__ ._ A _ ~ __ ~/ 

NA!SA Contractor Keport j~.ns(} 

NASA-CR-3986 1986001859 1 

Measurements of a Turbulent 

Horseshoe Vortex Formed 

Around a Cylinder 

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W. A. Eckerle and L. S. Langston 

GRANT NSG-3238 

JUNE 1986 

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NF02268 

1l 

NASA Contractor Report 3986 

Measurements of a Turbulent 

Horseshoe Vortex Formed 

Around a Cylinder 

w. A. Eckerle 

United Technologies Research Center 

East Hartford, Connecticut 

L. S. Langston 

University of Connecticut 

Storrs, Connecticut 

Prepared for 

Lewis Research Center 

under Grant NSG-3238 

NI\S/\ 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Branch 

1986 

SYMBOLS 

SUMMARY 

INTRODUCTION 

EXPERIMENTAL CONFIGURATION 

\~ind Tunnel . 

Flow Uniformity 

Test Section 

Test Model 

Design . 

Afterbody 

Probe Configuration 

Data 

RESULTS 

Five-Hole Probe 

Probe Traverser 

Acquisition System 

Hardware 

Software 

Boundary Conditions 

TABLE OF CONTENTS 

Surface Static Pressure Measurements 

Endwall .... 

Cylinder . . . . . 

Five-Hole Probe Measurements 

Endwall Region . . . . . 

Test-Section Midspan . . 

.' 

Boundary Layer Development in the Plane of Symmetry. 

Pressure Loss . . . . 

Surface Flow Visualizations 

Technique . . . . . . 

Endwall Visualization 

Cylinder Visualization 

Discussion of Vortex Formation 

CONCLUSIONS 

REFERENCES 

FIGURES 

APPENDIXES 

A - EXPERIMENTAL UNCERTAINTIES 

B - TABULATED DATA . . . . . . 

iii 

Page 

lV 

Vll 

1 

3 

3 

3 

4 

6 

6 

8 

9 

9 

10 

10 

10 

11 

13 

13 

16 

16 

17 

18 

19 

23 

24 

26 

28 

28 

29 

31 

32 

34 

35 

38 

104 

110 
Cf 

Cp 

Cps 

Cp 

T 

CpT 

D 

h 

H 

n 

PcPs 

Pp 

PS 

PS 

o 

PT 

PT o 

q 

qo 

R 

ReD 

Rea 

u 

SYMBOLS 

skin-friction coefficient, T/(1/2 P U~) 

pitot pressure coefficient, (p p - PSo)/qo 

static pressure coefficient (P S- Ps )/qo 

o 

loss coefficient, (PT - PT)/qo 

o 

mass-averaged loss coefficient, equation (10) 

cylinder diameter, 29.85 cm 

test-section entrance height, 30.48 cm 

boundary-layer shape factor, o/6x 

exponent in power law profile representation, 2/(H-l) 

five-hole probe pressures, figure 17 

local pitot pressure 

local static pressure 

reference static pressure near test-section entrance 

local total pressure 

reference total pressure near test-section entrance 

local dynamic pressure 

reference dynamic pressure near test-section entrance 

radial distance from instrumented-disk center, figure 25 

Reynolds number based on the cylinder diameter 

Reynolds number based on boundary-layer momentum thickness 

velocity in x-direction 

l.V 
u. 

+ u 

u 

Do 

u"" 

v 

w 

x,y,z 

y+ 

Yms 

Zo 

Zw 

Greek 

s 

o 

o 

n 

p 

)..l 

v 

<P 

* 

friction velocity, /Tlp 

universal velocity, ulu. 

local velocity magnitude 

reference velocity magnitude near test section entrance 

velocity at boundary-layer edge 

velocity in y-direction 

velocity in z-direction 

orthogonal coordinate system as defined in figure 25 

universal coordinate perpendicular to endwall, yu.lv 

distance of midspan from endwall, 0.511 D 

lower limit of mass-averaged loss integral, either 0 or D/2 

distance from test-section plane of symmetry to sidewall, 0.91 m 

position angle relative to plane of symmetry, figure 25 

boundary-layer thickness 

boundary-layer displacement thickness 

profile factor, equation (9) 

density 

viscosity 

kinematic viscosity, )..lIp 

pitch angle, figure 17 

v 
S 

S cal 

Smeas 

Sx 

corrected yaw angle, same sign convention as Seal' figure 17 

yaw angle correction for five-hole probe calibration, figure 17 

uncorrected yaw angle 

boundary-layer momentum thickness 

V~ 
SUMMARY 

As a uniform viscous fluid flow approaches wall-mounted structures such 

as a cascade of turbine airfoils, the boundary layers formed on the bounding 

walls (endwalls) separate in front of each airfoil. They then roll up into a 

horseshoe vortex system that is swept downstream around each airfoil. This 

vortex system and its formation can greatly influence both aerodynamic losses 

and heat transfer on endwall and airfoil regions. 

This experimental investigation involved the aerodynamic measurement of 

the formation of a symmetrical horseshoe vortex system in front of and around 

a single large diameter right cylinder centered between the side walls of a 

wind tunnel. Test conditions included a Reynolds number of 5.5 x 10 5 and 

endwall turbulent boundary layer thicknesses of 13 percent, both based on 

cylinder diameter. Detailed surface flow visualization and static pressure 

measurements, and extensive mean velocity and pressure measurements in and 

around the vortex system flow field were made. 

The results lend new insight into the formation and development of the 

vortex system. The actual vortex formation did not occur in the lateral plane 

of symmetry of the cylinder, but originated at a significant angular distance 

away from it. Also, contrary to the multiple vortex systems reported by 

others, only a single primary vortex and saddle point were found. The scale 

of the separation process occurring at the saddle point was found to be much 

smaller than the scale of the approaching boundary layer thickness. 

Although the data presented are for the symmetrical endwall flow around a 

cascade of cylinders, the results can be used to shed light on such phenomena 

as the nonsymmetrical endwall flow in axial turbomachinery. The data can also 

be used as a test case for three dimensional computational fluid mechanics 

computer codes. 

vii 
j 
INTRODUCTION 

As a result of the rapid development of computational hardware in the 

last decade, gas turbine engine designers have the opportunity to develop 

analysis techniques that can be used to significantly improve engine performance and durability. Numerical solutions of equations governing engine 

viscous internal flows are gaining acceptance as an alternative to costly 

experimentation in the development of new designs. To this end, the gas turbine community has been developing three-dimensional fluid dynamic codes that 

take advantage of extensive available computing power. Verification of these 

codes has been difficult because data characterizing these complex flows has 

been meager or nonexistant. Detailed measurements quantifying these flow 

fields are necessary to fully utilize the analysis techniques. 

In particular, a turbulent boundary layer approaching a local obstruction, such as when annulus wall boundary layers encounter airfoils and support 

struts, has not been well documented. Studies to date show that fluid outside 

the boundary layer has enough momentum to overcome the streamwise pressure 

gradient generated by the obstacle. Low momentum flow in the boundary layer, 

however, cannot negotiate the local adverse pressure gradient and separates 

from the wall. The separation process creates a reverse flow region in front 

of the obstacle, bringing higher momentum flow from outside the boundary layer 

close to the wall. As the reverse flow convects around the obstacle, the 

streamwise and reverse flow interaction leads to the formation of a vortex 

system. A leg of the vortex passes around each side of the obstacle creating 

the characteristic horseshoe-like shape when viewed from above. 

The reverse flow and vortex structure significantly alter local flow and 

heat transfer characteristics. The flow visualization of figure 1, obtained 

by Gaugler and Rusel1 (ref. 1) using the teChnique developed by Langston and 

Boyle (ref. 2), dramatically demonstrates the effect of this separation 

process on the endwall of a turbine vane cascade. The figure is a black and 

white print of the actual data. Blue ink dots (dark shade in fig. 1) were 

placed upstream of the separation zone and red dots (light shade) placed downstream of the separation. These two regions are distinct in the flow 

visualization. Almost the entire endwall in the passages is covered with 

light shade, indicating that the separation strongly impacts heat transfer and 

aerodynamic losses throughout the cascade's endwall region. This implies that 

details of the separation process must be accurately modeled to calculate flow 

parameters and temperature distribution through the cascade. 

The symmetrical separation of boundary layer flow normal to a single 

cylinder (or a cascade of cylinders) is perhaps the simplest of geometries 

that demonstrate the horseshoe vortex phenomenon (e.g., ref. 3), while the 

I 
vortex system formed on the endwall of a cascade of turbine airfoils (e.g., 

refs. 1 and 4), might be considered to be one of the most complex of the 

family of such flows. 

This paper deals with the experimental study of the simple cylinder 

vortex system. Aerodyamic measurements were made to define the horseshoe 

vortex system formed around a single cylinder mounted between endwalls in a 

wind tunnel. Because of the existance of the sidewalls of the tunnel, the 

cylinder model approximates one element of a cascade of cylinders. The tests 

were carried out at a relatively high Reynolds number with turbulent boundary 

layers on the endwalls. The objectives of the study were as follows: 

1. There have been a number of studies carried out to measure and 

explain cylinder endwall flow and these have been reviewed by Eckerle 

,(ref. 1). The conclusion of this review is that few or no measurements have 

been taken in the vortex region itself, especially in the region of vortex 

formation. Also, in most studies, the scale of the experiment was too small 

for accurate and detailed measurements. In the study presented here, measurements were made in the vortex region, and the cylinder model scale was about 

100 times larger than the pressure probe scale. 

2. Often it is possible to study and understand a simple member of a 

fluid flow family to explain and predict the behavior of a more complex member 

of that family. The study here represents the flow into a cascade of 

cylinders with zero angle of attack (no lift), at a Reynolds number based on 

cylinder diameter representative of many turbomachinery applications and with 

a large scale that would be difficult to achieve in an airfoil cascade. One 

objective then is to shed more light on the important problem of endwall flows 

in turbine cascades. 

3. The measurements were taken in such a way (i.e., inlet and exit 

conditions to a control volume with interior flow measurements) that they can 

be used as a test case for three-dimensional computational fluid mechanics 

computer codes. 

2 
EXPERIMENTAL CONFIGURATION 

The horseshoe vortex flow structure was investigated with a single 

cylinder immersed in a turbulent boundary layer. This simple and symmetric 

geometry created a strong secondary flow without the added complexity of an 

asymmetric flow field. Because of the symmtry, detailed flow measurements 

were required in only one quadrant of the test section. This represented a 

significant reduction in experimental data gathering since a large scale 

experiment was designed to minimize probe effects. 

Wind Tunnel 

Testing was conducted in the University of Connecticut Low Speed Wind 

Tunnel. This tunnel was an open circuit, suction type incorporating an inlet 

with a 9:1 contraction ratio, a 1.2 m long constant - area transition section 

for developing separate turbulent boundary layers on the top and bottom 

endwalls, and a 1.8 m long constant-area test section. Flow from the test 

section dumped into a large plenum and subsequently exhausted into the 

laboratory via a centrifugal fan and 75 HP motor. The maximum velocity that 

could be delivered to the test seciton, which had a 0.3 x 1.8 m cross section, 

was 30.5 m/sec. 

A settling chamber built for these tests at the tunnel entrance effectively isolated the tunnel from the laboratory. A bellmouth on the front of 

the chamber served to catch flow. The entrance height was 2.8 m, while the 

chamber width matched that of the 1.8 m wide tunnel. Prior to entering the 

chamber, the flow passed through a porous plate (23 pecent porosity), 15 cm of 

0.3 cm cell honeycomb, and a fine mesh screen. The porous plate created a 

pressure drop to smooth out local nonuniformities in the entering flow. The 

flow then fully developed as it passed through the honeycomb's high length/ 

diameter passages. This process removed streamwise vorticity from the 

entering flow. The fine mesh screen broke up any wakes created by the plate 

and honeycomb. After this conditioning process, the flow was contracted 

before passing through the transition section. Figure 2 is a photograph of 

the wind tunnel in its location inside the laboratory. 

Flow Uniformity. - Even though the tunnel was in close prox~m~ty to the 

laboratory walls, the settling chamber arrangement created a reasonably 

uniform flow field at the test-section entrance. A pitot pressure profile 

measured near the test section entrance at the tunnel centerline is contained 

in figure 3. Corresponding boundary-layer parameters are listed in Table I. 

3 
TABLE I. - BOUNDARY-LAYER PARAMETERS FOR CENTERLINE TRAVERSE 

Tunnel I 

Endwall a/h a*/h 6x /h 0*/6 x 

Floor 0.083 0.0122 0.0091 1.34 I 

Ceiling 0.092 0.0148 0.0109 1.36 I 

---- ----- - - - ~ 

The data are expressed as pressure coefficients using the total and 

dynamic pressures measured at the same streamwise location near the tunnel 

sidewalls for reference conditions. The profile is substantially symmetric, 

although the ceiling boundary layer was approximately 15 percent thicker than 

the floor boundary layer. Core-flow pressure coefficients in the profile are 

close to 1.0 indicating transverse uniformity of the entrance flow. Additional traverses acquired at 30.5 cm intervals across the test-section 

entrance plane contained a maximum core-flow total pressure deviation of less 

than one percent of the reference value. 

Test section. - With the attainment of good flow symmetry, only one endwall flow region needed to be documented. Since probes used in the test program were cantilevered from a positioner, which was an integral part of the 

test-section ceiling, probe interference effects were smaller for measurements 

near the test-section floor. The floor was modified to mate with the test 

model and to incorporate endwall instrumentation. 

Floor Modification: The existing plexiglass floor was replaced with two 

aluminum plates. A support plate, figure 4, was bolted to the test-section 

angle iron frame. The remainder of the floor was a rotatable instrumented 

disk, figure 5, that fit concentrically inside the support plate. The floor 

disk, which contained static pressure taps, holes to concentrically mount the 

test cylinder, and an access hole for passing cylinder instrumentation lines 

out of the test section, was clamped to the underside of the support plate. 

Clamping was accomplished with four toggle clamps and four cam follower 

assemblies equally spaced around the disk. 

The cam followers were mounted into slides, as shown in figure 6. This 

arrangement allowed the floor disk to be retracted from the support plate and 

rotated in the following manner. The toggle clamps were released, enabling 

the floor disk to rest on the cam followers. The cam followers were lowered, 

via the adjustment bolts shown in figure 6, until the O-ring seal was clear of 

the support plate. The floor disk, and therefore the static pressure taps, 

could then be rotated to position the taps as desired. With this design, 

4 
detailed endwall static pressure distributions were obtained with a m~n~mum 

number of pressure taps. Since the cylinder mounted concentrically on the 

instrumented floor disk, detailed cylinder surface pressure distributions 

could also be obtained with a minimum of pressure taps. 

The instrumented disk was accurately and repeatably located with index 

holes machined near the disk's outer edge. Since the disk had a large 

diameter, holes could easily be placed at one degree increments. A springloaded pin assembly, attached to the support plate, served as the reference 

for the disk angular location. Figure 7 is a photograph of a portion of the 

inverted test section floor showing the pin indicator, index holes, a toggle 

clamp, and a cam-follower assembly. 

The pressure tap locations on the instrumented disk are listed in Table 

II. The radial and angular positions correspond to the polar coordinate 

system shown in figure 5. 

TABLE II. - INSTRUMENTED FLOOR DISK STATIC 

PRESSURE TAP LOCATIONS 

[ S-degl_zo 1-10 I 0 110 I 20 I ±401~601 ±80Ig-o-1 IR-cm -- - - - - - - - - - - - - -

24.8 15.9 15.0 16.5 17.1 22.9 22.9 22.9 15.0 

32.4 18.4 17.8 19.1 19.7 30.5 30.5 30.5 

39.4 21.0 20.3 21.6 22.2 38.1 38.1 38.1 

23.5 22.9 24.1 24.8 

26.0 25.4 26.7 27.3 

28.6 27.9 29.2 29.8 

31.1 30.5 31.8 32.4 

33.7 33.0 34.3 34.9 

36.8 35.6 38.1 39.4 

41.9 40.6 43.2 44.5 

47.0 45.7 48.3 49.5 

53.3 50.8 55.9 58.4 

63.5 61.0 66.0 68.6 

71.1 ---- - --- - ------- ----- ---'-- -

Taps were staggered along the disk radius at angular locations S = -10, 0, 10, 

and 20 degrees. These taps provided pressures along any radial line every 

0.64 cm for 15 < R < 35.6 cm, every 1.27 em for 35.6 < R < 50.8 cm, and every 

2.54 cm for 50.8 < R < 71.1 em by successively rotating each of the four lines 

5 
of taps to a desired angular location. Additional taps permitted acquisition 

of pressures to check flow symmetry. Static taps were also machined in the 

support plate to define boundary conditions. Locations for these taps are 

indicated in figure 4. 

A photograph of the assembled test-section floor, taken with the floor 

inverted prior to installation in the tunnel, is shown in figure 8. The plug 

in the center of the instrumented floor disk was installed in the disk's 

access hole to permit tunnel checkout testing prior to the cylinder's installation. The small lines are stainless steel tubes that were epoxied to each 

of the pressure taps. 

The angle iron support members sagged under the weight of the new floor. 

Adjustable trusses, incorporated into the test section frame, leveled the 

tunnel floor to within 0.125 cm. 

Ceiling and Probe positioner: An integral part of the test-section 

ceiling and this test program was the probe positioner assembly. This 

assembly consisted of two positioning disks and a series of support plates. A 

sketch of the disks is contained in figure 9. The probe extended through the 

hole in the small disk to the test section. Movement of the small disk 

positioned the probe to the radial position of the large disk corresponding to 

the desired probe position. The large disk then rotated the probe to the 

desired traverse location. For a given position of the disks, the probe could 

be moved to any point inside a 40 cm diameter circle. The support plates, 

shown disassembled with the disks in figure 10, could be interchanged so that 

the positioning disks could be moved to different ceiling locations covered by 

the support plates. 

The positioning disks were 

installed on top of each disk. 

gear with a spacer plate. This 

mechanized as shown in figure 11. Gears were 

The smaller gear was raised above the larger 

arrangement permitted a D.C. motor and 

potentiometer to be connected to each gear. The motors and potentiometers 

accurately provided remote angular positioning of the disks. 

Test Model 

Design. - The experimental model was a cylinder that spanned the test 

section. The cylinder diameter was a compromise of two design constraints. A 

large-diameter cylinder, orders of magnitude larger than the probe, was 

desirable to minimize probe interference effects. At the same time the cylinder diameter was limited by the tunnel size. If the cylinder was too large, 

interference with the test-section sidewalls could alter the desired flow 

field. 

6 
Cylinder surface static pressures were calculated for inviscid flow 

through a cascade of cylinders to determine a desirable cylinder diameter. 

The plane of symmetry between the cylinders corresponded with the tunnel sidewalls. Calculations were performed for a range of cylinder diameters using a 

code developed at the University of Iowa. This code was based on the 

technique of Hess and Smith (ref. 5). The deviation of static pressure at 

ninety degrees from that for potential flow around a single cylinder was used 

to indicate the sidewall interference effects, since this pressure was most 

sensitive to the presence of the walls. A nominal cylinder diameter of 30.5 

cm was chosen. This size decreased the calculated 90-deg static pressure by 

only five percent yet provided a model scale 100 times that of a five-hole 

probe. 

The off-body static pressure distribution for this geometry was calculated using the inviscid analysis of Barber (ref. 6). Data from several 

angular planes are shown in figure 12 along with the distributions for potential flow around a single cylinder. Only a small effect of the sidewalls on 

pressures upstream of the cylinder can be discerned. The largest deviations 

occur in the 90-deg plane. Pressure coefficients in this plane are approximately five percent smaller (more negative) than those for a single isolated 

cylinder. The confining effect of the sidewalls, then, only insignificantly 

altered the pressure distribution leading to flow separation. 

A sketch of the test model is shown in figures 13 and 14. The cylinder 

was fabricated from commercially available tubing with a nominal D.D. and wall 

thickness of 30.5 cm and 2.54 cm, respectively. The tubing was accurately 

turned down to an D.D. of 29.85 cm and polished to obtain a smooth surface 

finish. The cylinder concentrically bolted to the instrumented floor disk V1a 

the attachment holes shown in figure 5. An 0 ring provided the seal between 

the cylinder base and the instrumented floor disk. The top of the cylinder 

remained unattached allowing the cylinder to rotate with the floor disk. The 

cylinder also mated with the probe positioner that formed a portion of the 

test-section ceiling. Ensuring a seal between the cylinder and probe 

positioner disks was difficult. Since the positioner consisted of disks that 

rotated over the cylinder, only a small force could be exerted to gain a seal. 

A soft foam-type material that easily compressed was affixed to the top of the 

cylinder. A ridge was machined into the cylinder top surface to support the 

gasket against shear forces created by the relative rotation between the probe 

positioner disks and the cylinder. A disk using an O-ring seal was installed 

near the top of the cylinder, as shown in figure 14, to prohibit leakage of 

ambient air through the inside of the cylinder to the test section. The foamtype gasket only needed to seal against the much smaller circumferential pressure variation. Figure 15 is a photograph of the cylinder mounted in the 

tunnel. 

7 
Designing the cylinder to rotate with the instrumented floor disk enabled 

detailed cylinder surface pressure distributions to be obtained with a minimum 

of pressure taps. The tap locations on the cylinder are given in Table III. 

Pressure taps were staggered along the cylinder axis at four angular positions 

corresponding with the staggered rows of taps on the instrumented floor disk. 

Additional taps were included to check flow symmetry. Static pressures could 

be obtained every 0.64 cm on the lower half of the cylinder. Lines connected 

to the pressure taps were routed out of the cylinder through the access hole 

in the center of the instrumented floor disk. 

TABLE III. - TEST CYLINDER STATIC PRESSURE TAP LOCATIONS 

S-deg 

-20 -10 0 10 20 ±40 ±60 ±80 90 

y-cm 

3.8 0.3 2.5 1.9 1.3 5.1 5.1 5.1 15.2 

8.9 3.2 5.1 4.4 3.8 10.2 10.2 10.2 

14.0 5.7 7.6 7.0 6.4 15.2 15.2 15.2 

8.3 10.2 9.5 8.9 22.9 22.9 

10.8 12.7 12.1 11.4 

13.3 15.2 14.6 14.0 

22.9 17.8 22.9 22.9 

20.3 

22.9 

25.4 

27.9 

Afterbody. - An afterbody was fabricated to mate with the downstream side 

of the cylinder. The afterbody was designed to eliminate unsteadiness introduced into the upstream separation region by vortex shedding in the cylinder 

wake. Figure 16 is a sketch of the afterbody design. The afterbody, fabricated from aluminum, consisted of two side plates connected by three braces 

for rigidity. The upstream edge of the side plates had a machined radius that 

tangentially mated with the cylinder at the 90-deg plane. Gasket material was 

placed on all the afterbody's edges to prevent leakage. The afterbody length 

displaced the base region to the exit of the test section. 

8 
During the initial phase of the program, tests with the afterbody 

installed indicated a nonsymmetric flow field around the cylinder. In addition, the endwall saddle-point location determined from flow visualization 

tests varied from test to test. The afterbody effectively divided the test 

section into two constant area passages downstream of the cylinder. Evidently 

an unacceptable bistable flow structure set up as the flow divided itself 

between the two passages. As a result, this test program was conducted without the afterbody. 

Probe Configuration 

Five-Hole Probe. - Interior fluid measurements were obtained with a fivehole probe. The tip geometry for the probe, United Sensor Model DC-.093-24-F, 

is shown in figure 17. The probe tip diameter was 0.24 cm instead of the 

stock configuration of 0.32 cm. In addition, the tip was ogival rather than a 

standard truncated cone. The corners of the truncated cone, even though they 

contain large obtuse angles, cause inconsistencies in the calibration. (See 

Camarata et ale ref. 7.) The ogival tip makes the probe calibration less 

sensitive to changes in Reynolds number. The probe tip was aligned with the 

shaft axis (which is the reason for the "shephard's crook") so that the tip 

rotated but did not translate as the probe was rotated about the shaft axis. 

The nomenclature for the pressure taps is in figure 17. Tap 1 was the impact 

pressure while taps 2 and 3 were for nulling the probe in yaw. Taps 4 and 5 

provided dynamic pressure and pitch angle from the calibration. 

The probe was calibrated in an air jet from a 3.8 cm diameter nozzle. 

The sign convention used for the calibration, which was accomplished at a 

dynamic head of approximately 6.6 cm of water, is in figure 18. Yaw angle, 

Seal' was defined as the angle between the plane formed by the tip and the 

shaft of the probe and the projection of the velocity vector on the plane 

perpendicular to the shaft. Pitch angle ~, defined as the angle between the 

velocity vector and the plane perpendicular to the probe shaft, was v~ried 

from -29 to +30 degrees. For each calibration pitch angle, the probe was 

nulled in yaw by rotating the probe about the shaft axis until P2 equaled P3 • 

The resultant yaw angle, measured relative to a flag mounted on the shaft, was 

Scal' Pressures from the remaining taps were recorded to generate calibration 

curves shown in figure 19. 

Measurements were likewise acquired in the wind tunnel. At a given 

spatial location in the flow field, the probe was rotated until the pressures 

from taps 2 and 3 were equal. The probe rotation, Smeas' was measured 

relative to the core flow direction upstream of the cylinder. The sign 

convention for Smeas was that shown in figure 17. The pressures PI' P4 , and 

Ps were recorded for each point. The data were reduced as follows. From the 

pressure ratio (P4-PS)/(PI-(P4+PS)/ 2), the pitch angle ~ was determined from 

9 
figure 19A. Knowing $, the parameter (P 1

-(P 4+P S)/2)/q was determined from 

figure 19B and local dynamic pressure was calculated. Also using $, figure 

19C provided the parameter (PT-P 1) to calculate local total pressure. Similarly, figure 19D provided the calibration yaw angle 6cal ' Flow yaw angle, 6, 

was the sum of 6cal and 6

meas ' The Bernoulli equation was used to calculate 

local static pressure from the local total and dynamic pressures. 

Probe Traverser. - An L.C. Smith Model BBR 16360 traverser positioned the 

probe. The traverser was mounted to the small gear with a bulkhead fitting as 

shown in figure 11. An access hole for installing and removing the probe was 

created through mating holes in the gear, spacer plate, and small positioner 

plate. Since the hole diameter had to be slightly larger than the 1.27 cm 

shephard's crook to allow passage of the probe, the bulkhead fitting which 

held the traverser was bored out and could not be used for sealing around the 

probe. Instead, ambient air was prevented from passing around the probe into 

the test section by a seal in the small positioning disk. With the probe in 

place and held by the traverser, a removable plug, shown in figure 20, was 

slipped over the probe tip inside the test section. (A recess, machined into 

the plug, allowed the plug to pass around the shephard's crook.) The plug fit 

into the positioner disk, as shown in figure 21, and bolted to the spacer 

plate. Sealing was accomplished by compressing a rubber washer between two 

steel washers in the plug, as shown in figure 22. The bulkhead fitting cap 

provided the sealing force through a long compression sleeve. This assembly 

also provided an effective technique for quick and safe removal of the 

delicate probes. 

Data Acquisition System 

Hardware. - Experimental data were acquired with an ADAC Corporation 

data acqu1s1t1on system (DAS) shown in figure 2. The main components of the 

system were a Digital Equipment Corporation (DEC) LSI 1102 microcomputer with 

32K words RAM, the DEC RT-ll operating system, a DEC VT100 terminal, ADAC dual 

8-inch floppy disk drives, ADAC analog to digital and digital to analog 

convertors with software support packages, and an Axion IMP miniprinter. This 

system also contained an ADAC 1664 TTL input/output board that enabled the 

data system to send and receive signals across 64 ports. A control circuit 

interfaced between the 1664 TTL board and a model 555-48 CBM 48-port scanivalve. 

A layout of the various components used with the DAS is shown in figure 

23. The overall instrumentation setup involved connecting the various static 

taps and probes to the laboratory scanivalve box. The box, controlled by the 

DAS, sequentially connected each pressure to a single differential pressure 

transducer. Output from the transducer was integrated and sent to a Hewlett 

Packard (HP) model 3455A digital voltmeter, rather than to the DAS analog to 

10 
digital (A/D) converter because the converter resolution of 0.0012 volts was 

not low enough to accurately convert the transducer's millivolt signal. The 

DAS accessed the voltmeter through an IEEE buss. Other experimental outputs, 

such as flow temperature and probe position, were converted using the DAS A/D 

converter. All data were recorded on 8 inch floppy disks and subsequently 

reduced. The reduced data could be printed on the miniprinter, allowing 

immediate analysis. 

The transducer was a Barocel (Gould type 590) with a range of 134.6 cm of 

water and a full scale output of ten volts. It was calibrated using a Von 

Essen-Delft type 250 Betz micromanometer accurate to 0.0010 cm of water. The 

transducer calibration was nearly linear (a least squares curve fit had a 

standard deviation of 0.00055 cm of water). Because the transducer was 

sensitive to the temperature rise caused by recirculating the room air through 

the tunnel, the transducer was mounted in an insulated box to slow the 

temperature transients. Temperature changes only shifted the calibration, 

without altering the slope. With the linear transducer calibration, temperature effects could be corrected by referencing all outputs to the output at 

zero pressure difference. The transducer reference pressure was connected to 

one scanivalve port to provide the zero pressure output for each test run. 

Teeing one pressure and the transducer reference pressure to the Betz micromanometer established a reference pressure that was hand recorded and compared 

with the transducer reading. This comparison indicated the accuracy of the 

calibration and provided a continual verification that the calibration had 

remained constant. 

Software. - A flow chart of the program used for acquiring data with the 

DAS is in figure 24. Initially the program read input constants from a 

scratch file. The constants included run number, number of channels and 

number of samples to be collected from the DAS A/D converter, number of ports 

on the scanivalve to be sampled, number of samples to be gathered from each 

port, scanivalve stepping rate, and barometric pressure at the beginning of 

the run. Since the values of these constants could be changed external to the 

program, it could be used for a variety of instrumentation setups. The 

program opened a data file and assigned the current run number to that file. 

Acquisition constants along with the current time and date were entered into 

the file for reference purposes. Data from the DAS A/D converter were then 

collected, with the converted voltages stored in the data file. The collection rate was manually set on the DAS A/D board, which could sample up to 

12 kHz. The program then used the following method to record signals from the 

scanivalve transducer: the program first sent the scanivalve to its home port 

and read the output signal from the scanivalve to ensure the scanivalve had 

stepped properly. The program then waited a specified period (15-20 seconds) 

for the transducer signal to be integrated before recording voltages from the 

HP A/D converter using the IEEE buss instrumentation. The transducer signal 

was slowly recorded (2 Hz) over 10-25 seconds (20-50 samples) to resolve low 

11 
frequency oscillations in the integrated signal. Next, the program sequentially stepped the scanivalve, repeating the above process for the number of 

ports defined by the acquisition constants. Finally, the program collected 

data from the DAS AID converter a second time at the end of the run and closed 

the data file. Thus, the outputs connected to the DAS AID board could be 

averaged over the duration of the run. 

A program was also developed to reduce static pressure tap data. This 

program read the data stored on floppy disks, averaged the samples, computed 

average and standard deviations, and converted the pressure data to coefficients using the formula: 

Cp s 

= P s - P so 

(PT-Ps)o 

where ps-p.so was the pressure calculated from the transducer signal using the 

transducer calibration, and (PT-ps)o was the difference between the core flow 

total and static pressures measured with a pitot-static probe near the 

sidewall of the documented quadrant at the test-section entrance. In addition, the program calculated the average test-section entrance velocity and 

velocity head for the run based on the reference pressures. 

A second program reduced the five-hole probe acquired data. This program 

contained tables of the calibration parameters shown in figure 19. Local 

static, total, and dynamic pressures, along with the local pitch and yaw 

angles, were calculated by linearly interpolating between the calibration 

points. The program used these results to calculate various velocity 

components and pressure coefficients required for analysis purposes. Both 

reduction programs could be run immediately following data acquisition to 

provide real-time analysis. 

12 
RESULTS 

The test results are described in four sections. Initially the testsection entrance boundary condition is documented along with the floor static 

pressure distribution near the sidewalls. Subsequently the static pressure 

distributions on the endwall and cylinder surfaces are presented followed by a 

characterization of the five-hole probe measurements. Comparisons of the data 

with potential-flow calculations and experimental results described in the 

literature are also discussed. The flow field implied by limiting streamlines 

indicated by endwall and cylinder surface flow visualizations is then 

integrated with the vortex characteristics deduced from the other measurements 

to characterize the vortex formation process. 

A schematic of the test section along with the coordinate system used 1n 

this effort are shown in figure 25. The origin of the coordinate systems 

coincides with the cylinder and disk center on the lower endwall. Angular and 

radial positions are denoted by a and R, respectively. Cartesian coordinates 

representing streamwise, vertical, and transverse locations, are x, y, and z, 

respectively. The experiment was designed to create vertical and horizontal 

planes of symmetry at the test-section centerline and midheight, respectively. 

As shown in figure 25, the lower quadrant on the right side of the testsection, when viewed facing downstream, was chosen for documentation. 

All of the presented results were measured with a nominal test-section 

entrance dynamic pressure of five centimeters of water. These conditions 

correspond to ReD = 5.5 x 10 5 . An uncertainty analysis for the data 

acquisition is included in Appendix A. A tabulation of the data is contained 

in Appendix B. 

Boundary Conditions 

The mean flow conditions near the test-section boundary were documented 

with the support plate static pressure taps and pitot-static probe traverses. 

The core flow turbulence intensity was measured with a hot-wire probe. Data 

were recorded with the cylinder installed in the test section. 

The floor static pressure distribution measured near the test-section 

entrance is shown in figure 26. Blockage created by the cylinder caused a 

slight transverse static pressure gradient. The peak pressure at the tunnel 

centerline was approximately seven percent of the reference dynamic pressure 

above the reference static pressure. Away from the centerline, static 

pressure symmetrically decreased and approached the reference value near the 

tunnel sidewalls. 

13 
Static pressure variation in the streamwise direction measured near the 

tunnel sidewalls is shown in figure 27. The two distributions are similar, 

with the pressure decreasing in the streamwise direction. At the x = 0 plane, 

the pressure was approximately 22 percent of the dynamic head below the 

reference condition. The data in figures 26 and 27 document the flow symmetry 

about the tunnel centerline. 

The flow field entering the test section was characterized with pitotstatic probe traverses. Since the experiment contained two planes of symmetry, only the quadrant shown in figure 25 was documented in detail. Results 

from traverses acquired at the tunnel centerline, z/D = 1.021, and z/D = 

2.043, are shown in figure 28. (Though a failure in the blower impeller 

precluded taking additional traverses with the cylinder installed, more 

closely spaced traverses acquired during shakedown tests indicated uniform 

test-section entrance conditions.) The velocity distributions are normalized 

by the freestream velocity at the edge of the boundary layer. Although the 

freestream velocity varied across the entrance plane due to the cylinder 

blockage, as shown in figure 29, the normalized profiles are nearly identical. 

From the perspective of a velocity power law, the profiles are well represented by the 1/5.7 power-law shape shown in figure 28. The basis for this 

exponent value is defined later in the discussion concerning the plane of 

symmetry boundary-layer development. 

The boundary-layer parameters calculated for the above three traverses 

are shown in Table IV. 

TABLE IV. - TEST-SECTION ENTRANCE BOUNDARY-LAYER PARAMETERS 

WITH CYLINDER INSTALLED 

x/D = -2.72 

z/D olD o*/D 6x /D 0*/6 x Cf Re6 

0 0.099 0.0154 0.0114 1. 35 0.0028 6149 

1.021 0.099 0.0160 0.0118 1.36 0.0029 6156 

2.043 0.097 0.0152 0.0113 1.35 0.0029 6037 

The skin-friction coefficient was calculated using a technique developed by 

Clauser. The skin-friction velocity, uT ' is given by IT/P. Using u

T to 

normalize the mean velocity distribution, the inner twenty percent of the 

boundary layer, excluding the viscous sublayer, can be universally represented 

by the following expression, where y+ has been substituted for yut/v: 

14 
u+ = U 

5.6 log y+ + 4.9 

UT 

+ for y > 10 (1) 

Defining the local skin-friction coefficient, Cf, as T/(1/2p~2), equation (1) can be rewritten as a universal family in terms of the velocity ratio 

u/U= and Re y with Cf as a parameter: 

u = {?- [5.6 log (Rey ~)+ 4.9] (2 ) 

Uoo 

A sample Clauser plot is in figure 30. With the experimental data acquired 

near the endwall plotted in this form, Cf was determined from the best fit 

to the data. The coefficients, shown in Table IV, are nearly identical across 

the entrance plane. 

The pitot-static probe was too large to acquire data in the viscous sublayer. A correlation developed by Burton (ref. 8) for the mean velocity in 

the sublayer was used in the calculation of displacement and momentum thicknesses. This correlation is given by 

y ~~ ~ C+ + (8~:4r) (3) 

The mean velocity distribution in the sublayer, calculated with this correlation and the above determined skin-friction coefficients, was matched with 

that from the pitot-static probe. The combined distributions were integrated 

to determine the two integral boundary-layer thicknesses. The data in Table 

IV show little variation in these parameters. The shape factor, o*/9 x , is 

also quite uniform and at a level typical of a constant-pressure turbulent 

boundary layer on a flat plate, as indicated by Schlichting 

(re f. 9). 

Turbulence in the core flow was measured using a hot-wire probe with a 

single wire oriented perpendicular to the main flow. The turbulence intensity 

was less than one percent. 

15 
Surface Static Pressure Measurements 

static pressure measurements were obtained on the endwall and cylinder 

surfaces using pressure taps located at the positions shown in Tables II and 

III. Detailed distributions were acquired in the quadrant shown in figure 25. 

Additional measurements were made in the other quadrants to check the flow 

symmetry. The pressures are presented in coefficient form using the polar 

coordinate system defined in figure 25. These measurements are important 

because they are the only nonintrusive measurements in these tests. They 

serve as a basis for comparison with the flow visualization patterns and fivehole probe results. 

Endwall. - Plane of Symmetry: The endwall static pressure distribution 

in the plane of symmetry, 8 = 0, is presented in figure 31. Radial locations 

are normalized by the cylinder diameter, and the ordinate corresponds to the 

cylinder leading edge. Upstream of the separation region, the distribution 

displays a characteristic rise in pressure due to the blockage of the 

cylinder. Unlike the potential-flow distribution shown by the solid line, the 

experimental distribution begins to decrease a short distance downstream of 

the saddle point determined from the endwall flow visualizations. The 

distribution displays a local minimum approximately two tenths of a cylinder 

diameter from the cylinder leading edge, then increases rapidly from that 

point to a value of one at the endwall-cylinder junction. The coefficient 

value of one indicates that loss-free core flow stagnated at the junction. 

Location of the saddle point in an adverse pressure gradient, not at the local 

peak pressure, is consistent with the work of Langston and Wagner (ref. 10). 

They applied Oswatitch's model to saddle-point behavior and predict that the 

saddle point occurs in an adverse pressure gradient. 

The data in figure 31 also provide an indication of the flow unsteadiness 

in this region. Data at several radial locations were acquired during four 

different runs. The data repeatability is quite good upstream of the saddle 

point and near the cylinder, indicative of relatively steady flow in these 

regions. In the separated zone between the cylinder and saddle point, a 

significant range in the measured pressures is apparent and is attributed to 

flow unsteadiness in the vicinity of the rather substantial pressure 

gradients. McMahon, et. al. (ref. 12) also found high turbulence levels in 

the corresponding region of their experiment. 

The experimental pressure distribution parallels the potential-flow 

distribution upstream of the saddle point. The experimental values, however, 

are slightly lower in magnitude. This difference is a result of the mean flow 

accelerating through the test section due to boundary-layer buildup on the 

uncontoured endwall surfaces. Experimental pressures in figure 31 are 

corrected for the thickening boundary layer. The correction represents the 

decrease in pressure associated with a one-dimensional flow passing through a 

duct with contracting sides simulative of the measured boundary-layer 

16 
thickening. The corrected pressures are close to the potential-flow values, 

though the values upstream of the saddle point are higher. This difference 1S 

consistent with the five-hole probe results which show that the static 

pressure was not constant through the boundary layer. Static pressures 

measured near the endwall are larger than core-flow values, which will be 

shown to be well represented by the potential flow solution. 

The experimental distribution in figure 31 is plotted with the limited 

results of Ram (ref. 13) and East and Hoxey (ref. 14) in figure 32. These 

experiments were conducted in large wind tunnels so that corrections for 

thickening boundary layers are insignificant. Static pressures measured 

upstream of the saddle point are close to the corrected values from this 

experiment, although Ram's data are slightly higher than the other two sets. 

Ram's results in the separation zone exhibit the same trend as data from this 

experiment. 

Documented Quadrant: Potential-flow and measured endwall static pressure 

contours throughout the documented quadrant are shown in figure 33. The 

potential-flow results are for a cascade of cylinders spaced to simulate the 

test-section sidewalls. These potential-flow calculations were discussed 

previously with respect to the cylinder design. Comparing these results, the 

pressure distributions are quite similar outside of the separation region. 

The experimental pressure coefficients (representing 1007 pressure tap 

readings) are slightly lower due to the small acceleration of the mean fiow 

caused by the endwall boundary layers. Inside the separation region, the 

experimental contours display a large dip near RID = 0.72. This dip, which 

was observed in the plane of symmetry data, persists around the cylinder up to 

approximately 8 = 60 deg. Beyond this angular plane, the dip is no longer 

present, and the the experimental contours are shaped more like that of the 

potential flow contours. This similarity indicates that the strong pressure 

field associated with the mean flow acceleration around the cylinder, which is 

represented by the potential-flow solution, negated the local pressure minimum 

created in the separation region. The experimental pressures near the 

cylinder and 90-deg plane are higher than the potential-flow values. 

Evidently, the separation in the cylinder wake retarded the approaching flow 

next to the cylinder, creating the higher static pressures. 

Cylinder. - The cylinder surface lateral pressure distribution at five 

angular positions is shown in figure 34. The distribution along the stagnation line (8 = 0) is constant except for the slight dip near the endwall 

region. The cylinder saddle-point location determined from the cylinder flow 

visualizations is in the range 0.031 < y/D < 0.068. For this range, the 

pressure distribution indicates that the cylinder saddle point was situated 1n 

an adverse pressure gradient, as with the endwall saddle point. 

17 
Proceeding around the cylinder from the stagnation line, the profiles up 

to the 45-deg plane are relatively flat, but they display a slight pressure 

increase near the endwall. The profiles at higher angular locations become 

increasingly distorted, taking on a bowed shape. This distortion can be 

attributed to the separation in the cylinder wake. Humphreys (ref. 15) and 

Farell and Blessman (ref. 16) show, for an approaching two-dimensional flow, 

spanwise variations in cylinder surface pressure distribution that were caused 

by instabilities in the downstream separation. Although the ReD of 5.5 x 

105 in this experiment is slightly larger than that for which these variations 

were observed, the variations were highly dependent on the end conditions. 

Wake instabilities for the low aspect ratio cylinder used in this experiment 

can be expected to be enhanced by the endwall separations. 

The cylinder angular pressure distribution is in figure 35. Profiles 

obtained near the endwall (y/D = 0.011), the quarter-span (y/D = 0.255), and 

the midspan (y/D = 0.511) are displayed. The distribution for potential flow 

through a cascade of cylinders is also shown. The experimental values agree 

with potential-flow values up to approximately 45 deg. At larger angles, the 

experimental pressures are higher than the potential-flow distribution. Data 

presented by Hoerner (ref. 17) for two-dimensional flow around a single 

cylinder is also in figure 35. Since the experimental profiles are in reasonable agreement with Hoerner's data, even up to the 90-deg plane, the cylinder 

surface mean pressure distribution is predominantly like that expected for 

two-dimensional viscous flow. The spanwise pressure variations created by the 

endwall separation are small due to the manner in which the endwall separation occurred. Core flow entered the endwall region near the plane of symmetry, immersing the entire cylinder span in loss-free flow. This flow was 

nearly uniformly accelerated around the cylinder, leading to a surface pressure distribution much like that for two-dimensional flow. 

Five-Hole Probe Measurements 

Data were acquired with a five-hole probe in the angular planes defined 

by 8 = -5, 0, 5, 25, 45, and 90 deg. The probe was traversed at 81 radial 

locations to define the flow field adjacent to and inside of the separation 

region. Data were recorded from y/D = 0.0085 to the test-section midspan. 

This smaller value, approximately one probe tip diameter from the endwall, 

represents the lowest point for which data could be acquired without endwall 

interference. This determination was primarily based on endwall static data 

acquired in this test program with and without the probe in proximity of a 

static pressure tap. Camarata et. al. (ref. 7) also used this guideline in 

their tests. The data acquired in the 8 = -5-deg plane are not presented in 

detail since they were acquired only to document the flow symmetry. A listing 

of all the reduced data, including static and total pressure coefficients, yaw 

angle, pitch angle, and velocity ratio, are included in Appendix B. 

18 
Endwall Region. - Data obtained up to 0.2 cylinder diameters from the 

endwall are discussed. The data in the region between ylD = 0.2 and the testsection midspan (y/D = 0.511) do not substantially vary from the midspan 

values. The endwall-region data are presented in the form of in-plane velocity vectors, static pressure contours, and total pressure contours. 

In-Plane Velocity Vectors: The in-plane velocity components for the 

angular planes given by S = 0, 5, 25, 45, and 90 deg are presented. The data 

are displayed as vectors centered at the measurement point. The in-plane 

pitch angles are based on the in-plane components, not on the total velocity 

measured with the five-hole probe. The vectors are normalized by the 

reference velocity measured at the test-section entrance. The ordinate and 

abscissa in the figures represent the cylinder O.D. and endwall, respectively. 

The plane of symmetry velocity vectors are shown in figure 36. Upstream 

of the endwall saddle point the vectors take on the appearance of a twodimensional boundary layer, though vortex stretching is present. The outer 

edge of the approaching boundary layer at RID = 0.94 is at ylD = 0.13. 

Downstream of the saddle point, reverse flow was not measured until 

RID = 0.766. The separation streamline between forward and reverse flow is 

very shallow. A straight line drawn from the saddle point to the streamline 

location at RID = 0.766 represents a separation angle of approximately four 

degrees. The shallowness of this line is markedly different from the multiple 

vortex models developed in the literature, e.g. that of Baker (ref. 18). 

Following the flow field from the saddle point toward the cylinder, the 

velocity vectors indicate that flow in the boundary layer and outside of the 

boundary layer pitched downward, rotated 180 degrees, and proceeded toward the 

saddle point. Blank areas are present in the traverses nearest the cylinder 

because the flow pitch angle was out of the probe calibration range 

(-29 ~ ~ ~ 30 deg). Data were acquired in these regions, however, to 

qualitatively determine the flow direction. The yaw angles determined for the 

traverse at RID = 0.638 are shown in figure 37. The shaded symbols, which 

represent data acquired outside the probe calibration range, are uncorrected 

for pitch angle effects. Based on the authors' experience with probe calibrations at large pitch angles, the corrections would be on the order of two to 

ten degrees. The data in figure 37 show that flow in the region 0.04 < ylD 

< 0.08 was in the direction of the cylinder. The change between forward and 

reverse flow was quite abrupt. The yaw angle changed approximately 140 deg 

between y/D = 0.037 and 0.045. This pattern typifies that of the other 

traverses where reverse flow was measured. 

19 
The plane of symmetry flow pattern deduced from the five-hole probe data, 

surface static pressure data, and surface flow visualizations is sketched in 

figure 38. Loss-free fluid from outside the boundary layer stagnated at the 

endwall-cylinder junction. Five-hole probe measurements at RID = 0.596 

contain substantial negative pitch angles up to ylD = 0.3, indicating that 

flow from approximately two approaching boundary thicknesses away from the 

endwall entered the juncture region. The reverse flow accelerated as it moved 

away from the endwall-cylinder juncture to accommodate the incoming flow, 

which separated at a shallow angle. The favorable endwall static pressure 

gradient is consistent with this pattern. At approximately RID = 0.72, 

reverse flow started stagnating with incoming flow. The abrupt reverse flow 

deceleration caused by the blockage is indicated by the strong endwall adverse 

pressure gradient in this region. The reverse flow did not roll up to form a 

vortex, however. The vectors clearly show that a closed vortex was not 

present in the plane of symmetry, though positive pitch angles in a portion of 

the reverse flow at RID = 0.72 and ylD = 0.02 may indicate the start of the 

vortex formation. Rather than rolling up, flow passed out of the plane and 

proceeded tangentially around the cylinder. Note that the reverse flow was 

confined to the lower 15 percent of the boundary layer as it passed out of the 

plane. 

The velocity vectors and corresponding flow pattern in the 5-deg plane 

are shown in figures 39 and 40, respectively. The data display similar trends 

to those observed in the plane of symmetry. Flow from both insid~ and outside 

the boundary layer pitched downward and formed a recirculation zone. Reverse 

flow closer to the cylinder accelerated toward the separation line. As in the 

plane of symmetry, the reverse flow a small distance away from the endwall 

eventually was blocked by the incoming flow and tended to pass tangentially 

out of the plane rather than to roll up into a vortex. The velocity 

magnitudes near the endwall for 0.74 < RID < 0.86 are small. These low inplane velocities correspond to flow from the plane of symmetry region passing 

tangentially through the plane. The rudiments of a vortex are again present 

in the traverse at RID = 0.72, where the reverse flow had a small positive 

pitch. 

Velocity vectors for the 25-deg plane are displayed in figure 41. The 

vectors show a well-formed vortex. The vortex, then, became fully formed 

somewhere between the 5-deg and 25-deg planes. The vortex center in the 25-

deg plane was at RID = 0.71 and ylD = 0.035. This was approximately one third 

of the incoming boundary-layer thickness from the endwall. The vortex itself 

was confined to a region less than one boundary-layer thickness from the 

endwall. The radial location of the vortex center is close to that of the 

local static pressure minimum on the endwall in this plane. 

20 
The velocity vectors in the 45-deg plane, figure 42, also define a fully 

formed vortex. Between the 25-deg and 45-deg planes, the vortex center moved 

radially outward to R/D = 0.735. As in the 25-deg plane, the in-plane 

velocities next to the endwall oetween the vortex and separation line were 

small because this region contained tangential flow from the plane of symmetry 

region. 

The vortex structure in the 90-deg plane was much weaker than that in the 

45-deg plane. The velocity vectors in figure 43 faintly show a vortex center 

at R/D = 0.80 and y/D = 0.07. The vortex was not symmetric, with the 

secondary flow near the endwall stronger than that on the core-flow side of 

the vortex. The reduced vortex strength, which was also indicated by the 

endwall static pressure distribution, can be attributed to the streamwise 

acceleration of the mean flow around the cylinder. 

Static Pressure Contours: Local static pressure was calculated from the 

five-hole probe results using Bernoulli's equation. Static pressure 

coefficient contours corresponding to the velocity vector plots are showll ~n 

figures 44 to 48. 

Upstream of the endwall saddle point, the static pressure contours in the 

plane of symmetry are nearly vertical except near the endwall surface. The 

pressures adjacent to the endwall were larger than those measured in the core 

flow. This trend was seen before in the comparison between potential-flow and 

corrected endwall static pressures in the plane of symmetry (fig. 31). The 

assumption of constant static pressure through the two-dimensional boundary 

layer at a given streamwise location upstream of the saddle point is 

inaccurate. The cylinder created a stronger adverse pressure gradient in the 

viscous sub layer. 

The pressure distribution closer to the cylinder was significantly skewed 

by the recirculating flow. A local pressure minimum at y/D = 0.04 and 

R/D = 0.73 is marked by the closed contours. The velocity vectors show that 

this small minimum is not associated with a vortex. The minimum pressure in 

the plane was adjacent to the endwall at the same radial location. This 

minimum is associated with the reverse flow first accelerating away from the 

cylinder and then decelerating when blocked by the streamwise flow. The 

coefficients near the cylinder are close to one. They indicate that low-loss 

fluid from outside the boundary layer passed next to the cylinder at a low 

velocity prior to £tagnating at the endwall cylinder junction. 

The pressure contours for the 5-deg plane, figure 45, are similar to 

those in the plane of symmetry. Closed contours are centered around a slightly lower local minimum at y/D = 0.04. The minimum pressure in the plane was 

next to the endwall at R/D = 0.73. Due to the acceleration of the flow around 

21 
the cylinder, the coefficients next to the cylinder are lower than those ~n 

the plane of symmetry. 

The contours in the 2S-deg plane, figure 46, clearly correspond to the 

well-formed vortex structure shown in the corresponding velocity vector plot. 

The center of the closed pressure contours corresponds with the vortex center 

indicated by the velocity vectors. The static pressure coefficient at the 

vortex center is 40 percent of the test-section entrance dynamic head below 

the test-section midspan coefficient measured at the same radial position. 

The pressure contours indicate that the pressure distribution upstream of the 

separation line was also substantially altered by the vortex structure. 

The closed contours in the 45-deg plane, shown in figure 47, again are 

centered about the vortex center that is indicated by the corresponding 

velocity vector plot. The pressure coefficient corresponding to the vortex 

center is 45 percent of the test-section entrance dynamic head below the 

midspan value at the same radial location. This pressure was not the smallest 

recorded pressure in the plane, however. The pressures adjacent to the 

cylinder were lower due to the two-dimensional acceleration of the flow around 

the cylinder. The contour lines representing the flow close to the cylinder 

are nearly vertical, as would be expected for a two-dimensional type flow. 

The region with vertical contours is larger than that shown for the 2S-deg 

plane. 

In the 90-deg plane, where the vortex strength was signficantly reduced, 

pressure profiles in figure 48 show that pressure at the vortex core was only 

slightly less than surrounding pressure. The contours tend to be vertical and 

increase in value radially outward. The pressure field associated with the 

two-dimensional acceleration of the flow around the cylinder was clearly 

dominant. The vortex had only a small local effect on the pressure distribution. 

Total Pressure Contours: Total pressure data from the five-hole probe 

measurements have been expressed as loss coefficients: 

Cp T 

= 

PT - PT o 

qo 

22 

(4) 
where the test-section entrance conditions are again used for references. The 

loss contours for the plane of symmetry are shown in figure 49. Upstream of 

the saddle point, the contours are nearly horizontal. like an attached twodimensional boundary layer. The edge of the boundary layer approaching the 

saddle point was at y/D = 0.13. Downstream of the saddle point, the low-loss 

contour bends around and touches the abscissa at R/D ~ 0.54. This pattern 

shows the radial extent of the low-loss fluid in front of the cylinder. The 

contours show the high total pressure loss associated with the low-loss fluid 

accelerating away from the endwall-cylinder junction. The region of highest 

loss, Cp = 0.6, occurred 'at R/D ~ 0.74, where reverse flow next to the 

T 

endwall interacted with streamwise flow. 

The loss distribution in the 5-deg plane is nearly identical to that of 

figure 49. For the 25-deg plane, however, the contours in figure 50 show high 

losses at the location corresponding to the vortex. The losses at the vortex 

center were 80 percent of the entrance dynamic pressure. Though these losses 

associated with the rollup were high, they were localized. The region of low 

losses adjacent to the cylinder location is larger than the same region in the 

plane of symmetry. 

The contours for the 45-deg plane, figure 51, are similar to those for 

the 25-deg plane. Again, a high-loss region is associated with the vortex 

core and a low-loss region is adjacent to the cylinder. 

For the 90-deg plane, the contours in figure 52 indicate that the highloss region is displaced to the same location as the vortex center. The highloss fluid created during the rollup process, then, simply accumulated at the 

vortex center and passed around the cylinder with the vortex. The magnitude 

of the losses in the vortex did not increase during the passage from the 25-

deg to the 90-deg plane. The size of low-loss fluid region adjacent to the 

cylinder increased only a small amount from that same region in the 25-deg 

plane. 

Test-Section Midspan. - Midspan values for a large aspect ratio cylinder 

should agree with the inviscid solution through the 45-deg plane. Beyond the 

45-deg plane, the separation in the cylinder wake influences flow near the 

cylinder. With a cylinder aspect ratio in this test of only one, however, the 

endwall separations could have altered the midspan values. This comparison 

with the potential-flow solution indicates that the horizontal plane of symmetry for the low aspect ratio cylinder of this test can be considered as an 

inviscid boundary. 

The midspan static pressure distribution measured in the plane of 

symmetry appears in figure 53 along with the potential-flow values. As with 

the endwall pressures, the coefficients are less than the potential-flow 

23 
values. By applying the appropriate boundary layer correction to the 

pressures measured upstream of the saddle point, the potential-flow solution 

agrees with experimental results. Although local corrections for pressures 

measured above the separated boundary layer cannot be calculated, the uniform 

difference between the measured and potential-flow values near the saddle 

point suggests that corrections applied to regions upstream of the saddle 

point are valid for regions slightly downstream of the saddle point as well. 

Since the flow decelerated and eventually stagnated at the cylinder leading 

edge, the boundary-layer correction for the pressures measured closer to the 

cylinder is small. The data in figure 53 show this trend. The difference 

between the distributions decreases to zero at the cylinder leading edge. 

The midspan pressure distributions for the 25-, 45-, and 90-deg planes 

are shown in figure 54 and are accompanied by potential-flow profiles for both 

a single cylinder and a cylinder cascade. Pressures measured at locations 

farther from the cylinder are less than the potential-flow values. 

Differences are again like the corrections applied to the plane of symmetry 

measurements. The pressures measured close to the cyl~nder in the 25- and 45-

deg planes agree with the potential-flow solution. The small pressure 

gradient imposed by the increasing endwall boundary-layer thickness was almost 

completely negated by the two-dimensional pressure field setup around the 

cylinder. Data measured in the 90-deg plane next to the cylinder are 

significantly less than the potential-flow values. This difference, which was 

also seen in the cylinder surface static pressure data (fig. 35), is 

attributed to the separation in the cylinder wake. 

The measured midspan yaw angle distributions for the 25-, 45-, and 90-deg 

planes are shown with potential-flow values in figure 55. The potential-flow 

angles correspond to flow through a cylinder cascade. The angles calculated 

for flow around a single cylinder are nearly identical to those for the 

cylinder cascade. The measured data in figure 55 are in agreement with the 

potential-flow distributions throughout the flow region. The largest 

deviations are in the 90-deg plane. A small crossflow moving radially outward 

from the cylinder was present at the midspan. The resultant yaw angle was 

approximately 3 deg throughout the plane. 

The agreement shown in the above comparisons indicates that the midspan 

flow can be represented as potential flow. The boundary condition at the 

midspan plane of symmetry, then, can be specified with a potential-flow calculation. In defining the boundaries for the calculation, the endwall contours 

should incorporate the previously discussed boundary-layer corrections. 

Boundary Layer Development in the Plane of Symmetry. - The boundary layer 

approaching the endwall saddle point was characterized using the five-hole 

probe measurements. Since the plane of symmetry flow upstream of the saddle 

24 
point is two dimensional, the boundary-layer displacement thickness, momentum 

thickness, shape factor, and wall shear stress were calculated with the same 

two-dimensional correlations used to characterize the boundary layer at the 

test-section entrance. 

The variation in the skin-friction coefficient along the plane of 

symmetry is shown in figure 56. The coefficients decrease in value from 

0.0028 at the test-section entrance to an assigned value of zero at the saddle 

point. The coefficients far upstream of the saddle point agree with the twodimensional correlation of Ludweig and Tillmann (ref. 19): 

C

f = 0.246e-l.561H Re -0.268 

e (5) 

The correlation breaks down and overpredicts the coefficients near the saddle 

point. 

The coefficients measured by East and Hoxey are also in figure 56. 

Because of the thicker boundary layer in their experiment, their values are 

lower than those of this experiment. The Ludweig-Tillmann correlation 

approaches their experimental value at the farthest upstream point but again 

overpredicts the experimental cOefficients near the saddle point. The saddle 

points for the two experiments are at the same normalized radial location. 

Calculated shape factors along the plane of symmetry are plotted in 

figure 57. The shape factor progressively increases from the test-section 

entrance value of 1.35. The shape factor at the saddle point could not be 

calculated since Burton's (ref. 8) laminar sublayer correlation is not defined 

for Cf = O. Extrapolation of the distribution in figure57 indicates the 

boundary layer separated where H = 2. The shape factors calculated by East 

and Hoxey show the same trend. An extrapolation of their data shows that the 

boundary-layer shape factor in their experiment was approximately the same at 

separation. 

For a given normalized radial location, the shape factor calculated for 

East and Hoxey's thicker boundary layer is less than the corresponding value 

from this experiment. The boundary-layer parameters for the two experiments 

can be correlated using the technique discussed by Schlichting (ref. 9). Mean 

velocity profiles are assumed to be represented by a power law profile: 

u = (!..)l/n 

Uec 0 

(6) 

25 
Using this velocity distribution and performing the required integrations, 

the following expressions relating the boundary-layer parameters are: 

1 n n+2 

0*/0 

n+l 

ex/O H = (7) 

(n+l) (n+2) n 

A profile factor n is given by: 

n = I _ (u<::) y (8) 

where u(e x) denotes the velocity in the boundary layer at y = ex' The 

significance of the profile factor is that velocity profiles for a favorable 

pressure gradient correspond to n < 0.46, for a constant pressure correspond 

to n = 0.46, and for an adverse pressure gradient correspond to n > 0.46. 

Using the power law formulation for the mean velocity, the profile factor can 

be related to the shape factor: 

n = 1 _ (e

x

/o)2/n = 1 _ (H-l )H-l 

H(H+l) 

(9 ) 

Thus a unique relationship exists between the shape and profile factors 

independent of the boundary-layer physical size. 

Several experimental profiles are plotted in figure 58 using the power 

law formulation. The profiles: acquired at points with significantly 

different shape factors, are correlated in this formulation. The relationship 

between the shape and profile factors (equation (9)) is shown in figure 59 

along with data from this and East and Hoxey's experiment. The predicted 

curve fits the data from this experiment and deviates only slightly from the 

East and Hoxey results. The experimental values for n are all greater than 

0.46, consistent with the adverse pressure gradient. 

Detailed data were not acquired in this study upstream of the separation 

line except in the plane of symmetry. The agreement shown in the plane of 

symmetry implies that the detailed East and Hoxey results can be used to 

characterize the flow upstream of the region where five-hole probe 

measurements were acquired in the present study. 

Pressure Loss. - The mass-averaged pressure loss at any streamwise plane 

in the test section is given by: 

26 
Zw Yms 

J J Cp u dy dz 

z 0 T 

r> 0 

vp Zw Yms 

(0) 

T 

J J u dy dz 

Zo 0 

where, because of the low Mach numbers, density is assumed to be uniform in 

the plane. The limits in equation (10) reflect the two planes of symmetry. 

The sidewall boundary layers were not measured and are not included in the 

loss calculation. This definition was used to calculate the average loss at 

the test-section entrance (x/n = -2.72) and 90-deg (x/n = 0.0) planes. 

As explained previously, Burton's (ref. 8) correlation was used to calculate velocities in the viscous sublayer of the entrance plane. Because this 

correlation could not be used in the separated region of the 90-deg plane, a 

parabolic segment was fit between the lowest five-hole probe data point and 

the endwall. The experimental values in equation (10) were integrated 

assuming straight line segments between the data points. 

Loss distributions for the entrance and 90-deg planes are in figures 60 

and 61, respectively. Each point represents the mass-averaged loss of a 

particular traverse. The losses calculated across the entrance plane are 

reasonably uniform at four percent of the reference dynamic pressure. The 90-

deg plane losses are nonuniform. Adjacent to the cylinder, the losses are 

quite low since low-loss fluid from the core flow occupied this region. 

Relatively high losses at z/n = 0.8 are associated with high-loss fluid that 

accumulated in the vortex core during the rollup process. Farther away from 

the cylinder, z/n > 1.15, losses level out at around five percent of the 

reference dynamic pressure. 

Control volume has only a small effect on these loss calculations. Average loss in the entrance plane does not depend on control volume because of 

the uniform loss distribution. Though the loss distribution in the 90-deg 

plane in nonuniform, average loss in the plane is approximately equal to the 

average of the traverses acquired outside of z/n = 1.5. The average value for 

the 90-deg plane, then, is not strongly weighted by losses outside the separation region. 

A check on the integration procedure for calculating the above losses was 

accompliShed by comparing the calculated mass flow through each of the planes 

(the denominator in equation (10)). Mass flow through the 90-deg plane was 

3.4 percent above that in the entrance plane. This agreement indicates that 

the above integration procedure provided accurate values for c.;-. T 

27 
A comparison for the above loss calculations is the loss for an 

equivalent turbulent boundary layer developing on a flat plate without a 

cylinder. Substituting the power law formulation for the velocity distribution (equation (6)) into equation (10) yields: 

Cp T 

n n 

n+l n+3 

( ) 

n+l 

n MS n 

n+l 8 

(1) 

where n = H~l from equation (7). The calculated loss coefficient at the t~stsection entrance centerline, using measured boundary-layer parameters, is CpT 

= 0.038. This value is very close to the 0.039 value calculated by 

integrating experimental data. In the absence of a pressure gradient, 

Schlichting (ref. 9) gives the following expression for the boundary-layer 

thickness as a function of streamwise distance: 

15(x) ( 

UcoX)-1/5 

0.37 x -

v 

(12) 

Equation (12) was used to estimate the flat-plate boundary-layer development 

of a flow starting with the test-section entrance conditions. The boundarylayer thickness was calculated for a length equal to x/D = 2.72 (the distance 

to the 90-deg plane). The calculated value of 8 was substituted into equation 

(11), resulting in a loss coefficient of 0.054. This value is identical to 

the measured loss in the 90-deg plane. It is concluded, then, that the 

overall loss associated with the horseshoe vortex formation is small. 

Langston, et. al. (ref. 4) found the same trend in their cascade experiment. 

The measured losses in the initial portion of the cascade were only slightly 

larger than those measured upstream of the saddle point. Significant losses, 

measured farther downstream in the passage, were associated with the interaction of the passage vortex with the airfoil suction surface in the region of 

uncovered turning. 

Surface Flow Visualizations 

Technique. - A qualitative picture of the flow field adjacent to the 

endwall and cylinder surfaces is indicated by the direction of the limiting 

streamlines in these regions. A technique developed by Langston and Boyle 

(ref. 2) was used to visualize these surface streamlines. This technique 

28 
involved attaching drafting film dotted with permanent ink on the endwall and 

cylinder surfaces. Best results were achieved with ink dots that had dried 

for several days before testing. Just prior to turning on the wind tunnel, a 

thin continuous coating of oil of wintergreen (synthetic methyl salicylate) 

was sprayed on the film. The ink dots dissolved and diffused into the oil 

coating. When the tunnel was turned on and quickly brought up to operating 

conditions, the dissolved ink flowed in response to the wall shear forces. 

Each ink dot acted as a stationary source of ink to produce a well-defined ink 

trace. Within a few minutes, the oil of wintergreen evaporated, and the ink 

traces left a permanent picture of the surface streaklines. These streaklines 

were used to locate separation and attachment points and lines. The nature of 

the flow processes near the cylinder and endwall surfaces was inferred from 

the patterns. 

This technique proved to be superior to other ink-type flow visualization 

techniques primarily because of the evaporation characteristics of the oil of 

wintergreen. The viscosity of the visualization medium is a critical factor 

with some of the other techniques. In regions with relatively high velocities, a high viscosity medium is required to resist the strong shear forces. 

In many cases, the medium is carried downstream, leaving a void in the flowvisualization pattern. Alternatively, a low viscosity medium is needed in 

relatively low velocity regions to avoid medium accumulation. The result of 

this compromise on visualizing the surface flow around an obstacle has been 

that the flow visualization pattern is void of the medium near the separation 

line and suffers from an agglomeration of medium near the saddle point. The 

endwall flow visualizations of Baker (ref. 18) and Moore and Forlini (ref. 20) 

indicate this problem. Consequently, the interpretation of the patterns 

regarding the nature of the internal flow field has been inconclusive. The 

oil of wintergreen viscosity is relatively low. Distinct ink traces were 

obtained even near the saddle point. The oil evaporates quickly in the high 

velocity regions, however, so that the ink is not carried out of these 

regions. 

One problem associated with this technique was recognized. If an excessive amount of oil was sprayed on the surface in the separated region, a small 

dam of oil was created around the cylinder by flow moving back toward the 

separation line. The dam altered the path of the reverse flow and caused a 

skewing of the streakline pattern in the separation region. This problem was 

mitigated by applying only a very thin oil coating in the separation region in 

front of the cylinder. Streaklines were obtained by repeated applications 

over several runs. 

Endwall Visualization. - A portion of the surface streaklines on the 

endwall in front of the cylinder is shown in figure 62. A saddle point can be 

identified where the forward and reverse streaklines combine in the plane of 

29 
symmetry. The separation line corresponding with the saddle point has been 

drawn on the visualization. The precise location of the line is somewhat 

difficult to determine from the ink traces. It is hard to discern where the 

ink traces are actually combining to form the separation line as opposed to 

merely converging. 

The saddle point radial location, measured from the cylinder center, is 

approximately 0.89 cylinder diameters. This normalized saddle point location, 

repeated during many flow visualization tests, agrees with the results of 

Boyle (ref. 21) and East and Hoxey (ref. 14) which were acquired for cylinders 

with diameters one half and twice the cylinder diameter of this experiment. 

Unlike the case of two-dimensional flow separation, where separation position 

can vary from test-to-test, the saddle-point position remained constant from 

run-to-run. Near the cylinder, an attachment point can be discerned in the 

plane of symmetry. The corresponding attachment line is not easily identifiable. No other singular points can be seen in the flow visualization. 

All of the streaklines between these two points indicate flow moving toward 

the separation line. 

A larger view of the streakline pattern around the cylinder is shown In 

figure 63. The saddle point (denoted by the + sign) and attachment point 

previously identified in the plane of symmetry are also evident in figure 63. 

A sketch of the flow pattern is shown in figure 64. The flow visualization 

pattern indicates another region of converging streaklines between the 

separation line and cylinder. (This convergence is also apparent in figure 

51, though not as dramatically.) A line of accumulated ink is formed by the 

streaklines beginning approximately 15 deg off the plane of symmetry. The 

steak pattern between the plane of symmetry and B = 15 deg indicates that 

reverse flow moved toward the separation line and then proceeded tangentially 

around the cylinder. Beyond the l5-deg plane, reverse flow streaklines 

abruptly stop leading to the line of accumulated ink. This pattern indicates 

that reverse flow adjacent to the endwall was entrained into the fluid 

interior in the vicinity of the 15-deg plane. Since the five-hole probe data 

show that the horseshoe vortex was formed between the 5-deg and 25-deg planes, 

this pattern suggests that flow adjacent to the endwall rolled into the vortex 

at approximately the l5-deg plane. Determination of whether the surface line 

corresponding to the accumulated ink is a limiting streamline is difficult. 

In the work of Lighhill (ref. 22), a separation line must originate from a 

singular point of a particular type, a saddle point, as the separation line 

identified in this experiment does. The flow visualization clearly shows that 

the line of accumulated ink does not extend from a saddle point in the plane 

of symemtry. In his terminology, then, a separation line is not associated 

with the flow adjacent to the endwall being entrained into the vortex. Tobak 

and Peak (ref. 23) have developed a concept that a separation line does not 

necessarily originate from a saddle point. They categorize separation lines 

originating at a saddle point as global lines of separation and separation 

30 
lines not originating from saddle points as local lines of separation. In 

this context, the line of accumulated ink could be interpreted as a local 

separation line. However, there is little evidence to indicate that the endwall flow outside the line of accumulated ink separated. The streaklines 

indicate that this flow simply moved tangentially around the cylinder adjacent 

to the line of accumulated ink. The streaklines suggest a convergence of 

streamlines in the vicinity of the accumulated ink but do not conclusively 

indicate a combining of streamlines as required for a separation line. 

Other endwal1 flow visualization results also indicate a single separation line and saddle point. The flow visualization pattern obtained by East 

and Hoxey (ref. 14), using oil, is similar to those of this experiment. A 

photograph of the endwa1l pattern, contained in figure 65, also shows a line 

formed by an accumulation of ink between the streamlined cylinder and the 

separation line. But a second saddle point clearly was not present in the 

plane of symmetry. The region adjacent to the separation line again appears 

to have been filled by ink emanating from the plane of symmetry region. The 

medium deposited between the accumulated oil and separation line does not show 

a second attachment line. The presence of a single saddle point in front of a 

cylinder was also observed by Langston and Boyle (ref. 2) in their endwal1 

visualizations which were obtained with the technique used in this experiment. 

Cylinder Visualization. - Flow visualizations obtained on the cylinder 

surface elucidate the flow pattern at the endwal1-cylinder junction. Streaklines that formed on the upper portion of the cylinder are shown in figure 

66. The vertical plane of symmetry is at the center of the pattern. Near the 

cylinder midspan, the ink in the plane of symmetry flowed downward. The shear 

forces near the stagnation line were too small to negate gravitational effects 

in this region. The ink in the plane of symmetry started flowing upward at 

approximately two approaching boundary-layer heights from the endwa11. This 

pattern implies that flow from outside the approaching boundary layer entered 

the separation region. This pattern was previously identified with five-hole 

probe results. A saddle point and associated separation line can be discerned 

where the flow separated near the top of the cylinder. The attachment point 

on the endwa1l flow visualization indicates that the flow reattached to the 

endwa1l close to the cylinder. The downward flow pattern on the cylinder 

surface adjacent to the endwal1 indicates that a vortex may have been formed 

at the endwal1-cylinder juncture. The close prox1m1ty of the separation and 

attachment lines means that the vortex would have been small. 

Surface streak1ines on the bottom portion of the cylinder, shown in 

figure 67, are similar to those on the top portion. The saddle point, 

however, is closer to the endwa1l and not as easily discerned. The difference 

can be attributed to gravitational effects. On the top of the cylinder, the 

gravitational forces enhanced the downward ink flow, creating an indicated 

31 
saddle point 0.068 cylinder diameters from the endwall. In the recirculation 

zone near the bottom of the cylinder, gravity retarded the corresponding ink 

flow, producing an indicated saddle point 0.031 cylinder diameters from the 

endwall. The actual saddle-point is probably in between these two biased 

values. The endwall attachment point is 0.013 cylinder diameters from the 

cylinder (figs. 62 and 63). If a vortex was present at the endwall-cylinder 

juncture, the vortex had an oblong cross section. 

Work by Sparrow, et. al. (ref. 24), Goldstein and Karni (ref. 25), and 

Goldstein, et. al. (ref. 26) using naphthalene sublimation, shows the presence 

of a vortex structure in the endwall-cylinder juncture region. Goldstein and 

Karni concluded that two vortices were present at the endwall-cylinder juncture in their experiment. The size of the hypothesized vortices was 

incredibly small. A trench that the vortices formed at the cylinder base was 

on the order of 0.4 8* wide. In their experiment, this distance was only 0.9 

mm. Unfortunately, the results of Goldstein and Karni and Sparrow are contradictory. For example, Goldstein and Karni measured higher Sherwood numbers 

near the endwall than measured in the freestream. Sparrow, on the other hand, 

shows reduced mass transfer near the endwall relative to that in the twodimensional flow region. In any case, the recirculation region near the 

endwall-cylinder juncture in this experiment probably contained a vortex. The 

close proximity of the cylinder saddle point and endwall attachment point 

precluded making five-hole probe measurements to document the recirculation 

zone. The recirculation region was so small, however, that the fluid dynamics 

in this region had little or no effect on the main vortex characteristics. No 

attempt was made to document the flow in this region. 

Discussion of Vortex Formation 

The vortex pattern deduced from the experimental data is shown in figure 

68. Near the plane of symmetry, low-loss fluid from outside the approaching 

boundary layer passed next to the cylinder, stagnated at the endwall-cylinder 

junction, where flow visualizations indicate a small vortex formed, and 

proceeded back toward the saddle point. Streamwise flow inside the boundary 

layer followed the same pattern, turning inside of the low-loss fluid. As a 

consequence of the reverse flow and incoming flow interaction, the reverse 

flow accelerated away from the cylinder. Reverse flow very close to the 

endwall passed beneath the incoming separated flow and proceeded to the saddle 

point region before turning to pass tangentially around the cylinder next to 

the separation line. Since the streamwise flow separated at a shallow angle, 

reverse flow passing a small distance away from the endwall was blocked by the 

incoming flow, forcing the reverse flow to decelerate. Rather than rolling up 

into a vortex, the reverse and incoming flow tended to turn and pass 

tangentially around the cylinder. Significant losses in total pressure are 

typically associated with two flows interacting in this manner. The high 

32 
losses measured in the center of the vortex subsequent to its formation, then, 

may indicate that this flow collected at the vortex center. Reverse flow away 

from the plane of symmetry followed the same pattern, but flow close to the 

endwall that passed beneath the separated incoming flow turned before reaching 

the separation line because flow from the plane of symmetry region already 

occupied the space next to the separation line. Moving away from the plane of 

symmetry, the endwall region next to the separation line and beneath incoming 

separated flow progressively filled, forcing the endwall flow to turn closer 

to the cylinder. Eventually the accelerating reverse flow could not adjust to 

the sharp turning required to pass tangentially around the cylinder in the 

same manner. Rather, the reverse flow tended to be entrained into the fluid 

interior leading to the formation of the vortex. The reverse and incoming 

flow apparently wrapped around the high loss fluid created in the plane of 

symmetry region. The endwall visualization pattern indicates that flow 

adjacent to the endwall became involved in the vortex beginning at 

S = 15 deg. The five-hole probe'measurements show that the vortex was present 

in the 25-deg plane but not the 5-deg plane. 

This flow pattern does not support the multiple vortex pattern given by 

Baker (ref. 18) and Moore and Forlini (ref. 20). That pattern was developed 

from endwall flow visualization; no interior measurements were acquired to 

verify this model. These experimentors interpreted the line of accumulated 

ink identified in this experiment as a separation line emenating from a second 

saddle point in the plane of symmetry. Based on the flow topology, a nodal 

point of attachment and corresponding attachment line must be present between 

the saddle points, though the nodal point and attachment line could not be 

discerned in the endwall flow visualizations. The flow visualization medium 

placed between the upstream separation line and the line of accumulated ink 

was carried away. For this combination of two endwall separation lines and 

two attachment lines, the experimentors inferred the four-vortex model 

sketched in figure 69. The system includes a main vortex, a pair of counterrotating vortices beneath the main vortex, and a small vortex tucked in the 

endwall-cylinder junction, all of which form in the plane of symmetry. 

This complex system was not present in this experiment. The endwall flow 

visualization clearly shows a single saddle point while the interior flow 

field measurements indicate a single horsehoe vortex that formed away from the 

plane of symmetry. 

33 
CONCLUSIONS 

This project documented the flow field in the endwall region around a 

cylinder. This documentation leads to the following conclusions: 

1. A single endwall saddle point and a single endwall attachment point 

were observed in the endwall flow visualization pattern. The 

multiple singular points required for the four-vortex model were not 

present. 

2. The five-hole probe measurements indicate that a single main vortex 

was formed. Though the rudiments of a vortex were observed in the 

plane of symmetry and the S-deg plane, the vortex was fully formed 

between the S-deg and 2S-deg planes. The flow visualization pattern 

indicates that the flow adjacent to the endwall initially rolled up 

near the lS-deg plane. 

3. The main vortex was confined to a region less than one boundary-layer 

thickness from the endwa11. The vortex core moved radially outward 

and slightly away from the endwall as the vortex passed around the 

cylinder. 

4. The vortex strength was significantly reduced between the 4S-deg and 

90-deg planes. 

S. The losses associated with the vortex rollup were localized and 

offset by the transport of core flow into the endwall region next to 

the cylinder. 

6. Measured flow conditions at the test-section midspan are close to 

those for potential flow through a cascade of cylinders. 

7. Because the cylinder was covered by low-loss fluid, the lateral 

pressure distribution was reasonably uniform. The angular 

distribution was like that for two-dimensional viscous flow around a 

cylinder. 

8. The plane of symmetry results in this experiment and that of East and 

Hoxey are in agreement. This agreement implies that the detailed 

data acquired by East and Hoxey can be used to characterize the flow 

upstream of the five-hole probe measurements acquired in this 

study. 

9. A key implication of these experimental results for gas turbine 

engines is that flow in the saddle-point region does not exhibit 

swirl. 

34 
REFERENCES 

1. Gaugler, R. E. and Russell, L. M., "Flow Visualization Study of a 

Horseshoe Vortex in a Turbine Stator Cascade,;; NASA Technical Paper, 

1884, 1982. 

2. Langston, L. S. and Boyle, M. T., itA New Surface-Streamline FlowVisualization Technique," Journal of Fluid Mechanics, Vol. 125, pp. 53-

57, 1982. 

3. Eckerle, W. A., "Horseshoe Vortex Formation Around a Cylinder," Ph.D. 

Thesis, University of Connecticut, Storrs, Connecticut, May 1985. 

4. Langston, L. S., Nice, M. L. and Hooper, R. M., "Three-Dimensional Flow 

Within a Turbine Cascade Passage," Trans. ASME, Journal of Engineering 

for Power, Vol. 99, January 1977, pp. 21-28. 

5. Hess, J. L., and Smith, A. M. 0., "Calculation of Potential Flow Around 

Arbitrary Bodies," Progress in Aeronautical Sciences, Vol. 8, D. 

Kuchelmann, ed., Permagon Press, 1967, pp. 1-138. 

6. Barber; T. J., and Weingold, H. D., "Vibratory Forcing Functions Produced 

by Nonuniform Cascades," Trans. ASME, Journal of Engineering for Power, 

Vol. 100, No.1, January 1978, pp. 82-88. 

7. Camarata, F. J., Hooper, R. M., and Nice, M. C., "Experimental 

Investigation of Passage Flow in Baseline Build of Large-Scale Turbine 

Cascades," United Aircraft Research Labs Report R75-212632, June, 1975. 

8. Burton, R. A., "A Simple Universal Velocity Profile Equation," Tech. 

Note, AIAA Journal, Vol. 3, No.4, 1965, pp. 784-785. 

9. Schlichting, H., Boundary-Layer Theory, McGraw-Hill, 1968, pp. 596-651. 

10. Langston, L. S. and Wagner, C. A., "A Streamline Model for a Saddle Point 

of Separation," Submitted to the Journal of Fluid Mechanics, October 

1983. 

11. Oswatitsch, K., "Die Ablosungsbedingung von Grenzschichten," Symposium on 

Boundary Layer Research, International Union of Theoretical and Applied 

Mechanics, Edited by Gortler, Springer Verlay, Berlin, 1958. 

12. McMahon, H., Hubbartt, J., and Kubendran, L., "Mean Velocities and 

Reynolds Stresses Upstream of a Simulated Wing-Fuselage Juncture," NASA 

CR 3695, June 1983. 

35 
REFERENCES 

13. Ram, V. V., "Untersuchungen uber die Eckengrenzschicht an einem 

Kreiszy1inder mit Seitenwand," Report 63/46, Institute of Fluid 

Mechanics, Technische Hochschule, Braunschweig, 1963. 

14. East, L. F. and Hoxey, R. P., "Low Speed Three-Dimensional 

Boundary Layer Data," Royal Aircraft Establishment, Tech. 

69041, Parts I and II, 1969. 

Turbulent 

Rep. No. 

15. Humphreys, J. S., "On a Circular Cylinder in a Steady Wind at Transition 

Reynolds Numbers," Journal of Fluid Mechanics, Vol. 9, Part 4, pp. 603-

611. 

16. Farell, C., and Blessmann, J., "On Critical Flow Around Smooth Circular 

Cylinders," Journal of Fluid Mechanics, Vol. 136, pp. 375-391. 

17. Hoerner, S. F., Fluid-Dynamic Drag, Published by the author, 1965. 

18. Baker, C. J., "Vortex Flow Around the Bases of Obstacles," Ph.D. Thesis, 

Univesity of Cambridge, Cambridge, England, September 1978. 

19. Ludweig, H. and Tillman, W., "Investigation of the Wall Shearing Stress 

in Turbulent Boundary Layers," NACA TM 1285, May 1952. 

20. Moore, J., and Forlini, T. J., "A Horseshoe Vortex in a Duct," Trans. of 

the ASME, Journal of Engineering for Gas Turbines and Power, Vol. 106, 

July 1984, pp. 668-676. 

21. Boyle, M. T., "Three Dimensional Separation and Vortex Formation," Ph.D. 

Thesis, University of Connecticut, Storrs, Connecticut, 1984. 

22. Lighthill, M. J., Laminar Boundary Layers, Edited by L. Rosenhead, Oxford 

University Press, pp. 60-82. 

23. Tobak, M. and Peake, D. J., "Topology of Three Dimensional Separated 

Flows," Ann. Rev. Fluid Mechanics, Vol. 14, pp. 61-85, 1982. 

24. Sparrow, E. M., Stahl, T. J. and Traub, P., "Heat Transfer Adjacent to 

the Attached End of a Cylinder in Crossflow," Internation Journal of Heat 

and Mass Transfer, Vol. 27, No.2, 1984, pp. 233-242. 

36 
REFERENCES 

25. Goldstein, R. J., and Karni, J., "The Effect of a Wall Boundary Layer on 

Local Mass Transfer from a Cylinder in Cross Flow," Trans. ASME, Journal 

of Heat Transfer, Vol. 106, May 1984, pp. 260-267. 

26. Goldstein, R. J., Chyu, M. K. and Rain, R. C., "Measurement of Local Mass 

Transfer on a Surface in the Region of the Base of a Protruding Cylinder 

with a Computer-Controlled Data Acquisition System," Journal of Heat 

Transfer, Gallies, 1983. 

37 
w 

00 

Figure 1 Turbine Cascade Endwall Flow Visualization 

0. 

0 

1--

Z 

W 

0 

LL 

LL 

W 

.p- O 

0 0 

w 

ex: 

:J 

(f) 

(f) 

w 

ex: 

(L 

I0 

Ia:: 

0.8 

0.6 

0.4 

0.2 

CENTERLINE TRAVERSE 

q=5.0 em H20 

OL-________ -L __________ ~ __________ L_ ________ ~ __________ _J 

o 0.2 0.4 0.6 0.8 1.0 

DISTANCE FROM TEST-SECTION FLOOR, y/h 

Figure 3 Pitot Pressure Profile Near Test-Section Entrance 
FLOW 

~0.3~2 5.s2. 521152115415. j ! '-

+ + + + + + + + + + + -h-L 10.2 ~_ t 

20.3 I 

+ It 15.2 ! 

PRESSURE TAP ~ + 

LOCATIONS 15.2 

-l1.031~ + 

15.2 

+ + 

15.2 

+ + ! ! 183 

15.2 

+ + 

15.2 

D.17'~ I + + 

0.08 'I I I 15.2 

0?4 ' + + O~32- t-t- tt 152 ~ 1.43 -. + 

: 20.3 i TAP GEOMETRY 

+ + + + + + -L 

-11-- 1 .

03 "Ju . ...J ..:>v . ...J LV.0 ! V.L 

I 1- 183 

DIMENSIONS IN CM 

Figure 4 Wind Tunnel Floor Support Plate 

1.43±t 

032--1 r I 

016-; U_ 

FLOW 

~ ACCESS HOLE FOR 

,- CYLINDER PRESSURE 

L~I ~I I TAP LINES 15.2 DIA 

, 097~~ 0.56 

, 

0.17 I 

0.08\ I 

-1'191 t--

TAP GEOMETRY 

CYLINDER 

ATTACHMENT HOLES 

(EOUALL Y SPACED ON 

26.3 DIA BOLT CIRCLE) 

DIMENSIONS IN CM 

, 

'\ '\ \1 

l ~ 

_.:r± 

feI 

i 

1. 

Figure 5 Wind Tunnel Floor Instrumented Disk 

(See Table" for Tap Locations) 

41 
INSTRUMENTED \ 

DISK \ 

r 

/ 

CAM 

FOLLOWER 

MOUNTING 

PLATE 

I I I I ",. .. "tA 

All ~ ".""IC - -'-1 

I ' I 

THREADED HOLE FOR 

CAM-FOLLOWER ADJUSTMENT 

BOLT 

SUPPORT 

PLATE 

HOLES FOR LOCKING BOLTS 

SLIDE 

BRACKET 

Figure 6 Cross·Sectional View of Cam· Follower Slide Assembly 

42 
+' 

w 

Figure 7 Photograph of Inverted Test·Section Floor Showing Indicator and 

Index Holes for Angular Positic)ning of Instrumented Disk 
Figure 8 Photograph of Inverted Test-Section Floor 
ACCESS HOLE 

FOR PROBE 

r-----

SMALL POSITIONER I' // 

DISK I J ....... 

LARGE POSITIONER 

DISK 

SUPPORT 

PLATE ~ ~ 

23.8 

- ---l 

~ 

I 

I 

I 

I 

I 

" 5~2 

L ---------------- "---- ::::::: _.1 

14 58.4 .1 

DIMENSIONS IN CM 

Figure 9 Probe Positioner Disks 

45 
"TI 

cS' 

c:: 

.... 

CD 

...... 

0 

." 

.... 

0 

eCD 

." +:- 0 

0\ en 

.-

o· 

~ 

CD 

.... 

» 

en 

en 

CD 

3 

e-

-< 
.p-

-...J 

PROBE HOLDER ROTATOR 

PROBE TRANSLATOR 

D.C. MOTORS BULKHEAD 

FITTING I I 

POTENTIOMETERS 

LARGE 

GEAR 

LARGE POSITIONER 

DISK 

FASTENING I I ...., NUT 

SMALL POSITIONER 

DISK 

SPACER 

PLATE 

POSITIONER SUPPORT 

PLATE 

Figure 11 Cross-Sectional View of Motorized Probe Positioner with Mounted 

Probe Traverser 
1.0 

{3 = 0 deg 

0.6 

0.2 

(J) 

Q. 45 

0 -0.2 

f--

z 

W 

(3 

u:: - 0.6 LL 

W 

0 

0 

w -1.0 

a: 

::::l 

CI) 

CI) 

-1.4 w 

a: 

0... 

0 - SINGLE CYLINDER 

f--

« -1.8 f--

--- CASCADE OF CYLINDERS 

CI) 

-2.2 

- 2.6 

-3.0u"----~--~----~--~--__ ~ ____ ~ __ ~ 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 

RADIAL DISTANCE FROM CYLINDER CENTER. RID 

Figure 12 Potential·Flow Static Pressure Distribution Around a 

Single Cylinder and Cascade of Cylinders 

48 
TAPPED MOUNTING --7 

HOLE-8 PLACES / 

ON 26.3 dia / 

SOL T CIRCLE / 

(EQUALLY SPACED)/ 

0.56 

0.97 

f.. 29.2 

VIEW A-A 

TAP GEOMETRY 

0.95 

1 ~t--: ----,.~ Icl± 

0.64 J.... ....-.... ~ 2.22 --1 

0.17 

0.08 

~.. 29.8 -

I: i 

I, 

i II ! Id-t= 

I I 

30.1 

I 

I 

O-RING GROOVE-2 

PLACES 

SEE VIEW A-A 

DIMENSIONS IN CM 

Figure 13 Cylinder Test Model 

49 
~ J, 25.72 

r 

• 1.59 

t IT 

I I 25.4 

I 

I 

j 

i 

I 

30.1 , 

I 

I 

.rL 

---t 

-

~ 

O·RING GROOVE 

0.71 WIDE BY 

0 DEEP 

po--

~ 6 

r. :.. 1.47 

l.J-,j 

DIMENSIONS IN eM 

Figure 14 Cross-Sectional View of Cylinder Showing Sealing Technique 

50 

VI 

N 

I 

26.3 

1 

30.4 

191 

1e-1111'" 

26.0 

- ~ 

-_._----------_._--_. 

- 60.96 ~ I r----fl 

I '---- -, 

, I I I , j I I I I 

I I j 

I I 

I I I I I 

I I I 

I I I ~~---------11.7 ------------~.~I 

Figure 16 Test-Cylinder Afterbody 

./ 

/ \ 

/ 14. 92 

I 

~2.54 \ 

\ 

\ CYLINDER 

~LOCATION 

"-

I- 0.40 

T r-.... 

I 

f 

I 

I 30. o 

I 

I 

I 

I -'-

DIMENSIONS IN CM 
a) 

.. 0 .. lI) 

\ c 

0 

:;:: 

as 

~ 

:::J 

C) 

~~ := 

c 

0 

0 

CD 

.c 

e 

Q. C""'I 

CD ""' '0 

::I: 

cD 

> 

i.i: ~ 

..... 

..... --1 ~ I-- CD 

u 

'" (!) 

0 

~ 

:::J 

C) 

i.i: 0-

I-
PITCH ANGLE 

CALIBRATION JET 

YAW ANGLE 

CALIBRATION JET 

VIEW A-A 

1; 

Figure 18 Sign conventions for Five·Hole Probe Calibration 

54 
CJ) 

a: 

ill 

Iill 

~ 

« 

a: 

't 

z 

o 

~ a: 

CD 

::i 

« 

() 

q= 6.5 em H20 PSAR =75.97 emHg TeAL =74 CF 

A B. 

3.0 1.6 ,..., -----r----.-------r-----, 

N 

-

La 

Cl. 0-

+ -- Cl.'<:t 

C\l 1.2 --La -I 

r:[ 0 

-

Cl. 

+ 

'<:t 

~ 

-

Cl.lI"J I 

.,.... 

I -1.5 S 

'<:t 

~ 

- 3.0 ':-:' __ ..l.-__ L-_-1.. __ --1 

-30 o 15 30 0.4~' ----~------~----~----~ -00 -15 o 15 30 

--.,.... 

Cl. 

I 

~ 

-15 

C. D. 

0.6 r, ---,----,------r----, 6.0"'" ----.---.....,----.-----, 

Cl 2.0 Q.) 

"0 

I 

...J 

« 

~ -2.0 

o I I =:....... I -? I - 6.0 1-' __ --L. __ --'-__ ---l'---_----J 

- 30 - 15 0 15 30 - 30 -15 o 15 30 

PITCH ANGLE - cf> - deg 

Figure 19 Five-Hole Probe Calibration Curves 

55 
5.40 

DIMENSIONS IN CM 

.-I 

C·SINK FOR 

#8-32 ON 

3.81 dia 

(3 PLACES) 

--i ~ 0.25 Tl-J1 

'I -v ~95 -Tl -

I 

I 

_1 

0.64 -..I I-

-.....I 

~-

--., 1.27 ~ 

Figure 20 Removable Plug for Small Positioner Disk 

56 
Q) 

-to 

ii: 

... 

Q) 

c 

o 

:;: 

"iii 

o 

Q. 

Cii 

E 

(/) 

,... 

N 
COMPRESSION 

SLEEVE 

BULKHEAD 

FITTING 

REMOVABLE 

PLUG 

RUBBER WASHER 

PROBE SUPPORT 

CAP 

FASTENING NUT 

PROBE TRAVERSER 

BASE 

SMALL GEAR 

SPACER PLATE 

SMALL POSITIONER 

DISK 

STEEL WASHERS 

Figure 22 Seal Around Probe Support in Probe Positioner 

58 
WIND TUNNEL 

PRESSURES 

SCANIVALVE 

PRESSURE 

SIGNAL 

ANALOG 

MONOMETER 

AVERAGE 

VOLTAGE 

TRANSDUCER I .. I INTEGRATOR 

SCANIVALVE CONTROL ~ I VOLTAGE 

(VIA 1664 TTL BOARD) 

VOLTMETER 

OTHER '\ VOLTAGE 

PARAMETERS f (VIA IEEE BUSS) 

8-INCH 

FLOPPY DISK 

DATA 

SYSTEM 

PRINTER 

Figure 23 Data Acquisition Instrumentation 

59 
READ 

CONSTANTS 

OPE~; 

DISK FILE 

• 

RECORD 

CONSTANTS 

, 

SAMPLE 

AID BOARD 

END 

OF 

RUN? 

NO 

r SET UP 

IEEE BUSS 

l 

I--

• 

SEND SV 

HOME 

/ 

YES 

PRINT 

ERROR 

CLOSE 

FILE 

~ 

STOP 

t 

CLOSE 

FILE 

I 

8 

NO 

YES 

r-' 

SV 

AT 

CORRECT 

PORT? 

YES 

WAIT FOR 

STEADY SIGNAL 

SAMPLE 

DIGITIZED 

VOLTAGE 

~ 

LAST 

PORT? 

NO 

~ 

STEP 

SV 

Figure 24 Data Acquisition Program Flow Chart 

60 

~ 
1.8 m 

T ~5~ 

I,. 1.8 m -I 

I 

I 

x 

, 

y 

~ !"""""'~""""""""'" --t 29.8 em I-- ~ OUADRANT DOCUMENTED 

Figure 25 Schematic Showing Test Section with Cylinder and Coordinate Systems 

61 
x/D=2.75 yrD = 00 C!l 

0.... 

o 

~ 

z 

w 

0.08 r' ---------------~ 

(3 

LL tb 0.04 

o 

o 

w 

a: 

::> 

(f) 

(f) 

w 

a: 

0.... 

0.0 

o 

~ - 0.04 .... ' __ --'-__ ---L. __ -1. __ ---1 __ ---1 __ --.J 

(f) 

C!l 

0.... 

o -0.30 ' ~ 

z 

w 

(3 

tt -2.0 

w 

o 

o 

w 

a: 

::> -0.1 

(f) 

(f) 

w 

a: 

0.... 

-3.0 -2.0 -1.0 0.0 1.0 2.0 

DISTANCE FROM TEST-SECTION CENTERLINE, z/D 

Figure 26 Test·Section Floor Entrance 

Static Pressure Distribution 

y/D =0.0 

3.0 

o z/D=2.72 

o z/D= -2.72 

o 

~ 0" :::Sl' 

~ 

(f) 

o -4.0 -0.8 -1.2 -1.6 -2.0 -2.4 

DISTANCE FROM CYLINDER MIDPLANE, xlD 

Figure 27 Static Pressure Distribution Near 

Test·Section Sidewalls 

62 

-2.8 
XID= -2.72 

1.1~------------~------------~------·------~------------~---------

lOT _,.fiJ ... • 

8 0.9 :J 

--:::J 

0 

~ 08t! o z/D =0.0 

a: 

0\ X zlD =1.021 

W >- l- T z/D=2.043 (5 

0 - POWER LAW 

-' 0.7 

w 

> 

0.6 

0.5~'~----------+------------+------.---------~-------------~-------------- 0.0 0.1 0.2 0.3 0.4 0.5 

DISTANCE FROM FLOOR, ylD 

Figure 28 Test·Section Entrance Velocity Distribution 
x/D = - 2.72 ylD = olD 

1.00 

0 

~ 

8 

~ 

0 

i= 0.95 <C 

a: 

>- f-

(3 

0 

---l 

W 

> 

0.90 

0 0.4 0.8 1.2 1.6 2.0 2.4 

DISTANCE FROM TEST-SECTION CENTERLINE, zlD ,~ -

Figure 29 Freestream Entrance Velocity Variation 

1.0,.------------------------------------------------------. 

8 0.8 

~ 

--;:) 

o 0.6 

~ a: 

i:: 0.4 

(3 

o 

---l 

W 

> 0.2 

Ox i 0 = - 2.7 2.. Z i 0 = 0 

Or:: ! I I I! I I , I 

10 20 50 100 200 500 1000 2000 500010,000 20,000 50,000 

REYNOLDS NUMBER, Re y 

Figure 30 Typical Clauser Diagram 

64 
1.0 

0 EXPERIME 

g RANGE MEASURED 

U) 

OVER 4 RUNS 0.. 

0 0.8 

I- - POTENTIAL FLOW Z 

w • COFH1ECTED FOR o' (3 

LL 

LL 0.6 I- 0 W 

0 

6 0 (OO8OfO w 

a: 90 00 ::::) 

U) 0.4 U1 

0-

W 

U) 000 SADDLE QOOOQ~ a: POINT 00 0.. 

0 LOCATION u 0 

~ 0.2 

IU) 

o ' I I 

0.5 0.6 0.7 0.8 0.9 1.0 1 .1 1.2 1.3 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 31 Endwall Static Pressure Distribution in Plane of Symmetry 
1.0 

° EXPERIMENT 

0 EAST & HOXEY 

(f) 

D- 0.8 ° [':, RAM (0* ID 0= 0.03) 0 

1-- -POTENTIAL FLOW 

Z tD • w CORRECTED FOR 0' 

(3 

LL 0.6 ° LL 

W 

0 Z 0 

w 

a: ~00080 ::J 0.4 Q"\ (f) ° Q"\ (f) 

w 0°[':, 

a: SADDLE 

D- POINT 

i= 

0 LOCATION ° 

« 0.2 

I-

(f) 

o ~ ____ ~ ____ ~~ ____ ~ ____ ~~ ____ ~ ____ ~ ______ ~ ____ -J 

0.5 0.6 0.7 0.8 0.9 1.0 1 .1 1.2 1.3 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 32 Comparison of Plane of Symmetry Static Pressure Distributions 
RID 

90 

2.5 

2.3 

2.1 

80 MEASURED 

10 

~7777577j lm~\~ L: ' ... ,-:' ! " II I 0 - FLOW 

0.9 

90 2.5~0 

2.31 -.1 

2.1 r-------...l 

POTENTIAL FLOW 

FLOW 

Figure 33 Comparison of Measured Endwall Pressure 

Distribution with Potential·Flow 

Pressure Distribution 

67 
1.0~~~~~~~Tn~~~~~~~~~~--~ 

(3 = 0 deg 

0.5 

0.0 rOO 0 0 00000000000000000 0 3~ 

(f) 

0.. 

() 

-0.5 1---

z 

ill 

[5 

LL 

~ 00000000000000000000000 LL 

ill 

0 

() -1.0 45 

ill 

c: 

:::> 

(f) 

(f) 

ill 

c: 

0.. -1.5 

() 

i= 

1

0 ~ 00 0 (f) 0000000000 0 000000000 

60 

-2.0 

o 

o 0 000 00 00 -2.5~ 000 0 0000 000000 90 

-3.0~'----~----__ ~-----L--__ ~ ______ L-__ ~ 

o 0.1 0.2 0.3 0.4 0.5 0.6 

DISTANCE FROM ENDWALL SURFACE, y/D 

Figure 34 Cylinder Surface Lateral Pressure Distribution 

68 
en a.. 

0 

1-" 

Z 

W 

g 

LL 

LL 

W 

0 

0 

w 

a: 

::::> 

en 

en 

w 

a: 

a.. '" 0 \0 

~ Ien 

1.0~.~cr----.-----.-----.------.-----.-----.-----.------' 

o 

-1.0 

-2.0 

-3.0 

-4.0 

o 

o zlD=0.011 

o zlD =0.255 

6. zlD = 0.511 (MIDSPAN) 

_ POTENTIAL FLOW THROUGH 

CASCADE 

---- HOERNER 

10 20 30 40 50 60 70 

ANGULAR POSITION ON CYLINDER SURFACE, 

Figure 35 Cylinder Surface Angular Pressure Distribution 

80 90 
REFERENCE 

I VELOCITY MAGNITUDE 

0.20 

0 ..- --

...-

-

-

-

- -->- 0.16 ." 

-- -- ...-

-1 

- .,...-

--

- -- ---

- ..--

- • ....J 

« .... --

3: "".. 

-- --- -- --

-

-

- --- 0 0.12 Z 

-- --

-

-

-

- --- -- w .,....,., - ~ --- -- - - - - - .,./ 0 7 --- -- - -- ...- -...j a:: - - - - - 0.08 

-- ...- 0 LL 

-

- -- ...- -

-

-

- () 

w .,--

-

-

-

-

- z ~ -- - - - - « ~ -- - - - - - (/) 

I- 0.04 

-

-

--

-

-

- ~ - - - - - ..- 0 ...... V - - - - - -.. - ~ --.. -

V 

-

- . - s=-

O It. 0.50 0.58 0.66 0.74 0.82 SADDLE POINT 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 36 Velocity Vectors in the Plane of Symmetry 
0 

->. 

-I 

-I 

~ 0 

z 

w 

~ ,..... 

v 

cr. 

L.L 

W 

() 

Z 

C/) 

~ 

0 

RID =0.638 0.20i~--------------------------------------------------~ 

10 

0.12 to 

10 

• 

• 

• 

0.041- • 

NOTE: SHADED SYMBOLS ARE UNCORRECTED 

o 

8 

o 

o 

0

0 

O~l ________ -L ________ ~ ________ ~~ ________ L-______ ~ 

o - 40 - 80 - 120 - 160 -200 

FLOW YAW ANGLE, e-deg 

Figure 37 Plane of Symmetry Flow Yaw Angles 

71 
0.20~----------=--------------------------------------------------------------, 

0 0.16 -.. 

>, 

-1 

...J 

« 

3: 0.12 0 

z 

w 

~ 

....... 0 N 0: 0.08 LL 

w 0 

() 

Z D 

« I-

(f) 0.04 

0 

O~~~~~~~~~ 0.50 0.58 0.66 0.74 0.82 SADDLE POINT'0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 38 Flow Pattern in the Plane of Symmetry 
REFERENCE 

VELOCITY MAGNITUDE 

0.20 

..- -- --

0 - - -- -- -- 0.16 ..- >. 

-- - -- - -1 .- -l -- - -- - - « .- -- ~ 

-- -- - -- - - 0 0.12 ..... -- - z -- -- - -- - - - --

w II"" 

-- -- - - / -- ~ - - - - 0 - -- -- - - - - - - a: :;;:: ........ 0.08 

-- - --. - - VJ LL -- - - - - - w r? --- () .,...... - - - - - - z - - - - - - « ~ - - - - - - b) 0.04 -- - - --- - - - - ..-

- - -- - 0 .. 

• -1; - -- - - . -... - - - t ~ - - .. .. .... 1 -I o I 

0.50 0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 39 Velocity Vectors in the 5·deg Plane 
0.20r---------------------------------------------------------------------------~ 

0 0.16 -.. 

>. 

--.l 

--.l 

« 

~ 0 0.12 

z 

w 

~ 

0 ....... 0: 

+=- LL 0.08 

w 

0 

z 

« 

f0.04 (f) 

0 

O~ ____ L_ ____ ~ ____ _L ____ _L ____ ~ ______ L_ ____ ~ ____ J_ ____ __.l_ ____ _L ____ ~ ____ ~ 

0.50 0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 40 Flow Pattern in the 5·deg Plane 
OH:l '~31N38 ~30NIlA8 V'lO~:l 38N'V1SIO l'VIO'V~ 

86'0 06'0 (:ffO PL'O 99'0 8S'O OS'O 

0 ... . - ~s:::=--- - -. - · . - ~ ~ ___ ~ ___ e.- . .. ~~--~- · • - - .. ., 

!fV~~~l • 

- -. . f - 0 - .. . , - - -. .. ~ ~ A l I }. 1 I (f) - ... pO'O - - - - ~ I --t - - - » - - - ----;~-~/.~ ~ /. I z -- - - - - -- -- :::::: ~ /. /':: ~ Z I 0 - - - _----_~/~ 7. /. / m 

tr\ 

-

-

- ----:::::::~/ ~ ~ ~ / 80'0 " -. r-- - -. -------~/ / /. JJ 

0 

-

- -- -- .. . 

-- ----,....--. /...-: / /'" / ~ 

- -- ... ----~~/ ,/' " - - ---.... - ... -~ ,..,.,../ / m 

z 

-

-

- L_ ~ ,..,.,.. /""" / /" " G~'O 0 - • L.~ ~ 

-

-

- • --------........ ./ / ~ » .:.---------- ~ ......... /'" ,/ r 

--

- .! 

--

- ------------- ......... /'" ,/ 9~'O '< 

~-------------'" 

/ /' 0 

-

-

- 0(:'0 

30nlIN8'v'V'l AIIOOl31\ I 

3~N3tl3:l3~ 
o 

-->-

-i 

-1 

~ o 

z 

w 

2 

a 

a: 

LL 

w 

o 

z 

~ o 

REFERENCE 

1---.... ,VELOCITY MAGNITUDE 

0.20~---T----~----~---'-----r----~--~r----r----'-----r---~----, 

0.16 

0.12 

0.08 

0.04 

or 

."., 

,/ 

,/ 

,/ 

,/ 

,/ 

/ 

/ 

i 

{ 

.,-

....,., 

.,/ 

.,/ 

/ 

,./ 

/" 

~ 

1 '-. 

-

---------

---.....-- - --- ---.....--- -- -----.....--... ---- --.....-- -- ".. - ~------

-

-

-

-

--

-

--

-... 

-

-

-

-

--

-

-

--

-

-

-

-

-

-

-

-

--

- OL- -:: ____ ~ ____ -L ____ _L _____ ~ ____ _L ____ ~ ______ L_ ____ ~ ____ ~ ____ _L ____ ~ ____ ~ 

0.50 0.58 0.66 0.74 0.82 0.90 0.9f 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 42 Velocity Vectors in the 45·deg Plane 
REFERENCE 

t- I VELOCITY MAGNITUDE 

0.20 

• 0 • • -->. 0.16 • • 

-1 

.....J • « • • ~ • • • 

0 0.12 z • , 

w • • ~ • • • • • 

0 • • , • • • .. • • a: • \ , • • LL 0.08 • • • -...J , " " • • -...J W • " " \ t II 

0 , '" \ z ~ .. • ",. '" 

« • " , "- ~ .... ... ~ " 

- " ...... ..... I- .... " - ....... (j) '" .... ~ - ....... 0.04 ..... """ -...-~ ..... 0 '" .... 

..... ---:..-- ::::: 

--

- -- .... ..... ------

-

- .... - - ---- - - o I 

---

----

0.50 0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 43 Velocity Vectors in the 90·deg Plane 
0.20 

0 0.45 

>. 0.16 

-' -' 0.98 « 

?; 

0 

Z 0.12 0.475 

w 

'-I ~ 00 0 

0: 

LL 0.08 

w 

0 

z 

« 

I-

(J) 0.04 

0 

0.74 0.82 0.90 0.98 

SADDLE POINT 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 44 Static Pressure Contours in Plane of Symmetry 
0.20 

• 0.90 0.80 0.70 0.65 0~)5 0.45 

0.60 0.50 

~ 016f I } /1 / J I I ( \ Cp 

s 

« 

3: 

o 012 z . 

UJ 

~ 

0 

........ a: 

LL 0.08 

\.0 UJ 

() 

Z 

(/) 

~ 

0 

0 

0.50 0.58 0.66 , /f 0.74 ., 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 45 Static Pressure ContolJlfs in 5·deg Plane 
0.20------~----~-----T----~~----r-----~---------~------------------~----~ 

0.35 0.375 0.35 '0.30 0.25 0.23 0.22 

0 

-->. 0.16 

-I 

....J « 

:s: 

0 

z aJ W 

0 ~ 

0 

a:: 

LL 

W 

0 

Z 

« 

l-

(/) 0.04 

0 

0.25 

0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CENTER OF CYLINDER, RID 

Figure 46 Static Pressure Contours in 25·deg Plane 
0.20 I 

j 016 ~]oo r 

0.55 0.35 

I-LJ I \" \ 

-0.25 

U 

" \ \ 

-0.20 -0.15 Cp S 

00 w 0.12 ...... ~ 

0 

a: 

LL 0.08 

w 

() 

z 

« I-

~ 0.04 

0 

0.98 

-0.55 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 47 Static Pressure Contours in 45·deg Plane 
00 

N 

0.20r-----r---~~--~~--~~--~~--_,----~----~----~----_r----_r-----

o 

>., 

-I 0.16 -I 

~ o 

z 

w 

~ 

o 

a: 

0.12 

u.. 0.08 

w 

o 

z 

~ Cf) 0.04 

o 

-2.0 

- 1.8 - 1 .6 - 1 .4 -1.15 -1.0 -0.9 -0.8 

0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 48 Static Pressure Contours in 90·deg Plane 
0 

-->-

..J' 

-l 

« 

~ 0 

z 

w 

~ 00 

VJ 0 

a: 

u.. 

w 

() 

z 

(f) 

~ 

0 

0.20 

0.16 

0.12 

0.08 

0.04 

Cp 

T 

____ - 0.02 

_----.-----.--------0.10 

~---------- 0.20 

_------ 0.30 

"'----. 0.40 

[0.60 

I 'l\. 1\ \1 \.. ~ 1 :;;; 1 i j 1 1 O~ 00.50 0.58 0.66 0.74 0.82 SADDLE 0.90 0.98 

POINT 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 49 Total Pressure Loss in Plane of Symmetry 
0.20 

0 

-->. 0.16 

-i 

..J 

« 

3: 

0 0.12 z 

0.02 

w 

~ 00 0 +' a: 

u.. 0.08 

0.10 

w 0.20 

0 

z 

« 

I-

(f) 0.04 

0.30 

0 0.40 

0 

0.50 0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 50 Total Pressure Loss in 25·deg Plane 
0 

-->-

..J 

..J 

~ 0 

z 

w 

~ 

0 

a: 

LL 

W 00 

~ VI 

« 

~ (5 

0.20, • 

0.16 

0.12 

0.04 

-~ ~ ~ ~ 0.02 =005 

~~. ===-- 0.10 -0.20 

" - 0.30 

Cp T 

0.40 

Ol~ ____ ~ ____ ~ ______ ~ ____ ~ ____ ~ ____ ~. _____ ~ ____ .~ ____ ~ ____ ~~ _____ ~ ____ ~ 

O.~ 0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 51 Total Pressure l.oss in 45·deg Plane 
0.20 

0 

-- 0.16 >. 

..1 cp 

--' T 

~ 0.02 

0 0.12 

z 

ill 

~ 0.10' 

0 

a: 0.08 00 LL 0.20 

'" ill 

() 

Z 0.30 

~ 0.04 (f) 

0 

0.40 

O~ ____ ~ __ ~~ __ ~~ __ ---'~ __ ---'~ __ ---'~ __ ---'~ __ ~ ____ ~~ __ -J ____ ~ ____ -J 

0.50 0.58 0.66 0.74 0.82 0.90 0.98 

RADIAL DISTANCE FROM CYLINDER CENTER, RI D 

Figure 52 Total Pressure Loss in 90·deg Plane 
1.0Qqc----------------------------------------------------~ 

Cf) 

Q. 

() 0.8 ~ 

z 

w 

<3 

E 0.6 

w 

o 

() 

w 

a: 

::> 0.4 

(J) 

Cf) 

w 

a: 

Q. 

() 

i= 0.2 

~ 

POINT 

LOCATION 

o EXPERIMENT 

o CORRECTED FOR o' 

POTENTIAL FLOW 

OL'------~ ______ ~ ______ ~ ______ ~~ ______ ~ ______ ~ ______ ~ ______ ~ 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 53 Midspan and Potential· Flow Static Pressure 

Distribution in Plane of Symmetry 

87 

1.3 
(J) 

Cl.. 

() 

....: 

z 

ill 

(3 

I.l.. 

I.l.. 

ill 

0 

() 

ill 

a: 

~ 

(J) 

(J) 

ill 

a: 

Cl.. 

() 

t= 

<{ 

f-

(J) 

0.6 r

, ---------------- ANGULAR PLANE (deg) 

25 

0.2 o 

45 

-0.2 --0--0 o 

~061 /15 ~---o _-0 

';t:Y""..cf 

-1.0 

-1.4 

~18[ °li POTENTIAL FLOW THROUGH 

A CYLINDER CASCADE 

POTENTIAL FLOW AROUND 

A SINGLE CYLINDER 

-2.2 0 EXPERIMENT 

-3.0~"~--~L------L------L------L----~L------L--~~ 0.5 0.6 0.7 0.8 0.9 1.0 1 .1 1.2 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 54 Midspan and Potential Flow Static Pressure 

Distribution in the 25·, 45·, and 90·deg Planes 

88 
-20~'-------L------~-------L--__ · __ ~ ______ ~ ______ -L ______ ~ 

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 55 Midspan and Potential· Flow Yaw Angle Distribution 
ClO.003r-----------------------------------------------------------------------~ ~ 

z 

w 

(3 

LL It 0.002 

o 

<-) 

z 

o 

t5 0.001 

a: 

LL 

I 

Z 

_ .......... "'-- - ...... =-- --- --- ----

o EXPERIMENT 

o EAST & HOXEY 

__ LUDWIEG-TILLMANN 

S2 

(f) O~~~~ ______ ~ ______ ~ ____ ~ ______ ~ ____ ~~ ____ _L ______ ~ ____ ~ ______ ~ 

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 56 Variation of Skin-Friction Coefficient Along the Plane of Symmetry 
:r: 

a: 

0 

0 

<{ 

LL 

\0 ill t-' a.. 

<{ 

:r: 

(f) 

2.2·· ..... , -------------·----------1 

2.0 I 

o EXPERIMENT 

o EAST & HOXEY 

1.8 

1.6 

1.4 ..... -.----------------. - -0 

1.2~' ____ ~ ____________ ~ ______ ~ ____ ~ __ . __ ~ ______ ~ ____________ ~ ____ ~ 

0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 

RADIAL DISTANCE FROM CYLINDER CENTER, RID 

Figure 57 Variation of Boundary-Layer Shape Factor Along the Plane of 

Symmetry 

2.6 2.8 
8 

::::> 

--::l 

0 

~ a: 

>- I-

(3 

0 

....J 

UJ 

> 

1.0 -------------------------------------o~nl i 

0.8 

0.6. 

0.4 

0.2 

x/D 

A -2.72 

o -1.53 

o -1.02 

ov~ __________ ~ __________ ~~ __________ ~ __________ ~ ____________ ~ 

o 0.2 0.4 ti..::.1 0.6 

(~) 2 

0.8 1.0 

Figure 58 Velocity Profiles in the Plane of Symmetry 

92 
I 

r:i 

0 

I-

() 

« 

LL 

w 

CL 

« 

I 

(J) 

2.0 , , 

1.8 

1.6 

1.4 

1.2 

1.0..........-

o 

PREDICTED FOR POWER LAW PROFILE 

o EXPERIMENT 

o EAST & HOXEY 

0.2 0.4 0.6 0.8 

PROFILE FACTOR,17 

Figure 59 Shape and Profile Factors in the Plane of Symmetry 

93 

1.0 
w 

a: ~ :::> 0... (/)10 

(/) . w~ 

a:z 

o...w 

00 

w- ott 

<{w 

a:o 

wo >(/) <f(/) (/)0 

~...J 

~ 

xlD= -2.72 

0.06"'" -----------------------~ 

0.04tr---- --- -~ ---------0----

AVERAGE LOSS J 

0.021-

O~I--------~--------~--------~~--------~------~ 

o 0.5 1.0 1.5 2.0 2.5 

DISTANCE FROM PLANE OF SYMMETRY, zlD 

Figure 60 Pressure Loss Distribution in the Test-Section Entrance Plane 

94 
\0 

Vt 

xlD = 0.0 

0.12 r· ----------------------------, 

c9 

ct- 0.10,-

10 I 0 

cr.) 

(f) 

o 

9 0.08tw 

a:: 

::J 

(f) 

(f) 

w 

a:: 

CL 

o 

w 

~ a:: 

w 

> <} 

(f) 

~ ::;:! 

o 000 

AVERAGE LOSS AT 

0.06t- _ ~ __ ~ _0 ___ ~ ~-~A=---1,,_ o 

o 

0.041----~--------------------:::::AT]---

0.02 to 

a' ° 

° 

0.5 0.7 

J.. 

0.9 

..L 

1 .1 

....L 

1.3 

....L 

1.5 

1 

1.7 

INLET PLANE 

_L 

1.9 

...L... 

2.1 

DISTANCE FROM PLANE OF SYMMETRY, zlD 

Figure 61 Pressure Loss Distribution in the 90·deg Plane 

..J. 

2.3 2.5 
'T1 

cO" 

c 

... 

CD 

0) 

I\) 

~ 

I» 

... -iii" 

'T1 

0" 

:E 

< Cii" 

C 

I» r " 0 

\.0 N" ~ I» 

~ 

-

0" • -J 

~ ::;:, 

~ 

I» --

CD 

... 

::;:, -u 

r 

0 

::;:, » 

z 

m 

-:::r 0 

CD (f) " 

m 

::;:, 

-< 

c. 

s:: 

:E 

s:: 

!!. 

m 

-; 

:IJ 

-< 
3NIl 

NOllV8Vd3S t 

MOl:J 
!! I 

cg I 

"'" 
SURFACE OF OBSTRUCTION 

... FREE STflEAIv1 

PLAN: OF SYMMETRY -7 -

Figure 65 Endwall Flow Visualization Pattern Obtained by East 

and Hoxey 

99 
t-' 

o 

o 

SADDLE POINT 

PLANE OF 

~SYMMETRY r TOP 

·Ii , ~ 

Figure 66 Flow Visualization on Top Part of Cylinder 

CYLINDER 

-- MIDSPAN 
a:z 

w« 

OCL 

Z(fJ 

::10 

>-- 0 2 

~ 

i 2 

0 

lI- ~ 0 Q) i aJ '0 • 'j C 

>. 

0 

• 

-0 

LL>- ~ Og: 

-

~ 

WW as 

· • Q. 22 

«2 ~ ....J>- Q) CL(fJ ~ 

~ ." , 0 

...I 

C ~ 

0 0 

C ~ 

0 

;: 

as ~ t , .~ 

'ii 

::J 

U) 

:; 

~ 

0 

It l ii: ,~ ,y 

,.... 

CD 

11: t , ~ , Q) 

~ 

::J 

tJ) 

~ ~'. Ii '* t 

'\ 

, I' t. , u: 

;:" , ,~ • I 

r-~~-1 
~~ VORTEX DISSIPATED 

--.--

~ SEPARATION LINE 

/ 

\ENDWALL 

Figure 68 Horseshoe Vortex Formation 

102 
lapow xalJol\oJn0.:l 69 aJn6!.:I 

SlNIOd 

31001t8 

3NIl 

IN3I"1H~ltillt 

3NIl 

NOllltt:lltd3S - ---

~ ___ . 81NIOd 

31aaltS 
APPENDIX A - EXPERIMENTAL UNCERTAINTIES 

This appendix outlines the procedure used to determine experimental 

uncertanties associated with the data in Appendix B. 

Appendix Tables 

1. Summary of Experimental Uncertainties 

Cps 

Cp T 

Ps 

Ps a 

PT 

P

To 

qo 

R 

ReD 

T 

D 

Do 

V· ~ 

w· ~ 

y 

S 

<I> 

a 

e 

Appendix Symbols 

static pressure coefficient, equation (A4) 

loss coefficient, (PTa - PT)/qo 

local static pressure 

reference static pressure near test-section entrance 

local total pressure 

reference total pressure near test-section entrance 

reference dynamic pressure near test-section entrance 

radial distance from instrumented-disk center, figure 25 

Reynolds number based on the cylinder diameter 

any linear function for which an uncertainty level is needed, 

equation (AI) 

local velocity magnitude 

reference velocity magnitude near test section entrance 

any independent variable 

uncertainty interval for an indepndent variable, equation (A2) 

vertical distance from endwall, figure 25 

position angle relative to plane of symmetry, figure 25 

local flow pitch angle, figure 17 

standard deviation 

local flow yaw angle, figure 17 

Uncertainty Analysis 

The accuracy of data presented in Appendix B was assessed using the 

uncertainty analysis of Kline and McClintock (ref. AI). Theorem 3 of Kline 

and McClintock states that if T is a linear function of n independent normally 

distributed variables, v, 

T T(v l , v 2' v3 .... v n ) (Al) 

104 
then the relationship between an uncertainty interval, Wi, for each of the 

independent variables and the corresponding uncertainty interval for T, WT, 

is: 

WT -[( G:J WI) 2 + (G:J W2) 2 + ••• i(::J Wn) 2] 1/2 (A2) 

uncertainty intervals were calculated based on 20 to 1 odds that the measured 

value lies within the calculated uncertainty. The uncertainty intervals, 

then, correspond to four times the standard deviation of the measurement: 

Wi=±20'i = 4 cr i (A3) 

Surface Static Pressure Coefficients. - The surface static pressure 

coefficients are given by 

CPS 

P - P S s 0 

= P - P

s TO 0 

(A4) 

Since Ps was connected to the reference port of the Barocell differential 

o 

pressure transducer, the numerator and the denominator represent separate 

transducer measurements. With the transducer calibration fitted with a 

straight line, using the method of least squares, the standard deviation 

between the calibration and fitted line is 

O'p = 0.00547 cm of water 

The uncertainty of any differential pressure measurement, then, is: 

Wt,p = 4cr p = 0.02186 cm H20 

105 
Applying equation (A2) to equation (A4) gives the expression for the 

uncertainty in the pressure coefficient: 

Wc Ps ~( acp )2 - S W + - a(PS - P

S ) ~P 

o 

( 

acp )2] 1/2 

a (PT : P ) W~p o So 

= [ 1 (Cp ) 2] 1/2 W~p -2 + _S 

qo q o 

(AS) 

For these tests qo = S cm of water, and the largest measured absolute value 

of Cp was approximately 6.4 cm of water. Substituting these values into 

S 

equation (AS) yields the desired uncertainty: 

Wc 

Ps 

0.0119 

The odds are 20 to 1 that the surface pressure coefficients contained in 

Appendix B are within ± 0.00S9 of the tabulated value. 

Five-Hole Probe Measurements. - Uncertainty in the five-hole probe 

measurements were calculated in a manner similar to that shown for the surface 

static pressure coefficients. The calculations were more difficult, because 

of the added complexity of the calibration parameters. Each of the three 

pressure parameter curves shown in figure 19 was fitted with fifth order 

curves so that the appropriate derivatives required for equation (A2) could be 

evaluated. As with the surface coefficients, worst-case values of the derivatives were used to calculate the following uncertainties: 

Wc = 0.0324 

P s 

Wc = 0.0124 

PT 

Wu = 0.0170 

Uo 

Wcp 0.3 deg 

position Parameters. - The five-hole probe radial position, R, and 

angular position, S, were determined from the static pressure taps in the 

instrumented floor disk. Since the taps were accurately machined into the 

disk, the uncertainties in these values are small: 

106 
WR = 0.08 em We = 0.4 deg 

At the beginning of each traverse, the probe was manually shimmed to 0.25 

em off the floor. The vertical position from that point was determined from 

the L. C. Smith probe traverser calibration. The uncertainty of the ycoordinate due to the uncertainty introduced by the calibration is: 

Wy = 0.10 em 

uncertainty in the flow yaw angle, e, was introduced by four calibrations: the L. C. Smith probe rotation, the two probe positioner potentiometers, and the pitch angle correction (fig. 19). The uncertainty associated 

with these calibrations is: 

We = 1.0 deg 

Summary of Uncertainties. - A summary of the calculated uncertainty 

intervals is contained in Table AI. 

TABLE AI. - SUMMARY OF EXPERIMENTAL UNCERTAINTIES 

Qt}an- Cp -Surf. Cp Cp U <P e R e y tHy S T S Uo 

Uncer- ±O.O059 ±0.OO62 ±0.0162 ±0.0085 ±0.15 ±0.5 ±0.04 ±0.2 ±O .05 

tainty deg deg em deg em 

- - ---

107 

I 

I 
Error Due to Unsteadiness 

Flow unsteadiness affects five-hole probe measurements. Bennett (ref. 

A2) has shown that turbulence intensities of 25 percent can lead to the 

following changes in the measurements: 

yaw angle 

pitch angle 

q 

Cp T 

2.0 deg 

0.2 deg 

1 percent 

3.5 percent 

These changes are larger than the typically quoted five-hole probe 

accuracies of 0.5 percent. Based on the measurements of McMahon, et. al. 

(ref. 12), unsteadiness near this level probably only occurred where the mean 

velocities were low. In this study, low mean velocities were only recorded 

near the endwall and in the shear layer between forward and reverse flow in 

the plane of symmetry region. The effect of unsteadiness on most of the 

measurements, then, was probably small. Only in a small region near the plane 

of symmetry are changes as large as those indicated above expected to be 

caused by unsteadiness. 

Aerodynamic Effect of Five-Hole Probe 

Some error was introduced into the five-hole probe measurements by the 

physical presence of the probe. Since the cylinder blockage was two orders of 

magnitude larger than that of the probe tip, probe interference effects were 

found to be small. Static pressures measured with the probe are in good 

agreement with endwall static pressures throughout most of the separation 

region. With the probe tip near the endwall in the plane of symmetry, though, 

core flow entering the endwall region near the cylinder passed around the 

large diameter probe support prior to reaching the measurement location. The 

reverse flow direction near the endwall was affected by the probe support. 

The yaw angle measurements for the traverse at RID = 0.638 (fig. 37) show a 

variation near the endwall. The yaw angle decreased to approximately -173 deg 

whereas the flow visualization shows a limiting streamline angle of 180 deg. 

This effect was only encountered near the cylinder in the plane of symmetry. 

108 
REFERENCES 

AI. Kline, S. J., and McClintock, F. A., "Describing Uncertainties in SingleSampl e Experiments," Mechanical Engineering, Jaunary 1953. 

A2. Bennett, J. C., "Use of Five-Hole Pneumatic Probe in Unsteady Flows," 

Experimental Diagnostics in Gas Phase Combustion Systems, Progress in 

Aeronautics and Astronautics, Vol. 53, Volume Editor: B. T. Zinn, 1977. 

109 
APPENDIX B - TABULATED DATA 

This appendix contains a tabulation of the conditions specifying the 

inlet boundary conditions, endwall and cylinder surface static pressure 

coefficients, and data gathered via a five-hole probe. The coordinate system 

for presenting these data is contained in figure 25. Values of terms used to 

nondimensionalize quantities in the table are listed below. The reference 

conditions are nominal values for the test program. 

Appendix Tables 

1. Values of Terms for Nondimensinalizing Data 

2. Inlet Profiles 

3. Cylinder Surface Static Pressure Distributions 

4. Endwall Static Pressure Distributions 

5. Five Hole Probe Data 

CPS 

Cp T 

D 

Ps 

P

So 

PT 

PT o 

PHI 

qo 

R 

ReD 

e 

U 

Uo 

y 

z 

D 

29.85 em 

Appendix Symbols 

static pressure coefficient, (PS - Ps )/qo 

o 

loss coefficient, (PT - PT)/qo 

o 

cylinder diameter 

local static pressure 

reference static pressure near test-section entrance 

local total pressure 

reference total pressure near test-section entrance 

local flow pitch angle, figure 17 

reference dynamic pressure near test-section entrance 

radial distance from instrumented-disk center, figure 25 

Reynolds number based on the cylinder diameter 

local flow yaw angle, figure 17 

local velocity magnitude 

reference velocity magnitude near test section entrance 

vertical distance from endwall, figure 25 

distance from vertical plane of symmetry, figure 25 

Values of Terms for Nondimensionalizing Data 

Ps o 

0.1006 MPa 

PT o 

0.1011 MPa 

110 

qo 

486 Pa 

Uo 

29.0 m/sec 
Inlet Profiles 

z/D=O.O z/D=1.021 

---------------------------- ---------------------------- Y/D CPT CPS U/Uo Y/O CPT CPS U/Uo 

0.0051 0.591 0.059 0.592 0.0051 0.607 0.044 0.590 

0.0140 0.467 0.060 0.688 0.0136 0.477 0.043 0.693 

0.0226 0.396 0.059 0.738 0.0221 0.415 0.043 0.736 

0.0311 0.343 0.060 0.773 0.0306 0.357 0.043 0.775 

0.0396 0.287 0.059 0.808 0.0391 0.300 0.043 0.810 

0.0481 0.235 0.059 0.840 0.0477 0.253 0.042 0.840 

0.0651 0.134 0.060 0.898 0.0562 0.201 0.043 0.870 

0.0736 0.099 0.059 0.918 0.0647 0.153 0.043 0.897 

0 .. 0821 0.057 0.060 0.940 0.0732 0.111 0.043 0.920 

0.0906 0.029 0=060 0.955 0.0817 0=071 0.044 0.941 

0.0991 0.015 0.060 0.962 0.0902 0.038 0.043 0.958 

0.1077 0.002 0.061 0.968 0.0987 0.015 0.043 0.971 

0.1162 -0.003 0.061 0.971 0.1072 0.003 0.044 0.977 

0.1247 -0.006 0.060 0.972 0.1157 -0.004 0.045 0.979 

0.2013 -0.006 0.062 0.972 0.2009 -0.003 0.045 0.979 

0.2864 0.001 0.062 0.968 0.2860 -0.001 0.047 0.977 

0.3715 0.000 0.064 0.968 0.3711 0.002 0.047 0.975 

0.4566 0.001 0.064 0.967 0.4562 0.004 0.048· 0.974 

0.5417 0.004 0.065 0.965 0.5413 0.004 0.050 0.973 

z/D=2.043 

------------------------------

YIn CPT CPS U/Uo 

0.0051 0.619 0.0048 0.614 

0.0136 0.484 0.0031 0.716 

0.0221 0.417 0.0028 0.762 

0.0306 0.353 0.0030 0.803 

0.0391 0.299 0.0037 0.835 

0.0477 0.241 0.0027 0.869 

0.0562 0.204 0.0020 0.891 

0.0647 0.149 0.0030 0.921 

0.0732 0.112 0.0031 0.941 

0.0817 0.068 0.0030 0.964 

0.0902 0.032 0.0033 0.982 

0.0987 0.011 0.0032 0.993 

0.1072 0.001 0.0029 0.998 

0.1157 -0.003 0.0029 1.000 

0.2009 -0.001 0.0035 0.999 

0.2860 0.002 0.0050 0.997 

0.3711 0.002 0.0049 0.996 

0.4562 0.004 0.0058 0.995 

0.5413 0.004 0.0072 0.994 

III 
Cylinder Surface Static Pressure Coefficients 

f3 

Y/D 0 5 10 15 20 25 30 35 40 45 

=================================================================================================== 

0.511 0.996 0.965 0.B86 0.741 0.553 0.330 0.037 -0.267 -0.58B -0.90B 

0.489 0.999 0.972 0.882 0.732 0.557 0.314 0.044 -0.243 -0.5B6 -0.921 

0.468 0.995 0.969 0.889 0.752 0.549 0.301 0.053 -0.259 -0.573 -0.883 

0.447 0.996 0.968 0.B83 0.750 0.543 0.303 0.023 -0.276 -0.5B8 -0.922 

0.426 0.998 0.965 0.883 0.740 0.551 0.326 0.030 -0.272 -0.596 -0.926 

0.404 0.999 0.972 0.8B3 0.733 0.553 0.309 0.040 -0.248 -0.593 -0.929 

0.383 0.995 0.969 0.B89 0.749 0.548 0.300 o.lm -0.266 -0.579 -0.890 

0.362 0.997 0.969 O.BBb 0.751 0.542 0.303 0.024 -0.274 -0.590 -0.924 

0.340 0.999 0.965 0.884 0.741 0.552 0.326 0.031 -0.276 -0.601 -0.927 

0.319 0.999 0.972 0.8B4 0.733 0.550 0.310 0.039 -0.251 -0.597 -0.929 

0.298 0.996 0.971 0.891 0.75(; 0.550 0.299 0.040 -0.268 -0.562 -0.B99 

0.277 0.996 0.969 0.882 0.750 0.543 0.303 0.026 -0.276 -0.5B9 -0.922 

0.255 0.995 0.962 0.B81 0.738 0.54B 0.321 0.023 -0.279 -0.606 -0.930 

0.234 0.996 0.971 0.B81 0.730 0.550 0.310 0.041 -0.248 -0.594 -0.929 

0.213 0.991 0.966 0.888 0.750 0.548 0.300 0.043 -0.267 -0.577 -0.890 

0.191 0.991 0.963 0.862 0.749 0.543 0.304 0.027 -0.271 -0.587 -0.918 

0.17(t 0.987 0.957 0.B81 0.736 0.551 0.323 0.030 -0.273 -0.599 -0.916 

0.149 0.985 0.963 0.875 0.730 0.552 0.313 0.041 -0.243 -0.584 -0.9i5 

0.128 0.979 0.957 0.881 0.747 0.550 0.304 0.053 -0.250 -0.566 -0.877 

0.106 0.975 0.954 O.B72 0.744 0.544 0.310 0.03B -0.255 -0.567 -0.896 

0.OB5 O. ~'75 0.948 0.873 0.740 0.554 0.333 0.048 -0.251 -0.567 -0.BB7 

0.064 0.978 0.958 0.B76 0.734 0.561 0.330 0.068 -0.220 -0.552 -O.B7~ 

0.043 0.986 0.965 0.888 0.759 0.570 0.329 O.OBO -0.221 -0.528 -0.836 

0.011 1.000 0.981 0.902 0.776 0.582 0.35B 0.093 -0.199 -0.504 -0.827 

112 
Cylinder Surface Static Pressure Coefficients 

(continued) 

f3 

Y/D 50 55 60 65 70 75 80 85 90 

=====:=================================================================::E================ 

0.511 -1.227 -1.535 -1.800 -2.048 -2.233 -2.379 -2.447 -2.457 -2.366 

0.489 -1.239 -1.550 -1.819 -2.062 -2.250 -2.388 -2.456 -2.479 -2.426 

0.468 -1.235 -1. 545 -1.832 -2.074 -2.25b -2.409 -2.471 -2.486 -2.432 

0.447 -1.242 -1.545 -1.831 -2.084 -2.283 -2.432 -2.498 -2.523 -2.454 

0.426 -1.242 -1.554 -1.832 -2.078 -2.279 -2.427 -2.521 -2.545 -2.494 

0.404 -1.258 -1.565 -1. 841 -2.093 -2.281 -2.438 -2.526 -2.560 -2.517 

0.383 -1.251 -1.566 -1.854 -2.100 -2.296 -2.450 -2.533 -2.566 -2.523 

0.362 -1.247 -1.559 -1.852 -2.102 -2.30B -2.458 -2.544 -2.578 -2.524 

0.340 -1.246 -1.559 -1.843 -2.099 -2.306 -2.468 -2.547 -2.590 -2.551 

0.319 -1.263 -1.570 -1.858 -2.107 -2.314 -2.461 -2.5b2 -2.598 -2.543 

0.298 -1. 258 -1.575 -1.863 -2.115 -2.318 -2.462 -2.554 -2.590 -2.551 

0.277 -1.249 -1.560 -1.844 -2.115 -2.311 -2.475 -2.566 -2.600 -2.55~ 

0.255 -1.255 -1. 570 -1.857 -2.106 -2.313 -2.472 -2.570 -2.603 -2.569 

0.234 -1.255 -1.564 -1.847 -2.101 -2.314 -2.465 -2.557 -2.603 -2.553 

0.213 -1.248 -1.566 -1.857 -2.096 -2.310 -2.459 -2.548 -2.591 -2.545 

0.191 -1.238 -1.547 -1.840 -2.101 -2.298 -2.458 -2.562 -2.590 -2.533 

0.170 -1.234 -1.547 -1.834 -2.083 -2.296 -2.448 -2.542 -2.569 -2.544 

0.149 -1.249 -1.550 -1.827 -2.075 -2.280 -2.435 -2.531 -2.563 -2.518 

0.128 -1.227 -1.541 -1.825 -2.069 -2.275 -2.431 -2.514 -2.542 -2.496 

0.106 -1.211 -1.520 -1.800 -2.058 -2.261 -2.421 -2.503 -2.532 -2.490 

0.085 -1.205 -1.509 -1.791 -2.030 -2.243 -2.409 -2.486 -2.507 -2.465 

0.064 -1.198 -1.501 -1.776 -2.021 -2.219 -2.368 -2.448 -2.507 -2.456 

0.043 -1.174 -1.489 -1.771 -2.012 -2.211 -2.360 -2.448 -2.474 -2.423 

0.011 -1.120 -1.443 -1.724 -1. 980 -2.177 -2.327 -2.411 -2.452 -2.388 

113 
Endwall Static Pressure Coefficients 

f3 

RID 0 5 10 15 20 25 30 35 40 45 

=================================================================================================:= 

0.5021 1.005 0.982 0.902 0.762 0.596 0.370 0.116 -0.173 -0.470 -0.789 

0.5319 1.001 0.978 0.095 0.786 0.640 0.435 0.209 -0.045 -0.311 -0.585 

0.5532 0.976 0.959 0.897 0.787 0.638 0.453 0.238 0.004 -0.247 -0.505 

0.5745 0.939 0.914 0.859 0.760 0.634 0.461 0.259 0.040 -0.192 -0.428 

0.5957 0.867 0.864 0.810 0.714 0.593 0.439 0.260 0.056 -0.156 -0.374 

0.6170 0.802 0.785 0.732 0.646 0.543 0.392 0.230 0.048 -0.144 -0.333 

0.6383 0.701 0.681 0.645 0.567 0.469 0.331 0.181 0.013 -0.163 -0.350 

0.6596 0.609 0.582 0.549 0.469 0.380 0.252 0.119 -o.o:n -0.197 -0.359 

0.6809 0.513 0.461 0.402 0.325 0.260 0.159 0.027 -0.103 -0.246 -0.391 

0.7021 0.381 0.354 0.314 0.251 0.167 0.070 -0.050 -0.171 -0.305 -0.444 

0.7234 0.341 0.327 0.275 0.231 0.154 0.056 -0.058 -0.181 -0.322 -0.449 

0.7447 0.362 0.331 0.304 0.241 0.204 0.125 0.007 -0.123 -0.253 -0.391 

0.7660 0.397 0.446 0.434 0.379 0.285 0.192 0.083 -0.040 -0.172 -0.302 

0.7872 0.484 0.491 0.459 0.400 0.325 0.233 0.125 0.010 -0.116 -0.245 

0.80B5 0.471 0.471 0.456 0.402 0.339 0.251 0.146 0.037 -0.OB2 -0.199 

0.8298 0.488 0.482 0.459 0.407 0.345 0.260 0.162 0.056 -0.060 -0.173 

0.8511 0.476 0.481 0.452 0.403 0.343 0.263 0.172 0.074 -0.031 -0.144 

0.8723 0.478 0.473 0.443 0.401 0.341 0.2b6 0.182 0.OB6 -0.014 -0.123 

0.8936 0.459 0.457 0.435 0.389 0.337 0.264 0.181 0.093 -0.007 -0.111 

0.9149 0.453 0.453 0.425 0.385 0.331 0.265 0.18b 0.099 0.001 -0.098 

0.9362 0.439 0.444 0.408 0.371 0.322 0.258 0.184 0.101 0.007 -0.088 

0.9574 0.428 0.420 0.395 0.3b6 0.313 0.254 0.183 0.101 0.013 -0.076 

0.9787 0.418 0.411 0.387 0.351 0.303 0.246 0.176 0.097 0.010 -0.074 

1.000!; O.40t 0.399 0.379 0.341 0.294 0.243 0.176 0.097 0.016 -0.066 

114 
Endwall Static Pressure Coefficients 

(continued) 

f3 

RiD (; 5 10 15 20 25 30 3S 4(1 45 

=============================================================:a==================================== 

1.0213 0.392 0.382 0.358 0.329 0.283 0.233 0.166 0.094 0.017 -0.063 

1.0426 O.37b 0.364 0.347 0.321 0.273 0.224 0.100 0.091 0.017 -0.058 

1.0638 0.369 0.358 0.336 0.307 0.263 0.217 0.152 0.084 0.013 -0.061 

1.0851 0.353 0.346 0.327 0.294 0.25g 0.212 0.152 0.086 0.015 -0.054 

1.1064 0.341 0.330 0.312 0.286 0.247 0.201 0.142 0.080 0.015 -0.053 

1.1277 0.326 0.316 0.305 0.2i7 0.240 0.193 0.139 0.078 0.017 -0.050 

1.1489 0.319 0.312 0.292 0.2b6 0.231 0.185 0.129 0.072 0.011 -0.055 

1.1702 0.308 0.301 0.283 0.256 0.225 0.lB2 0.129 0.072 0.013 -0.051 

1.1915 0.296 0.2BB 0.271 0.246 0.216 0.172 0.122 0.070 0.011 -0.049 

1.2340 0.273 0.267 0.255 0.229 0.200 0.160 0.115 0.066 0.011 -0.048 

1. 2766 0.259 0.254 0.239 0.215 0.187 0.148 0.106 0.059 0.005 -0.049 

1.3191 0.244 0.236 0.224 0.204 0.174 0.140 0.100 0.053 0.003 -0.045 

1.3617 0.226 0.221 0.210 0.186 0.163 0.130 0.092 0.048 0.002 -0.045 

1.4043 0.212 0.207 0.196 0.175 0.153 0.122 0.OB6 0.045 0.003 -0.043 

1.4468 0.201 0.197 0.lB7 0.166 0.139 0.112 0.075 0.037 -0.004 -0.051 

1. 4814 0.194 0.187 0.175 0.159 0.133 0.108 0.073 0.038 -0.001 -0.045 

1.5319 O.lBl 0.177 0.167 0.147 0.12B 0.104 0.070 0.035 -0.002 -0.043 

1. 5745 0.172 0.167 0.157 0.140 0.122 0.097 0.065 0.034 -0.003 -0.042 

1. 6170 0.163 0.159 0.151 0.135 0.114 0.090 0.060 0.029 -0.007 -0.046 

1.6516 0.157 0.152 0.142 0.128 0.109 0.085 0.058 0.026 -0.008 -0.044 

1.7021 0.148 0.145 0.136 0.127 0.103 0.082 0.056 0.024 -0.009 -0.043 

1. 7872 0.136 0.131 0.122 0.111 0.097 0.072 0.050 0.021 -0.010 -0.042 

1.8723 0.126 0.122 0.115 0.104 0.087 0.068 0.044 0.018 -0.012 -0.043 

1. 9574 0.118 0.114 0.107 0.094 0.080 0.063 0.041 0.015 -0.012 -0.040 

2.0426 0.107 0.105 0.099 0.OB8 0.074 0.060 0.037 0.012 -0.013 -0.038 

2.1277 0.102 0.099 0.091 0.083 0.071 0.054 0.034 0.013 -0.011 -0.038 

2.2128 0.095 0.094 0.086 0.079 0.065 0.051 0.030 0.011 -0.013 -0.040 

2.2979 0.093 0.089 0.083 0.074 0.062 0.048 0.030 0.010 -0.012 -0.036 

2.3830 0.087 0.OB5 0.079 0.071 0.062 0.04B 0.031 0.010 -0.012 -0.034 

115 
Endwall Static Pressure Coefficients 

h:ontinuedi 

f3 

RID 50 5S 60 65 70 75 80 85 90 

=================================================================z===================-==== 

0.5021 -1.086 -1.368 -1.633 -1.868 -2.070 -2.212 -2.309 -2.283 -2.221 

0.5319 -0.862 -1.126 -1.372 -1.598 -1.782 -1.896 -1. 963 -1.993 -1. 915 

0.5532 -0.765 -1.006 -1.227 -1.409 -1.564 -1.695 -1.783 -1.812 -1.812 

0.5745 -0.668 -0.891 -1.105 -1.280 -1.416 -1.511 -1.574 -1.609 -1. 574 

0.5957 -0.587 -0.783 -0.971 -1.146 -1.296 -1.406 -1.475 -1.478 -1.457 

0.6170 -0.531 -0.725 -0.907 -1.066 -1.198 -1.282 -1.341 -1.368 -1. 341 

0.6363 -0.529 -0.701 -0.850 -0.979 -1.096 -1.191 -1.250 -1.289 -1.288 

0.6596 -0.524 (; 'Ii' - .0,1 -0.831 -0.955 -1. 050 -1.109 -1.157 -1.178 -1.186 

0.6809 -0.531 -0.664 -0.767 -0.906 -1.000 -1.077 -1.126 -1.123 -1.114 

0.7021 -0.563 -0.694 -0.805 -0.914 -0.986 -1.036 -1.062 -1.073 -1.050 

0.7234 -0.594 -0.712 -0.821 -0.910 -0.982 -1.033 -1.061 -1.066 -1.053 

0.7447 -0.526 -0.653 -0.776 -0.875 -0.949 -0.911 -1.017 -1.030 -1.016 

0.7660 -0.437 -0.563 -0.676 -0.787 -0.885 -0.946 -0.993 -1.000 -0.985 

0.7872 -0.371 -0.490 -0.608 -0.712 -0.800 -0.864 -0.921 -0.945 -0.948 

0.8085 -0.323 -0.440 -0.550 -0.64B -0.733 -0.804 -0.859 -0.896 -0.910 

0.B298 -0.292 -0.404 -0.512 -0.611 -0.692 -0.755 -0.804 -0.838 -0.856 

0.8511 -0.257 -0.363 -0.464 -0.559 -0.642 -0.712 -0.762 -0.790 -0.807 

0.8723 -0.229 -0.336 -0.436 -0.528 -0.605 -0.666 -O.71S -0.755 -0.770 

0.8936 -0.216 -0.316 -0.408 -0.494 -0.564 -0.634 -0.686 -0.726 -0.745 

0.9149 -0.200 -0.296 -0.388 -0.466 -0.539 -0.601 -0.643 -0.685 -0.713 

0.936: -0.181 -0.271 -0.355 -0.439 -0.514 -0.575 -0.622 -0.654 -0.681 

0.9574 -0.166 -0.255 -0.339 -0.418 -0.485 -0.541 -0.589 -0.624 -0.647 

0.9787 -0.16! -0.245 -0.327 -0.400 -0.465 -0.522 -0.572 -0.610 -0.631 

1.0000 -0.149 -0.236 -0.314 -0.394 -0.455 -0.511 -0.555 -0.589 -0.611 

116 
Endwall Static Pressure Coefficients 

(continuedl 

f3 

RiD 50 55 DO 65 70 75 SO 85 90 

========================================================================================== 

1. 0213 -0.142 -0.220 -0.295 -0.363 -0.428 -0.485 -0.527 -0.559 -0.581 

1. 0426 -0.133 -0.212 -0.286 -0.356 -0.412 -0.464 -0.507 -0.540 -0.561 

1.0638 -0.136 -0.209 -0.278 -0.343 -0.400 -0.451 -0.498 -0.529 -0.550 

1.0851 -0.127 -0.201 -0.270 -o.:m -0.394 -0.444 -0.484 -0.516 -0.538 

1.1064 -0.122 -0.191 -0.257 -0.319 -0.378 -0.426 -0.463 -O.49b -0.518 

1.1277 -0.117 -0.184 -0.251 -0.309 -0.362 -0.40B -O.44B -0.479 -0.503 

1.1489 -0.122 -0.184 -0.245 -0.303 -0.354 -0.404 -0.444 -0.475 -0.497 

1.1702 -0.112 -0.178 -0.239 -0.298 -0.348 -0.394 -0.431 -0.463 -0.483 

1.1915 -0.111 -0.169 -0.226 -0.283 -0.335 -0.378 -0.415 -0.445 -0.463 

1.2340 -0.104 -0.162 -0.220 -0.271 -0.317 -0.358 -0.391 -0.422 -0.444 

1.2766 -0.103 -0.156 -0.209 -0.257 -0.302 -0.343 -0.379 -0.407 -0.428 

1.3191 -0.095 -0.152 -0.202 -0.253 -0.292 -0.333 -0.365 -0.392 -0.412 

1.3617 -0.094 -0.144 -0.192 -0.237 -0.281 -0.317 -0.349 -0.374 -0.396 

1.4043 -0.091 -0.137 -0.184 -0.228 -0.263 -0.300 -0.333 -0.357 -0.378 

1. 4468 -0.099 -0.141 -0.187 -0.228 -0.267 -0.302 -0.335 -0.360 -0.379 

1.4894 -0.088 -0.133 -0.175 -0.218 -0.253 -0.287 -0.315 -0.340 -0.360 

1.5319 -0.085 -0.126 -0.166 -0.203 -0.241 -0.273 -0.298 -0.324 -0.345 

1. 5745 -0.082 -0.121 -0.161 -0.199 -0.230 -0.264 -0.291 -0.317 -0.335 

1. 6170 -0.OB4 -0.121 -0.159 -0.195 -0.228 -0.259 -0.288 -0.311 -0.329 

1. 6596 -0.081 -0.11B -0.153 -0.191 -0.221 -0.252 -0.276 -0.302 -0.321 

1.7021 -0.078 -0.115 -0.149 -0.183 -0.215 -0.245 -0.267 -0.292 -0.309 

1.7872 -0.075 -0.10B -0.144 -0.175 -0.201 -0.230 -0.256 -0.280 -0.296 

1.8723 -0.073 -0.105 -0.137 -0.166 -0.195 -0.224 -0.250 -0.270 -0.289 

1.9574 -0.068 -0.101 -0.130 -0.162 -0.187 -0.212 -0.236 -0.260 -0.275 

2.0426 -0.068 -0.098 -0.126 -0.154 -0.183 -0.207 -0.227 -0.249 -0.264 

2.1277 -0.066 -0.092 -0.122 -0.148 -0.171 -0.200 -0.219 -0.239 -0.255 

2.2128 -0.066 -0.091 -0.117 -0.144 -0.169 -0.192 -0.218 -0.237 -0.251 

2.2979 -0.061 -0.088 -0.113 -0.142 -0.163 -0.186 -0.209 -0.230 -0.247 

2.3830 -0.060 -0.086 -0.110 -0.133 -0.161 -0.184 -0.202 -0.223 -0.240 

117 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

-5.000 DEG 

0.809 

============================================================ 

Y/D 

0.0083 

0.0131 

0.0159 

0.0214 

0.0294 

0.0377 

0.0460 

0.0543 

0.0625 

0.0706 

0.0787 

0.0871 

0.0954 

0.1036 

().1117 

O. 119<7' 

0.1334 

0.1472 

0.1607 

0.1746 

0.2157 

0.2568 

0.3387 

0.4210 

0.5055 

PHI 

DEG 

5.0 

13.9 

11.3 

-1. 1 

1.5 

4.2 

7.4 

4.0 

4.8 

7.5 

2.2 

4.6 

1.0 

1.3 

-0.3 

-c). 3 

0.3 

-0.7 

-0.5 

-1.6 

-2.1 

-2.5 

-2.4 

-1.7 

-0.8 

THETA 

DEG 

-104.6 

-101.1 

-97.9 

-74.2 

-47.7 

-31.9 

-23.6 

-18.1 

-14.1 

-11.5 

-10.0 

-9.2 

-8.2 

-7.5 

-7.3 

-6.9 

-6.5 

-6.1 

-5.6 

-5.1 

-5.1 

-5.8 

-5.9 

-6.1 

-7.2 

118 

CPT CPS U/Uo 

0.519 0.443 0.195 

0.547 0.431 0.145 

0.548 0.430 0.148 

0.542 0.425 0.184 

0.493 0.417 0.300 

0.449 0.436 0.255 

0.450 0.435 0.339 

0.443 0.441 0.341 

0.370 0.447 0.427 

0.328 0.437 0.485 

0.299 0.438 0.512 

0.256 0.443 0.549 

0.228 0.449 0.568 

0.149 0.455 0.629 

0.124 0.462 0.643 

0.087 0.456 0.677 

0.047 0.464 0.699 

0.016 0.465 0.720 

-0.004 0.468 0.732 

-0.006 0.476 0.729 

-0.003 0.496 0.712 

-0.003 0.517 0.697 

0.004 ().532 0.681 

0.005 0.536 0.677 

0.007 0.550 0.666 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

-5.000 DEG 

0.888 

============================================================ 

Y/D 

0.0085 

0.0144 

0.0213 

0.0296 

0.0376 

0.0459 

0.0541 

0.0624 

0.0704 

0.0787 

0.0870 

0.0952 

0.1033 

0.1118 

0.1199 

0.1336 

0.1472 

0.1607 

0.1745 

0.:'156 

0.2566 

0.3387 

0.4208 

0.5054 

PHI 

DEG 

-1.6 

-2.8 

-0.1 

-1.6 

O. 1 

1.5 

1.4 

1.3 

1.3 

1.5 

1.2 

1.1 

1.1 

1.0 

0.8 

0.8 

0.6 

0.5 

0.5 

-0.4 

-0.7 

-1.3 

-1.7 

-1.7 

THETA 

DEG 

-45.9 

-32.1 

""""'"":'" '"7 -4-_--. _'\ 

-16.9 

-13.8 

-11.4 

-9.5 

-8.3 

-7.5 

-7.1 

-6.5 

-6.1 

-5.8 

-5.5 

-5.4 

-5.0 

-4.6 

-4.4 

-4.1 

-4.1 

-4.7 

-4.5 

-4.6 

-5.0 

119 

CPT CPS U/Uo 

0.533 0.440 O. 164 

0.508 0.443 0.219 

0.493 0.439 0.261 

0.446 0.445 0.330 

0.426 0.439 0.366 

0.374 0.445 0.424 

0.338 0.439 0.472 

0.317 0.437 0.497 

0.267 ,.,. ,. ..... v • .,."'tJ. 0.540 

0.241 0.434 0.570 

0.196 0.436 0.607 

0.153 0.436 0.641 

0.126 0.432 0.665 

0.081 0.433 0.697 

0.058 0.433 0.713 

0.023 0.432 0.739 

0.002 0.431 0.75::::, 

-0.008 0.430 0.760 

-0.011 0.436 0.758 

-0.008 0.438 0.755 

-0.009 0.443 0.752 

-0.003 0.454 0.741 

-0.002 0.461 0.736 

-0.001 0.465 0.732 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

-5.000 DEG 

0.936 

============================================================ 

Yin 

0.0083 

0.0152 

0.0228 

0.0311 

0.0393 

0.0473 

0.0556 

0.0636 

0.0721 

0.0801 

0.0939 

0.1076 

0.1213 

0.1351 

O.148t:-

0.1622 

0.1760 

0.2170 

0.2580 

0.3403 

0.4224 

0.5067 

PHI 

DEG 

-0.7 

..,.. <=" -.-, .. ....J 

0.0 

-0.4 

(j. (; 

1.3 

O. 1 

1.3 

1 .J.. • ~ _, 

1.6 

1.2 

1.7 

1.5 

1. ::;:. 

1.3 

1.5 

1.1 

0.7 

0.0 

-0.6 

-1.0 

-1. (j 

THETA 

DEG 

-29.1 

-20.5 

-14.6 

-11.7 

-9.4 

-7.9 

-7.1 

-6.1 

-5.4 

-4.8 

-4.1 

-3.6 

-3.2 

-2.9 

-2.6 

-..::. '"' • c-..J 

-2.4 

-2.0 

-2.5 

-2.7 

-3. () 

-3.3 

120 

CPT CPS U/Uo 

0.546 0.414 0.200 

0.532 0.411 0.239 

0.485 0.412 0.321 

0.456 0.412 0.362 

0.419 0.415 0.407 

0.391 0.409 0.447 

0.355 0.404 0.491 

0.325 0.405 0.521 

0.278 0.407 0.561 

0.251 0.403 0.588 

0.200 0.400 0.632 

0.140 0.395 O.6E:::: 

0.085 0.398 0.720 

0.062 0.395 0.737 

0.025 0.397 0.76C 

0.007 0.395 () .. 773 

0.000 0.396 0.777 

-0.007 0.397 0.781 

-0.006 0.398 0.779 

-0.004 0.409 0.771 

-0.001 0.416 (>. 7£::5 

-0.001 0.419 0.763 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA~ 

Five-Hole Probe Data 

(continued) 

-5.000 DEG 

1.021 

============================================================ 

YiD 

0.0084 

0.0157 

0.0233 

0.0316 

0.0396 

0.0479 

0.0561 

0.0644 

O. Cl724 

0.0807 

0.0943 

0.1081 

0.1219 

0.1354 

0.1492 

0.1628 

O. 1766 

0.2174 

0.2588 

O.34(i5 

0.4230 

o C"c~~ • ....s _.1/.':;. 

PHI 

DEG 

-1.4 

-0.3 

-0.1 

-0.8 

-0.4 

0.2 

0.4 

0.0 

().5 

(i.l 

0.7 

0.7 

0.9 

0.9 

1.0 

1.2 

1.2 

0.7 

0.5 

-0.2 

-I). "2-

-U.6 

THETA 

DEG 

-13.3 

-10.4 

-8.4 

-7.1 

-6.1 

-5.4 

-4.8 

-4.3 

-3.8 

-3.6 

-3.3 

-3.0 

-2.7 

-2.5 

-2.4 

-2.3 

-2.1 

-1.8 

-2.2 

-2.4 

-2.6 

-2.8 

121 

CPT CPS UiUo 

0.544 0.371 0.292 

0.508 0.367 0.354 

0.474 0.365 0.401 

0.441 0.365 0.440 

0.409 0.365 0.475 

0.372 0.36:· 0.515 

0.347 ().361 (f. 54() 

0.304 0.360 0.580 

0.268 0.360 0.610 

0.244 0.356 0.633 

0.180 0.356 0.681 

0.131 0.353 0. 7 18 

0.080 0.353 ().752 

0.056 0.351 0.771 

().022 0.352 0.791 

-0.001 0.348 0.808 

-0.013 0.351 0.814 

-0.014 0.347 0.817 

-0.011 0.349 0.814 

-0.009 (}.353 0.810 

-0.001 0.357 0.802 

-0.012 0.370 0.801 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

-5.000 DEG 

1.191 

============================================================ 

Y/D 

0.0083 

0.0160 

0.0244 

0.0323 

0.0406 

0.0488 

0.0572 

0.0654 

0.0733 

0.0817 

0.0954 

0.1089 

O. 1229 

0.1365 

0.1501 

0.1776 

0.2185 

0.2597 

0.3418 

0.4238 

().5()83 

PHI 

DEG 

1.2 

0.7 

-0.9 

-0.3 

-1.3 

-0.6 

-0.6 

0.2 

0.1 

0.2 

0.0 

0.4 

0.1 

0.4 

o s= .-1 

0.4 

0.5 

0.0 

-0.2 

-0.3 

-0=4 

THETA 

DEG 

-7.0 

-6.2 

-5.4 

-4.8 

-4.3 

-3.9 

-3.7 

-3.4 

-3.2 

-3.1 

-2.9 

-2.7 

-2.5 

-2.3 

-2.2 

-1.8 

-1.8 

-1.9 

-2.1 

-2.4 

-2.4 

122 

CPT CPS U/Uo 

0.543 0.284 0.416 

0.494 0.272 0.484 

0.441 0.276 0.533 

0.419 0.271 0.557 

0.383 0.272 0.587 

0.328 0.275 O. 6~.O 

0.313 0.267 0.648 

0.278 0.273 0.669 

0.247 0.270 0.695 

0.211 0.268 0.722 

0.154 0.269 0.760 

0.108 0.270 0.789 

0.076 0.267 0.811 

0.040 0.265 0.834 

0.008 0.270 0.850 

-0.015 0.265 0.866 

-0.010 0.264 0.863 

-0.011 0.265 0.864 

-0.009 0.268 0.861 

-0.004 0.266 0.859 

-0.004 0.269 0.857 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

<conti nued) 

-5.000 DEG 

1.532 

============================================================ 

Y/D 

0.0085 

0.0140 

0=0196 

0.0278 

0.0361 

0.0441 

0.0524 

0.0606 

0.0690 

0.0770 

0.0852 

0.0991 

0.1125 

0.1264 

0.1399 

0.1537 

0.1810 

0.2221 

0.2632 

0.3453 

0.4273 

0.5112 

PHI 

DEG 

0.1 

-0.3 

-0.6 

(j.3 

-0.9 

-0.3 

-0.4 

0.1 

0.0 

-0.1 

0.0 

0.2 

0.0 

0.1 

0.6 

0.4 

0.7 

0.5 

0.1 

-0.3 

O. 1 

-0.3 

THETA 

DEG 

-2.8 

-2.7 

-2.5 

-2.5 

-2.2 

-2.2 

-2.0 

-2. i) 

-1.8 

-1.8 

-1.7 

-1.7 

-1.6 

-1.6 

-1.6 

-1.6 

-1.3 

-0.9 

-1. 1 

-1.4 

-1.5 

-1.5 

123 

CPT 

0.559 

0.520 

0.482 

0.429 

0.401 

0.371 

(1.323 

0.296 

0.261 

0.224 

0.197 

0.139 

0.100 

0.053 

0.021 

-0.005 

-0.014 

-0.017 

-0.012 

-0.004 

-0.004 

-0.004 

CPS 

0.175 

0.171 

0.166 

0.166 

0.166 

0.167 

0.163 

0.161 

0.160 

0.160 

0.161 

0.159 

0.156 

0.159 

0.154 

0.157 

0.161 

0.157 

0.156 

0.154 

O. 161 

0.160 

U/Uo 

0.516 

0.556 

0.593 

0.636 

0.658 

0.680 

0.717 

0.736 

0.761 

0.785 

0.801 

0.838 

0.863 

0.888 

0.908 

0.921 

0.924 

0.927 

0.925 

0.922 

0.918 

0.919 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.596 

============================================================ 

Y/D 

0.0078 

0.0101 

0.0148 

0.0186 

0.0227 

().027i) 

0.0313 

0.0354 

0.1261 

0.1344 

0.1468 

0.1605 

0.1946 

0.2165 

0.2575 

0.2985, 

0.3395 

0.3799 

('.4628 

PHI 

DEG 

-2.2 

-8.7 

-12.2 

-13.8 

-15.0 

-17.9 

-22.8 

-27. 1 

-27.1 

-26.1 

-21.5 

-18.7 

-11.6 

-8.5 

-6.9 

-3.8 

-1.3 

-3.4 

-1.7 

THETA 

DEG 

-156.7 

-158.4 

-163.1 

-173.6 

179.0 

177.5 

177.4 

178.3 

-0.5 

13.4 

1.9 

1.2 

-0.5 

-8.6 

-4.6 

-6.6 

-0.7 

-1.8 

-1. 6 

124 

CPT CPS U/Uc 

0.132 0.802 0.257 

0.144 0.795 0.247 

0.160 0.781 0.241 

0.166 0.770 0.25;:, 

0.171 0.764 0.255 

0.173 0.759 0.261 

0.179 0.751 0.263 

0.193 0.745 0.249 

0.024 0.889 0.295 

0.029 0.892 0.261 

0.017 0.894 0.298 

C'.017 0.897 0.295 

0.007 0.907 {).2t7'3 

0.007 0.905 0.297 

0.001 0.912 ().295 

-0.002 0.915 0.295 

-0.004 0.921 0.288 

0.002 0.910 {).297 

-0.001 0.906 0.310 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.638 

============================================================ 

Y/D 

0.0083 

0.0125 

0.0181 

0.0233 

0.0288 

0.0329 

0.0371 

0.08:24 

0.0865 

0.0948 

0.1056 

0.11<71 

0.1328 

0.1466 

0.1602 

0.1740 

0.2151 

0.2562 

(l.3384 

0.4203 

0.5053 

PHI 

DEG 

-1.9 

-3.1 

-6.0 

-14.8 

-2(). () 

-23.7 

-28.5 

-27.6 

-26.7 

-24.6 

-21.2 

-18.3 

-15.7 

-13.0 

-11.9 

-10.2 

-7.3 

-5.3 

C" "":'" -.J •. ..:.. 

-3.0 

-1.4 

THETA 

DEG 

-172.6 

-176.1 

-179. 1 

-178.8 

-177.9 

-177.7 

-177.2 

-: .. 6 

-2.9 

-3.2 

-3.4 

-~ '_'. ~ ,_9 

-3.3 

7 C-

-''':''' ,J 

-3.2 

-3. () 

-2.4 

-2.0 

-2. (j 

-1.4 

-1.3 

125 

CPT CPS U/Uo 

0.211 0.669 0.345 

().,229 0.663 (). 33C~ 

0.255 0.64::: 0.315 

0.281 0.638 0.285 

0.302 0.626 0.268 

0.315 0.620 0.255 

0.331 0.61:. 0.237 

0.096 0.754 0.387 

0.083 0.758 0.399 

0.065 0.764 0.414 

0.038 0.772 0.436 

0.031 0.785 0.42'7 

0.02(; 0.799 0.425 

0.019 0.805 0.420 

0.012 0.810 0.422 

0.010 0.816 0.417 

0.002 0.830 0.410 

0.000 0.834 0.407 

0.002 0.842 0.395 

0.002 0.840 0.39::;' 

0.002 0.842 0.395 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.681 

============================================================ 

YiD 

0.0082 

0.0113 

0.0138 

0.0162 

0.0186 

0.0216 

0.0220 

0.0228 

0.0237 

0.0504 

0.0545 

0.0585 

0.0666 

0.0750 

0.0832 

0.0911 

0.0995 

0.1078 

0.1160 

0.1244 

0.1341 

O.143~ 

0.1558 

0.1677 

0.1803 

0.1943 

0.2093 

0.2363 

0.2637 

0.3048 

0.3460 

0.3877 

0.4282 

0.4689 

PHI 

DEG 

2.1 

-0.4 

_r"'J ,..., 

.:.. "' 

-2.5 

-5.3 

-9.9 

-7.6 

-12.5 

-13.6 

-28.0 

-25.6 

-2:::: .. 6 

-18.7 

-18.0 

-17.0 

-16.2 

-15.8 

-14.1 

-13.3 

-13.1 

-11. 7 

-11.2 

-10.3 

-9.8 

-9.5 

-9.1 

-9.1 

-8.7 

-7.2 

-7.1 

-5.8 

-5.3 

-4.2 

-3.6 

THETA 

DEG 

-178.9 

-178.3 

-178.1 

-178.1 

-178.0 

-178.0 

-177.9 

-177.5 

-177.5 

-7.8 

-6.8 

-3.2 

-3.0 

-1.8 

-1.9 

-1.3 

-1.4 

-1.2 

-1.3 

-1.2 

-1.1 

-1. (> 

-0.7 

-0.5 

-0.2 

-0.2 

0.2 

0.3 

0.2 

0.0 

-0.6 

-0.4 

-0.2 

-0.2 

126 

CPT 

0.298 

0.326 

0.348 

0.372 

0.398 

0.432 

0.436 

0.444 

0.453 

0.369 

0.341 

0.316 

0.271 

0.195 

0.172 

0.099 

0.062 

0.041 

0.015 

0.010 

0.002 

-0.001 

-0.002 

-0.004 

-0.006 

-0.005 

-0.009 

-0.008 

-0.002 

-0.008 

0.002 

0.005 

-0.003 

-0.002 

CPS 

0.565 

0.555 

0.542 

0.534 

0.523 

0.505 

0.506 

0.500 

0.495 

0.548 

0.553 

0.558 

0.579 

0.605 

0.610 

0.638 

0.654 

0.659 

0.675 

0.684 

0.695 

0.702 

0.708 

0.715 

0.719 

0.723 

0.729 

0.739 

0.746 

0.757 

0.761 

0.771 

0.770 

0.776 

U/Uo 

0.369 

0.345 

(l.332 

0.307 

0.279 

0.251 

0.241 

0.235 

0.228 

0.288 

().322 

().354 

0.387 

0.447 

0.467 

0.513 

().533 

0.548 

0.557 

0.553 

(i .. 55C· 

0.546 

0.542 

0.538 

0.536 

0.531 

0.529 

0.519 

0.502 

0.501 

0.491 

0.474 

0.483 

0.475 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.723 

============================================================ 

YID 

0.0083 

0.0104 

0.0124 

0.0152 

0.0166 

0.0179 

0.026:, 

(). ()28?: 

(). (>:,()4 

0.0342 

0.0426 

O.05f)9 

0.0577 

0.0644 

0.0755 

0.0837 

0.0850 

0.0917 

0.098'7' 

0.1054 

C .1. 11~~ ...:::.~. 

0.1193 

0.1329 

0.1466 

0.1601 

0.1741 

0.2150 

0.2561 

0.3381 

0.4202 

0.5048 

PHI 

DEG 

2.0 

4.7 

C" 7 .J •• 

5.8 

15.2 

21.4 

_'?c ~ 

~'-'.~ 

-14.1 

-11.0 

-9.4 

-9.4 

-7.9 

-9.0 

-8.3 

-8.4 

-8.4 

-8.5 

-8.1 

-9.2 

-9.2 

-6.9 

-9.2 

-8.8 

-8.5 

-8.4 

-8.0 

-7.5 

-5.7 

-3.7 

-2.9 

-1.5 

THETA 

DEG 

-178.2 

-178.5 

-178.6 

-178.2 

-178.5 

-175.3 

-15.0 

-14.0 

-11.3 

-10.1 

-6.1 

-4.5 

-3.0 

-2.7 

-2.0 

-1.8 

-1.7 

-1.8 

-1.4 

-1.5 

-1.3 

-1.3 

-1.0 

-1.0 

-0.8 

-0.5 

0.1 

-0.1 

-0.3 

-0.1 

-0.1 

127 

CPT CPS U/Uo 

0.394 0.531 0.274 

0.406 0.528 0.255 

0=426 0.515 0.241 

0.455 0.506 0.197 

0.467 0.502 0.176 

0.480 0.498 0.148 

0.478 0.495 0.164 

0.486 0.478 0.190 

0.469 0.490 0.205 

0.461 0.487 0.228 

0.419 0.476 0.324 

0.356 0.478 0.407 

0.333 0.470 0.444 

0.267 0.486 0.496 

0.198 0.501 0.549 

0.136 0.519 0.587 

0.137 0.524 0.581 

0.100 0.541 0.599 

0.056 0.561 0.618 

0.041 0.579 0.616 

0.015 0.599 0.621 

0.014 0.609 0.615 

-0.009 0.619 0.624 

-0.006 0.628 0.615 

-0.009 0.638 0.609 

-0.006 0.645 0.601 

-0.010 0.657 0.594 

-0.011 0.668 0.586 

-0.004 0.696 0.555 

-0.001 0.709 0.540 

-0.003 0.712 0.538 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.766 

============================================================ 

Y/D 

0.0077 

0.0090 

0.0104 

0.0131 

0.0157 

0.0200 

0.0241 

0.0282 

0.0323 

0.0405 

0.0487 

-:). (:r568 

0.0651 

0.0732 

0.0776 

0.0814 

0.0858 

0.0980 

0.1062 

0.1105 

0.1146 

0.1348 

0.1555 

0.1760 

0.1965 

0.2377 

0.2786 

0.3199 

0.3608 

0.4020 

0.4430 

0.484 

PHI 

DEG 

-27.9 

4.4 

-15.3 

-25.8 

-10.8 

-8.3 

-6.2 

-6.8 

-6.0 

-5.0 

-4.6 

-3.1 

-3.2 

-2.9 

-3.8 

-3.4 

-3.2 

-4.5 

..,. ""7 -._.,. / 

-3.6 

~ c- -,L.. t......f 

-5.3 

-5.1 

C" .... -....,. -."1 

-5.0 

-4.1 

-3.6 

-;r .". -.':" • ..J 

-3.3 

-2.7 

-2.2 

-1. 7 

THETA 

DEG 

-102.2 

-44.5 

-41.1 

-40.0 

-21.9 

-18.2 

-12.9 

-11. 2 

-9.0 

-6.3 

-5.0 

-3.6 

-2.7 

-2.2 

_':> ':> ....... 

-1.9 

-1.8 

-1.5 

-1.4 

-1.4 

-,-1.1 

-0.9 

-0.6 

-0.4 

0.0 

0.0 

0.1 

-0.1 

-0.3 

0.0 

0.0 

0.0 

128 

CPT CPS U/Uo 

0.485 0.512 0.063 

0.475 0.519 0.077 

0.467 0.519 0.122 

0.472 0.517 0.105 

0.456 0.523 0.145 

0.457 0.515 0.167 

0.434 0.511 0.235 

0.418 0.515 o .... "',-. • ..:!-J7 

0.426 0.506 0.261 

0.382 0.506 0.335 

0.337 0.513 0.387 

0.281 0.510 0.456 

0.259 0.512 0.479 

0.218 0.506 (l.525 

0.190 0.508 0.550 

0.157 0.506 0.561 

0.145 0.512 0.585 

0.118 0.515 0.606 

0.071 0.516 0.643 

0.057 0.520 0.650 

0.055 0.527 0.647 

0.003 0.551 0.668 

-0.006 0.575 0.657 

-0.008 0.582 0.653 

-0.009 0.584 0.652 

-0.009 0.599 0.640 

-0.004 0.609 0.629 

-0.003 0.617 0.621 

-0.003 0.626 0.613 

-0.001 0.635 0.607 

0.003 0.638 0.602 

-0.002 0.636 0.601 
ANGLUAF: PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.809 

============================================================ 

Y/D 

0.0079 

0.0100 

0.0120 

0.0142 

0.0183 

0.0265 

0.0345 

0.0429 

0.0512 

0.0594 

0.0674 

()IF {)757 

0.08::::.9 

0.0922 

0.1058 

0.1196 

0.1331 

0.1466 

0.1743 

0.2154 

0.2562 

0.3383 

0.4206 

0.5054 

PHI 

DEG 

-4.3 

-5.1 

-4.6 

-8.7 

-6.7 

-4.7 

-4.0 

-3.5 

-3.9 

-3.0 

-3.2 

-2.9 

-2.8 

-2.7 

-2.9 

-3. 1 

-3. 1 

-3.4 

-2.9 

-2.2 

-2.4 

-2.2 

-2.0 

-1 •. :;. 

THETA 

DEG 

-13.5 

-11.3 

-8.3 

-7.0 

-4.5 

-3.4 

-2.7 

-2.2 

-1.9 

-1.6 

-1.5 

-1.4 

-1.3 

-1.1 

-0.9 

-0.7 

-0.6 

-0.5 

-0.3 

0.1 

0.3 

-0.1 

0.0 

-0.1 

129 

CPT CPS U/Uo 

0.474 0.516 0.105 

0.468 0.515 0.134 

0.460 00514 0.164 

0.454 0.513 0.182 

0.432 0.510 0.239 

0.396 0.510 0.307 

0.358 0.509 0.365 

0.314 0.509 0.421 

00276 0.509 0.464 

0.232 0.507 0.510 

0.196 0.505 0.547 

0.150 0.504 0.588 

0.112 0.503 0.621 

0.080 0.506 0.643 

0.032 0.506 0.680 

0.008 0.510 0.694 

-0.004 0.516 0.699 

-0.003 0.525 0.691 

-0.012 0.534 0.691 

-0.007 0.538 0.685 

-0.010 0.546 0.681 

-0.002 0.563 0.662 

-0.005 0.572 0.658 

-0.002 0.576 0.653 
ANBLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.851 

============================================================ 

Y/D 

0.0085 

0.0137 

0.0220 

0.0302 

0.0375 

0.0465 

0.0548 

0.0631 

0.0711 

0.0794 

0.0929 

0.1067 

0.1205 

0.1342 

0.1477 

0.1614 

0.1752 

0.2162 

0.2571 

0.3393 

0.4216 

0.4496 

0.5059 

PHI 

DEB 

3.8 

-0.4 

-2.5 

-2.4 

-3.3 

-~ -.. ~ ::,: 

~ ..... - . .j • .:.. 

-2.6 

-2.3 

-2.2 

-2.0 

-1. 7 

-1.7 

-1.4 

-1.6 

-1.7 

-1.7 

-1.9 

-1.5 

-2.0 

-2.0 

-2.1 

-2.5 

THETA 

DEG 

-10.4 

-7.5 

-4.7 

~ ~ 

-~./ 

~ .., -"';'.L 

-2.8 

-2.4 

-2.2 

-2.0 

-1.8 

-1. 7 

-1.4 

-1.1 

-0.9 

-0.8 

-0.7 

-0.4 

0.4 

0.6 

0.6 

0.4 

0.2 

0.1 

130 

CPT CPS U/Uo 

0.489 0.477 0.184 

0.467 0.473 0.245 

0.436 0.474 0.298 

0.405 0.471 0.352 

0.367 0.469 0.405 

0.332 0.470 0.445 

0.293 0.469 0.488 

0.247 0.468 0.534 

0.218 0.471 0.558 

0.181 0.467 0.593 

0.126 0.469 0.636 

0.073 0.46'1' 0.677 

0.034 0.469 0.705 

0.010 0.469 0.722 

-0.005 0.472 0.729 

-0.009 0.471 0.733 

-0.015 0.475 0.735 

-0.010 0.483 0.727 

-0.006 0.487 0.720 

-0.004 0.497 0.711 

-0.003 0.508 0.704 

-0.002 0.515 0.699 

-0.004 0.519 0.696 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.890 

=:========================================================== 

Y/D 

0.0085 

0.0108 

0.0163 

0.0218 

0.0301 

0.0381 

0.0464 

0.0547 

0.0629 

0.0708 

0.0792 

0.0930 

0.1065 

O. 1204 

O. 1338 

O. 1477 

0.1750 

(i. 257(; 

0.3394 

0.4214 

(j.5(;52 

PHI 

DEG 

-3.0 

-5.6 

-,. '""' -'-'. ~ 

-4.1 

-4.2 

-4.0 

-3.2 

-3. (j 

-3.6 

-3.2 

-2.7 

-2.5 

-2.2 

~ -, -..:.. . ..;.: 

-1.9 

-2.1 

-2.1 

-1.9 

-2.4 

-2.7 

-3.1 

THETA 

DEG 

-5.1 

-4.9 

-4.5 

-3.6 

-2.8 

-2.4 

-2.1 

-1.8 

-1. 6 

-1.5 

-1.5 

-1.2 

-1.2 

-1. 1 

-0.9 

-0.6 

0.0 

0.4 

0.2 

0.0 

0.0 

131 

CPT CPS U/Uo 

0.515 0.449 o ""':7 • k....j" 

0.476 0.449 0.274 

0.451 0.448 0.318 

0.419 0.448 0.365 

0.381 0.446 0.416 

0.340 0.446 0.463 

0.300 0.441 0.509 

0.258 0.443 0.547 

0.219 0.440 0.584 

0.184 0.442 0.612 

0.144 0.443 0.643 

0.088 0.441 0.686 

0.047 0.443 0.714 

0.012 0.443 0.736 

0.000 0.441 0.748 

-0.006 0.442 0.751 

-0.003 0.441 0.750 

-0.009 0.443 0.752 

0.004 0.454 0.736 

-0.006 0.479 0.726 

-0.005 0.483 0.722 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

0.936 

============================================================ 

'lID 

0.0083 

0.0110 

0.0166 

0.0221 

0.0301 

0.0383 

0.0467 

0.0549 

0.0632 

0.0712 

0.0794 

0.0933 

0.1069 

0.1206 

0.1343 

0.1479 

0.1752 

0.2164 

0.2575 

0.3394 

0.4216 

O.5t)6(! 

PHI 

DEG 

-0.4 

0.6 

-0.6 

-1.9 

-1.9 

-1.5 

-0.8 

-0.5 

-0.2 

-0.8 

-1.2 

-0.6 

-0.7 

-0.3 

-0.7 

-0.7 

-0.7 

-0.9 

-1.4 

., "7 -.::., • .J 

-2.8 

-2.7 

THETA 

DEG 

-3.4 

-2.8 

-2.3 

-1.8 

-1.4 

-1.2 

-1.3 

-1.1 

-1.1 

-0.9 

-0.9 

-0.9 

-0.8 

-0.8 

-0.6 

-().2 

0.2 

0.6 

0.4 

0.4 

0.2 

0.1 

132 

CPT CPS U/Uo 

0.508 0.434 0.241 

0.496 0.435 0.263 

0.467 0.434 0.315 

0.446 0.425 0.359 

0.410 0.430 0.401 

0.371 0.427 0.449 

0.325 0.425 ().5(i() 

0.285 0.425 0.539 

0.236 0.428 0.579 

0.205 0.424 0.610 

0.163 0.423 0.643 

0.110 0.424 0.683 

0.061 0.420 0.720 

0.028 0.424 0.740 

-0.005 0.423 0.763 

-0.003 0.418 0.764 

-0.013 0.423 0.769 

-0.013 0.420 0.770 

-0.013 0.423 0.768 

-0.002 0.428 0.758 

0.000 0.440 0.746 

0.004 0.446 0.742 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

1.021 ============================================================ 

YID 

0.0085 

0.0118 

0.0174 

0.0229 

0.0312 

0.0393 

0.0475 

0.0558 

0.0637 

0.0720 

0.0803 

0.0941 

0.1076 

0.1214 

Ci.134'7 

0.1487 

0.1762 

0.2172 

0.2580 

0.3403 

0.4224 

O.5Ut-tPHI 

DEG 

1.0 

0.3 

-0.7 

-(;.3 

-0.3 

-0.2 

-0.1 

(i.2 

(I '-:> - ....... 

0.2 

0.6 

(i.5 

0.6 

0.7 

0.8 

0.8 

0.7 

0.8 

0.4 

-0.3 

-(1.5 

-1.0 

THETA 

DEG 

-1. 7 

-1.5 

-1. 2 

-1.0 

-1.0 

-0.9 

-0.8 

-0.8 

-0.8 

-0.9 

-0.9 

-{).8 

-0.9 

-0.7 

-0.6 

-0.3 

0.1 

0.5 

0.2 

0.1 

O. 1 

-0.1 

133 

CFT 

0.514 

0.497 

0.468 

0.433 

0.399 

0.361 

0.313 

0.279 

0.242 

0.202 

0.178 

0.113 

0.065 

0.028 

0.002 

-0.002 

-0.009 

-0.014 

-0.008 

0.000 

-0.003 

0.000 

CPS 

0.389 

0.385 

0.383 

0.384 

0.379 

0.379 

0.379 

0.375 

0.375 

0.375 

0.372 

0.371 

0.370 

0.366 

0.367 

0.367 

0.366 

0.367 

0.366 

0.369 

0.371 

0.372 

U/Uo 

0.311 

0.344 

0.386 

0.429 

0.470 

0.510 

0.555 

0.588 

0.619 

0.650 

0.671 

0.718 

0.752 

0.778 

0.794 

0.797 

0.802 

0.804 

0.801 

0.794 

0.795 

0.792 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

1. 191 

============================================================ 

YID 

0.0083 

0.0132 

0.0187 

0.0239 

0.0322 

0.0406 

0.0488 

0.0571 

0.0654 

0.0734 

0.0816 

0.0954 

0.1090 

0.1228 

0.1363 

0.1502 

0.1775 

0.2185 

0.2595 

0.3417 

0.4237 

0.5074 

PHI 

DEG 

1.1 

0.2 

-0.2 

-0.4 

-0.4 

-0.4 

-0.2 

rO. 1 

O. 1 

0.3 

0.3 

0.4 

0.2 

0.7 

0.4 

0.3 

0.2 

0.4 

o. 1 

0.4 

O. 1 

-0.4 

THETA 

DEG 

-0.1 

-0.1 

-0.1 

-0.2 

-0.2 

-0.2 

-0.4 

-0.4 

-0.4 

-0.5 

-0.4 

-0.4 

-0.4 

-0.3 

-0.3 

-0.1 

0.3 

1.0 

1.0 

0.6 

0.4 

0.2 

134 

CPT CPS U/Uo 

0.526 0.305 0.412 

0.495 0.298 0.456 

0.457 0.295 0.495 

0.434 0.293 (}.522 

0.396 0.294 0.558 

0.345 0.292 0.602 

0.301 0.292 0.638 

0.264 0.291 0.666 

0.235 0.288 0.69(; 

0.199 0.289 0.716 

0.169 0.287 0.738 

0.111 0.288 0.775 

0.057 0.284 0.812 

0.024 0.289 0.829 

0.004 0.282 0.845 

-0.016 0.284 0.856 

-0.006 0.283 0.850 

-0.011 0.287 0.851 

-0.014 0.279 0.857 

-0.008 0.281 0.853 

-0.007 0.282 0.851 

-0.002 0.280 0.850 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

0.000 DEG 

1.362 

============================================================ 

YID 

0.0085 

0.0136 

0.0192 

0.0261 

0.0340 

0.0424 

0.0506 

0.0586 

0.0668 

0.0751 

0.0834 

0.0972 

0.1108 

0.1246 

0.1383 

0.1520 

0.1793 

0.2203 

0.2612 

0.3436 

0.4257 

0.5078 

PHI 

DEG 

1.6 

0.6 

-0.1 

-0.1 

0.1 

0.0 

-0.1 

0.1 

-Oii2 

0.0 

-0.1 

(l.2 

0.3 

0.4 

0.4 

().3 

0.3 

0.1 

0.2 

0.1 

-0.1 

-t).3 

THETA 

DEG 

0.0 

-0.1 

-0.2 

-0.2 

-0.3 

-0.3 

-0.3 

-0.4 

-0=4 

-0.5 

-0.4 

-0.4 

-0.4 

-t).3 

-0.3 

-0.1 

0.2 

0.7 

0.7 

0.5 

0.3 

(l.2 

135 

CPT CPS U/Uo 

0.534 0.236 0.481 

0.499 0.231 0.520 

0=467 0.224 0.555 

0.423 0.225 0.593 

0.375 0.225 0.632 

0.344 0.220 0.660 

0.303 0.219 0.691 

0.259 0.220 0.722 

0.220 0.221 0.748 

0.171 0.220 0.780 

0.147 0.219 0.797 

0.083 0.215 0.838 

0.041 0.215 0.863 

0.014 0.215 0.877 

0.002 0.217 0.884 

-0.010 0.217 0.891 

-0.013 0.215 0.894 

-0.006 0.216 0.889 

-0.007 0.216 0.890 

0.000 0.214 0.887 

-0.001 0.212 O.88E, 

-0.004 0.216 0.888 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole P~obe Data 

(continued) 

0.000 DEG 

1.532 

============================================================ 

YiD 

0.0085 

0.0140 

0.019E: 

0.0281 

0.0361 

0.0444 

0.0527 

0.0610 

0.069(1 

0.0772 

0.0855 

0.09<73 

0.1129 

0.1266 

O. 14(12 

Ci.1540 

0.1813 

0.2221 

0.2635 

0.3456 

0.4272 

().5()97 

PHI 

DEG 

1.8 

0.7 

0.6 

().2 

O. 1 

0.1 

O. 1 

0.0 

O. 1 

0.2 

0.3 

(,.3 

0.4 

0.3 

0.5 

0.4 

0.3 

0.3 

0.3 

O. 1 

O. 1 

-0.2 

THETA 

DEG 

0.0 

-0.1 

-0. 1 

-().2 

-0.2 

-0.3 

-0.3 

-0.4 

-0.4 

-0.3 

-0.3 

-0.3 

-0.3 

-0.2 

-0.2 

-0.1 

0.3 

0.8 

0.8 

0.6 

0.4 

o '":> ...... 

136 

CPT CPS U/Uo 

0.539 0.189 0.722 

0.490 0.180 0.75E 

0.449 0.178 0.781 

0.407 0.176 0.80:. 

0.361 0.175 0.825 

0.316 0.174 0.845 

0.269 0.173 0.864 

0.237 0.174 0.876 

0.196 0.172 0.891 

0.156 0.173 0.905 

O. 118 0.170 0.918 

0.069 0.169 0.934 

0.024 0.170 0.947 

0.003 0.169 0.954 

-0.009 0.169 0.957 

-0.012 0.170 0.958 

-0.014 0.170 0.958 

-0.016 0.169 0.959 

-0.009 0.168 0.957 

-0.004 0.169 0.956 

-0.003 0.168 (). 9~t6 

-0.003 0.171 0.955 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.596 

============================================================ 

Y/D 

0.0082 

0.0101 

0.0119 

0.0137 

0.0155 

0.0175 

0.1032 

0.1100 

0.1248 

0.1382 

0.1509 

0.1649 

O. 1787 

0.2199 

0.2604 

0.3012 

0.3431 

0.4244 

0.5067 

PHI 

DEG 

-4.0 

-7.9 

-10.4 

-16.4 

-20.9 

-26.6 

-27.2 

-25.9 

-21,8 

-19.1 

-17.4 

-15.8 

-15.8 

-13.1 

-10.8 

-9.4 

-7.8 

-4.1 

-1.1 

THETA 

DEG 

138.2 

137.2 

133.7 

131. 1 

129.8 

125.1 

19.2 

18.3 

17.3 

16.9 

17. 1 

17.5 

18.2 

19.7 

21.4 

23. (; 

23.6 

24. ~t 

'")c" ,...., 

..:.....J.L 

137 

CPT CPS U/Uo 

0.078 0.836 0.295 

0.087 0.839 0.272 

0.106 0.831 0.251 

0.111 0.836 O.23() 

0.129 0.828 0.207 

0.130 0.831 0.197 

0.020 0.869 (}.335 

0.023 0.870 0.329 

0.014 0.873 0.335 

0.013 0.874 0.336 

0.010 0.872 0.344 

0.006 0.873 0.::::".48 

0.001 0.870 0.359 

-0.005 0.871 0.367 

-0.007 0.874 0.366 

-0.004 0.878 0.355 

-0.004 0.883 0.348 

0.000 0.885 0.339 

-0.006 0.890 0.341 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.638 

============================================================ 

YID 

0.0083 

0.0115 

0.0142 

0.0170 

0.0198 

0.0668 

0.0703 

0.0785 

0.0868 

0.0951 

0.1031 

O. 1115 

o. 1197 

0.1332 

0.147(1 

0.1605 

O. 1744 

0.2154 

0.2563 

0.3386 

0.4207 

0.5051 

PHI 

DEG 

2.0 

-1.2 

-10.0 

-22.6 

-28.0 

-27.7 

-26.1 

""'? C- -L.L • ....J 

-19.8 

-17.2 

-15.5 

-14.0 

-11.9 

-11.3 

-10.6 

-10.3 

-10.7 

-9.6 

-8.4 

-5.6 

-3.1 

-0.7 

THETA 

DEG 

146.1 

144.0 

141.8 

140.2 

137.1 

8.9 

8.4 

7.8 

7.1 

6.8 

6.4 

6.8 

6.5 

7.4 

7.9 

9.2 

10.0 

11.8 

13.0 

14.1 

15.3 

15.4 

138 

CPT CPS U/Uo 

0.208 0.665 0.356 

0.263 0.655 0.286 

0.298 0.648 0.235 

0.335 0.639 0.164 

0.345 0.623 0.176 

0.137 0.715 0.386 

0.126 0.719 0.394 

0.089 0.728 0.429 

0.069 0.733 0.445 

0.047 0.747 0.454 

0.036 0.756 0.457 

0.023 0.766 0.459 

0.024 0.766 0.458 

0.011 0.775 0.463 

0.009 0.776 0.464 

0.002 0.776 0.470 

-0.003 0.777 0.475 

-0.009 0.790 0.468 

-0.007 0.798 0.457 

0.000 0.811 0.435 

0.003 0.817 0.424 

0.000 0.819 0.425 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.681 

============================================================ 

Y/D 

0.0082 

0.0105 

0.0131 

0.0159 

0.0186 

0.0213 

0.0241 

0.0491 

0.0525 

0.0608 

0.0698 

0.0784 

0.0870 

0.0940 

0.1147 

0.1255 

O. 1346 

O. 1542 

0.1751 

0.2169 

0.2581 

0.3403 

0.4218 

0.5060 

PHI 

DEG 

3.1 

1.6 

0.1 

-1.4 

-4.5 

-9.8 

-17.1 

-26.2 

-24.3 

-19.7 

-16.4 

-15. 1 

-14.0 

-12.9 

-11.5 

-10.9 

-10.5 

-9.7 

-9.1 

-7.5 

-6.0 

-4.4 

-2.9 

-1.2 

THETA 

DEG 

159.7 

161.9 

162.3 

167.6 

168.9 

170.0 

170.1 

6.5 

6.3 

co C" ..J • ..J 

4.3 

4.5 

4.9 

4.3 

4.4 

4.7 

4.9 

5.5 

6.0 

8.0 

8.9 

9.7 

10.3 

10.4 

139 

CPT CPS U/Uo 

0.311 0.497 0.438 

0.365 0.481 0.391 

0.421 0.463 0.341 

0.466 0.447 0.295 

0.504 0.426 0.265 

0.549 4.020 0.221 

0.575 0.383 0.205 

0.376 0.512 0.335 

0.363 0.513 (l.352 

0.300 ().533 0.407 

0.231 0.549 0.470 

0.184 0.563 ().5i)2 

0.131 0.578 0.539 

0.090 0.587 0.568 

0.021 0.616 0.602 

0.005 0.625 0.608 

0.000 0.635 0.604 

-0.007 0.658 0.591 

-0.005 0.671 0.578 

-0.010 0.699 0.558 

-0.005 0.720 0.534 

-0.005 0.745 0.510 

-0.002 0.754 0.499 

-0.005 0.757 0.546 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.723 

============================================================ 

Y/D 

0.0084 

0.0102 

0.0130 

0.0157 

0.0185 

0.0199 

0.0213 

0.02:::.4 

0.0293 

0.0334 

0.0375 

0.0431 

0.0485 

0.0540 

0.0623 

0.0704 

0.0786 

0.0869 

0.0952 

0.1032 

0.1115 

0.1197 

(1.1335 

0.1472 

0.1606 

0.1745 

0.2155 

0.2565 

0.3386 

0.4208 

0.5050 

PHI 

DEG 

5.4 

6.1 

6.5 

13.9 

16.4 

24.0 

22.6 

7.0 

8.2 

4.6 

0.6 

-0.8 

-3.7 

-2.8 

-4.1 

-4.6 

-4.5 

-4.7 

-4.7 

-4.7 

-4.9 

-4.9 

-5.6 

-5.4 

-5.7 

-5.7 

-5.1 

-4.6 

-3.4 

-2.7 

-1.3 

THETA 

DEG 

156.5 

156.4 

156.3 

150.8 

141.9 

136.5 

126.4 

20.2 

14.4 

11.3 

8. 1 

6.0 

5.1 

4.2 

3.9 

3.6 

""T I:" _i • ..J 

3.3 

":'" .., _i • .L 

3.2 

3.4 

..., .." 

"';". -' 

3.4 

3.6 

4.0 

4.5 

6.1 

6.9 

7.4 

8.0 

B.2 

140 

CPT CPS U/Uo 

0.426 0.494 0.281 

0.441 0.490 0.261 

0.460 0.478 0.247 

0.483 0.469 0.219 

0.506 0.463 0.173 

0.505 0.459 0.190 

0.528 0.450 0.148 

0.575 0.413 0.110 

0.566 0.407 0.164 

0.535 0.409 0.237 

0.488 0.419 0.305 

0.417 0.442 ().375 

0.362 0.453 0.42c]' 

0.305 0.471 0.473 

0.233 0.492 0.524 

0.178 0.502 0.567 

0.138 0.510 0.594 

0.095 0.515 0.624 

0.059 0.526 0.644 

0.035 0.532 0.658 

0.017 0.545 0.662 

0.009 0.553 0.662 

-0.003 0.570 0.658 

-0.001 0.581 0.648 

-0.004 0.593 0.641 

0.000 0.602 0.631 

-0.004 0.627 0.614 

-0.003 0.647 0.597 

-0.003 0.669 0.578 

0.003 0.681 0.562 

0.001 0.684 0.561 
ANGLUAH PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.766 

===========================================================~ 

Y/D 

0.0083 

0.0107 

0.0131 

0.0146 

0.0160 

0.0174 

0.0187 

0.0215 

0.0228 

0.0242 

0.0267 

().029t. 

0.0323 

0.0350 

0.0391 

0.0434 

0.0520 

0.059'7'-

0.0686 

0.0799 

0.093:'"", 

0.1069 

0.1209 

O. 1340 

0.1551 

0.1751 

0.2158 

0.2575 

0.3394 

0.4209 

0.5040 

PHI 

DEG 

0.0 

0.4 

4.5 

18.3 

1.1 

-1.0 

-20.6 

""'I~ """"!" - ";:-.. ) .. ..;. 

-25.4 

-12.7 

-5.8 

-0.8 

5.0 

6.3 

4.5 

3.4 

4.3 

1.7 

.., E::-

.:... J 

0.8 

0.0 

-Ci.5 

-1.2 

-2.1 

-2.5 

-3.1 

-3.0 

-2.6 

-2.5 

-2.1 

-1.4 

THETA 

DEG 

129.6 

126.5 

125.1 

117.8 

112.4 

106.6 

101.5 

70.0 

70.7 

55.7 

33.3 

28.5 

21.5 

15.7 

14.3 

11.3 

7.8 

6.7 

5.7 

4.7 

4.5 

4.3 

4.1 

4.2 

4.2 

4.5 

5.6 

6.3 

6.6 

7.4 

7.5 

141 

CPT CPS U/Uu 

0.480 0.489 0.176 

0.486 0.482 0.179 

0.499 0.478 0.152 

0.511 0.470 0.134 

0.515 0.469 0.126 

0.526 0.468 0.071 

0.531 0.465 0.063 

0.527 0.463 0.095 

0.532 0.458 0.100 

0.528 0.455 0.130 

0.495 0.455 0.200 

0.507 0.450 ().2(J5 

0.498 0.453 0.221 

0.456 0.462 0.288 

0.457 0.454 0.298 

0.409 0.470 0.3417-

0.348 0.467 0.429 

0.310 0.469 0.47« 

0.227 0.478 0.543 

0.164 0.482 0.595 

0.096 0.487 O.64L 

0.036 0.491 0.688 

0.010 0.502 0.699 

-0.003 0.506 0.705 

-0.008 0.525 0.695 

-0.011 0.539 0.687 

-0.006 0.559 0.669 

-0.009 0.580 0.656 

-0.003 0.605 0.631 

-0.003 0.619 0.620 

-0.004 0.623 0.617 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.809 

============================================================ 

Y/D 

0.0083 

0.0107 

0.0135 

0.0170 

0.0215 

0.0298 

0.0378 

0.0460 

0.0544 

0.0626 

0.0708 

0.0789 

0.0871 

0.0954 

0.1035 

O. 1119 

0.1201 

0.1335 

0.1472 

0.1611 

0.1747 

0.2157 

0.2569 

0.3389 

0.4211 

0.5052 

PHI 

DEG 

5.1 

18.9 

-6.8 

-2.8 

-. C" -..::..-...1 

-0.8 

-1.0 

-0.5 

0.6 

0.7 

0.9 

0.7 

1.1 

0.3 

0.3 

0.2 

-0.2 

-0.5 

-1.1 

-1.4 

-1. 9 

-2.1 

-2.4 

-2.4 

-1. 9 

-1.7 

THETA 

DEG 

67.8 

58.9 

44.1 

....,r::- -"1' 

L....J • ...:.s 

17.9 

11.8 

8.8 

6.8 

5.3 

4.2 

3.4 

3.2 

2.7 

':> c:- L. oJ 

2.2 

2.1 

2.1 

2.0 

1.9 

.., .., L • ..:.. 

2.5 

-". ~ 

....,:..~ 

3.8 

4. 1 

4.6 

4.6 

142 

CPT CPS U/Uo 

0.492 0.503 0.071 

0.494 0.496 0.105 

0.478 0.500 0.148 

0.460 0.499 0.202 

0.436 0.496 0.261 

0.403 0.498 0.315 

0.338 0.504 0.397 

0.298 0.50:. 0.445 

0.249 0.500 0.501 

0.193 0.503 0.551 

0.147 0.499 0.596 

0.108 0.498 0.628 

0.082 0.494 0.650 

0.047 0.497 0.675 

0.031 0.491 0.692 

0.008 0.491 0.708 

0.003 0.495 0.709 

-0.003 0.495 0.713 

-0.004 0.495 0~713 

-0.002 0.497 0.710 

0.000 0.504 0.704 

-0.006 0.512 0.703 

-0.002 0.524 0.691 

0.003 0.541 0.675 

-0.002 0.556 0.668 

0.001 0.554 0.667 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.851 

============================================================ 

YID 

0.0082 

0.0106 

0.0141 

0.0201 

0.0284 

0.0367 

0.0449 

O.052!7' 

0.0614 

0.0696 

0.0773 

0.086(' 

0.0939 

0.1065 

0.119'7 

0.1269 

0.1349 

0.1763 

Ci.2582 

0.3409 

O. - 4--- '..'- ... ,1 

0.5069 

PHI 

DEG 

-1.0 

-4.0 

-2.9 

-1.0 

-0.1 

1.0 

1.6 

2.0 

3.0 

2.4 

2.8 

2.6 

1.9 

1.6 

1.4 

1.3 

1.1 

0.3 

-1.2 

-1.9 

-2.1 

-1.5 

THETA 

DEG 

54.7 

41. I) 

30.3 

19.7 

13.2 

9.8 

7.7 

6.8 

5.8 

5.2 

4.9 

4.5 

4.3 

4.0 

..)./ 

3.6 

3.5 

3.5 

4.5 

4.4 

4.7 

4.8 

143 

CPT CPS U/Uo 

0.513 0.469 0.134 

0.508 0.472 0.141 

0.493 0.474 0.179 

0.472 0.473 0.235 

0.429 0.473 0.313 

0.376 0.475 0.386 

0.326 0.476 0.445 

0.283 0.473 0.494 

0.242 0.471 0.536 

0.197 0.468 0.579 

0.165 0.464 0.609 

0.136 0.464 O. 6~::,2 

0.085 0.461 0.674 

0.043 0.459 0.705 

0.014 0.456 0.729 

0.000 0.461 0.733 

-0.005 0.458 0.739 

-0.008 0.463 0.739 

-0.009 0.479 0.729 

-0.004 0.496 0.713 

0.000 0.506 0.703 

-0.006 0.510 0.704 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole P~obe Data 

(continued) 

5.000 DEG 

0.890 

===================;======================================== 

YID 

0.0083 

0.0149 

0.0218 

0.0298 

0.0381 

0.0464 

0.0547 

0.0628 

0.070'7 

0.0792 

0.0874 

0.0958 

0.1038 

0.1121 

0.1204 

0.1339 

0.1477 

0.1615 

0.1750 

0.2161 

0.2571 

0.3.392 

0.4214 

0.5059 

PHI 

DEG 

-0.2 

-1.0 

0.5 

-0.1 

0.0 

0.4 

0.7 

0.8 

0.7 

0.9 

0.7 

0.9 

0.7 

0.7 

0.6 

0.3 

0.2 

0.0 

0.0 

-0.6 

-0.8 

-1. 6 

-2.0 

-1. 6 

THETA 

DEG 

20.3 

13.2 

9.8 

7.5 

6.0 

5.0 

4.3 

3.9 

- c- "::;'.-1 

"< .., "_ .. ~ 

2.9 

2.8 

2.6 

2.4 

_. ? "< '-' 

,., ,..., "'- • .L. 

'): ,., ..:... L. 

,..., ~ 

L. "_, 

2.5 

-,.. ..., _'\. --' -:0 c ..:.-. ~ 

3.4 

7 C ...,:1 • ..J 

3.4 

144 

CPT CPS U/Uo 

0.484 0.470 0.214 

0.449 0.467 0.290 

0.403 0.465 0.363 

0.356 0.464 0.424 

0.307 0.461 0.482 

0.270 0.455 0.524 

0.226 0.455 0.565 

0.181 0.451 0.607 

0.132 0.450 0.647 

0.098 0.447 0.675 

0.068 0.445 0.698 

0.037 0.443 0.721 

0.021 0.444 0.732 

0.006 0.443 0.742 

0.004 0.440 0.746 

-0.001 0.439 0.749 

-0.002 0.439 0.750 

-0.008 0.437 0.756 

-0.003 0.432 0.756 

-0.004 0.437 0.753 

-0.007 0.444 0.750 

0.000 0.456 0.738 

0.002 0.459 0.734 

0.002 0.461 0.733 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

0.936 

============================================================ 

Y/D 

0.0083 

0.0153 

(). ()22~5 

0.0305 

0.038;-' 

0.0471 

0.0554 

0.0634 

0.0716 

0.0798 

0.0937 

O. 1073 

0.1210 

0.1345 

0.1483 

o. 1757 

0.2168 

0.2577 

0.3400 

0.4219 

0.5066 

PHI 

DEG 

-1.3 

-1.2 

-1.1 

-0.3 

0.3 

0.7 

0.9 

1.0 

1.1 

1.4 

1.4 

1.4 

1.2 

1.5 

1.1 

0.9 

O •. ;;,. 

-0.3 

-1.0 

-1.3 

-1. 2 

THETA 

DEG 

14.2 

10.3 

8.3 

6.8 

5.9 

4.9 

4.2 

4.0 

'7 co ....;.,.,.J 

-:r ~ -' • .::> 

2.9 

2.6 

2.3 

2.2 

2.4 

-;r '7 ~. _ .. 

3.6 

3.8 

3.4 

3.6 

3.4 

145 

CPT CPS U/Uo 

0.497 0.433 0.265 

0.461 0.431 0.329 

0.430 0.428 0.377 

0.382 0.427 0.437 

0.348 0.425 0.477 

0.305 0.425 0.520 

0.255 0.423 0.567 

0.216 0.420 0.60=· 

0.183 0.417 0.632 

0.141 0.417 0.665 

0.084 0.413 0.709 

0.049 0.410 0.7=.6 

0.014 0.407 0.761 

-0.001 0.404 0.773 

-0.011 0.408 0.777 

-0.009 0.403 0.778 

-0.016 0.408 0.780 

-0.010 0.412 0.773 

-0.001 0.416 0.765 

-0.001 0.417 0.764 

-0.010 0.431 0.762 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

1.021 

============================================================ 

Y/D 

0.0083 

0.0157 

0.0230 

0.0311 

0.0395 

0.0478 

0.0561 

0.0640 

0.0722 

0.0805 

0.0944 

0.108(! 

0.1218 

0.1353 

0.1491 

0.1765 

0.2175 

0.2584 

0.3407 

0.4227 

0.5069 

PHI 

DEG 

-0.3 

-0.8 

-0.6 

-O.B 

-0.6 

-0.5 

-0.1 

0.0 

0.0 

0.1 

0.3 

0.5 

0.6 

0.6 

0.4 

0.4 

0.3 

0.1 

-0.7 

-0.7 

-0.9 

THETA 

DEG 

8. 1 

6.3 

5.3 

4.6 

4.0 

-;r C" _"r • ...J 

3.1 

2.9 

2.7 

., C" 

L.~ 

2.2 

2.0 

1.9 

1.8 

1.9 

2.4 

-;r ., 

_'. L 

3. () 

2.7 

2.8 

'") c:- ..:... ~ 

146 

CPT CPS U/Uo 

0.485 0.382 0.365 

0.435 0.377 0.434 

0.386 0.374 0.490 

0.347 0.370 0.532 

0.296 0.371 0.576 

0.249 0.369 0.618 

0.20B 0.366 0.653 

0.164 0.366 0.686 

0.126 0.365 0.713 

0.093 0.362 0.738 

0.049 0.358 0.770 

0.013 0.359 0.792 

-0.002 0.357 0.803 

-0.004 0.356 0.805 

-0.008 0.355 0.808 

-0.006 0.351 0.809 

-0.006 0.346 0.812 

-0.011 0.354 0.811 

-0.006 0.357 0.B06 

-0.001 O.36() 0.801 

-0.004 0.363 O.BOl 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

1. 191 

============:=============================================== 

Y/D 

0.0083 

0.0164 

0.0247 

t). ()33CJ 

0.0410 

0.0493 

0.0576 

0.0656 

O. 074l~' 

0.0821 

0.0959 

0.1095 

0.1232 

0.1370 

O. 1505 

(1. 1778 

0.2191 

0.2600 

0.3420 

0.4242 

0.5087 

PHI 

DEG 

0.1 

-0.8 

-1. 0 

-t).9 

-0.9 

-0.8 

-0.6 

-(j.5 

-0.4 

-(>.5 

-0.3 

-0.3 

-().2 

-0.2 

-0.2 

-0.2 

0.0 

-0. 1 

-0.3 

-0.4 

-0.8 

THETA 

DEG 

4.5 

3.6 

3. 1 

2.7 

..., -:r ~ •. -=-

2. () 

1.8 

1.6 

1.4 

1.3 

1.1 

1.0 

0.9 

0.9 

1.0 

1.6 

2.4 

2.4 

1.9 

1.7 

1.6 

147 

CPT CPS U/Uo 

0.484 0.286 0.480 

0.417 0.277 0.553 

0.359 0.275 0.606 

0.314 0.272 0.643 

0.262 0.273 0.682 

0.219 0.271 0.714 

0.174 0.273 0.744 

0.137 0.271 0.769 

0.093 0.269 0.799 

0.063 0.269 0.817 

0.022 0.269 0.842 

0.002 0.267 0.855 

-0.004 0.266 0.859 

0.002 0.262 0.858 

-0.006 0.267 0.859 

-0.004 0.266 0.859 

-0.009 0.264 0.863 

-0.007 0.265 0.861 

0.000 0.267 0.856 

-0.001 0.265 0.858 

0.001 0.263 0.858 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

5.000 DEG 

1.532 

============================================================ 

Y/D 

0.0083 

0.0142 

0.0200 

().028t) 

0.0363 

0.0446 

0.0530 

0.0612 

0.0694 

0.0774 

0.0857 

0.0995 

0.1131 

0.1269 

0.1407 

O. 1542 

0.1816 

0.2226 

i). 2635 

0.3457 

0.4279 

0.5114 

PHI 

DEG 

1.1 

.0 

-0.4 

-().3 

-0.7 

-0.3 

-0.5 

-0.5 

-0.3 

-0.2 

-0.3 

-0. 1 

-0.1 

-0.2 

-().5 

-0.5 

-0.5 

-(}.3 

-0.1 

-0.2 

-0.3 

-0.4 

THETA 

DEG 

1.9 

1.6 

1.4 

1.3 

1.2 

1.1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.4 

0.4 

0.4 

0.5 

0.8 

1.2 

1.4 

1.2 

0.9 

0.9 

148 

CPT CPS U/Uo 

0.481 0.175 0.587 

0.423 0.168 0.640 

0.385 0.164 0.672 

0.330 0.162 0.713 

0.273 0.160 0.753 

0.223 0.159 0.786 

0.172 0.161 0.816 

0.133 0.162 0.840 

0.094 0.156 0.866 

0.057 0.157 0.887 

0.029 0.159 0.901 

-0. (h) 1 0.158 0.918 

0.004 0.154 0.918 

-0.013 0.159 0.924 

-0.011 0.157 0.924 

-0.007 0.155 0.923 

-0.004 0.153 0.922 

-0.005 0.15::::: 0.923 

-0.006 0.154 0.923 

-0.004 0.154 0.921 

-0.001 0.155 0.92(.> 

0.001 0.155 0.919 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 OEG 

0.553 

============================================================ 

Y/O 

0.0084 

0.0120 

(). ()15S: 

0.0215 

0.0296 

0.0379 

0.0461 

0.0545 

0.0627 

0.0707 

0.0789 

0.0928 

0.1063 

0.1201 

0.1338 

0.1474 

0.1609 

0.1748 

0.2159 

0.2570 

O. ::::.:::;.82 

0.4211 

0.5060 

PHI 

DEG 

-0.2 

-3.6 

co -00 -..J.I 

-8.7 

-10.3 

-12.2 

-12.8 

-13.4 

-13.7 

-13.8 

-13.6 

-13. 1 

-12.5 

-12.0 

-11. 2 

-10.5 

-9.9 

-9.4 

-8.3 

-5.9 

-3.8 

-2.5 

-0.8 

THETA 

DEG 

69.0 

67.6 

65.6 

6:::: .• 6 

61.0 

58.7 

57.2 

55.9 

54.6 

53.6 

53.0 

52.2 

51.7 

51.4 

51.3 

51.2 

51.2 

51.2 

51.5 

51.6 

51. 9 

52.2 

52.1 

149 

, 

CPT CPS U/Uo 

0.008 0.476 0.718 

0.013 0.459 0.727 

0.021 0.450 0.727 

0.020 0.440 0.735 

0.016 0.429 0.745 

0.012 0.420 0.753 

0.007 0.414 0.761 

0.002 0.408 0.769 

0.001 0.399 0.775 

-0.001 0.393 0.780 

-0.002 0.394 0.780 

-0.002 0.388 0.784 

-0.002 0.383 0.187 

-0.005 0.382 0.789 

-0.008 0.381 0.792 

-0.004 0.377 0.792 

-0.004 0.377 O. 7'7'2 

-0.007 0.377 0.793 

-0.015 0.377 0.799 

-0.003 0.380 0.789 

0.000 0.380 0.787 

-0.001 0.382 0.787 

-0.002 0.383 0.787 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.596 

============================================================ 

Y/D 

0.0088 

0.0136 

0.0157 

0.0239 

0.0319 

0.0402 

0.0485 

0.0568 

0.0649 

0.0731 

0.0813 

0.0924 

0.1060 

0.1197 

0.1332 

0.1468 

0.1607 

0.1744 

0.2156 

(J.2567 

().3:::,S:'j 

0.4205 

(i.5r:)53 

PHI 

DEG 

-1. 5 

-4.9 

-7.0 

-10.5 

-13.1 

-15.3 

-16.4 

-17.0 

-17. 1 

-16.9 

-16.2 

-15.7 

-14.4 

-13.5 

-12.1 

-11. 3 

-10.5 

-9.8 

-8.3 

-5.9 

-;0 .., 

-'.) •. ? 

-2.4 

-1.0 

THETA 

DEG 

81.5 

77.2 

75.3 

68.1 

61. 9 

57.1 

52.8 

49.5 

46.9 

44.8 

43.4 

42.2 

41. 4 

41.2 

41.1 

41.2 

41.2 

41.6 

42.4 

42.8 

43.5 

43.9 

43.8 

150 

CPT 

0.041 

0.080 

0.098 

0.107 

0.105 

0.110 

0.089 

0.062 

0.043 

0.030 

0.026 

0.000 

0.001 

-0.004 

-0.001 

-0.011 

-0.007 

-0.007 

-0.011 

-0.002 

0.000 

-0.005 

0.000 

CPS 

0.431 

0.414 

0.407 

0.402 

0.395 

0.376 

().373 

0.361 

0.362 

0.358 

0.352 

0.354 

0.354 

0.355 

0.356 

().362 

0.365 

().365 

0.373 

0.380 

0.386 

().392 

0.394 

U/Uo 

0.727 

0.711 

0.704 

0.701 

0.706 

0.717 

0.733 

0.760 

0.771 

0.783 

0.789 

0.804 

0.803 

0.806 

0.802 

0.806 

0.801 

0.801 

0.799 

0.789 

0.784 

0.783 

0.778 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.617 

============================================================ 

Y/D 

0.0085 

0.0133 

0.0189 

0.0244 

0.02<:]'6 

0.0351 

0.0421 

0.0490 

0.0571 

0.0652 

0.0735 

0.0817 

0.0900 

0.0980 

0.1091 

0.1198 

0.1337 

0.1475 

0.1611 

0.1749 

(>&2157 

0.2569 

0.3389 

0.4211 

0.5057 

PHI 

DEG 

-0.3 

-4.3 

-8 . ..::' 

-10.9 

-12.9 

-15.2 

-17.0 

-17.8 

-18.1 

-18.0 

-17.5 

-16.5 

-15.9 

-15.1 

-14.0 

-12.9 

-11.7 

-10.7 

-9.9 

-9.3 

-8.0 

-5.7 

-3.5 

-1.9 

-0.8 

THETA 

DEG 

87.6 

82.9 

77.4 

71.7 

66.3 

61.4 

55.9 

51.0 

46.8 

43.1 

40.6 

38.8 

37.3 

36.7 

36.1 

36.0 

36.1 

36.4 

36.6 

36.9 

38.1 

38.8 

39.7 

40.0 

40.1 

\ ') 1 

CPT CPS U/Uo 

0.078 0.382 0.735 

0.128 0.367 0.711 

0.166 0.355 0.693 

0.190 0.352 0.677 

0.200 0.343 0.677 

0.199 0.339 0.680 

0.182 0.330 0.69c]' 

0.153 0.327 0.721 

0.129 0.318 0.744 

0.094 0.316 0.768 

0.071 0.310 0.787 

0.044 0.312 0.802 

0.024 0.318 0.811 

0.015 ().32() 0.816 

0.006 0.327 0.817 

0.001 0.332 0.817 

-0.003 0.340 0.814 

0.001 0.346 0.808 

-0.001 0.351 0.806 

-0.004 0.355 0.806 

-0.003 0.367 0.797 

0.001 0.377 0.788 

0.002 0.386 0.782 

-0.002 0.395 0.779 

0.000 0.396 0.777 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.638 

============================================================ 

Y/D 

0.0085 

0.0120 

0.0162 

0.0210 

0.0255 

0.0304 

0.0352 

0.0408 

0.0463 

0.0514 

0.0570 

0.0625 

0.0681 

0.0763 

0.0842 

0.0928 

0.1009 

0.1092 

0.1202 

0.1337 

0.1475 

0.1611 

0.1749 

0.2160 

0.2571 

0.3392 

0.4210 

0.5067 

PHI 

DEG 

-0.7 

-". c::" - . .:;. ~ 

-5.8 

-9.2 

-11.4 

-13.7 

-15.9 

-17.1 

-17.5 

-18.6 

-18.5 

-17.7 

--17.8 

-17.0 

-16.3 

-15.1 

-14.4 

-1~,. 4 

-12.5 

-11.4 

-10.0 

-9.2 

-8.9 

-7.4 

-4.9 

-3.5 

-1.9 

-1.1 

THETA 

DEG 

93.8 

90.3 

85.9 

80.5 

75.3 

70.1 

65.0 

59.4 

54.2 

50.5 

46.7 

43.3 

40.8 

38.1 

35.7 

34.1 

"7~ ? ...;:,_ .... - 32.6 

32.4 

32.7 

33.0 

33.5 

33.9 

35.0 

36.0 

37.2 

37.6 

37.6 

152 

CPT CPS U/Uo 

0.108 0.289 0.777 

0.159 0.292 0.741 

0.211 0.290 0.706 

(>.252 0.282 0.683 

0.272 0.277 0.672 

0.295 0.270 0.660 

0.287 0.265 0.669 

0.282 0.264 0.675 

0.275 0.253 0.687 

0.246 0.257 0.706 

0.219 0.251 0.728 

0.195 0.251 0.744 

0.176 0.248 0.759 

0.122 0.257 0.788 

0.095 0.261 0.802 

0.055 0.266 0.824 

0.033 0.277 0.831 

0.017 0.280 0.8.38 

0.001 0.295 0.839 

-0.005 0.309 0.834 

-0.001 0.314 0.829 

-0.007 0.321 0.828 

-0.005 0.333 0.820 

-0.006 0.354 0.807 

0.005 0.357 0.799 

0.002 0.375 0.789 

0.005 0.379 0.785 

0.005 0.378 0.785 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.660 

============================================================ 

Y/D 

0.0083 

0.0131 

0.0176 

0.0218 

0.0257 

0.0300 

0.0340 

0.0380 

0.0423 

0.0465 

0.0519 

0.0574 

0.0629 

0.0696 

0.0765 

0.0847 

0.0930 

0.1011 

(J.I094 

0.1204 

o. 13:.9 

0.1476 

0.1612 

0.1751 

0.2161 

0.2571 

0.3392 

0.4214 

0.5056 

PHI 

DEG 

1.0 

-3.1 

-6.0 

-10.1 

-13.4 

-16.5 

-18.8 

-2().2 

-20.6 

-20.4 

-19.6 

-17.6 

-17.1 

-15.4 

-14.8 

-13.6 

-12.9 

-12.4 

-11. 6 

-10.6 

-9.6 

-9.1 

-8.5 

-8.1 

-6.0 

-4.7 

-3.1 

-1.7 

-0.8 

THETA 

DEG 

101. 5 

97.9 

93.1 

88.0 

81.8 

75.8 

69.4 

62.6 

55.7 

49.9 

44.1 

40.3 

37.2 

34.7 

~ ..... ~ 

.,),4 • . ~. 

30.6 

29.3 

28.3 

28.0 

27.9 

28.2 

28.9 

29.4 

30.0 

31.2 

32.2 

33.6 

34.0 

34.1 

153 

CPT CPS U/Uo 

0.159 0.194 0.804 

0.260 0.172 0.754 

0.348 0.158 (i.7()2 

0.422 0.144 0.659 

0.466 0.131 0.635 

0.496 0.121 0.619 

0.490 0.113 0.630 

0.492 0.116 0.626 r\ JlC::O ~I. -r~ i 0.120 0.649 

0.427 0.128 0.667 

0.376 0.132 0.701 

0.3:;:.6 0.150 0.717 

0.281 0.159 0.748 

0.231 0.183 0.766 

0.183 0.192 0.791 

0.127 0.209 0.815 

0.080 0.218 0.837 

0.044 0.236 0.849 

0.030 (l.252 0.847 

0.005 0.261 0.856 

0.001 0.281 0.847 

-0.004 0.295 0.842 

-0.005 0.309 0.835 

-0.010 0.319 0.831 

-0.002 0.350 0.807 

-0.001 0.362 0.799 

-0.001 0.376 0.791 

0.002 0.381 0.785 

-0.001 0.386 0.784 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.681 

============================================================ 

Y/D 

0.0083 

0.0129 

0.0178 

0.0226 

0.0264 

0.0305 

0.0347 

0.0389 

0.0430 

0.0482 

0.0540 

0.0623 

0.0703 

0.0785 

0.0868 

0.0952 

0.1059 

0.1197 

0.1334 

0.1470 

0.1606 

0.1744 

0.2154 

0.2564 

0.3386 

0.4207 

0.5053 

PHI 

DEG 

0.9 

-2.3 

-5.1 

-9.3 

-12.1 

-16.3 

-19.7 

-21.2 

-21. <) 

-20.1 

-18.4 

-17.0 

-15.3 

-13.3 

-12.4 

-11.6 

-10.8 

-9.7 

-8.8 

-8.4 

-8. 1 

-6.9 

-5 .. 3 

-4.3 

-2.8 

-1.8 

-0.9 

THETA 

DEG 

105.2 

101.7 

96.8 

91.1 

85.2 

78.3 

70.2 

62.0 

54.0 

45.9 

40.0 

34.3 

30.6 

28.3 

26.5 

25.6 

24.9 

24.9 

25.3 

26.0 

26.7 

27.1 

28.5 

29.7 

31.3 

31.7 

31.8 

154 

CPT CPS U/Uo 

0.205 0.108 0.828 

0.317 0.083 0.775 

0.418 0.065 0.719 

0.512 0.046 0.665 

0.577 0.026 0.631 

0.608 0.020 0.610 

0.620 0.015 0.604 

0.608 0.011 0.618 

0.574 0.025 0.633 

0.517 0.034 0.670 

0.456 0.047 0.705 

0.359 0.077 0.751 

0.280 0.103 0.786 

0.207 0.129 0.815 

0.136 0.152 0.844 

0.096 0.171 0.85t.. 

0.047 0.189 0.874 

0.007 0.228 0.875 

0.003 0.240 0.873 

-0.007 0.260 0.864 

-0.005 0.276 0.854 

-0.007 0.285 0.850 

0.000 0.322 0.823 

-0.003 0.343 0.812 

-0.004 0.360 0.802 

-0.003 0.369 0.797 

0.002 0.371 0.792 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.702 

============================================================ 

Y/D 

0.0083 

0.0110 

0.0138 

0.0170 

O.{)2(;1 

0.0232 

0.0260 

(1.0288 

0.0315 

0.0343 

0.0371 

0.0398 

0.0426 

0.0468 

0.0522 

0.0577 

0.0632 

0.0684 

0.0740 

0.0795 

0.0878 

0.0961 

0.1041 

0.1123 

0.1232 

0.1342 

O. 1477 

0.1616 

0.1754 

0.2165 

0.2574 

0.3397 

0.4218 

0.5065 

PHI 

DEG 

..,. c- .-.,~ ~ 

2.4 

2.0 

,.., ~ ...:... _I 

1.0 

0.3 

-2.0 

-1. 6 

-5.3 

-6.1 

-12.4 

-12.4 

-11.6 

-12.4 

-11.2 

-10.2 

-9.4 

-9.5 

-9.5 

-8.8 

-8.6 

-8.3 

-8.2 

-7.0 

-6.2 

-6.4 

-5.6 

-5.5 

-5.2 

-4.4 

-3.9 

-2.5 

-1.6 

-0.6 

THETA 

DEG 

105.7 

104.7 

102.7 

100.4 

96.7 

92.6 

87.3 

81.2 

75.2 

68.4 

61.3 

54.7 

47.9 

40.4 

34.3 

30.9 

28.1 

26.4 

25.5 

24.2 

23.4 

22.5 

22.1 

21.9 

21.9 

22.3 

23.0 

23.6 

24.2 

25.8 

26.9 

28.3 

28.9 

29.0 

155 

CPT CPS U/Uo 

0.274 0.025 0.838 

0.345 0.009 0.804 

0.421 -0.003 0.763 

0.498 -0.022 0.724 

0.577 -0.039 0.680 

0.653 -0.051 0.631 

0.711 -0.058 0.589 

0.778 -0.085 0.554 

0.820 -0.106 0.535 

0.829 -0.103 0.523 

0.847 -0.105 0.508 

0.821 -0.114 ().542 

0.798 -0.106 0.555 

0.689 -0.081 0.625 

0.604 -0.050 0.668 

0.515 -0.016 0.709 

0.421 0.015 0.751 

0.355 0.031 0.783 

0.301 0.050 0.806 

0.260 0.075 0.815 

0.178 0.105 0.847 

0.123 0.128 0.865 

0.087 0.148 0.875 

0.055 0.179 0.875 

0.021 0.210 0.877 

0.014 0.228 0.871 

0.000 0.251 0.865 

0.003 0.266 0.855 

0.001 0.282 0.847 

-0.004 0.313 0.831 

-0.003 0.329 0.821 

0.002 0.348 0.806 

-0.005 0.357 0.804 

-0.001 0.360 0.801 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.723 

============================================================ 

Y/D 

0.008::::. 

0.0118 

0.0153 

0.0187 

0.021 ::' 

0.0244 

0.0271 

0.02'7'8 

0.0326 

0.0354 

0.0381 

0.0405 

0.0450 

0.0492 

0.0547 

0.0602 

0.0653 

0.0709 

0.0765 

0.0820 

0.0876 

0.0954 

(i. 1 (}4f) 

0.1121 

0.1232 

0.1341 

0.1477 

0.1616 

0.1751 

0.2161 

0.2570 

0.3392 

0.4214 

0.5061 

PHI 

DEG 

5.0 

4 0 

6.5 

6.9 

8.7 

9.9 

9. :. 

10.5 

4.9 

7.5 

3.9 

-3. 1 

-1.8 

-4.2 

-3.6 

...,.. ~ 

-''':'. ~r 

-5.4 

-:: .. 9 

-4.0 

-4.3 

-4.1 

-4.6 

-4.3 

-4.3 

-4.5 

-4.1 

-4.2 

-4.1 

-4.1 

-3.9 

-3.1 

-2.1 

-1.5 

-0.8 

THETA 

DEG 

101.9 

100.8 

99.2 

96.2 

92.6 

88.5 

83.5 

77.3 

71. 8 

63.2 

37.9 

51.1 

41.8 

35.9 

30.9 

28.0 

25.7 

24.2 

23.6 

22.4 

21.6 

20.9 

2().2 

20.0 

19.9 

20.0 

20.6 

21.4 

22.1 

23.6 

25.2 

26.1 

26.8 

26.8 

156 

CPT CPS U/Uo 

0.373 -0.031 0.811 

0.425 -0. (>::::,6 0.782 

0.502 -0.049 0.740 

0.579 -0.059 0.693 

0.649 -0.088 0.663 

0.706 -0.094 0.623 

0.766 -0.108 0.584 

0.814 -0.127 0.559 

0.857 -0.142 Ci.533 

0.873 -0.129 0.506 

0.849 -0.142 0.541 

0.886 -0.154 0.519 

0.781 -0.103 0.567 

0.679 -0.094 0.64:3 

0.580 -0.043 0.680 

0.507 -0.026 0.720 

0.438 0.003 0.747 

0.363 0.032 0.778 

0.316 0.075 0.780 

0.261 0.080 0.811 

0.224 0.108 0.818 

0.157 0.122 0.849 

0.108 0.148 0.863 

0.069 0.169 0.872 

0.025 0.189 0.887 

0.006 0.214 0.883 

-0.002 0.233 0.877 

-0.002 0.251 0.867 

-0.002 0.262 0.860 

-0.003 0.296 0.841 

-0.004 0.312 0.832 

-0.005 0.334 0.819 

0.000 0.342 0.811 

0.002 0.344 0.808 
ANGLUAR PLANE: 

RADIUS/CYLINDER D!A: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.745 

============================================================ 

Y/D 

0.0083 

0.0108 

0.0136 

0.0167 

0.0198 

0.0229 

0.0259 

0.0285 

O.03i2 

0.0339 

0.0367 

0.0395 

0.0437 

0.0478 

0.0519 

0.0560 

0.0616 

0.0684 

0.0764 

0.0847 

c~. f)9'3(J 

0.1010 

O. 1094 

0.1177 

0.1259 

0.1367 

0.1478 

0.1613 

0.1752 

0.2162 

0.2572 

0.3392 

0.4213 

0.5061 

PHI 

DEG 

4.5 

2.6 

5.6 

7.0 

8.4 

9.6 

11.0 

11.9 

14.2 

9.4 

9.8 

iO.6 

7.8 

8.4 

5.4 

4.5 

3.6 

1.6 

0.9 

-0.3 

-1. I) 

-1.5 

-2.3 

-1.9 

-2.4 

-2.7 

-2.8 

-3.1 

-3.3 

_-:r ~ 

~ .... -2.8 

-1. 8 

-1.2 

-0.8 

THETA 

DEG 

89.3 

89.9 

8~'. 4 

87.7 

84.5 

80.4 

76.1 

70.7 

65.3 

60.6 

54.9 

49.3 

42.0 

37.2 

33.9 

31.0 

28.0 

25.8 

23.4 

21.9 

21.2 

20.5 

19.8 

19.5 

19.4 

19.5 

19.8 

20.2 

20.5 

21.6 

22.5 

24.0 

24.6 

24.7 

157 

CPT CPS U/Uo 

0.518 0.072 0.640 

0.505 0.040 0.675 

().523 0.057 0.648 

0.549 0.054 0.629 

0.581 0.032 0.622 

0.603 0.038 0.599 

0.635 0.021 0.587 

0.654 -0.001 0.589 

0.670 0.006 0.569 

0.680 0.014 0.552 

0.654 0.013 0.577 

0.654 0.005 0.584 

0.588 0.044 0.606 

0.549 0.049 0.634 

0.487 0.075 0.662 

0.456 0.081 0.680 

0.390 0.092 0.720 

0.318 0.115 0.753 

0.253 0.128 0.787 

0.207 0.150 0.802 

0.15:::;, 0.170 0.82:, 

0.113 0.186 0.837 

0.064 0.195 0.861 

0.037 0.206 0.869 

0.020 0.219 0.872 

0.001 0.231 0.876 

0.003 0.244 0.868 

-0.008 0.256 0.867 

-0.003 0.268 0.857 

-0.003 0.292 0.844 

0.000 0.308 0.832 

-0.002 0.328 0.820 

-0.001 0.335 0.816 

0.000 0.342 0.811 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.766 

============================================================ 

Y/D 

0.0085 

0.0120 

0.0169 

0.0217 

().0259 

0.0297 

0.0338 

0.0380 

0.0421 

0.0463 

0.0532 

0.0601 

0.0681 

0.0764 

0.0843 

0.0928 

0.1009 

0.1092 

O. 1175 

0.1253 

O. 1340 

0.1475 

O. 1611 

0.1749 

0.2160 

0.2571 

0.3392 

0.4212 

0.5061 

PHI 

DEG 

3.9 

3.6 

3.6 

6.8 

9.6 

11.2 

10.9 

10.4 

10.4 

10.3 

8.2 

6.3 

4.7 

2.9 

1.7 

1.0 

0.1 

-0.5 

-1.0 

-1. 4 

-1.5 

-1.9 

-2.3 

-2.4 

-2.6 

-2.6 

-2.0 

-1.4 

-0.9 

THETA 

DEG 

79.9 

80.8 

79.5 

74.8 

69.7 

64.6 

58.5 

52.1 

45.6 

40.1 

33.6 

29.1 

25.0 

23.1 

21.5 

19.8 

19.0 

18.5 

18. 1 

18.0 

18.0 

18.2 

18.6 

18.8 

19.8 

20.7 

22.2 

22.6 

22.8 

158 

CPT CPS U/Uo 

0.548 0.118 0.578 

0.537 0.104 0.600 

0.554 0.093 0.594 

0.573 0.089 0.581 

0.588 0.080 0.576 

0.585 0.084 0.575 

0.600 0.083 0.562 

0.567 0.082 0.592 

0.576 0.079 0.587 

0.522 0.086 0.626 

0.465 0.106 0.656 

0.412 0.120 0.685 

0.315 0.139 0.738 

0.253 0.152 0.771 

0.190 0.158 0.807 

0.140 0.164 0.834 

0.094 0.181 0.851 

0.061 0.187 0.867 

0.034 0.192 0.880 

0.023 0.200 0.881 

0.005 0.214 0.884 

-0.005 0.225 0.883 

-0.009 0.235 0.880 

-0.006 0.245 0.872 

-0.005 0.272 0.856 

-0.001 0.286 0.846 

-0.003 0.309 0.832 

-0.001 0.318 0.826 

-0.001 0.323 0.823 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.787 

============================================================ 

Y/D 

0.0085 

0.0140 

0.0196 

0.0250 

0.0302 

0.0358 

0.0413 

0.0469 

0.0538 

0.0606 

0.0686 

0.0769 

0.0852 

0.0934 

0.1015 

0.1098 

0.1178 

0.1263 

0.1343 

0.1482 

0.1t-17 

0.1750 

0.2166 

0.2577 

0.3398 

0.4219 

0.5065 

PHI 

DEG 

2.7 

0.8 

• c:- l •. J 

1.8 

3.6 

5.3 

4.8 

5.3 

5.0 

5.0 

4.0 

3.8 

2.9 

2.0 

1.5 

0.9 

0.5 

o ,.., • .0.. 

-0.1 

-0.5 

-0.8 

-1.1 

-1.7 

-1.7 

-1.5 

-1.2 

-0.7 

THETA 

DEG 

71. 1 

71.4 

68.3 

63.0 

58.1 

51.1 

45.4 

39.8 

34.4 

3(}.3 

26.5 

23.8 

21.8 

20.3 

19.3 

18.4 

17.8 

17.4 

17.3 

17.4 

17.8 

18.0 

18.6 

19.6 

20.7 

21.1 

21.2 

159 

CPT CPS U/Uo 

0.501 0.207 0.540 

0.514 0.180 0.553 

0.521 0.171 0.556 

0.520 0.158 0.567 

0.515 0.168 0.563 

0.502 0.171 0.572 

0.475 0.182 0.586 

0.437 0.189 0.612 

0.390 0.197 0.643 

0.348 0.196 0.675 

0.299 0.204 0.705 

0.244 0.204 0.743 

0.197 0.207 0.772 

0.156 0.210 0.796 

0.114 0.211 0.822 

0.078 0.212 0.843 

0.045 0.214 0.861 

0.020 0.220 0.871 

0.007 0.225 0.877 

-0.004 0.232 0.879 

-0.005 0.237 0.876 

-0.003 0.245 0.871 

-0.003 0.266 0.859 

-0.001 0.278 0.850 

-0.001 0.297 0.839 

0.002 0.306 0.832 

0.000 0.311 0.831 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.809 

=====:====================================================== 

Y/D 

0.0084 

0.0140 

0.0194 

0.0246 

0.0302 

0.0356 

0.0412 

0.0468 

0.0547 

0.0630 

0.0713 

0.0796 

0.0907 

0.1014 

O. 1125 

O. 1235 

0.1344 

0.1480 

0.1615 

0.1754 

<).2165 

0.2575 

0.3397 

0.4218 

0.5063 

PHI 

DEG 

1.1 

-0.2 

0.4 

-0.3 

0.1 

0.7 

2.6 

::·.6 

3.6 

3.3 

2.9 

~'< 4 

'"') 'Z ...... "_" 

1.8 

1.2 

0.9 

0.7 

0.1 

0.0 

-0.5 

-1.2 

-1.5 

-1.6 

-1.2 

-0.8 

THETA 

DEG 

67.0 

64.0 

59.5 

55.0 

50.1 

45.6 

41.5 

37.1 

32.6 

28.7 

25.4 

23.1 

20.8 

19.0 

17.9 

17.1 

16.7 

16.6 

16.9 

17.1 

17.6 

18.2 

19.4 

19.6 

19.7 

160 

CPT CPS U/Uo 

0.482 0.240 0.527 

0.487 0.221 0.540 

0.487 0.211 0.55C> 

0.484 0.206 0.557 

0.472 0.214 0.56,=' 

0.444 0.207 o c:-q? • .J,~ 

0.415 0.211 0.612 

0.387 0.213 0.6.33 

0.360 0.222 0.647 

0.302 0.226 0.686 

0.261 0.224 0.718 

0.216 0.222 0.725 

0.156 0.228 0.785 

0.116 0.222 0.814 

0.059 0.223 0.847 

0.035 0.223 0.861 

0.016 0.221 0.873 

-0.004 0.231 0.879 

-0.004 0.235 0.877 

-0.003 0.239 0.874 

-0.003 0.255 0.865 

-0.006 0.270 0.858 

0.002 0.285 0.844 

0.000 0.294 0.841 

0.007 0.289 0.839 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.851 

============================================================ 

Y/O 

0.0085 

0.0125 

0.0167 

0.0208 

0.0249 

0.0289 

0.0337 

0.0384 

0.0440 

0.0523 

0.0605 

0.0687 

0.0769 

0.0851 

0.0934 

0.1017 

0.1097 

0.1208 

0.1346 

0.1481 

0.1615 

0.1755 

0.2165 

0.2576 

0.3399 

0.4218 

0.5065 

PHI 

DEG 

2.6 

1.0 

0.4 

0.5 

0.8 

0.5 

1.1 

1.1 

1.5 

1.6 

2. 1 

2. 1 

2.0 

2.2 

1.9 

1.7 

1.7 

1.4 

1.2 

0.9 

0.7 

0.6 

-(>.2 

-0.8 

-1.0 

-0.6 

-0.5 

THETA 

DEG 

61.1 

57.5 

53.1 

48.8 

45.1 

42.1 

38.4 

35.8 

-:r~ ~ ....:1,.: • .L 

28.7 

25.9 

23.6 

21.2 

20.0 

18.6 

17.6 

16.9 

15.9 

15.2 

15.0 

15.1 

15.2 

15.6 

16.0 

17.1 

17.3 

17.5 

161 

CPT CPS U/Uo 

0.492 0.251 0.507 

0.492 0.238 0.520 

0.479 0.238 0.532 

0.470 0.236 0.542 

0.451 0.237 0.559 

0.432 0.237 0.574 

0.420 0.238 0.584 

0.400 0.238 0.601 

0.370 0.235 0.628 

0.332 0.238 0.657 

0.294 0.241 0.682 

0.261 0.241 0.706 

0.222 0.236 0.736 

0.185 0.233 0.763 

0.139 0.233 0.792 

0.114 ().232 0.809 

0.079 0.234 0.829 

0.045 0.232 0.851 

0.014 0.228 0.871 

-0.004 0.231 0.879 

-0.012 0.231 0.884 

-0.009 ().233 0.881 

-0.008 0.241 0.876 

-0.007 0.249 0.871 

-0.004 0.264 0.860 

-0.001 0.270 0.855 

-0.005 0.274 0.855 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEB 

0.894 

============================================================ 

Y/D 

0.0086 

0.0131 

0.0172 

0.0228 

0.0280 

0.0336 

0.0419 

0.0499 

0.0584 

0.0664 

0.0747 

0.0831 

0.0913 

0.0993 

0.1076 

O. 1186 

0.1321 

0.1459 

0.1595 

O. 173~, 

0.2144 

0.2554 

0.3376 

0.41.97 

0.5043 

PHI 

DEB 

1.6 

1.1 

0.8 

1.1 

0.9 

1.3 

1.7 

1.8 

1.9 

2.0 

2. (> 

2. 1 

1.9 

1.9 

1.8 

1.7 

1.6 

1.3 

1.0 

0.7 

.0 

-0.6 

-0.9 

-0.8 

-0.8 

THETA 

DEB 

52.9 

48.3 

44.8 

39.7 

36.1 

33.2 

29.1 

26.5 

24.2 

22.0 

20.7 

19.4 

18.0 

17.1 

16.3 

15.6 

15.1 

15.0 

15.1 

15.1 

15. 1 

15.4 

15.8 

16.0 

16.2 

162 

CPT CPS U/Uo 

0.506 0.242 0.502 

0.485 0.237 0.528 

0.473 0.234 0.541 

0.442 0.235 0.568 

0.423 0.234 0.586 

0.391 0.236 0.611 

0.349 0.234 0.646 

0.309 0.234 0.676 

0.273 0.234 0.702 

0.232 0.233 0.732 

0.200 0.229 0.755 

0.164 0.230 0.778 

0.129 0.224 0.804 

0.098 0.223 0.823 

0.070 0.220 O. 84~, 

0.038 0.218 0.863 

0.011 0.216 0.879 

-0.002 0.214 0.888 

-0.004 0.213 0.889 

-0.003 0.214 0.888 

-0.003 0.217 0.887 

0.001 0.221 0.882 

0.001 0.230 0.877 

0.000 0.237 0.873 

0.000 0.241 0.871 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

25.000 DEG 

0.936 

============================================================ 

Y/D 

0.0086 

0.0142 

0.0200 

0.0256 

0.0336 

0.0419 

0.0502 

0.0584 

(1. ()664 

0.0747 

0.0831 

0.0913 

0.0993 

0.1076 

0.1186 

0.1321 

0.1459 

0.1595 

0.1732 

0.2144 

().2554 

0.3376 

0.4196 

0.5043 

PHI 

DEG 

1.7 

0.7 

0.6 

0.8 

1.0 

1.1 

1.3 

1.4 

1 ..,. ~ .. ~~ 

1.3 

1.4 

1.5 

1.3 

1.4 

1.4 

1.3 

1.2 

0.9 

0.7 

0.1 

-0.4 

-0.6 

-(1.9 

-0.9 

THETA 

DEG 

44.4 

39.6 

7C'" '"'" -,,;.~ . ..: 

32.2 

28.5 

25.5 

22.9 

21.2 

19.5 

18.3 

17.1 

16.3 

15.6 

15.1 

14.4 

14.1 

14.0 

14.0 

14.0 

13.9 

14.1 

14.4 

14.5 

14.7 

163 

CPT CPS U/Uo 

0.501 0.243 0.506 

0.469 0.239 0.540 

0.441 0.238 0.567 

0.411 0.237 0.593 

0.381 O.23.!; 0.619 

0.335 0.234 0.657 

0.301 0.231 0.683 

0.263 0.231 0.712 

0.229 0.228 0.737 

0.185 0.229 0.766 

0.152 0.224 0.790 

0.117 0.221 0.814 

0.081 0.223 0.834 

0.055 0.219 0.852 

0.028 0.215 0.870 

0.003 0.215 0.884 

-0.003 0.212 0.890 

-0.004 0.212 0.890 

-0.006 0.210 0.892 

-0.003 0.211 0.890 

0.002 0.208 0.889 

-0.001 0.218 0.885 

0.001 Ci.222 0.881 

0.001 0.225 0.880 
ANGLUAR PLANE: 

RADIUS/CYLINDER OIA: 

Five-Hole Probe Data 

(continued) 

45.000 OEG 

0.553 

============================================================ 

Y/O 

0.0083 

0.0122 

(J.0163 

0.0219 

0.0274 

0.0330 

0.0412 

0.0494 

0.0575 

0.0657 

0.0792 

0.0930 

0.1066 

0.1204 

0.1342 

0.1477 

0.1612 

0.1750 

0.2574 

0.3402 

0.4222 

0.5058 

PHI 

DEG 

0.3 

-1.9 

-3.2 

-4.5 

-5.3 

-6.0 

-7.5 

-8. 1 

-8.3 

-8.3 

-8.3 

-8.2 

-8.2 

-8.0 

-7.4 

-7.0 

-6.3 

-5.8 

-4.1 

-3. () 

-1.9 

-1.2 

THETA 

DEG 

46.6 

46.1 

44.9 

43.8 

42.9 

42.4 

41.5 

40.7 

40.0 

39.2 

38.9 

38.2 

37.8 

37.6 

37.5 

37.5 

37.4 

37.3 

37.5 

37.9 

38.1 

38.1 

164 

CPT CPS U/Uo 

-0.001 -0.552 1.234 

0.004 -0.558 1.246 

0.013 -0.573 1.249 

0.009 -0.592 1.258 

0.011 -0.599 1.260 

0.015 -0.606 1.261 

-0.004 -0.620 1.274 

-0.013 -0.630 1.282 

-0.011 -0.635 1.283 

-0.011 -0.641 1.286 

-0.013 -0.653 1.291 

-0.015 -0.658 1.293 

-0.012 -0.661 1.293 

-0.015 -0.670 1.298 

-0.010 -0.671 1.297 

-0.009 -0.674 1.297 

-0.005 -0.673 1.29=. 

-0.004 -0.675 1.296 

0.002 -0.695 1.3(12 

0.000 -0.073 1.305 

0.001 -0.700 1.303 

-0.001 -0.693 1.302 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.596 

============================================================ 

Y/D 

0.0082 

0.0126 

(1.(}167 

0.0208 

0.0250 

0.0291 

0.0331 

0.0372 

().0413 

0.0497 

0.0579 

0.0686 

0.0796 

0.0935 

O. 1070 

0.1208 

0.1343 

0.1471 

0.1624 

0.1761 

0.1887 

0.2588 

0.3401 

0.4218 

0.5054 

PHI 

DEG 

0.9 

-2.1 

-3.8 

-4.7 

-5.8 

-7.0 

-8.0 

-8.5 

-8.7 

-9.3 

-9.6 

-9.8 

-9.6 

-9.4 

-9.0 

-8.6 

-8.3 

-8.0 

-7.2 

-6.2 

-5.7 

-3.9 

-2.5 

-1.7 

-0.8 

THETA 

DEG 

54.2 

52.6 

50.6 

48.4 

46.8 

45.4 

44.3 

42.7 

41.5 

39.5 

37.8 

35.8 

34.6 

33.9 

33.4 

33.1 

33.1 

33.1 

33.0 

32.9 

33.0 

-:'- co ._"'t.~ • "J 

34.2 

34.4 

34.3 

165 

CPT CPS U/Uo 

0.029 -0.378 1. 161 

0.057 -0.417 1.166 

0.078 -0.435 1.165 

0.090 -0.444 1.164 

0.099 -0.446 1.161 

0.094 -0.457 1.167 

0.090 -0.471 1.175 

0.086 -0.476 1.179 

0=081 -0.494 1.189 

0.073 -0.503 1.196 

0.054 -0.512 1.207 

0.035 -0.523 1.22(i 

0.015 -0.529 1.230 

0.002 -0.540 1.240 

-0.007 -0.547 1.246 

-0.006 -0.555 1.249 

-0.012 -0.560 1.254 

-0.012 -0.565 1.255 

0.008 -0.566 1.254 

0.000 -0.564 1.251 

-0.001 -0.530 1.237 

-0.001 -0.566 1.252 

-0.001 -0.579 1.257 

-0.003 -0.579 1.258 

-0.002 -0.559 1.249 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.638 

============================================================ 

Y/D 

0.0083 

0.0125 

0.0173 

0.0219 

0.0263 

0.0302 

0.0343 

0.0385 

0.0426 

0.0466 

0.0551 

(i. 06 -::;.1 

0.0714 

0.0796 

0.09::::.1 

0.1069 

0.1206 

O. 1343 

0.1481 

0.1616 

O. 1 7~· 1 

0.2161 

0.2575 

0.3399 

0.4218 

0.5062 

PHI 

DEG 

-0.3 

-'"' "'-. "'- '"' 

-3.8 

-5.0 

-6.3 

-8.0 

-8.5 

-9.1 

-9.4 

-9.8 

-10.3 

-10.7 

-10.7 

-10.5 

-9.9 

-9.5 

-9.0 

-8.4 

-7.8 

-6.9 

-6.1 

-4.8 

-3.9 

-2.6 

-1.7 

-1.2 

THETA 

DEG 

62.6 

60.0 

56.2 

53.4 

50.6 

48.8 

46.4 

44.3 

42.5 

40.3 

37.3 

34.8 

32.5 

31.2 

29.5 

28.6 

28.2 

28.3 

28.5 

28.6 

28.7 

29.1 

29.8 

30.6 

30.8 

30.9 

166 

CPT CPS U/Uo 

0.075 -0.382 1. 143 

0.127 -0.391 1. 124 

0.183 -(;.392 1.100 

0.213 -0.396 1.088 

0.234 -0.404 1.082 

0.233 -0.413 1.086 

0.237 -0.417 1.086 

0.237 -0.423 1.089 

0.232 -0.425 1.092 

0.222 -0.427 1.098 

0.192 -0.436 1. 115 

0.154 -0.443 1.135 

0.121 -0.448 1.152 

0.090 -0.451 1. 167 

0.038 -0.450 1.188 

0.007 -0.451 1.202 

-0.007 -0.448 1.206 

-0.016 -0.446 1.209 

-0.014 -0.441 1.206 

-0.010 -0.433 1.201 

-0.006 -0.431 1.199 

-0.002 -0.417 1. 191 

-0.005 -0.409 1.189 

-0.004 -0.401 1.185 

0.000 -0.393 1.181 

-0.005 -0.385 1.179 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.681 

============================================================ 

Y/D 

0.0086 

0.0141 

0.0197 

0.0238 

0.0279 

0.0321 

0.0359 

0.0402 

0.0446 

0.0525 

0.0608 

0.0688 

0.0770 

0.0854 

0.0937 

0.1144 

0.1345 

O. 1570 

O. 1771 

0.2586 

0.3412 

0.4231 

0.5053 

PHI 

DEG 

0.7 

-2.7 

-4.7 

-6.8 

-8.6 

-9.4 

-10.2 

-11.3 

-11. 6 

-11.5 

-10.7 

-1,).2 

-9.9 

- '7' .,J ~ 

-9.0 

-8.2 

-6.7 

-5.4 

-4.7 

-3.1 

...... '""' -"'::' • .L 

-1.4 

-1.0 

THETA 

DEG 

69.9 

66.5 

62.0 

59.2 

55.9 

52.3 

49.4 

45.2 

41 c:; ........ 

36.3 

31.9 

29.2 

27.3 

25.8 

24.8 

23.3 

22.9 

23.5 

24.2 

25.9 

~7 '? .,;.... r • .L. 

27.6 

27.7 

167 

CPT CPS U/Uo 

0.133 -0.405 1.128 

0.243 -0.449 1.098 

0.350 -0.456 1.051 

0.402 -0.476 1.036 

0.435 -0.481 1.023 

0.468 -0.485 1.008 

0.492 -0.491 0.999 

0.493 -0.496 1.001 

0.484 -Oe502 1.009 

0.433 -0.507 1.036 

0.357 -0.492 1.065 

0.289 -0.487 1.0'=74 

0.242 -0.479 1. 112 

0.187 -0.465 1.130 

0.132 -0.450 1.148 

0.051 -0.428 1.173 

0.004 -0.401 1. 182 

-0.006 -0.377 1. 176 

-0.002 -0.362 1.168 

-0.003 -0.330 1.155 

-0.005 -0.317 1. 150 

0.000 -0.309 1.144 

-0.001 -0.303 1. 142 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued> 

45.000 DEG 

0.702 

============================================================ 

Y/D 

0.0085 

0.0126 

0.0162 

0.0207 

0.0247 

0.0289 

0.0330 

0.0371 

0.0413 

0.0454 

0.0493 

0.0537 

0.0575 

0.0618 

0.065'7' 

0.0770 

0.0852 

0.0934 

0.1069 

0.1208 

0.1342 

0.1481 

0.1617 

O. 1755 

0.2162 

0.2577 

0.3394 

0.4218 

0.5058 

PHI 

DEG 

1.3 

-0.7 

-2.1 

-3.7 

-5.1 

-8.2 

-8.9 

-10. 1 

-11. 0 

-11.7 

-11.3 

-10.5 

-10.3 

-9.8 

n 'j -7 ..... 

-8.5 

-8.2 

-8.0 

-6.7 

-5.8 

-5=2 

-4.7 

-4.4 

-4.0 

-3.4 

-3. () 

-2.3 

-1.6 

-1.2 

THETA 

DEG 

73.3 

71.9 

69.3 

66.3 

63.3 

59.2 

54.9 

49.9 

44.3 

39.5 

35.8 

31.9 

30.2 

28.1 

26.4 

24.1 

23.2 

..,? 'j 4'-_ • .L. 

21.1 

20.5 

20.4 

21.0 

21.7 

?.., ..... _.L..4 

23.3 

24.1 

25.1 

..,E:" r .... ~ • ...J 

25.7 

168 

CPT CPS U/Uo 

0.196 -0.480 1.134 

0.288 -0.503 1.102 

0.392 -0.528 1.066 

0.481 -0.538 1.028 

0.570 -0.566 0.998 

0.628 -0.577 0.974 

0.682 -0.600 0.958 

0.710 -0.603 0.945 

0.693 -0.613 0.959 

0.670 -0.606 0.967 

0.627 -0.603 0.988 

0.549 -0.580 1.015 

0.511 -0.571 1.030 

0.448 -0.557 1.053 

0.402 -0.545 1.069 

0.293 -0.505 1.101 

0.237 -0.480 1. 115 

0.188 -0.461 1.128 

0.117 -0.428 1.145 

0.066 -0.400 1.155 

0.022 -0.389 1. 169 

0.002 -0.365 1.167 

-0.008 -0.355 1.167 

-0.009 -0.340 1. 161 

-0.009 -0.318 1.152 

-0.003 -0.307 1.145 

0.001 -0.288 1.134 

-0.005 -0.280 1.133 

0.000 -0.276 1.130 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.723 

============================================================ 

Y/D 

0.0085 

0.0114 

0.0155 

0.0211 

0.0252 

0.0293 

0.0331 

0.0361 

0.0387 

0.0415 

0.0442 

0.0470 

0.0497 

0.0539 

0.0577 

0.0662 

0.0743 

0.0826 

0.0933 

0.1074 

0.120[: 

0.1344 

0.1485 

0.1620 

0.1756 

0.2166 

0.2580 

0.3401 

0.4223 

0.5064 

PHI 

DEG 

2.6 

1.6 

1.2 

0.6 

-0.4 

-1.4 

-2.5 

-4.3 

-4.8 

-5.5 

-5.9 

-7.2 

-7.4 

-6.8 

-6.4 

-5.7 

-5.4 

I:" ., 

-~.~ 

-4.7 

-4.4 

-4.2 

-4.0 

-3.6 

-3.4 

-3.2 

-3.0 

-2.9 

-2.0 

-1.4 

-1. 1 

THETA 

DEG 

74.1 

73.2 

71.4 

68.3 

64.7 

60.5 

56.0 

50.9 

46.7 

43.2 

38.6 

34.5 

32.1 

28.7 

26.7 

23.0 

21.5 

20.6 

19.9 

19.3 

18.9 

18.9 

19.3 

19.8 

20.4 

21.6 

22.4 

23.7 

24.2 

24.4 

169 

CPT CPS U/Uo 

0.269 -0.531 1.123 

0.329 -0.550 1.105 

0.421 -0.564 1.070 

0.568 -0.594 1.013 

0.657 -0.626 0.984 

0.748 -0.645 0.947 

0.820 -0.667 0.921 

0.849 -0.677 0.910 

0.859 -0.681 0.906 

0.867 -0.698 0.912 

0.826 -0.683 0.926 

0.759 -0.663 0.951 

0.723 -0.660 0.968 

0.636 -0.621 0.992 

0.596 -0.615 1.010 

0.456 -0.559 1.051 

0.366 -0.528 1.078 

0.296 -0.492 1.094 

0.221 -0.452 1.109 

0.149 -0.417 1.126 

0.093 -0.390 1.139 

0.039 -0.369 1.153 

0.009 -0.350 1.158 

-0.004 -0.337 1.158 

-0.010 -0.325 1.156 

-0.006 -0.299 1.142 

-0.003 -0.288 1.137 

-0.003 -0.267 1.127 

-0.005 -0.258 1.124 

-0.001 -0.251 1.119 
ANGLUAH PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.745 

====================================================== =====~ 

Y/D 

0.0090 

0.0118 

0.0159 

0.0200 

0.0239 

0.0281 

0.0322 

0.0364 

0.0405 

0.0447 

0.0486 

0.0527 

0.0582 

0.0664 

0.0747 

0.0830 

0.0939 

0.1076 

0.1214 

0.1350 

0.1485 

0.1622 

0.1759 

0.2170 

0.2582 

0.3394 

0.4225 

0.5064 

PHI 

DEG 

4.4 

4.2 

4.6 

5.8 

5.8 

6.4 

6.3 

6. 1 co ..,. ,..J •• .;.: 

3.7 

2.0 

2. 1 

0.7 

-f). 2 

-0.9 

-1.2 

-1.9 

-2.1 

-2.1 

-2.2 

-2.2 

-2.2 

-2.3 

-2.6 

-2.4 

-2.0 

-1. 5 

-1.2 

THETA 

DEG 

68.9 

69.3 

68.8 

66.7 

64.4 

60.4 

55.2 

49.9 

43.9 

37.6 

33.1 

29.5 

26.0 

22.9 

21.1 

19.8 

18.8 

18.0 

17.6 

17.7 

18.0 

18.6 

19.2 

20.7 

21.5 

22.7 

22.8 

23.4 

170 

CPT 

0.435 

0.438 

0.488 

0.558 

0.636 

0.695 

0.765 

0.802 

0.824 

0.791 

0.727 

0.679 

0.574 

0.464 

0.387 

0.312 

0.242 

0.156 

0.090 

0.032 

0.006 

-0.008 

-0.007 

-0.003 

-0.004 

-0.007 

-0.003 

-0.006 

CPS 

-0.531 

-0.544 

-0.557 

-0.574 

-0.591 

-0.608 

-0.622 

-0.632 

-0.635 

-0.631 

-0.613 

-0.602 

-0.567 

-0.522 

-0.484 

-0.451 

-0.421 

-0.386 

-0.361 

-0.337 

-0.327 

-0. ::::.11 

-0.302 

-0.277 

-0.265 

-0.244 

-0.237 

-0.225 

U/Uo 

1.047 

1.052 

1.034 

1.007 

0.978 

0.956 

0.926 

0.911 

0.901 

0.917 

0.941 

0.961 

0.9S-6 

1.029 

1.047 

1.067 

1.085 

1.109 

1.128 

1.142 

1. 14'7' 

1.148 

1.144 

1.131 

1.126 

1. 118 

1.114 

1. 110 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.766 

============================================================ 

y/r. 

0.0093 

0.0120 

0.015;:' 

0.0213 

0.0291 

0.0373 

(.1.0457 

0.054<) 

0.0623 

r~ r't.II-\-:-" '_1. V I "'_' .... ) 

0.0787 

0.0869 

0.0951 

0.1037 

0.1119 

O. 134 .:;, 

0.1556 

0.1768 

(1.2585 

0.3402 

().422S' 

() .. 5i)47 

PHI 

DEG 

4.8 

4.7 

c:- .., ..J • .L.-

6.6 

8.3 

9.2 

7.8 

6.3 

4.9 

3.4 

2.1 

1.4 

1.1 

0.3 

O. 1 

-0.5 

-1.0 

-1.4 

-1. 8 

-1.5 

-1.2 

-0. S' 

THETA 

DEG 

61.2 

62.4 

62.5 

61.2 

c:"c" C" 

..J...J • .J 

47.3 

37.4 

31.0 

26.3 

23=6 

21.4 

20.7 

19.3 

18.4 

18.0 

17.7 

18.2 

19.1 

21.0 

21.9 

22.4 

.L."::'. ~....., -I 

171 

CPT CPS U/Uo 

0.547 -0.434 0.941 

0.517 -0.452 0.967 

0.521 -0.462 0.970 

0=559 -0.463 0.951 

0.619 -0.478 0.927 

0.644 -0.485 0.917 

0.621 -0.471 0.921 

0.558 -0.456 0.948 

0.478 -0.424 O. 9T~. 

0.404 -0.398 0.996 

0.345 -0.376 1.015 

0.290 -0.384 1.046 

0.243 -0.385 1.069 

0.171 -0.334 1.078 

0.112 -0.331 1. 104 

0.020 -0.312 1.136 

-0.001 -0.278 1.131 

-0.014 -0.276 1.136 

-0.011 -0.240 1. 118 

-0.003 -0.217 1.105 

-0.003 -0.210 1.101 

-0.004 -0.205 1.100 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.787 

============================================================ 

Y/D 

0.0088 

0.0116 

0.0156 

0.0197 

0.0278 

0.0361 

0.0443 

0.0526 

0.0607 

0.0689 

0.0772 

0.0854 

0.0938 

0.1074 

0.1210 

0.1347 

0.1485 

0.1621 

0.1759 

0.2170 

0.2572 

0.3391 

0.4218 

0.5051 

PHI 

DEG 

2.9 

..., ~ 

L. "_I 

2.2 

~ -". ~. "';1 

5.0 

6.3 

6.6 

6.3 

C" Ll .J. • 

4.5 

3.6 

2.7 

2. 1 

1.4 

0.7 

O. 1 

-0.3 

-0.5 

-0.9 

-1.4 

-1. 5 

-1.6 

-1.4 

-1. 1 

THETA 

DEG 

52.6 

53.6 

54.4 

53.9 

50.5 

44.9 

38.2 

32.6 

28.4 

25.0 

22.7 

20.8 

19.8 

18. 1 

17.2 

16.9 

17.2 

17.5 

18.0 

19. 1 

19.7 

20.7 

21.1 

21.3 

172 

CPT 

0.545 

0.538 

0.531 

0.533 

0.537 

0.542 

0.521 

0.476 

0.427 

0.383 

0.319 

0.271 

0.211 

0.128 

0.060 

0.018 

0.001 

-0.006 

-0.007 

-0.004 

-0.003 

-0.001 

0.000 

-0.003 

CPS 

-0.330 

-0.359 

-0.365 

-0.371 

-0.369 

-0.368 

-0.355 

-0.348 

-0.333 

-0.323 

-0.316 

-0.306 

-0.303 

-0.292 

-0.282 

-0.273 

-0.267 

-0.256 

-0.250 

-0.232 

-0.222 

-0.205 

-0.192 

-0.186 

U/Uo 

0.886 

0.906 

0.913 

0.915 

0.912 

0.909 

0.913 

0.934 

0.952 

0.970 

0.999 

1.017 

1.045 

1.079 

1.105 

1.120 

1.125 

1.123 

1.122 

1.112 

1.107 

1.098 

1.092 

1.090 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.809 

============================================================ 

y/n 

0.0090 

0.0119 

0.0147 

O.02(i3 

0.0286 

0.0368 

0.0452 

0.0518 

0.0607 

O. (}690 

0.0774 

0.0853 

0.0940 

O. 1077 

0.1213 

O. 1351 

0.1483 

0.2580 

0.3399 

0.4225 

0.5069 

PHI 

DEG 

'") <" .... ~-' 

0.6 

0.2 

0.6 

1.0 

2.0 

3.3 

3.7 

-,. Q -' .. 

4. 1 

3.7 

"7 "7' .";T. ,_"r 

..., -'. ",,".t::1 

2.0 

1.5 

1.0 

0.5 

-1.0 

-1.4 

-1. 2 

-1.0 

THETA 

DEG 

48.4 

49.2 

49.4 

49.2 

46.1 

42.2 

37.4 

33.6 

29.5 

26.3 

23.6 

21.5 

20.2 

18.5 

17.4 

16.8 

16.9 

18.8 

19.7 

20.0 

20.2 

173 

CPT CPS U/Uo 

0.506 -0.240 0.857 

0.497 -0.262 O. 87~' 

0.499 -0.272 O.88r) 

0.501 -0.294 0.891 

0.496 -0.295 0.894 

0.482 -0.291 0.899 

0.462 -0.281 0.906 

0.442 -0.275 0.913 

0.398 -0.262 0.929 

0.347 -0.260 0.955 

0.308 -0.256 0.974 

0.256 -0.255 0.999 

0.196 -0.255 1.029 

0.117 -0.252 1.065 

0.055 -0.249 1.093 

0.014 -0.242 1.108 

-0.001 -0.239 1. 114 

-0.011 -0.207 1.104 

-0.002 -0.193 1.093 

-0.003 -0.183 1.089 

-0.005 -0.176 1.087 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.851 

============================================================ 

VIr. 

0.0118 

O.017Ll 

0.0243 

(). ()3{)~ 

0.0392 

O. (J475 

0.0558 

0.0638 

(i .. (}719 

0.0803 

0.0885 

0.0965 

0.1048 

O. 1187 

0.1321 

0.1460 

0.1595 

0.1734 

0.2145 

0.2556 

0.':373 

0,4197 

O.5Ci39 

PHI 

DEG 

0.8 

-0.2 

O. 1 

0.6 

0.8 

0.9 

0.9 

1.3 

1.2 

1.4 

1.3 

1.2 

1.1 

0.9 

0.7 

0.6 

0.3 

I). 1 

-0.5 

-0.9 

-1.2 

-1.1 

-1.0 

THETA 

DEG 

44.4 

41.8 

37.9 

34.7 

31. 3 

28.0 

25.8 

23.9 

22.1 

20.8 

19.7 

19.0 

18.2 

17.4 

17.0 

17.0 

17.0 

17.0 

17.3 

17.5 

18.0 

18. 1 

18.4 

174 

CPT CPS U/UD 

0.476 -0.189 0.844 

0.464 -0.195 0.855 

0.449 -0.198 0.865 

0.414 -0.199 0.886 

0.375 -0.197 0.907 

0.337 -0.194 0.926 

0.287 -0.191 0.951 

0.244 -0.191 0.973 

0.207 -0. 194 0.993 

0.164 -0.192 1.014 

0.130 -0.194 1.032 

0.091 -0.195 1.051 

0.072 -0.197 1.061 

0.028 -0.196 1.081 

0.003 -0.196 1.093 

-0.003 -0.197 1.095 

-0.006 -0.198 1.097 

-0.006 -0.194 1.095 

-0.003 -0.187 1.091 

-0.001 -0.185 1.089 

0.000 -0.175 1.084 

0.002 -0.169 1.08« 

0.001 -0.161 1.077 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0=894 

============================================================ 

Y/D 

0.0085 

0.0140 

0.0196 

0.0275 

0.0358 

0.0441 

0.0523 

0.0606 

0.0687 

0.0770 

0.0852 

0.093=, 

0.1015 

0.1097 

0.1181 

O. 1316 

0.1522 

0.1728 

0.2139 

0.2140 

0.254'7' 

0.3371 

0.4192 

0.5037 

PHI 

DEG 

1.5 

0.6 

0.4 

0.5 

0.9 

1.0 

1.2 

1 . r=; 

~ 

1.5 

1.7 

1.6 

1.7 

1.7 

1.7 

1.6 

1.3 

1.1 

0.8 

O. 1 

-0.3 

-0.7 

-0.8 

-0.8 

-0.9 

THETA 

DEG 

42.8 

40.5 

37.4 

33.6 

30.5 

27.3 

25.2 

23.2 

21.6 

20.2 

19. 1 

18.4 

17.7 

17. 1 

16.6 

16.2 

16.0 

16.2 

16.2 

16.6 

16.7 

16.8 

17.1 

17.1 

175 

CPT CPS U/Uo 

0.508 -0.147 0.799 

0.482 -0.161 0.825 

0.461 -0.163 0.838 

0.436 -0.166 0.854 

0.403 -0.163 0.872 

0.359 -0.162 0.896 

0.318 -0.166 0.921 

0.276 -0.165 0.942 

0.234 -0.163 0.964 

0.186 -0.165 0.989 

0.154 -0.167 1.066 

0.105 -0.170 1.032 

0.07:3, -0.l71 1.048 

0.038 -0.173 1.006 

0.015 -0.173 1.076 

-0.002 -0.176 1.085 

-0.004 -0.178 1.087 

-0.007 -0.182 1.090 

-0.004 -0.178 1.087 

-0.004 -0.174 1.085 

0.002 -0.166 1.079 

0.001 -0.161 1.077 

0.001 -0.154 1.074 

-0.001 -0.150 1.073 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

0.936 

============================================================ 

Y/D 

0.0092 

0.0120 

0.0202 

0.0283 

0.0366 

0.0449 

0.0532 

0.0614 

0.0694 

0.0777 

0.0861 

0.0943 

O. 102:~. 

0.1106 

0.1189 

().1325 

0.1461 

0.1598 

0.1736 

0.2147 

0.4199 

0.5042 

PHI 

DEG 

1.0 

0.6 

0.3 

0.5 

0.7 

0.5 

0.9 

0.7 

0.9 

0.7 

0.8 

1.0 

(1.9 

0.7 

0.6 

0~6 

0.4 

0.3 

0.1 

-0.2 

-0.9 

-{).9 

THETA 

DEG 

36.9 

35.7 

31.7 

28.8 

26.2 

24.0 

........ c- 4.£..",,,,J 

20.9 

19.6 

18.7 

17.9 

17.3 

16.7 

16.4 

16.0 

15.8 

15.7 

15.6 

15.6 

15.7 

15.9 

1"'" -J. Q , 

176 

CPT CPS U/Uo 

0.506 -0.120 0.784 

0.489 -0.126 0.798 

0.440 -0.130 0.831 

0.403 -0.134 0.855 

0.355 -0.132 0.881 

0.315 -0.133 0.904 

0.274 -0.138 0.930 

0.223 -0.134. 0.954 

0.193 -0.140 0.973 

0.146 -0.141 0.998 

0.106 -0.144 1.019 

0.073 -0.143 1.034-

0.042 -0.148 1 • (-1"'"-::' ___ --.J~ 

0.021 -0.141 1.058 

0.004 -0. 145 1.068 

-0.002 -0.148 1.072 

-0.002 -0.149 1.073 

-0.003 -0.147 1.073 

-0.005 -0. 149 1.074 

-0.005 -0.150 1.075 

-0.001 -0.140 1.068 

-0.001 -0.137 1.0t7 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA; 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

1. 021 

=~========================================================== 

Y/D 

0.0078 

0.0098 

0.0154 

0.0210 

0.0289 

0.0371 

0.0455 

0.0537 

0.0621 

0.0701 

0.0783 

0.0865 

0.0948 

0.1029 

0.1108 

0.1195 

0.1332 

0.1741 

0.2152 

0.2564 

().3385 

(). 42Cj::~ 

0.5043 

PHI 

DEG 

1.8 

1.0 

0.0 

-0.4 

-0.4 

-0.1 

-0.1 

-0.2 

0.0 

0.0 

0.0 

-0.1 

-().2 

-0.1 

-0.1 

-0.2 

-0.1 

-0.1 

-0.2 

-0.4 

-0.9 

-1.0 

-0.9 

THETA 

DEG 

29.6 

28.9 

27. 1 

25.0 

22.8 

21.3 

19.6 

18.4 

17.3 

., "- .1o."'t 

15.8 

15.3 

14.8 

14.6 

14.2 

13.9 

13.6 

13.2 

13.2 

13.1 

13.1 

1 :::;-" 1 

13.3 

177 

CPT CPS U/Uo 

0.514 -0.075 0.748 

0.487 -0.088 0.775 

0.435 -0.100 0.815 

0.398 -0.104 0.840 

0.345 -0.111 0.875 

0.305 -0.109 0.896 

0.254 -0.108 0.924 

0.201 -0.111 0.954 

0.167 -0.112 0.972 r. 110 V • .L.L' -0.111 0.996 

0.083 -0.109 1.013 

0.061 -0.112 1.025 

0.031 -0.118 1.04::::, 

0.018 -0.124 1.052 

0.010 -0.117 1.052 

-0.003 -0.116 1.058 

-0.002 -0.119 1.059 

-0.003 -0.122 1.061 

-0.004 -0.123 1.062 

-0.002 -0.123 1.061 

0.002 -0.121 1.058 

0.005 -0.117 1.055 

0.000 -0.121 1.059 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

1.106 

====~======================================================= 

VII) 

0.0077 

0.0096 

0.0153 

0.0207 

0.0287 

0.0370 

0.0453 

0.0536 

0.0618 

0.0699 

0.0781 

0.0864 

0.0944 

0.1028 

0.1110 

0.1193 

0.1328 

0.1737 

0.2151 

0.2562 

0.3383 

(I.419S· 

0.5048 

PHI 

DEG 

1.7 

0.9 

0.0 

-C'.2 

-0.3 

-().3 

-0.2 

-0.4 

-0.3 

-0.4 

-0.3 

-0.2 

0.0 

-0.2 

-0.1 

0.3 

-0. 1 

-0.1 

-0.5 

-0.5 

-0.5 

-0.8 

-0.7 

THETA 

DEG 

25.1 

24.5 

23.0 

21.5 

19.8 

18.3 

17.0 

16. 1 

15.2 

14.5 

13.9 

13.3 

12.9 

12.5 

12.3 

12. 1 

11.8 

11.7 

11.7 

11.5 

11.6 

11.4 

11. 4 

178 

CPT CPS U/Uo 

0.502 -0.072 0.755 

0.478 -0.082 0.777 

0.435 -0.093 0.812 

0.386 -0.097 0.843 

0.355 -0.100 0.863 

0.314 -0.097 0.885 

0.275 -0.101 0.908 

0.234 -0.100 0.930 

0.193 -0.100 0.952 

0.163 -0.098 0.967 

0.132 -0.102 0.985 

0.099 -0.105 1.003 

0.065 -0.102 1.018 

0.045 -0.105 1.030 

0.020 -0.105 1.042 

0.013 -0.108 1.046 

-0.002 -0.105 1.052 

-0.002 -0.102 1.051 

0.000 -0.110 1.054 

0.002 -0.112 1.053 

-0.003 -0. 108 1.054 

-0.001 -0.106 1.053 

-0.004 -0.102 1.052 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

45.000 DEG 

1. 191 

============================================================ 

Y/[' 

0.0079 

(1.0099 

0.0152 

0.021(' 

0.0290 

0.0374 

0.0456 

0.0536 

0.0621 

0.0701 

0.0785 

0.0867 

0.0947 

0.1030 

0.1113 

O. 1193 

0.1331 

0.1743 

0.2153 

0.2562 

0.3386 

O. 42(L~ 

0.5048 

PHI 

DEG 

1.3 

0.8 

-0. ~, 

0.0 

-0.6 

-0.7 

-().5 

-0.6 

-0.4 

-0.5 

-0.5 

-0.8 

-0.7 

-0.4 

-0.6 

-(~. 3 

-0.6 

-i).2 

-0.4 

-i).2 

-(!.6 

-0.6 

-C'.9 

THETA 

DEG 

21.1 

20.7 

19.3 

17.8 

16.8 

15.7 

14.7 

13.9 

13.1 

12.5 

11.8 

11.5 

11. 1 

10.8 

10.4 

10.2 

10.0 

10.0 

9.7 

9.8 

9.8 

9.6 

9.7 

179 

CPT CPS U/Uo 

0.523 -0.063 0.735 

0.503 -0.067 0.751 

0.449 -0.079 O. 7<7'4 

0.404 -(;. (j7B 0.821 

0.357 -0.082 0.851 

0.306 -0.076 0.87<7' 

0.250 -0.083 0.913 

0.228 -0.088 0.927 

0.194 -0.086 0.944 r ... .. ,-,.. 

.... '. J.O·_ .... -0.086 0.961 

0.119 -0.081 0.981 

0.102 -0.088 0.993 

0.095 -0.090 0.997 

0.054 -0.088 1.017 

0.034 -0.085 1.02b 

0.025 -0.097 1.035 

0.005 -0.093 1.043 

-0.002 -0.092 1.045 

0.003 -0.097 1.045 

-0.001 -0.095 1.047 

-0.001 -0.094 1.046 

-0.0('4 -0.092 1 • ~)4 7 

0.004 -0.092 1.043 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.553 

:=~====================~==================================== 

Y/D PHI THETA CPT CPS U/lL=-

DEG DEG 

0.0099 0.7 1.3 0.002 -1.832 1.682 

0.0131 -0.4 1.3 0.003 -1.871 1.694 

(I. ~)2C'=, -1.4 0.9 -0.002 -1.895 1.702 

(). ()26tl -1. 9 O.t.. 0.002 -1.<710 1. 7'-)5 

0.0404 -2.8 0.1 -0.002 -1.937 1.714 

0.054(' "7 .-. -''':' . ..,;;.. -().2 -0.004 -1.953 1.720 

0.0677 "7 c;- -._"t. ~ -0.5 0.000 -1.968 1.723 

0=0815 -3.7 -0.7 -0.003 -2.001 1.733 

()'" (;95f) -3.8 -0. <7' 0.001 -2.006 1.734 

0.1158 -4.0 -1.1 0.002 -2.029 1.740 

0.1362 -4.1 -1. 2 0.004 -2.047 1.744 

0.1773 -4.0 4 ~ 

- J.. •• :) 0.002 -2.073 1.752 

(}.21S1 -'~" 9 -1.2 0.003' -2. ()79 1 -,-<=".~ • i w':: 

0.2595 -3.9 -1.2 0.001 -2.075 1.753 

0.3005 -4.1 -1. 1 -0.002 -2.070 1.752 

0.3416 -4.1 -1. 1 0.007 -2.055 1.746 

0.3824 -4.1 -1.0 0.003 -2.031 1.740 

O. 423:~, -4.2 -1.0 0.005 -2.000 1.730 

0.4625 -4.5 -0.9 0.004 -1. 974 1.723 

0.5080 -4.4 -0.7 0.001 -1.921 1.709 

180 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.596 

===========================================================: 

Y/D 

0.0089 

0.0144 

0.0200 

0.0252 

0.0335 

0.0417 

0.0500 

0.0638 

0.0773 

0.0911 

0.1046 

0.1184 

O. 1322 

0.1731 

0.2142 

0.2554 

0.3373 

0.4196 

0.5037 

PHI 

DEG 

0.4 

-0.9 

-2.0 

-2.3 

-2.9 

-3.3 

-3.4 

-3.6 

-3.7 

-3.7 

-3.5 

-3.4 

---=:- .--, •• ~ _1 

-3.3 

-3.0 

-2.9 

-2.9 

-3.0 

-:r ,..... -...;..~ 

THETA 

DEG 

7.7 

6.9 

6. 1 "" c- ...J • ...J 

4.5 

3.7 

3.0 

2.1 

1.7 

i.5 

1.3 

1.3 

1.2 

0.8 

0.9 

1.0 

1.0 

1.2 

1.5 

181 

CPT CPS U/Uo 

0.029 -1. 469 1.562 

0.037 -1.512 1.573 

0.041 -1. 526 1.576 

0.043 -1.537 1 r:;--"r, • ...J/7 

0.043 -1.549 1.583 

0.040 -1.561 1.588 

0.037 -1.563 1.589 

0.027 -1.567 1.594 

0.013 -1.602 1.60t]' 

0.004 -1. 611 1.614 

0.001 -1.629 1.621 

-0.001 -1.634 1.623 

-0.002 -1. 655 1.630 

0.003 -1. 685 1.638 

-0.001 -1.703 1.645 

0.005 -1.708 1.644 

0.002 -1. 717 1.648 

0.004 -1.697 1.641 

0.003 -1. 645 1.625 
ANGLUAR PLAt-.JE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.638 

============================================================ 

Y/D 

0.0106 

0.0150 

0.0192 

0.0233 

0.0274 

0.0341 

0.0410 

0.0478 

0.0548 

0.0682 

0.0821 

0.0955 

0.1367 

0.1778 

0.2187 

0.2599 

0.3417 

0.4242 

0.5084 

PHI 

DEG 

-0.1 

-1.1 

-1.8 

-2.5 

-2.7 

-3.4 

-3.7 

-4.2 

-4.3 

-4.6 

-4.6 

-4.5 

-3.9 

-3.6 

-3.5 

-3.5 

-3.3 

-3.:3 

-3.4 

THETA 

DEG 

11.3 

10.5 

9.4 

8.3 

7.4 

6.3 

5.2 

4.5 

..,.. c:- "':'1. -' 

.... ..,.. ..:: . ..:-

1.3 

0.7 

c).2 

0.2 

0.3 

0.5 

0.7 

1.1 

1.5 

182 

CPT CPS U/Uo 

0.050 -1.304 1.502 

0.083 -1.328 1.498 

0.105 -1.328 1.491 

0.117 -1.336 1.490 

0.125 -1.343 1.489 

0.134 -1.350 1.489 

0.132 -1.351 1.490 

0.129 -1.358 1.493 

0.116 -1.363 1.499 

0.095 -1.378 1.511 

0.068 -1. 386 1.522 

0.040 -1.401 1.537 

-0.007 -1.431 1.561 

-0.005 -1. 444 1. ~;65 

-0.005 -1.450 1.567 

0.002 -1.467 1.570 

-0.001 -1.455 1.567 

-0.003 -1. 432 1.560 

0.001 -1.381 1.54::::, 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.681 ============================================================ 

Y/D 

0.0090 

0.0144 

0.0200 

0.0280 

0.0363 

0.0446 

0.0528 

0.0610 

0.0690 

0.0773 

0.0856 

O. (1937 

0.1019 

0.1102 

(J. 1184 

0.1321 

O. 1454 

(I. 159::. 

O. 1732 

0.2142 

0.2552 

0.3375 

0.4195 

0.5039 

PHI 

DEG 

0.3 

-1.0 

-2.0 

-2.9 

-3.9 

-4.2 

-4.8 

-4.9 

-5.1 

-5.1 

-5.0 

-4.5 

-4.5 

-4.4 

-4.3 

-4.1 

-3.7 

..." -:r -._"t. "_"I 

-3.4 

-2.8 

-2.6 

-2.5 

,.., I::" 

-":: • ..J 

-2.6 

THETA 

DEG 

17.0 

15.6 

13.8 

11.5 

9.5 

7.7 

6.3 

5.0 

4~0 

3.1 

2.4 

2.0 

1.7 

1.5 

1.4 

1.4 

1.5 

1.4 

1.3 

1.6 

1.7 

2.1 

2.3 

2.6 

183 

CPT CPS U/Uo 

0.094 -1.121 1.424 

0.151 -1. 148 1.413 

0.197 -1.161 1.402 

0.243 -1. 174 1.390 

0.278 -1. 177 1.378 

0.267 -1. 179 1.383 

0.251 -1. 185 1.391 

0.234 -1.192 1.399 

0.199 -1.210 1.418 

0.159 -1. 211 1.432 

0.135 -1.222 1.445 

0.090 -1.219 1.459 

0.063 -1.231 1.472 

0.049 -1.239 1.480 

0.023 -1. 252 1.493 

0.009 -1. 245 1.495 

0.001 -1. 255 1.501 

-0.001 -1.262 1.505 

-0.002 -1.267 1.507 

-0.007 -1.271 1.509 

-0.002 -1.282 1. 511 

-0.004 -1.285 1.51::· 

0.002 -1. 261 1.503 

0.006 -1.247 1.497 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.723 

============================================================ 

Y/D 

0.0085 

0.0144 

0.0198 

0.0282 

0.0363 

0.0445 

0.0528 

0.0610 

0.0692 

0.0773 

0.0855 

0.0939 

O. 1021 

0.1102 

0.1184 

0.1322 

0.1457 

0.1595 

0.1730 

0.2142 

(>.2554 

(l.3373 

0.4194 

0.5042 

PHI 

DEG 

0.2 

-1.4 

-2.7 

-4.0 

= -:r --.I. _"t 

-6. 1 

-6.8 

-6.9 

-6.7 

-6.0 

-5.6 

-5.3 

-5.0 

-4.7 

-4.5 

-4.0 

-:r c- -._'. ,J 

-3.2 

-3.0 

-2.8 

-2.6 

-2.4 

-2.6 

-2.6 

THETA 

DEG 

21.2 

19.7 

17.6 

14.6 

12.4 

9.3 

~ -> / . ..::.. 

5.0 

'7 ..., 

_-'.4 

2.1 

1.2 

0.6 

0.3 

0.0 

-0.2 

-0.1 

0.1 

0.3 

0.3 

0.8 

1.2 

1.7 

2. () .., .a: •. -.) 

184 

CPT CPS U/Uo 

0.138 -1.066 1.389 

0.219 -1.096 1.370 

0.303 -1.099 1.340 

0.377 -1. 109 1. 316 

0.417 -1. 112 1.302 

0.425 -1. 124 1.303 

0.408 -1.131 1.313 

0.371 -1.146 1.332 

0.32:::- -1. 149 1.351 

0.280 -1. 152 1.368 

0.233 -1.150 1.385 

0.185 -1. 150 1.402 

0.129 -1. 150 1.422 

0.089 -1.150 1.436 

0.061 -1. 158 1.448 

0.023 -1. 156 1.460 

0.003 -1.160 1.468 

-0.001 -1.151 1.467 

-0.001 -1. 155 1.468 

-0.001 -1. 158 1.469 

0.001 -1.154 1.468 

0.002 -1.151 1.466 

0.004 -1.132 1.459 

0.003 -1.101 1.448 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.766 

============================================================ 

Y/D 

0.0091 

0.0146 

0.0202 

0.0254 

0.0309 

0.0365 

0.0420 

0.0475 

0.0527 

0=0585 

0.0637 

0.0692 

0.0776 

0.0857 

0.0938 

0.1022 

0.1104 

0.1187 

0.1321 

0.1459 

0.1595 

O. 173"::" 

0.2144 

0.2556 

0.3376 

0.4196 

0.5041 

PHI 

DEG 

0.8 

-0.2 

-1.4 

-2.4 

-3.4 

-4.4 

-5.7 

-6.5 

-7.1 

-7.4 

-7.5 

-6.1 

-5.4 

-4.7 

-4.2 

-3.8 

-3.2 

-.~c "" • -:r ...;, 

-2.6 

..... -:r -L. "_"t 

-2.1 

-2.1 

-2.0 

-2.0 

-1.7 

-2.0 

-2.1 

THETA 

DEG 

27.2 

26.2 

24.9 

"?~ C" L.~'. _, 

21.3 

18.9 

15.2 

11.6 

8.4 

5.2 

2.8 

1.0 

-0.2 

-1.0 

-1.1 

-1.1 

-1.1 

-1.0 

-0.7 

0.3 

0.1 

0.4 

1.1 

1.5 

2.0 

2.4 

2.7 

185 

CPT CPS U/Uo 

0.241 -1.044 1.343 

0.328 -1. 060 1.316 

0.444 -1.080 1.279 

0.532 -1.085 1.246 

0.615 -1.108 1.222 

0.667 -1. 122 1.206 

0.724 -1.143 1. 191 

0.744 -1. 153 1.187 

0.721 -1.164 1.201 

0.661 -1.158 1.224 

0.594 -1. 143 1.245 

0.548 -1.124 1.255 

0.453 -1. 122 1.292 

0.373 -1.098 1.313 

0.294 -1.087 1.339 

0.238 -1. 069 1.353 

0.175 -1. 064 1.374 

0.118 -1.061 1.394 

0.047 -1.046 1.414 

0.014 -1.042 1.424 

0.002 -1.037 1.427 

-0.004 -1.033 1.427 

-0.002 -1.031 1.425 

-0.006 -1.028 1.426 

0.000 -1.021 1.422 

0.003 -1.009 1.461 

0.000 -0.989 1. 411 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.787 

============================================================ 

Y!I) 

0.0085 

0.0140 

0.0198 

Ci.025<) 

0.0307 

0.0361 

0.0416 

0.0471 

0.0527 

0.0582 

0.0634 

0.0690 

O.074Ll 

0.0799 

0.0855 

0.0907 

I).0t7'62 

CI.I01B 

0.1101 

0.1184 

O.1-::.U:? 

(). 145&., 

0.1593 

0.1730 

0.2141 

0.2552 

0.3372 

0.4194 

0.5041 

PHI 

DEG 

1.8 

1.1 

1.0 

0.6 

(>.2 

-0.7 

-1.3 

-2.8 

-2.9 

-3.6 

-3.5 

-3.3 

-3. (j 

...,. ..... -":". L 

-2.8 

-2.7 

-.L.6 

-2.4 

-2. () 

-2. (j 

-1.8 

-1. '7' 

-1.8 

-1.8 

-1.8 

-2.4 

-1. 9 

-2.0 

-2.2 

THETA 

DEG 

27.9 

27.4 

26.5 

25.2 

,"" , .--. "-' 

20.5 

16.8 

12.3 

8. 1 

4 . '"' ..:.. 

1.5 

-0.3 

-1.7 

..... ...,. -..::.. . ..;,.. 

-2.7 

-2.7 

-2.6 

-2.4 

..... '"' -,-c,L 

-1.9 

-1.4 

-1.0 

-0.4 

0.0 

0.9 

1.3 

1.7 

2.2 

2.4 

186 

CPT 

0.321 

0.366 

0.476 

0.570 

0.658 

0.740 

0.795 

0.825 

0.823 

0.766 

0.687 

0.613 

0.542 

0.486 

0.418 

0.369 

0.316 

0.275 

0.209 

0.143 

0.068 

0.019 

0.001 

-0.006 

-0.006 

-0.001 

0.000 

0.003 

0.005 

CPS 

-1.041 

-1.064 

-1.087 

-1.100 

-1. 118 

-1. 136 

-1. 158 

-1.173 

-1. 16<7' 

-1.160 

-1.137 

-1.122 

-1.105 

-1. 092 

-1.077 

-1. 062 

-1.053 

-1.043 

-1. 027 

-1. 021 

-1.005 

-0.998 

-0.985 

0.985 

0.981 

-0.994 

-0.971 

-0.961 

-0.946 

U/Uo 

1.311 

1.303 

1.269 

1.237 

1.208 

1.182 

1.167 

1.161 

1.160 

1. 181 

1.204 

1 '"''''' • ..:.....:...c 

1.251 

1.267 

1.288 

1.302 

1.318 

1.33() 

1.348 

1.370 

1.392 

1.407 

1.409 

1. 411 

1.409 

1.412 

1.404 

1.399 

1.393 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.809 

============:=============================================== 

Yir0.0085 

0.0144 

(). C)2CH~} 

().0254 

0.0309 

0.0362 

0.0417 

0.0472 

0.0528 

0.0582 

0.0638 

0.0692 

0.0772 

O. ')855 

0.0939 

O. 11)19' 

0.1102 

0.1184 

O. 1322 

0.1451 

0.159[, 

0.1731 

0.2140 

0.2554 

0.3373 

0.4195 

0.5041 

PHI 

DEG 

..,. ...., .J • .::. 

3.6 

4.5 

5.0 

= ..,. ..J •. .:> 

5.6 

= 7 ......J = "_, 

4.6 

4.0 

2.9 

2.4 

1.6 

1.2 

0.5 

-0.1 

-0.1 

-0.2 

-0.6 

-i). 9 

-1.1 

-1.2 

-1.2 

-1.6 

-1.8 

-2.1 

-2.2 

-2.4 

THETA 

DEG 

24.9 

25.6 

25. () 

23.8 

21.9 

19.4 

15.8 

11.8 

8.3 

4.6 

2.0 

0.0 

-1.6 

-"::'.L. " " 

-2.2 

" ...., -L • .£.. 

-1.9 

-1.8 

-1.4 

-1.1 

-0.6 

-0.1 

0.9 

1.2 

1.9 

...., ..,.. ..:... __ "t 

2.8 

187 

CP1 CPS U/Uc 

0.518 -1.034 1.232 

0.456 -1.061 1.267 

0.504 -1.062 1.248 

0.571 -1.082 1.229 

0.635 -1.094 1.208 

0.684 -1.104 1.192 

0.749 -1. 122 1.172 

0.756 -1.136 1.174 

0.745 -1. 125 1.175 

0.711 -1. 117 1 1 A' ...... _0 

0.636 -1. 091 1.206 

0.591 -1.088 1.224 

0.504 -1.057 1.246 

0.417 -1.036 1.272 

0.350 -1.028 1.295 

0.270 -1.006 1.318 

0.200 -0.986 1.336 

0.141 -0.985 1.358 

0.065 -0.969 1.38f) 

0.024 -0.967 1.394 

0.001 -0.957 1 <:qq • -_" , J 

0.000 -0.955 1.398 

0.003 -0.950 1.395 

-0.003 -0.948 1.397 

0.001 -0.935 1.391 

-0.001 -0.927 1.389 

0.004 -0.905 1.379 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.851 

============================================================ 

Y/D 

0.0092 

0.0146 

0.0201 

0.0256 

0.0311 

0.0364 

0.0420 

0.0474 

0.053(-

0.0585 

0.0637 

0.0695 

0.0774 

0.0858 

0.0940 

0.1021 

0.1104 

0.1186 

0.1321 

0.1460 

0.1597 

0.1733 

0.2142 

0.2556 

0.3375 

0.4195 

0.5040 

PH! 

DEG 

2.1 

1.9 

2.1 

3.1 

3.5 

4.8 

4.7 

5.4 

5.0 

5.1 

4.7 

4.2 

3.9 

"_I.T ~ _, 

..... '"J '" "_I 

1.9 

1.4 

1.1 

0.6 

0.4 

-0.1 

-Co.3 

-0.8 

-1.2 

-1.8 

-1.9 

-2.1 

THETA 

DEG 

13.6 

15. 1 

16.6 

16.8 

16.6 

16.0 

14.5 

12.7 

11. 0 

9.2 

7.4 

6.0 

4.6 

3.4 

2.6 

2.0 

1.3 

0.9 

0.7 

0.6 

0.7 

0.8 

1.4 

1.7 

2.3 

2.7 

2.9 

188 

CPT CPS U/Uo 

0.652 -0.887 1. 111 

0.568 -0.917 1. 161 

0.546 -0.927 1.175 

0.548 -0.931 1.176 

0.529 -0.922 1.180 

0.543 -0.925 1.176 

0.536 -0.919 1. 176 

().524 -0.921 1.182 

0.514 -0.919 1.185 

0.485 -0.909 1.193 

0.459 -0.896 1.199 

0.421 -0.892 1.213 

0.366 -0.891 1.235 

0.311 -0.886 1.255 

0.246 -0.877 1.277 

0.198 -0.874 1.295 

0.124 -0.874 1.323 

0.087 -0.871 1.336 

0.031 -0.870 1.356 

0.008 -0.869 1.364 

-0.007 -0.867 1.369 

-0.007 -0.865 1.369 

-0.007 -0.859 1.366 

-0.008 -0.855 1.365 

0.002 -0.852 1.361 

0.000 -0.844 1.358 

-0.001 -0.827 1.352 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.894 

=========================~================================== 

Yin 

0.0086 

0.0145 

0.0200 

0.028::-. 

0.0363 

0.0446 

0.0530 

0.0612 

O. (J692 

0.0774 

0.0857 

0.0940 

0.1022 

0.1103 

0.1185 

O. 1321 

0.1459 

O. 1597 

0.1732 

0.2144 

().2553 

(l.3375 

0.4196 

0.5040 

PHI 

DEG 

0.6 

0.0 

-0.2 

-{).3 

0.1 

0.6 

C'.8 

0.9 

1.3 

1.3 

1.3 

1.2 

1.1 

1.4 

1.0 

1.0 

0.5 

0.4 

-0.1 

-0.7 

-1.0 

-1.6 

-2. () 

-2.1 

THETA 

DEG 

10.7 

11.6 

12.1 

12.0 

11.5 

10.4 

9.0 

7.6 

6.5 

5.5 

4.6 

3.9 

.j. - " L 

2.7 

2.1 

1.5 

1.3 

1.2 

1.2 

1.3 

1.5 

1.9 

~ < 4 __ -

2.7 

189 

CPT CPS U/Uo 

0.583 -0.796 1. 101 

0.490 -0.817 1.152 

0.479 -0.832 1. 164 

0.476 -0.844 1.170 

0.440 -0.846 1.186 

0.420 -0.834 1.18S 

0.391 -0.828 1.199 

0.359 -0.824 1. 211 

0.306 -0.830 1.235 

0.272 -0.818 1.243 

0.206 -0.815 1.268 

0.175 -0.812 1.279 

0.118 -0.797 1.296 

0.092 -0.811 1. 311 

0.049 -0.806 1.326 

0.017 -0.806 1.338 

0.002 -0.798 1.340 

-0.005 -0.803 1.345 

0.003 -0.811 1. 345 

-0.001 -0.800 1.342 

0.004 -0.796 1.339 

-0.002 -0.796 1.:-41 

0.004 -0.783 1.334 

-0.007 -0.768 1.332 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

0.936 

============================================================ 

Y/D 

0.0088 

0.0142 

0.0198 

0.0278 

0.0360 

0.0443 

0.0527 

0.0609 

0.0771 

0.0855 

0.0937 

0.1017 

0.1100 

0.1183 

0.1321 

0.1456 

0.1594 

0.1730 

0.2140 

0.2549 

0.3373 

0.4193 

0.5037 

PHI 

DEG 

0.9 

O. 1 

-0.3 

-0.4 

-0.5 

-0.2 

-0.3 

0.1 

0.3 

0.4 

0.6 

0.5 

0.5 

0.6 

0.5 

0.4 

0.2 

O. 1 

-0.4 

-0.7 

-1.1 

-1.5 

-1.7 

THETA 

DEG 

11. (I 

12.1 

12.4 

11. 6 

10.4 

9.0 

7.7 

6.9 

5.6 

4.9 

4.4 

4.0 

...,. c;- -"I. ~ 

'" "_I • ..., .i;.., 

2.8 

2.6 

..., ...,. 4_ ...;,. 

2.2 

~ . ...., ..::.. . ...::. 

2.1 

..., 

L _ "7 _ .,. 

...... c;- ':"11: __ J 

2.9 

190 

CFT 

0.619 

0.517 

0.459 

0.425 

0.398 

0.365 

0.324 

0.287 

0.199 

0.155 

0.124 

0.087 

0.052 

0.028 

0.006 

-0.002 

-0.006 

-0.007 

-0.002 

-0.001 

-0.002 

0.000 

0.003 

CPS 

-0.711 

-0.731 

-0.740 

-0.743 

-0.750 

-0.751 

-0.740 

-0.743 

-0.743 

-0.739 

-0.737 

-0.738 

-0.737 

-0.735 

-0.740 

-0.737 

-0.737 

-0.739 

-0.736 

-0.735 

-0.729 

-0.724 

-0.715 

U/UD 

1.045 

1.102 

1. 132 

1. 146 

1.163 

1. 177 

1.190 

1.207 

1.243 

1.258 

1.270 

1.285 

1.298 

1.307 

1.316 

1. 319 

1.320 

1.321 

1.318 

1.318 

1.316 

1.313 

1.308 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

1.021 

============================================================ 

Y/D 

0.0083 

0.(1111 

0.0166 

0.0221 

0.0304 

0.0384 

0.0467 

(). ~)549 

0.06::::,L 

0.0714 

0.0794 

0.0878 

0.0960 

0.1043 

O. 112~. 

O. 1206 

O. 1341 

(i. 1479 

0.1617 

O. 175~. 

0.2164 

(). 257~, 

0.3395 

0.4216 

0.5057 

PHI 

DEG 

1.5 

0.5 

o. 1 

-0.2 

-0.3 

-0.2 

-0.1 

-0.1 

-{). 1 

-0.2 

O. 1 

0.0 

0.0 

-0.2 

-0.1 

-0.1 

-().2 

-0.2 

-0.3 

-().2 

-0.4 

-0.6 

-1.0 

-1.4 

-1.7 

THETA 

DEG 

8.5 

9.2 

10.0 

10.2 

9.5 

8.7 

7.8 

6.9 

6.3 

5.6 

5.1 

4.5 

4.2 

3.8 

3.6 

3.3 

3.0 

2.9 

2.8 

2.7 

2.6 

2.6 

2.7 

2.8 

3.0 

19l 

CPT CPS U/Uc 

0.683 -0.596 0.956 

0.610 -0.615 1. (H)3 

0.500 -0.627 1.062 

0.439 -0.642 1.0<7'7 

0.386 -0.642 1. 121 

0.347 -0.639 1.137 

0.308 -0.644 1. 156 

0.271 -0.640 1. 170 

0.231 -0.646 1.190 

0.200 -0.640 1.200 

0.157 -0.639 1. 218 

0.131 -0.63<7' 1.228 

0.101 -0.643 1.242 

0.090 -0.643 1.246 

0.063 -0.641 1.256 

0.041 -0.645 1.266 

0.035 -0.638 1.266 

0.010 -0.638 1.276 

0.000 -0.639 1.280 

0.002 -0.643 1.281 

-0.007 -0.648 1.286 

-0.001 -0.652 1.286 

0.001 -0.650 1.284 

0.002 -0.641 1.281 

-0.001 -0.629 1.277 
ANGLUAF: PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

1.106 

===========================================================~ 

Y/D 

0.0083 

0.0103 

0.0159 

0.0214 

0.0293 

0.0376 

0.0461 

0.0542 

0.0625 

0.0707 

0.0787 

0.0870 

0.0954 

i}~ 1 ()33 

0.1117 

I). 1199 

0.1337 

0.1472 

0.1611 

0.1746 

0.7157 

().25t,S--

0.3388 

0.4209 

0.5054 

PHI 

DEG 

1.4 

0.5 

-0. 1 

-0. 1 

0.0 

-f) '":> -. ~ 

0.0 

0.2 

0.0 

0.1 

0.2 

O. 1 

O. 1 

(l.U 

(i. (J 

-0.1 

-().3 

-0.3 

-0.5 

-0.6 

-()~ 7 

-0.9 

-1.1 

-1. 2 

-1.4 

THETA 

DEG 

6.8 

7.2 

8.0 

8.0 

7.6 

7.7 

6.2 

5.7 

5.0 

4.5 

4.2 

3.8 

"7 c- '':''. --.J 

-:r 7 

";'. "-" 

3& () 

2.9 

2.7 

....., c:- .L • ...J 

~ <:" ..::.. • \-1 

..., <:" 

.&....~ 

....., -:0-

L. •. .;. 

....., .,.. L • ..... :-

2.2 

2.3 

~ C" 

"::".-1 

192 

CPT 

0.664 

0.600 

0.496 

0.440 

0.392 

0.366 

0.328 

0.324 

0.297 

0.278 

0.241 

0.223 

0.209 

0.181 

0.145 

0.132 

0.090 

0.045 

0.023 

0.005 

-0.001 

0.000 

0.000 

0.002 

0.002 

CPS 

-0.525 

-0.542 

-0.559 

-0.566 

-0.567 

-0.568 

-0.567 

-0.564 

-0.569 

-0.569 

-0.567 

-0.571 

-0.573 

-0.572 

-0.569 

-0.570 

-0.572 

-0.547 

-0.573 

-0.573 

-0.575 

-0.576 

-0.572 

-0.569 

-0.562 

U/Uo 

0.928 

0.971 

1.031 

1.061 

1.084 

1.096 

1.113 

1. 114 

1.128 

1.136 

1.152 

1. 161 

1.168 

1.179 

1.193 

1.199 

1. 218 

1.237 

1.245 

1.252 

1.255 

1.255 

1.254 

1.252 

1.249 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

1. 191 

=========================================================~== 

Y/D 

0.0084 

0.0105 

0.0161 

0.0216 

0.0296 

0.0379 

0.0462 

0.0541 

t.'.0627 

0.0706 

0.0789 

0.0873 

0.0955 

O. 1035 

0.1118 

0.1201 

0.1336 

0.1474 

0.1609 

0.1784 

0.2159 

().2562 

().3391 

0.4211 

0.5052 

PHI 

DEG 

1.0 

0.4 

-0.4 

-0.4 

-0.3 

-0.3 

-0.4 

-C'" 3 

-()= :3 

-0.4 

-0.3 

-0.1 

-{).2 

-0.4 

-0.4 

-0.5 

-0.4 

-0.4 

-0.3 

-0.4 

-c).5 

-0.6 

-1.0 

-1.2 

-1.4 

THETA 

DEG 

5.2 

5.6 

6.3 

6.5 

6.2 

5.8 

C" 00::- ..J • '_' 

5.0 

4.7 

4.5 

4.2 

4. 1 

4.0 

3.8 

3.8 

3.6 

3.7 

3.2 

3. (j 

2.8 

2.6 

"'I = ..::. • ..J 

2.4 

" C" ...... -' 

2.6 

193 

CPT CPS U/Uo 

0.695 -0.477 0.884 

0.641 -0.488 0.920 

0.547 -0.507 0.979 

0.475 -0.508 1. 016 

0.422 -0.512 1.044 

0.381 -0.514 1.064 

0.331 -0.514 1.088 

0.286 -0.509 1. 106 

0.263 -0.511 1. 117 

0.200 -0.510 1.145 

0.172 -0.507 1.155 

0.124 -0.508 1. 176 

0.113 -0.516 1. 184 

0.092 -0.520 1.195 

0.090 -0.519 1.195 

0.050 -0.521 1. 212 

0.027 -0.522 1.223 

0.004 -0.513 • ,"?,":.q l • ..:.. .... ~ 

-0.006 -0.518 1 ,"?,= .......... _._1 

-0.007 -0.517 1.235 

-0.005 -0.518 1.234 

-(l.OOl -0.519 1.233 

-0.002 -0.516 1.23:' 

0.003 -0.509 1.227 

0.001 -0.506 1.227 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

1.362 

============================================================ 

Y/D 

0.0085 

0.0147 

0.0216 

0.0296 

0.0378 

0.0462 

0.0544 

0.0625 

0.0707 

0.0790 

0.0873 

0 .. ()952 

(.1. 1 ()35 

~ i. ! 1 J 7 

0.1201 

0.1337 

O. 1475 

0.1611 

0.1748 

0.2159 

0.2569 

0.3391 

0.4212 

0.5061 

PHI 

DEG 

0.5 

-0.6 

-0.9 

-1 .. i) 

-1.0 

-1.0 

-0.9 

-0.8 

-o.e; 

-0.8 

-0.8 

-0.6 

-0.7 

--0,6 

-(1.6 

-0.5 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.7 

-0.7 

-0.9 

THETA 

DEG 

5.2 

5.7 

5.9 

5.9 

5.6 

5.3 

5.0 

4.7 

4.6 

4.3 

4.1 

3.9 

3.8 

3.7 

3.6 

..,. ~ 

..:i • ..J 

3.4 

3.4 

3.4 

3.4 

"?" ~ 

..:i • ..J 

3.4 

_ 

"7 ~ .... ~ 

..,. "7 

.,.j. -' 

194 

CPT CPS U/Uo 

0.635 -0.404 0.877 

0.519 -0.422 0.951 

0.429 -0.431 1.001 

0.375 -0.432 1.028 

0.331 -0.433 1.050 

0.291 -0.435 1.070 

0.250 -0.434 1.089 

0.233 -0.432 1.099 

0.199 -0.435 1. 112 

0.177 -0.438 1.123 

0.156 -0.433 1. 130 

0.125 -0.431 1.143 

0.103 -0.435 1.154 

0.081 -0.436 1.164 

(1.068 -0.434 1.169 

0.040 -0.436 1.182 

0.008 -0.436 1.195 

-0.004 -0.435 1.200 

-0.006 -0.438 1.202 

-0.003 -0.435 1.199 

-0.003 -0.434 1.199 

0.001 -0.434 1. 197 

-0.001 -0.430 1.196 

0.002 -0.425 1.193 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

1.532 

========~=================================================== 

Y/D 

0.0084 

0.0149 

0.0218 

0.0300 

0.0381 

0.0465 

0.0547 

O.062S· 

0.0711 

0.0792 

0.0875 

0.0955 

O. 103':;' 

0.1121 

0.1204 

0.1339 

0.1478 

0.1613 

0.1751 

0.2161 

0.2571 

().3393 

0.4215 

0.5060 

PHI 

DEG 

1.7 

0.3 

-0.2 

-0.3 

-0.4 

-().5 

-0.4 

-0.4 

-0.6 

-0.2 

-0.2 

-().3 

-0.3 

-0.3 

-0.2 

-0.1 

-0.2 

-0.2 

-0.1 

0.0 

-0.2 

-0.4 

-0.3 

-(}.5 

THETA 

DEG 

3.9 

4.5 

4.7 

4.6 

4.5 

4.3 

4.1 

3.9 

-:- f oJ. I 

-:r L ._'. ~ 

-:- C" 

''':'' ...J 

3.4 

3.3 

3.1 

3.0 

3.0 

3.1 

3.2 

..,.. ...., ~ . ..:... ...". -:r "';" • .J 

..,.. ...., ...;1. L 

3.1 

3.2 

3.4 

195 

CPT CPS U/Uo 

0.617 -0.337 0.848 

0.498 -0.356 0.926 

0.430 -0.362 0.966 

0.365 -0=367 1.001 

o ..,..,.,..., . .":,,,,-~ -0.367 1.023 

0.271 -0.365 1.046 

0.229 -0.367 1.066 

0.199 -0.370 1.082 

0.158 -0.370 1.101 

0.136 -0.366 1. 109 

0.103 -0.368 1.125 

0.077 -0.362 1.134 

0.054 -0.361 1.143 

0.029 -0.364 1.155 

0.019 -0.371 1.163 

0.003 -0.368 1.168 

-0.004 -0.372 1.173 

-0.005 -0.368 1.172 

-0.007 -0.369 1.173 

-0.005 -0.364 1.170 

-0.002 -0.364 1.169 

-0.005 -0.368 1.172 

-0.002 -0.359 1.167 

-0.008 -0.359 1.169 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(conti nued) 

90.000 DEG 

1.702 

============================================================ 

Y/D PHJ THETA CPT CPS U/Uo 

DEG DEG 

0.0085 1.7 3.1 0.661 -0.302 0.800 

0.0150 0.5 3.6 0.550 -0.317 0.876 

0.0220 IJ.3 3.6 0.483 -0.331 0.921 

0.0300 O. 1 ..,. c:- ''';'' ..J 0.427 -C) .. 324· 0.947 

0.0382 ().3 ..,. ..,. ..,:,. _\ 0.364 -0.318 0.977 

0.0465 ().2 ~ ':l _'a ..:... 0.347 -0.325 0.989 

0.0549' 0.2 3.0 0.306 -0.324 1.009 

0.0631 0.4 2.8 0.258 -0.322 1.031 (~. ()71:' 0.3 2.7 0.216 -0.319 1.050 

0.0794 0.3 2.6 0.188 -0.321 1.064 

0.0876 0.3 2.5 0.165 -0.326 1.077 

0.0959 0.3 2.4 0.133 -0.326 1.092 

0.1039 O. 1 2.4 0.105 -0.325 1.105 

0.1122 O. 1 2.4 0.076 -0.326 1. 118 

0.1206 0.2 '"' ..,. ..:::.... "-"I 0.052 -0.319 1.126 

O. 1:"540 0.2 .L '"' •. ~ :;. 0.019 -0.326 1. 143 

0.1479 0.2 2.3 -0.005 -0.325 1.153 

0.1613 0.2 2.3 0.000 -0.323 1. 15(1 

0.1752 ().2 ., ~ 

.L •. ::, 0.001 -(J.325 1. 151 

0.2163 O. 1 2.4 -0.007 -0.326 1.154 

().2573 0.1 2.6 -0.005 -0.324 1.153 

(i. 3394 f). ? ~ "< ~. "_, -0.002 -0.320 1.149 

0.4216 O. 1 2.4 0.003 -0.325 1.149 

0.5061 -().3 2.7 -0.006 -(}.322 1. 1<=;':) 

196 
ANGLUAR PLANE: 

RADIUS/CYL7NDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

2.043 

============================================================ 

Y/O 

0.0083 

0.0142 

0.0211 

0.0294 

0.0374 

0.0458 

0.0540 

0.0623 

0.0702 

0.0785 

0.0868 

0.0951 

(i. 10:,1 

0.111'S 

{).1225 

0.1360 

O. 1497 

0.1633 

0.1772 

0.2183 

0.2593 

O.3L11:. 

.-. ,.~....,..-- '_1 .. ",+,,::,.':''J 

0.5069 

PHI 

DEG 

2. () 

1.0 

0.3 

(l.2 

0.3 

-0.1 

0.0 

-0.1 

-0. 1 

0.0 

-0.1 

0.0 

-0.2 

-0.1 

(). () 

-0.1 

-0. 1 

-0.1 

-0.2 

-().2 

-0.4 

-0.2 

0.1 

-0.2 

THETA 

DEG 

1.1 

1.4 

1.6 

1.6 

1.6 

1.5 

1.4 

1.4 

1.3 

1.3 

1.2 

1.1 

1.2 

1.1 

1.1 

1.0 

1.0 

1.0 

1.0 

1.0 

1.0 

0.8 

0.8 

1.0 

197 

CPT CPS U/Uo 

0.611 -0.253 0.801 

0.522 -0.268 0.86'1 

0.444 -0.274 0.911 

0.369 -0.278 0.953 

0.309 -0.274 0.982 

0.249 -0.276 1.013 

0.208 -0.281 1.036 

0.168 -0.278 1.054 

0.129 -0.279 1.072 

0.091 -0.281 1.091 

0.062 -0.282 1.105 

0.034 -0.281 1. 117 

0.02:. -0.282 1.122 

0.006 -0.283 1.130 

-0.001 -().282 1.133 

-0.001 -0.282 1.133 

-0.002 -0.282 1.134 

-0.003 -0.278 1.132 

-0.002 -0.276 1. 1:51 

-0.005 -0.281 1.134 

-0.001 -0.276 1. 130 

0.002 -0.277 1.130 

0.004 -0.284 1. 131 

-0.0(i6 -0.272 1.130 
ANGLUAR PLANE: 

RADIUS/CYLINDER DIA: 

Five-Hole Probe Data 

(continued) 

90.000 DEG 

2.375 

============================================================ 

Y/D 

0.0085 

0.0142 

0.0209 

0.0293 

0.0372 

0.0456 

0.0538 

0.0621 

0.0703 

0.0783 

0.0867 

0.0949 

0.1092 

0.1113 

0.1251 

0.1386 

0.1524 

0.1659 

0.1798 

().22()8 

0.2619 

0.3440 

0.4261 

0.5082 

PHI 

DEG 

2.1 

1.0 

0.4 

0.2 

0.1 

O. 1 

0.0 

0.0 

-0.1 

-0.1 

-0.2 

-0. 1 

0.0 

-0.1 

0.0 

-0.1 

0.0 

0.0 

0.0 

0.0 

0.0 

-0.1 

-0.1 

-0. 1 

THETA 

DEG 

2.0 

2.0 

2. 1 

2.1 

2.0 

2.0 

1.9 

1.9 

1.8 

1.7 

1.7 

1.7 

1.5 

1.5 

1.4 

1.3 

1.3 

1.2 

1.1 

1.1 

1.1 

1.1 

0.9 

0.7 

198 

CPT CPS U/Uo 

0.666 -0.230 0.751 

0.560 -0.244 0.826 

0.483 -0.249 0.875 

0.414 -0.257 0.918 

0.354 -0.256 0.950 

0.314 -0.253 0.969 

0.261 -0.253 0.996 

0.227 -0.255 1.014 

0.191 -0.256 1.032 

0.161 -0.257 1.047 

0.120 -0.256 1.066 

0.086 -0.257 1.082 

0.060 -0.255 1.093 

0.034 -0.254 1.105 

0.008 -0.255 1. 117 

-0.004 -0.254 1.122 

-0.007 -0.254 1.123 

-0.003 -0.255 1.122 

-0.005 -0.255 1.122 

-0.002 -0.255 1. 121 

0.000 -0.252 1. 119 

-0.001 -0.252 1.119 

0.000 -0.251 1. 118 

-0.002 -0.252 1.120 

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. 

NASA CR-3986 

4. Title and Subtitle 5. Report Date 

Measurements of a Turbulent Horseshoe Vortex June 1986 

Formed Around a Cylinder 6. Performing Organization Code 

7. Author(s) 8. Performing Organization Report No. 

W.A. Eckerle and L.S. Langston None 

10. Work Unit No. 

9. Performing Organization Name and Address 

11. Contract or Grant No. 

University of Connecticut NSG-3238 Department of Mechanical Engineering Storrs, Connecticut 06268 13. Type of Report and Period Covered 

12. Sponsoring Agency Name and Address Contractor Report 

National Aeronautics and Space Administration 14. Sponsoring Agency Code 

Washington, D.C. 20546 

505-62-21 (E-3027) 

15. Supplementary Notes 

Final report. Project Manager, Louis J. Goldman, Internal Fluid Mechanics 

Division, NASA Lewis Research Center, Cleveland, Ohio 44135. W.A. Eckerle, 

United Technologies Research Center, East Hartford, Connecticut 06108; L.S. 

Langston, University of Connecticut, pepartment of Mechanical Engineering, 

Storrs, Connecticut 06268. 

16. Abstract 

An experimental investigation was conducted to characterize a symmetrical horseshoe vortex system in front of and around a single large-diameter right cylinder 

centered between the sidewalls of a wind tunnel. Surface flow visualization and 

surface static pressure measurements as well as extensive mean velocity and pressure measurements in and around the vortex system were acquired. The results 

lend new insight into the formation and development of the vortex system. Contrary to what has been assumed previously. a strong vortex was not identified in 

the streamwise plane of symmetry, but started a significant angular distance away from it. Rather than the multiple vortex systems reported by others, only a 

single primary vortex and saddle point were found. The scale of the separation 

process at the saddle point was much smaller than the scale of the approaching 

boundary layer thickness. Results of the present study not only shed light on 

such phenomena as the nonsymmetrical endwall flow in axial turbomachinery but 

can also be used as a test case for three-dimensional computational fluid 

mechanics computer codes. 

17. Key Words (Suggested by Author(s)) 18. Distribution Statement 

Horseshoe vortex formation; Cylinder on Unclassified - unlimited 

endwall junction flows; Three-dimensional STAR Category 02 

aerodynamic measurements 

J 

19. Security Classif. (of this report) 120. Security Classif. (of this page) 21. No. of pages 22. Price" I 

Unclassified Unclassified 206 A10 i 

* For sale by the National Technical Information Service, Springfield, Virginia 22161 

NASA-Langley, 1986 
--'-----.---.---.. '-~~---.