS'I' I.AEI6.8 7 l'O',,,,x,'sGO~' - I' 1,F1El<'.R) W~ITFCIOUT'260)V
?SO F~Q~ATI'OV EQJIVALFNCE ARRAY'.15C/' '.AFlli.8» WRITE (!OUT,?40) Cl.r=lt7) tRW, ,. , __ ", _
240 F~RI1ATI'O',7C~X.'RWC',II.,) •• ~X)/' ,.7FI6.8) "H'lj5i~=2b D~ lOOn l=l.NI'ljST~
T~I!.En.12)WRITF(TOUT.4qo) 4(}fl FQP>4AT(tI')
WRITE(yOUT.500)i.iNSTR(I) ~oo Fnp'1ATI'OTNSTR('.12"):',I7)
I ? 1 4. 5 Ii
103
15
AEDC-TR-76·39
DATF: :: 15157 11/5fV40
r. l~ 17 lR )9 20 21 22 23 24 2~ 26 27 2A 29 30 31 GO TO (~l 0 ,5~Q ,.5.]Q.,5.lt.(L,5;;.QtSnJ!u.HL,..58..2...U9fu 600.610.620.630.640.650
1·660.670.SAO.690.700.710.720.730.740.750,760 - ), I._. ___ ... __~~ ..
510 WqlTE(JOUT.~ll)TNSTR(l) 511 FOR'1AT ( '" , ,20 X " ~EJ'J!}_ ()~9U.G.G ING.QlLtPl)J~!1.SflN' • I3)
GO TO !OOO' 52 (l W q If E (J OJ! T , 5 Z \).1 N s...t~I~2~1_--=-:. 521 FnR~AT('.'.?OX.'O~TATN INPUT FRO~ nSRN9,I3)
GO TO ]000 530 WRITE(TOUT.531)TNSTR(3) 531 FOR~AT ('''' .20)(. 'S~Hf)_Ji~\>ll.UIJU]lHPULJQ_l)SR.N'_d')L __ .. _. _______ _
GO TO loon ?40 II" qJJ E.L1QU T .• ;;'tllJ~S T R J . .::47:)c::--==:-:-;::;--:-:-:-;;=:-:-:-~--=---=-=:------------__ 54i FOR~AT('.'.20)("PRI~TING TIME INTERVAL: •• I3)
GO TO.100P .. 550 WRITE(TOUT.551)r.HARl(INSTRI5r) 55) FOR~AT J ,_ .... 2tl)( .•. ' L"!PPT ... A"i!LOUTPUT PRESSURES IM... __ , ..... ,/I""4x..l'---_______ _
GO TO ]()()O _ ._.5 ~(l .1 l'"_tlN.!i.L~_t~J ..... EQ..Jll.J.1RllE.il..Oill..:<.-=5:>!.6 .... 2-'--) ________________ _
JF(tNSTRI~).NE.0)WRTTEltnUT.561)
5" 1 F DR \fAll! ~ • • i' 0 l!.t !J>~lN.L 0 AT /I AF'T~ . .<.E-'-'Rc..!.Y___'_I..!..T.hE_'_'R--"A..!.T.A.I""O"'N-'-• .Ll ___ ~ _____ _
562 FDP\fAT(''''.20X,'PRINT DATA ONLY WHFN CONVERGE~') GO TO 1000 . ______ .
570 IF(TNSTR(7).EQ.I)WRITFIIOUT.S71) J'" (U:LSrRJ71 .0. 2 .. H1Rl!f..lliUT ,572)
571 FOR\fAT(' ••• 20X,'LTNFARLV FXTHAP~O~L~AT~E~T~O~N~E~X~T~T~I~M~E~I~N~T~~~R~V~A~L--A-~S~A-N~l---INITIAL GUIOS5')
57? FOP'1AT('+I,20X;'OO-Nnf-fi'TR~POC4Tr::TO NF"XT TIMf INTERVAL') GO TO ]000. _ .. _.~ .. ___ ._ .. ___ .
590 WRITE (TOUT."i81) (CHAR2(J.3-JNSTR (8» .J::l.2) 5'H.FOP\fAJ.(!.~!_!~Q.)(.~USE t .21\4.' DEGRn: REVERTED SERTFS AS If\lJTIAL GlJF"S
IS T3 M~SS F"LUX-~ACH NUMAFR WAVE EQUATION') GO TO Inoo _. __ ~ __ . ______ .
59!) TF(TNSTR(9) .E~.1)WqITE(JOUT.591) I F I I NSTR (9) • E~. 2 L~.BlI.E.JJ OU.T. 5921 __
591 FOR\fAT('.'.20)("USF TTERiTIVE SOLUTTON TO ENF"RGY ANn WAVF" EQUATtON l?' I . . __ ._ ... _.
592 FOR\fAT('.'.20X"USF APPROXIMATF EXPANSIONS FOR ENERGY AND WAVE FQU 1 ATTONS')
GO TO 1000 600 I I'" (JNSTH( 10) • ~(L...QntRJ.TW.OUT.!i1.9J,::-,)'---___ _
J I'" ( INS T R ( 10) • E (). 1 ) WR ITE ( TOUT. I'> 0 2) IF (TNST'! I lQ) .r:.Q"'?J.WRlIUl.Q!lT.(03)
601 fOR~AT('+'.20X"DO NOT INVOKE AVERAGING OPTION') M? FOR"IA T (1+' • 20X. I A\lfRII..GI;.IlIl.\,VF,S~~ ._c:.lLFi~.f.t-I.L_U(EA.TJJlN \lUJ:l.....~VfBAGf V
'ALlIES OF" 0REVIOUS ITERA"ON') 603 FOR'1AT('.'.20X,'AVf.RAGE VALUES OF CURRENT ITERATION WITH UNAVERAGE
10 V~LUF"S 3f P9E"V-yOUS-tTF.RATYONI) GO TO 1000
610 WRITE-(TO·uf;ii,fi·)YNSTR(ll) b11 frlP\fAT('+1.20.)( •. "'~.l)_f!E~!'!..L.WFT_G!'U~_liI\LVEO BEYOND ',n.' ITERATIONS'
11 GO TO 100Q _ '_. __ . ______ .
620 Jf(Yf\lST'!(12).EQ.l)WRITEITOUT.621) IF (LNSTP 11.2.1 IL'it .... lJ WRITE (TOUT .(22) !l.-,-,N",S:..!T-,-,R,-,I .. l--"2~)-".-,,Jc:::" ... 1-'-'-,=2.J..) _________ _
104
AEDC-TR-76-39
DATE '" 75157 11I5R/40
62] .OR~AT(,+,.20X,'DO NOT TNVOKf ERROR CUTTING OPTION') ._622 FQRIlAT('3_._.t2.0XL'JH.tlI2E....£RI'iI.1~S BY'oI3,' WHEN TIME-DIEfERENCES ARE L
lESS THoN',I3,' TIMfS THE ERPOAS') r.O TO 1000 .. _______ . _____________________________ _
630 IFIINSTA(13).~Q.O)WRITE('OUT.631) I F ( 1"'5 T R (13J • 'I E a O_J .w RlI£ilJlU1~ 6.~3 2 .... 1L--__ _
631 FOR~ATI .. ,.?O)(.'PRINT ALt nATA') .. 632 F:OR~AT(i •• _.2.Q.X_'_'_e...IliNT 0'11 y TtMFS AND PRESSUREsq
60 TO 1000 61+0 1-1'".1 I filS T R ( 141... Ell.1.tiLR1IT11JllJ.Lt1LUL--:::c---:--__ =-=-:::--:,-:--________ _
, IF ( Y NS TA ( 11+) • G T .1 ) WR TTE ( I Ol/T, 642) INS TR ( 14) tT NSTR ( 12) 641 FOR \1 A T I f+ , , 2D )(,'00. __ "'1.1 L.Lr-J.VI)~L.n~ . .LI £l.S~I !-'lNuG_O,,-,,-PLTLI O",N,,--,-' L) _--::-__ -,---,--:--__ _
642 fOP'1ATI'.'.20X,'SET DT :'.13,'*DT YE TJME-DTEFfRENCFS ARE LESS THA . __ . .!..IIJ.' "LUL.I.l~ TLlHi.<;.E-t:,E,nR.!:lRJ,lO.!:lf./-'!S..!.'L) _______________________ _
('.0 TO 1000 . _6511.1 E ( lNS T R_Ll.5.L .. .EQ.LJ!3.L_\'IB1 T f I J au T .6,5.1L ____________ . ____ _
IEIINSTRIlS) .NE.03) WRTTf(IOUT.65?)INSTR(lS) 651 f(lR'1AT J'_".i.ZJJ.x~'.IlQ_.NOI __ REAO.._s...O...LJlI1J)~L£ROM PfR.MANFNT 'lATA SElf I 652 EOR'1AT(O+t.?O~.'RfAO SOllJTYON fROM PERMANENT DATA SETt.13)
----6-6-i1~}1LgUlLQ!L~-. f,-6-1:--) y-,N-,-S-cT::-:R::-:'Cn:--"':--)------------------------_66.1EDR'1Al.L'_!.!...t...2..!Ut. 'FTRST RECORD TO 'BE llRL.EB.Al.LD.L:.:.i.L • .LI4~I ___________ _
GO TO 1000 __ 6] 0 ..II/ fillEJI O!H..t..6llil fi5.1P'-'( .... 1-L7,L)_---=
f,71 fOR'1ATI •••• 20X,'LaST RECORD TO AE Rf.AD:'.I4) GQ TO IO~ ___ ~~_~:__:__~~,---~-________ -------------------
690 I"'(TNSTA(lfl) .EQ. OJ) WPYTEfIOUT.6flll _ I F..!1 N.5.J RH B .L.....N£. 03 I W R I I£.LUlUL..ll6.aAL.2,L) -LX !-'IN;;>,SLT Rru.! L! BI:1.L) _:--=-_--::-_---:::-____ _
681 FOR'1ATt •••• ~Ox •• DO NOT WAITE SOLUTION ON PERMANENT nATA SET') 682 F'DRIlA T_(I +.' .• 20lt.t..' l'IJnlL..5.OLUll~ PERMANENT DATA SET', 01
r,0 TO lOOO ___ 69Q_. l'IRl.I£J.llWL.h.911 INSIACl91
691 EOR'1ATI' ••• ?O~XL.-,'E~J~A~.S~T~R~E~C.~,D~R::-:O~T~O~A::-:f::-W~~::-:I~T~T~E~N~I-,'-.~1-,47)---------------------GO TO ULQ1L _ ___. ______ ~ __
700 IE«IN<;TRIlll .Nf.O).IINt).!TNSTR(20).NE'.0)) WRtTEIIOUT.70U INSTRli'? II() .._ __ ______ . _____ . _____ _
IF' ( I I N<; IR ( 11 ) • EO. 0) • OR. IT NS IR (20) • FQ. 0) ) WR ITE' ( TOUT. 70 2) .1OlIQP.'1AIL' __ !...'J2.<l1t,tlNCREMENT YNSTRCll.LJi'i. ,.13.' WHENfYfq WEIGHT '5 H
ilIlLVEO' ) 70i' F'ORI1A T ('.', 20~j •. DON.QL':1.onIl"_ClN~TRllJi.J ________ . _______ _
GO TO 1000 no IE (INSTB (2.1l_oE.fJ I OJ J'iRllilLDJlJ,,711L ______ _
IfIINSTR(21) .~f.OIWRITEIJOUT.712)
_711 F'OR.'1li T { • +' 9 20X~_ • .DO_.NQLruaNGLLHRAPJlLAlJ.Q1! __ !lE.ll.D.N II \lSTR 1711' I 712 FORI1AT 1'.'.?OX.'lNvnKE .XTRAPOLATJON OPTION (SET IN5TR(7)=21 WHEN
II ,IE 18HT I S HALVED ') __ . _____ _ GO TO 1000
720 WRITE: (IOUT.721)1N5.IFI(22J. . _____________ ._. ___ 721 fOR'1ATI' ••• 20X.'SET INSTAI?3)=? WHEN ITER >='.17)
GO )'0 1000.... . ___ . ____ ... _____________ . ________________ _ 130 TeIYNSTR(23).EQ.0)WRITE(TDUT.731)
J E I T NS Hl (23) • E~. 1 ) WR Y IF! LOllI!.1~2) __ . _. __________ _ TfIINSTR(23).~Q.2)WRTTf(ynUT.7331
731 F::IR'1AT (f", 20X ~.!Dn NOT._ .. USL SM.f\LLPF:RLLJR8~LIJ2~_fl!.EA!~SJ ONS'.!..) ____ _ 732 EOR'1ATI'.'.20X"USf SMALL PFRTURRATION fKPANSIONS AS INYTIAL GUESS
______ J F'O~ ~I:)(.'t q'-1.L...ltfl£R.YAl..'i. __ ,-----..
105
AEDC~TR-76-39
nUMP DATE:: 75157 Il/<;A/40
713 ~DR~AT('+'.?OX,'U5~ SMAll PFRTURAaTION ~XPAN5YON AS SOLUTION') _GO Tn lOQO __________________________________________ _
140 TI'"IYNSTRI;>4) .EQ.O)WRITF.ITOllT.7411 I I'" I J NSTR I 24) • \lE:.i') \VP TTf IIOllT...!]4_~I _________ _
HI ~OR~AT(I ... 20~.n:lI'"C;tJLT5 ~ROM ')MPFRT NOT PRINT!'O,) 142 ~OP~AT I' +', <,OX. '_Rf511US ~RO'1.. S"1e.[R_LA..I1.L._F'_FU1tl_EJ"_!l. __________________ _
GO TO 1000 7'50 IF" ( I /115Ta (25_1.L~ ~,,-ll j!.!llJ.E.Jl Cillh7.5.lL ______________ _
1F"(INSTRI;>5).EQ.2)WRYTEITOLJT.752) 70:;1 ~OR'1AT I 1+' .?OX, 'ASSLJ~f:. PLf.NIJ.M IS_ IS[tHROPlr.!L _____ _ 752 FOR'1AT('+'.?ox.'S~T TP ANn TPT :: ~A)(ITSfN TP.TCTO)')
GO TO 1000 ----------------7~O WRJTEITOUT.761IINSTRI2b)
_ 7"1 _~OR,,~:r .l1+'.!.ZO!<n.--'B.El!.f~~_LliL'£)(lIr~CSI)?e:.~~_9~LCSOJ.l~lJl!'!~' TIME IN ICRE~E~TS AFTER CHOKE')
GO TO 1000 1000 CONTI""F
WRITEIYOUT,lllO) ('JtJ=I'26) .JV 1110 ~OR~AT(III.;>61' J'.T?)/' '.132('-')1' 1.2610;)
11=0 _________________________________ _ 1)0 1020 1=1.1 TF"(\lVT (Tl.GT. Yl) II=NVT III
10;>0 C(lNTl\lIJ~
WR T TEl T ('IU T • I 040) I ('J. Y:: 1 .? I •• J= 1 .]) • I J • IT v (J, t "_A~F" A.J.J..!_U_t J= 1,.:;1) • 1 1=1.1,)
1 o_~o ~OR'4A T ( 'OC'lnw nR(!S _ IiER'iUS_ Tl Mf'j'(\ __ L!.lJ.l.5)(t' I'H_'--LLil.!..!..LTL) -c-' .... , __ _
I AX.'ARF"AI'.II.,.y),.3X)/' '.QQI'=').501/' '.Y3.6El~.A» YF"(\lCTL.El.AIRETURN 1 RETJR\I E\lO
106
AEDC-TR-76-39
50LVFR DATE", 75157 11/58/40
.. ·5UR~OUTJ"'N,,"=-. '-=Sc::O.,...L7CWE:::c.P;::-(:-:,,:7,--------------------._.l.MP.k:l..nJ .. ~ALII8 (II-H.M,O:'Z .$f
CDM'lOIlJ AR,,,n.50) .AREATSi3) .ARF.AM(3) .rV(3.50) .AIlO) .1"(7) .9(301 • .. L T.\I~ .. ! ~u.lJf.LA'Lil1,__'.'_'.R'-"W'--'(..L7-:':' ________ =::__.,--_=____,.-------
COM'lON PC.RC,TC.AC.MOCTC.FAE'EAPF.EAf,MOTSTR.INfIN.TM50GS,GPO2r,5 • .. .1 . .5.G.QR .... _ .. _ ... __ .
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2 'lGPOGM.MGOGMl.R.GR,OOR.PI.PERR.AWOKW.OOAl.OOKF.KF.KW .... CQ.M~Q~1>.Wf.JS!:J. TSw. TSPt TSa. TSWIl!.ISV .CTO.CTA .Py.pVOTSV. fAUlt
CQMMON T.T!.OT.TSTR.OT02.TSTOP.OOOT.OTOPV ._ .CQ~MQN .ft.l t.AZ .• .A.J.i.1L~.s. A6. A7. A8. 119. UJl!.A 11. A12. A 13. A 14, A15. Al6. AlI
COMMOIll PN. PP. PPT. PO. PT. prTO. PEO. MOE. MJD. MOl". MOPT • MDCT • MOPE .MDTSO .MOCTO. TEO. Tp. TPT • TeTO. PP. PPT. PEO. RCTO • ACTO. MCT, AE.
_ ... ": .... ftr:>E_L ... ...A! .... _...:::MN:":-"'. _::'M-'"D::-:-_--::o::-::--_-=:-:----:::-::-::-:-:_-:::::-::-:-_-:-=-::-:-__ _ COM\10N PIIIl. PPI. PPTl. POI. PTlt PCTOI. PEOI. MDEl •
...... !:12Qtj._.\10Flj ... J~OPTl.~M~Q':'C=-T71~.~MO:=-PE~l~.M'-CD=-T::-:S=-0:-1:-.~M~O~C~f:cO~l:-9~-:T,:-,:E",O;-;1:-,,~_T-=P:-!1~. __ _ TOTI. TCTOI. PPl. RPTI. REOI. RCTOI. ACTOI. MCTI. AEI. AOEl. 4£1. MNI. MOl
CDM!o!DIII P1IIl'. PP2. PPT2. PO? PTl'. PCTOl'. PEOl', MDEl', M~Dl'. ~DF2. M~D~P~T~l'~.~M~o~C~T~l'~.~M=O=P~E~2L.~MD~TS~Ol'~.M~D~C~T~O~2~.~~T~E~O~2~'~~T~P~l'~.~ __ TPTl', TCTOl'. RP? RPT? REOl'. RCT0l'. ACT02. MCT2. AEl' •
...... ~. __ IIPE.2._ AJ" 2L .. ~.!_ .. MD.l' COM~OIll P1II3. PP3. opT3. P03. PT3. PCT03. PE03. MDE3,
. ___ .~ .. _):1!.lQJ.1....-\.1Di"3.t. '1..Q.~.J:!l1C.IkJiQ.e.u .... ",M~D::T~S:::-O::-3 .... fI..,.1D~C~T;-0!,3~i --:T~E~Q;-:3::--'L __ T~P;!3~.,--__ TPT], TC1 03. RP3. PPT3. RE03. RCT03. ACT03. MCT3, AE3. A PO t. M" 3 • . ... ~NJ.L ..... Hlll
COM~O~ PS~PO.TSOTO.RSORO.MSOMO COM "ION $ Y, $Y I, ~Y.2Jjij(..l.!.SX2.t.!nX. SEl. $E2. SEMAX. 'EP, SDE COM"ION yNSTP(26),IDEAUG.TTN.TOUT.NP.IP.JTER.NVT(3).!.NT.yPAGE,
. _ .. _ .... _1~f:)A3E. ~!:!ill . .t3) .J. Y M I, IT Y ME .ND .NN .NCT. I ELG .IFUH • IFLr,2 p tELG3. YfLG4 , l'rFLG5'TFL3~.IrLG7.IFLG8.TFLr,q.ll.T2.13,I4.r5
COM401ll J.J.! ~2' J~ '.-!'u J5 !.>!I',. ,)7 ,J8, J9,Jl Q. J 11. Jl2 .J}3 .J14 .J15.JI6 .J11. 1 JIB.J19,J20.J21.J2l'.J23.J24.J25.J26
COM'101ll ~C'fL i 'Jt~GER $.~:-.. .~ --------.--...
.. _._B.I;t\\,.,!,B. TN""'l'iLK£.!.KW C ELLIPTTC ENERGY EQUA~T7r~O~N~G~I~V~YN~G~,~P~R~F.~.S~S~U7.R~F.~. ~F~R~O~M~M~A~S~S~F~L~U~X~---------------
GUESSl (.F)l) ::PS()PQ.u£.lJj.?~M.!-'2S.QRIJ~ ... -,:(=A=5~*O","=1=-) 1I=:1I~l'=-;-;-) :-::-=-::::-:-;-::-_____ _ C ELLTPTTC ENrRGV EQUATTON GIVYNG MACH NUMBER FROM MASS fLUX
. _.r,UF5S?JDJJ=r)<;ll>l.T «GUF'SSI (01) UA'" -1.) IITOGM1) C fLLIPTTC ENrR3Y/CD~TIIIIUITY EQl/ATrON GIVING MACH NUMBER FROM AREA RATTO
.' G.l,IfSS3J[)U:;:GUE..~!l./Oli C APPROXYMATF U~STEADY ~W~A~V~E~E~Q~U~A~T~t~07.N~G~f7.V~y7.N~G~M~A~C~H-N~U~M~B~.E~R~F~R~O~\1~M~A:'S~S=-=F~L~U7.X~--
GVESS4 (01) "OOGP.L".1.lJL,,:ns.Q!Ull.~~JllU $Q)(",.OOI
.. _ .. JHt.JQ.Jl.Q •. ~(J.,J!l..!.:::!:4.!!.O.!.) L .... TFLL"-'Z.G ________ . ____________ _ 10 'Xl=GUES51($Y)
_._ GO_.LCL5.L ~o YF($y.r,F.~SOMO)GO TO 25
$)( 1 ::GlIF'SS2 ($.)') (;0 TO 0;0
.2.5 $)(I=I.DO ______________________ _ -$,,;'0 . ···--r
.. _ .. _.BE.'LJRN
107
AEDC-TR·76·39
~--'--~~-'-----------------------
SOLVI'"R - ~... -.----~--
30 $Xl=GUFSS3('Y*~"i) .~. _~ G.O~ __ LQ 51L ________ ~ ____ .
40 II'"(TNSTR(~).EQ.l)r.O TO 4S __ $U :GiJ.ESSH$.,(L __ ~._
GO TO 0;0 __ 45.._S.lU~Q_IL ____ ~ __
DO 46 T=I,7
nATE " 7510:;7 11/58/40
_ A1l_.1IU =$.Xlt~R\II..lll~'..Jl ______________________ _ 50 II'"(INSTA(9'.EQ.2)RETURN
_ WR I TE (Il)nuG..t.l O.Il..U.Y.t..ll'CllO"'X""-,.ll$LE""M.aA-"X _______ -__:_-____ -__:_-----: ____ ---100 I'"OR~AT(' SOLVER'I'O$Y='.1'"}6.8.' $OX=',EI6.8,' $EMAX='.F16.81
l' 0 N~' • 5l\..t..!Jt~'~.!.1Jl_ltt..!..!'.lliU~t 2.lu_!JUl'I=.l.L! • ax. 'Y I N-l I , • 9X •• E (N I •• ? 9X.'EIN-I),.10X"OE'.12x.'EP'.12X.1DX'I' ',132('·1),
. _______ 1.'1;;;.0 _______________ ------------------120 GO TO(1100.1200,1300.14001.TFLr. ~13{)$El~=l$.'{~Lll _______________________ _
II'"('N.NF.O)GO TO 180 140 $E2=$EL___ _ _____ ~_~ __ ~ ____ ~~_ .. __
$Y2=Syt , .11t2;;_SXL_ $X 1 :SX?+S')X
J~Q$'j='Ii"l+L __ ._ GO TO 120
l~O 'EP='El*SE~ ~ $OF=DARSI'liEl)-nAAS($F2)
_ .~_~-'n.lE.1111E.3Ufu.2JH1.Llli! U 1. $V 1. $X2. !fiV2. SO dif2. $DE. $Ep. $r)X 700 FOR4ATI' ',J3.9fI4.6) ,
I I'" (JABS (!liE'lL. LEA $EMA!U.fIElURN II'"I~fP.r,T.O.)GO TO 220 $[)X=.5*$DK ~ __ . ______ . __ ~
210 $lq:$X?+$,)X ___ GO TJ2. u_L ____ _
220 JI'"(~DE.LT.O.)GO TO 140 !Ii[)X=-$f:\)(~ __ ~_ . ________ ~ ______ --'--___ _
GO TO ?10 C E 'J ERG Y :: QUA U 0 N G I'i I N fL MAS.£._r.l..illLE!li) ~M"__'P:.cR""EU2S ... S.I.I.UR!>Jf"---___ _
1100 $YI=$Xl**TnG-~XI*·APlOG 'Ii Y.l =u 5N~ Tt ~~ Yll. _____ _ GO TO 130
r F'JF"qr,y r::QUIlTION r.1Vtt-JAt1AS!;_ELI1X_J'RQ~L"1A.CH NUMBER 1200 $Vl=$XI*(1.+r,4102.'liXl*.~i**MGPGM2
GO TO 130 _ ~ ______ ~ _______________ _ r A~fA q~TIO V~RSUS ~ACH NUMQI'"R
1 ~Oo 'lin" (TOG~ 1* U ._.G'11D.2..*.$_l\.l~*.!Z1l uGPGMl21U 1 GO TO 130
C U'lSTfMW "'I\S5 FLUX FROM "1ACH "ItJ"lAE.R._ 1400 $Yl=$Xl*(1.+r.41n2*'liXl).*MC,POGM
GO TO 130 ~ ______ ~ __ ~_~ __ . ___ ~~. ____ _ f'J[\
108
A E DC-T R -76-39
PRINT DATE" .. 75157 11/58/40
~ ~~ -~~-~ ~ - -~-.--=:------SUR~OUTINC', PRINT (It)
--I11PL'ICIT "iEAL*8 (A-H.M,O-Z,$1 COM~ON AR~~(3.50).AREATS(3).ARE"AM(31.TV(3.50).A(10).E(7).B(30).
__ ~1~!j:lh.I!1f.U.Yl.31 •. Rlttll __ _ COM~ON PC.RC,TC.AC.MnCTc.FAF.EAPF.EAF.MOTSTR.INEIN.TMGOr,S.GPO2GS.
_ 1 SGOR.. ___ . ____ ~_~~ COM~ON G.3Ml.GPl.OOG.GPl02.GMl02.GPlOG,GMlOG,GOGP1,GOGMl •
. .. -L-QO.ru1L..O..Q.ae.J .. .Gf.OGM I • SGM I n2. TOGM I ,TOG. MGeGM2. raGe I • OeMl? 2 MGPOGM,M30GMI.R,GR.OOR,Py.PERR.AWOKW,OOA1.OOKE.KE,KW
__ ~ ~ .c.rut"lQII/ J.SLlt T S"i..!.liW. TSP. IS At TSI/A. ISV. C To. C TA. PV. pva TSV. TAll'" COM~ON T,TI.DT.TSTR,nT02.TSTOP.OOOT,OIOpV
no c.w~~aN Al. 42. A.hM .• A.5...tA6 ... a.LMtl..2-'.Al.0. All. Ai? Al3. Al4, A15. Al6. A 17 CDM~ON PN. PP. PPT. PO. PI. PcIO. PEO. MOE.
MOD. ~OF. MDPT • MorT. MOPE ,MDTSO ,MOCTO, TEO. TP. TPT • ICTO. RP. RPT. REO. RCTO • ACTO. MCT. AE,
._ ~P(-1._ ~J5-,-__ ~~_. __ ~c:M,,::O,-:-_--::=c,----_--::c::-: COM~ON PNI. PPI. PPTl. prll. PTl. peTOI. PEOI. MOEl •
. _~-_ ~_"t:)Ql.J __ ._~OI"L..._MPP.HJlM!lC.J lL'1~Uern.!5Jtt.!'}lO,-"C,",:T-"O~l-"'_-,LT."-E~O~l-"-'_-LT!:.P~IL' __ _ TPTI. TC10l. RPI. RPTI. REOI. RCIot. ACTOI. MCTI. AEI.
_~~~---A':>.EL-Af..l.J..'_.-:JMJ.:jN..I.IJt._.....!!:"ll~Oul ______________ -:-______ _ COM~ON PN2. PP2. PPT? PO? PT2. PCTOZ. PE02. MDEZ.
__ ~_~~-'.~_.~Q[2L_~Ia.l1ru:I4_"'-QP(Z~O~TL>S~0,,-,2~!M,",OI.L<:~T!LQ~2""'~.:LY~E~O~2 .... _-,-,~T-:P.~2~.,--__ _ TPT2. TCT02. RP2. RPT2. REO? ReTO? ACTO?,. MCT2. AE2.
_ ~.~ __ ~E.2.L_ AFlL_ '1NC.L __ ~ __ ~ __ ~~~ CDM~D~ p~3. PP3. PPT), PO). PT3. PCT03.
WlD3 •. ~~DF3. '1DPTl~ Moen. MDPEJ.MDTS03.MOCY03. TPT3, TCT03. RP1. RPT3. RE03. RCTO]. ACT03.
.. APO. AF..3.L_._.>.1N.}L_~ COM~O~ pS~PO.TsoTO.QSORO.MSOMO
PE03. YE03, MCT3,
~ CDM'10~. JY ,HI ,~Y2-,HL~t.iDlL.Ji.E.L$E2.$EMAXL.'.!CE..,P~.~$l.LD ... E_--=_-=-_____ _ CDM~O~ INSTR(26).TOERUG.TTN.rOUT.NP,IP.rTER.NVT(3).y.~T,tPAGF.
_~~~~_.!~~t..1Jfl~l. IIIME ,NO.N~.NCT.IELG" IELGI. IEU;2. IELG3. IELG4, 2IFLG§.TFLS6.YC'LA7.TELG8.TELG9,Il.T2.13.I4.IS ~ C0P1'10~ _Jl .• J2. Jh"'4~J.'li.JL..JLt.JR. J9. Jl o. Jil. Jl Z .J13. J14 .JIS. J16 .J},.. 1 JIQ.JIQ,J20.J219J22.JC).J24.J2§.J?h C9M~ON NC TL ~ _ _ ... ___ ~ __ . __________________ _ DIM~NSTON V(24.4) ElWLVA!. F;NCL~~.!~ . .=..V-,-( .... l.r.. • .>..I!-) ... ) ______________________ _ l'.JT~GER $\1 REAL~8 INC"IN.'<F.~KJ;/ ___ _ lP:TP+] IF (JP.NF.\lP) RrrUR~L TP=O
_. I 1=.J.16~L IF(rN5TR(13).~E.0)GO TO Jon jF(yPAGE.EQ.O)GQ To.1O.0. ~_ ~ _____ ~~ _ .~~_.~ __ ~ JF(rpAGF.L~.NPAGE)AO TO 140
Ion WRllE (JOUT d20U I~.I=.Ltl~ __ ~ ___ ~~ 120 EOR~AT(')'.RX.'T'.IJX.'TSTR.,13X.'Tl'.14X"PT'.14X.'Pp'.14X.
_. _1 '~O'.d_.!XJ.'p"I·_,.1~.x. 'PPT' !'lX. 'ND'I' • .6X, 'PCTO, .13X, 'PEG' .13X. 'Mere -.13)(,'MO' 2.!4K,·M"I'.13X.'MOCT'.12X,'MDPT',13)(,'MOO,.BX"NM'I' ,.7)(,'MOE',13X. 3. 'M,)E' ~ 12K.' M')PE '. i-2X~-' MnTSo'·~,Tfx •• MOCTO' .12)(. 4'TP'.14X,'TPT'.13X.'TFO'.7X.'NCT'I' '.6X.'ICTO'. 5 13X;'RP I ~ 14)( •• QPii ~ flX.'RF:O'~T2X;oR:;;:c-;T-:;:O-':,20,·1-;3"'X'-"--"''-:A'';'E:-:i:-.-;1:-:4:-;X:;-':-':-A:-:p:::;e:;;",=-.------
... ~I.3..lL~.'.A.FI .• _7X. '~JTEB_'~_' .71~X.'E ('.y I,') '.6X) .5X,' OT '.6)(, 'J16'
109
AEDC-TR-76-39
-I' '4132(1-", IP/l3E=1;
PRI~T DATE" 75157 11/5~/40
-140 wlli"TE-( T OUr.T60' T. TSm-;rt;P-r;;:;p-;PO.PN,PPT ,ND ,PCTO ,PEO. 14CT. "10 ,MN. __ lt~On, Mf'lpr ,·".1Dll, ~N.!!:1Jlf~"'DF, "tQP~.MD~S.ll.Mf)CTO, TP. TPT. TEO. ~CT, TCTO. RP,
2RPT,REn.RCTO'Aq~ATS.TTER.E.f'lT,11 _ J 6.0 F'ORI4/1 T (~II '-_" BE 1" .6. Et Ii.. _____ . __ . ________________ _
JP/l3E=TPAGE+6 _____ .R.E. Y.!ll't"'l ___ _ 300 JF'ITPAGF'.EQ.O'GO TO 320
_ T F' J I PAGE' ~.l..IT.L~~Mlf.' G!L.T_O __ .360 320 W~IT~ITOUT,340' 340 F'ORI4AT 1'1 't_6)~_1 or '..111.)( t '~!'T' ,.1.1)(., '_I'iIR.!.li ox" PT...! .ll X. 'PP' ,11 X..1 ___ _
l'P~'.llX"P~'IIOX.'PFO'.lOX.·PCTO'I' '.1321 ' _'" ___ ..iEl!.;;~:;L
360 WRYTEIYOUT,380IT,PPT.TSTR.PT.PP,PO.PN.PEO.PCTO 3[\0 F'ORI4AT (' I ,9E11..~ __ _
IPA3E=TPA3F+l II'" ('JCTL.E',l.lOI qr:IURIL.L ____ . ____ . ___ _ RET JRf.j
___ E .. ·'iD_
110
AEDC-TR-76-39
AINO~ DITE " 75157 11/58/40
SUR~O-UTiNE' ~i~OM(*) I"4P\,.'ICU_I'.F.ItL~.B_( A-H.Mt~ COM 110 "J I R C" II!. ( 3 • 50 I • II RF" ITS ( 3) • I-=R-=E-:-IIC-:~-:-(-=3-:-) -. -=T77y-:-( -=J-. ::-5-=07") -. 7"A 7( :-1 0-::7") -:, E~(7:;;-):-.-:B:-:-:( J::":O:":):-,---
1 T Y. (3 ;., T 'E L 11..'( ! 11_!.fi\lLtIl __ ---,-::--:::-::-_-=:--,-=-::::-_-:-:-:-=-:::-:-:---=-:-:-:-::-::-::---::-::-:-::--:::--_ en~110N Pc.Rr.Te,~c.MnCTc.ElfiEIPF.EAF.MDTSTR.tNFIN~TMGOGS,GPOlaS •
.. L S."OR.. -------.------------:cc-:------------eOMI10~ r,.3Ml.r, P l.00G.QPl02or,Ml02.r,PlOG.GMlOG,GOGP1.GOGMl.
__ .J .. nOGMl .nO.3Pl t_GE..QG.MJ • SGM) 02. TOGMI. TOG. MGpGM2. TOGpl .GpGI112. 2 I1G POGM.M30GMl.P,r,R.OOR.PT.PERR.IWOKW.OOA1.OOKF,KF,KW COMI10~ .TSLI. rS"i!..TSw, TSp uSA. TSWfl. TSY. C TO .CTA .pv .pVQTSY. T Awt COMI10~ T. T 1. DT. TS TR. OT02~.TSTOP. OOOT .OTOPY COMI10111 111.12 '.A '3 ~fllu A5.t.4fuA7.!A1hA.2..!.Al..!!..!.A 11. A 12.1 IJ. 114. fA15. A 16. A 17 COMI10~ P"J. PP. ppT. PD., pT. peTO. PEO. MOE.
": __ M')O._ , .. _I1JJF ___ LMDPLL..!iOCT • MOPE • MOTSO ,MOCTO. TEO. Tp. TPT • Telo. RP. RPT. REO. RCTO ,ACTO. MCT·. AE. ft,PE .' AF •. _ M."l .• ___ "111.
cnMI10N P"Jl. PPI. PPTI. POI. PTI. PCTOI. pEOI, MOEI, M,)D 1 • I1[W 1., MOPT l.!_!1DC Il.L-'if)PE.!-l.:L,,,,M~D-=-T::;-S~O~l ..... M,-,-Q,:"C~T!-O~l L' --:T:,:,E::cO~l~'L-_T~P:-!l~'L-__ TPTI. TeTOI. RPI. ~pTl. REOI. ReTOl, ACTOI. MeTI. AEl.
II PE 1 t . I\f 1 '-Jlli.l..L-.!IDl--=-c:---=-=-=---:::-::-:::-7:----:~:_:::_---:~:---_ COMI10N PN2. PP2. PPT2. po?, pT2. PCTO?. PEOl, MOE?'.
1.4')02. 140"'2, .MPYl.?_'!._ "lllJ:I2:-,.,--,-M""0"-P-,:E~2'-"'..c.M""D,-,-T.."S",O-",2,-,,.~M~Q~C-=T-,,O-':'2 ..... _-'-cT':'-E-=-Q=-2.L. __ .y.wPw2~. __ _ TPT2, TeT02,' RP2, RpT2, RE02. RCT02. ACT02. MeT?. AE2. A;>E? A.2 •. _.~N_2.! ___ '1ll2
COMI10N PN3. PP3. PPT3. P03. pTJ. peTOJ. PE03, MOEl. M,)O.3 •. 1401'3 I M..QP.l;;\J_._~llCI.h2!,::,D=P~e:~3 ..... ",M~D-=-T~S,,!O_,!-J ..... Mw.O",C~T=-O~3~. --:T:,:,E::cO~3~.,,--_T,,:P~3~.,--__ TPI). TerO), RP3. RPTJ, RE03. ReT03. ACTOJ. MCT3, AEJ. ~PE3. _ A.3, ... _MN1!. ___ ._~D.J...
COMI10N PSOPO.TSOTO.RSORO,MSOMO COMI10~ ~ v. 1-n • $Y_2 tilU..t'!"l!..2.t.!.D.lli.lli...ll.!E..2. 'lEMA)(. 'iEP, 'iDE eOMIlON tNSTQ(?6).rOEBUG.TIN.10UT.NP.=-IP~.~YT~E~R~.N~V~T~(3~'~ .• -t-.~N~T~.-I~P~A~G~E-.------
1 NPA 3E. ~~J, T.T (~) .~.d.'1ll.l.I..lMfJNO .NN, NCT oIFLlh J Fl Gl. I flG? tIEL GJ. IFLG4. 2I.l~~'Tfl"6.J.Lr,7.YFlGS.TfLG9,Il.Y2,I3.I4.15
eOM140'll Jl, Ji;' • JhJ4. • .)_~ ._JI?..t..J..U~~lig .Jl 0 ,Jl1. J12 • .,113 • .,114 ,..115 • ..116 • .,117. 1 JI~.JIQ.J?O.J21.J22.J23.J24.J25.J26 CO"'110~ ~CTL JIjT:GER $'11
!:l. AL"'S J I'!""J "I_ •. _'S..F....t.!<w 1=0 II. ( I ) = 1.
10 T=l+l II"(I.r.T.b)(;O TO 2fL. . .. _. _____ .. __ I'll"!-l A ( r + 1 ) = II. ( I 111 ( 1\ (8) ~I MJ ) 11..._ .. _____ ____ _ w~y TE (TDE.~lI(;.15) I. I 1. Pll
15 FORIlI T (I 1=', 17 •. ' r 1= I. T 7. ,_ 1'11."_'_d 7-'. _____________ _ GO TO In
20 W~JTE(yf')E'01UG,JOJA _ ._~ ____ ~ __ _ )0 FnRI1AT(.O~I"JOI1I/ ••• lOE1'.~)
no 40 T=1 ~ L _______ . ___ . 40 A (11 =A (TlIIII. (Q) fill (1-11
W~ITE(TOE~Ur,.30)1I.
RET JR~ E"JO
111
AEDC-TR-76-39
O~H: = 75157 11/5~/40
SUR~OUTIN~ REVERT(*) . J "1PI • ..'I cr L ~.~.!I..!\ (A-H. M. Q~Z-'-'-"~L) :--__ -,-_=--:-.~---_-_:_-----COt-l110~ /lR"iI\l3,50) ,IIREATS(3) .AREAM(3) ,TV(3.50) .A(10) 01':(7) .8(30).
I _TV. (3) 2 T.J£l.l~.Y 1..3 Ll..RW.(7) COMI10N PC.RC.Tc,AC.MnCTc.EIIE.EAPE.FAF,MOTSTR.INFIN.TMGOr,S.GPO2r,S.
l_ S<,OR. __ ~ __ ~_~ .~~._~~ ______ _ COMI10~ G,5Ml.GP1,Onr,.r,PIO?GMl02,GPlOG.GMlOG,GOGPl,r,05MI.
1 OOGMl.! O_!l~u_GPf')~5.GM 1 02. 10GMl. TOG. MGPGM2, TOGP 1. GPGI112. ? I1r,POGM,M50GMl.R.GR.nOR.PT.PERR.i\WOKW,OOIl1.OOKF.KF.KW COMI10./\J._rS!.J.J.~.J.DW.Ll?~.! TSII. T~. TSV.C TD.CTA,PV .PVOTSV. T /jUW COMI10N T,Tl.OT.TSTR,nT02,TSTOP.OOQT,OTOPV COMI10.~ 111.112 •. 4 3! At. .1\5 !.!I!>J.l!l-,.I\~.!..I!~._~l 0, All. Ai? _.1113.1\ 14. A 1 '5.1\ 16. II 17 COMI10N PN. PP. PPT. PO. PT. PCTO. PEO. MOE •
. _ ...':. _.~'l()~L .. ~F • MOPT • MoeT • MPPE .MOT50 ,MOCTO. TEO, Tp. TOT • TCTO. RP. RPT. REO. RCTO • ACTO. MeT. AE •
.. A OE, . .AL...!. -':'M.,.,N---"._--"M""OL-_--:,---__ --:=-__ :::-:-.,--_--:~----:-__ _ COMI10~ p~l. PPI. PPTI. POI. PTI. PCTOI. PE01, MOEI.
M ~o 1 t. _110 r: Li~.!1Q£'T~ D r Tl. MD PEl. 140 T Sol. MDCI.".O.&.l CL' _..LT .... E ... O~l-".---'T.LP'""lw.'--__ ToT1, TCIOl. RPI. RPTI. REOl, RCTOI. ACTOI. MCTI. AEI.
~_~~~Eli___AEl.~. __ ~M~N~l~.'--~Mlln~l~ __ ~~ ____ ~=_~-=~ __ ~~~ __ ~~~ __ __ COMI10N PN2. pp2. PPT2. pOZ. pT2. pC102. PEOl, MOEZ.
~~ _- _J':1.1I2?..L..~.~DE2 .. , -'M""DILP!:.-'-T&.2 .... --"!M~D ..... eJ.T.<.2-'!.--"'M!l.JD"'p":E.L2'-'.C!:M!J,D!JTwSl.IOLl2~.'-'M:!ln1JC~T"'0"'2"'-"-' _.LTE~O~Z-!.._--'.Tl:p..r;;ZJl' __ _ TPT2. TCTO~. RP2. RPT2, REO? RCT02. ACT02. MC'Z. AE2.
~~~_~I\l>.E2~.~_. A.f2.i.~~_!1NZ.~M . .:cD"'2'"___~ ____ _::c,-----:--:-:--:----::-::-c::_---:-__ COMI10N PN3. PP3. PPJ3. 1"03. PT3. PCT03. PE03, MOE3 •
. __ ~~2Q1L__~QrJ~.~M~O~P~T~3~.~M~0~C~T~3~.~M~D~P~E~3~.M~O~T~S:70~3~.~M~0~C~T~O~3~. __ 7T~E~O~3~.,----,T~P~3~'L-__ _ TPT3, TCT03. RP3. RPT3. RE03. RCT03. ACT03. MCT3, AE3. APE3. ~r:3. MN3. Mo3
-- CO~M-110N PSOPO;TsoYO.RSORo;-,;qSOMO . n~J:I_I1QN _H; ~n ... !iY2. $)( 1. $)(;>. !inK. $E 1. "EO!. 'JiEMAK. 'liEP. !iDE
COM~ON tNSTR(26).IDEBUG.TJN.IOUT.NP.IP.ITER.NVT(3).r.~T.IPAGE. __ --.!~£'Ai:t~!.1fu.1..u3) • J. 1M 1. IT I ME. NIh ~N .NCT dF'LG. I FLGI .rELGZdELG3. XFLG4.
21 n 65. T FL 56.1 F"LG7 .1 FLG8. Tn r,9 oJ 1 • T Z. I3. I (H 15 _ ~c.oM.~9~ _ .J.t, J..2.!.J3.. •. ,.L4.!.,15 .~6 .. J1_ .. 4~-,_.J9 .• ..>!lO. J 11. J 12. J 13. J 14 • .1 15. J 16. JU. 1 Jlg,JI9,J20.J21.J22.J~3.J249J25.J?6 . C0':1110N!H;;JL ... ~ ___ . ___ ~_ _.~ .... __ ~ .. _~~ _ .. _. ___________ _ INEGER $\1
... R...EAL~fLl~!pl"'<F" . .!'5.w_~_ A(l)=l./A(l) A(z)z-a(2)/A(J)~·3 . R (3) .. (;>. <t.a (2) .... 2-a ( 1 ) *A (:l) ) 1 II ( 1 ) U5 R(4)S(~.*~ll)DA(2)"A(3)-A(1)*"2*A(4)-~."A(2)""3)/A(1)*"7 B (.;; =~(i<:: * 0 (I ' .... -2 i a (21 "A~( 4).)~"~A il) U2*1I (3) **2·c.:+C=1'-'4..!..-""'-'A'-'(L!2"'1'-c .. ~*c..4~_-----
p. Jut L!.!J.! t\.l5 t -.2 t~ .. p. jJ~~~" 2!!A (]U_ail.L!*;-9"-:-c;-:-~;--:;-:-777-::--:-:-:;:-:-~-:::-_ A(6)=(7 ... a(I)* .. 3*A(2)*A(5)+7 ... A(1) .... 3*A(3)*A(4).S4 ... A(1) .. A(Z' .... 3
~ .. A(3)-A(1) .... 4 .. a(~)-2A.*A(1)* .. 2.A(2)**2 .. A(4)-ZA.*A(1) .... 2"I\(Z) C lOA (3) "*2-42. 11 6 (2; 1ID5; IA (-i'· .... ll ~~~ ............ ---~~--~--.. ~~--.... -~~--
A(7)=(R ... A(1) ... 4*A(2)*A(6).~ ... A(I)* .. 4*A(3)*A(5).4.*~( 1) .... 4*1\(4)* .. Z iI .12\J~.iI (U *"2"" (2) ';"3*" (4) ;Tg·o~-i~ 11 ""2"1\ (21 ""2*A (3! 11*2+ R 13?*~(2) .. *6-A(1) .... 'i*A(7)-36.*~(1) .. *3*A(2) .... Z .. A(5)-
--C 72·~itA(lf'j"j*i\(2f"Ai3) *11 (4) -12.*A (1) **3*11 (3) .... 3-330.*A( 1) itA (Z) o .. *4 .. A(3))/I\(1) .... 13 . 00 lOT .. 1 .7 --.- -- - ~ -~ .. ~--.... -~-. ---~- .~.~----
10 A (II =R (Il.. ._ .. ~ ... _~_.~~._._.~~ WRITf(IOE3Ur,,20)A
. a.Q. F'OR'1AJ(·.(J3~V(.>tl.!.L!.~UQF~3.5L_ RETJR~
.~~ t':.'I!L.~~ _.
112
c:
AEDC·TR·76·39
C;MP~RT [lATE., 75157 11151'1/40
SUR~OUTTN~ ~MO~RT(~) I'H'L'ICYT '?E~L"A (A-:H,~\'O-Z,:ti!.. ._ _ COM'10N aR C:'II ( -i. 50) • /lRF' A TS (3) ,ARF II M (.]) • TV ( 3,50) • II ( 10) • F (71 • q (30) •
1 TV.(3) .TJELAY(.]) ,RW(7) COM~O~ PC.RC,Tc.Ae.MOCTe.F'I\F.FAP •• FAF.MnTSTR.INFIN.TM30~S.GPO?n~.
1 SGOA' _ eOM'10~ r,.~Ml.GP1,OOG,GPlO?,GM10?GP10G.GMlOG.GOGP1.r.03Ml.
1 003101 1 • 00 3P 1 • GPOGM 1 ,<;r:;MjD2.. IQGM It '.OSi. '1rlPGM?, TOGP 1, GPG 111 ~! ? '1~POGu.M30GMI,p.AR.00R.P,.PEAA •• WOKW.OOAl.00KF.~F.KW
COM'10N TSU,TS".TSw.T<;P.TS8.T~WI\.TC;V.CTD.CTI\.pv.pvorsv,T~IIW cnM~ON T.TI,oT.TSTR,DTO?,TSTOp,nonT.DToPV COMIAON AI,II?A3.1\4./lc:;,A6.A7.AA,,\9 •. AIO.AII.Al;>.III.J,A14.AIc:;.A16'All.._ rOM'10N P~, PP. oPT. po. PT. ,.>cTO. PF:O. 1.10F.
W)f). "'r) •• MnPT • Mr:lr:J .. ,._.I:
AEDC-TR-76-39
nATE" 75157 111<;1'\/40
cn " pr:Ol II A()) C11 :: 0.510 II PfO] II A(I) .. ~E:l_/.!E.Ql __________________ _
r. F.'llIoTJ(1'J 2 ~(l C~;> = -1.)0 ---------------
AI;» :: III / r)S:lRTI TP\ ) II /12 CA? " -AP~l II A(2) CC? :: -PPI II A(2) Cr;I? :: 0.::1')0 II PPl_ It A (2) _II 1\.,0 l ___ JP_L _. ________________ _
r. F'JUIITJ(1'J 3 CA:) -1.)0 CQ3 :: -IP~l - pnl II A16) It OOKF II 112 CC) :: -Al"l II ~OKF II II? C11 :: -CC1 II AI~
(" DUATJ(1'J 4 CII4 = -].10 C~4 " -IIW')KW II A2 CC4 " -Cb4 II 111<;
C F JIIA T t O'J 5 CA'> :: -1.,)0 C~c; " nTO"'V CC'" = 1-85
---------------_._----
c:)c:; = r~5 Cfc; = CA5 II ~npFl • Mnr:) + MOPTll
(" FOUIITIO'J 6 Cl\~ :: 1.00 CRIi ::: 1.00 (,Cli " -1.,)0 Y.ITFLr.2.'JE:.I)GO TO 91
r FouaTIO'J 7 CA7 :: 1.00 CR7 "-1.00 CC7 = -1.10
C F,}UaTP)'J A CAR = -1.10 11(1) " 1.)0 -~CTI A(4) :: 1.10 + r,MIO? .. MCTI Cf-lR :: MnCiC <; 1\ (3) I A (4) ,;<. (GOGMI .. 2.1)0)
r E:)lIATTO'J 9 ('1\9 :: :'1.10 AI"') :: 1.10' r,MIo?" MrTI .. II 2 CRQ" -r. " /II]) " PFOI I A(4) / AI"»
C F111ATro'J 10 C/IIO :: -l.r)(\ C 'II 0 :: Q 3M I " II (1) " T c: 01 / II (4) / /lJ '" I.
C F,}UaTIO'J 11 ~I CAll = -1.00
1r:ITFLr.?)~9.Q99Q.IOO
Inn [~11 :: 0."'10 CC II :: cfH I (H) TO 101
90 C~'I=I.nO-III1 CC11=1I17
C F11)~ T TO\J 17 101 11(9) = - 3MI / '10T<;01 .. " ?
AIIO) :: (;'11 I '1nT<;OI "" 1 CII.l2 =11 (9) " '1 ':In 1
114
AEDC-TR-76-39
i 1/<;8/40 -~ - -- --~-----. _ .. _-------
C91? " A(JO) II MDf'll H2 I F" I JI"Lr.2 .• EQ" lJ Al~J_;:;P1ULPI':Ol __________ _ rF"(TF"Lr.;>.~E.I)A(6)"pnl/pr.TOl II (7) ::: 1\ ( ~) .... TOG A ( A ) " II ( 6) 1111 GP I OG "H,JD:; TO:; 1I_IIL1L~ __ Gf>lD_~Jl\L __________________ _ NU2' " TM~OGS II A(7) - GP02GS II A(A) 1 F" I J FLG2) 94 19.9_~'U_9.J _____ ._. ____ . ____________________ _
93 CCI? " NUIO / POI/ PFOI COl? :; "lU2D / I PI)L _1I __ I"EOLL_ ...... _2. _____ _ GO TO 95
94 CCI?" "lUll/POI/PCTOI. - ------_._--.----- -------------CDl?:/I,1t12DI (POI OPCTO]) 11*2
95 I F" II FLG2. \jE .. 1) GQJ_IL9'L2 ________________________ _ r. f.:}UATJO\l D
CAl 3 ~ ( 9) II MDO 1 ___________ _ C913 :; ~llO) It ~1OCTl II" ? B(1) " PNI / PEO.!_ B(2) :; All) .... TOr.· BOt =!H1L .... 1I GPJ.OJL ~Ul\l=TOG*~(2)-GP10G .. A(3) NIJ? \l" T MGO 3S*B ( ;> L-GP_Q2.G~"JtL1L CCI3=NUIN/P"JI/PfOl CD13=NlI?NI (PNlllp~JUJ H2
C nUIIT!O\l 14 C ~ 1.4_ .. =: _-1 • .0.0 .. ______ ~__::,.--__ -=,__:_-:------:----------'-------CA14 TSA II SGOP / DSQPT( TEOI ) II A2 CC 14 =.0" 51)0_ II. PE'OL~_.l:R.L14"-/'--T1JfI:.:O!!..1'__ _________________ -
C FQUATJn\l 17 92 GO rOI9699B)tIFLG9 _______________ _ 9R CA17"A2
__ C911:::-@.."Ic.IJl.L GO TO "17
96 C1\17" RPI CA17 " - ~ II PPI
C E~l,II\TI()\l 18 _. ____________________________________ _ 97 CAl'!: -1.')0
C91'~ ::: Q.500_. ___ _ CCl~ " PPTI - PPI
C E'W"TJO~ 1"1 Cl\l~ " q I> PPI C"I]'i " R II 1Pl CC)9 :: -A2 IF" (IFLG2) ?,"I992.,_:3 _______________ _
C0l>OOIl**OOl>1I0ll001l1l1l1l01l1l1ll>1I01l01lIlllIl0*OIl*O*1I0*O*O*******************************1 r. SuPE~SO\lIC ARaNCH CIIIIOOO*OIlOIlOIlIlOOOIlIlIlOOIlIlIlIlIlOIlIlIlIlIlIlO**O***II***********************************'
? I~(TOE~UG.En.03)GO 107Q COl :::: TNI"IN C'11 INFTN eCl = T"JFJN C:ll = I'WIN CA7 :::: 1 NFIN CR7 '" Y'JF"1N CC7 :: T"lFTN C4A :::: TNFIN
115
AEDC-TR-76-39
C"lP TNFTN CI\9 J"JFIN C~Q T'IFTN CC~ = TNFTN C ~ 1 0 = J N "',r ."J
DATI': " 15151 11/5'1/40
C31'l :: yN"'{"J C"l11 INC"I"J C312 ::: INC"I~
-----------
CII13 = yN"'!"J C'\l1 IN"'l"J r.C13 = TN:"Y'I CDI3 " TN"!'! CII14 :: IN"!''J CSlI4 " TN""!"! CC14 TNC'J"J
C F:lUATIO'J II 70 SALPII = -CCII / CAll
C FrlUATIO'J IA SAL P l8 = -CAI'I / CAIA S'lETlB :: -CCle / C.fdA
C FfWATTo'J 1"1 A(1) :: -1.00 I CAl 9 SAL Pl9 CAl9 ~ SALPIA ~ AliI S'lETI9 " eel9 ~ All) SGA~19 '" CAl9 0 SAETIA ~ All)
C f11J~TIO'J 2 /', I?) = -1.00 IrA? SAl P2 = ICP? • C02 ~ SBI"T19) 0 A5.1') ___ . ______ _ S"lF.T? " C~7 0 SALPI9 0 AI?) 'iGt.~2 ., ICC? 0 FAPF • Cr)? 0 SGA"I19) .. __ lt_A1?.l ___ _
C F'lUIITTO'J 3 1\(1) = -1.00 I CA1 SAL:>3 " CC) ~ A (3) -- .-.. --- .---- -----------
S'lET3 " C)3 0 A(3) SGA~3 :: C"l3 0 fllF 0 ~(3)
C F)U~TI('\'J 17 All,) ::: -C317 J CAl7 SALPI7 ::: SALPIB 0 AJ4) C;QFTI7 = SAFTIA 0 A(4)
C F::lIIATIO'J 4 SIL P4 ~ C~4 ~ SALPII
C F1UIITIf1\i 0; SAL~5 ~ CAS. CR5 ~ SBET? C;qFTS " C ~5 0 "ALP2 .• l;ts " 5A.1. P3. _______ . ___ _ Sr,A~S = ces * S'lET3 SFPC;S " C"lS 0 SAA~? • Ctc; "SA~M3 + Cf5.
C F1UftTTO'J 4 CO'JTT"JJFO S3FT4 = C~4 * SALP17 Sr,ft~4 " C34 * S8ETI7
C F1UnTTO'J S CO'J1TNUfO STOP; " SALPS + SIILPl'7' -II -'5AFTS AIS) " -1.00 I 'iIOTS SlETS = S"AMS " AIS) SETAS ::: C15 " A(5) SI(A P 5 " ISAns'" SAF.T17 + C;FPSS) .. A(5)
C EJUftTIO'J 4 CO'JTINJE~
116
DATE II 75157
S~T~4 9 CAit + SAfIit * SpIA~ SEPS. r -/S9EI4 * S7fT5 t SALP" I SfTA4 SZ1"4 = -(SAfT' * SKAP5 + SAAM4) I SETA4
LE1U/I.JlJ)IL 6. _ _ ___ .. __ . ___ _ A (6) .. -C'l6 / CI\6
__ . __ ...5.AU'~._'" nSEe~_.A..LILL6)L__ S~1'T6 c 57fT4 * A(6)
C E:'lIIA IJO\l....l2... ___ ------,::--: __ -----------------Sr,~~12 '" C012 * PCIOl ** ?
___ .1iAL!>.l.2_JL.LC.Cl..2...* PUO! t CA!Z * SAl P6) I SGA"'!? S~ET12 = r.~12 * 5~fT6 / SGAM12
__ .Ul.lMeuG.. EikI1llCiO.....I"'-O_8 ... 0"---____________ _ SEPS3 ,. I 'JrI N
~GA~6 z 1\l1'1N SEPS6 '" I 'JET N
__ 5ZL16~=~I~\lF~INL_ ______________ _ SETA6 .. I\lETN
_Slil.llL.!L..1. \I F 1 N SLA"I6 " I\lrIN 5.,1/6 '" I \lEI N S"!U6 .. I\lrIlId
___ ~~~I~'J~E~JuN __________ . ___ _ sen1 " I\lFHJ
._ .. _ .. ~I' ....JXL\lILE...II.lJN'--___________ _ SEPS7 ,. I\lFTN 57FT! m 1~_XLrnN ______________________ __ SETH .. }\lnN
___ . .5.LO.lL_LDlE.J..y-"J!fII _____________ _ SKAPI ., !\lrIN
___ ._..5.A.U'1LJI101LJ.Y-"l".o:.E.Llno.fII _____________ _ SALP9 II I\lFIN S9EI9 .. BIEIN SGA"I9 .. I'JI"JN
___ .5.1.E.1.2..~--&I.ilN'---____ ~ _____ _
SALPIO ,. INn"! .. __ .. _ . .li9.E..U.l....!'.....1J:,!F~T'I:"-I-__ -----------
SIILP13 Ii: JNET\I ___ . SBEIl3 .. INn\l
SGA~13 .. TNn" __ ... SALP.l"t_-'L IN!' .... X...,\I'---_________ _
S8nu " YNFPJ ___ 5.G.A.~.H_..!" ... lf1!IJ..I_"\I __________ _
SFPSU .. Jt~n Ij
_____ szrLL~~.~I~N~E~I~\I __ --------SFTA14 " INn" 5IOli~. '!' I"IFl'L. __ . ___ ._' _______ _ SGA~17 " TN,,":!'''
. ,.5f P s.1.1 _::II llif,-,Y...lI'IIL...... __ ~O A(7) " 0.500 * SALP12
__ --..ti;2.L"' DSJRIIA!I) U ;2 s SAEnZ) V(l) .. -1\(1) • V(e')
_.__ .. 'i'(i.'L~AIJ'1 - _V'--(,..,Z .... l _______ _
r.------------C.SOBLBOOIS
r.------------1=0
117
A E DC-T R -76-39
11l58/4()
AEDC-TR-76-39
SMPF.IH DATE .. 75157 11/5A/40
DO 200 I( .. 1 ... _.1.F"_l?A~JJaMAGIYIK»I.GT.I.D-12)GO TO 200
B()S) .. D~fAl(YII() )/1"['11 WRI IE-'-I DE3\J.lh.91K.!.YJJ ) • Y I 2) • A 14. !Hl51
9 FoR~ATI' ~= •• ll.' Yz'.4F.13.~.' A14=1-.~E71~3-.=5-'~'~B~(~15=c, .. ~.-.E~13~.~5~'~-------I F" DAile; 1 ~Jl5.ll. G T • 0 AR5 I A 14) ) GO TO ..z.0"-'9'--_-------------_ I II I .1
___ .. F.PS (12) " . ..YlKL-_________________________ _ 200 CoNTINUF
~H;;~~(~~~d~(~f~;_:_L·T__:nA-::FI:-:S:-:I;-:n:-;:R;-:E~IJ.~~l~(~Y:-:I~l~)~)~)~)7.Y:-:(71~)-.. 7:V:-:(~2~)------EPS(1c)=YIll .. _._ .... ___ _
'=1 205 IELG8".L._ .. _____________________________ _ I( .. 1 IF" IT .e:Q.l) GO rD .. 2Jl.!.._ WRITE(TOUT.210)T
21 0 FOR~A T ( • OSMIOE~J j SU~E:RS..O.NIC1J .. '_,_lJ ._'_S.oLUllD.N.S. fOUND ') IDF3UG .. 06
____ J.EL1HL=L.L _ .. K .. 0
220 K=I<+I. TF"(~.GT.2)r.0 TO ~o e: PS <12; .. Y (K)
;.-==-=======---===--C CDMPJ)JE" IN.CREI1E'HS. -------.----.------------i.===================
230 EPS (6) " SALP!) II F.PS1l2) .. S8.ET6 ______ .... [1"5(4) .. S[PSII II I'"PS(12) .. SIET4 EIOS (5) .. SZEr5 II F.PS (121 + SEI.A!L"_EF?lHitl.+._St<.AP.5. __ ._. [IOS(17) .. StlLI)17 II FPS('5) + SBETl7
.E"'SllL" SALf'3.~ . .EE'.S.lH~ELL~.lZ.l + SGAM.1-[1"5(2) .. SALP2 II F"PS(171 + SRET2 II FPS(5) + SGAM2 EPS(19; .. 5ALI)19 II EPSI5l_+_ SBEU9 ...... Ef'.s'U11._'Ls.G4.1tl'L [I)S(18) '" SALPlFI * rPSIS) .. SBETl8 EPSIll) ::: SALPll .. EPS(12) EI)S(l) " 0.1)0
.EPS(J) '" O.:>Q . __ . _____ .. _. EPS(8) ::: O.~O
EPS (9) :: O.DO EPS(lO) " 0.00 EPS!l3) ::: 0.00 EI)<;(l4) ::: 0.00 WR.I H. (JDE311G, 20)j hI::l ,241_,E.P.S ___ . ____ . ____ _
c------------------------. C COMPUTF" PROPE~TY VALUES.
c------------------------00 240 I ::: 1919_. J :: IEXTP(J) HI J. EI) ... !)JGO_U1._ ... 2."-4=O=-=-~---------VIJ.l) ::: V(,J.2) .. FPC:; !I)
24r) CONTliIlllE T~o=TCTI) MDE .. ~[)O - MJr P~O ::: MnE * nSQPTITfO) I (~l .. A~ * AF) GO TOI?39.23A) tlfL(i~ ....
118
239 PPT z PPTI 41 (RPT 1 RPTl; *41 G TPI = peT 41 42 II OOR I RPT GO TO 237
DATE" 75157
AEDC-TR-76-39
11/514/40
._ .. --231Lli'J.Al.1,.C-LTllo ___________________ --,-_________ _ PPT=RPT II R .. TPT 1 A2
_._~~~~* aA~2~*_O~0~R~/L_T~E~O~ ____________________ _ MD " MaCH(PD) YE(IINSTBj23).NE.2).AND.lYNSTRI?41.EQ.01)GO TO ?4! Jlb .. JI"+1
. __ .cALL!. __ E'RlfliT _ . ___ . __ . ___________ ----' ____________ _ J16=Jll\-1 WR IrE. (I OU T, 24 2J . _______ _
2112 FOR\.1AT(t.~I)
_. ___ --.2!tLlF I I II"I G~I .AND. ITPEBIIG.EQ. 03; ) RETURN WRITE (YOE'lUG'32) V .
C~~--.~_-_=_~.-.-..,--_'e...,_~'"_=.~~.~----=-:-~ ______________ ~ _______ _ C S~A~L PERTURBATION RESIDUALS .c----.-~..,..,~~-,.,,,.'"'_-_..,,,._"_"'_..,.,,._'"_"'==,,.~. __ ~ _________________ _
DO ('50 r :: 1019 ___ 250 OIT! .. TNI",TM
(;)(2) " CA(, II EPS(~I .. CB? 41 EPSIl7) + CC2 II EAPE .. C02 II EPSIl9) _. _____ ~(31 .. CIIJ II !'"PSI]) + CA3 II fAE .. CO II EPSIl7) .. CO] II EPSI121
0(4) ::: CA4 II EP5(4) .. C~4 It EPS(l7) .. CC4 II EP5(11) _Jll5J~-,,-1I-,,-5_' -=-II---,,-E P"-S,,,-,-I 5",-,-) _ .. "---'C..,B:L:5~II"-'f'_'p:..S"__lu?"_J)'____'+'____'"C .... C_5<--.;.1I'--I:E.<:P-,Sul ... 3L.Li--",+---,-c ... p""S_.::.4I---<:.E,,-P .. S .... I .. 'LI _
II .. CE5 Q(6) " cA!', II EPS(61 .. CAli II fPSI!!) Q ('J') " lNEIIN ~BJL_~_l~~~ _______ ~ _____________________ _ Q (9) " IN!'"'I"1 Q (1.0.1. !L l~H~----_------:c-:--::--:-=-:--------------o ( 11) .. Call It fPS ( II) .. cell 41 E'PS ( 12)
_______ lHI2) " CAl? II 1"1'5(6) .. CCl? It perOI It EPS!l?l .. CPl? II pCTOI till 2 j/ II O:PSIl2) till 2
CH 13l !LJ .\!FiN. Q ( 1 4 ) ,. I '1FT N (Hll.L.;;C1U.1 II EP51111 t C917 II EPSOAI Q(IB) " CalB II I':P5(lA) + CBIS II EPS(5) t CelS Q.U2L'LC.U'L.!!_fPS/19) + CAlC) II EPSOM t CClli II EPSI171 w~TTF.ITnE~UG.131 <rtI=1o(0).Q
c--------------_-~ .. __ ._. C EXACT R~SInuAL6 C -~-.~_~~-~_---_~..,.-.~.~.
DO 40 T=1.19 _ItQ_Q( UtlAD].~ ____ _
Q(Z)=MnPE+Al*op*APE/nSQRT(TPF*A2 o (3) :MDF'+ ~F<!OO~f~IPP""-PD~Al!il_lI!~ __ Q(4)"MnpT+AWO~WII(PP-PTIIAI5)ItA2 Q (5 )=Rp1- =lPT 1 ~H1J2~~.f. M[1F'J:L~..n:-,-T-"O-,=-P-,-V _______________ _ Q(6)=Mno+~DpT-MOCT
11".1 1I"LG2125-'H9qq9..La~':i,:-:----:-:=::~_ 254 QIll)=PT-(1.OO-a17,*PN-a11 o pO
GD TO ;>56 _____________________ . ____________ _ 25~ QIIl)=pT-O.SDO*(PN+PO) 256 B (l~) =1.00/pC1L. __________________ _
~(13)=TOG~1IlM~rSO~1I2
Q(12)~MnQ*II~~gllJl_~(PDIIBI121)**TQG-(pn*B(12"II*GPlOG'
119
AEDC·TR·76·39
SMPERT
GO TO (?51.2521.II'"lG9 2S1 Q(17)"PP-PPTIO!RP/RPTI,o*G
GO TO 253 252 Q(17)=PP-RP*R*TP/A2 253 (1)~'=PP-0.5DO*!RPT.RPTli
__ -----.GI19,=TP-PP*OOR/RPOA2 GO TO .19
!lATE .. 7S157 I1/S8/40
~** •• ****.*******.** •• ********* •• **.************************************ r. SJRSO~JC 9RaNCH C·***·*···***·*·····***·*******··****·******··****************************** C-------------------------------__ L-CQ~p~E_cn~5J_~_~SLiE~O~R~S~O~L~LJ~T~TllONN ________________________________________ ___
C-------------------------------C EQUATIOI/ 19 3 SAL o 19 .. -CBI9 1 CAl9
SBETl9 .. -CC19 1 CA19 C E~UATIOI/ 2
_________ B..i.il.. .. ~-.A.l.o.!. 0""O"--'I'-'C..tAu;2'---_..,---_~ ___ __,_--------------SALol.' '" ( CAl.' + C02 * SBFT19 ) * 8(4) S8ET2 .. C,Z * SALP19 * BI4' SGA~2 .. cce * EAPE * 8(4;
C DLJATIO"J S SALPS .. CBS * SALP2 SeET5 .. C95 * SAET2 SGA~5 .. C95 * S6AM2 • CES
C E~LJATTO"J! B SALPB = -CAB 1 CBA
_....J:..£QUA1l..rul~ __ _ SALP18 .. -CAIS 1 CBIS
________ 5.9£11JLJ;~.c.c ... 1 ",-B_'L~ --'CwR"-l..,A~ __________________________ ___ C EQUATIO~ 5 CO"JTJNUEO
SKAPS = CAS *~~A~L~PAl~A~.~SnB~ELT~S ____________________ __ 8 (S) .. 1.00 1 SKAPS
_______ ~5S __ .!O. __ ... ....SAU'_~_'*~Bu(""Su' ______________________ _ SZETS .. - ces * B(S) _______ ._.5n~_= - _C05... ..... __ Ili5.L) _____________ __
SlOTS .. - ( e~5 * SBfTle + SGAM5 ) * B(5) C EQUATIOI/ 10 .
SALPIO .. - C810 * SALPB 1 CAIO _LE.illlA.UO"LIL __
SALol1 .. ~ CRIll CAll ____ ---.S_BEll.L~_:...cI...JCk.lLlL--1/'___1.C..!'ALAl...Ll __________ _
C EQUATlO"J 17 SEPS}1 '" CAIL...c~~4C~B~J1L_ .. ~S~EuP~S~5L_ ______________ _ 8(6) =-eB17 1 SEPS17 . 5AL~ LL!iL SZET_S_ !I-'U6.L ___ : ________ ___ S~ET17 = SETA5 .. 8(6) 5~'UL!'__5HlJ5.~Jli6~. _______ _
C EQUATlO'l 1 B(V = -1.00 1 CAl SALPl = CBl .. B(1)
_______ ~9FTl =. C'll * SALPIO .. !H1) SGA~l = CC1 * EAE .. R(7)
__ c...J::~VAllJl'.1 3 SEPS3 = CA3 + CC3 * SALP17 8(1'11 '" -1.00 I SEPS3
120
SMP!'"~T
SAL P 3 ~ CC3 .. SRET17 * BIR) 59ET3 '" C~3 .. *_13 LBJ_
DATE .. 75157
5GA"13 " ( CC3 * SGAM17 + CR3 .. EA!'" ) II R(e) C E:lUATl(l~ 4 ________ .
51'"P~4 = CA4 + C~4 * ( SAFTl7 • SALP17 .. SAlP3') B (9) =- lADO .LSEP..5.~
AEDC-TR-76-39
1110;8/40
SALP4 = I CR4 II SALP17 II SAFT3 • CC4 * SBFTIl ) .. B(9) S!:lH.4 " C.C.4. II 5A.LE.l..L....:*'---'9l..J('-'9 .... )'--_____________________ ~ SGA"14 = C~4 * I SAlPl7 II 56AM3 • SGAM17 ) * R(9)
C E~UAlIO'l (, ._. ___ . ______________ --,.. _____ _
9(}0) ,. - C96 I CII" SAlcf, ::: 51lLP 4 II B UO_L __ S9ET6 = 59ET4 II AIIOI
__ .SGA~HL.;: .. _~.c.C1LL_.J:ll_. ____________________ _ S~PS6 ::: S31144 .. BIIO)
C E.:lUAr1.Q~ ... 1 . ____ .. __ .. 5ZFT7 ::: CA7 II SGAM6 + CC] II S8ETI
.BUI.! ;;_~ L.llJLLSZEU ... __ _ SALP7", I CAT .. SIILP6 • CR] .. I'SRnJ + SALP:l * SALP4 ); II Bell; 59FT7 " I_CA? * S8FT6 + CB7 II SALP3 .. S6FT4 ) .. Bltl) SGAM7 " CC7 .. SALPI *BIlll
... 5EP..5.L,=_L.c.A·L~~!L.!.....C.8.1.. .. SGAM3 • Cr.7 II SGAMI + C!:!f' II SAL P3 II
'II SGAM4 I" 9 1111 .CEJlliA.llQ'i._LCJ!.'tILt\lLlf.!L..... _____ _
SZET(, " SAlP6 + SGAM6 .. SALP7 SETA6 '" S9ET6 • SGAM6 II SBET7 SlOT6 " SGAM6 II SGAM]
_____ ~~~~_S!~~L.£GA~Mm6~*~5~E~P~S~] _____________________ __ C E:lU4TIO'l 14 ___ .. _...JUl.2L..;;" CCli. .. SAl PI 0
SALP14 '" CB14 + 8(121 II SGAM7 S9EIl4 " 311?! .. SAl P7 S(;4"114 " 9(12) II 5BET7
__ . __ --.5Ef'.Sl..iL.;L.9..U2J.~-'lS..L7 ______________________ _ C F.~Ut\TJO\l 9 ______ ~~l_= C39~~P~8L-~~-= __ ----__ ----------__ ---
SZFT9 ~ Ca9 + 8(13) ~ Sr,aM7 SGA~9 =-8(13) I SZETQ SaL D9 = SGA~9 ~ SALP]
_. 590'il.::;. .. S.Gl\'1':L!._S.B.Ell ______________________ ___ SGb~9=SGA49·SEPS7
C E.2UA!.Ht.'LH . ..cJ1flJll~!L.. 8(14) '" - 1.00 I CA14
_ ... _ .. _---SZ£~::;._LSilll!t. ... S4LP9 + SBETl4 ) .. 6(14) StTA14 '" 1 SALPl4 .. S8ETQ + SGAM14 ) It 8 (141 510114."1 SALP14. !!. SGA"t9 ~. SEP..5H_l . ...!. . .B..L1Al. __ ..
C E~UATln'l 6 CO'l'INUEn _ .. _ S LlL'ML "'._ S.ZEl.b ._L S.l11J.6_._~9.
S"1U6 .. S~TA6 • SIOT~ * SRET9 .. __ .. _...5!ill!l. _".-S.IiIlP6 + SlOT \L..*:.......;;SuGuQ"'M""Q'--_______________ _ C E~UATrO\l 7 CO~T'NUEn
SH &...7 . .!LSA LP1 __ LS.GAM.1_! .5.Ali'~ __ SlOT7 = S9ET7 • SAAM7 .. 5RET9
... SKAPL"'_ . .5.EP.5.1_Jo--.5GliMl. ~ SGAM9 h __
C E~UaTTO~ 1? _._. ___ .5.ALE'_lZ._'".....I:>£OL - PDI It SAl ~
121
AEDC-TR-76-39
SMPI'"RT DATE .. 75157 11/58/40
S~fTI2 " ~P~l • SPfTq __ SGA'112 _= __ ~Dl_"_~'19 ___ _
SA? .. rnl? • SALPl2 ... 2 592 " CAl2 • SLAM£> _. __ CBI2._. _SZEI11L_~ .LCl~ SAl Pl2 • 2.00 II ent? ..
~ SALPl? • Sr,A~l? SC2 '" 2.00 II C')12 II SALP12. II_SBE1l2 _ ________--::-_-::-___ -----:--__ _ S1? " r~12 • S~U6 • CAl2 .. SETA14 • CCI2 .. SPETl2 + 2.00 .. Col2 ..
t.l SPEll2 • _%A"112 __ _________________ ._ SF? " r~12 • SRfTI? •• ~ sr:? " CAI2 I> S'-IU6. I;Rl2 .. 'lynTl4 _+ c'Ci2._"~MI2 • C~12 ..
'II SGAMl? •• ? C J:":}UATJO'J 1'3
SALP)3 :: - P~l .. ShLPQ SBFTl3 _0; "I;OL.- X~L.· 5pr::tL... __ . __________________ _ 5GA~13 :: - PNI. SGAMQ Sl\~:: Cn13 .. S~L.PI'3 <HI 2 ______________________ .---,--_--:: _______ _ SB~ " r~ll .. SfTA7 • CAl) • SZFTl4 • eCl3 .. SALP13 + 2.00 .. COl) ..
1il S~L.P)3 .. 5GA"1)3 _________ ._ SC'3 " ?OO • COl) • StlLP11 • SAET13 5:»_ " CA13 • !ilQIL..! CI:H3~. SETtll4 • CC13 .. SAfID • 2.00 • rOll.
~ SR~T13 • SGA~13 SE3 = coD" S3ETl3 <HI 2 _____________ _ sr:'3 .. rAil" SKAP7. CAll" 5TOT14 • eC13 • S"AMI3 • Col3 ..
'iI 5GAMl3 •• 2 JJ=JDERUG
- .. _----------- -----------
CALL'_QSIM_JL (51\2 ,~2J5CZ.15D2.5E?Sf2.~.fI3.5C1.5D3,5r:3.SE3. Ii.)( 1 • Y) c-------.----
C S1RT 'I('I1TS
C-----------1=0 DO 1 !iJ~_=_h4__ __________ _ Ir:«DAPS('IMAG()«(~))).GT.l.n-12).DR.(DABS(DYMAG(Y(K))).GT.I.D-1211
1 GO TO 15 _ _ ____ _ B(14)=nREALIXIK»)/POI B (15) "ORE Ill( Y (K IIlPN 1_ _ _________ . ______ _ WqTT£IT~E'llJC;.(9)K.XI!() ,Y(lO .A!4.RI!4) .AIIS)
_69 F l)P"1/tI t' '<=' J..U-, '_..!=-.' _t.2.F.L1..!it_' ___ v" '--t.2E 13.5.· al4=' tEl). 5. I • ~ ( 14) ,'I ( 15) " I .?F 13.5)
IF I (DAI'lS Ig I 14) j .GT .n.485 1~14») .0'1. IDABS(fi11S) j .GJ...nAB5JAHllJ ____ _ 1 50 TO 15
1=1+1 JJIIl=1< EPSI121=XnC) EPS(l1):V(K)
15 CO~.lTI~IJE I-(T.LF.l)r,n TO 340 K=J R(l4)=qJJII») 8<l5)=V(JJ(l) ) 00 320 T:?oe: J:oJJ (1)
Jr:('4RS(O~FtlLIX(J))).GT.n~RSI~114)))GO TO 300 II =J R(14)=qJ)
301) I ~ DA[-ls 10~EAL I V I.)) ) ) .(n .n ... ~s (p (1';) ) )_GO 1(L3_2Q ____ _
122
AEDC-TR-76-39
SMPERT DATE" 75157 11/5A/40
I2=J .... ___ Bl.l.5.1_=_'U,LL._. _______________________ _
320 CONTINUE _I r.lll. ~JE.12) £lLTO .3!t.O I" I _____ ~_U2.J,.xul .... ) __ _'_ ______________________ _ EPS(13;=YII?)
_._-lilL.'EI138=0 1(=1
_____ li".J .. l .. E.O"lJ.)JlG.uO........LI.uO ........... 1.L7 ________________ ---------WRITE(TOUT.16) Y
.... _ U EDR'IAJ (' O'S~.F'.E.!U.L'...!..l...J3l.O • ...!.I_.!>S.urjLr.IJlJJ.TJ.'.uO"'N_"S...LEuOl.l.U1"-Nuri.!.., L..) _____________ _
JDF3UG::::06 ___ ..........l.f.L38=1
1(:::0 .. _._lJLJ.<_" K .. 1.... .. __ ._. _____ _
IF«~GT.4)GO TO 60 .. E"5.112) =HKI ____ .. __________ . E"S(13)=Y(I()
_.c,. .. "".,._"=,.~,. .. -. .,..,,.-_-,._"_"'.,..-"__ ______________________ _ C CO~PUT' INrRE~ENTS C.------.,.~D,.--".,.,.----. .,. .... ~---_-- ..
17 EI>S(6) '" SLIIM6 I> fPS(12) .. SMU6 .. EPS(13) .. SNU6 EPS 11 J p" 5..E..1Jl. L_'!..... .E.f>s (] 2) .. 5 r Q il..~...n .... SLJI'--'I....;3l.L)__"' .. '___"'SwK'_"A..cP..L7 ________ _ EI>S(9) ::: SALP9 .. FPSIl2) .. SBET9 .. I':PS(13) .. SGAM9 FPSIIQ_" SlEI14 .. EPSIl2) "SETA!4 <I FPS!l3j t STOTU E"S(4) " SALP4 .. FP5(12) .. SBET4.<I EPS(13) .. SGAM4
. _ EP5.13L.;:: _SALf>3 .. EPS (41 .;, SBET3 It EPS II 2) .. SGAM3 EPS(}) :: SALPI I> EPS(9) .. 5BETl <I EPS(7) .. 5GAMI EP5.il1L.::;......sI\~l.Ll' FPS(3) .. SBFTl7 .. FPS(4) t SGAM17 EPS(lI) " SAL"}l I> EP5(13) .. SAETll It EI>SIl2)
. ______ E~lJl.L::;.....S til P 10 I> FPS 17 i EI>S 11 A) '" ..:.tS..ll." .... P-=-S~5-"-::-It-=-=-F:P=-S!::...;:L( ~17.L..L.) - .. -S~Z~F.~. T~5::--.. ---:E~P::-S::-(-:3:-:)-.. ---::S:-::E:-::T::-A-:5:--.. ---::E:-:P:::S-:(-:I;-:-)-.. -
jil SI.aJ5. __ .... ___ . EP':;(5) " SALPIB It EP5(18; .. SElETlA
_E."5..(f31 .. =.......s.jUJ~3_! .. _EI:..JP""5oL(LJ7L1)':___-___==_=__-::_=_::__:___:-__::_..,__,_:_:_---_~ EP5(2) = SALP2 * ~PS(17) .. 5RET2 I> 'PS(lS) .. SGAM2
. .E.P.sH..2.l .....':. . ....5.A.LE.19 I> EPS () A) .. SBETl9 .. EPS Cl71 Wr<ITE (¥nE9Ur;.20) (I. Y"'I.24) .EP5
20 rDR_\1AT (3 It' ..... 6J5..lt!...!..E..e.5...l...!...o..lb .... -'.1..!..t.4....11_I).3 (I' • ,~,..L)..L) __ _ c--------------G--~-----------______________ _ C COMPUTE .S\1/1LL.P£"Iil.llBBAI.lilN PROP~RTY VIlL"'-U .... E-"-S ___________ _
C--------------------------------------------.. DO .. 30 1d . .19. .... ___ _ 25 J=yooXTP(I)
IE(J.EQ.O)GO TO 30 V(J.l)=V(J.?)+fPS(Y)
30 CONTINUE .. ______ . _____ .. __ .. ________ _ AD TO(141.342).TFLG9
341 PI>T= .PPH .... .!I. l~E'L..L..1!£JJi.._~!.......G _____ .. ____ . ___ _ TPT :: ppT I> OOR I RPT .. ~2
GO TO 143 342 TPT:::fCTO
PPT=~PTUR~TPT/~a
341 PCTO PEO TCTO " TEO
123
AEDC-TR-76-39
SMPEPT OATE" '" 75157 1115A140
REO = PEO II OOR I TEO II a? ____ qrlL"._H.EJL. _______________________________ _
ACTO '" nS~RTIGR II TCTO) . ___ . "1I1CI!t .=_ BCIJL~----.AIT~~
MO = ~~r.HIPD) . ___ .. MN .. "_'-1~CHl ~l._::_--c---~ __ -----------
IF«INSTR(23).NF.2).AND.(1NSTRI24).EQ.0»GO TO 28 __ . __ .-..>illl=-J.l6.d._--'--______________ . ____________ _
CALL' PRTNT .JH=J16-L _. __ WRITE I TOUT.29)
29. FOR\1AJ I '.+Q.!.l ____ . ______ _ 28 IF I (IFI.r-;8.Ft~.0) .ANn. I IDFRUG.EQ.03) ) RETURN
_____ ~RI TI': (IDE3UG' 32) Y 37 FOR'1AT(tOSMALLI PERTUR~ATTON PROPERTIES'.131/' '.8E\l>.B»
--~-"--~"-".~~~.,.-~-."'-"'-".-'".,,.-.,..,..------""-"'-'----------------------C S'1ALL pr::RTIJRBATJO\l RESIDUALS
. c....,.':".-.,..-.,..,..,. . .,. . .,. . .,. . .,..-.-.,..,----"'-"'-=~~..,.,.~.,,--DO 35 1=1.19
35 QII' .. 1.D70 O(l) " CAl II r::pSIll + ef31 II 101'5(9) + eel • FAE. COl. EPSIlO) 0(2) '" CA.2 . ..I:I_.EP..5..1 ... 2.L) ---'--........... c~e"-2_II.c.......JE....,p'-'S"'--'-1 1 .... 71-)<.........+':--'C .... C ..... 2--=--:·,..-Lf .... AuP ...... E.........,+'--'-C .... D .... 2........c: • ......,E"'-P ... Su( .... 1""'9CL) __
0(3) = CA3 II 101'5(3) .. ce3 .. EA!" + CC3 * EpS(l7) .. e03 • F.PS(12) . __ . JHlt..l.. .. =U:.M. _1I_.EP..S..ilu'--'+'-----"Ccr.:A"'4c......cIl-..loE"-P""'S'-'-I.AIJ,7.L) ......:..+ ........ C"'-C;:!,4-'...II-"-.EL..P""-S ... ( ~1 .... 1 L.' _......,... _____ _
QIS) :: CAS II EPS(5) .. CB<; It EpSI2, • CCS .. fPS(3) + cos .. EPS(4) • . __ .1l_.c.E.5 __ . ____ .. --:-__ -~--=-::-:-__ --:------=-=-::-:-~---------
Q(F,) :: CA~ It EpS(6) .. CBF, • EPS(4) .. CC6 • EpS(7) .u __ Q..W_.-",--,=AJ_*EE'.5..t6) .. CB7 • fPS (3) .. CC7 .. EPS (11
Qlfll :: CAB It EpS(7) .. CRR • EPS(8) __ .Q..l9.L..;:: .. J:A 9 ... !. L~_+,--,C""B,,-,9L......C·'-....Lf"...cP~S....,Iu.8u' ________________ _
Q I I 0) '" CillO II EPSll0) + CRIO • EPSIB) ___ .Q.1ll) :CAIL!.. EPSIIlI + CBll • EPSIl3) + cell II EpS!l2)
AilS) " PI"OI • fPSIl?) - POI II EP5(9) . _____ Jll1.2L..:..J:.Jll2....ll . ..EPSI6' .. CBI? • EPSl14' • CCl2 II BIl5' + COl? ..
'il 1'1(15) 11* 2 . ... BUbL.=-.p"OL.tI.EPSI13) - PNl .. EPS(9)
Q(13) '" CA13 II EPS(7) + re13 • EPSIl4) + ce13 • 8(16) • (:013 • . __ .l!...lU.16) .... 2...
Q(J4) " CII14 • fpS(l4) • CBI4 It fPS(9) + cellt It EPSIlO) _. H_ .Q.I171 :: C.~17 _It .Fp2.lW_.L~ EPS (18)
DIU'll '" CIIlA I; EPS(lS) + CR18 .. FPS(5) .. CCIR ___ JUt 9. L~J;Al'~ .. 11"'£ PS...,C .... l..29CL)-...:!+--"C-'-'R""1,L9......::.·-'-.E"'p"'S ..... I."-1 ",BL.) _. c:..+ _C",-Cl<..Ll 9z-.. .::......JE...,p'-S"--'-( 1 .... 7!...'L...... ___ _
W~ITEIHIE=!UGtl3) l''I=1020).Q ·_. __ l.3 ... .E.QB'1AIJ!.Q.~E.SJ..!)JHLS fROM SMI\I L PE~TURBATION EQUATIONS'.
1 21/' ,.1016X.12.5X».21/' •• 10EI3.5» __ C -.~_~.~-.~."'~.- ---~ ---
r EXACT RESlnUA~5 ___ .c. ... _~.--.~~_~..""."'_~~"::"'.-~ ... _. _______________________ _ DO 1110 T"'I.19
140 Q(II=I.o7Q Q(1)=MOF-AlI;PEO*Af/DSQRT(TEor·A2 Q(2) =MM'E.+Al.IIJ~~~..EL.Q..sRU1.I.P.t~, _______________ _ Q(3)=MnF+AFIIOOKF*IPP·poiIlA2
__ . __ ._Qt3J.=.t'!DF.+A.f~~~-PQ.:;.*-!'-~.J..l"_6L.).::.. .. f!.Ah2_. ______________ _ 0(4)=~npT+AWO~W~IPp-PTIIA15)*A2
_____ ~JlD_=R~~_~Tl-(MopE .. MOF+M~D~P_T~J'_II~D~T~O~P~v'--__________________ ___
124
AEDC-TR-76-39
SMPF.lH DATE .. 15151 11/5A/40 _ ..... _-_ .. _--------------------------
Q(~I=MnO·~DPTmMOCT . __ JULL:;MnQ-:'IDF-"'-"iDI:..E __ _
B(91=1.OO.GMI0Z·MCT .... ___ a(1j)1;::J. ... MH1M.W2.~I~t~ ___ . ___________________ _
Q(Bl=MncT-MC'*MDCTC*A(91*·MGPOGM __ .. aLllL:;BlLOlLB.19J.·~ _____________________ _
Q(Ql=PFO-PC Il 8(111 1lIl GOGMl . _P .. _Q tlDJ",'[£Jl~.c'!!'~Uu)ululL-_______________________ _
IF(IFLG21144.9999.145 ___ .UiLJlilUEP.1-: ~_~.1-L1"'::*.LP-,-,Nc::· ... A-L)-,-7.:.41L:.PJ.LD ___________________ _
GO TO 146 ..... ..145 (H1Ll =PT":"_O_.5DO*.i!"J\I.±.~
14~ R(121=I.DO/PEO _______ .~~T~OyG~~Al~lItlM~~LTS~O~IIII~2~ _____ ~ _____ ~ ____ ~ ______________ _
QI121=MnD*1I2-9(131 1l «PD4IR(1211· II TOG-(PD4IS(1211*41GPI0GI _____ ._----.JliL31~_D_CJ: •• 2-B I 131 II I IPNIIR I 1211 UTOG- IPNIISI 12; I UGplOGI
Q(141=MOTSO-SGOR*PEOIITSA/nSQRT(TF.OI*A2 ____ ... ___ G.O. .I<1ll4L.1!2.LL1f1.-1 u.G9'L..._--,--____________________ _
141 Q(171=PP-PPTl.(RP/RPTl' •• G ___ . GO TO 143
142 Q(17)=PP-~PIIRIITP/A2 m __ ..li.:L Q I) 91 =RP-O. SOo. (RPT.RPT) I
Q(19)=TP-PP*OO~/RP*A2 .. _1:.!!.. '!.! .... II. II 1111* * II 11* 1111 II II II II lIiI II II "*11 II II 11111111 II 1111 It illI *iI II ** ***11 * * * * **1111 * ........ * .... "**111111""1111 1111
C OUTPUT ~1I1I1*iliIll*IIIIIIIIIIIIIIII*****iI***lillI.I •• II*illliI.*iI.iI**iI***"****.iI** ..... ***iI.* •• * ••• ·
C----------------------------------_uL .c_Q.N'L~.H_T-R£5lQUALS TO PERCENTAGES
C----------------------------~-----... 19_ QCLIt9 .. 1.;: 1ll9. J=T~XTP(11
.. __ ------li I J. EO. 0 I GO TO 49 IFIT.EO.6)GO TO 45
____ ._...l1:.Ll.a.E!hll.1i!l TL
O"--'4:r..1L-____________________ _ IF(I.Eo.SIGO TO 42
... __ .lEIl....£11.l211HL.J: . .lJO'--"4 .... 3 _________________ _ IFIJ.EQ.13IGO TO 42
____ . __ .. .GlLIQ._AL-._· __________________ _
41 J=lO GO .TO 4.6
42 J:::12 . _____ . ___ G.(LIQ _4.6 .
43 J=q .... _._ .... _GfLIQ _-"-6. __ _
45 J=ll 4(, IF tV tJ.2) .~LO.DOI.G~LIO....AJ' ___ _
Q I T I =INn 'I' .GO TO 4 eL.
47 Q(TI=QIY)&1.D2/V(J,21 ____ . __ .49._ CO.t-j.Il!:i~_ .. _
W~ITE (FIE~UG.21) (,. I=I.201.() _ 21 f.OR"~T L'llqES1.!l.U.ALS...£FOM EXACT EQUATIONS'.
1 21/' 1,10(6X.I2,5XII,2(~' t,lOE13.511 . __ .u.L1ELU1l.A~lU..G.O....I_(L D."lLO~ ___________ _
IrIJFLG?)220.Q9q9.1~ ... __ lIlLJtRLlE..(TOE9LJG • .3lJ (T. y"t.1 O).At I J. I=1.30) .R
125
AEDC-TR-76-39
SMPEPT DIITE " 75157 11/58/40
31 FOR~AT('OA ARRAY'I' '.10(~X.r2.sX)/' '.lOE13.s/ I 0.,'R ARRAY'. h 13 U.L. '..tULlE'll(. I 2,5 X! ! .t..llL!._...:.'-"wlLlOblJE:....L.l..!.3~.'"'5.Ll..LI _________________ _
WRJTE(JOE~Ur,.lOI CAl, CRI. reI. COl. CA2. C82. CC2. C~2. 1 CAJ •.. CB3, Cc.3.t-1:.Il.U._C.b..{u_.CB4. CC4. CAS. CR5. ce5. C!)S. 2 C~S. CA6. CR~. CC6. CA7. CR7. CC7. C/l8, CBR. C1I9. C89. 3 CAI0. CBIO~All..o.CBllACLll..o.CII!2.CB!2'CC!2.CO!?CA!3.CBI1. 4 CCI3.r.!)13.CIl14~CA14.CC14.CA17,CBI7.C/l18.CAlA.CClA.C/l19. 5_.c.a 19. •. cc1.9.. ..... ________ _
10 FOR~AT(II5MPERTI/. ,.~(.=.1/'0 •• 7X.·CAl'.13X.'CAl'.13X •• CCl •• 1 13X, 'CDl '1 .. '. ' • .4El..fu..BL!!l..!...L7X. 'CA2' ,13X. 'CB2' .13)(. 'CC2', 13X, 2 'C'2 ' /' 1.4.16.A/'O·,7X,'CA3'.13X"CB3 •• 13x,'CC3,.13X.'CD3' 3 I I I, 4Et!>. 81' 0' .7 X.I' CA4' .• 13llt •. C9.-'>. ... _ •. ux....!...C.CA.!.i'..!_'--. 3E 1 &.8" o •• 4 7X. ' Co5 ' .13X.'CR5,.13X"rC5 •• 13X"COSI.13X.'CE5t/' '.sFI6.8
. .5...1 ' O' .• 1.Ji..t.!...C.Ab.!..1.1lX. 'C86'.1 n'.!J.:C6'1' '.306.8"0' .7X. 'CA71 ,13X. 6 'C~7'.13X"CC71/' '.3EI6.8/'0,.7X.'CAS •• 13X,lce8'1' 1.2E16.8 7 1'0 ' ,7)(. 'CA9
' tl))(u •. !CR2.!.L!_Lt.2f..l...6......lU0' .6x,'ciilO' ,12X. 'CBI0'1' I.
A 2F 16.A/'O'.6x.'r.all'111X.'CBI1'.12X,'CCll'I' '.3.16.8/'0'. q 6)(,' C ~.12 I. IZl\ •• C912 '.12X.!..c.Cl.2..' tl.2X.!..!..C.Q12 'I' • ....L4E.l.6...liL! ..... o-'-, .... "..6"X ..... ___ _ A 'CA13 1 .12X"cgI3 1 .12X"ccI3'.12X,'CDI3'/' '.4.16.8/ I O'.6X,
. __ !L'CU4 •• 12X.!CB.L4 • ....L.12XL!.tEI4.1. '.3E16.BI ·ol.!?X.'CAI1I.1ZX. C IC~17'1' '.2~16.A/.O •• 6X •• CAlS'.12X •• CR18 •• 12XI.CCIA.I. '1 I) 3E 16.91' (l' • 6X. • C A 19' .l.2.X ... !.1:Bl.'l!....t..l21tJ_'.1:.tl q 'I' '. 3£.lb...lll. _______ _ WR!TE(TnE~ur,.II) 5ALPI. SBETI. Sr,/lMl. SALP2. S8ET2. SGAM2. SALP3
1 • SBET3. SG4'13. SEP.S.3L S.JI.Lf>4LSB.E.I4.L.5.GlI.Mit.LSEPS4. SALPS. SBET5 2 • Sr,AM~. S"PS5. SZ.T5. SFTAs. SlOTS. SKAPS. 5ALP6. S8ET6. SGAM6 .3 • SEPS6. SlET"LS£!A6. STQ.I.6_L.s.~. SLAM6. SMU". SNU6. SAlPZ it • SAET7. Sr,A~1. SfP57. SZET7, SETA7. SIOT7. SKAP7. SALPS. SALpq <; • S9ET9. SGA'19, SZEI9.5ALP10.SALP.U,.s.AETll.SAI PI2.SBETI2.SGAMI2 " .SALPI3.SR.TI3.Sr.AM13.5ALPI4.SBFT14.Sr,/lM14.5FP514.SZET14.5ETA14 7 .5IOT14.SALPI7.SRET17,SGIl.'117 •. SEf>S.l1.t...SA.LP.lB...SBEIla.SAI pI9.SBETI9
II FOR~AT('ll.6X"SALPI·.11x.'S8ETl,.llX"SG/lMl'I' '.3Fl~.A/'0'.6X. I • So'lL P? 1,11 x t
' SREI2.~~5G.A'12..!L! ___ ' ,3E I ~. f!I' 0' .6X •• SALP)' .1 ! X.
? 'S~ET".IIX"Sr,AM3'.IIX"SFPS3'1' ,.4EI6.A/'O'.6X.'SI\LP4'.11X. 3 '5'lET4 ' ,IP .• 'SGA M4'.9 _ ... _....l1.!U. • .5EPS4'..L. ',4El6.8/'0 •• 6X. 4 ISdLP~,.11X"5qET5'.11x.'SR/lM5',11X"SEPSS~.I)X"SZETS',11X. ~ • S~T A~' .11 X. 'S I OT~' 'Ill( •• SI(AP,,\'.I" _ '!..6~l1> .JU .. ! .. ~..! !M.i.!'~1UP6' .11 X. 6 'S~ET~ •• ilX"SRA~6'.11X.'SFPS6'.1IX.'SZET6 •• 11X"SfTh6 •• 11)(. 7 l'iTOTf,'.11X"5KAP2,--~f;l.~fil'0'.6X"SLAM" •• 11X,'S'1U6 '.IIX, A 'S~U6'1' '.3~16.Q/'O •• ,,~.'SALP7,.11X"SAET7,.11X.oSGAM7,.11X. 9 'S~PS7' .\1 x. 'S7E T7' • 11 X, • SETA 7' '.11)(. '.5 LOT]'_' 'Lli)(t..!5K.~~L' _.'-'."---___ _ A ~.16.~/'n •• 6X.'SALPA'I' "'16.A/'O'.6X.'5ALP9'.1IX,'SAET9'. E1 llX, '<:;011149' .111<"SZE."(t'I' __ '--1~.E...11l..lL8/'O' .5)(, 'SALPIO'I C ' 't FI6.A/'0'.SX.'SALPll'.10x.'SAETll'I' '.2.16.A/'O·.sX.'SALP12 I) '.10 x. I S3E H2' ,lOX ,t SGAM12.!.!'.'_...'--U.E.L/';>....JU. 0' .5)(. 'SALP 13' t1 OX. E ·S~lTI3'.10X •• SGAMI3'/I '.3EI6.A/'O'.5X.'SALPI4,.lOX,'SRETI4', F" 1 0 ~. I SGA ~ 14' ,lOX, I Sf'PS 14 • ,1 (l x, • S ZE 11.4 ' . .1 0)(, '.SE 111.1.4. ..... d 0 x.. o_S..LO.I.l1t..!.. __ _ G I' '.7"1~.R/'O,,~X.'SALPI7·.10X.'SBETI7',lOX"SGhMI7 •• 10X. H • S~P51 7' /' ',4Ft ~. AI' O •• o;X, • Si'i.LP 18' dJ»(!_'.S.B.Ella!L'._.!...!.i',",E~1,-,61LL • .... 8LI ___ _ I 'O',5x,'5ALPlq·,IOX.'SQFT19'I' '.2E16.8 )
W>lT Tf" (InE311R, J 2) ? .. I\!'-,S8?_ • ...5.tb!'!.02,SF2.SF2.SA3.S93,SC3.523.SE3.SF3 \ .FAE.FAP~.FAI'"
\2 FDR~/lTfll •• 7X,I5A?'.11)("'iA?·.13X"SC?.13X"S02',13X.'5.2', 1 1 1 X • I c; ~ ? , I' I. "'- E I 6 • 'II • 0 , , IX •• SA 3 , • 1 3 ~ .' 5 R3' '~'l 3 X~' 'ISC 39;-11 X-.--'--------? 'C; ')3 I .13 x • • 5,3' • I 3 X, • SF 3' I' '. 6~ 1 "'- •. B.L!.lL'...LVt.L~f ~_u.?J5_'_'-,-'-"A,-,-P-"E,-,'--,.,----__ _ ::I 13X, '"~F' 4 I' •• ~Fl!\.fl) TF(TFLr.A.~Q.I)STnp
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126
AEDC-TR-76-39
rlS t \.II/L nATE" 75157
SUR~OUTTN~ ~STMUL(.?R2.r?n2.F2.F?A3,R3.C3.n].F3.F3.InERUG.XX.V)
tI4PL.'lCJT ~EAL."8. (A-t:bQ~Z..l .. _._._ ... _._. CO~PLEx"1& X(??..4),Y(4).SIr,MA.UPSLON.PHI.PSI.OMF.GA.l~RO.A1.B1.Cl.
-Vi. y2.Y3. Y4 .o'!!:. ,R (2,2.4. 2.1 .CHlFIIII~.lUU.<U .. _ ... _. ______ _ rOMPLEx"1~ ST3 MA1.uP SLN1.PHT1.PSTl.OMFGAl OIM~NSTON I rI (4) ,JJJ(41. _ ... ___ .. _. __ .--------___ . _____ _ DATA ZFRO/(O.~o.o.nn)/.ONF/(1.no.o.nO)/.cINFIN/(1.n70.1.n70II
C---"'-"'.-_-----,.,._.,.--"',.-"',. . .,._,."''''''' . .,._~ ___ . ____ . __ _ C C~MPUTF QUaRTIC CDFFFTCJFIIITS
C---------------------------.,.-. ALP~I=~2 .. ~3-A3 .. F2 9~TAI=~2 .. )3-A3 .. D2 GAMI4I=A? .. ~3-A3 .. F2
_ ALP-tU=AJ .... B.2..-A?i*.BL __________ _ 8~TAlr=.3 .. C?-A2 .. C1 T)::L Tl I=ALPHI"9ETAl.L .. _ ...... _._ FPSLII=ALoHY*ALPHTY+RFTI'*RFTArl lETAII=~ETAY*ILPHYI+GA~~'''9ETAII EThTI=r,~MI4I"ALPHIJ BU.sQ=SET Al I H2 .. __ . ____ . __ ._. _______ . ARJY=ALPHYI"R~ThIY AIYSQ=/lLP-tIIHC:' SYGI.1A=i'FR1 UPSLON=lE~O P-tY::lERO PSl:o:ZERD .... ___ . ___ ._._ .. ___ . ___ ._ .. _____ ... 0I.1F.3A=7.RD DO 9 1=1.2 no 7 J=l,? DO &. '<=1,4
~ X(I.J,K,=eJNFI~
7 CO"lTI"lUE. R COMTI"l11J:
-_ ... __ ._----_. -----
.. _-_._- ._---_ .. _-----
5 I G 1.11\:: 1\ 2 .. A L"H I .... 2 + C 2 .. OEL TI L.+_ E 2 .. I> _lill.S!L __ ._ ... _. __ ..... UPSLO~ = ~.~o ~ I\? ~ AL P41 ~ ~~T~T + R2 .. DFLTlr • r2 * FPSLtI •
I> 2.)0 .. E2*A~HI + n.? I> 9n<;Q ....... _ .. . P~T = ~? .. ( ~"TAT *~ 2 + ?oo ~ ALPHI ~ GAMMI ) + R2 .. EPSLTT +
.. C? I> ZElII.II •• 2 .. A IlSQ .~.f2.....!._Bll.sQ~Bill.'._~...D..2.....! __ A!H . .LI ____ _ PST = ?OO I> ~rTAT ~ r,AI.1~T 1>11.2 + A2 .. lETArT + C2 .. FTATY +
.. ?OO" F2 .. AH't • 02 .. AIISrl _ OMFGA = 11.2 .. ~AMMT .... 2 • R? .. ETAty • F? .. A1TSQ Srr,I.1A1=S!"MI\ UPSLN 1 =lJPSl(lN PSIl"PSI P-tIl=PI-IY OI4F:;Al=OM~GA Y'(I0EPUG.fQ.03'Gn TO 9
C-------------------r P~TNT CJF.~TCTf~T5 r------------------- _ .... __ . ____ .... __ ._. _ .. __ ... W~ITF(T~E~UA.I)A?P?r?~?F2.F2.ft1.B3,r3.D3.F3.F3,I\LPHY,RrTAY.
- Ghl.1~' .dL"HT T ,~FTI\Tl.I)ELTT t .FPSLT T ,7ElAt I.,ETAH,flI TSQ,AAY I.!A.l15..rl .. __ 1 F~~~II.T(ll~C;IMJL'/' ,.~(.=.)/·OI.7X.'A?14X •• A2'.14X.'C?.'.14X. ) 'f''' I .14 X • , ~? I • \4 X •• F 2' I' '. bE 16. All 0 , .7 x • ' .. 11. l' •. 1.4)( .•• A}' t.l4.ll..!. '.e.3!. L..
2 14X.'~11.14X,'F3'.14X.'F]'I' '.~F16.R/IO'.6X.'ALPHT'.11X. "3 '8,,",1\ T' ,II x. '('.a"''''Y' tl OX,, A[PHU' .lOX, '.AE.T..All.'.!.lM<".!n::I..Ir L'-' ______ _
127
AEDC-TR-76-39
()SI"1UL DATE = 75157 11/58140
4 1 0 )( • , FP SLII J ' I • ~- , , 7 E 1 6 • 8 I' 0 , • 5)(. ' Z FT A I I ' • 1 1 X • ' f TA J Y , • 1 1 X • . 2 '.[1_1.15(;" !.U.lU~ll.!.ll2l< .. l.!.A.ll.5~2..t2Ell.&L.,.-:-__________ _ WqTTE(TnE~UA.2)SIAMA.UPSlnN.PHl.PSI.OMEAA.ZERO
.2 I'"OR\4A T ( 'O.'~' D~X .... !i IC,MA '~~'.2J_X_L'_~!E?..l.IlN' • 2AX. 'PHI • • (9)(. 'PH 1'1' '. lBfl~.B/'0 •• 14X"OMEGA,.(7)("ZERO'I' '.4EI6.8)
C-~~~-----,:---~~-.~_--:-~~~_.~_ ... __ ~ _________ . r. FI~D qODTS TO OUAqTyr.
. C-:-.~-----':"--':'.~_-:::-_-.~~:::.':" 9 N=4
Y I'" (DREft.L(5JJl~1.."!L.O_~!lQJJ3JLI0~Q.~ _______ _ N:3 IF (')Re:~Le)P5LO_"i) .NE • .lto_D.O_lGn ... TD _lL_. ______ . ___ ~ N:?
____ ._. ___ .1 f. . .l2BE A L (I>H I ~E..'..10u.u.D,-,Qu)..lOG!.'.<QL-LT-"Q,---"2_,,O _____________ _ r. LI~FAq
N = 1 _ . __ . _~_. __ .. __________ . 10 O"1I'"GA=nMEr,A/PSI
PSI=.ONF ____ .. ~_ _ _ . __ . ___ .. __ . ___________ _ CIIL LI flIiNDC·(~. D'11'"611, ZERO, 71'"Rn. lFRO. ZERO. VI, V2. V3. V4)
______ .JiCLnL45_~ ____________ . __ r. OJAn~HTJC
('0 PSl=p~T/P>ir OMFGA=n"1Er,A/P>i1
~-. ~~-- "- --- .. -~--:- -'~---'---'-.. ----
PHI=ONF _~._ .~ ____ . ___________ . __ . CtlLli QANDC(~.PSJ.OMEGt\.ZFRO.ZERO.VloV2,V3.V4) GO }O 45 ____ . ______________ _
r. CUR1C 30 PHI=PHI/UI>SLO~
PSY=PSJ/UI>SLO~
04I'"GA=OMEAA/UPSLON. UPSLON=ONJ;:' Ct\.LLI Q!I"'Oct"l,"'-H.t!.E.S.I..!.l1!1E..Cl.ru~'I'h_'(UY:hYll. __ _ GO TO 45
C QUARTIC 40 UPSLON=UPSLON/5TGMa
PHI "PHT ISH."'. PSJ=PST/SYG'-1A
_ O~'-1F Gi\=O~ll: SA.!.').! G.M~._. _________ _ SI(;'1A=oNE CIILL' Q~NDC (N.UPS\'ON,PHI .P'H_.OMEGA_.'(t .. 'L2.,-Y.1.~Y4)
C----------------------------------__ J: LL~JLt.l, 1.'-!._Y~J..LJfS .!..1'"-'-'O"'R'-'-I'"-'"II"C'cH'--'Y'.....C.qo.:0"-'O'--T'--_________ _ C----------------------------------__ . 4.5...._liU =v L_. ___ _
V(2)=Y? Y())=Y3 V(4)=Y4 DO 100 1=1,4 IF(T.GT.N)GO TO 100
.~ Ill::: -", .... 5..!..iB.2 tl:2.!.llllJ..LA2_---:--:-------::-:-:---__ --Cl=CDSORT(Bl*~2-(n2~Y(I)+I'"?~V(I)**2+F2)/A2)
)( (1.1. I) =31+CL X(?d.T)=31-Cl 81=-.5* (83+.c3l)V (1) tiA3 ~_~_ . ____ ._. ______ _ Cl=COSORT(RI*l)?-(n~oY(I)+F3~V(T)*~2+F3)/A3)
II. U1.,a'.I) =.:n~c.l __
128
AEDC·TR·76·39
I)S T .... IIL DIITE = 7<;10;7 11/0;""40
)( (;>.2. T) =~I·C:l
100 CO~'TPHJf
r----------------------------------c: P~IN' PlOTs Tl ~UAQTlr A~O CONICS
r----------------------------------W~JTE(T~t~U9.2)SIGMA.UPSLON.PHI'pSI.OMEGA'lERO IIR 1 TE ( T r)E ~tI".::I) Y. ( T • T = I.;» ,)(
3 fOR"AT(·Ol,15X.'Yl·t3(l)(,'V2'.]/)(,·V3',30lC,'V4'/' '.8E16 .. 81._!JU-,--__ . __ _ I ?('I •• ;>(,(I.I,.,tQtIIlTJ0'4'.T;>.;>7(.-.)).'-I'I' ";>('1'011(1.1). 2 'P:lSITJV~I.ll(h')"II,ll('-')"NfGATlVf·tl?(I.I) ,'.1 ' ) __ ]/'nx RonTS ~A5En ON'Vl'" '.AFI6.A/'OX ROOTS ~ASEn nN V2'" '.A 4 n<"Il/'OX POOTe; ~ASFn ON v3'/I • .AF.:lb.8/'O)( ROOTS 9ASEn Ofll_ Y.lt'l 6 • '9AF'16.R)
r. - - -- - -- - -------- ~ ~ - --~-- ~~~~.-.-.:-.:----":':- - -- ~------~-~~.:-_-~ ___ _ r. c~.rK ALL X A~O V VaLUES IN ORTr.TNAL sve;TFM OF cnNICS c -- - - -- -- ---.-- .---.--- :---.--":':---------------:-":':--.--~:-:_:-~ ____ . __ . ______ _
no 130 L=lo;> 00 120 1=1.4 no 114 .)=1,;> DO lIS K=I.2 Jr('RFAL(V(T)).r,T.I.n~q)r,o TO Il~ GO TO(loe.l10).L '
lOA R(J.K.T.l)=A?X(J.K.,) •• ?q;>*X(J.~.T)+C:2.X(J.K.J)*V(Y)+n?*v(l). 1 E2 11 V (T) 1II>2+f2
GO TO 115 11 0 R (J ,K, T. 2) =A3*)( (J.I<:, I 1.1111 2.'33*)1. (J,K d) +C3 11 )( lJ.K i..ll.!_'UI) +o3 l1 y (T I.
I F3"Y(T)·";>+F'3 J 1') CONTINI.IE 114 cO~lr I"JII. 120 CO'llTI"JUi'" J 30 COf\JTINlw
WClITE(!DE3UG.4'R _____ ._. 4 f:lP~AT('O~EST'UAL ARPAY'.4(/' ',AfI6.8))
c---~-----------------------C 5:ltlT OIIT EXTRa"J.OiJ5 Rnnrc;
C---------------------------13'" L=I) DO 160 J=1.4 no 180 r=I.? DO 140 0(=1.2 T~(CD.qS(~(T.I.J.K)).LT.I.n-10)Gn Tn 140 GO TO 1[10
14(l CONTI'JIW L=L+l JF(L.Lr.4)GO TO 190 WRITE" (fOUr,14S)
14~ fOR .... AT('O~STM~L: ~ORF T~A'" FOUR ROOTS FOUND') STOP
150ITT(U=T ,)JJ(L'=J'
1'~ 0 CON TI NUF 150 COMTINIIF
LLL =L DO ?'OO [,,=1,4 XX (Ll =rTNC'f~1 I'(L~GT.LLL)GO TO .190 XX (LI)=X (ITT (U .1.J,)J(U) GO TO ?OO
lqO V(U=CPJfTN 200 CONTI NilE
WClTTE(T~E~UG.?;>O)xx.v
220 rORI1AT(llSORTi'"') ROOTS: XXlV',?'(/' .,8E1.6aflU WRITE('nf~UA.240)'TI.JJJ
-------------
;>4(1 FOQ~AT('OJIJ l\"Jn JJJ VALUE.5.J':O'LJHIll.tLJJJtlO .. 'L!.._!. 'IU_",_' t.41.2L-_ 1 ' JJJ= •• 41,",1
RfTJR'l E 'Jrl
129
AEDC-TR-76-39
OATE = 7510;7 - --- ----- - .. _._-
!,;LJI'l~OUTTN'" CU'JI)f:(hJ,R,C.I).F,Xl.x2.XJ.X4) II.1PL'I C TT ~O"lPLJ;:~ l~ I\~(,-,o~l L COMPLD .. t .. ! nATA I/CO.OO,1.nO)/.CINFIN~(1.n70.1.D70)1 GJ TOI10,20.10.0;),N
C QJI\RTlC
f:
5 ~=CI4.nO"C*~-I~""?"F)-D"*?)/2.00) Al = 1 C* (BII )~4. ?Q*e:Uf> • .Dill ... 112:-(lr·"1)/27.00) /1=1\.41+112 R9=CDSQRTIIA .... ?)+((~"D-4.I)OIlF-(lroll?)/3.DO)I.1I311?7.noI fI=-A CALL' CIIRRT (A,'1R.R) PS TAR=eIlD -4. ()Q.llf ~r.IIC lJ.. nO RI=-PSTAR/(l.,O·RI R=(~.Rl.(C/l.I)O)1
p:r)S1RT«(R·"2/4.I)OI-C·RI P~=~DSQRTIO.?'5I)n"R"O?-E) II"'?=. <;nO.~'O;:!-"l Df'1l2=? DO *P*Pl . _ _ .. ____ ... __ . ___ .. 11'"(~DAJ.1S(AR2-DPQ2) .liT. rnARSIAR2.PP(2)IPQ=-PQ DD: (C'H~S (P» rAt [tIL /I T I 'It; T -IE UROS ~1=(I.O.O.OI RI:(i1/?Dn).p r1 ;: (fV? • [) 0 I • P:~ ..... . __ .. _._ X I = ( -'I 1 • C "lc;()R T (R I 00 ;>-4. f) n"" I 41 C 1 I ) I (2. nOli II 1 ) X?=(-~1-C)5QRT(J.1I00?-4.f)nIAI"f:I)I/(;>.nO"III) J.11=(fl/?[)O)-P r.I = (R/?[)n) _D~ x 1= (-'11 • C "lS(l'l T er1) 0" ?-4. I) n II ~ I "Cl ) II ( 7..00 11 /\ I ) X4=(-Rl-C"lS1RT(Rlo"?-4.nn O/ll ll rl»/(?nO Il /ll) oOT.JR'~ .
f: CJRIC 10 C::>~ITI'JIIr:
P=("-(A .... 7./3.[)CJ) Q=n-(q·r/1.~nl.(C?nnOH·ol)/?1.[)n)
ZI=-CQI?101.ccnSQ~T(U."?/4.f)OI·CP·"3/?7.DO)) 7?=-(J/?"l01-(cnSQATC(Q· .. ?/4.nO)+C DoO l/?7.nOI» !~CCDARSCZl).3~.C~~~~(7?111=71 Fi:::()iiI'lS(Z2).:'E".Cr,~R<;(ll)IZ=Z2 T~C~nAR~(Z) .~Q. O.O)XI=-(A/l.nO) Y>CCDAqS(7) .E"Q. 0.0IX2=-CR/l.nOI T.crDA~<;(Z) .~Q. n,O)X3=-(R/3.nO) Ie' Cr.nA~"I71 .C''}. O.OIAFTllRIIJ RqQ=CO.nO,o.nrll CIII L rllRRT (l,'lRR,ol) R=-O"/L1.10 0 R\» wl=-(.~~01+CC1.nO"o.~II?nn)"y
W?=-C.~~O)-C(1.nO"".SII?~n)OI XI=-C~/3.")O).~\.~
~C"-(~/1.')n) -\II "~1 HJ;>"f< XJ=-C~/1.101'~?"~1.wl·k
X4=::I'I"TN R~T ,Jk'J
C QJA')R~Tlr 211 hl=."''''''
Q=r)S~PTCAIOO?-C)
XI=~I." ~c=III-D
X 3=r.!hJ>TIIJ X4=CI'I>TN kC"TJR'IJ
C LI"JP~ 30 Xl=-H
~"=CI'J"TN X1=C!'lJi'"TN X4=C!"JrTN RC'TJk'IJ I'"\l()
130
II/O:;A/40
990
CUB~T
5UR~OUTIN~ CU~QT(AA.RR.QQ)
TI1PLiJCTT e0I1PLEX*16tA-G~Q~Z) Q"AL~AH.HIA.Hl~.HTH
REAL"''''PI.SSSS r.O~1:lLEX*1 ~I
CONT I"IUE' 1=(0.01.)
AEDC-TR-76-39
11/5A/40
II = 1 Zl=aA+~R
... - .... ------.. _ .. - ....... _ ..... _-------------Z?=U-RR ' ..... _ ............ ___ . I"(COAR~(Z?) .GF. COARS(Zl»A=Z2 I"(COM-1~(7ll. .GF. COARSpc»A=zL .... R=DCOIIJ,J(; (a) H1./\ =.tA+~) L.2 ... DL ... . _ ... ____ _ HIB=-I*(A-R)/~.OO
HtH=DAT AN.2 (.1113, H LlI.l ..... . H=(HIA**2tHIR**?')**.'5DO PI=1.14159265358979300 __ . SC;5S=3.DO ijCi;:.(H** U . ...o.n/..3"n.oJ..L~_L Dens ( (HTH+ (IT -11 *2.DQ*PTl/SS5S) t Til (
IHt (Y 1-1) *2.r)O*PI) 15<;<;5») RETi.lRN EIlO
DSTN( (HI
IN TV G L~V~L 21 DREAI. DATE:: 75157 1l/'5A140
FUIIJCTJnllJ ')REAU((~C) COI.1PLEX*l~. C.fCC ................ _._. ______ . ________________ _ R~AL .. A O(?).D~EAL EQUIVALENCE IC,D(l» C=CC ORE aL=n (1) RqJRIIJ E'JD
IN TV G L~V~L 21
FUNeTi~\j 1II1Ar,(Tij COMPLEX*15 y.n REAL"" O(?).DTI1AG FQIITVALENCE (J.o II)) I:: rt OTMAG:n(2) RETJRIIJ EIlD
DATE" 75157 11/SA/40
------------_ .. _-- -------
131
AEDC-TR-76-39
A
All
E
F
k
M
Moo
m
m
1\ m
n
P
P
NOMENCLATURE
Area
Solution weighting parameter, Eq. (25)
Momentum correction coefficient in wall crossflow model, Eq. (7)
Flap correction coefficient in the flap flow model, Eq. (8)
Weight used in computing test section pressure, Eq. (10)
Arrays of coefficients in the small perturbation equations
Computational error
Function
Flow coefficient, as in kf and kw
Mach number
Steady, asymptotic test section Mach number
Mass flow rate
Convenient quantity with units of mass flow rate defined as
If Peto r;r- Ats
R VT eto
J ~2-1 Nondimensional mass flow rate defined as rn Eq. (B-3) -.-, rno
N ondimensional mass flow rate defined as m/ me, Eq. (B-l)
Convenient quantity with units of mass flow rate defined as
Pi Pc V R 1Tc Aet
Iteration number
Pressure
Nondimensional pressure, P/Po
132
R
T
t
t*
tF
v
X,Y
a
p
7
SUBSCRIPTS
c
ct
d
e
AEDC-TR-76-39
Perfect gas constant
Temperature
Time
Midpoint of a time interval
Final time in an area time curve
Volume, as in V p or Vts
Scratch variable used to develop small perturbation expansion, Eq_ (27)
Variables in numerical reversion procedure (Fig. 10)
Constant defined as
Ratio of specific heats
Flap gap
(
_2 );~11 "1+1
"I , Eqs. (4) and (5) R
Array of small perturbations of the variables from the exact solution (Table A-I)
Perturbation in the main valve area
Perturbation in the flap area
Perturbation in the plenum exhaust valve area
Density
Porosity, percent of test section wall area drilled out to allow crossflow
Charge condition
Charge tube (or supply tube)
Diffuser end of test section
Main tunnel exit, main valves
133
AEDC-TR-76-39
f
i
max
n
p
pe
pt
t, ts
tsw
w
o
SUPERSCRIPT
*
Flaps
Array index
Maximum value as in Ap e m a x
Nozzle end of test section
Plenum
Plenum exhaust
Plenum - Test Section
Test section, as in Pt or Ats
Test section wall, as in Atsw , the total wall area
Test section wall, as in Aw, the effective flow area
Stagnation condition
Test value in numerical reversion (Fig. lO)
Sonic conditions
134