Calhoun: The NPS Institutional Archive

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Theses and Dissertations Thesis and Dissertation Collection

1980

Analysis and testing to improve the flow from

the plenum of a subsonic cascade wind tunnel.

Moebius, Richard Carl

Monterey, California. Naval Postgraduate School

http://hdl.handle.net/10945/18924

Downloaded from NPS Archive: Calhoun

ANALYSIS AND TESTING TO IMPROVETHE FLOW FROM THE PLENUM OF ASUBSONIC CASCADE WIND TUNNEL

Richard Carl Moebius

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISANALYSIS AND TESTING TO IMPROVETHE FLOW FROM THE PLENUM OF ASUBSONIC CASCADE WIND TUNNEL

by

Richard Carl Moebius

March 1980

Thesis Advisor Raymond P. Shreeve

Approved for public release; distribution unlimited

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Analysis and Testing to Improve the Flowfrom the Plenum of a Subsonic CascadeWind Tunnel

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Richard Carl Moebius

* PERFOPMINO OROANIZ ATION NAME ANO ADDRESS

Naval Postgraduate SchoolMonterey, California 93940

13. PROGRAM ELEMENT. PROJECT TaskAREA ft WORK UNIT NUMBERS

II CONTROLLING OFFICE NAME ANO AOOREIS

Naval Postgraduate SchoolMonterey, California 93940

12. REPORT OATE

March 1980IS. NUMBER OF PAGES

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Subsonic Cascade

Flow Improvement

Finite Element Flow Analysis

20 ABSTRACT (Conllnuo on fry an* l+mnttrw my •!•«*—Rwj

The original design of the plenum and bellmouth contractionarrangement of a subsonic cascade test facility did not producesufficiently uniform flow conditions at the bellmouth exit plane.Pneumatic measurements revealed sizeable blade-to-blade variationsin velocity and flow angle. A finite element numerical analysisof the inviscid flow field was carried out which both confirmed

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the need for and guided the design of a modification to thebellmouth contraction from the plenum. Following the modif-ication, in which the original contraction was changed to twotwo-dimensional contractions in series, and a program ofdevelopment tests, acceptably small variations in velocityand flow angle were measured at the bellmouth exit plane.

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Analysis and Testing to Improvethe Flow from the Plenum of aSubsonic Cascade Wind Tunnel

by

Richard Carl MoebiusLieutenant, United States Navy

B.S., Pennsylvania State University, 1973

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOL

March 1980

DUDLEY KNOX LIBRARY

NAVAL POSTGRADUATE SCHOOL

MONTEREY, CA 93940

ABSTRACT

The original design of the plenum and bellmouth contrac-

tion arrangement of a subsonic cascade test facility did not

produce sufficiently uniform flow conditions at the bellmouth

exit plane. Pneumatic measurements revealed sizeable blade-

to-blade variations in velocity and flow angle. A finite

element numerical analysis of the inviscid flow field was

carried out which both confirmed the need for and guided the

design of a modification to the bellmouth contraction from

the plenum. Following the modification, in which the original

contraction was changed to two two-dimensional contractions

in series, and a program of development tests, acceptably

small variations in velocity and flow angle were measured

at the bellmouth exit plane.

TABLE OF CONTENTS

I. INTRODUCTION 10

II. FACILITY AND MEASUREMENT APPROACH 13

A. CASCADE AND INSTRUMENTATION 13

B. PNEUMATIC PROBE SURVEYS 14

1. Probe and Installation 14

2. Data Acquisition and Reduction 14

C. OTHER TECHNIQUES 16

1. Tufts 16

2. Static Pressure Distribution 17

3. Velocity Meter 17

III. PROGRAM OUTLINE 18

IV. PRELIMINARY TEST RESULTS 19

V. FINITE ELEMENT FLOW MODEL PREDICTIONS 21

VI. PLENUM DESIGN MODIFICATION AND TEST RESULTS 25

VII. CONCLUSIONS 27

APPENDIX A

APPENDIX B

APPENDIX C

APPENDIX D

FINITE ELEMENT FLOW ANALYSIS 55

PRELIMINARY TEST PROBE DATA 8 6

PLENUM DEVELOPMENT TEST PROGRAM 106

PLENUM MODIFICATION DRAWINGS 125

LIST OF REFERENCES 131

INITIAL DISTRIBUTION LIST 132

LIST OF TABLES

I. Measured Quantities 28

II. Plenum/Bellmouth Test Configurations 29

LIST OF FIGURES

1. Cascade Facility 30

2. Plenum - Configuration #0 31

3. Bellmouth and Test Plane 32

4. Cascade Nomenclature (Test Plane at Bellmouth Exit)-- 33

5. Pneumatic Probe and Traversing Probe Mount 34

6. United Sensor DC-125 5-Hole Pneumatic Probe -- 35

7a. Blade- to- Blade Dynamic Pressure Distributionat the Test Plane (at 501 Span, Velocity =

230 ft/sec) Configuration #0 36

7b. Blade- to-Blade Dynamic Pressure Distributionat the Test Plane (at 50% Span, Velocity =

270 ft/sec) Configuration #1 37

7c. Blade- to-Blade Total Pressure Distribution at theTest Plane (at 50% Span, Velocity = 230 ft/sec)Configuration #0 38

7d. Blade- to- Blade Total Pressure Distribution at theTest Plane (at 50% Span, Velocity = 280 ft/sec)Configuration #1 39

7e. Blade- to-Blade Yaw Angle Distribution at theTest Plane (at 50% Span, Velocity = 230, 280 ft/sec)Configurations #0 and #1 40

8a. Spanwise Dynamic Pressure Distribution at theTest Plane (at X = 30 in., Velocity = 280 ft/sec)Configuration #1 -- - 41

8b. Spanwise Total Pressure Distribution at the TestPlane (at X = 30 in., Velocity = 280 ft/sec)Configuration #1 42

8c. Spanwise Yaw Angle Distribution at the TestPlane (at X = 3Q in., Velocity = 280 ft/sec)Configuration #1 43

9. Plenum and Bellmouth Finite Element FlowAnalysis Models-- 44

10. Finite Element Analysis Velocity DistributionUsing Model 1- 45

11. Finite Element Analysis Velocity DistributionUsing Model 2 --- 46

12. Comparison of Dynamic Pressure Distributions(Pneumatic Data at 50% Span, Velocity = 270 ft/sec)Configuration #1 47

13. Flow Model Analyzed in Reference 8 48

14. Plenum - Configuration #7 (Side Views) 49

15. Plenum - Configuration #7 (Plan View) 50

16a. Blade- to-Blade Dynamic Pressure Distribution atthe Test Plane (at 50% Span, Velocity = 270 ft/sec)Configurations #1 and #7 51

16b. Blade- to-Blade Yaw Angle Distribution at theTest Plane (at 50% Span, Velocity =270 ft/sec)Configurations #1 and #7 52

17a. Spanwise Dynamic Pressure Distribution at theTest Plane (at X = SO in., Velocity =270 ft/sec)Configuration #7 53

17b. Spanwise Yaw Angle Distribution at the TestPlane (at X = 50 in. , Velocity = 270 ft/sec)Configuration #7 54

ACKNOWLEDGEMENTS

The author wishes to express his sincere gratitude to

Professor Ray Shreeve, Lab Manager Jim Hammer, and Technician

John Morris for their willing assistance in every facet of

this study. Their efforts have assisted in making this a

most worthwhile and rewarding engineering experience.

I. INTRODUCTION

In 1963 construction was completed on the Naval Post-

graduate School's subsonic cascade test facility. Its primary-

function was to be used to provide information applicable to

compressor and turbine blade design. As described in Ref. 1,

several unique features were incorporated in the design of

the cascade to ensure a two-dimensional, periodic flow at the

test blading. Previously the lack of good two-dimensionality

in other facilities had plagued efforts to correlate air

turning angles and blade surface pressure distribution data

[Ref. 2].

Initial evaluations of the facility were carried out and

reported in references 1 and 3. The test section entrance

flow was examined and initially found to be unacceptably non-

uniform. Several measures were taken at that time to correct

the deficiency, but an examination of subsequent data revealed

that only partial success was obtained. In particular, an

investigation was performed using NACA 65 series blades as

inlet guide vanes [Ref. 4]. Difficulty in obtaining two-

dimensionality was reported and a strong recommendation was

made that the test section inlet flow conditions be improved.

In preparing for tests of new compressor blade designs,

the goal of the present study was to take whatever steps

were necessary to first obtain a two-dimensional and periodic

flow at the entrance to the cascade test section.

10

For purposes of this report, a two-dimensional and periodic

flow will be considered to exist when the dynamic pressure

variations are less than +_ 1%, total pressure variations are

less than _+ .5%, and flow angles are within _+ 1 . 5 degrees

of their centerline value.

Preliminary pneumatic measurements indicated that the

flow from the plenum itself was not uniform. A numerical

analysis of the flow field through the plenum chamber and

contraction bellmouth was therefore performed using the finite

element method, (FEM) . Based on the results of the prelimin-

ary measurements and the FEM analysis, plenum redesign and

development test programs were carried through. The final

pneumatic survey results showed acceptable levels of dynamic

pressure, total pressure, and flow angle variations.

This report documents the experimental and analytical

steps taken to obtain a suitable plenum geometry for the

cascade facility. Following a description of the cascade

and measurement techniques given in Section II, the steps

taken in the development of a successful plenum arrangement

are first outlined in Section III and then described in the

following three sections. In order to present a clear account

of the development, details of each section of the work have

been confined to appendices. First, the FEM program is given

in detail in Appendix A. Data from the original plenum con-

figuration are given in Appendix B and the plenum development

test results in Appendix C. Finally, detailed drawings of

11

the construction of the modification to the plenum and

bellmouth are given in Appendix D.

12

II. FACILITY AND MEASUREMENT APPROACH

A. CASCADE AND INSTRUMENTATION

A description of the Naval Postgraduate School's Recti-

linear Cascade as it was originally designed is given in

reference 1. The layout of the complete facility is shown

in Figure 1. The addition of two fine mesh screens at the

bellmouth entrance to improve flow stability is the only

modification to the plenum which is reported in reference 1.

A follow-on study into the cascade performance was conducted

by Bartocci and is reported in reference 3. Plenum turning

vanes were installed by Bartocci to direct plenum inlet air

towards the bellmouth entrance and to decrease the total

pressure fluctuations. Multiple views of the plenum chamber

and the bellmouth contraction arrangement as it was at the

inception of the present work are shown in Figure 2.

All testing in the present study was conducted with the

cascade test section walls vertical, with all inlet guide

vanes (Fig. 1) and test blading removed. The effects of

changes in plenum geometry were evaluated primarily by con-

ducting pneumatic probe surveys at the exit of the bellmouth,

hereafter referred to as the test plane. Additional informa-

tion was obtained using tufts for surface flow visualization

in the plenum and from static pressure distributions displayed

on water columns. A Datametrics Series 100 VT Air Velocity

Meter was also used to measure velocities in the plenum.

13

B. PNEUMATIC PROBE SURVEYS

1. Probe and Installation

The installation for probe surveys at the test plane

is shown in Figure 3. A wooden two-by-four was used to

traverse the probe in the blade-to-blade direction. The

coordinate system adopted is shown in Figure 4. The X-wise

displacement of the probe was manually set by sliding the

bar. The displacement in the Y direction and rotation of

the probe were adjusted using the traversing probe mount shown

in Figure 5, which was attached to the two-by-four and incor-

porates potentiometers for the measurement of the immersion

(Y) and yaw (g) displacements.

The five hole United Sensor D- 125 probe shown in

Figure 6 was used to determine total and static pressure,

and yaw and pitch angle. A U-tube water manometer connected

to the ?2 an d P-z ports was used to indicate when the probe

was correctly aligned with respect to yaw angle. An approx-

imate value for the static pressure was obtained by pneumat-

ically averaging P- and P.,. An exact calibration of the

probe was not carried out since only relative measurements

(showing the degree of uniformity across the test plane) were

required.

2

.

Data Acquisition and Reduction

Probe and other reference pressures were multiplexed

via a Scanivalve to a single transducer referenced to atmos-

pheric pressure. The transducer and Scanivalve were connected

to a B and F scanning data system. Signal conditioning

14

circuits in the data system were adjusted so that pressures

were recorded in units of 10 inches of water. Data was

printed and also output on punched paper tape.

A Hewlett-Packard Model 9830A Programmable Calculator

System with a two Megabyte mass memory disc unit and X-Y

plotter were used to process the probe survey data from the

paper tape.

The measured quantities and uncertainty intervals are

given in Table I. The uncertainties in the pneumatic quanti-

ties were calculated from the 2a intervals of 25 consecutive

readings at the test plane center. The position and yaw

angle uncertainties were determined by the accuracy to which

the appropriate scales could be read.

Since test plane Mach number did not exceed .25,

compressibility effects were ignored. Test plane Reynolds

number was 1.5 x 10 per foot scale, with variations of _+ 5% .

In addition to the measured yaw angles, the following (rela-

tive) dimensionless flow properties were evaluated from the

measurements in Table I, and their distributions across the

test plane were examined:

Dynamic Pressure (Q)

q = Q(X,Y)f

uncertainty = + .01,^REF

where Q(X,Y) = PT(X,Y) - P

S(X,Y)

Q.REF = PT C3Q, 5) - P

S(3Q, 5) = Q(30, 5)

and the uncertainty in Q is + .008.

15

Total Pressure (Al^)

_ AP (X,Y)APT = —pr , uncertainty = + .05,

1 ^REF

where APT(X,Y) = P

pL- P

T(X,Y) ,

and the uncertainty is + .049.

Static Pressure (APg)

_ AP (X,Y)AP- = —^

, uncertainty = + .015,b ^REF

where APg(X,Y) = Pg(X,Y) - Pw , uncertainty = + .01.

Note that the uncertainties in AP- and AP~ are rather

high since these quantities are derived from small differences

between two larger quantities. Note also that the values of

QRF Pchanged over the period of a test run due to variations

in the plenum pressure. The value of Q R pp at each (X,Y) was

therefore derived from the plenum pressure reading taken at

the time of the Q(X,Y) measurement. This technique assumed

a linear relationship between Q(30, 5) and Ppj

.

C. OTHER TECHNIQUES

Qualitative information which was simple to obtain,

greatly accelerated the development of the final plenum con-

figuration.

1. Tufts

Tufts were attached to the plenum walls and were

observed and photographed using a Polaroid camera during testing

16

(Average velocities of less than 10 ft/sec allowed the

presence of an observer in the plenum.) A tufted probe was

also used extensively.

2

.

Static Pressure Distribution

The uniformity, but particularly the steadiness, of

the cascade sidewall static pressures displayed on water

manometer columns were monitored as changes in configurations

were made.

3. Velocity Meter

Velocities from the sound baffles in the plenum were

measured using a Datametrics Series 100 VT Air Velocity Meter.

17

III. PROGRAM OUTLINE

The goal was to obtain a plenum and contraction arrange-

ment which would give at the test plane (outside the boundary

layers) maximum peak-to-peak variations of + 1% in dynamic

pressure, + . 51 in the total pressure, and +1.5 degrees in

the flow yaw angle.

The program was carried out in three steps. First, tests

were made to determine the performance of the existing plenum

configuration. Second, a finite element analysis was carried

out which confirmed that the existing bellmouth could not

generate a sufficiently uniform flow at the test plane. The

analysis also guided the design of a suitable modification

to the plenum. Third, an experimental program was carried

out during which a major modification was made in the plenum

geometry and a plenum and contraction configuration which

gave satisfactory flow was subsequently developed.

These three steps in the program are documented in the

following three sections of this report.

A summary of the configurations tested during the program

is given in Table II. Effects of configuration changes were

evaluated at the test plane by conducting blade-to-blade

probe surveys (first at 50% span) and spanwise surveys at

selected locations. The other measurement techniques listed

in Section III.C. often were used first to determine whether

a particular configuration should be measured in detail.

18

IV. PRELIMINARY TEST RESULTS

Blade-to-blade probe surveys were obtained with the

original plenum arrangement (Conf iguration 0) at 10, 30, 50,

and 90% span. The results at 50% span are shown in Figures

7a, 7c, and 7e. (The remaining data are given in Appendix

B.) The results showed unacceptable variations in total and

dynamic pressure in both the blade-to-blade and spanwise

directions. Spanwise variation of the various parameters

can be seen by comparing values at given blade-to-blade loca-

tions in the results at 10, 30, 50, and 901 spans. The yaw

angles were also outside the required bounds.

The source of the total pressure variation was traced to

the screens at the bellmouth inlet. Clearly, the normal flow

into the bellmouth would generate a velocity which would vary

in magnitude and direction over the face of the screen,

thereby generating a corresponding variation in the total

pressure drop.

The screens were removed (Configuration 1 ) and the

measurements repeated. Blade-to-blade survey results are

shown in Figures 7b, 7d, and 7f. A spanwise survey was con-

ducted at X = 30 inches and is shown in Figure 8. The total

pressure variation (AP~T ) across the test plane was seen to

have decreased to + .5%. The variation in Cj was within

tolerance in the spanwise direction; however, an unaccept-

able gradient still existed in the blade- to- blade direction

19

at all spanwise stations surveyed. The yaw angles in Figures

7e and 7f suggested that the flow was still converging through

the center 50% of the test plane. In addition, observed

spanwise variations in flow angle near the ends in the blade-

to-blade direction suggested the presence of large scale

vorticity. This was verified using a small string tuft at-

tached to the end of the pneumatic probe.

The question then was, - was the measured velocity field

simply the result of the geometry of the bellmouth contrac-

tion, or could something be done in the plenum itself to

correct the profile? An analysis of the flow from the plenum

was required to answer this question.

20

V. FINITE ELEMENT FLOW MODEL PREDICTIONS

A two-dimensional finite element analysis was used to

analyze the potential flow field through the plenum and bell-

mouth contraction. Two questions were of specific interest.

First, what was the velocity profile created by the bellmouth

contraction at its exit plane, and secondly, what distance

downstream was required to attain an acceptable uniform

velocity profile? The details of the analysis and the Fortran

programs developed for the IBM 360 to answer these questions

are given in Appendix A.

The plenum, bellmouth, and exit passage were modeled in

two ways as shown in Figure 9. Model 1 was the most simpli-

fied representation, and was used to obtain a first estimate

of the velocity profile developed by the bellmouth contrac-

tion. Due to the vertical axis of symmetry in Model 1, only

half of the model needed to be included in the calculations.

A more realistic model was that shown in Figure 9 as Model

2. In Model 2 the flow entered the plenum from one side as

in the actual plenum.

The computer analysis of each model was performed in a

similar manner. Namely, the exit boundary condition, which

specified flow to be parallel to the exit walls, was applied

at boundary planes located at progressively increasing dis-

tances downstream of the bellmouth exit plane (Fig. 9). For

each boundary plane, the computed velocity profiles across

21

the bellmouth exit plane and the boundary plane were compared

with the results from the previous run. The following simi-

larities were noted in the results of the two models:

1) The exit boundary plane velocity profiles were always

more nearly uniform than the bellmouth exit plane velocity

profiles.

2) As the exit boundary planes were moved farther down-

stream, the exit plane velocity profile became more nearly

uniform. The bellmouth exit plane velocity profiles changed

during this process.

3) As the exit plane velocity profile approached a

uniform condition, the still non-uniform bellmouth exit plane

velocity profile did not change as the exit boundary was

moved even farther downstream.

The results of Model 1, shown in Figure 10, indicated

that at exit plane (GH) , 41.5 inches downstream of bellmouth

exit plane (CL) , the velocity profile had relaxed to give a

maximum variation of 0.3%. The velocity profile at plane

(CL) had a variation then of 14% between peak velocity at

the contour wall and minimum velocity at the axis of symmetry.

Similarly, the results of Model 2, shown in Figure 11, indi-

cated that at exit plane (LM) , 50 inches downstream of the

bellmouth exit plane (FS) , there existed only a 1.3% velocity

variation. This velocity profile was not, however, symmetri-

cal due to the asymmetry of the flow model. Higher velocities

existed on the inlet side of the exit plane. The velocity

profile at plane (FS) also exhibited the asymmetry and a

22

15% variation between maximum and minimum velocities. Figure

12 shows a comparison between the measured profile of Q for

Configuration 1 at 50% span, and that calculated from the

velocity profile of Figure 11.

While the magnitudes are different, the trends in the

computed and measured distributions of Q are clearly similar.

Since the analysis is a two-dimensional one, the magnitudes

should not be expected to fully agree. While a three-dimen-

sional inviscid analysis could be expected to be more repre-

sentative, the inclusion of viscosity would be necessary to

closely approximate the actual flow.

There is sufficient documentation in the literature to

presume significant amounts of vorticity exist in this flow.

The rectangular duct shape in itself can create sizeable

corner vorticity [Ref. 5 and Ref. 6]. Velocity gradients in

the boundary layer, under the influence of transverse pressure

gradients, can produce sizeable amounts of vorticity also

[Ref. 7]. As was stated by C. Truesdell [1954], "Even in

nearly irrotational flows the relatively small amount of vor-

ticity present may be of central importance in determining

the major flow characteristics."

An analysis of the flow in the orthogonal plane (i.e.,

in the spanwise direction), was not performed. However, an

approximate analytical solution for a similar but simpler

model sheds light on the probable trends in the velocity

distribution. For this analysis, the flow field is created

by a circular cylinder immersed in the flow between two

23

parallel walls. This is illustrated in Figure 13. The

velocity distribution across the stream at the plane of

maximum contraction is. given in Ref. 8 as the following

vx

= U 1 -

sinli (itd/H) cos C2ttY/H)

cosh 2 OX/H) - cos2OY/H)

1/2 sinh2 Ob/H) sin

2(27rY/H)

[cosh2(7TX/H) - cos

2(ttY/H)]

2

The important result to note is that as the ratio b/H

increases, the magnitude of the velocity variation decreases

Using a similar argument for the cascade bellmouth contrac-

tion, one would expect a difference in the maximum velocity

variations, between the blade-to-blade and spanwise direc-

tions, of almost an order of magnitude. This was consistent

with experimental observation.

24

VI. PLENUM DESIGN MODIFICATIONAND TEST RESULTS

The measurements reported in Section IV and the analysis

reported in Section V suggested that the bellmouth contraction,

as designed, could produce an acceptably uniform velocity

profile in the spanwise direction, but not in the blade-to-

blade direction. Several perturbations were subsequently

made in the original plenum geometry, and the test results

supported this conclusion. A complete account of the tests

leading to, and subsequently verifying, the design of a

modification to the plenum is given in Appendix C.

The basic idea in the modification was to arrange two

two-dimensional contractions in series, each with sufficient

length to allow relaxation to uniform velocity of the accel-

erated flow. The spanwise contraction of the original bell-

mouth contour was retained, and a new contraction section in

the blade-to-blade plane was built down into the original

plenum. The contours and construction of the new section are

given in Appendix D. The final configuration (Configuration

7) of the plenum, including features which were determined to

be necessary as a result of subsequent development testing

(Appendix C) , is shown in Figure 14 and Figure 15. Referring

to these figures, the baffles were installed to dampen flow

oscillations observed in earlier tests. The flow diverter

fastened to the west end ceiling was installed to deflect

25

high velocity air from along the ceiling, downward through

the baffles toward the plenum center. The velocity and yaw

angle distributions (Configuration 7 at 50% span) are shown

in Figure 16. Measurements from Configuration 1 are shown

for comparison. The results of a spanwise traverse at X = 50

for Configuration 7 are shown in Figure 17. The variations

in both dynamic pressure and yaw angle were seen to have been

brought to within the prescribed limits of +_ 1% and + 1.5

degrees respectively.

26

VII. CONCLUSIONS

The original design of the plenum and bellmouth contrac-

tion arrangement did not produce sufficiently uniform flow

conditions at the bellmouth exit plane. While the large area

contraction ratio (40:1) ensured uniformity in the total

pressure when no screens were introduced, the original bell-

mouth contraction contours in the blade-to-blade plane gave

unacceptable variations in velocity and flow angle at the

inlet guide vane station. The inlet guide vanes would nor-

mally be adjusted to control air-inlet angle to the test

cascade.

Following the design and installation of a modification

to the plenum, in which the original contraction was changed

to two two-dimensional contractions in series, and a program

of development tests, acceptably small variations in velocity

and flow angle were measured at the inlet guide vane station.

Future tests will involve installation of the inlet guide

vanes and an evaluation of the flow downstream at the cascade

test blading location.

27

TABLE I

MEASURED QUANTITIES

Item Description Method Uncertainty

X Blade- to- Blade

dimensionX= in. East endX = 60 in. West end

Tape measure + .1 in.

Y Spanwise dimension

Y = in. South wallY = 10 in. North wall

Immersion

Potentiometer onprobe mount

+ .01 in.

3 Flow yaw angle Yaw angle

Potentiometer onprobe mount

+ .25 deg.

PT(X,Y) Total pressure at

the test planePressure P-. onPitot probe

+ .1 in. H2

PPL

Plenum total pressure Static tap in

plenum chamber

V *

+ . 1 in. H2

PS(X,Y) Static pressure at

the test planePneumatic averageof P

7and P^ on

Pitot probe

+ .15 in. H2

PW

Static pressure at

X=30 in., Y=0 in.

Static tap on southwall

+ .1 in H2

pATM

Atmospheric pressure Mercury barometer + .01 in.H2

i

PTARE

Tare reading acrosspressure transducer

P - PATM ATM

+ .01in.H2O

Note: All pressures are gauge pressure.

28

TABLE II

PLENUM/BELLMOUTH TEST CONFIGURATIONS

ConfigurationNumber Description Figure

Number

Original design 1 and 2

1 Removed screens frombellmouth entrance

1 and 2

minus screens

2 Simulated "relaxation" conceptAdded plywood vertical wall

C-l

3 Added eastern and westernlower contractions

C-4minus fillets

4 Same as above, but movedturning vanes 3 ft. to the east

As above

5Inserted cardboard filletsbetween upper and lowercontraction

C-4

6 Removed plenum turning vanesC-4

minus turningvanes

7 Installed baffles andflow diverter

14 and 15

29

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APPENDIX A

FINITE ELEMENT FLOW ANALYSIS

A.l Method

A computer program was developed to solve LaPlace's

Equation (two-dimensional potential flow) in terms of the

stream function, \p . The purpose of the analysis was to sub-

stantiate the premise that the measured velocity distributions

in the blade-to-blade directions were a result of the inlet

contraction design. The finite element method analysis, FEM,

was used to solve this continuum problem. The detailed pro-

cedures for an FEM analysis are presented in Ref. 9, with

numerous specific fluid flow applications in Ref. 8.

An FEM analysis results in a piecewise approximation of

the field variable in the governing flow equation. In the

present case, the flow is governed by LaPlace's Equation,

2V \p

= , where ^ is the field variable. The solution was

sought for the flow through a two-dimensional contraction

with the same physical shape as the bellmouth of the NPS

Rectilinear Cascade. Two different models were used to

represent the incoming flow and plenum boundaries.

The first step in applying the FEM was to divide the

continuum into a discrete number of elements. Model 1 is

shown in Fig. A-l with the appropriate boundary conditions

specified. Only one-half of the contraction required analy-

sis due to symmetry. The discretization of the area ABGH

55

was carried out with a framework of graphically estimated

lines of constant velocity potential, <$>= constant, and

streamlines of constant i|* . This method was both accurate

and efficient since it gave smaller elements where velocity

gradients were high (p r boundary geometry changes occurred,

as in the contraction contour) , and larger elements where

gradients were small.

The next step was to assign nodes to the element vertices

and to select an interpolation function to represent the var-

iation in ty over the element [Ref. 9, Chap. 5]. A linear

two-dimensional interpolation polynomial was chosen.

The third step was to determine the matrix equations

expressing the properties of a single element. Galerkin's

method of weighted residuals was chosen to accomplish this

task [Ref. 9, Chap. 4].

The fourth step required an assembly of the sets of matrix

equations for each element into a large system matrix. The

system matrix was modified at this point to introduce the

specified boundary conditions [Ref. 9, Chap. 3]. The boundary

conditions were specified in terms of node values of the field

variable of its first derivative.

Fifth, tne combined set of system equations were solved

simultaneously for the nodal values of the field variable.

In the present case, a computer library subroutine called

"LEQTIF" was used. However, any equivalent linear equation

solver could be used here.

56

Once the values of \\> at each of the nodes were deter-

mined, the final step was to obtain a value for the average

velocity between any two adjacent nodes. Since \\i was assumed

to vary linearly between nodes, and the velocity was given

by, for example,

3dU = — ,

8YY <-

X

the average velocity was calculated using

U =^2 - »1

Y2

- YX

A. 2 Computer Program

A listing of the Fortran IV FEM program "LAPFEM," written

for the NPS IBM 360, is given in Table A- I. Table A-II is a

listing of terms not defined in the program comments. The

data required for input is given in each "READ" statement.

The data used for Model 1 with (GH) as the exit plane (see

Fig. 9) are given in Table A-III.

Referring to Fig. A-l, and using for example the element

number 1, the correspondence between element and system

coordinates was as follows:

57

System Element General Element

ICOR (1,1) = 7

ICOR (1,2) = 1

ICOR (1,3) = 2

In general, the rules are as follows:

1) Correspond all elements in either a clockwise or an

anti-clockwise manner.

2) If an element has 1 side on a boundary, then

ICOR (1,1) and ICOR (1,2) will be the two nodes

of that side.

3) If an element has two sides on boundaries, as does

element #1, then the correspondance proceeds anti-

clockwise along the bounded sides first, as shown

above

.

The finite element construction for Model 2 is shown in

Fig. A- 2. The data used when the exit plane was at (LM) are

presented in Table A-IV. The results are shown in Fig. 11.

As one can see, a larger number of system elements are re-

quired when there is no axis of symmetry.

The values output from "LAPFEM" are as follows:

1) Values of ijj at each node point.

2) Velocities between specified nodes.

58

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TABLE A- II

DEFINITION OF TERMS NOT DEFINED INTHE "LAPFEM" PROGRAM COMMENTS

ITYPE

NEL

NSNP

IIEL

ICOR

A

U

SYSA(I,II)

SYSF(I,II)

ELA I II

ELF II

AREA

I, II

X,Y

Specifies type of boundary condition

Total number of system elements

Total number of system nodal points

Number of element

A term to correspond single element nodenumbers (1,2,3), with system node numbers(1,2,5,4,5,..., NEL)

System matrix of coefficients of i>

Column vector of unknown values of ty

C* 1 »*2'"'

' '^NSNP^

Column vector of external node values

System A matrix

System F matrix

Elemental A matrix

Elemental F matrix

Element area

Matrix row and column respectively

X and Y locations of each node

65

• TABLE A- III . DATA FOR MODEL 1 ANALYSISC5/27/79 17.40.49

FILE : LAPDAT FT05F00J. Pi M/WAl PGS7G3 ^C'JA^E «; c hog i

141 ^10 35 61 2 3 4 5 6 7 12 13 13 19 2<+ 2 5 ?'o

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66

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LE : LAPO^T FT05F00 1 P

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<tO 24 31 3041 26 25 2 742: 21 26 Zl43 22 2 7 33 )

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35 40 34 3557 40 35 413 8 41 35 3659 41 36 42oO 42 3c 3761 37 42 426 2 44 33 3963 44 39 4564 45 39 4065 45 40 4666 46 40 41 367 46 41 47 )

08 47 1 4269 47 4 2 4370 43 42 4371 43 49 4 872 50 44 45li 50 45 5174 51 45 4675 51 46 5276 52 46 4777 52 47 5378 53 4 7 4879 53 4 8 548J 54 48 4931 54 49 5532 56 53 5133 56 51 5784 57 51 5285 57 52 58'16 58 52 3387 58 5 3 5988 59 53 5439 59 54 609 0. 60 54 5591 55 61 692 62 56 5793 o2 57 6394 63 57 5 395 63 53 6496 04 58 5997 64 59 6598 65 59 6099 65 60 66IOC 66 60 6110 1 61 67 6610 2 68 o2 o3103 68 63 6910* 69 6 2 6410 5 69 o4 70106 70 64 65

NAVAL PlSTostOUME SCi-TlL.

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83

Exit-> Boundary

Planes

Bellmouth Exit Plane

Area ABCL

Area ABGH 181 Elements115 Nodes

Figure A-l. FEM Model 1

2/, 3/ \%/ i a/.5/ p/| * '•

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85

APPENDIX B

PRELIMINARY TEST PROBE DATA

The following figures are data from tests of Configura-

tion #0 and Configuration #1. The results showed unacceptable

variations in total and dynamic pressure in both the blade-to-

blade and spanwise directions. The yaw angles were also

outside the required bounds.

86

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APPENDIX C

PLENUM DEVELOPMENT TEST PROGRAM

Several alternative designs were proposed to obtain a

uniform, steady flow at the exit plane of the original bell-

mouth contraction, which was the location for the inlet guide

vanes for the cascade test section. Some considerations

governing the selection of the approach to be followed were:

1) It was desirable to maintain the benefits of a largesettling volume.

2) A simple construction was needed, one which was easyto alter if necessary.

3) Minimum boundary layer buildup was required prior toand within the cascade test section.

4) Equal boundary layer growth on opposite sides of theproposed design was required.

A modification of the plenum and bellmouth was carried out

which satisfied all of the above requirements.

As shown by the FEM analysis in Appendix A, the velocity

distribution created by an East-West contraction required an

additional length of non-converging duct in order to relax

(to a uniform condition). Configuration 2, Fig. C-l, was

tested as a rough simulation of the "relaxation" concept.

The arrangement was generated by using the existing plenum

turning vanes and a sheet of 3/4 inch plywood. The measured

distribution of Q shown in Fig. C- 2 showed a 2% variation

through most of the tunnel width except in the deadwater

regions [evidenced by PT

readings) at either end. The yaw

106

angles in Fig. C-3 were similar to Configuration 1 except as

expected at the ends of the test plane. A major modification

was made to the plenum to obtain two separate contractions

in series with adequate lengths for relaxation. In Configur-

ation 3, the east and west contours of the bellmouth were

covered by vertical walls dropping down to a newly constructed

set of East-West contraction contours. The construction

sketched in Fig. C-4 (and detailed in Appendix D) allowed

some relaxation of the velocity distribution created by the

new East-West contours before the flow entered the original

North-South bellmouth contours. The cardboard fillets shown

in Fig. C-4 were not installed in Configuration 3. Measure-

ments of Q and yaw angles were made and the results are shown

in Fig. C-5. The non-uniformities were acceptable through

the center 40 inches of the test section. The velocity dis-

tributions, however, peaked rapidly at both ends and the

sudden increase in yaw angles indicated a strong influx of

fluid from the East and West walls toward the tunnel center.

The close confinement of the deviant yaw angles to the tunnel

ends, at X = 10 inches and X = 50 inches, was thought to be

partially caused by the proximity of the plenum turning vanes

to the lower contraction.

In Configuration 4, the vanes were moved three feet

towards the east end of the plenum and the measurements were

repeated. The results shown in Figures C-7 and C-8 were

similar to those from Configuration 3; however, the peak

107

velocities at the ends were decreased slightly and the yaw

angles varied across the entire 40 inch channel width.

At this point the west end lower contraction surface and

vertical wall was tufted with three-inch strips of light

string in order to examine the surface flow. A tufted rod

was used to probe the flow outside the wall boundary layer.

Figure C- 9 shows a sketch of the tuft positions with air flow

through the test plane at a dynamic pressure of 15 inches of

water. The positions were traced from a Polaroid photograph

taken from within the lighted plenum. The view was taken

from the east end of the plenum looking west at a 45 degree

upwards angle. The following observations were made.

1) Flow on the vertical wall in the vicinity of theupper contraction converged more rapidly than thecontraction walls.

2) Large regions of deadwater existed in the uppercorners.

3) Strong corner vortices (verified by the hand heldprobe) were present at the junction of the ceiling,upper contraction walls, and vertical walls.

These observations pointed to the presence of substantial

secondary flow of the boundary layer fluid. Cardboard

fillets were installed in Fig. C-4 to eliminate the dead-

water areas. Pneumatic measurements taken with this con-

figuration are shown in Figures C-10 and C-ll. The results

indicated little change in the Q distribution; however, the

peak yaw angles were notably increased.

The effect of the position of the turning vanes was ques-

tioned. When the plenum turning vanes were displaced three

108

feet to the east, it was apparent that very little flow was

passing through any but the top turning vane passage. The

vanes were therefore removed altogether as their functional

benefit was questionable. The results of probe measurements

for this Configuration 6 are shown in Figures C-12 and C-13.

The distribution of Q was seen to be similar to the previous

one but an increase was noted in the peak values of the yaw

angles. The yaw angles measured at 20% and 701 span were

consistant with the proposed existance of strong contra-

rotating vortices centered at about X = 10 and 45 inches.

An audible low frequency pressure pulsation was noted

and the static pressures in the cascade test section gave

an unsteady measurement of +_ 0.75 inches of water on the

manometer columns. These observations suggested that the

plenum turning vanes had served as a damping structure and

perhaps as a spoiler which deterred the formation of large

scale vortex motions.

The Datametrics Air Velocity Meter was used to probe the

plenum chamber. Flow velocities through the sound baffles

were quite uniform. However, at a distance of eight feet

downstream of the sound baffles approximately 75% of the

flow was seen to have passed through the upper one-half of

the plenum at this location. It was also noted that little

flow was actually moving around the east end lower contrac-

tion contour.

It was clear at this point that in order for the lower

contraction to work properly, it was necessary to prevent

109

the flow from forming a smoothly accelerating jet from the

distributed source represented by the sound baffles, to the

line sink represented by the bellmouth exit plane.

Consequently, the plenum was reconfigured as shown in

Section VI, Figures 14 and 15. Baffles were positioned to

behave as spoilers and to better distribute the flow below

the contraction. A 4-by-12 foot construction of 1/8 inch

masonite was installed on the west end ceiling to divert the

high velocity fluid from the ceiling down through the baffles

The measurements of Q and flow angles for this final Configur-

ation 7 are presented in Section VI.

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124

APPENDIX D

PLENUM iMODIFICATION DRAWINGS

The following drawings show the construction of the east

and west lower contractions.

Construction Materials:

Figures D-l through D-4

1. All framing material is construction grade pine.

2. The surface covering is 1/8 inch untempered masonite

paneling in 4 x 8 ft sheets.

3. Countersunk wood screws secure the masonite to the

framing.

4. Framing is secured to the cement wall with power-

driven nails.

Figure D-

5

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constructed from welded 1/8 inch steel plate.

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Figure D-4. Lower Contraction Contour

129

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Figure D-5. Upper Contraction Contour

130

LIST OF REFERENCES

1. Rose, C. and Guttormson, D.L., Installation and Test ofa Rectilinear Cascade , Master's Thesis, Naval PostgraduateSchool, Monterey, California, 1964.

2. Johnsen, I. A. and Bullock, R.O., Aerodynamic Design ofAxial-Flow Compressors , NASA SP-36, Chap. VI, NationalAeronautics and Space Administration, 1965.

3. Bartocci, J.E., An Investigation of the Flow Conditionsat the Lower Measuring Plane, and in the Plenum Chamberof the Rectilinear Cascade Test Facility , Master's Thesis

,

Naval Postgraduate School, Monterey, California, 1966.

4. Wheeler, W.R., Experimental Determination of Turning Angleand Losses of Axial Compressor Inlet Guide Vanes , Master'sThesis, Naval Postgraduate School, Monterey, California,1972.

5. Streeter, V.L., Handbook of Fluid Dynamics, Chap. 10,McGraw-Hill, 196T7"

6. Prandl, L. , On Fully Developed Turbulence , Proceedings ofthe International Congress of Applied Mechanics, Zurich,Switzerland, 1926.

7. Bansod, P. and Bradshaw, P., "The Flow in S-Shaped Ducts,"Aeronautical Quarterly

, pp. 131-140, June 1971.

8. Chung, T.J., Finite Element Analysis in Fluid Dynamics ,

McGraw-Hill, 1978.

9. Huebner, K.H., The Finite Element Method for Engineers ,

Wiley and Sons, 1975.

131

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2

Cameron StationAlexandria, Virginia 22514

2. Library, Code 0142 2

Naval Postgraduate SchoolMonterey, California 93940

3. Department Chairman, Code 67 1

Department of AeronauticsNaval Postgraduate SchoolMonterey, California 93940

4. Assoc. Prof. R. P. Shreeve, Code 67 Sf 1

Department of AeronauticsNaval Postgraduate SchoolMonterey, California 93940

5. LT Richard Carl Moebius, USN 1

2271 St. Marshall Dr.VA. Beach, VA 23454

6. Turbopropulsion Laboratory 10Code 67Naval Postgraduate SchoolMonterey, California 93940

132

thesM656

Analysis and testing to improve the flow

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