AD-A264 476

Control System Analyses forthe Driver Gas Fill System of

the BRL 1/6th ScaleLB/i'S Test Facility

Duane T. HoveGregory P. Mason

ARL-CR-46 April 1993

prepared by

Sparta, Inc.3828 Carson Street, Suite 102Torrance, California 90503

under contract

~MAY 18 1993.

APPRtOVED FOR PUBLIC RELEASE; DISTRIBUTIoN is UNLIMTD.

93-11013

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1. AGENCY USE ONLY (Leave biank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVEREDApril 1993 Final, Aug 90-Feb 92

4. TITLE AND SUBTITLE S. FUNDING NUMBERS

Control System Analyses for the Driver Gas Fill System of the BRL 1/6thScale LB/TS Test Facility C: DAAA15-90-D-1002

Task 16. AUTHOR(S)

Duane T. Hove and Gregory P. Mason

7. PERFORMING ORGANIZATION NAME(S) AND ADORESS(ES) 8. PERFORMING ORGANIZATIONREPORT NUMBER

Sparta, Inc.3828 Carson St., Suite 102Torrance, CA 90503

9. SPONSORING/ MONIT.RING AGENCY NAME(S) AND AOORESS(ES) 10. SPONSORING/MONITORINGAGENCY REPORT NUMBER

U.S. Army Research LaboratoryATTN: AMSRL-OP-CI-B (Tech Lib) ARL-CR-46Aberdeen Proving Ground, MD 21005-5066

11. SUPPLEMENTARY NOTE:,Contracting Officer Representative is Mr. Richard Pearson; Alternate Contracting Officer Representative isMr. Klaus Opalka, Nuclear/Directed Energy Division, U.S. Army Research Laboratory, Aberdeen Proving

Ground, MO 21005-5066. Contract No.: OAAA15-90-D-1002; Delivery Order 0001.i2a. DISTRIBUTION/ AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Approved for public release; distribution is unlimited.

13. ABSTRACT (Maximum 200 words)

This report covers the design of an automatic control system for the gas supply of a blast simulator facility,The control system regulates the output temperature of a heat exchanger used to evaporate liquid nitrogen andheat the resulting gas to high temperature. An analytical model is developed for the two ph.;se flow throughthe heat exchanger. A design is developed for the valves used in the control system. The properties of thevalves in the design and the analytical model of the flow are used to analyze the dynamics of the controlsystem.

14. SUBJECT TERMS 15. NUMBER OF PAGES42

heat exchange; control theory; cryogenics; blast simulation; liquid nitrogen; ..PCCO

shock tubes 16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACTOF REPORT OF THIS PAGE OF ABSTRACT

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

NSN 7540-01-280-5500 Standard Form 298 (Rev 2-89)Pesr~tired by .N1145 Sid -Z i-S298- 102

INTENTIONALLY LEFT BLANK.

TABLE OF CONTENTS

PAFe

FOREWORD .............................................. v

PREFACE ................................................. vii

1. INTRO DUCTION .................................... .... 1

1.1 Objectives .......................................... 11.2 Requirem ents ........... ......................... .... 11.3 S cope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. GAS SUPPLY SYSTEM DESCRIPTION ....................... 3

2.1 Layout ........................................ ..... 32.2 Control Valves ........................................ 3

3. THERMAL HYDRAULIC ANALYSIS ........................... 5

3.1 M odel .............................................. 53.2 C alculations ......................................... 7

4. CONTROL SYSTEM ANALYSIS ............................. 18

4 .1 M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 84.2 C alculations ......................................... 21

5. CO ST ESTIM ATE ....................................... 24

6. SUMMARY................................. ...... 28

6.1 Conclusions ........................................... 286.2 Recommendations . ..................................... 28

7. REFERENCES .......................................... 29

NOMENCLATURE ........................................ 31

DISTRIBUTIO N LIST ..................................... 33

iii

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iv

FOREWORD

This report is submitted to the Ballistics Research Laboratory in partial fulfillment ofDelivery Order 0001 of Contract No: DAAA1 5-90-D-1 002.

The BRL Project Officer is Mr. Richard Pearson. The SPARTA Program Manager is Mr.Gregory Mason. Mr. Daniel Nowlan performed the elegant control system dynamicanalysis and Dr. Irving Osofsky provided valuable technical advice.

Raeession For

" 'T 1-" <

Ar - b 1 - v Ioe,

D~ist 0r 1 • all l llll lli I I i n I I I I l l I l

INTENTIONALLY LEFT BLANK.

vi

PREFACE

On 30 September 1992, the U.S. Army Ballistic Research Laboratory (BRL) was

deactivated and subsequently became part of the U.S. Army Research Laboratory (AMIL) on

I October 1992.

vii

INTENTIONAt.LY LEFT BLANK.

viii

1. INTRODUCTION

The US Army Ballistic Research Laboratory (BRL) is currently modifying an existing shocktube located ;-* the Aberdeen Proving Grounds to demonstrate Large Blast/ThermalSimulato- +echnologies and to provide high fidelity air blast environmonts for nucleareffects testing. This facility will be the first large shock tube to use heated driver gas toachieve desired air blast waveforms in the test section. The driver gas must be heatedand the driver quickly pressurized to minimize heat loss to the driver walls; this requiredinnovative solutions to pumping hot gas.

Under BRL sponsorship SPARTA developed and demonstrated a driver filling methcoawhich pumps liquid nitrogen (LN) through a previously heated Pebble Bed Heater (PBH)thereby vaporizing the liquid and raising its temperature to the desired value in one pass(Figure 1). A bypass system allows precise control of the output gas temperature byselectively mixing LN with the heated gas exiting the Pebble Bed Heater. This approachhas the advantages that: pumping a liquid is more efficient than pumping a gas (if indeedpumping a hot gas can be done at all), the LN pump is much smaller and much morerobust than a gas compressor system and the constant displacement pump mass flowrate is independent of back pressure.

SPARTA installed a 22 ton Pebble Bed Heater working unit at BRL and successfullydemonstrated its performance (Reference 1). Manually operated valves were used toroute the liquid nitrogen to the Pebble Bed Heater in these initial tests. However, anautomatic control system is preferable to manual operation for safety, precise gastemperature control and efficiency of operation.

1.1 Objectives

The objectives of the present study were to design an automatic control system whichmeets established requirements, analyze its performance, prepare drawings and providea system cost estimate.

1.2 Requirements

Four driver gas design conditions were established by BRL (Table 1). The driver fillingstrategy is to pump a constant temperature gas (at or above the design temperature) untiithe driver gas reaches the design pressure (Reference 2). During the filling process, thePBH back pressure will rise from ambient to the peak value approximately linearly(depending on the magnitude of the heat loss to the walls).

1.3 Scope

Valves and valve properties were selected from vendor supplied information. Appropriatevalve settings were established based on a thermal hydraulic model which consideredpressure drops in the primary and bypass paths. Control system response wasestablished based on analytical models of the valve/actuator motion. Cost estimates werebased on vendor quotes and engineering estimates by experienced personnel.

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2. GAS SUPPLY CONTROL SYSTEM DESCRIPTION

The control system analysis starts with a control system layout and performancecharacteristics of the specific valves used to direct the flow to the PBH and the bypasssystem.

2.1 Control Systerr Layout

Liquid nitrogen is pumped from a tank through a series of pipes and valves to the PebbleBed Heater. Numerous diagnostic measurements, exhaust valves, check valves andcontrol valves are used to control the fluid flow as indicated in Figure 2 which is takenfrom Reference 3. The PBH control valves denoted as V7 and V8 are of specific interestto this study.

The PBH controls perform the functions of regulating the outlet temperature of the PBHmixer to a specified setpoint. The PBH operates by receiving LN from the high pressurepumping system and branching the LN flow into two subsystems, the primary pebble-bedand the bypass thermal mixer. Precise control of valves 7 and 8 in the primary andbypass lines is required to produce a stable outlet temperature of the PBH.

2.2 Control Valves

Globe valves have been selected for the PBH valves because of their ruggedconstruction, cryogenic rating and high capacity. Valve position control is achieved by theuse of a closed feedback control loop to the actuators using the outlet temperature of themixer as the feedback sei sor point. Valtek Mark One valves and Linear Spring actuatorswere chosen to develop valve performance characteristics and establish cost estimates(Reference 4).

TABLE 1 DRIVER GAS DESIGN CONDITIONS

CASE NUMBER MAXIMUM MAXIMUM GAS GASBACK BACK TEMPERATURE TEMPERATUREPRESSURE PRESSURE )(MPa) (ATM) (K) (R)

1 12.8 129 663 1193

2 7.8 79 468 842

3 2.9 29 361 6504 098A

0810 288 518

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3. THERMAL HYDRAULIC ANALYSIS

Engineering procedures were developed from analytical models based on conservationof fluid momentum and energy. All Pebble Bed Heater thermal hydraulic processes arerelatively slow so transients are not important.

3.1 Moael

The relationship defining the temperature of the nitrogen gas leaving the thermal mixeris

rhT(CPT+hV) - rh7(C, T -, h,) ,rhSCP TLN EQ (1)

Conservation of mass gives

rhT - r77 + mn EQ (2)

Substituting (2) into (1) and solving for temperature gives

rm h.T-Tpa-- ( Tpa- T+- ) EQ (3)

For convenience we define a reference temperature

TR=TP8-TLN+h, EQ (4)CP

Both mr, and m8 are a function of time during the operation of the PBH due to changingback pressure and, near the end of the run, changing PBH exit temperature. Controlvalves located on the primary PBH supply line (V7) and the mixer bypass supply line (V8)are assumed identical with respect to flow capability.

The mass flow rates are determined by equating the pressure drops in the primary andbypass legs. In the primary system the pressure drops are due to the pipes, valve 7, theelbows and the PBH; in the bypass system the pressure drops are due to the pipes andvalve 8. Following Reference 5 we have for the primary leg

Pipes_

DELP = f L _ C1 U7 2 EQ (5)2 D

5

Elbows

DELP2=N 2 fgo C2U 72 EQ(6)2

Valve

DELP3 = .pUA L7 C3 X EQ (7)CV x -

uVPebble Bed Hea ter

DELP4- p UP2 fp -C4 Up2 EQ (8)2

Here the pressure drop constant was selected such that the pressure drop equalled 20

psi based on BRL measurements on the existing PBH.

For the bypass leg

Pipes

DELP5- pU2f C 1 U.2 EQ (9)2 D

and

Valve

DEL,_[F p UA4 C 3 (X)U2 EQ (10)CVx X

Summing pressure drops

U.72 ( C1 + C2 + C3 X C4 U82 C5 + C6 EQ (11)

Equation 11 can be rewritten as

6

U72 C7 (x) - U8

2 C8 (x) EQ (12)

and therefore

Us (EQ (13)

where it is understood that the terms C7 and C8 are functions of x.

Since the liquid nitrogen is essentially incompressible, Equation 3 can be rewritten as

112

Tu- Tr, - T - (U1 +I.. -C8+ )- TR EQ(14)( U7 U8 C7 )

which gives the output gas temperature as a function of valve position. Setting the output

temperature at the desired or set point control temperature

T=Tc

and performing a bit of algebra, there results

L C3 EO (15)

"CL 7K TR -1 C5 + C6 - (C1 + C2 + C4(ST, - Tc 9 L

3.2 Calculations

Sample calculations are made to indicate nominal valve settings and their sensitivities.The basic procedure is to set one valve (e.g., V7) at a single setting and control the PBHoutput temperature with the other valve (V8). It is desirable that the valves be operatedin mid range, if possible, simply to avoid fine settings and/or slamming into the stopsunnecessarily. The design test conditions are addressed first at their peak backpressures. Then the effect of back pressure is considered.

3.2.1 Design Test Conditions

A broad range of PBH output temperatures are achievable if the PBH is heated to 2000OR (1110 OK). The peak design temperature of 1193 OR (663 OK) is achieved with asecondary valve relative opening of 0.2 to 0.5 as the primary valve relative openingranges from 0.25 to 1.0 (Figure 3).

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Considering each design case individually, the sensitivity to outlet temperature isestablished by calculating the required valve settings for the nominal design condition andfor the next lowest outlet design condition (Figures 4 to 7). Initial bed temperatures werepicked based on enthalpy scaling from present test results (i.e., thermal energy requiredis proportional to the mass and temperature of gas required). However, while technicallyfeasible to operate at PBH temperatures near the desired outlet temperature for the lowerpressures, a minimum bed overheat of 500 "R was evolved by trial and error to insurerobust valve control (see for example, Figure 8 compared to Figure 6 and Figure 9compared to Figure 7).

3.2.2 Effect of Back Pressure

All of the pressure drop mechanisms considered except the PBH assumed that thenitrogen was liquid; therefore, only the PBH pressure drop will be a function of backpressure. We have

DELP4 - f (Re) E U,2 EQ (16)

The Reynolds number range considered is about 10 to 1000 and according to Reference5, the pressure drop across a porous media is not a strong function of Reynolds numberin this range. Further, the mass flow is constant and the nitrogen gas phase follows theperfect gas law which results in

DELP4 - T EQ (17)P

Thus, at a given bed temperature, the pressure drop is inversely proportional to the backpressure. Figures 10 and 11 indicate valve setting combinations required at a lower backpressure for each of the elevated design temperature conditions. While there is someeffect (e.g., the required V8 relative opening is lowered about 0.1 for a 70 percent V7opening), the required valve positions are well within the operating capability of the gassupply system and the long pumping cycle (order of minutes) allows plenty of time for theautomatic control system to adjust.

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4. CONTROL SYSTEM DYNAMIC ANALYSIS

A dynamic model of the valve operation and control system was developed to assessautomatic valve performance.

4.1 Model

Once the primary valve has been set, the mass flow rate through the bypass valve is

dh8 = MFR x(.) EQ (18)L

where MFR = mass flowrate with the valve fully open (back pressure dependent).

The valve seat is positioned by a spring loaded pneumatically actuated piston. Modernglobe valves are fast acting and highly damped so the actuator is modeled as a dampedspring mass system. The force balance equation for the pneumatic actuator is

mk+ f,9+ kx- F(t) EQ (19)

Defining a valve position forcing function as

X, (t) M F(t) EQ (20)k

and defining the following constants

k EQ (21)

ff =EQ (22)24 km

Equation 19 becomes

,k+ 2 ý + 0, x - X,(t) C02 EQ (23)

The Laplace transform of EQ 23 is

18

x(s) - X,(s) o2W + (s+ 2•oj )x(O) (s) + (s+ 2[a)c,)x(O) G(s) EQ (24)s2+ 2C to, s+wo0, o )

where X•(s) is the transformed valve position forcing function, x(O) is the valve actuatorinitial position determined from Figures 4 to 7 and

O~2

G(s) - EQ (25)s2 + 2cons + (0)

Since pumping time (minutes) is long compared to the valve response time ( ~ seconds)and valve damping is high, a proportional control system was selected. Setting theactuator forcing function proportional to the difference between the measured outputtemperature and the control or setpoint temperature

Xt = K (T- T,) EQ (26)

Substituting (EQ 18) into (EQ 3) gives

T- T L- MFR TR x(t) EQ (27)dITL

Taking the Laplace transforms of (EQ 26) and (EQ 27) and combining with (EQ 24) gives

T(s) = Tps(s) - • . G(s) K(T(s)- (s - 2ýx(O) EQ (28)

or

T (s) - Tp(s) + K1G(s) [Ta(s) - T(s) - (s + 2 n) x(O) EQ (29)L KW n

where the nondimensional

K-•- K MFTR EQ (30)rhT L

Solving for T(s) in (EQ 29) gives

19

T(s) - TpB (s)+ K1 G(s) T,(s) - K(s + 2Co•) x(O)G(s) EQ(31)1 + K, G(s) K=,,n (1 - K, G(s))

Because T, (the setpoint temperature) is a constant value, the Laplace transform is

Tc (s) T EQ (32)S

The temperature of the outlet gas of the PBH (primary flow), Tp, entenng the thermalmixer can also be considered a constant because

1. This temperature will be maintained at a nearly constant value until the pebble-bedtemperature at the end (bottom) of the pebble-bed starts dropping. This typicallywould occur when approximately 80 % of the process flow has been used.

2. During the last 20% of the flow period, the gas temperature at the outlet willdecrease slowly compared to the response rate of the control valves.

Thus, the Laplace transform of T., is

TP8(s) - T9 EQ (33)

S

Substituting (EQ 32) and (EQ 33) into (EQ 31) gives

Ts 1 - Tp -, KT TcG(s) K, (s+2to,))x(O)G(s) EQ (34)T (s) 1 + K, G(s) - K(on' (1 + K, G(s))

and taking the inverse transform of (EQ 34) gives

T(t) - TPB -K Tý +.K,(Tp 5- T,)- K, x(O) *1+ K1 1 1+ K K W EQ (35)

e- , (o t l+K )+ 1 - ....... sin(°•nt4 1+K -K _ )~coso1 1+ K- _ 1

High gain (K, >> 1) is required to result in the steady state value of T approaching T,.Inspection of EQ 35 indicates that for Tp. of the order of 2000OR and T, of the order of1000 OR, K1 must be of the order of 50 to achieve controlled mixed gas temperatureswithin 5 percent of the desired temperature T,.

20

The resulting solution for valve position (from EQ 27) becomes

x(t) rh T K, ( Tp- T,)

L MFR TR 1 + K1

- KZ.2 e'os(o),t4 1 , K71 ý2si (o ý 1+ - jEq (6

where the nondimensional

L 1+-K1K Tpg- T,

4.2 Calculations

Example calculations were made to demonstrate valve performance using the following

characteristics from Valtek literature:

w,, = spring cylinder actuator natural frequency = 2.5 cps= damping ratio = 0.7

Selecting an initial position of the primary valve as 70 percent open, the peak design

condition of 2000 OR and 129 atm back pressure, an initial valve position of half open and

a K1 of 50, the setpoint temperature is achieved in less than a quarter of a second (Figure

13). Note that the valve motion is minimal due to the excellent choice of initial position;

Figure 14 provides a better view of the motion by changing the scale of the ordinate.

21

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5. Cost Estimate

Components of the control system are itemized in Table 2 along with a suggested venderand catalog prices. Unburdened hardware costs total $56,000. The estimated price toprocure, assemble, program, install and checkout the system is $200,000. Includinghardware purchases, the period of performance is expected to be six months.

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6. Summary

Conclusions and recommendations reached as result of this design study are summarizedbelow.

6.1 Conclusions

* An automated control system for the BRL 1/6th scale shock tube is

feasible and practical using off the shelf hardware.

* Globe valves of the type selected for valves 7 and 8 give positive control over

the output gas temperature with reasonable valve actuator positions.

* Drver gas backpressure has a small effect on control valve position based on

the Pebble Bed Heater pressure drop model developed here.

* The analytical models should be calibrated with test data for each design

condition.

6.2 Recommendations

* Assembly, programming, installation and checkout of an automated control

system should begin immediately.

* The time dependent driver gas filling model developed in Reference 2 should be

coupled to the gas supply system quasi-steady and dynamic control models in asystem simulation to develop detailed control strategies for each test condition.This simulation should be used to establish test procedures, train operators andanalyze test data.

* Pebble Bed Heater and mixer nozzle pressure drop data should be obtained for

a variety of flow conditions and a more detailed model developed for use in thecontrol system model.

* A control system analysis should be performed for the existing valves which are

being retrofitted for automatic control and the models should be calibrated with testdata.

28

7. REFERENCES

1. Osofsky, I., Hove, D., Mason, G. and Tanaka, M., "Development of a Pebble-BedLiquid Nitrogen Evaporator/Superheater for the BRL 1/6th Scale Large Blast/ThermalSimulator," LA-92-TR-001, SPARTA, Inc., January 1992.

2. Hove, D., and Osofsky, I., "An Analytical Moaei for the BRL Heated Driver Gas SupplySystem," Twelfth International Symposium on Military Applications of Blast Simulation,Perpignon, France, October 1992.

3. Mason, G. M., "Procedures for the Operation of the Driver Gas Fill System for the BRL1/6th Scale LB/TS Test Facility," LA91-21 -TR, SPARTA, Inc., December 1991.

4. VALTEK Brochures: Mark One Body Assembly, Linear Spnng Cylinder Actuators andBeta Control Valve Positioners.

5. Blevins, R., Apolied Fluid Dynamics Handbook, Van Nostrand Reinhold Company,1984.

29

INTENTIONALLY LEFT BLANK.

30

Nomenclature

A areaCV valve characteristicCP specific heat at constant pressured diameterf friction factorF f=ceG transfer functionh, heat of vaporizationL actuator full travelk spring constantK gain constantm massN number of unitsRe Reynolds numbers transform variablet timeT temperatureU fluid velocityx position

Greek

a natural frequency"; dampingp density

Superscnpts

* derivative wrt time- • second derivative wrt timeSubscripts

7 valve 7 or primary line8 valve 8 or bypass linePB pebble bedp pipeT total90 elbowLN liquid nitrogenR referenceC control

i i i i I I3I I

INTENTIONALLY LEFT BLANK.

32

No. of No. ofCopies Organization C Orqanization

2 Administrator CommanderDefense Technical Into Center U.S. Army Missile CommandATTN: DTIC-DDA ATTN: AMSMI-RO-CS-R (DOC)Cameron Station Redstone Arsenal, AL 35898-5010Alexandria, VA 22304-6145 1 CommanderCommander U.S. Army Tank-Automotive CommandU.S. Army Materiel Command ATTN: ASONC-TAC-DIT (TechnicalATTN: AMCAM Information Center)5001 Eisenhower Ave. Warren, MI 48397-5000Alexandria, VA 22333-0001

1 DirectorDirector U.S. Army TRADOC Analysis CommandU.S. Army Research Laboratory ATTN: ATRC-WSRATTN: AMSRL-OP-CI-AD, White Sands Missile Range, NM 88002-5502

Tech Publishing2800 Powder Mill Rd. 1 CommandantAdelphi, MD 20783-1145 U.S. Army Field Artillery School

ATTN: ATSF-CSIDirector Ft. Sill, OK 73503-5000U.S. Army Research LaboratoryATTN: AMSRL-OP-CI-AD, (CWAs. only)I Commandant

Records Management U.S. Army Infantry School2800 Powder Mill Rd. ATTN: ATSH-CD (Security Mgr.)Adelphi, MD 20783-1145 Fort Benning, GA 31905-5660

2 Commander (U,,=ss. only)1 CommandantU.S. Army Armament Research, U.S. Army Infantry School

Development, and Engineering Center ATTN: ATSH-CD-CSO-ORATTN: SMCAR-IMI-I Fort Benning, GA 31905-5660Picatinny Arsenal, NJ 07806-5000

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