analysis and testing to improve the flow from the plenum of a ...calhoun: the nps institutional...
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Calhoun: The NPS Institutional Archive
DSpace Repository
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
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ANALYSIS AND TESTING TO IMPROVETHE FLOW FROM THE PLENUM OF ASUBSONIC CASCADE WIND TUNNEL
Richard Carl Moebius
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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
T192032
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UNCLASSIFIEDStCumTV CLASSIFICATION OF THIS "AC.C fWnmn Omtm Enlmrooi)
REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM
•*»0"T m UM«<* 2. GOVT ACCESSION MO J RECIPIENT'S CATALOG NUHIEK
4 TITLE fmd Iu»ml«>
Analysis and Testing to Improve the Flowfrom the Plenum of a Subsonic CascadeWind Tunnel
>. type of report pepioo covcreoMaster's Thesis;March 198
«. »l«FO»MIMO OAG REPORT NUMBER
7. »uTHO*nj • . CONTRACT OR GRANT NOMlCKrtj
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
132Ti MONITORING AGENCY NAME A AOO»SSSflf tltlformnt Irom Controlling Ollle*)
Naval Postgraduate SchoolMonterey, California 93940
It. SECURITY CLASS, (ol iMt report)
Unclassified
IS*. DSCLASSIFICATION/OOWNGRAOinGSChEOuLE
IE. DISTRIBUTION STATEMENT for ihlt M*9*r<)
Approved for public release; distribution unlimited.
17. DISTRIBUTION STATEMENT (ol tna mtrntrmet «»«rt< In Block 30. II dltioront hmm Moportj
II SUPPLEMENTARY NOTES
IS KEY WORDS (Contlnuo am rovoroo ttoo II nmemmomrr ono) Utoniity my Bloc* nimmoot)
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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EDITION OF I MOV «S is OBSOLETES/N 010 2-014- MO 1
UNCLASSIFIEDSECURITY CLASSIFICATION OF TNIS PAOE (Whan Dmlo Mnlorod)
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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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14 ' 3 UNCLASSIFIEDS/N 0102-014-6601 sgeu«tw claudication o» t*u »*ocrv»*« o*
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Approved for public release; distribution unlimited
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
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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.
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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
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LIST OF TABLES
I. Measured Quantities 28
II. Plenum/Bellmouth Test Configurations 29
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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
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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
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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.
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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.
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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
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the construction of the modification to the plenum and
bellmouth are given in Appendix D.
12
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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
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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
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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.
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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
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(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
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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
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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
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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.
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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
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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
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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
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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.
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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
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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.
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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.
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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.
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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
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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
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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.
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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:
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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.
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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
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• 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
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28. 127.52 8.5 96.29. 63.529.5 31.530. 0.058. 160.58. 127.58. 95.57.3 62.556.5 30.555.5 CO100. 160.95. 125.585.5 9 2.79. 62.76. 30.75. 0.014U. 160.152.5 120 .
12$. 104.110. 81.99. 55.9*. 26.93.5 CO16 0. 90.145. 81.131. 6o. 5117.5 47.5109.5 23.10 7. 5 CO166.5 - 76.5 •
155. 68.144. 56.134. " 38. 5128. 18.5125.5 0.0173. 67.5U4. 59.5
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LAPJAT F~0''F00i 'H livn > i F ;-'il
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LE : LAPO^T FT05F00 1 P
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NAVAL PlSTostOUME SCi-TlL.
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Exit-> Boundary
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Figure A-l. FEM Model 1
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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.
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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
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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
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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
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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
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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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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
The upper contour is part of the original bellmouth
constructed from welded 1/8 inch steel plate.
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33 in
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Figure D-4. Lower Contraction Contour
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Figure D-5. Upper Contraction Contour
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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.
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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
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thesM656
Analysis and testing to improve the flow
3 2768 002 04656 7DUDLEY KNOX LIBRARY