Flowfield Downstream of a Compressor Cascadewith Tip Leakage

Chittiappa Muthanna

Thesis submitted to the Faculty of the Virginia PolytechnicInstitute and State University in partial fulfillment of the

requirements for the degree of

Masters of Sciencein

Aerospace Engineering

William J. Devenport, ChairRoger L. Simpson

Saad A. Ragab

November 20, 1998Blacksburg, Virginia

Keywords : Compressor, Cascade, Flowfield, Turbulence

Copyright 1998, Chittiappa Muthanna

Flowfield Downstream of a Compressor Cascadewith Tip Leakage

Chittiappa Muthanna

(ABSTRACT)

An 8 blade, 7 passage linear compressor cascade with tip leakage was built. Theflowfield downstream of the cascade was measured using four sensor hot-wireanemometers, from which the mean velocity field , the turbulence stress field andvelocity spectra were obtained. Oil flow visualizations were done on the endwallunderneath the blade row. Also studied were the effects of tip gap height, and bladeboundary layer trip variations. The results revealed the presence of two distinct vorticalstructures in the flow. The tip leakage vortex is formed due to the roll up the tip flow asit exits the tip gap region. A second vortex, counter-rotating when compared to the tipleakage vortex, is formed due to the separation of the flow leaving the tip gap from theendwall. Increasing the tip gap height increases the strength of the tip leakage vortex,and vice versa. Changing the boundary layer trip had no effect on the flowfield due thefact that boundary layers on the blade surface had separated.

As the vortices develop downstream, the tip leakage vortex convects into thepassage “pushing” the counter rotating vortex with it. As it does so, the tip leakagevortex dominates the endwall flow region, and is responsible for most of the turbulencepresent in the downstream flow field. This turbulence production is primarily due toaxial velocity gradients in the flow, and not due to the circulatory motion of the vortex.Velocity spectra taken in the core of the vortex show the broadband characteristicstypical of such turbulent flows. The results also revealed that the wakes of the bladesexhibit characteristics of two-dimensional plane wakes. The wake decays much fasterthan the vortex. Velocity spectra taken in the wake region show the broadbandcharacteristics of such turbulent flows, and also suggest that there might be somecoherent motion in the wake as a result of vortex shedding from the trailing edge of theblades. The present study reveals the complex nature of such flows, and should providevaluable information in helping to understand them.

This study was made possible with support from NASA Langley through grantnumber NAG-1-1801 under the supervision of Dr. Joe Posey.

Acknowledgements

First and foremost, I would like to thank my parents for their guidance and

support. They instilled in me a sense of values and lessons that have enabled me to

accomplish everything that I have set out to do. For that, I am forever grateful.

Special thanks are in order to my advisor, and mentor, Dr. William J. Devenport,

for his guidance, patience, and for giving me this opportunity. He has been the ideal

teacher, and his perseverance and motivation led me to accomplish things which I

thought were beyond me.

I would like to thank Dr. Ken Wittmer, who taught me everything there is to

know about the hot-wire system and helped me take much of the data. Without his

experience, I would still be in the tunnel taking data to this day.

I would also like to thank my friends in the lab, Semere Bereketab, Christian

Wenger, and Yu Wang, who voluntarily helped me with the taking of the measurements.

I would also like to thank Greg Dudding, Bruce Stanger, Kent Morris, and Gary Stafford

in the Aerospace shop whose tireless work helped transform the tunnel from paper to

reality.

And lastly to my friends; Alex, Joe, and especially my roomate Tone, thanks for

just being there.

Chittiappa.

iv

Table of Contents

CHAPTER 1. INTRODUCTION................................................................................................................1

1.1 COMPRESSOR CASCADE EXPERIMENTS. ................................................................................................2

1.2 COMPRESSOR ROTOR EXPERIMENTS ....................................................................................................3

1.3 CONTEXT OF THE PRESENT STUDY .......................................................................................................6

CHAPTER 2. APPARATUS AND INSTRUMENTATION.....................................................................8

2.1 LINEAR COMPRESSOR CASCADE...........................................................................................................8

2.1.1 Test Section. .................................................................................................................................8

2.1.2 Suction slots. ..............................................................................................................................10

2.1.3 Blade row...................................................................................................................................11

2.1.4 Pressure taps..............................................................................................................................12

2.1.5 Screens .......................................................................................................................................12

2.2 TRAVERSE SYSTEM. ...........................................................................................................................13

2.3 FLOW VISUALIZATIONS ......................................................................................................................13

2.4 HOT WIRE ANEMOMETRY ..................................................................................................................13

2.5 CASCADE CALIBRATION AND SET UP. .................................................................................................15

CHAPTER 3. RESULTS AND DISCUSSION.........................................................................................21

3.1 INFLOW MEASUREMENTS....................................................................................................................22

3.2 BLADE MEASUREMENTS.....................................................................................................................23

3.3 OIL FLOW VISUALIZATIONS ...............................................................................................................24

3.4 MEAN FLOW FIELD.............................................................................................................................25

3.4.1 Overall Form of the Flow ..........................................................................................................25

3.4.2 The Tip Leakage Vortex .............................................................................................................26

3.4.3 The Blade Wake .........................................................................................................................28

3.5 TURBULENT FLOW FIELD ...................................................................................................................29

3.5.1 Overall Form of the Flow ...........................................................................................................29

v

3.5.2 Tip Leakage Vortex ....................................................................................................................30

3.5.3 The Blade Wake .........................................................................................................................32

3.6 SPECTRAL RESULTS............................................................................................................................34

3.7 EFFECTS OF TIP GAP VARIATIONS ......................................................................................................35

3.8 TRIP EFFECTS......................................................................................................................................38

3.9 REPEATABILITY..................................................................................................................................38

3.10 SUMMARY OF RESULTS ....................................................................................................................39

CHAPTER 4. CONCLUSIONS ................................................................................................................41

CHAPTER 5. REFERENCES...................................................................................................................43

1

Chapter 1. IntroductionThe current trend for engine manufacturers is to design large aspect ratio aircraft

engines. However, in today’s environmentally conscience world, the noise associated

with such designs needs to be minimized. Much of the noise is a result of the turbulence

field created by the fan blades impacting on the downstream stator vanes. In order to

predict this noise, it is necessary to have a complete description of this turbulence field

which is concentrated in the fan blade wakes and the tip-leakage vortices in such

configurations. In addition to the noise problem, current trends within the industry have

been to model such fluid flows computationally. In order to develop accurate models, a

detailed experimental study has to be performed in order to verify the modeling solutions.

To this extent, measurements of the flow field downstream of a linear compressor

cascade with tip gap have been made.

There have been numerous studies performed on axial compressors rotors and

linear compressor cascades. The studies have concentrated on the tip gap flow, the

passage flow and the flow downstream of the rotors/blades. In a compressor, the rotating

motion of the blades induces a pressure difference across the blades. This pressure

difference drives a flow through the gap between the blade and the casing of the

compressor. This tip gap flow and its interaction with the lower endwall are the source of

turbulence in the downstream flow field, and it is this flow field that is the subject of this

investigation. However, due to difficulties associated with making measurements in

rotating turbomachinery, the flow can be simulated by building a cascade of blades

placed in a flow. Flow over the blades produces a pressure difference between the

surfaces, and similar to that seen in rotating turbomachinery, a tip gap flow is induced

between the blade and lower endwall. One drawback of a cascade configuration is the

fact that rotational effects which include the relative motion of the endwall and

centrifugal and coriolis forces cannot be simulated. The central presumption of any

linear cascade study including this one is thus that these effects do not have a direct

influence on the physical structure of the flow field.

Previous studies have given some insight as to the flow structures present in such

cascades. These structures in the flow found in the blade passages in compressor

cascades are shown in Figure 1.1. As the tip gap flow exits the tip gap region, it rolls up

2

to form the tip leakage vortex which may become the dominant flow feature within the

blade passage. Also present in the blade passage may be secondary vortices which are

not as dominant as the tip leakage vortex. For example, a vortex may be formed due to

separation of the tip-gap flow from the blade tip surface which rolls up to form the tip

separation vortex as shown in Figure 1.1. The vortices influence is not only limited to

the blade passage, but also has a significant affect on the downstream flow field as well.

1.1 Compressor cascade experiments.

Kang et al (1993, 1994) made measurements in a 7 blade linear compressor

cascade at design and off design conditions. The blades had a NACA 65-1810 profile,

and had a chord length of 7.87 in, and the Reynolds number based on this chord length

for the study was approx. 300,000. Measurements were made with a 5 hole pressure

probe at 16 positions which ranged from 0.075c upstream of the blades to 0.5c

downstream of the trailing edges. They also preformed flow visualizations on the blade

tip using oil films and paint traces. The tip gap flow was shown to be almost

perpendicular to the camber line of the blade, and this tip gap flow rolls up to form the tip

leakage vortex as it exits the tip-gap region. At about the mid-chord of the blade, the tip

gap flow begins to separate and rolls up to form a tip separation vortex. In addition to the

tip leakage vortex and tip separation vortex, there is a secondary vortex formed due to

separation of flow at the leading edge of the tip of the blade. Pressure measurements

downstream of the blade row show that the tip leakage vortex dominates much of the

endwall flow region and vorticity plots have indicated high vorticity in the vicinity of the

core region of the flow. These measurements show that the vortex forms close to the

suction side of the blades and begins to move away from the suction side and lower

endwall with downstream distance.

Yocum et al (1993) made measurements in an 18 blade cascade with a split-film

probe. Measurements were made for Reynolds numbers ranging from 57,000 to 200,000

at different stagger angles. The measurements were made primarily to study stall

conditions, but the unstalled cases are more insightful as to the nature of the flow. In

these experiments, measurements taken at the trailing edge plane of the blade rows

3

showed that of the three vortical structures, the tip-leakage vortex engulfs the other two

vortices. Also present in these measurements, is an indication of a passage vortex

originating from the pressure side of the blade. However, in most cases, the tip leakage

vortex seems to be the most dominant structure of the two. It was also observed that for

larger tip gaps, the tip leakage vortex moved further away from the suction side of the

blade and closer to the pressure side of the next blade in the cascade.

Storer et al (1990) performed an incompressible study of a 5 blade compressor

cascade at a chord Reynolds number of 500,000. A flattened pitot-probe and a two-hole

probe were used to make pressure measurements within the tip gap along the chord line

of the blade. Similar to that seen in Kang et al. (1993), the tip gap flow is seen to

separate from the blade tip. Results taken at different tip gaps indicate that for smaller tip

gaps (less than 1.0% of the chord), there is no clear indication a tip leakage vortex in the

flow, but for tip gaps greater than 2.0% of the chord, there is a tip leakage vortex formed

on the suction side of the blade.

Flow visualizations were done by Bindon (1989) on a 7 blade cascade with exit

Reynolds number of 250,000 under the tip gap of the blade. He also made single hole

pressure probe measurements, and these results show that there is a separation bubble

formed on the blade tip, with the leakage flow going over it. Some of this tip leakage

flow may separate to form a tip-separation vortex but studies have shown that the tip

leakage flow which stays attached to the blade tip is nearly perpendicular to the blade

surface as it exits the tip-gap. This shear flow then rolls up to form the tip leakage vortex

at the suction side of the blade.

1.2 Compressor Rotor Experiments

Experiments performed on compressor rotors differ from those in cascades in that

the rotational effects between the tip-gap and endwall are now present. These rotational

effects lead to two different pictures of the flow in turbomachinery, one where there is a

tip-leakage vortex present, and the other where there is no indication of a tip-leakage

vortex, but instead a region of high shear flow on the lower endwall.

4

Phillips et al(1980) performed smoke flow visualizations in a single fan

compressor stage in a rotating rig. The rotor consisted of 22 blades and the visualizations

were performed at “low” Reynolds numbers. These pictures did not give any indication

of the presence of a tip leakage vortex, instead they show that the large scale motions in

the endwall region due to rotational effects swamp and disperse these vortical structures

as they emerge from the tip-gap.

Bettner et al.(1982) made static pressure measurements, and hot wire

measurements in a single stage low speed compressor, with NASA 65 series airfoils at

design conditions. Similar to that seen in the cascade measurements, results here show

evidence of tip vortices extending into the flow.

Inoue et al.(1985, 1988), using hot wires and wall mounted pressure transducers,

made measurements on a compressor rotor with the same NASA 65 series airfoil shape at

design conditions and different tip clearances. These measurements clearly showed the

development of a tip leakage vortex within the passage of a compressor rotor. For large

tip gaps, the vortex tended to cross the passage, ending up closer to the pressure side by

the blade trailing edge.

Chesnakas et al (1990) made LDA measurements on a GE single stage rotor and

stator configuration in an axial compressor. The blade profiles were a RAF-6 prop blade

with twist and the rotor was run at design conditions. Plots of the cross flow velocity

vectors did not indicate the presence of any vortical flows within the blade passage, but

instead shows that the tip-gap flow produces a region of high shear flow on the lower

endwall of the apparatus.

A numerical investigation using RANS/Baldwin-Lomax computations performed

by Crook et al.(1993) identified the tip leakage vortex as a high loss region which

increases in size with downstream distance.

Laksminarayana et al(1981) made measurements in a 21 blade rotor using a triple

hot-wire rotating with the compressor blades at design conditions. The blade profiles

were a NASA 65 series, and the Reynolds number based on chord was 300,000. These

measurements showed that the tip-leakage vortex had moved to the middle of the passage

between the blades at the blade trailing edges. In a later experiment by Lakshminarayana

et al.(1982) in the same setup as that described in his previous study in 1981, but this

5

time concentrating on measurements primarily in the blade passage goes on to indicate

that there is no roll up of the tip-gap flow into vortices within the blade passage, instead

claiming that the roll up to the vortex occurs after the blade passage.

Popovski et al.(1985), using LDV, hot wires, and a 5 hole pressure probe made

measurements on the same test apparatus as Lakshminarayana et al.(1982), and found the

presence of a tip-leakage vortex within the passage contrary to the work by

Lakshminarayana (1982). Results from subsequent experiments by Lakshminarayana et

al. (1987, 1995) on the same test apparatus but at off design conditions i.e. different blade

loading, did not reveal the presence of a tip leakage vortex being formed within the blade

passage, but regions of high shear flow on the lower endwall. In another study by

Lakshminarayana et al. (1990), using an LDV and at design conditions in the same test

apparatus described previously, revealed the presence of a tip-leakage vortex and showed

that the vortex moved across the passage toward the pressure side with downstream

distance while rapidly decreasing in strength.

Poensgen et al.(1996), using single and triple hot wire probes measured

turbulence levels in a single stage axial compressor. The study was primarily done to

investigate stall conditions i.e. different blade loadings, but at unstalled conditions which

are near design conditions, the measurements found regions of elevated turbulence

kinetic energy in the vicinity of the core. In those cases where the vortex was not

formed, the tip gap flow mixes with the mainstream flow and produces regions of high

shear and flow separation.

These differing pictures as to the nature of the flow downstream of the rotor

highlights the differences that may arise due to different flow conditions. Much of the

studies that were done at off design conditions for rotors show that there is no formation

of a tip leakage vortex. All of the cascade experiments (including those done at different

flow conditions) and those rotor experiments at design conditions revealed the presence

of a tip-leakage vortex. These results imply that especially for rotating apparatus where

the endwall behavior has a greater effect, the flow conditions play a much more

significant role as to the nature of such tip gap flows.

6

1.3 Context of the Present Study

While the above discussion mainly concentrated on compressor rotors and

cascades, a more recent study as to the turbulent nature of tip leakage vortices has been

performed by Moore et al.(1994, 1995), and Devenport et al.(1997) using a turbine

cascade. This turbine cascade has subsequently been replaced by the current compressor

cascade that is the topic of this study. Though the operating principles of turbines and

compressors are different, the nature and form of the tip leakage vortex seen in a turbine

cascade can be compared to that seen in the compressor cascade. Moore et al.(1994,

1995) used hot wire measurements to show elevated turbulence kinetic energy levels

around the tip leakage vortex region. The results included all components of the

Reynolds stress tensor and showed that the most intense turbulence kinetic energy levels

were in a region adjacent to the tip leakage vortex where the flow was being lifted from

the endwall.

Devenport et al.(1997) performed a follow up study on the same turbine cascade

using a four sensor hot wire probe to measure the velocity and turbulence fields further

downstream. Results here showed that the vortex dominates much of the endwall flow

region, and similar to Moore et al’s findings, had the highest turbulence levels where the

flow was being lifted off the wall. The results indicated that the turbulence appears to be

generated by streamwise velocity gradients in the flow. The secondary flow field was

seen to decay at a much higher rate than the turbulence field.

While all the previous studies have given a detailed description of the flow field

downstream, much of it has been limited to within one chord length downstream of the

blade row. Measurements are needed at further downstream locations to better describe

the development of such flows. Turbulence data from Poensgen et al.(1996), is also

limited primarily to turbulence kinetic energy, while there is very little on the

components of the Reynolds stress tensor. One notable exception is the work by Moore

et al (1994, 1995), where the Reynolds stress tensor was presented for a turbine cascade,

which has similar flow features when compared to a compressor cascade. However, as

the study by Devenport et al (1997) demonstrated, that detailed and accurate

measurements of the turbulence field can be achieved with the use of a four sensor hot

wire probe.

7

The turbine cascade mentioned in Moore et al.(1994, 1995), and Devenport et

al.(1997), has been replaced with linear compressor cascade. The present investigation is

the first in a two part study performed on the flow field downstream of a compressor

cascade with tip gap and stationary endwall. The objectives of the overall study are to

obtain a detailed description of the mean and turbulent flow fields downstream of a linear

compressor cascade with tip leakage. The present study utilizes the four sensor hot wire

probe to measure both the mean and turbulence fields up to four chord lengths

downstream of a linear compressor cascade with tip leakage with a stationary endwall.

The results presented here precede a future study where the stationary endwall will be

replaced with a moving endwall. The moving endwall is used to simulate some of the

rotational effects that would be present in a compressor rotor. This study also

complements a numerical investigation of the same cascade configuration. Coupled with

the experimental results, accurate computational models can be developed which can then

be used for analysis of similar configurations. Benefits of such models include much

better initial designs of rotors, and cheaper and quicker analysis of configuration when

compared to the time involved in setting up an experimental study. With the results

obtained from this venture, a detailed description of the turbulence field will be obtained

to further aid in the understanding and predicting the nature of such flows in rotating

turbomachinery.

This report presents the results for the linear compressor cascade with the

stationary endwall. Chapter 2 of the reports describes the apparatus used in the study.

Specifically, an overview of the construction, and set up of the cascade, and a brief

description of the measurement system that was used to make the measurements.

Chapter 3 presents the results from the measurements in terms of the mean velocity field,

the turbulence stress field, and spectra measurements that were taken. Also presented in

Chapter 3 are the flow visualizations, and the inflow measurements of the tunnel.

Concluding remarks are presented in Chapter 4.

8

Chapter 2. Apparatus and Instrumentation

The Virginia Tech Low Speed Cascade Wind Tunnel was used. This facility was

built specifically for the present study by modifying the turbine cascade tunnel described

in Moore et al. (1994,1995), and Devenport et al. (1997). Hot wire anemometry was used

to make detailed measurements of the flow field downstream of the cascade.

2.1 Linear Compressor Cascade

Shown in Figure 2.1 is the 8-blade, 7-passage linear compressor cascade. Using

computational fluid dynamics, various configurations as to the number of passages, and

the sizes of the blades were looked at. Figure 2.2 shows the results of the calculations

performed by Moore et al(1996). in which a 4 passage cascade is compared to an infinite

cascade. The figure shows that a 4 passage cascade is sufficient to simulate an infinite

passage cascade. By increasing the number of passages in the cascade, the differences

between the two (infinite and finite passage cascades) are reduced, and the sidewall

influence will be minimized within the middle passages. From these calculations, and

limitations on the space available to build the cascade, an 8-blade 7-passage

configuration was chosen.

Construction of the cascade was completed in two stages, the inlet section, and

the downstream section. The tunnel is powered by a 15 hp motor with a fan. This then

proceeds to a diffuser, a settling chamber, a series of flow conditioning screens, a

contraction and then into the test section as shown in Figure 2.1. The contraction exit was

modified from the previous width of 33” to 30”, but retained a height of 12” to have a

contraction ratio of 3.88:1 at the entrance of the test section. Any gaps between the

contraction exit and test section were sealed with duct tape and caulk.

2.1.1 Test Section.

The test section is shown in figure 2.3. The inlet section has a rectangular cross

section perpendicular to the flow direction, with dimensions of 30” x 12”. The frame was

made from steel C-section, and was bolted to the floor of the laboratory to reduce

9

movement and vibration of the structure while it was running. The floor of the inlet

section was fabricated form 0.75” fin-form plywood, which has a solid smooth epoxy

surface finish, and was screwed into the steel frame of the tunnel. 0.25” thick plexiglass

was used to make the sidewalls and the roof of the tunnel. A cross section of the

sidewall–roof construction for the inlet section can be seen in figure 2.4. As seen in the

picture, one sheet was screwed to the legs of the frame, while the other was attached to

the first piece using double sided carpet tape. Two sheets were used, such that the second

sheet was to serve as a ledge onto which the roof of the inlet section was supported as

seen in the figure. The roof was removable so as to allow access to the inlet section and

was reinforced with aluminum C-sections.

One foot downstream of the contraction exit, mean velocity, and turbulence

intensity distributions were measured using hot-wire anemometers described in Section

2.4. Figure 2.5 shows the contours of mean streamwise velocity and contours of

turbulent intensity at this measurement plane. The vertical axis corresponds to the height

above the lower endwall, and the horizontal axis corresponds to the distance from the

sidewall. The velocity contours show that the flow is uniform within the inlet sections,

with as little as 1% variation across the cross section of the inlet section. However, the

mean velocity measurements can be influenced by temperature changes in the flow, and

this 1% variation can be attributed to the temperature drift that was observed during the

measurement. This implies that the variation in mean velocity across the cross section is

less than 1%. The turbulent intensity contours also show that the free stream turbulent

intensity is only 0.3%, and that there is little variation across the cross section. The

results also show a uniform boundary layer on both the upper and lower endwalls of the

section.

The downstream section of the tunnel can also be seen in figure 2.3. The frame

was made of steel C-section and was bolted to the floor, similar to that done to the inlet

section. The floor of the downstream section was constructed from two materials; a

0.25” aluminum plate occupied the area under the blade row, and the remainder of the

floor was 0.75” fin-form plywood, similar to that used in the inlet section. The aluminum

sheet was used under the blades enabling pressure taps to be drilled into the surface

(Figure 2.3). These pressure taps were used in the calibration process described later.

10

The downstream section had a rectangular cross section of 64” x 10”, the

reduction in height being due to the presence of suction slots described in section 2.1.2.

Similar to the inlet section, the roof of the downstream section was also made of 0.25”

plexiglass, and reinforced with aluminum C-section, of which there are two roof sections,

both identical in dimension. One of the sections has a series of slots in it, enabling

measurements to be made at different locations, whereas the other roof section is solid

(measurements can be taken at the other roof section simply by interchanging the roof

pieces). Unlike the inlet section, the sidewalls (also referred as tailboards) are a single

sheet of plexiglass. The roof now rests on a steel sheet, aluminum plates and aluminum

flanges. The sidewalls are also made of 0.25” plexiglass, and are hinged at one end so

that their angle could be adjusted. On the outside of the sidewalls are two movable

flanges attached on the top and bottom to fix the position of the sidewalls. One end of

the sidewalls are hinged at the trailing edge of the two outermost blades, and by lowering

the flanges the position of the sidewalls can be adjusted. Once positioned, the sidewall is

fixed into place by the use of clamps, which force the flanges onto the upper and lower

endwalls. This arrangement is shown in figure 2.6.

2.1.2 Suction slots.

As seen in the plan view of the cascade (figure 2.1), the exit plane of the inlet

section is at an angle of 24.9° to the sidewall. As a result, the two sidewalls are at

unequal lengths, one being almost 5 times as long as the other. Hence the size of the

boundary layers at the two sidewalls will be different, the boundary layer at the longer

side being larger than that at the shorter sidewall. To obtain uniformity of the flow as it

enters the blade row, these boundary layers were removed using suction slots between the

downstream section and the inlet section. The shape and arrangement of the suction

slots, and the two sections is shown in figure 2.7.

The suction slots removed both the upper and lower endwall boundary layers of

the flow. Preliminary measurements taken using a 7-hole yaw probe suggest that the

boundary layers extended in height from 0.25” to 1” across the width of the tunnel. The

suction slots were set up (see figure 2.7) such that there was a reduction in cross section

height from 12” to 10”, as previously mentioned. At the exit of the suction slot passage,

11

the opening could be adjusted so as to vary the amount of boundary layer that is being

bled. This was primarily used during the calibration and set-up of the cascade which is

described in section 2.5. As shown in figure 2.7, the boundary layers from the suction

slot were tripped with a 0.25” strip of glass beads 1” downstream of the leading edge of

the suction slots. The glass beads had a diameter of 0.02”, and were attached in a single

layer on double sided tape at a density of about 1750 beads per square inch of tape. Also

present were sidewall suction slots, which were formed by the gap between the leading

edges of the first and last blades and the inlet sidewall. An aluminum sheet 0.03” thick

was used as a flap which served as the slot covering, and one edge of the flap was

attached to the inlet sidewall with double sided tape. Once again, these were used during

set up of the tunnel described in section 2.5.

2.1.3 Blade row

The blade row of the cascade consisted of 8 cantilevered GE rotor B section

blades (Wisler (1981)). Figure 2.8 shows the cross section of blade which has rounded

leading and trailing edges and maximum thickness at 60% chord location. The cross

section coordinates supplied by G.E. aircraft engines, are given in table 1. The blades

were fabricated from aluminum on a numerically controlled milling machine, which had

an accuracy of 0.001”. The surface of each blade was then hand finished to give a

smooth surface. Each blade was made with a chord length of 10” and a span of 11”.

A support structure for the blades was made of 3”x1” aluminum box sections as

shown in Figure 2.9. The blades are screwed onto the flanges on the support structure

with four screws. This allowed for adjustment of the sweep and lean of the blades. This

was done so as to enable the blade row to be moved as one unit, and allowed for

individual adjustment of the blades once mounted in the cascade. The blades were

initially set such that they were flush with the aluminum floor, and the tip gaps was set by

placing shims under the support structure, which enabled the tip gap to be varied

simultaneously for all blades.

The stagger angle of the cascade was 56.9°, and the inlet angle of the flow was

65.1°. The blade spacing was 9.29”, which corresponds to the GE design conditions.

The tip-gaps under the blades were adjusted and set to have a nominal tip gap of 0.165” ±

12

0.015” for most measurements. Presented in table 2 are the actual tip gaps measured at

the completion of these experiments. The boundary layers on both the suction and

pressure sides of the blades were tripped 1” from the leading edge of the blade using a

0.25” strip of 0.02” diameter glass beads extending from root to tip similar to that used

with the suction slots. The roots of the blades were sealed with 1/32” thick steel sheets

that conformed to the blade surface (maximum gap between the blade and sheer was less

than 0.03”), and these sheets were attached to the plexiglas roof with double sided tape.

2.1.4 Pressure taps

As mentioned previously, 0.03” diameter pressure taps were drilled into the

aluminum floor section, which were used for the calibration and set up of the tunnel. In

addition to those drilled into the aluminum plate, aluminum pressure taps were fabricated

and embedded in the fin-form plywood endwall in both the inlet and downstream

section. These aluminum pressure taps are shown in figure 2.10. The aluminum pressure

taps were screwed into the floor, and the edges were sealed with clear scotch tape to

ensure smooth flow over the pressure port. The ports were then connected to pressure

transducers using 1/16” diameter plastic tubing.

2.1.5 Screens

Once the cascade was assembled, screens were made and placed at the exit plane

of the downstream section so as to enable the back pressure of the cascade to be adjusted

and thus provide a pressure difference across the suction slots. The screens were

constructed using an aluminum frame with the screen material used in home windows

and screen doors. The screen material had an open area ratio of 69.5%. The screens

were held in place by clamps attached to the frame of the tunnel. By placing more

screens, the back pressure could be increased, and this was further adjusted by placing

strips of 1” masking tape across the screens. This was used in the calibration and set up

of the tunnel which is described in section 2.5.

13

2.2 Traverse System.

A traverse system was built specifically for this cascade tunnel. The traverse

consisted of a two-axis movement system. Movement of each axis was controlled by

individual stepper motors manufactured by Compumotor (model S57-83-MO) which

were controlled through a PC. These were mounted to a TechnoIsel double rail guide and

carriage system, which held the hot wire sensors in place. Lead screws, manufactured by

TechnoIsel, and accurate to 0.003” per foot, were driven by the motors. The carriages are

attached to lead screws, using anti-backlash nuts which were also manufactured by

TechnoIsel. Using a cathetometer, the system was found to be accurate to 0.005” in both

axis’ directions. This arrangement was mounted on an aluminum I-beam and is shown in

Figure 2.11. The whole traverse system arrangement could be moved and mounted at the

required downstream position.

2.3 Flow Visualizations

Surface oil flow visualizations were performed on the lower endwall in the blade

passage with tip gap, extending 16” behind the blade row towards the exit of the

downstream section. A mixture of 5 parts titanium dioxide, 13 parts kerosene and a drop

of oleic acid was painted on black self adhesive paper which was fixed to the lower

endwall. The tunnel was run for about 5 minutes until all the kerosene evaporated, and

then a fixative was used to preserve the traces. The paper was removed, and various

details of the flow were photographed.

2.4 Hot Wire Anemometry

Velocity measurements were made using a computerized hot-wire system. Single

hot-wire probes were used to measure the boundary layer profile of the flows. Four

sensor wire probes were used to make 3-component velocity measurements. The single

hot wire probes were TSI incorporated model 1218-T1.5. The single hot wire probe is a

boundary layer type probe, with the wire axis perpendicular to the flow direction and the

tips of the prongs bent at a 90° angle to the stem. The four sensor probe (type AVOP-4-

100) was manufactured by the Auspex corporation. It is a miniature Kovaznay type

14

probe with four sensors arranged in two orthogonal X-wire arrays on eight stainless steel

prongs. All sensors, both in the single hot wire, and quad-wire probes were made from

etched tungsten wire of 5 microns in diameter. The measurement volume for the four

sensor probe is approximately 0.5 mm3. A diagram of the probe and sensor geometry is

given in figure 2.12.

Each sensor was operated separately by a Dantec 56C17/56C01 constant

temperature anemometer unit. The anemometer bridges were optimized to give a

frequency response greater than 20 kHz. Hot wire signals were buffered by 4x10 buck-

and-gain amplifiers containing calibrated RC-filter to limit their response to 50KHz. The

amplitude and phase of each sensor, bridge and amplifier combination placed in a jet of

velocity close to the wind tunnel free stream was measured by simulating its impulse

response using an 8 Watt YAG laser manufactured by Spectra Physics (model number

GCR 170). The beam was directed at each sensor in turn, the prongs being masked using

a pinhole, and was pulsed on the wire. The output signal from the corresponding

amplifier was recorded using an 8 bit RS2000 A/D converter unit. The time averaged

impulse response signals were then fourier transformed to obtain amplitude and phase

response curves. Presented in figure 2.13, are the magnitude response curves of each of

the individual sensors, and from these figures, we can see that the wires have a flat

amplitude response from zero Hz to a 3dB point close to 22 kHz.

While performing the measurements in the cascade tunnel, output voltages from

the anemometer unit were recorded by an PC using an Analogic 12 bit HSDAS-12 A/D

converter with an input range of 0-10V. The signals were stored on magneto optical

disks, which permitted reduction of the data at a later time. The probes were calibrated

for velocity by placing them in the uniform jet of a TSI calibrator and using Kings Law

to correlate the wire output voltages to the cooling velocities. The velocity calibrations

were done before and after taking data for each measurement grid. This was done to

account for changes in wire characteristics during each run. In the case of the four-wire

probe, velocity components were determined by means of a direct angle calibration,

where the probe is pitched and yawed over a range of angles, and then using look up

tables to give the relationship between cooling velocities and flow angle. A detailed

description of this calibration method is given in Wittmer et al. (1997) (Experiments in

15

Fluids submission). Hot-wire signals were corrected for ambient temperature drift using

the method of Bearman (1971).

The probes were mounted on the traverse and aligned with the mainstream flow

direction. As a safety precaution so as not to break any sensors, the minimum distance

the quad wire probe was placed above the lower endwall was 0.1”, the distance verified

using a cathetometer. One aspect of the four sensor probe was its near wall performance,

specifically, the effects that the large velocity gradients present in the near wall would

have on the measurements taken by the probe. Wittmer performed a study by placing the

four sensor probe in a pipe flow and taking measurements close to the walls of the pipe.

By comparing the measured values to actual values for such pipe flows, it was found that

the four sensor probe could give accurate measurements near the endwall, and as such

could be used in the cascade tunnel.

The approach free stream velocity was measured using a pitot-static probe with its

tip 6” above the lower endwall, and 2” from the sidewall by blade 8, at a distance of 86”

upstream of the leading edge of the blade row. The pitot-static probe was connected to

SETRA model 239 pressure transducer with an input range of 0-5 in.water with an ouput

of 1V/in.water. The output was sampled by one channel of the A/D converter. The

temperature of the approach free stream was measured using an OMEGA instruments

thermocouple, whose output was also sampled by one channel of the A/D converter.

Both the pressure signal, and the temperature signal were also stored on the magneto

optical disks with the hot-wire signals to enable reduction of the data at later times.

2.5 Cascade calibration and Set up.

Once the inlet section and downstream section were attached, the cascade had to

be adjusted to ensure that it operated correctly. Specifically, the angle of the sidewall

tailboards in the downstream section had to be adjusted to eliminate tangential pressure

gradients across the cascade, and the back pressure had to be adjusted to ensure proper

operation of the suction slots. The turning angle is defined as the angle of the flow

downstream of the blade row relative to the flow upstream of the blade row, and for this

configuration, the design condition was 12.9° as specified from G.E. aircraft engine

16

company (Wisler (1981)). Since the flow direction is parallel to the sidewalls, the

turning angle can be determined from the position of the sidewalls.

Pressure measurements were taken at four locations in the downstream section,

and the co-ordinate system used to define the locations is shown in Figure 2.14. The

origin of the co-ordinate system is located on the lower endwall of the downstream

section, centered at the middle of the passage between lines extended along the leading

edges of blades 4 and 5. The z-axis (tangential direction) extends along a line which

corresponds to the leading edge line of the blades in the blade row, and is defined to be

positive in the direction shown in figure 2.14. The y-axis extends upward from the lower

endwall. The x-axis completes the right hand coordinate system as indicated, and

hereafter, any positive x location will be referred to as an ‘axial’ position by analogy with

a turbomachine. All distances are normalized on the axial chord of the blade, ca = 5.46”.

Measurements were taken at 4 axial locations corresponding to x/ca = 0.137, 0.870,

3.297, and 6.593 as indicated in figure 2.14 . Measurements were taken with the

embedded pressure taps described in section 2.1.4, and also pressure taps that were

drilled into the aluminum floor panel. The pressure taps in the aluminum floor piece

corresponded to the locations at x/ca = 0.137, and 0.870. The remaining locations utilized

the fabricated aluminum pressure taps that were embedded into the fin-form plywood of

the lower endwall. The pressure readings were taken using the Scanivalve system

described by DeWitz (1988). The system uses a J-type scanivalve controlled by a IBM

PC computer. Pressures were sensed using a SETRA model 239 pressure transducer with

a range of 0-5 in. of water.

Using these readings, the angle of the sidewall tailboards was adjusted to

minimize the tangential pressure gradients across the downstream section of the tunnel.

The turning angle of the tunnel was determined to be 12.5° ± 0.1°, the uncertainty here

based on uncertainties in measurements of the positions of the sidewalls. This compares

favorably to the design condition of 12.9° for this blade geometry. Figure 2.15 presents

the pressure measurements obtained from the scanivalve system for this tailboard angle.

The pressure coefficient, Cp, defined as

(p – pref)/(po – pref)

17

is plotted against the z/ca position for each row of pressure ports. The results at the axial

locations x/ca = 0.137, and 0.870 correspond to locations under the blades, so there are

ports on the pressure side and suction side of the blades. At the x/ca = 0.137 axial

location, the readings indicate a slight pressure difference (indicative of a pressure

gradient) under the blades i.e. a difference of approximately 0.03 across the width of the

section. At the x/ca = 0.870 axial location, there is a slightly larger pressure difference of

about 0.05, with a much more scattered distribution when compared to that at x/ca =

0.137. This could be due to the fact that the flow above the lower endwall has various

vortical structures present within the blade passage, which affects the pressure readings

on the surface. However, at the x/ca = 3.297, and 6.593 axial locations, the pressure

difference is approximately 0.01 across the width, implying that there is a very small net

tangential pressure gradient across the width of the tunnel. The sensitivity of the pressure

readings with respect to the sidewall tailboard position was found by varying the position

of the tailboards so as to change the turning angle by one degree in either direction. This

one degree change resulted in a pressure difference of about 0.13 under the blades, and a

pressure difference of about 0.06 at the downstream locations across the test section.

These values of pressure difference that were obtained for a turning angle of 12.5°

implied an uncertainty of about 0.16° based on the pressure readings.

Once the turning angle was established for the cascade, the back pressure had to

be set using screens placed at the tunnel exit to ensure the correct operation of the suction

slots. As mentioned previously, the suction slots also had adjustable slats to either

completely or partially close them. In order to determine whether the suction slots were

operating correctly, it was decided to measure the boundary layers on the lower endwall

in the middle of the blade passages at the leading edge line of the blade row. If the slots

were operating correctly, then the boundary layer profiles would be similar in shape to

one another. The passages at the extremes of the blade row were ignored in the

comparison, since these would have been subject to interference from the sidewalls, and

the sidewall slots. Tufts placed on the leading edge of the suction slots were used to

provide a qualitative indicator of separation of the flow over the leading edge of the

suction slots. If the suction slots were operating correctly, then there would be no

separation seen on the leading edge of the suction slot. Each of the boundary layer

18

profiles were compared by taking hot wire measurements using the single hot wire probe

mentioned in section 2.4 at each of the passages.

Different configurations were tested, with different numbers of screens at the

tunnel exit, with the suction slots opened and closed, with the sidewall slots opened and

closed, and with vortex generators placed upstream of the suction slots. The vortex

generators were made of 1/32”aluminum shaped similar to a delta wing, and were used to

ensure that the flow over the suction slot would stay attached and be turbulent. The

optimum configuration that was found involved placing four screens (30% of the area

was covered with masking tape attached to one of the screens) at the exit plane, fully

opening the suction slots and the side slots, and without the vortex generators. This

corresponds to a Cp = -0.13 between the ambient pressure and the static pressure

measured at the mid-height of the inlet section.

Figure 2.16 shows the boundary layer profiles for this configuration in terms of

the mean streamwise velocity (U), and the mean square velocity (u2), normalized on the

inlet free stream velocity. As shown in the picture, the profiles look similar in shape,

especially in the passages 2,3,4,and 5(passage 3 corresponds to that between blades 3 and

4, passage 4 is between blades 4 and 5, and so on, where the blade numbers are shown in

figure 1) where the variation in the mean velocity is less than 1%, and the variation in

turbulence intensity is less than 2%. The profiles for passages 1 and 6 also show some

indication of being affected by the sidewalls since their profiles vary by as much as 8% in

the mean velocity and almost 10% in the turbulence intensity from the other passage

profiles. These results show that the inlet boundary layers to the blade row was

tangentially uniform for the cascade tunnel which suggests that the flow periodic in the 3

middle passages.

After set up of the tunnel, measurements were made with the single hot wire

probe at an axial location x/ca = 2.289” across the width of the tunnel. Presented here in

figure 2.17 are the contours of the turbulence intensity (u2) normalized on the approach

free stream velocity. The contours show the tip leakage vortices and the wakes from the

blades as the regions of elevated tke contours. These regions are similar in size and

shape across the three middle passages, indicative of the periodic nature of the flow in

this region.

19

Table 1: Blade Co-ordinates (normalized on chord)

Lower surface Upper surfacex/c y/c x/c y/c

0.000000 0.000000 0.000000 0.0000000.000435 0.000596 0.000060 -0.0014910.001413 0.001047 0.000923 -0.0031690.002926 0.001323 0.002598 -0.0050090.004966 0.001388 0.005091 -0.0069750.007524 0.001209 0.008414 -0.0090210.010599 0.000777 0.012579 -0.0111020.014200 0.000137 0.017595 -0.0131800.019048 -0.000748 0.023465 -0.0152380.029117 -0.002550 0.030187 -0.0172910.039178 -0.004300 0.037745 -0.0194000.049233 -0.006001 0.045855 -0.0215900.096961 -0.013419 0.093151 -0.0334780.144562 -0.019783 0.140592 -0.0439400.192059 -0.025156 0.188155 -0.0530270.239468 -0.029599 0.235822 -0.0607890.286809 -0.033171 0.283572 -0.0672780.334100 -0.035929 0.331389 -0.0725440.381356 -0.037929 0.379254 -0.0766400.428588 -0.039220 0.427156 -0.0796130.475794 -0.039826 0.475098 -0.0814870.522983 -0.039750 0.523069 -0.0822620.570167 -0.038991 0.571058 -0.0819380.617353 -0.037568 0.619059 -0.0804920.664516 -0.035603 0.667097 -0.0776700.711679 -0.032997 0.715151 -0.0732770.758887 -0.029596 0.763179 -0.0671580.806192 -0.025241 0.811130 -0.0591630.853654 -0.019769 0.858947 -0.0491430.901342 -0.013007 0.906564 -0.0369540.949328 -0.004778 0.953911 -0.0224610.959464 -0.002843 0.963827 -0.0191070.969617 -0.000834 0.973727 -0.0156450.979787 0.001253 0.983610 -0.0120720.989977 0.003419 0.993477 -0.0083890.993047 0.004088 0.996438 -0.0072600.997043 0.003561 0.999467 -0.0046671.000000 0.000000 1.000000 0.000000

20

Table 2 : Measured tip gap heights (inches)Blade Leading Edge Mid Chord Trailing edge1 0.157 0.157 0.1572 0.148 0.152 0.1533 0.148 0.152 0.1574 0.148 0.152 0.1545 0.147 0.151 0.1636 0.147 0.154 0.1647 0.147 0.155 0.1648 0.148 0.169 0.172

21

Chapter 3. Results and Discussion

Surface oil flow visualizations and four sensor hot wire measurements were taken

to give a detailed description of the flow field downstream of the linear compressor

cascade with tip leakage. The co-ordinate system used to present the data is shown in

Figure 3.1. The origin of the co-ordinate system is located on the lower endwall of the

downstream section, centered at the middle of the passage between the leading edges of

blades 4 and 5. The z-axis extends along the leading edge line of the blade row, and is

defined to be positive in the direction shown in figure 3.1. The y-axis extends from the

lower endwall, and the positive direction corresponds to the height above the lower

endwall. The x-axis completes the right hand coordinate system as indicated, and

hereafter, any positive x location will be referred to as an ‘axial’ position. All distances

are normalized on the axial chord of the blade, ca = 5.46”.

Measurements were taken at 5 axial locations corresponding to x/ca = 1.366,

2.062, 2.831, 3.077 and 4.640 as indicated in Figure 3.1. Due to the periodic nature of

the flow, measurements were taken downstream of the passage between blades 4 and 5

(as indicated in Figure 3.1). Velocities are presented in terms of the mean components

(U, V, W), and the fluctuating components (u, v, w). Relative uncertainties for the

measured quantities were computed for 20:1 odds (95% confidence), and are presented in

Table 3.1. The mean streamwise velocity, U, is aligned with the mainstream flow

direction downstream of the cascade which makes an angle of 53.6° with the x-axis as

shown in Figure 3.1. All velocities are normalized on the approach free stream velocity

(U∞) of 87 ft/s, which was measured with a Pitot static probe positioned 6” above the

lower endwall and 72” upstream of the passage between blades 7 and 8. In all the cross

sectional plots, the aspect ratio of the axes has been adjusted so as to reveal the flow as it

would be seen by an observer looking upstream in the negative U direction (see Figure

3.1).

22

3.1 Inflow measurements

Measurements were made upstream of the blade row to obtain inflow

characteristics of the flow field. Measurements were made with the single hot wire

sensor of the area 2” axially upstream of the blade passage between blades 4 and 5. The

results of these measurements are shown in Figure 3.2 which are the contours of the mean

streamwise velocity, and the turbulence intensity normalized on the approach free stream

velocity (U∞). Observing the contours of the mean velocity, we can see the upstream

influence the blades have on the flow, revealed by the areas of velocity deficit at

approximately z/ca = -0.8 and 0.9. This distance is also consistent with the blade spacing

of 1.7ca (9.29”). From the contours of turbulence intensity, the turbulence intensity

levels in the passage are about 0.3% of free stream and shows a variation of about 0.1%

across the width of the passage. This implies that flowfield upstream of the blade

passage is uniform and shows very little variation across the width and height of the

passage.

Further uniformity of the inflow is revealed from figure 2.16, which are the

boundary layer profiles taken at the mid passage, at x/ca=0 (corresponds to the line

extending along the leading edges of the blades). These profiles were obtained with the

single hot wire probe, and the profiles for the middle passages are very similar to one

another. As previously mentioned the profile for passage 1 and passage 6 are affected by

the sidewall suction slots so are different from the middle passages. Given in Table 3.2

are the boundary layer parameters, displacement thickness( δ* ) and momentum thickness,

(θ), normalized on the axial chord, ca. The values in the table show that the boundary

layers in the middle passages are similar to one another, and the passages towards the

ends are affected by the sidewall suction slots as revealed by the difference in the

momentum thickness.

These results, along with the measurements presented in section 2.1 of the cross

section of the inlet section reveal the uniformity and quality of the inflow. With free

stream turbulence intensity levels as little as 0.3%, and with less than 1% variation of the

flow across the cross section, there should be no contamination of the flow field within

the blade passages and downstream of the cascade.

23

3.2 Blade Measurements

Due to the difficulty in obtaining surface pressure measurements on the blades,

two dimensional computations were performed by Moore et al.(1996) to obtain the

pressure distribution on the blade surface. The results of these 2D calculations are

presented in Figure 3.3. Plotted on the figures are the blade loading (the difference

between the total pressure and surface pressure divided by the difference between total

pressure and inlet stagnation pressure) distribution around the surface of the blade. Also

shown on the figure are the various blade loadings for different inlet angles. For this

study, the inlet angle was 65.1°, and the figure reveals the pressure difference between

the pressure side and the suction side of the blades. It is this pressure difference that

drives the flow under the gap between the blade tip and lower endwall resulting in the tip-

gap flow. It is this tip-gap flow which rolls up to form the tip-leakage vortex formed in

the blade passage.

Using the single hot wire probe, measurements were made of the blade boundary

layers at a distance of 0.0625” upstream of the trailing edge of the blades on both the

pressure side and the suction side of the blades. The results are presented in figure 3.4.

Data for the pressure side was only take to a height of about 0.04” away from the

endwall, anything closer, and the probe would touch the surface of the blade. Fig 3.4a-b

shows the variation of the normalized mean velocity with height above the blade surface,

the difference in the two being Fig 3.4b is plotted as a semi-log plot. Fig 3.4c shows the

variation of the turbulence intensity with height above the blade surface. The profile on

the pressure side of the blade shows a shape characteristic on turbulent boundary layers,

where it can be seen in Fig 3.4c, the profile has a logarithmic shape to it. These profiles

suggest a boundary layer thickness of about 0.07ca (0.38”), and from this a displacement

thickness of about 0.147” can be estimated.

However, the suction side boundary layer profile does not show this characteristic

shape, but instead suggests that the boundary layer has separated from the blade surface.

Looking at the turbulence intensity profiles, there is a peak in the suction side profile,

which is indicative of separation of the boundary layer. From these profiles, the

boundary layer seems to have separated at about a height of 0.05ca (0.3”) above the blade

surface. Also seen in the plots is the non uniform free stream values. This is because the

24

flow is curved around the surface of the blade, and as expected, the velocities are higher

on the suction side than on the pressure side. As the distance away from the surface

increases, the velocity is seen to approach 0.7 U∞, and as will be shown later, this value

corresponds to the theoretical value for the mainstream flow velocity for the current

cascade configuration.

3.3 Oil Flow Visualizations

Oil flow visualizations were done on the lower endwall of the cascade. The

visualizations were photographed and are presented in Figure 3.5a and Figure 3.5b.

Figure 3.5a shows the flow pattern of the lower endwall in the passage between blades 4

and 5 ( the position of the blades are indicated as Region 1). Figure 3.5b is a close up of

flow pattern of the lower endwall flow in the tip gap region underneath blade 4 (the

position of the blade is also shown on the figure).

Observing the details of the flow visualization in figure 3.5a, we see that there are

dark regions where the paint has been swept away from the surface. These regions have

been labeled to better identify them. Region 1, corresponds to the location directly

underneath blade 4 which is the tip gap region. In this region there is high shear flow as

a result of the tip-gap flow, and this is what is responsible for removing the paint and

leaving the dark streak as indicated. Observing figure 3.5b, which is a close up of the

same flow pattern, in Region 1, there are some streaks of paint which were probably

drawn from the adjacent area. These streaks will correspond to the flow direction, which

is almost perpendicular to the blade shape. This is similar to what has been observed in

previous studies as described in Section 1.

Assuming now, that the dark regions in the flow visualization correspond to

regions of high shear flow, then Region 2 as indicated in Figures 3.5a, and 3.5b is

indicative of a very strong shear flow. From previous studies, the only other feature in

the flow which has such high shear flow could only be the tip-leakage vortex. This

region is probably indicative of where the vortex lifts flow off of the wall. Further

evidence that this might be indicative of the tip-leakage vortex is the fact that this region

is seen to extend beyond the blade region, and from subsequent the hot-wire results, it

was seen that the tip-leakage flow is the dominant feature in the endwall region.

25

Another interesting feature is the dark region labeled as region 3 in the figures.

This also implies that there is a structure that has a high shear flow associated with it.

Previous studies have all suggested that there might be a passage vortex present, which

could form due to corner stall on the pressure side of the blade. However, this structure

suggested by region 3, is on the suction side of the blade, and looking Fig. 5b., the streak

lines indicate that this vortex is in the opposite sense as the tip leakage vortex. Further

downstream, the oil flow patterns indicate that the influence of this vortex has diminished

and is possible engulfed by the tip leakage vortex. The oil flow visualizations do not give

any indication of a passage vortex due to corner stall on the pressure side as there are no

regions indicative of high shear flow near the pressure side of the blade.

3.4 Mean Flow Field

3.4.1 Overall Form of the Flow

Figures 3.6a – 3.10a present contours of mean streamwise velocity (U),

normalized on the approach free stream velocity (U∞). Contour labels on the plots

indicate the magnitude of the normalized quantity. Figures 3.6b – 3.10b present the mean

cross-flow velocity vectors (V,W). The relative magnitude of these vectors can be

compared to the reference vector (0.5 U/U∞) indicated in each of the plots. In both sets

of plots, the vertical axis corresponds to the height above the lower endwall (positive y

direction in figure 3.1), and the horizontal axis corresponds to the z position (z direction

in figure 3.1). Both these quantities are normalized on the axial chord, (ca = 5.46”).

These figures reveal the wakes from blades 4 and 5 which are the vertically

oriented regions of mean velocity deficit. The wake from blade 4 is centered at z/ca =-1.2

and the wake from blade 5 is centered at z/ca = –2.9 at the most upstream location (figure

3.6a), and at z/ca = -5.4(from blade 4) and -7.1( from blade 5) at the most downstream

location (Figure 3.10a). This separation distance of 1.7ca is consistent with the blade

spacing of 9.29”. The tip-leakage vortex from blade 4 can be seen to dominate the lower

endwall region, revealed as the region of high axial velocity deficit, and occupying the

area between the wakes of blade 4 and 5 from the lower endwall to approximately

y/ca=0.5. In the secondary flow vector plots (figures 3.6b-3.10b), the tip leakage vortex

is the region of circulatory flow between the wakes locations (the wakes are not clearly

26

visible, but maybe inferred from the z position as revealed in the mean velocity plots

(figures 3.6a-3.10a)).

The mainstream velocity downstream of the cascade can be estimated

approximately if we consider this to be a uniform two-dimensional incompressible flow,

and if we assume the axial velocity remains constant. Thus for a cascade where the inlet

angle is 65.1°, and turning angle is 12.5°, the computed value using the equation

U∞cos(inlet angle) = Umainstream cos(exit angle)

of the mainstream flow of such an flow is 0.70 U∞ . This compares favorably with the

measured value in the mainstream of 0.72 U∞,. This difference could be a result of the

inlet flow being accelerated due to the increasing boundary layer displacement thickness.

The mainstream velocity increases slightly with downstream distance as well to about

0.73 U∞ The slight acceleration is also probably due to a some acceleration as the upper

and lower endwall boundary layers in the downstream section also grow with

downstream distance as well as the tip-leakage vortex adding some displacement.

3.4.2 The Tip Leakage Vortex

At x/ca = 1.366, the vortex from blade 4 can be seen to be roughly halfway

between the wakes of blades 4 and 5, at z/ca=-2.15(figure 3.6a). However, as it travels

downstream, the vortex is seen to move towards the wake of blade 5, z/ca=-4.30 at

x/ca=2.831 in figure 3.8a, and starts to merge with the wake, which can be seen at z/ca=-

5.65 at x/ca=3.77 in figure 3.9a. In fact, at x/ca=3.770 and 4.640, the vortex from blade 3

is now visible in figures 3.9a and 3.10a respectively, and has merged with the wake from

blade 4 in lower endwall region. The vortex also begins to influence a larger region

further downstream. At x/ca=1.366, the vortex region extends to about y/ca = 0.4 (where

the mean streamwise velocity is approximately 0.65U∞, and it increases to y/ca=0.6 at

x/ca=4.640. The mean streamwise contours show a strong velocity deficit (compared to

the mainstream velocity) in the vortex. The peak deficit at x/ca = 1.366 is 0.44U∞,

located at y/ca=0.17 and z/ca=-2.14. Figure 3.11 shows the variation of peak deficit

(normalized on the approach free stream velocity (U∞)),on the vertical axis, of the vortex

with downstream position (normalized on the axial chord), given on the horizontal axis.

There is initially a large drop off in the deficit from x/ca = 1.366 to 2.062, but then it

27

starts to fall much more slowly. Overall, there is a 2.5 fold decrease in the deficit as the

vortex develops downstream. At x/ca=1.366 and 2.062, this high deficit region is a

distinct minimum in the contours. However, as the vortex develops downstream, this

minimum starts to merge with the low speed region at the endwall region that forms due

to the no slip condition. From the secondary vectors, this low speed region is seen as

where the flow is being lifted off the wall at approximately z/ca=-7.25 at x/ca=4.640.

This growth suggests that the vortex is becoming the dominant feature of the flow field

in the endwall flow region.

As stated above, the vortex moves across the endwall, from the wake of blade 4

towards blade 5. Also, though the secondary flow vectors show some circulatory motion

around the vortex, it is not strictly speaking the secondary mean velocity field of the

vortex. This is because the vortex axis and the mainstream axis are not aligned with one,

evident from the motion of the vortex across the passage. The vortex axis can be defined

as the locus of points of peak mean streamwise vorticity, where the vorticity is computed

as the curl of the mean velocity vector and ignoring streamwise derivatives. Figures

3.12-3.16 show the contours of streamwise vorticity. The axis definitions are similar to

that presented in figure 3.6-3.10, and once again the aspect ratio of the plots have been

adjusted as in figure 3.6-3.10. From these figures, the vortex axis can be found (which is

defined as the point where the vorticity is a maximum), and its position relative to the

mainstream direction is shown in figure 3.17 ( the wake axis is parallel to the mainstream

axis). The vertical axis in the figure is the z position of the vortex core, and the

horizontal axis is the downstream location, and both axes have been normalized on the

axial chord, ca. The vortex axis is at an angle of 56° to the x-axis. From this angle, if we

were to assume that the vortex behaves as a infinite line vortex located at y/ca=0.2, the

effective total circulation can be calculated to imply a total circulation of 0.11U∞ca. The

velocity components are rotated, and the secondary flow vectors are plotted so that they

are now aligned with the vortex axis, as shown in Figures 3.18-3.22 (axis definitions are

similar to those in figures 3.6-3.10). From these figures, the circulating flow can now be

clearly seen rotating around the core of the vortex. In each of the figures, a reference

vector is given to indicate the magnitude of the vectors.

28

The decay of the rotating vortex is apparent from these vector plots. This decay is

clearly seen in Figure 3.23 which is a plot of the V velocity profiles through the vortex

core taken in the z-direction. These plots show a distinct vortex core indicated by a peak

velocity deficit, and from these plots the variation of an apparent core size, and peak

tangential velocity can be plotted. These are presented in figure 3.24. The peak

tangential velocity is seen to decay by a factor of 3, and the core radius decreases by a

factor of 2 from x/ca = 1.366 to x/ca=4.640. With these parameters, the apparent

circulation can be calculated and is presented in Table 3.3.

Looking at the vorticity contours, figures 3.12-3.16, we see that there is a region

of negative vorticity to the right of the vortex center. At x/ca=1.366 (Figure 3.12), this

region is very well defined, with a negative vorticity of about –1.15U∞ at z/ca=-2.6. This

may indicate that there is a secondary vortex rotating in the opposite sense as the tip

leakage vortex. This similar to the vortex suggested by the oil flow visualizations, and

that it does not get engulfed by the tip-leakage vortex within the blade passage. This

region of negative vorticity is still seen at the subsequent downstream locations, but it

decays very quickly to about –0.1U∞ at x/ca=4.640 and z/ca=-6.00 (Figure 3.16).

However, this vortex is not well defined in the secondary flow vectors, so it would

suggest that the tip-leakage vortex has a much greater influence in the endwall region.

3.4.3 The Blade Wake

Figure 3.25 shows the profiles of the mean streamwise velocity through the blade

wakes at y/ca = 1.0 taken in the z-direction. The mean streamwise velocity, normalized

on the approach free stream velocity is given on the vertical axis, and the z-position in

plotted on the horizontal axis. These profiles were measured through the wake behind

blade 4 above the lower endwall corresponding to y/ca=0.93. From Figure 3.25, the

wake shows a 3 fold decay in the deficit from x/ca = 1.366 to x/ca=4.640. Similar to that

seen in the vortex core, there is a sharp decrease in the deficit from x/ca=1.366 to

x/ca=2.062, and then this seems to fall more slowly. The wake is also seen to increase in

size as it travels downstream. Figure 3.26 shows the variation of the peak deficit, and the

half-width of the wake with downstream distance. The half-width of the wake is defined

as the distance from the location of maximum deficit to the location of half the maximum

deficit. From Figure 3.26, the decrease in the deficit shows the decay of the wake and the

29

increase in half width shows that the wake is indeed growing. Using these values,

normalized velocity profiles can be plotted.

Shown in figure 3.27a are the normalized mean velocity profiles. These profiles

are compared to the normalized mean velocity profile for standard wake data taken from

Wygnanski et al.(1986) which is shown in Figure 3.27b. On the vertical axis is the

normalized quantity (U – Ue)/Uw, where Ue is the edge velocity and Uw is the maximum

velocity deficit. Plotted on the horizontal axis is η, which is defined as y/lw, where lw is

the half width of the wake. Comparing the profiles from the wake from blade 4, and the

standard 2-D wake data, we see that they are very similar to each other in that they are

the same shape, and size. This would suggest that as you proceed downstream, the wake

behaves similar to that of a 2-D wake.

3.5 Turbulent Flow Field

3.5.1 Overall Form of the Flow

The structure and development of the turbulence field downstream of the

compressor cascade can be seen in plots of the turbulence kinetic energy (tke), the

distribution of the normal and shear stresses, and the tke production. The turbulence

kinetic energy is given by

and the contours of tke (normalized on U∞2) are presented in figures 3.28-3.32 for each

downstream measurement plane. The contours of the individual stress components are

given in figure 3.33-3.37 for each of the measurement planes. The values of the stress

levels are indicated by the flood legend beside each plot. The tke production is computed

by calculating the contributions due to the individual stress components, and ignoring

mean streamwise derivatives with the equation;

( )wvu222

2

1 ++

∂∂+

∂∂−

∂∂+

∂∂−

∂∂+

∂∂−

∂∂

∂∂−

∂∂

−−−1111111

2

1

2

1

2

x

W

z

U

y

W

z

V

x

V

y

U

z

W

y

V

x

Uuwvwuvwvu

30

In the above equations, the overbars represent mean square quantities which will be

referred to as u, v, and w terms henceforth. The x1, y1, and z1 axes are axis aligned with

the velocity directions (different from x, y, and z directions defined in figure 3.1). The u2,

uv, and uw terms of the equation are the contributions to the production due to the

gradients in the axial velocity, (hereafter referred to as streamwise contributions), and the

remaining terms (v2,w2,vw) are the contribution due to the gradients of the cross flow

(hereafter referred to as crossflow contributions). Figures 3.38-3.42 show the contours of

tke production, and figures 3.43-3.47 show the contours of the streamwise , and cross

flow contributions to the tke production. In all plots, the vertical axis corresponds to the

height above the lower endwall, and the horizontal axis corresponds to the z-position,

identical to that described for figures 3.6-3.10.

Similar to the mean velocity field (figures 3.6-3.10), the tip-leakage vortex and

the blade wakes can be seen in the contours of tke in figures 3.28-3.32. These features

can be inferred from the figures by observing where the tke levels are higher than that in

the mainstream. The wakes from blades 4 and 5 can be seen as the vertical regions of

elevated tke levels around (z/ca = -1.2 and –2.9) at the most upstream location in figure

3.28. The tip leakage vortex from blade 4 is indicated by the region of elevated tke levels

adjacent to the endwall between the wakes of the two blades. Similar to that seen in the

mean flow field, the vortex is seen to dominate the endwall flow region.

3.5.2 Tip Leakage Vortex

At x/ca=1.366 (figure 3.28), the tip leakage vortex contains two distinct regions of

elevated tke. There is the region just surrounding the core of the vortex near z/ca=-1.9,

and there is also an arch shaped region which extends from where the flow is being lifted

off the endwall near z/ca = -2.5 to seemingly merge with the first region. From figures

3.33a-3.33c, we see that the largest contribution to the tke in the region where the flow is

being lifted off the wall is from the u2 normal stress. Around the core of the vortex, the

v2 and w2 term are more dominant. In terms of shear stresses, figures 3.33d-3.33f, the uw

component is greatest where the flow is being lifted off the wall, and the uv component is

the greatest around the core of the vortex. Observing the contours of tke production

(figure 3.38), the region where the flow is being lifted off the wall and surrounding the

31

core of the vortex have the largest production levels. Figure 3.43, which shows the

production broken into streamwise and crossflow contributions, we see that the

streamwise contributions are much larger in that arch shaped region around the core of

the vortex. This suggests that the turbulence is being produced due to gradients in the

streamwise velocity associated with the vortex rather than the circulating motion of the

vortex.

As the flow progresses downstream, the tke contours show that the vortex grows

in size. At x/ca=2.062 (figure 3.29), it occupies a region of approximately 1ca (an increase

from 0.7ca at x/ca=1.366) in the z direction and extends in height to 0.41ca (from 0.39ca )

in the y-direction. There is a decay in the peak tke levels in the vortex where the

maximum tke level at x/ca=1.366 is 0.00966, and at x/ca=2.062, the maximum level in the

core is 0.0087. Similar to that seen at x/ca=1.366, there are still high tke levels where the

flow is being lifted off the wall at z/ca=-3.5, and to the left of the core at z/ca=-3. The

contours also show that this region where the flow is being lifted off the wall is beginning

to merge with the vortex. The anisotropy shown in distribution of the shear normal

stresses at this downstream location is still similar to that seen at the previous

measurement location, where the u2 stress is dominant near the lifting flow region, and v2

and w2 dominant around the core of the vortex. The distribution of the shear stresses is

also similar in form, uw dominating the lifting flow region, and uv around the core.

However, the levels are less than that seen at the previous measurement location,

indicating that the vortex is decaying.

Observing the production contours (figure 3.39), the region where the flow is

being lifted off the wall still has the highest levels of tke production. However, unlike at

x/ca=1.366 where the region around the core had production levels that were

approximately half of that in the region where the flow was being lifted off the wall, at

x/ca=2.062, the production levels around the core are three times as less than that in the

lifting flow region. Looking at the production contributions in figure 3.44, the production

is primarily due to the streamwise contributions, similar to that seen at x/ca=1.366.

Further downstream, at x/ca=2.831, the tke contours (figure 3.30) now show that

the tke levels in the vortex has decayed by almost half of those at x/ca=1.366. The

distribution of the tke levels has also changed from the two previous locations in that the

32

region where the flow is being lifted off the wall now seems to have merged with the

region surrounding the core of the vortex. Looking at the stress distributions at this

location (Figure 3.35), the distribution of the normal stresses around the core has

changed. At x/ca=1.366, the u2 normal stress dominated the lifting flow region, but at

x/ca=2.831, the u2 normal stress now dominates an arch shaped region above the core of

the vortex, while v2 dominates the region to the left of the core, and w2 under the core,

and closer to the endwall. In figure 3.30, the tke contours show a higher tke levels in a

region to the left of the core, which can be explained by the normal stress distributions,

where all three components seem to extend into this region left of the core. The

distribution seen in the normal stresses is still similar to those seen at the two previous

measurement planes. However, the levels of the turbulence stresses is lower than the

previous location, and this is highlighted in the production contours where the levels are

at least half of the previous location. Similar to the previous planes, the highest levels of

production are still in the lifting flow region.

At the two most downstream locations, i.e. x/ca=3.770 and 4.640, the tke contours

(Figs 3.31 and 3.32) now show that the region where the flow was being lifted off the

wall has merged with the endwall boundary layer and the vortex. The turbulence stress

distributions (Figs 3.36 and 3.37) have also changed at these locations, where the u2, v2,

and w2 stresses are all approximately the same, and larger than that seen in the lifting

region. The shear stresses are all negligible when compared to the normal stresses,

values of the peak normal stress 4 times as high as the peak shear stresses , and this is

further highlighted in the production contours. The total production at these downstream

locations are at least 3 times as less when compared to the previous measurement planes,

and observing the different contributions, we see the crossflow contributions are much

lower than the streamwise contributions.

3.5.3 The Blade Wake

The tke levels seen in the blade wakes at x/ca=1.366 (Fig 3.28) are similar to those

seen in the vortex region, 0.00826 in the wake compared to 0.00966 in the core region.

In the wake region, the most contribution to the tke is due to the w2 normal stress (figures

3.33a-3.33c). The wake from blade 4 shows a double peaked u2 profile, with the two

33

peaks at z/ca=-1.15 and –1.3. In terms of shear stresses, the contribution due to uw is

greatest, with the uv, and vw terms negligible in the wake region. The wake also has a

antisymmetric uw profile. Looking at the tke production contours in figure 3.38, the

wake shows a double peaked form due to the uw contribution seen in figure 3.33f.

Splitting up the production contributions (figure 3.43), we can see this double peaked

form in the streamwise contribution to production.

At x/ca=1.366, the tke levels seen in the wake and the vortex were similar,

however, at x/ca = 2.062, we see that the wake has decayed more than the vortex, with

peak tke levels being half of that seen in the vortex. The turbulence stress distributions

are similar to that seen at x/ca=1.366, but with the levels reduced. This would seem to

suggest that the vortex was beginning to become the dominant source of turbulence in the

flow. In the wake region, the production levels shown in figure 39 are small when

compared to those seen in the vortex region. The streamwise and crossflow contributions

to the production (figure 3.44) show that in the wake the contributions are small when

compared to the vortex region. This would explain the much greater decay in tke seen in

the wake since there is much less turbulence production here.

The tke and tke production levels seen in the wake at x/ca=2.831 are lower than

that seen at x./ca=2.062. Compared to the vortex, the maximum tke is about half of that

in the vortex, again implying that the vortex is becoming the dominant feature of the

flow. The turbulence stress distributions shown here are still similar to those seen at

x/ca=1.366 and x/ca=2.062, however the levels are much lower than before. When we

compare the production contours to x/ca=2.062, the production in the wake is negligible

when compared to the vortex.

At the two most downstream locations, i.e. x/ca=3.770 and 4.640, the tke contours

in the wakes also show that they are approximately half of that seen in the vortex, and

there is no significant production levels in the wakes of the blades. However, the

distributions of the u2 normal stress and uw shear stress is still similar to those seen

further upstream. Similar to that done with the mean velocity flow field, comparisons

can be made with standard wake data in terms of the normalized turbulence stress

distributions.

34

Given in figure 3.48a and 3.49a are the distributions of the normalized turbulence

normal stress (u2) and shear stress (uw) respectively for the wake. Figure 3.48b and

3.49b shows the distributions of the corresponding normal and shear stress respectively

for a standard 2-D wake from Wygnanski et al.(1986). Plotted on the vertical axis is the

normal stress u2 in Fig 3.48a and the shear stress uw in Fig 3.49a , both normalized on

Uw2 (the maximum deficit, similar to that used section 3.3.3), against η (as defined in

section 3.3.3). As can be seen in Fig 3.48a, the u2 distribution shows a similar shape to

that of the standard 2-D distribution at the downstream locations. The distribution at

x/ca=1.366 is similar in form, but has values less than that for the others due to the fact

that the wake has not yet fully developed. Comparing the uw distribution to that of the

standard wake data, the distributions are also similar to one another. These results, in

addition to the mean velocity profiles presented in section 3.3.3, suggest that as the wake

develops downstream of the cascade, it begins to behave similar to that of a two

dimensional wake away from the endwall region.

3.6 Spectral Results

Measurements of the velocity spectra were also made using the four sensor hot

wire probe. These velocity spectra measurements were taken in both the wake from

blade 4, and the tip leakage vortex. For the wake, the measurements were taken at the

wake center at a distance of 5”(y/ca = 0.92) above the lower endwall. Measurements

were taken at the center of the tip leakage vortex. The normalized autospectra are

presented in figures 3.50, 3.51, and 3.52. The autospectra are normalized on cU∞ and are

plotted against the nondimensionalized frequency fc/U∞. The legend in the figures

corresponds to the axial measurement location. For all sets of spectra, they have the

typical broadband character of fully turbulent flows, with the –5/3 slope in the inertial

subrange, with the drop off at higher frequencies. In the vortex core, there are no distinct

spectral peaks that might indicate the presence of periodically organized structures such

as eddies. However, there might be some wandering motions of the vortex core, and

these wandering effects, if present, might corrupt the turbulence measurements. However,

a study by Wenger et al (1998) in which two point measurements of this flow field

35

provided conclusive evidence that there was no wandering of the tip leakage vortex

present to corrupt the measurements.

In the wake however, at the most upstream locations, there is a distinct spectral

peak at a normalized frequency of about 3 in the Gww autospectra plot (figure 3.52), but

there are no distinct peaks in the other autospectra figures. This would indicate that there

is some periodic motion within the wake of the blade, which is believed to be as a result

of vortex shedding off of the rounded trailing edge of the blade. This shed vortex seems

to dissipate very rapidly, as there are no peaks evident at x/ca = 3.770 and 4.640. This

peak corresponds to a frequency of 420Hz. For round trailing edges, a Strouhal number

(defined as fc/Uref ) of 0.2 is indicative of trailing edge shedding. If we were to take

f=420Hz, and a Uref = 60 ft/s (corresponding to the edge velocity of the wake) for the

current cascade, the characteristic radius ( c ) is 0.0625”, which implies that the Strouhal

number for the blade is 0.04. However taking the displacement thickness of 0.147”

obtained from the blade pressure side surface profiles, which acts to increase the

characteristic radius of the trailing edge, a Strouhal number of about 0.13 is implied. But,

on the suction side of the blade, the boundary layer was found to have separated at about

0.3”. Assuming that this separated layer acts to increase the characteristic radius, a

Strouhal number of about 0.18 is implied. This would suggest that there might be some

trailing edge shedding from the blade.

3.7 Effects of Tip Gap Variations

Measurements were taken to study the influence of different tip gap heights on the

downstream flow field. The tip gap height was both doubled, to 0.320”, and halved, to

0.0825”, and cross sectional planes were measured at the axial location x/ca = 2.831. As

described in section 2.1.3, the tip gap was varied by replacing the shims underneath the

blade support structure. Measurements were taken with the four-sensor hot wire probe

and the results are presented in figures 3.53- 3.66, using the same coordinate system

described earlier.

Figure 3.53 and 3.54 show the contours of mean streamwise velocity and mean

cross-flow vectors for the double tip gap and half tip gap respectively. Comparing these

to the nominal tip gap of 0.165”, the case with the double tip gap shows that the tip

36

leakage vortex, defined as the region with high axial velocity deficit, is larger than

before, and its position has moved such that it has migrated across the entire blade

passage (in this case the vortex from blade 4 has reached the wake from blade 5). At the

nominal tip gap of 0.165”, the vortex only moved across 75% of the passage width. For

the case with half tip gap (Figure 3.54), the vortex has only moved across 50% of the

passage. The size and extent of the vortex has also changed, where in the case of the

double tip gap, the vortex now extends to about y/ca = 0.5, and for the half tip gap

extends to only about y/ca = 0.3, (compared to y/ca = 0.4 for the nominal tip gap).

Looking at the mean cross-flow vectors (Figures 3.53, and 3.54), we see a region of

apparently circulatory flow, but now for the case of the double tip gap, the magnitude of

the vectors are almost twice that of the nominal tip gap, and for the half tip-gap, the

vectors are about 65% of the vectors seen in the nominal tip gap. These results indicate

that for the case of the double tip gap, the vortex has increased in strength and for the

case of the half tip gap, the vortex has decreased in strength.

Figures 3.55 and 3.56 show the contours of mean streamwise vorticity for both

the double and half tip gap respectively. When compared to the vorticity figure for the

nominal tip gap (figure 3.14), we see that the peak vorticity has increased by about 50%

in the vortex core for the double tip gap, and has reduced by about 30% for the half tip

gap. There are still regions of negative vorticity in both plots and for the double tip gap,

it is almost twice the value as that seen for the nominal tip gap. and about 50% higher for

the half tip gap. This varaition with the tip gap height would suggest that this vortex is

formed within the tip gap region. From these vorticity plots, we can then plot the cross-

flow vectors such that they are aligned with the vortex axis. For the double tip gap, the

vortex axis is at an angle of 63° to the x-axis, and for the half tip gap, the vortex axis is at

an angle of 45° to the x-axis. These vortex aligned cross flow vectors are shown in

Figures 3.57 and 3.58 for the double and half tip gap respectively.

For the double tip gap, the circulatory motion around the vortex can be clearly

seen, and when compared to the nominal tip gap cross flow vectors (Figure 3.16), the

magnitude of the vectors are approximately twice as large. However, for the half tip gap,

the characteristic circulating motion usually associated with a vortex is not that clearly

defined, and the magnitude of the vectors are approximately twice that seen with the

37

nominal tip gap (the scale of the reference vector has been changed for clarity). This

would imply that the strong tangential flow as a result of the tip gap does not roll up to

form a vortex, but instead remains as a high shear flow region for the half tip gap

condition.

The contours of the tke for both gap heights are given in Figures 3.59 and 3.60.

Comparing the levels to the nominal gap height (figure 3.30), for the double tip gap, the

levels are about the same, but the high tke region is seen to occupy a much larger region

which is approximately the same size as the passage width. In the case of the half tip

gap height, the region where flow is lifted off the wall is much more clearly defined , and

turbulence levels here are 20% higher when compared to the nominal gap height.

Presented in figures 3.61 and 3.62, are the turbulence stress distributions for the double

and half tip gaps respectively. In the case of the double tip gap, the normal stress (u2) is a

maximum where the flow is being lifted off the wall. The normal stress (v2) has two

distinct regions around the core, and (w2) is a maximum at the core center. Compared to

the nominal gap height, the (u2 ) stress was a maximum above the core, v2 to the left and

under the core and w2 distributed under the core, and where the flow is being lifted off the

wall. The shear stresses however, show a similar distribution in uv, and vw, but the uw

stress component is a maximum where the flow is being lifted off the wall. In the case of

the half tip gap height, the stress distributions are similar to that seen with the nominal

gap height, with the exception of the u2 component, which has a maximum where the

flow is being lifted off of the wall.

In terms of tke production (Figures 3.63 and 3.64, for the double tip gap, and half

tip gap respectively), for both cases, it is the region where the flow is being lifted off the

wall with the highest production levels. Peak production levels for the double tip gap are

3 times as high as those seen in the nominal gap height. Peak production levels for the

half tip gap height are the same when compared to the nominal tip gap height. Figures

3.65 and 3.66 show the production split into the streamwise contributions and crossflow

contributions. For both the double and half tip gap height, the most production is from

the region where the flow is being lifted off the wall as the streamwise contribution.

Crossflow contributions are small compared to the streamwise contribution. Compared

to the nominal tip gap height, where the production levels are about a third of those seen

38

with the other two cases, there is no distinct region of high production levels where the

flow is being lifted off the wall.

These results reveal that changing the tip gap height of the cascade does have a

significant influence on the downstream flow field. However, since measurements were

not taken at all axial locations, it is difficult to say just what the effects are in terms of the

development of the vortex and the surrounding flow field.

3.8 Trip effects

Measurements were taken to study the effects of the blade boundary layer trip

strips. This was done by doubling the trip width, from 0.25” to 0.5” while using the same

density of glass beads attached to the strips. Measurements were taken with the four

sensor hot wire probe at x/ca=2.831 axial location, and the results are presented in figures

3.67 – 3.69, using the same coordinate system described earlier.

Figure 3.67 show the contours of mean streamwise velocity for the double trip

strip. Compared to Figure 3.8, which shows the velocity contours for the single trip strip,

we see that the vortex and wake are similar in shape and position. The same is seen if we

compare the turbulence kinetic energy distribution, given in Figure 3.68 for the double

trip gap. Comparing the distribution of tke to that of the single trip (Figure 3.30), we see

that the distribution is similar between the two. Figure 3.69 shows the distribution of the

turbulence stresses for the double trip strip. Once again, if we compare this distribution

to that for the single trip strip (Figure 3.35), we see that the two are similar in that the

normal stresses (u2,v2,w2) and the shear stresses (uv, vw, uw) all show the same pattern

and distribution between the two cases. This implies that the blade boundary layer trips

have no effect on the nature, and structure of the flow field downstream of the cascade,

which would suggest that the blade boundary layers are stalling and separating from the

blade surface as revealed in the blade boundary layer profiles presented in section 3.2.

3.9 Repeatability

As with all experimental studies, the repeatability of the experiment was

established for this study. Measurements were initially taken for all 5 downstream

39

locations with a measurement grid consisting of approximately 670 data points. This was

enough to give sufficient detail to describe the flow field at these locations, but more

detail was needed for the wake and vortex region. As a result, the measurements were

retaken, but with approximately 1350 data points, concentrating primarily in the wake

and tip leakage vortex. Presented in figure 3.70 are the turbulent kinetic energy (tke)

contours of both sets of measurements superimposed on each other. Plotted on the y-axis

is the height above the lower endwall normalized on the axial chord, and on the x-axis is

the z position normalized on the axial chord as well (see figure 3.1 and section 3 for a

description of the co-ordinate system). The color contours are the results from the first

data run of 670 points, and the contour lines represent the second data run of 1350 points.

The values of the contours are given by the legend for the shaded contours, and labeled

for the contour lines. From this figure, good repeatability can be established since the

two sets of results are very similar to one another. They both show the same structure of

the flow, in terms of regions of high tke, and the shape of the vortex.

The wake also is very similar in form. There is also a good agreement in the

values of tke obtained for these quantities. Given that between the two runs, the position

of the probe was varied, the tip gaps were varied, and the hot-wire sensor was used in

other studies, there are a lot of factors that were changed, and could have affected the

second run, but the two sets of results show that there is good repeatability in the

experimental facility.

3.10 Summary of Results

From these results and observations, there seems to be the presence of two distinct

vortices in the flow. These two vortices are shown in Figure 3.71, which is a sketch of

the flow pattern due to one blade. The figure shows the tip leakage vortex still attached

to the blade near the leading edge, and then by half chord, it moves towards the endwall.

Also shown is a counter-rotating vortex generated by the separation of the flow leaving

the tip gap from the endwall. As the tip-leakage vortex travels downstream, it convects

across the endwall as shown, and “pushes” the counter rotating vortex further into the

passage. This counter rotating vortex has negative vorticity when compared to the tip

leakage vortex, and it is this region of negative vorticity that is seen in the vorticity

contour plots (Figs 3.12-3.16).

40

In the wake, the overall decay is about 90%, as compared to a 70% decay in the

vortex in the mean flow field. However, the distribution of the turbulence stresses in the

vortex changes as it develops downstream, but remains the same, albeit at much lower

levels, for the wake. The tip-leakage vortex is responsible for much of the contribution to

turbulence production. A large percentage of the production is from the region where the

flow is being lifted off the wall, which would result in strong axial velocity gradients.

This could be a source of this turbulence production. Similarly, in the core, there is a

large axial velocity deficit, which could also produce turbulence as a result of these axial

velocity gradients. From spectral measurements, there is no evidence of wandering

motions within the tip-leakage vortex, and there seems to be some evidence of vortex

shedding off of the rounded trailing edge of the blade in the wakes.

Table 3.1 : Uncertainties in the measurements calculated at 20:1 oddsQuantity Uncertainty (20:1 odds)U, V, W ±1% U∞

u2 ±3% u2

v2, w2 ±6% v2 , ±6% w2

uv, vw, uw ±3% ¥�u2v2)tke (k) ±3.5% k

Table 3.2: Boundary Layer Parameters for the Inflowθ/ca δ*/ca

Passage 1 2.37 x 10-2 3.08 x 10-2

Passage 2 1.84 x 10-2 2.30 x 10-2

Passage 3 1.68 x 10-2 2.05 x 10-2

Passage 4 1.66 x 10-2 2.04 x 10-2

Passage 5 1.72 x 10-2 2.13 x 10-2

Passage 6 1.57 x 10-2 2.02 x 10-2

Table 3.3: Apparent Circulation of the corex/ca Apparent Circulation

1.366 0.140 U∞ca

2.062 0.094U∞ca

2.831 0.084 U∞ca

3.77 0.103 U∞ca

4.64 0.121 U∞ca

41

Chapter 4. Conclusions

A linear compressor cascade with tip leakage was designed and built, and the flow

field downstream of the cascade was studied. Oil flow visualizations were performed on

the lower endwall in the vicinity of the tip gap region of the blades. Four sensor hot wire

measurements were taken at five downstream locations, and results in terms of mean

velocities, turbulent quantities, and velocity spectra were obtained to document the flow

field. From these results, the following can be said about the experimental facility and

the corresponding flowfield.

• Due to the pressure difference across the blades, a flow is induced in the tip gap of the

blades, which is seen to be almost perpendicular to the chord line of the blade.

• This tip gap flow rolls up to form the tip leakage vortex, which moves from the

suction side of the passage to the pressure side with downstream distance.

• There is a second vortical structure formed within the passage which has the opposite

vorticity when compared to the tip leakage vortex.

• The tip leakage vortex is much stronger than the secondary tip vortex, and as such

dominates the lower endwall flow region.

• The tip leakage vortex is a source of high turbulence in the flow field. Much of the

turbulence is generated in the region where the flow is being lifted off the lower

endwall.

• Much of the turbulence in the tip-leakage vortex is generated due to axial velocity

gradients in the flow, and not the circulating motion of the vortex.

• Reynolds stress measurements reveal the tip vortex flow region to be highly

anisotropic.

• Velocity spectra in the tip-leakage vortex show the broadband characteristics typical

of such turbulent flows.

• Two point measurements performed by Wenger et al (1998) proved that there was no

wandering of the vortex present to corrupt the turbulence measurements.

• The wakes of the blades exhibit characteristics typical of 2-D plane wakes.

42

• Velocity spectra in the wake region show the same broadband characteristics of such

turbulent flows.

• The wake decays much faster than the vortex, revealing that the vortex becomes the

dominant feature of the flow.

• Velocity spectra suggest that there might be evidence of coherent motions in the wake

as a result of vortex shedding from the trailing edge of the blade.

• Increasing the tip gap increases the strength of the tip leakage vortex, which in turn

influences a much larger region near the lower endwall

• Decreasing the tip gap reduces the strength of the tip leakage vortex to an extent that

would possibly prevent roll up to form a vortex, instead only showing regions of high

shear flows.

• Changing the boundary layer trip had no effect on the flow field due to the fact that

the boundary layers on the blade had separated.

The present study reveals the complex nature of such a flow field. This study is

part of an ongoing investigation of such a flow field. As mentioned earlier, a two-point

measurement study has been done to further understand such flows. A future study is

currently underway where the stationary endwall in this study will be replaced by moving

endwall to simulate rotational effects which would be present in such rotating

turbomachinery. Complementing the experimental aspect of this study is a computational

study being performed on the current cascade. Together, these projects should be able to

provide valuable information that would help in the understanding of such fluid flows.

43

5. References

• Bearman, P.W., “Corrections for the effect of Ambient Temperature Drift on Hot-Wire Measurements in Incompressible Flow”, DISA Information, Vol 11, 1971.

• Bettner, J., L., Elrod C., “The Influence of Tip Clearance, Stage Loading, and WallRoughness on Compressor Casing Boundary Layer Development”, ASME paper 82-GT-153, 1982.

• Bindon, J.P., “The Measurement and Formation of Tip-Clearance Loss”, ASMEJournal of Turbomachinery, Vol. 111,pp. 257-263, 1989.

• Chesnakas, C.J., Dancey, C.L., “Three-Component LDA Measurements in an AxialFlow Compressor”, AIAA Journal of Propulsion and Power, Vol. 6, No. 4,pg. 474-481,1990.

• Crook, A.J., Greitzer, E.M., Tan, C.S., Adamczyx, J.J., “Numerical Simulation ofCompressor Endwall and Casing Treatment Flow Phenomena”, ASME paper 92-GT-300, 1992.

• Devenport, W.J., Wittmer, K.S., Muthanna, C., Bereketab, S., Moore, J., “TurbulenceStructure of a Tip-Leakage Vortex Wake”, AIAA paper 97-0440, 1997.

• DeWitz, M.B., “The Effect of a Fillet on a Wing/Body Junction Flow”, MS Thesis,Dept. of Aerospace and Ocean Engineering, Virginia Tech, 1988.

• Inoue, M., Kuroumaru, M., Fukuhara, M., “Behavious of Tip Leakage Flow Behindan Axial Compressor Rotor”, ASME paper 85-GT-62, 1985.

• Inoue, M., Kuromaru, M., “Structure of Tip Clearance Flow in an Isolated AxialCompressor Rotor”, ASME 88-GT-251, 1988.

• Kang, S., Hirsch, C., “Experimental Study on the Three-Dimensional Flow within aCompressor Cascade with Tip Clearance: Part I-Velocity and Pressure Fields, andPart II-The Tip Leakage Vortex”, ASME Journal of Turbomachinery, Vol. 115,pg.435-443, 1993.

• Kang, S., Hirsch, C., “Tip Leakage Flow in Linear Compressor Cascade”, ASMEJournal of Turbomachinery, Vol. 116, pp. 657-664, 1994.

• Lakshminarayana, B., Ravindranath, A., “Interaction of Compressor Rotor BladeWake with Wall Boundary Layer/Vortex in the End-Wall Region”, ASME paper 82-GT/GR-1, 1981.

• Lakshminarayana, B., Pouagare, M., Davino, R., “Three Dimensional Flow Field inthe Tip Region of a Compressor Rotor Passage-Part II: Turbulence Properties”,ASME paper 82-GT-234, 1982.

44

• Lakshminarayana, B., Murthy, K.S., “Laser Doppler Velocimeter Measurement ofAnnulus Wall Boundary Layer Development in a Compressor Rotor”, ASME paper87-GT-251, 1987.

• Lakshminarayana, B., Zaccaria, M., Marathe, B., “The Structure of Tip ClearanceFlow in Axial Flow Compressors”, ASME Journal of Turbomachinery, Vol.117, pp.336-347, 1995.

• Moore, J., Moore, J.G., Heckel, S.P., Ballesteros, R., “Reynolds Stresses andDissiapation Mecahnisms in a Turbine Tip Leakage Vortex”, ASME paper 94-GT-267, 1994.

• Moore, J.G., Schorn, S.A., Moore, J., “ Methods of Classical Mechanics applied toTurbulence Stresses in a Tip Leakage Vortex”, ASME paper 95-GT-220, 1995.

• Moore, J., Moore, J. G., Liu, B. “CFD Computations to Aid Noise Research, ProgressReport, 2/96 – 10/96”, Virginia Tech, 1996.

• Poensgen, C.A., Gallus, H.E., “Rotating Stall in a Single-Stage Axial FlowCompressor”, ASME Journal of Turbomachinery, Vol. 118, pp. 189-196,1996

• Popovski, P., Lakshminarayana, B., “An Experimental Study of the CompressorRotor Flow Field at Off-Design Condition using Laser Doppler Velocimeter”, ISABE85-7034, Proceedings from International Symposium on Air Breathing Engines, 7th,September 2-6, (A86-11601-02-07) AIAA, 1985.

• Storer, J.A., Cumpsty, N.A., “Tip Leakage Flows in Axial Compressors”, ASMEpaper 90-GT-127,1990

• Wenger, C.W., Devenport, W.J., Wittmer, K.S., Muthanna, C., “Two-pointMeasurements in the Wake of a Compressor Cascade”, AIAA paper 98-2556, 1998.

• Wisler, D., C., “Core Compressor Exit Stage Study, Volume IV – Data andPerformance report for the Best Stage Configuration”, NASA Report # CR-165357,1981.

• Wittmer, K.S., Devenport, W.J., Zsoldos, J.S., “A Four-sensor Hot-Wire ProbeSystem for Three Component Velocity Measurement”, Experiments in Fluids, to bepublished in 1998.

• Wygnanski, I., Champagne, F., and Marasli, B., “On the large-scale Structures inTwo-Dimensional, Small Deficit, Turbulent Wakes”, Journal of Fluid Mechanics,vol.168, pp. 31-71, 1986.

• Yocum, A.M., O’Brien, W.F., “Separated Flow in a Low-Speed Two DimensionalCascade: Part I- Flow Visualization and Time-Mean Velocity Measurements”, ASMEJournal of Turbomachinery, Vol. 115, pp. 409-420, 1993

Figure 1.1: Sketch illustration the flow structures found in a compressor cascadeTip leakage vortices are formed due to roll up of the tip gap flow as itexits tip gap regions. Tip separation vortices are formed due to separationof tip gap flow over the separation bubble in the tip gap region.

tip leakage vortices

tip separation vortices

suction side

pressure side

Inlet flow direction

lower endwall

45

Figure 2.1: Virginia Tech Linear Compressor Cascade

blade row

blade row

Inlet section downstream section

blower expansioncontraction

screens

inlet section downstream section

12”

30”

48”26”44”

31” 48”

95” 73” 36” 86” 70”56”

95” 73” 36” 86” 70”56”

blower expansion screens contraction

Side View

Plan (Top) View

section A-A

46

Figure 2.2 : Computations done on various cascade configurationsThe pressure contours indicate that a 4 passage cascade issufficient to simulate an infinite cascade. (calculations performed by Moore et al, (1996))

47

Figure 2.3 : Plan View of the inlet section and downstreamsection of the compressor cascade(Section A-A as indicated on Figure 2.1)

Inlet Section

Blade 1

U∞

Blade 8

Downstream Section

12.5° turningangle

leading edge of suction slot

aluminum floor section

exit plane with4 screens + tape

adjustable sidewall (tailboards)

adjustable sidewall (tailboards)

fin-form plywood floor

location of pitot staticprobe

contractionexit

Hot wire measurementlocation (Figure 2.5)

Hot wire measurementlocation (Figure 2.17)

section B-B

48

Figure 2.4 : Inlet sidewall and roof configuration

Fin form plywood floor section

Plexiglass roof

Plexiglasssidewalls

legs

Aluminum support flanges for the roof

49

Figure 2.5: Single hot wire measurements taken 12” downstreamof the contraction exit. Shown are contours of meanstreamwise velocity and turbulence intensitynote: legend above figures indicate contour values

0 10 20Widthwis e pos ition (in.)

0

2

4

6

8

10

12

He

igh

tab

ove

end

wa

ll(i

n.)

0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.80 0.81 0.82 0.83 0.84 0.85 0.87 0.88 0.89 0.90 0.92 0.93 0.94 0.96 0.97 0.99 1.00

Contours of mean stream wise velocity Contours of turbulence intensity

0 10 20Widthwis e pos ition (in.)

0

2

4

6

8

10

12

Hei

gh

tab

ove

en

dw

all

(in

.)

9.68E-06

8.13E-06

8.13E-06

8.13E-06

1.15E-05

9.68E-061.37E-05

1.0E-06 2.0E-06 4.0E-06 8.1E-06 1.6E-05 3.3E-05 6.6E-05 1.3E-04 2.7E-04 5.4E-04 1.1E-03 2.2E-03 4.4E-03

50

Figure 2.6 : Figure showing the arrangement of tailboard, andclamps holding the tailboards in place.

Clamp holding sidewall in place

Clamps holding sidewallto blade

Sidewall (plexiglass)

Fin form plywood floor

Adjustableflanges

Blade

51

Figure 2.7 : Sketch illustrating the suction slotarrangement (note: not to scale)(Section B-B as indicated in Fig 2.3)

1”

0.75” fin form plywood floor

0.25” aluminum floor

blade

blade trip

suction slot

adjustable flange

U∞

4” (axially)

tip gap

52

Figure 2.8 : Cross Section of the GE rotor B-section bladeused in the cascade tunnel

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1x/c

-0.1

0

0.1

y/c

53

Figure 2.9 : Illustration of blade support structure, showing how two bladesare supported in the cascade tunnel. This is repeated for all eightblades in the cascade (note:not to scale)

blade 1Blade 2

plexiglass roof

3” aluminum box section

shims used to set tip gap.

1/8th aluminum sheetused to seal blade root.

screws used to zerolean and sweep of blades

screws used to zerolean and sweep of blades

1/8th aluminum sheetused to seal blade root.

frame of tunnel

54

Figure 2.10 : Schematics of the aluminum pressure taps

30/1000”

1/16” copper tubing

Tygon® tubing

1” diameter

2” diameter

Fin form plywood floor

Fin form plywood floor

55

Figure 2.11 : Traverse system

I beam

stepper motors

carriage

56

Figure 2.12 : Four sensor hot wire probe

Probe Prongs(length ~ 40mm)

Ceramic Tubes(length ~ 10mm)

Stainless Steel Casing(length = 63mm, diam. = 4.3mm)

Delrin Block, (length = 50mm,7.9mm square cross-section)

Electrical Leads(length ~ 50mm)

DUPONT BergConType Connector

57

Figure 2.13 : Magnitude response of each sensor of thefour sensor hot wire. The figures show a flatresponse curve, followed by a drop offindicating the response of the hot wire

103 104 105 106

frequency (Hz)

100

101

102

103

104

105

106

107

Ma

gn

itud

e

Wire 2

103 104 105 106

fre quency (Hz)

100

101

102

103

104

105

106

107

Ma

gn

itud

e

Wire 3

103 104 105 106

fre quency (Hz)

100

101

102

103

104

105

106

107

Mag

nitu

de

Wire 4

103 104 105 106

freque ncy (Hz)

100

101

102

103

104

105

106

107

Ma

gn

itud

e

Wire 158

x/ca = 0.870

x/ca = 0.137

x/ca = 3.297

x/ca = 6.593

Figure 2.14 : Coordinate system showing the pressure tap locations used for the cascade set up.

59

Figure 2:15 :Cp variation across downstream section at indicated x/ca locationsDistributions show a constant Cp across the cross section for x/ca = 3.297 and 6.593 implying there is no pressure difference.

-15 -10 -5 0 5z/ca

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

Cp

0.1370.8703.2976.593

60

Figure 2.16 : Boundary layer profiles at taken at the leading edge line at the middle of indicated passages. Profiles showgood similarity in passages 2,3,4, and 5.

61

10-2 10-1 100

log y (in.)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1U

/U∞

pas s age 1pas s age 2pas s age 3pas s age 4pas s age 5pas s age 6

10-2 10-1 100

log y (in)

0.001

0.002

0.003

0.004

0.005

u2/U

2 ∞

pas s age 1pas s age 2pas s age 3pas s age 4pas s age 5pas s age 6

Figure 2.17 : TKE contours downstream of cascade. Contoursshow that the flow structures are similar to one another indicative of the periodicity of the tunnel.

-50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0V3

-8

-6

-4

-2

0

V2

widthwis e pos ition

-8

-6

-4

-2

0

he

igh

tab

ove

low

er

end

wa

ll

1.79E-03 1.79E-031.79E-03 1.79E-03 1.79E-03

6.31E-03 6.31E-036.31E-03 5.58E-03 6.31E-03

62

Blade 3

Blade 4

Blade 5

Blade 6

Fig 3.1: Co-ordinate system used to present measurements

63

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2z/ca

0.2

0.4

0.6y/

c a9.29E-01

9.00E-01

8.94E-01

9.30E-01

9.30E-01

8.89E-01

8.89E-01

9.32E-018.89E-01

9.04E-01

Contours of Mean Streamwise Velocity (U/U∞)

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2z/ca

0.2

0.4

0.6

y/c a

1.00E-05

9.00E-06

8.00E-06

1.00E-05

1.00E-05

1.00E-051.00E-05 1.54E-05

Contours of Normalized Turbulence Intensity (u2/U2∞)

Figure 3.2 : Single hot wire measurements made 2” upstream of the blade row in front of blades 4 and 5.

64

Figure 3.3 : Loading on blade from computational calculationsfrom Moore et al.(1996) revealing the pressure difference on the blade surface. Note: For the compressor cascade, the inlet anglewas 65.1°

65

0 0.05 0.1 0.15 0.2y/ca

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

U/U

∞

S uction S idePres s ure s ide

10-3 10-2 10-1 100

y/ca

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

U/U

∞

S uction S idePres s ure s ide

0 0.05 0.1 0.15 0.2y/ca

00

.00

10

.00

20

.00

30

.00

40

.00

50

.00

6

u2 /U∞

S uction s idePre s sure s ide

Figure 3.4 : Boundary layer profiles made on the pressure sideand suction side of the blade 4.Note: The peak in the u2 profile on the suction sideis indicative of a separated boundary layer.

Fig 3.4a : Mean velocity profile Linear scale

Fig 3.4b : Mean velocity profile Semilog scale on horizontal axis

Fig 3.4c : turbulence intensity profile Linear scale

66

Figure 3.5: Oil Flow visualization on the lower endwall.Dark regions indicate regions of high shear.

Region 1

Region 2

Region 3

Region 1

Region 2Region 3

67

Figure 3.6: Mean streamwise contours, and secondaryflow vectors for x/ca = 1.366

-3.5-3-2.5-2-1.5-1-0.499996z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.45

0.28

0.65

0.45

0.63

0.70

0.58

0.70

0.65

0.58

0.63

0.58

0.62

x/ca = 1.366

Fig 2a

-3.5-3-2.5-2-1.5-1-0.499996z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 1.366

0.5 U/U∞

Fig 2b

68

Figure 3.7: Mean streamwise contours, and secondaryflow vectors for x/ca = 2.062

-4.5-4-3.5-3-2.5-2z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.062

0.5 U/U∞

Fig 3b

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.40

0.70

0.57

0.48

0.520.43

0.58

0.63

0.70

0.65 0.63

0.70

0.57 0.52

x/ca = 2.062

Fig 3a

69

Figure 3.8: Mean streamwise contours, and secondaryflow vectors for x/ca =2.831

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.49

0.53

0.70

0.63

0.62

0.65

0.61

0.61

0.490.49

0.65

x/ca = 2.831

Fig 4a

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.831

0.5 U/U∞

Fig 4b

70

Figure 3.9: Mean streamwise contours, and secondaryflow vectors for x/ca = 3.770

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.55

0.53

0.70

0.700.65

0.55

0.63

0.65

0.580.62

x/ca = 3.770

Fig 5a

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 3.770

0.5 U/U∞

Fig 5b

71

Figure 3.10: Mean streamwise contours, and secondaryflow vectors for x/ca = 4.640

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.58

0.63

0.70

0.64

0.68

0.58

0.60

0.62

x/ca = 4.640

Fig 6a

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 4.640

0.5 U/U∞

Fig 6b

72

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4 5

x/ca

Cor

e D

efic

it/U

�

Figure 3.11: Variation of peak deficit in core of vortexwith downstream distance. Figure revealsa 2.5 fold decay.

73

Figure 3.12: Mean streamwise vorticity contours for x/ca = 1.366

-3.5-3-2.5-2-1.5-1-0.499996z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

-0.20

1.60

1.90

3.40 -1.12

-0.40

-0.20

x/ca = 1.366

Figure 3.13: Mean streamwise vorticity contours for x/ca = 2.062

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.90

-0.30

0.30

-0.20

-0.400.30

-0.50

x/ca = 2.062

74

Figure 3.14: Mean streamwise vorticity contours for x/ca = 2.831

Figure 3.15: Mean streamwise vorticity contours for x/ca = 3.770

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.54

0.18

1.00

-0.20

-0.08

-0.08

-0.08

-0.14

x/ca = 2.831

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.57

0.29

0.14

-0.11

0.14

0.57

0.57

x/ca = 3.770

75

-8

-7

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5

x/ca

z/ca Vortex axis

Wake axis

Figure 3.16: Mean streamwise vorticity contours for x/ca = 4.640

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.59

0.200.15

0.59

0.45

0.30

0.15

x/ca = 4.640

Figure 3.17: Vortex axis position relative to wake axis. Vortexaxis was defined as the locus of peak vorticity.

76

Figure 3.18: Secondary flow vectors for x/ca = 1.366 aligned withvortex axis

-3.5-3-2.5-2-1.5-1-0.499996z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 1.366

0.5 U/U∞

Figure 3.19: Secondary flow vectors for x/ca = 2.062 aligned withvortex axis

-4.5-4-3.5-3-2.5-2z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.062

0.5 U/U∞

77

Figure 3.20: Secondary flow vectors for x/ca = 2.831 aligned withvortex axis

Figure 3.21: Secondary flow vectors for x/ca = 3.770 aligned withvortex axis

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.831

0.5 U/U∞

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 3.770

0.5 U/U∞

78

Figure 3.23: Velocity profiles through core of vortex at variousdownstream positions

Figure 3.22: Secondary flow vectors for x/ca = 4.640 aligned withvortex axis

-7-6-5-4-3-2z/ca

-0.1

-0.05

0

0.05

0.1

0.15

V/U

∞

x/ca=1.366

x/ca=2.062

x/ca=2.831

x/ca=3.770

x/ca=4.640

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 4.640

0.5 U/U∞

79

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 1 2 3 4 5

x/ca

Rad

ius/

ca

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

V/U

inf

Apparent core radius

Peak TangentialVelocity

Figure 3.24: Variation of core size and peak tangential velocitywith downstream distance

Figure 3.25: Mean velocity profiles of the wake at variousdownstream locations

-6-5-4-3-2-1z/ca

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

U/U

∞

1.3662.0622.8313.7704.062

x/ca location

80

0

0.05

0.1

0.15

0.2

0.25

0.3

0 1 2 3 4 5x/ca

Def

icit/

U�

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Hal

fwid

th/c

Deficit

Half width

Figure 3.26: Peak deficit in the wake and half width variation ofthe wake variation with downstram distance

Figure 3.27: Comparison of Mean velocity profiles (Fig a) withstandard wake data from Wygnanski et al(1986) Fig(b).

Fig a Fig b

-6-5-4-3-2-10123456η

-1.5

-1

-0.5

0

(U-U

e)/U

w

1.3662.0622.8313.7704.062

x/ca location

-6-5-4-3-2-10123456η

-1.5

-1

-0.5

0

(U-U

e)/U

w

81

Figure 3.28 : TKE contours for x/ca=1.366

Figure 3.29 : TKE contours for x/ca=2.062

-3.5-3-2.5-2-1.5-1-0.499996z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.10E-02

1.10E-02

5.09E-03

5.79E-04

9.66E-03

8.26E-03

8.26E-03

2.18E-03

8.26E-03

x/ca = 1.366

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.02E-02

6.99E-03

2.74E-03

9.28E-03

8.73E-03

5.96E-03

2.74E-035.09E-03

4.26E-03

x/ca = 2.062

82

Figure 3.30 : TKE contours for x/ca=2.831

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

5.31E-03

6.34E-03

2.63E-03

8.33E-04

2.18E-03

2.63E-03

1.50E-03

x/ca = 2.831

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

4.20E-03

3.29E-03

1.53E-03

2.11E-04

3.43E-03

4.21E-04

1.37E-03

4.21E-04

1.37E-03

1.71E-03

2.24E-03

1.53E-031.71E-03

x/ca = 3.770

Figure 3.31 : TKE contours for x/ca=3.770

83

Figure 3.32 : TKE contours for x/ca=4.640

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

3.26E-03

2.41E-03

2.09E-03

5.26E-04

2.66E-03

2.66E-03

1.22E-03

5.26E-04

5.26E-04

1.00E-031.22E-03

2.98E-03

2.22E-03

x/ca = 4.640

84

Figure 3.33 : Turbulence stress contours for x/ca=1.366

85

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

8.00E-03

7.50E-03

7.00E-03

6.50E-03

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

8.00E-03

7.50E-03

7.00E-03

6.50E-03

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

8.00E-03

7.50E-03

7.00E-03

6.50E-03

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure f : Contours of uwFigure d : Contours of uv Figure e : Contours of vw

Figure 3.34 : Turbulence stress contours for x/ca=2.062

86

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

-4.5-4-3.5-3-2.5-2z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

8.00E-03

7.50E-03

7.00E-03

6.50E-03

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

8.00E-03

7.50E-03

7.00E-03

6.50E-03

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

8.00E-03

7.50E-03

7.00E-03

6.50E-03

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

Figure 3.35 : Turbulence stress contours for x/ca=2.831

87

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5.5-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5.5-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure 3.36 : Turbulence stress contours for x/ca=3.770

88

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

-6-5-4z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

4.00E-03

3.75E-03

3.50E-03

3.25E-03

3.00E-03

2.75E-03

2.50E-03

2.25E-03

2.00E-03

1.75E-03

1.50E-03

1.25E-03

1.00E-03

7.50E-04

5.00E-04

2.50E-04

0.00E+00

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

4.00E-03

3.75E-03

3.50E-03

3.25E-03

3.00E-03

2.75E-03

2.50E-03

2.25E-03

2.00E-03

1.75E-03

1.50E-03

1.25E-03

1.00E-03

7.50E-04

5.00E-04

2.50E-04

0.00E+00

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

4.00E-03

3.75E-03

3.50E-03

3.25E-03

3.00E-03

2.75E-03

2.50E-03

2.25E-03

2.00E-03

1.75E-03

1.50E-03

1.25E-03

1.00E-03

7.50E-04

5.00E-04

2.50E-04

0.00E+00

-6.5-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

1.00E-03

9.00E-04

8.00E-04

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

-2.00E-04

-3.00E-04

-4.00E-04

-5.00E-04

-6.00E-04

-7.00E-04

-8.00E-04

-9.00E-04

-1.00E-03

-1.10E-03

-1.20E-03

-1.30E-03

-1.40E-03

-1.50E-03

-6.5-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

1.00E-03

9.00E-04

8.00E-04

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

-2.00E-04

-3.00E-04

-4.00E-04

-5.00E-04

-6.00E-04

-7.00E-04

-8.00E-04

-9.00E-04

-1.00E-03

-1.10E-03

-1.20E-03

-1.30E-03

-1.40E-03

-1.50E-03

-6.5-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

1.00E-03

9.00E-04

8.00E-04

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

-2.00E-04

-3.00E-04

-4.00E-04

-5.00E-04

-6.00E-04

-7.00E-04

-8.00E-04

-9.00E-04

-1.00E-03

-1.10E-03

-1.20E-03

-1.30E-03

-1.40E-03

-1.50E-03

Figure 3.37 : Turbulence stress contours for x/ca=4.640

89

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

-7-6-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

4.00E-03

3.75E-03

3.50E-03

3.25E-03

3.00E-03

2.75E-03

2.50E-03

2.25E-03

2.00E-03

1.75E-03

1.50E-03

1.25E-03

1.00E-03

7.50E-04

5.00E-04

2.50E-04

0.00E+00

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

4.00E-03

3.75E-03

3.50E-03

3.25E-03

3.00E-03

2.75E-03

2.50E-03

2.25E-03

2.00E-03

1.75E-03

1.50E-03

1.25E-03

1.00E-03

7.50E-04

5.00E-04

2.50E-04

0.00E+00

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

4.00E-03

3.75E-03

3.50E-03

3.25E-03

3.00E-03

2.75E-03

2.50E-03

2.25E-03

2.00E-03

1.75E-03

1.50E-03

1.25E-03

1.00E-03

7.50E-04

5.00E-04

2.50E-04

0.00E+00

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

1.00E-03

9.00E-04

8.00E-04

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

-2.00E-04

-3.00E-04

-4.00E-04

-5.00E-04

-6.00E-04

-7.00E-04

-8.00E-04

-9.00E-04

-1.00E-03

-1.10E-03

-1.20E-03

-1.30E-03

-1.40E-03

-1.50E-03

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

1.00E-03

9.00E-04

8.00E-04

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

-2.00E-04

-3.00E-04

-4.00E-04

-5.00E-04

-6.00E-04

-7.00E-04

-8.00E-04

-9.00E-04

-1.00E-03

-1.10E-03

-1.20E-03

-1.30E-03

-1.40E-03

-1.50E-03

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

1.00E-03

9.00E-04

8.00E-04

7.00E-04

6.00E-04

5.00E-04

4.00E-04

3.00E-04

2.00E-04

1.00E-04

0.00E+00

-1.00E-04

-2.00E-04

-3.00E-04

-4.00E-04

-5.00E-04

-6.00E-04

-7.00E-04

-8.00E-04

-9.00E-04

-1.00E-03

-1.10E-03

-1.20E-03

-1.30E-03

-1.40E-03

-1.50E-03

Figure 3.38 : TKE production contours for x/ca=1.366

Figure 3.39 : TKE production contours for x/ca=2.062

-3.5-3-2.5-2-1.5-1-0.499996z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.07E-02

5.03E-03

2.57E-035.00E-04

3.67E-03

3.67E-03

5.00E-04

6.62E-03

5.03E-03

x/ca = 1.366

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

5.03E-03

3.78E-03

3.78E-03

5.00E-04

1.25E-041.25E-04

7.50E-04

x/ca = 2.062

90

Figure 3.40 : TKE production contours for x/ca=2.831

Figure 3.41 : TKE production contours for x/ca=3.770

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

7.50E-047.55E-05

1.74E-03

7.50E-04

7.55E-05 7.55E-05

1.14E-03 1.53E-03

x/ca = 2.831

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

4.42E-05

7.50E-04

1.25E-04

4.48E-04

7.50E-04

1.25E-04

1.25E-04

7.50E-04

4.42E-056.05E-04

x/ca = 3.770

91

Figure 3.42 : TKE production contours for x/ca=4.640

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

9.23E-06

3.04E-04

3.24E-04

4.22E-05

9.23E-06

2.10E-04

4.22E-05

3.24E-04

3.24E-04

7.50E-042.56E-04

3.24E-04

4.22E-05

9.23E-06

x/ca = 4.640

92

Figure 3.43 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=1.366

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.08E-02

8.77E-03

5.03E-03

5.03E-03

6.22E-03

1.05E-03

1.05E-03

x/ca = 1.366

Streamwise contributions

-3.5-3-2.5-2-1.5-1z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

6.22E-03

1.05E-03

4.11E-03

1.05E-03

1.91E-03

x/ca = 1.366

Crossflow contributions

93

Figure 3.44 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=2.062

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

2.57E-031.80E-03

2.45E-04

2.45E-04

x/ca = 2.062

Crossflow contributions

-4.5-4-3.5-3-2.5-2-1.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

3.63E-03

3.63E-03

6.73E-04

8.77E-03

6.73E-04

6.73E-04

x/ca = 2.062

Streamwise contributions

94

Figure 3.45 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=2.831

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

6.85E-046.85E-04

1.74E-04

1.74E-041.74E-04

5.67E-04

x/ca = 2.831

Crossflow contributions

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4y/

c a

1.63E-03

1.63E-03

9.32E-04

1.05E-031.44E-03

x/ca = 2.831

Streamwise contributions

95

Figure 3.46 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=3.770

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.07E-04

1.46E-04

1.07E-04

1.30E-042.19E-04

1.07E-041.30E-04

x/ca = 3.770

Crossflow contributions

-6-5.5-5-4.5-4-3.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

7.72E-04

4.11E-04

6.94E-04

6.94E-04

4.11E-043.67E-04

4.54E-04

4.11E-04

x/ca = 3.770

Streamwise contributions96

Figure 3.47 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=4.640

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

-1.06E-04

-9.04E-05 -1.06E-04-9.04E-05

x/ca = 4.640

Crossflow contributions

-7.5-7-6.5-6-5.5-5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.61E-04

3.96E-04

7.42E-04

2.97E-04

2.97E-04

5.18E-04

1.61E-04

1.61E-041.61E-04

x/ca = 4.640

Streamwise contributions97

Figure 3.48: Comparison of turbulent normal stress (u2) profiles (Fig a)with standard wake data from Wygnanski et al(1986) Fig(b).note: horizontal axis are not to same scale.

Figure 3.49: Comparison of turbulent normal stress (uw) profiles (Fig a)with standard wake data from Wygnanski et al(1986) Fig(b).note: horizontal axis are not to same scale.

-6-5-4-3-2-10123456η

0.0

00

.03

0.0

50

.07

0.1

00

.13

0.1

50

.18

0.2

0

u2 /Uw2

1.3662.0622.8313.7704.062

x/ca location

-6-5-4-3-2-10123456η

0.0

00

.03

0.0

50

.07

0.1

00

.13

0.1

50

.18

0.2

0

u2 /Uw2

-6-5-4-3-2-10123456η

-0.0

50

.00

0.0

50

.10

uw/U

w2

1.3662.0622.8313.7704.062

x/ca location

-6-5-4-3-2-10123456η

-0.0

50

.00

0.0

50

.10

uw/U

w2

Fig a

Fig a

Fig b

Fig b

98

Figure 3.50 : Autospectra for u velocity component

100 101 102 103

f c/Uref

10

-91

0-8

10

-71

0-6

10

-51

0-4

10

-31

0-2

Guu

/(U

ref

c)

2.0622.8313.7704.640

Take n through the vorte x ce nte r

100 101 102 103

f c/Uref

10

-91

0-8

10

-71

0-6

10

-51

0-4

10

-31

0-2

Guu

/(U

ref

c)

1.3662.0622.8313.7704.640

Take n through the wake ce nte r

-5/3-5/3

99

Figure 3.51 : Autospectra for v velocity component

100 101 102 103

f c/Uref

10

-91

0-8

10

-71

0-6

10

-51

0-4

10

-31

0-2

Gw

w/(

Ure

fc)

2.0622.8313.7704.640

Take n through the vortex ce nte r

100 101 102 103

f c/Uref

10

-91

0-8

10

-71

0-6

10

-51

0-4

10

-31

0-2

Gvv

/(U

ref

c)

1.3662.0622.8313.7704.640

Taken through the wake ce nter

-5/3

-5/3

100

Figure 3.52 : Autospectra for w velocity componentNote: Peak in the wake is indicative of coherentmotion such as vortex shedding from trailing edge

100 101 102 103

f c/Uref

10

-91

0-8

10

-71

0-6

10

-51

0-4

10

-31

0-2

Gw

w/(

Ure

fc)

1.3662.0622.8313.7704.640

Take n through the wake ce nte r

100 101 102 103

f c/Uref

10

-91

0-8

10

-71

0-6

10

-51

0-4

10

-31

0-2

Gw

w/(

Ure

fc)

2.0622.8313.7704.640

Take n through the vorte x ce nte r

-5/3

-5/3

101

Figure 3.53: Mean streamwise contours, and secondaryflow vectors for x/ca =2.831 w/ double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.831Double tip gap

0.5 U/U∞

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.72

0.70

0.65 0.46

0.50

0.53

0.58

0.46 0.50

0.58

0.630.62

x/ca = 2.831Double tip gap

102

Figure 3.54: Mean streamwise contours, and secondaryflow vectors for x/ca =2.831 w/ half tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.61

0.52

0.50

0.68

0.62

0.70

0.68

0.63

0.62

0.68

x/ca = 2.831Half tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.831Half tip gap

0.5 U/U∞

103

Figure 3.55: Mean streamwise vorticity contours for x/ca = 2.831 w/ double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.47 1.26

0.54

-0.40

-0.20

0.40

-0.14

-0.14

x/ca = 2.831Double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

-0.14

-0.14

-0.30 0.69

-0.26

0.30

-0.08

x/ca = 2.831Half tip gap

Figure 3.56: Mean streamwise vorticity contours for x/ca = 2.831 w/ half tip gap

104

Figure 3.57: Secondary flow vectors for x/ca = 2.831 aligned withvortex axis w/ double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.831Double tip gap

0.5 U/U∞

Figure 3.58: Secondary flow vectors for x/ca = 2.831 aligned withvortex axis w/ half tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

x/ca = 2.831Half tip gap

0.5 U/U∞

105

Figure 3.60 : TKE contours for x/ca=2.831 w/ half tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

8.33E-04

4.74E-03

6.34E-03

6.06E-03

5.66E-03

2.18E-03

5.31E-032.18E-03

5.31E-03

x/ca = 2.831Half tip gap

Figure 3.59 : TKE contours for x/ca=2.831 w/ double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

2.175E-03

2.175E-03

7.496E-036.061E-03

5.660E-03

6.336E-03

6.685E-03

7.496E-03

6.912E-03

5.660E-03

5.314E-03

8.333E-04

x/ca = 2.831Double tip gap

106

Figure 3.61 : Turbulence stress contours for x/ca=2.831 w/ double tip gap

107

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure 3.62 : Turbulence stress contours for x/ca=2.831 w/ half tip gap

108

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure 3.63 : TKE production contours for x/ca=2.831 w/ double tip gap

Figure 3.64 : TKE production contours for x/ca=2.831 w/ half tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5-2.25z/ca

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

7.55E-051.14E-03

1.53E-03

5.00E-04

7.50E-04

2.76E-04

3.42E-04

7.55E-05

5.00E-04

x/ca = 2.831Half tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

2.034E-03

3.174E-031.826E-04

2.034E-03

3.419E-04

1.143E-033.174E-03

3.419E-04

7.550E-057.550E-05

7.550E-05

7.550E-05

x/ca = 2.831Double tip gap

109

Figure 3.65 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=2.831 w/double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

4.83E-05

2.12E-04

1.05E-03

1.58E-04

1.58E-041.58E-04

x/ca = 2.831

Crossflow contributions

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4y/

c a

2.57E-03

1.05E-03

7.14E-041.63E-03 1.63E-03 1.05E-03

1.05E-03

x/ca = 2.831

Streamwise contributions

110

Figure 3.66 : Streamwise and Crossflow contributions to TKEproduction contours for x/ca=2.831 w/double tip gap

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.63E-03

2.57E-03

7.14E-047.14E-04

x/ca = 2.831

Streamwise contributions

-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

5.67E-043.10E-04

-1.77E-043.10E-04-1.77E-04

x/ca = 2.831

Crossflow contributions

111

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

0.49

0.53

0.70

0.63

0.62

0.65

0.61

0.62

0.500.50

0.65

x/ca = 2.831

-5.5-5.25-5-4.75-4.5-4.25-4-3.75-3.5-3.25-3-2.75-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

5.31E-03

6.34E-03

2.63E-03

8.33E-04

2.18E-03

2.63E-03

8.33E-04

x/ca = 2.831

Figure 3.67: Mean streamwise velocity contoursfor x/ca =2.831 w/ double trip strip

Figure 3.68: Mean turbulence kinetic energy contoursfor x/ca =2.831 w/ double trip strip

112

Figure 3.69 : Turbulence stress contours for x/ca=2.831 w/ double tripstrip

113

Figure c : Contours of w2Figure a : Contours of u2Figure b : Contours of v2

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6y/

c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

6.00E-03

5.50E-03

5.00E-03

4.50E-03

4.00E-03

3.50E-03

3.00E-03

2.50E-03

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.5-5-4.5-4-3.5-3z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

-5.5-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure d : Contours of uv Figure e : Contours of vw Figure f : Contours of uw

-5.5-5-4.5-4-3.5-3-2.5z/ca

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

y/c a

2.00E-03

1.50E-03

1.00E-03

5.00E-04

0.00E+00

-5.00E-04

-1.00E-03

-1.50E-03

-2.00E-03

-2.50E-03

-3.00E-03

Figure 3.70 : TKE contours at x/ca=2.062 highlighting repeatability of the facilityColor contours were taken first, and contour lines were taken aftervarying tip gap heights and blade boundary layer trips.

9.18E-03

1.00E-029.18E-03

9.25E-04

3.40E-03

2.16E-03

4.64E-03

5.13E-04

1.00E-02

2.58E-03

-4-3.5-3-2.5-2z/ca

0.2

0.4

0.6

0.8

1

1.2

1.4

y/c a

1.0E-02

9.6E-03

9.2E-03

8.8E-03

8.3E-03

7.9E-03

7.5E-03

7.1E-03

6.7E-03

6.3E-03

5.9E-03

5.5E-03

5.0E-03

4.6E-03

4.2E-03

3.8E-03

3.4E-03

3.0E-03

2.6E-03

2.2E-03

1.8E-03

1.3E-03

9.3E-04

5.1E-04

1.0E-04

k / U 2∞

114

blade

tip gap

tip leakage vortex

counter-rotating vortexgenerated by separation offlow laving tip gap from endwall

Inflow

blade

tip gap

blade

region near leading edgeof blade

region at about half chordof blade

Figure 3.71 : Sketch illustrating flow pattern observed in the linear compresor cascade. Shown are the tip leakage vortex anda counter rotating vortex. The tip leakage vortex is seen toconvect across the lower endwall pushing the counterrotating vortex with it.

115