Nov 20, 1998 - perpendicular to the camber line of the blade, and this tip gap flow rolls up to form the tip ..... 100) was manufactured by the Auspex corporation.
Flowfield Downstream of a Compressor Cascade with Tip Leakage Chittiappa Muthanna
Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of
Masters of Science in Aerospace Engineering
William J. Devenport, Chair Roger L. Simpson Saad A. Ragab
November 20, 1998 Blacksburg, Virginia
Keywords : Compressor, Cascade, Flowfield, Turbulence
Copyright 1998, Chittiappa Muthanna
Flowfield Downstream of a Compressor Cascade with Tip Leakage Chittiappa Muthanna (ABSTRACT) An 8 blade, 7 passage linear compressor cascade with tip leakage was built. The flowfield downstream of the cascade was measured using four sensor hot-wire anemometers, from which the mean velocity field , the turbulence stress field and velocity spectra were obtained. Oil flow visualizations were done on the endwall underneath the blade row. Also studied were the effects of tip gap height, and blade boundary layer trip variations. The results revealed the presence of two distinct vortical structures in the flow. The tip leakage vortex is formed due to the roll up the tip flow as it exits the tip gap region. A second vortex, counter-rotating when compared to the tip leakage vortex, is formed due to the separation of the flow leaving the tip gap from the endwall. 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 the fact that boundary layers on the blade surface had separated. As the vortices develop downstream, the tip leakage vortex convects into the passage “pushing” the counter rotating vortex with it. As it does so, the tip leakage vortex dominates the endwall flow region, and is responsible for most of the turbulence present in the downstream flow field. This turbulence production is primarily due to axial 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 characteristics typical of such turbulent flows. The results also revealed that the wakes of the blades exhibit characteristics of two-dimensional plane wakes. The wake decays much faster than the vortex. Velocity spectra taken in the wake region show the broadband characteristics of such turbulent flows, and also suggest that there might be some coherent motion in the wake as a result of vortex shedding from the trailing edge of the blades. The present study reveals the complex nature of such flows, and should provide valuable information in helping to understand them. This study was made possible with support from NASA Langley through grant number 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.
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
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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
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Chapter 1. Introduction The 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.
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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.
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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.
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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-4100) 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 buckand-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 x/c y/c 0.000000 0.000000 0.000435 0.000596 0.001413 0.001047 0.002926 0.001323 0.004966 0.001388 0.007524 0.001209 0.010599 0.000777 0.014200 0.000137 0.019048 -0.000748 0.029117 -0.002550 0.039178 -0.004300 0.049233 -0.006001 0.096961 -0.013419 0.144562 -0.019783 0.192059 -0.025156 0.239468 -0.029599 0.286809 -0.033171 0.334100 -0.035929 0.381356 -0.037929 0.428588 -0.039220 0.475794 -0.039826 0.522983 -0.039750 0.570167 -0.038991 0.617353 -0.037568 0.664516 -0.035603 0.711679 -0.032997 0.758887 -0.029596 0.806192 -0.025241 0.853654 -0.019769 0.901342 -0.013007 0.949328 -0.004778 0.959464 -0.002843 0.969617 -0.000834 0.979787 0.001253 0.989977 0.003419 0.993047 0.004088 0.997043 0.003561 1.000000 0.000000
Upper surface x/c y/c 0.000000 0.000000 0.000060 -0.001491 0.000923 -0.003169 0.002598 -0.005009 0.005091 -0.006975 0.008414 -0.009021 0.012579 -0.011102 0.017595 -0.013180 0.023465 -0.015238 0.030187 -0.017291 0.037745 -0.019400 0.045855 -0.021590 0.093151 -0.033478 0.140592 -0.043940 0.188155 -0.053027 0.235822 -0.060789 0.283572 -0.067278 0.331389 -0.072544 0.379254 -0.076640 0.427156 -0.079613 0.475098 -0.081487 0.523069 -0.082262 0.571058 -0.081938 0.619059 -0.080492 0.667097 -0.077670 0.715151 -0.073277 0.763179 -0.067158 0.811130 -0.059163 0.858947 -0.049143 0.906564 -0.036954 0.953911 -0.022461 0.963827 -0.019107 0.973727 -0.015645 0.983610 -0.012072 0.993477 -0.008389 0.996438 -0.007260 0.999467 -0.004667 1.000000 0.000000
20
Blade 1 2 3 4 5 6 7 8
Table 2 : Measured tip gap heights (inches) Leading Edge Mid Chord Trailing edge 0.157 0.157 0.157 0.148 0.152 0.153 0.148 0.152 0.157 0.148 0.152 0.154 0.147 0.151 0.163 0.147 0.154 0.164 0.147 0.155 0.164 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 tipgap 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 1 2
(u + v + w ) 2
2
2
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;
−u
2
2 ∂V ∂U − −v ∂x1 ∂y1
2
−w
∂W − ∂z1 uv
∂U ∂V − vw + ∂y1 ∂x1
∂V ∂W + ∂z1 ∂y1
− uw
∂U ∂W + ∂z1 ∂x1
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 crossflow 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 odds Quantity Uncertainty (20:1 odds) U, V, W ±1% U∞ 2 u ±3% u2 2 2 v ,w ±6% v2 , ±6% w2 uv, vw, uw ±3% ¥ u2v2) tke (k) ±3.5% k Table 3.2: Boundary Layer Parameters for the Inflow θ/ca δ*/ca Passage 1 2.37 x 10-2 3.08 x 10-2 -2 Passage 2 1.84 x 10 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 -2 Passage 5 1.72 x 10 2.13 x 10-2 Passage 6 1.57 x 10-2 2.02 x 10-2 Table 3.3: Apparent Circulation of the core x/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 HotWire Measurements in Incompressible Flow”, DISA Information, Vol 11, 1971.
•
Bettner, J., L., Elrod C., “The Influence of Tip Clearance, Stage Loading, and Wall Roughness on Compressor Casing Boundary Layer Development”, ASME paper 82GT-153, 1982.
•
Bindon, J.P., “The Measurement and Formation of Tip-Clearance Loss”, ASME Journal of Turbomachinery, Vol. 111,pp. 257-263, 1989.
•
Chesnakas, C.J., Dancey, C.L., “Three-Component LDA Measurements in an Axial Flow Compressor”, AIAA Journal of Propulsion and Power, Vol. 6, No. 4,pg. 474481,1990.
•
Crook, A.J., Greitzer, E.M., Tan, C.S., Adamczyx, J.J., “Numerical Simulation of Compressor Endwall and Casing Treatment Flow Phenomena”, ASME paper 92-GT300, 1992.
•
Devenport, W.J., Wittmer, K.S., Muthanna, C., Bereketab, S., Moore, J., “Turbulence Structure 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 Behind an Axial Compressor Rotor”, ASME paper 85-GT-62, 1985.
•
Inoue, M., Kuromaru, M., “Structure of Tip Clearance Flow in an Isolated Axial Compressor Rotor”, ASME 88-GT-251, 1988.
•
Kang, S., Hirsch, C., “Experimental Study on the Three-Dimensional Flow within a Compressor Cascade with Tip Clearance: Part I-Velocity and Pressure Fields, and Part 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”, ASME Journal of Turbomachinery, Vol. 116, pp. 657-664, 1994.
•
Lakshminarayana, B., Ravindranath, A., “Interaction of Compressor Rotor Blade Wake with Wall Boundary Layer/Vortex in the End-Wall Region”, ASME paper 82GT/GR-1, 1981.
•
Lakshminarayana, B., Pouagare, M., Davino, R., “Three Dimensional Flow Field in the 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 of Annulus Wall Boundary Layer Development in a Compressor Rotor”, ASME paper 87-GT-251, 1987.
•
Lakshminarayana, B., Zaccaria, M., Marathe, B., “The Structure of Tip Clearance Flow 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 and Dissiapation Mecahnisms in a Turbine Tip Leakage Vortex”, ASME paper 94-GT267, 1994.
•
Moore, J.G., Schorn, S.A., Moore, J., “ Methods of Classical Mechanics applied to Turbulence 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, Progress Report, 2/96 – 10/96”, Virginia Tech, 1996.
•
Poensgen, C.A., Gallus, H.E., “Rotating Stall in a Single-Stage Axial Flow Compressor”, ASME Journal of Turbomachinery, Vol. 118, pp. 189-196,1996
•
Popovski, P., Lakshminarayana, B., “An Experimental Study of the Compressor Rotor Flow Field at Off-Design Condition using Laser Doppler Velocimeter”, ISABE 85-7034, 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”, ASME paper 90-GT-127,1990
•
Wenger, C.W., Devenport, W.J., Wittmer, K.S., Muthanna, C., “Two-point Measurements in the Wake of a Compressor Cascade”, AIAA paper 98-2556, 1998.
•
Wisler, D., C., “Core Compressor Exit Stage Study, Volume IV – Data and Performance 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 Probe System for Three Component Velocity Measurement”, Experiments in Fluids, to be published in 1998.
•
Wygnanski, I., Champagne, F., and Marasli, B., “On the large-scale Structures in Two-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 Dimensional Cascade: Part I- Flow Visualization and Time-Mean Velocity Measurements”, ASME Journal of Turbomachinery, Vol. 115, pp. 409-420, 1993
45 Inlet flow direction
pressure side
suction side
tip separation vortices lower endwall
tip leakage vortices
Figure 1.1: Sketch illustration the flow structures found in a compressor cascade Tip leakage vortices are formed due to roll up of the tip gap flow as it exits tip gap regions. Tip separation vortices are formed due to separation of tip gap flow over the separation bubble in the tip gap region.
46 screens contraction blower
expansion
inlet section
downstream section
blade row 44”
48”
26”
section A-A
12” 56”
95”
73”
36”
86”
70”
36”
86”
70”
Side View
56”
95”
73”
48”
31”
blower
expansion
screens
30”
contraction
blade row
Inlet section
Plan (Top) View Figure 2.1: Virginia Tech Linear Compressor Cascade
downstream section
47
Figure 2.2 : Computations done on various cascade configurations The pressure contours indicate that a 4 passage cascade is sufficient to simulate an infinite cascade. (calculations performed by Moore et al, (1996))
48
leading edge of suction slot
location of pitot static probe Inlet Section
Blade 8
Hot wire measurement location (Figure 2.17) adjustable sidewall (tailboards)
section B-B
U∞
contraction exit
12.5° turning angle Downstream Section exit plane with 4 screens + tape
Hot wire measurement location (Figure 2.5) Blade 1
aluminum floor section fin-form plywood floor adjustable sidewall (tailboards)
Figure 2.3 : Plan View of the inlet section and downstream section of the compressor cascade (Section A-A as indicated on Figure 2.1)
49
Aluminum support flanges for the roof
Plexiglass roof
Plexiglass sidewalls
legs Fin form plywood floor section
Figure 2.4 : Inlet sidewall and roof configuration
50
12
10
10 He ig ht abo ve e ndwall (in.)
He ight abo ve e ndwall (in.)
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
12
8 6 4 2 0
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
1.37E-05
8
9.68E-06
9.68E-06
8.13E-06
6 8.13E-06
8.13E-06
4 1.15E-05
2
0
10
20 Widthwis e pos ition (in.)
Contours of mean stream wise velocity
0
0
10
20 Widthwis e po s ition (in.)
Contours of turbulence intensity
Figure 2.5: Single hot wire measurements taken 12” downstream of the contraction exit. Shown are contours of mean streamwise velocity and turbulence intensity note: legend above figures indicate contour values
51
Blade Sidewall (plexiglass)
Clamps holding sidewall to blade
Adjustable flanges Clamp holding sidewall in place
Fin form plywood floor
Figure 2.6 : Figure showing the arrangement of tailboard, and clamps holding the tailboards in place.
52
U∞
blade
4” (axially) blade trip
tip gap
0.25” aluminum floor
1”
0.75” fin form plywood floor
suction slot
adjustable flange
Figure 2.7 : Sketch illustrating the suction slot arrangement (note: not to scale) (Section B-B as indicated in Fig 2.3)
53
0.1
y/c
0 -0.1
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
x/c
Figure 2.8 : Cross Section of the GE rotor B-section blade used in the cascade tunnel
1
1.1
54 screws used to zero lean and sweep of blades
3” aluminum box section
screws used to zero lean and sweep of blades shims used to set tip gap.
frame of tunnel
1/8th aluminum sheet used to seal blade root.
1/8th aluminum sheet used to seal blade root.
plexiglass roof
Blade 2
blade 1
Figure 2.9 : Illustration of blade support structure, showing how two blades are supported in the cascade tunnel. This is repeated for all eight blades in the cascade (note:not to scale)
55 30/1000”
Fin form plywood floor 1” diameter
Fin form plywood floor
2” diameter
1/16” copper tubing
Tygon® tubing
Figure 2.10 : Schematics of the aluminum pressure taps
56
stepper motors
I beam
carriage
Figure 2.11 : Traverse system
57
Delrin Block, (length = 50mm, 7.9mm square cross-section)
Ceramic Tubes (length ~ 10mm)
Probe Prongs (length ~ 40mm)
Stainless Steel Casing (length = 63mm, diam. = 4.3mm)
Figure 2.12 : Four sensor hot wire probe
DUPONT BergCon Type Connector
Electrical Leads (length ~ 50mm)
10
7
10
6
10
5
10
4
10
3
1
10
0
10
10
7
10
6
10 5
10 2 10
3
10
4
10
5
10
6
10 4 10 3 10
2
10
1
10
0
fre que ncy (Hz)
10 3
10 4
10 6
10 6
10 5
10 5
Magnitude
Magnitude
10 7
10
4
10
3
10
2
10 2
10 1
10 1
10 4
10 5
fre que ncy (Hz)
10 6
Wire 4
7
10 0 10 3
10 5
fre que ncy (Hz)
Wire 3 10
58
Wire 2
Magnitude
Magnitude
Wire 1
10 6
10
4
10
3
10 0 3 10
10
4
10
5
fre que ncy (Hz)
Figure 2.13 : Magnitude response of each sensor of the four sensor hot wire. The figures show a flat response curve, followed by a drop off indicating the response of the hot wire
10
6
59
x/ca = 0.137 x/ca = 0.870
x/ca = 3.297
x/ca = 6.593
Figure 2.14 : Coordinate system showing the pressure tap locations used for the cascade set up.
60
0.5 0.4 0.3
Cp
0.2 0.1 0
0.137 0.870 3.297 6.593
-0.1 -0.2 -0.3 -15
-10
-5
0
5
z/ca Figure 2:15 :Cp variation across downstream section at indicated x/ca locations Distributions show a constant Cp across the cross section for x/ca = 3.297 and 6.593 implying there is no pressure difference.
61 0.005
1 0.9
pas s ag e pas s ag e pas s ag e pas s ag e pas s ag e pas s ag e
0.004
0.8 0.7
0.5
pas s ag e pas s ag e pas s ag e pas s ag e pas s ag e pas s ag e
0.4 0.3
1 2 3 4 5 6
u 2 /U 2∞
0.003
0.6
U/U ∞
1 2 3 4 5 6
0.002
0.2
0.001
0.1 0
10
-2
10
-1
log y (in.)
10
0
10
-2
10
-1
log y (in)
Figure 2.16 : Boundary layer profiles at taken at the leading edge line at the middle of indicated passages. Profiles show good similarity in passages 2,3,4, and 5.
10
0
V2
he ight above lo we r e ndwall
62
-8 -6
1.79E-03
1.79E-03
1.79E-03
1.79E-03
1.79E-03
-4 -2
6.31E-03 6.31E-03
0
-50
-45
-40
5.58E-03
6.31E-03
-35
-30
-25
-20
-15
V3
widthwis e pos itio n
Figure 2.17 : TKE contours downstream of cascade. Contours show that the flow structures are similar to one another indicative of the periodicity of the tunnel.
6.31E-03
-10
-5
0
63
Blade 6
Blade 5
Blade 4
Blade 3
Fig 3.1: Co-ordinate system used to present measurements
64
Contours of Mean Streamwise Velocity (U/U ∞)
0.6
8.94E-01 8.89E-01
9.30E-01
y/ca
9.29E-01 9.00E-01
0.4
8.89E-01 9.30E-01
0.2 9.04E-01
-1.2
-1
-0.8
-0.6
9.32E-01
-0.4
-0.2
0 z/ca
0.2
0.4
8.89E-01
0.6
0.8
1
1.2
1
1.2
Contours of Normalized Turbulence Intensity (u2/U 2∞)
0.6
8.00E-06 1.00E-05
y/ca
9.00E-06 1.00E-05
0.4 1.00E-05
0.2
-1.2
1.00E-05
-1
-0.8
1.54E-05
-0.6
-0.4
-0.2
0 z/ca
1.00E-05
0.2
0.4
0.6
0.8
Figure 3.2 : Single hot wire measurements made 2” upstream of the blade row in front of blades 4 and 5.
65
Figure 3.3 : Loading on blade from computational calculations from Moore et al.(1996) revealing the pressure difference on the blade surface. Note: For the compressor cascade, the inlet angle was 65.1°
66
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.3
0.2
0.2
0.1
0.1
0.005 0.004 0.002
0.3
S uction s ide Pre s s ure s ide
0.003
0.4
2
S uction S ide Pre s s ure s ide
u /U ∞
0.4
U/U ∞
U/U ∞
0.006
0.8
0
0.05
0.1 y/ca
0.15
0.2
0 10 -3
0.001 0
0
S uctio n S ide P re s s ure s ide
10 -2
10 -1
10 0
y/ca
Fig 3.4a : Mean velocity profile Linear scale
Fig 3.4b : Mean velocity profile Semilog scale on horizontal axis
Figure 3.4 : Boundary layer profiles made on the pressure side and suction side of the blade 4. Note: The peak in the u2 profile on the suction side is indicative of a separated boundary layer.
0
0.05
0.1 y/ca
0.15
0.2
Fig 3.4c : turbulence intensity profile Linear scale
67
Region 3
Region 2 Region 1
Region 2 Region 3
Region 1
Figure 3.5:
Oil Flow visualization on the lower endwall. Dark regions indicate regions of high shear.
68
Fig 2a 1.4
x/ca = 1.366 1.2
0.45
1
y/ca
0.65
0.8
0.63 0.70
0.6 0.58 0.70
0.4
0.65 0.58
0.2
0.45 0.62
0.58
0.28
0.63
0 -0.499996
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Fig 2b 1.4
x/ca = 1.366 1.2
y/ca
1
0.5 U/U∞
0.8
0.6
0.4
0.2
0 -0.499996
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.6: Mean streamwise contours, and secondary flow vectors for x/ca = 1.366
69 Fig 3a 1.4
x/ca = 2.062 1.2
1
y/ca
0.58
0.8 0.63 0.70
0.6
0.70
0.4
0.57 0.48 0.70
0.2 0.65
0 -1.5
0.40
0.63
0.43 0.52
0.57
-2
-2.5
0.52
-3
-3.5
-4
-4.5
z/ca
Fig 3b 1.4
x/ca = 2.062 1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0
-2
-2.5
-3
-3.5
-4
-4.5
z/ca
Figure 3.7: Mean streamwise contours, and secondary flow vectors for x/ca = 2.062
70 Fig 4a 1.4
x/ca = 2.831 1.2
y/ca
1
0.61
0.8
0.6
0.62
0.70
0.65
0.63 0.65
0.4
0.53
0.2
0.49
0.61
0.49
0.49
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Fig 4b 1.4
x/ca = 2.831 1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.8: Mean streamwise contours, and secondary flow vectors for x/ca =2.831
71 Fig 5a 1.4
x/ca = 3.770 1.2
1
y/ca
0.65
0.8
0.65
0.70
0.63
0.6 0.70
0.4 0.55 0.55
0.2
0.53 0.62 0.58
0
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Fig 5b 1.4
x/ca = 3.770
1.2
y/ca
1
0.5 U/U∞
0.8
0.6
0.4
0.2
0
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Figure 3.9: Mean streamwise contours, and secondary flow vectors for x/ca = 3.770
72 Fig 6a 1.4
x/ca = 4.640 1.2
1
y/ca
0.64
0.8 0.70
0.6
0.68 0.63 0.62
0.4
0.58
0.2 0.58 0.60
0
-5
-5.5
-6
-6.5
-7
-7.5
z/ca
Fig 6b 1.4
x/ca = 4.640 1.2
y/ca
1
0.5 U/U∞
0.8
0.6
0.4
0.2
0
-5
-5.5
-6
-6.5
-7
-7.5
z/ca
Figure 3.10: Mean streamwise contours, and secondary flow vectors for x/ca = 4.640
73
0.5 0.45 0.4 0.35 Core Deficit/U
0.3 0.25 0.2 0.15 0.1 0.05 0 0
1
2
3
4
x/c a
Figure 3.11: Variation of peak deficit in core of vortex with downstream distance. Figure reveals a 2.5 fold decay.
5
74
1.4
x/ca = 1.366 1.2
y/ca
1
0.8
0.6
0.4 -0.20
-0.20 1.60
0.2
-0.40
3.40
-1.12
1.90
0 -0.499996
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.12: Mean streamwise vorticity contours for x/ca = 1.366
1.4
x/ca = 2.062 1.2
y/ca
1
0.8
0.6 -0.20
0.4 0.30
0.2
-0.30 -0.50
1.90 0.30
0 -1.5
-2
-2.5
-3
-0.40
-3.5
-4
-4.5
z/ca
Figure 3.13: Mean streamwise vorticity contours for x/ca = 2.062
75 1.4
x/ca = 2.831 1.2
1
y/ca
-0.08
0.8
0.6 -0.08
-0.08 0.18
0.4 -0.14
-0.20
0.54
0.2 1.00
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.14: Mean streamwise vorticity contours for x/ca = 2.831
1.4
x/ca = 3.770 1.2
y/ca
1
0.8
0.6 0.14
0.14
0.4
-0.11 0.29
0.2
0.57
0.57
0.57
0
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Figure 3.15: Mean streamwise vorticity contours for x/ca = 3.770
76
1.4
x/ca = 4.640 1.2
y/ca
1
0.8
0.6
0.4
0.15 0.15 0.20
0.2
0
0.30 0.45
0.59
0.59
-5
-5.5
-6
-6.5
-7
-7.5
z/ca
Figure 3.16: Mean streamwise vorticity contours for x/ca = 4.640
0 -1
0
1
2
3
4
5
-2
z/ca
-3 Vortex axis
-4
Wake axis
-5 -6 -7 -8 x/ca
Figure 3.17: Vortex axis position relative to wake axis. Vortex axis was defined as the locus of peak vorticity.
77 1.4
x/ca = 1.366 1.2
y/ca
1
0.5 U/U∞
0.8
0.6
0.4
0.2
0 -0.499996
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.18: Secondary flow vectors for x/ca = 1.366 aligned with vortex axis
1.4
x/ca = 2.062 1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0
-2
-2.5
-3
-3.5
-4
-4.5
z/ca
Figure 3.19: Secondary flow vectors for x/ca = 2.062 aligned with vortex axis
78 1.4
x/ca = 2.831 1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.20: Secondary flow vectors for x/ca = 2.831 aligned with vortex axis
1.4
x/ca = 3.770
1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Figure 3.21: Secondary flow vectors for x/ca = 3.770 aligned with vortex axis
79 1.4
x/ca = 4.640 1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0
-5
-5.5
-6
-6.5
-7
-7.5
z/ca
Figure 3.22: Secondary flow vectors for x/ca = 4.640 aligned with vortex axis
0.15
0.1
V/U ∞
0.05
0
-0.05 x/c a =1.366 x/c a =2.062
-0.1
x/c a =2.831 x/c a =3.770 x/c a =4.640
-2
-3
-4
-5
-6
-7
z/c a
Figure 3.23: Velocity profiles through core of vortex at various downstream positions
80 0.14
0.45 0.4
0.12
0.35 0.1
0.25
0.08
0.2
0.06
V/Uinf
Radius/ca
0.3
0.15 0.04 0.1
Apparent core radius
0.02
Peak Tangential Velocity
0.05 0
0 0
1
2
3
4
5
x/ca
Figure 3.24: Variation of core size and peak tangential velocity with downstream distance
0.85 0.8 0.75 0.7
U/U ∞
0.65 0.6
x/ca location 1.366 2.062 2.831 3.770 4.062
0.55 0.5 0.45 0.4
-1
-2
-3
-4
-5
-6
z/ca
Figure 3.25: Mean velocity profiles of the wake at various downstream locations
81 0.3
0.16 0.14
0.25
Deficit/U
0.2
0.1
0.15
0.08 0.06
0.1
Halfwidth/c
0.12
0.04 Deficit
0.05
0.02
Half width
0
0 0
2 x/ca 3
1
4
5
Figure 3.26: Peak deficit in the wake and half width variation of the wake variation with downstram distance
0
0
-0.5
x/c a location 1.366 2.062 2.831 3.770 4.062
-1
-1.5
6
5
4
3
2
1
0
η
-1
Fig a
-2
-3
-4
-5
-6
(U-U e)/U w
(U-U e)/U w
-0.5
-1
-1.5
6
5
4
3
2
1
0
η
-1
-2
-3
-4
Fig b
Figure 3.27: Comparison of Mean velocity profiles (Fig a) with standard wake data from Wygnanski et al(1986) Fig(b).
-5
-6
82 1.4
x/ca = 1.366 1.2
1
y/ca
8.26E-03 2.18E-03
0.8
0.6 8.26E-03
5.79E-04
0.4
5.09E-03
1.10E-02
0.2
9.66E-03 1.10E-02
8.26E-03
0 -0.499996
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.28 : TKE contours for x/ca=1.366
1.4
x/ca = 2.062 1.2
y/ca
1
0.8
5.09E-03 2.74E-03
4.26E-03
0.6 2.74E-03
0.4
6.99E-03
0.2
9.28E-03 8.73E-03
1.02E-02
5.96E-03
0 -1.5
-2
-2.5
-3
-3.5
-4
z/ca
Figure 3.29 : TKE contours for x/ca=2.062
-4.5
83 1.4
x/ca = 2.831 1.2 2.63E-03
1
y/ca
1.50E-03
2.18E-03
0.8
0.6
8.33E-04 2.63E-03
0.4 6.34E-03
0.2 5.31E-03
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.30 : TKE contours for x/ca=2.831
1.4
x/ca = 3.770 1.2 1.37E-03
1
4.21E-04
1.53E-03
y/ca
1.71E-03
0.8
4.21E-04
2.11E-04
0.6
1.53E-03
1.37E-03
3.29E-03
0.4
1.71E-03 4.20E-03
0.2 3.43E-03 2.24E-03
0
-3.5
-4
-4.5
-5
-5.5
z/ca
Figure 3.31 : TKE contours for x/ca=3.770
-6
84 1.4
x/ca = 4.640 1.2
1
1.22E-03 1.22E-03
5.26E-04
y/ca
1.00E-03
0.8 5.26E-04
5.26E-04
0.6
2.09E-03 2.22E-03
0.4
2.98E-03
0.2
2.41E-03
3.26E-03
2.66E-03
2.66E-03
0
-5
-5.5
-6
-6.5
-7
z/ca
Figure 3.32 : TKE contours for x/ca=4.640
-7.5
85 1.6
1.6
1.6
1.4
1.4
1.4
1
0.8 0.6
3.00E-03 2.50E-03 2.00E-03 1.50E-03
y/ca
0.6
3.00E-03 2.50E-03 2.00E-03 1.50E-03
y/ca
0.8
1.00E-03 5.00E-04 0.00E+00
4.50E-03 4.00E-03 3.50E-03
0.6
3.00E-03 2.50E-03 2.00E-03 1.50E-03
1.00E-03 5.00E-04 0.00E+00
1.00E-03 5.00E-04 0.00E+00
0.4
0.4
0.2
0.2
0.2
-1
-1.5
-2
-2.5
-3
0
-3.5
-1
-1.5
z/c a
-2
-2.5
-3
0
-3.5
2
Figure b : Contours of v
2
1.6
1.4
1.4
1.4
1.2
1.2
1.2
1
y/ca
1.50E-03 1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
-3.00E-03
0.2
0.2
Figure d : Contours of uv
-3.5
5.00E-04 0.00E+00 -5.00E-04
-2.00E-03 -2.50E-03 -3.00E-03
-3.00E-03
0.2
-3
2.00E-03 1.50E-03 1.00E-03
-1.00E-03 -1.50E-03
0.4
-2.5
2
0.6
0.4
-2
-3.5
0.8
0.4
z/c a
-3
1
2.00E-03 1.50E-03
y/ca
2.00E-03
-2.5
y/ca
1
-2
Figure c : Contours of w
1.6
-1.5
-1.5
z/ca
1.6
-1
-1
z/ca
Figure a : Contours of u
0
5.50E-03 5.00E-03
0.8
0.4
0
7.00E-03 6.50E-03 6.00E-03
1
5.50E-03 5.00E-03 4.50E-03 4.00E-03 3.50E-03
8.00E-03 7.50E-03
1.2
7.00E-03 6.50E-03 6.00E-03
1
5.50E-03 5.00E-03 4.50E-03 4.00E-03 3.50E-03
8.00E-03 7.50E-03
1.2
7.00E-03 6.50E-03 6.00E-03
y/ca
8.00E-03 7.50E-03
1.2
0
-1
-1.5
-2
-2.5
-3
-3.5
0
z/ca
Figure e : Contours of vw
Figure 3.33 : Turbulence stress contours for x/ca=1.366
-1
-1.5
-2
-2.5
-3
z/ca
Figure f : Contours of uw
-3.5
86 1.6
1.6
1.6
1.4
1.4
1.4
1
0.8 0.6
3.00E-03 2.50E-03 2.00E-03 1.50E-03
y/ca
0.6
3.00E-03 2.50E-03 2.00E-03 1.50E-03
y/ca
0.8
1.00E-03 5.00E-04 0.00E+00
4.50E-03 4.00E-03 3.50E-03
0.6
3.00E-03 2.50E-03 2.00E-03 1.50E-03
1.00E-03 5.00E-04 0.00E+00
1.00E-03 5.00E-04 0.00E+00
0.4
0.4
0.2
0.2
0.2
-2
-2.5
-3
-3.5
-4
0 -1.5
-4.5
-2
-2.5
z/c a
-3
-3.5
-4
0 -1.5
-4.5
2
Figure b : Contours of v
2
1.6
1.4
1.4
1.4
1.2
1.2
1.2
1
y/ca
1.50E-03 1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
-3.00E-03
0.2
0.2
Figure d : Contours of uv
-4.5
5.00E-04 0.00E+00 -5.00E-04
-2.00E-03 -2.50E-03 -3.00E-03
-3.00E-03
0.2
-4
2.00E-03 1.50E-03 1.00E-03
-1.00E-03 -1.50E-03
0.4
-3.5
2
0.6
0.4
-3
-4.5
0.8
0.4
z/c a
-4
1
2.00E-03 1.50E-03
y/ca
2.00E-03
-3.5
y/ca
1
-3
Figure c : Contours of w
1.6
-2.5
-2.5
z/ca
1.6
-2
-2
z/ca
Figure a : Contours of u
0 -1.5
5.50E-03 5.00E-03
0.8
0.4
0
7.00E-03 6.50E-03 6.00E-03
1
5.50E-03 5.00E-03 4.50E-03 4.00E-03 3.50E-03
8.00E-03 7.50E-03
1.2
7.00E-03 6.50E-03 6.00E-03
1
5.50E-03 5.00E-03 4.50E-03 4.00E-03 3.50E-03
8.00E-03 7.50E-03
1.2
7.00E-03 6.50E-03 6.00E-03
y/ca
8.00E-03 7.50E-03
1.2
0 -1.5
-2
-2.5
-3
-3.5
-4
-4.5
0 -1.5
z/ca
Figure e : Contours of vw
Figure 3.34 : Turbulence stress contours for x/ca=2.062
-2
-2.5
-3
-3.5
-4
z/ca
Figure f : Contours of uw
-4.5
87 1.6
1.4
1.6
1.4 6.00E-03 5.50E-03
1.2
1.2
5.00E-03 4.50E-03 4.00E-03
1
1.00E-03 5.00E-04 0.00E+00
y/ca
y/ca
0.8
0.8
1.00E-03 5.00E-04 0.00E+00
0.6
0.4
0.4
0.4
0.2
0.2
0.2
-3.5
-4
-4.5
-5
0
-5.5
-3
-3.5
z/c a
-4
-4.5
-5
0
-5.5
2
Figure b : Contours of v
2
1.6
1.4
1.4
1.4
1.2
1.2
1.2
1
y/ca
1.50E-03 1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
-3.00E-03
0.2
0.2
Figure d : Contours of uv
-5.5
5.00E-04 0.00E+00 -5.00E-04
-2.00E-03 -2.50E-03 -3.00E-03
-3.00E-03
0.2
-5
2.00E-03 1.50E-03 1.00E-03
-1.00E-03 -1.50E-03
0.4
-4.5
2
0.6
0.4
-4
-5.5
0.8
0.4
z/c a
-5
1
2.00E-03 1.50E-03
y/ca
2.00E-03
-4.5
y/ca
1
-4
Figure c : Contours of w
1.6
-3.5
-3.5
z/ca
1.6
-3
-3
z/ca
Figure a : Contours of u
0
2.50E-03 2.00E-03 1.50E-03 1.00E-03 5.00E-04 0.00E+00
0.6
-3
3.50E-03 3.00E-03
0.8
0.6
0
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
1.4 6.00E-03 5.50E-03
y/ca
1.6
0 -2.5
-3
-3.5
-4
-4.5
-5
-5.5
0 -2.5
z/ca
Figure e : Contours of vw
Figure 3.35 : Turbulence stress contours for x/ca=2.831
-3
-3.5
-4
-4.5
-5
z/ca
Figure f : Contours of uw
-5.5
88 1.6
1.4
1.6
1.4
1.4
4.00E-03 3.75E-03
1.2
3.50E-03 3.25E-03 3.00E-03
4.00E-03 3.75E-03
1.2
2.75E-03 2.50E-03
y/ca
2.25E-03 2.00E-03 1.75E-03
0.8
1.50E-03 1.25E-03 1.00E-03 7.50E-04
0.6
5.00E-04 2.50E-04 0.00E+00
4.00E-03 3.75E-03
1.2
2.75E-03 2.50E-03
1
2.25E-03 2.00E-03 1.75E-03
y/ca
1
3.50E-03 3.25E-03 3.00E-03
0.8
1.50E-03 1.25E-03 1.00E-03 7.50E-04
0.6
5.00E-04 2.50E-04 0.00E+00
0.2
0.2
0.2
-5
0
-6
-3.5
-4
-4.5
-5
-5.5
1.50E-03 1.25E-03 1.00E-03 7.50E-04
0.6 0.4
z/c a
2.25E-03 2.00E-03 1.75E-03
0.8
0.4
-4
2.75E-03 2.50E-03
1
0.4
0
3.50E-03 3.25E-03 3.00E-03
y/ca
1.6
0
-6
5.00E-04 2.50E-04 0.00E+00
-3.5
-4
-4.5
z/ca 2
Figure a : Contours of u
Figure b : Contours of v
1.6
-5
-5.5
-6
z/ca 2
Figure c : Contours of w
2
1.6
1.6 1.00E-03
1.4
6.00E-04 5.00E-04 4.00E-04
1.2
1.00E-03 9.00E-04
1.4 1.2
3.00E-04 2.00E-04 1.00E-04 0.00E+00
y/ca
-1.00E-04 -2.00E-04 -3.00E-04 -4.00E-04 -5.00E-04
0.8
-6.00E-04 -7.00E-04 -8.00E-04
0.6
-9.00E-04 -1.00E-03 -1.10E-03
0.4
-1.20E-03 -1.30E-03 -1.40E-03 -1.50E-03
0.2
1.4
9.00E-04 8.00E-04 7.00E-04 6.00E-04
1.2
5.00E-04 4.00E-04 3.00E-04
1
0.00E+00 -1.00E-04 -2.00E-04
0.8
-3.00E-04 -4.00E-04 -5.00E-04
0.6
-6.00E-04 -7.00E-04 -8.00E-04 -9.00E-04
0.4
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
2.00E-04 1.00E-04
y/ca
1
1.00E-03
-1.00E-04 -2.00E-04 -3.00E-04
y/ca
9.00E-04 8.00E-04 7.00E-04
0.8
-4.00E-04 -5.00E-04 -6.00E-04
0.6
-7.00E-04 -8.00E-04 -9.00E-04
0.4
-1.00E-03 -1.10E-03
0.2
-1.20E-03 -1.30E-03 -1.40E-03 -1.50E-03
-1.00E-03 -1.10E-03 -1.20E-03 -1.30E-03 -1.40E-03
0.2
-1.50E-03
0
-3.5
-4
-4.5
-5
-5.5
z/c a
Figure d : Contours of uv
-6
-6.5
0
-3.5
-4
-4.5
-5
-5.5
-6
-6.5
0
z/ca
Figure e : Contours of vw
Figure 3.36 : Turbulence stress contours for x/ca=3.770
-3.5
-4
-4.5
-5
-5.5
z/ca
Figure f : Contours of uw
-6
-6.5
89 1.4
4.00E-03 3.75E-03 3.50E-03 3.25E-03 3.00E-03 2.75E-03
1.2
1.6
1.6
1.4
1.4
1.2
1.2 4.00E-03 3.75E-03
2.50E-03 2.25E-03 2.00E-03 1.75E-03 1.50E-03
y/ca
1.25E-03 1.00E-03 7.50E-04
0.8
5.00E-04 2.50E-04 0.00E+00
2.75E-03 2.50E-03
0.6
0.4
0.4
0.2
0.2
0
-5
-6
2.25E-03 2.00E-03 1.75E-03
0.8
0.6
0
-7
z/c a
4.00E-03 3.75E-03
3.50E-03 3.25E-03 3.00E-03
1
y/ca
1
1.50E-03 1.25E-03 1.00E-03 7.50E-04 5.00E-04 2.50E-04 0.00E+00
3.50E-03 3.25E-03 3.00E-03
1
2.75E-03 2.50E-03
y/ca
1.6
2.25E-03 2.00E-03 1.75E-03
0.8
1.50E-03 1.25E-03 1.00E-03 7.50E-04
0.6
5.00E-04 2.50E-04 0.00E+00
0.4 0.2
-5
-5.5
-6
-6.5
-7
0
-7.5
-5
-5.5
-6
z/ca 2
Figure a : Contours of u
Figure b : Contours of v
1.6 1.4
-6.5
-7
-7.5
z/ca 2
Figure c : Contours of w
1.6
1.6
1.4
1.4
2
1.00E-03
1.2
1.2
6.00E-04 5.00E-04 4.00E-04
y/c a
3.00E-04 2.00E-04 1.00E-04 0.00E+00
0.8
-1.00E-04 -2.00E-04 -3.00E-04 -4.00E-04 -5.00E-04
0.6
-6.00E-04 -7.00E-04 -8.00E-04 -9.00E-04 -1.00E-03 -1.10E-03
0.4
1
5.00E-04 4.00E-04 3.00E-04 2.00E-04 1.00E-04
0.8
0.00E+00 -1.00E-04 -2.00E-04
0.6
-3.00E-04 -4.00E-04 -5.00E-04 -6.00E-04 -7.00E-04 -8.00E-04 -9.00E-04
0.4
-1.20E-03 -1.30E-03
0.2
-1.40E-03 -1.50E-03
1.00E-03 9.00E-04
1.2
9.00E-04 8.00E-04 7.00E-04 6.00E-04
y/ca
1
1.00E-03
8.00E-04 7.00E-04 6.00E-04 5.00E-04 4.00E-04 3.00E-04 2.00E-04
1
1.00E-04 0.00E+00
y/ca
9.00E-04 8.00E-04 7.00E-04
0.8
-1.00E-04 -2.00E-04 -3.00E-04 -4.00E-04 -5.00E-04 -6.00E-04
0.6
-7.00E-04 -8.00E-04 -9.00E-04
0.4
-1.00E-03 -1.10E-03 -1.20E-03 -1.30E-03 -1.40E-03 -1.50E-03
-1.00E-03 -1.10E-03
0.2
-1.20E-03 -1.30E-03 -1.40E-03
0.2
-1.50E-03
0
-5
-5.5
-6
-6.5
z/c a
Figure d : Contours of uv
-7
-7.5
0
-5
-5.5
-6
-6.5
-7
-7.5
0
-5
z/ca
Figure e : Contours of vw
Figure 3.37 : Turbulence stress contours for x/ca=4.640
-5.5
-6
-6.5
-7
z/ca
Figure f : Contours of uw
-7.5
90 1.4
x/ca = 1.366 1.2
1
6.62E-03
y/ca
5.00E-04
0.8
3.67E-03
0.6
0.4
2.57E-03
3.67E-03 5.00E-04
5.03E-03
0.2 1.07E-02 5.03E-03
0 -0.499996
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.38 : TKE production contours for x/ca=1.366
1.4
x/ca = 2.062 1.2
7.50E-04
y/ca
1
0.8
1.25E-04 1.25E-04
0.6
0.4
3.78E-03 5.00E-04
0.2 3.78E-03
0 -1.5
-2
-2.5
-3
5.03E-03
-3.5
-4
-4.5
z/ca
Figure 3.39 : TKE production contours for x/ca=2.062
91 1.4
x/ca = 2.831 1.2
1 7.55E-05
y/ca
7.55E-05
0.8
0.6 7.50E-04
0.4
1.74E-03
7.55E-05 7.50E-04
0.2
1.53E-03
1.14E-03
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.40 : TKE production contours for x/ca=2.831
1.4
x/ca = 3.770 1.2 1.25E-04
1
y/ca
1.25E-04
0.8
0.6
1.25E-04 4.48E-04 7.50E-04 7.50E-04
0.4
0
4.42E-05
4.42E-05
0.2
7.50E-04
6.05E-04
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Figure 3.41 : TKE production contours for x/ca=3.770
92 1.4
x/ca = 4.640 1.2
4.22E-05
9.23E-06
1
y/ca
4.22E-05
0.8
9.23E-06
0.6 3.24E-04 3.24E-04 3.04E-04
0.4
3.24E-04 3.24E-04 2.10E-04
0.2 2.56E-04
9.23E-06
7.50E-04 4.22E-05
0
-5
-5.5
-6
-6.5
-7
-7.5
z/ca
Figure 3.42 : TKE production contours for x/ca=4.640
93 Streamwise contributions 1.4
x/ca = 1.366 1.2
y/ca
1
0.8 5.03E-03
0.6
6.22E-03
0.4
1.05E-03 5.03E-03 8.77E-03
1.05E-03
0.2 1.08E-02
0
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Crossflow contributions 1.4
x/ca = 1.366 1.2
1.91E-03
y/ca
1
0.8
0.6
0.4
1.05E-03 1.05E-03
0.2 6.22E-03 4.11E-03
0
-1
-1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.43 : Streamwise and Crossflow contributions to TKE production contours for x/ca=1.366
94 Streamwise contributions 1.4
x/ca = 2.062 1.2
y/ca
1
6.73E-04
0.8 6.73E-04
0.6
0.4
3.63E-03
0.2 6.73E-04
3.63E-03 8.77E-03
0 -1.5
-2
-2.5
-3
-3.5
-4
-4.5
-4
-4.5
z/ca
Crossflow contributions 1.4
x/ca = 2.062 1.2
y/ca
1
0.8
0.6
0.4 2.45E-04
0.2
2.45E-04 2.57E-03 1.80E-03
0 -1.5
-2
-2.5
-3
-3.5
z/ca
Figure 3.44 : Streamwise and Crossflow contributions to TKE production contours for x/ca=2.062
95 Streamwise contributions 1.4
x/ca = 2.831
1.2
y/ca
1
0.8
0.6 1.63E-03
0.4
1.63E-03
0.2
9.32E-04 1.05E-03 1.44E-03
0
-2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
-5
-5.25 -5.5
z/ca
Crossflow contributions 1.4
x/ca = 2.831
1.2
y/ca
1
0.8
0.6
0.4 1.74E-04
0.2 1.74E-04
1.74E-04 6.85E-04 5.67E-04
0 -2.5 -2.75
-3
6.85E-04
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
z/ca
Figure 3.45 : Streamwise and Crossflow contributions to TKE production contours for x/ca=2.831
96 Streamwise contributions 1.4
x/ca = 3.770 1.2
y/ca
1
0.8
0.6
0.4
7.72E-04
6.94E-04 4.11E-04 3.67E-04 4.11E-04
4.11E-04 6.94E-04
0.2 4.54E-04
0
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Crossflow contributions 1.4
x/ca = 3.770 1.2
y/ca
1
0.8
0.6
0.4 1.07E-04
0.2
1.30E-04
1.46E-04
1.07E-04
1.30E-04 1.07E-04
2.19E-04
0
-3.5
-4
-4.5
-5
-5.5
-6
z/ca
Figure 3.46 : Streamwise and Crossflow contributions to TKE production contours for x/ca=3.770
97
Streamwise contributions 1.4
x/ca = 4.640 1.2
y/ca
1
0.8
0.6 2.97E-04
0.4
1.61E-04
1.61E-04 2.97E-04 5.18E-04 3.96E-04
0.2
1.61E-04 1.61E-04
7.42E-04
0
-5
-5.5
-6
-6.5
-7
-7.5
z/ca
Crossflow contributions 1.4
x/ca = 4.640 1.2
y/ca
1
0.8
0.6
0.4
-1.06E-04
0.2
-9.04E-05 -9.04E-05
0
-5
-5.5
-6
-6.5
-7
-1.06E-04
-7.5
z/ca
Figure 3.47 : Streamwise and Crossflow contributions to TKE production contours for x/ca=4.640
2
0.10
2
6
5
4
3
2
1
0
-1
η
-2
-3
-4
-5
0.00
0.00
0.03
0.03
0.05
1.366 2.062 2.831 3.770 4.062
0.05
2
u /U w
0.07
x/c a lo cation
0.07
2
0.10
u /U w
0.13
0.13
0.15
0.15
0.18
0.18
0.20
0.20
98
6
-6
5
4
3
2
1
0
η
-1
-2
-3
-4
-5
-6
Fig b
Fig a
0.05 2
0.00
uw/U w
0.00
1.366 2.062 2.831 3.770 4.062
6
5
4
3
2
1
0
η
-1
Fig a
-2
-3
-4
-5
-6
-0.05
x/c a location
-0.05
2
uw/U w
0.05
0.10
0.10
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.
6
5
4
3
2
1
0
η
-1
-2
-3
-4
-5
-6
Fig b
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.
10 -2
10 -2
99
10 -3
2.062 2.831 3.770 4.640
10 -4
10 -4
10 -3
1.366 2.062 2.831 3.770 4.640
-5/3
10 -5 -7
10
10
-8
10
10
10 0
10 1
10 2
f c/U ref
10 3
10
-9
10
10 -6
G uu /(U ref c)
10 -5 10 -6 -7 -8 -9
G uu /(U ref c)
-5/3
10
0
10
1
10
2
f c/U ref
Take n through the wake ce nte r
Take n through the vorte x ce nte r
Figure 3.50 : Autospectra for u velocity component
10
3
10 -2
10 -2
100
10 -3
2.062 2.831 3.770 4.640
-5/3
10 -4
10 -4
10 -3
1.366 2.062 2.831 3.770 4.640
10 -5 -7
10
10
-8
10
10
10 0
10 1
10 2
f c/U ref
10 3
10
-9
10
10 -6
G ww /(U ref c)
10 -5 10
-6 -7 -8 -9
G vv /(U ref c)
-5/3
10
0
10
1
10
2
f c/U ref
Take n through the wake ce nte r
Take n through the vorte x ce nte r
Figure 3.51 : Autospectra for v velocity component
10
3
10 -2
10 -2
101
10 -3
2.062 2.831 3.770 4.640
10 -4
10 -4
10 -3
1.366 2.062 2.831 3.770 4.640
-5/3
10 -5 -7
10
10
-8
10
10
10 0
10 1
10 2
f c/U ref
Take n through the wake ce nte r
10 3
10
-9
10
10 -6
G ww /(U ref c)
10 -5 10 -6 -7 -8 -9
G ww /(U ref c)
-5/3
10
0
10
1
10
2
f c/U ref
Take n through the vorte x ce nte r
Figure 3.52 : Autospectra for w velocity component Note: Peak in the wake is indicative of coherent motion such as vortex shedding from trailing edge
10
3
102 1.4
x/ca = 2.831 Double tip gap
1.2
y/ca
1
0.62
0.63
0.8
0.6
0.72 0.58
0.4
0.70
0.53
0.58
0.2
0.50
0.46
0 -2.25 -2.5 -2.75
-3
0.50 0.46
0.65
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
1.4
x/ca = 2.831 Double tip gap
1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0 -2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.53: Mean streamwise contours, and secondary flow vectors for x/ca =2.831 w/ double tip gap
103 1.4
x/ca = 2.831 Half tip gap
1.2
y/ca
1
0.8
0.62 0.68
0.6
0.62
0.70
0.4 0.61
0.2
0.68
0.68
0.52 0.50 0.63
0 -2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
-5
-5.25
z/ca
1.4
x/ca = 2.831 Half tip gap
1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0 -2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
z/ca
Figure 3.54: Mean streamwise contours, and secondary flow vectors for x/ca =2.831 w/ half tip gap
104 1.4
x/ca = 2.831 Double tip gap
1.2
y/ca
1
0.8
0.6 -0.20
-0.14
0.4 0.54
0.40
0.2
1.47
0
-2.5 -2.75
-3
-0.14
1.26
-0.40
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.55: Mean streamwise vorticity contours for x/ca = 2.831 w/ double tip gap
1.4
x/ca = 2.831 Half tip gap
1.2
y/ca
1
0.8
0.6
0.4
0.2
-0.14
-0.08
-0.14 -0.26 -0.30
-2.5 -2.75
-3
0.30
0.69
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.56: Mean streamwise vorticity contours for x/ca = 2.831 w/ half tip gap
105 1.4
x/ca = 2.831 Double tip gap
1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0 -2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.57: Secondary flow vectors for x/ca = 2.831 aligned with vortex axis w/ double tip gap
1.4
x/ca = 2.831 Half tip gap
1.2
0.5 U/U∞
y/ca
1
0.8
0.6
0.4
0.2
0 -2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.58: Secondary flow vectors for x/ca = 2.831 aligned with vortex axis w/ half tip gap
106 1.4
x/ca = 2.831 Double tip gap
1.2
1
y/ca
2.175E-03
0.8
8.333E-04
0.6 5.314E-03
0.4
6.336E-03 2.175E-03 7.496E-03
0.2
6.061E-03
7.496E-03
6.685E-03 6.912E-03 5.660E-03
0 -2.25 -2.5 -2.75
-3
5.660E-03
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.59 : TKE contours for x/ca=2.831 w/ double tip gap
1.4
x/ca = 2.831 Half tip gap
1.2
y/ca
1
0.8 8.33E-04 2.18E-03
0.6
0.4
0.2
4.74E-03
2.18E-03 5.31E-03
6.34E-03 5.31E-03
6.06E-03 5.66E-03
-2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.60 : TKE contours for x/ca=2.831 w/ half tip gap
107 1.6
1.6
1.6
1.4
1.4
1.4
1
1.00E-03 5.00E-04 0.00E+00
y/ca
y/ca
0.8
0.8
1.00E-03 5.00E-04 0.00E+00
0.6
0.4
0.4
0.4
0.2
0.2
0.2
-3
-3.5
-4
-4.5
0
-5
-2.5
-3
-3.5
z/ca
-4
-4.5
0
-5
2
Figure b : Contours of v
2
1.6
1.4
1.4
1.4
1.2
1.2
1.2
1
y/ca
1.50E-03 1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
-3.00E-03
0.2
0.2
Figure d : Contours of uv
5.00E-04 0.00E+00 -5.00E-04
-2.00E-03 -2.50E-03 -3.00E-03
-3.00E-03
0.2
-5
2.00E-03 1.50E-03 1.00E-03
-1.00E-03 -1.50E-03
0.4
-4.5
2
0.6
0.4
-4
-5
0.8
0.4
z/ca
-4.5
1
2.00E-03 1.50E-03
y/ca
2.00E-03
-4
y/ca
1
-3.5
-3.5
Figure c : Contours of w
1.6
-3
-3
z/ca
1.6
-2.5
-2.5
z/ca
Figure a : Contours of u
0
2.50E-03 2.00E-03 1.50E-03 1.00E-03 5.00E-04 0.00E+00
0.6
-2.5
3.50E-03 3.00E-03
0.8
0.6
0
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
y/ca
6.00E-03 5.50E-03
1.2
0
-2.5
-3
-3.5
-4
-4.5
-5
0
-2.5
-3
-3.5
Figure e : Contours of vw
-4
-4.5
-5
z/ca
z/ca
Figure f : Contours of uw
Figure 3.61 : Turbulence stress contours for x/ca=2.831 w/ double tip gap
108 1.6
1.6
1.6
1.4
1.4
1.4
1
1.00E-03 5.00E-04 0.00E+00
y/ca
y/ca
0.8
0.8
1.00E-03 5.00E-04 0.00E+00
0.6
0.4
0.4
0.4
0.2
0.2
0.2
-3
-3.5
-4
-4.5
0
-5
-2.5
-3
-3.5
z/ca
-4
-4.5
0
-5
2
Figure b : Contours of v
2
1.6
1.4
1.4
1.4
1.2
1.2
1.2
1
y/ca
1.50E-03 1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
-3.00E-03
0.2
0.2
Figure d : Contours of uv
5.00E-04 0.00E+00 -5.00E-04
-2.00E-03 -2.50E-03 -3.00E-03
-3.00E-03
0.2
-5
2.00E-03 1.50E-03 1.00E-03
-1.00E-03 -1.50E-03
0.4
-4.5
2
0.6
0.4
-4
-5
0.8
0.4
z/ca
-4.5
1
2.00E-03 1.50E-03
y/ca
2.00E-03
-4
y/ca
1
-3.5
-3.5
Figure c : Contours of w
1.6
-3
-3
z/c a
1.6
-2.5
-2.5
z/ca
Figure a : Contours of u
0
2.50E-03 2.00E-03 1.50E-03 1.00E-03 5.00E-04 0.00E+00
0.6
-2.5
3.50E-03 3.00E-03
0.8
0.6
0
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
y/ca
6.00E-03 5.50E-03
1.2
0
-2.5
-3
-3.5
-4
-4.5
-5
0
-2.5
-3
z/ca
Figure e : Contours of vw
Figure 3.62 : Turbulence stress contours for x/ca=2.831 w/ half tip gap
-3.5
-4
-4.5
-5
z/c a
Figure f : Contours of uw
109 1.4
x/ca = 2.831 Double tip gap
1.2 7.550E-05 7.550E-05
1
7.550E-05
y/ca
7.550E-05
0.8
0.6
0.4
2.034E-03
2.034E-03 1.143E-03 3.174E-03
0.2
3.174E-03
1.826E-04
3.419E-04
3.419E-04
0
-2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.63 : TKE production contours for x/ca=2.831 w/ double tip gap
1.4
1.2
x/ca = 2.831 Half tip gap
3.42E-04
y/ca
1
0.8 2.76E-04
0.6 7.55E-05
0.4 1.53E-03
5.00E-04
5.00E-04
0.2
7.50E-04
7.55E-05 1.14E-03
-2.25 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
z/ca
Figure 3.64 : TKE production contours for x/ca=2.831 w/ half tip gap
110
Streamwise contributions 1.4
x/ca = 2.831
1.2
y/ca
1
0.8
0.6 1.63E-03
1.63E-03
7.14E-04
0.4
1.05E-03
2.57E-03
1.05E-03
0.2
0
1.05E-03
-2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
-5
-5.25
z/ca
Crossflow contributions 1.4
x/ca = 2.831 1.2
y/ca
1
0.8 4.83E-05
0.6
0.4 2.12E-04 1.58E-04
0.2
1.58E-04
1.58E-04 1.05E-03
0
-2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
z/ca
Figure 3.65 : Streamwise and Crossflow contributions to TKE production contours for x/ca=2.831 w/double tip gap
111
Streamwise contributions 1.4
x/ca = 2.831
1.2
y/ca
1
0.8
0.6
0.4 1.63E-03
7.14E-04
7.14E-04
0.2
2.57E-03
0
-2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25
-5
-5.25
z/ca
Crossflow contributions 1.4
x/ca = 2.831 1.2
y/ca
1
0.8
0.6
0.4
0.2
5.67E-04 3.10E-04 -1.77E-04
0
-2.5 -2.75
-3
3.10E-04
-3.25 -3.5 -3.75
-4
-1.77E-04
-4.25 -4.5 -4.75
z/ca
Figure 3.66 : Streamwise and Crossflow contributions to TKE production contours for x/ca=2.831 w/double tip gap
112 1.4
x/ca = 2.831 1.2
y/ca
1
0.61
0.8
0.6
0.62
0.70
0.65
0.63 0.65
0.4
0.53
0.2
0.49
0.62
0.50
0.50
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.67: Mean streamwise velocity contours for x/ca =2.831 w/ double trip strip
1.4
x/ca = 2.831 1.2 2.63E-03
1
y/ca
8.33E-04
2.18E-03
0.8
0.6
8.33E-04 2.63E-03
0.4 6.34E-03
0.2 5.31E-03
0 -2.5 -2.75
-3
-3.25 -3.5 -3.75
-4
-4.25 -4.5 -4.75
-5
-5.25 -5.5
z/ca
Figure 3.68: Mean turbulence kinetic energy contours for x/ca =2.831 w/ double trip strip
113 1.6
1.6
1.6
1.4
1.4
1.4
1
1.00E-03 5.00E-04 0.00E+00
y/ca
y/ca
0.8
0.8
1.00E-03 5.00E-04 0.00E+00
0.6
0.4
0.4
0.4
0.2
0.2
0.2
-3.5
-4
-4.5
-5
0
-5.5
-3
-3.5
z/c a
-4
-4.5
-5
0
-5.5
2
Figure b : Contours of v
2
1.6
1.4
1.4
1.4
1.2
1.2
1.2
1
y/ca
1.50E-03 1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
1.00E-03 5.00E-04
0.8
0.00E+00 -5.00E-04 -1.00E-03 -1.50E-03 -2.00E-03 -2.50E-03
0.6
-3.00E-03
0.2
0.2
Figure d : Contours of uv
-5.5
5.00E-04 0.00E+00 -5.00E-04
-2.00E-03 -2.50E-03 -3.00E-03
-3.00E-03
0.2
-5
2.00E-03 1.50E-03 1.00E-03
-1.00E-03 -1.50E-03
0.4
-4.5
2
0.6
0.4
-4
-5.5
0.8
0.4
z/c a
-5
1
2.00E-03 1.50E-03
y/ca
2.00E-03
-4.5
y/ca
1
-4
Figure c : Contours of w
1.6
-3.5
-3.5
z/ca
1.6
-3
-3
z/ca
Figure a : Contours of u
0
2.50E-03 2.00E-03 1.50E-03 1.00E-03 5.00E-04 0.00E+00
0.6
-3
3.50E-03 3.00E-03
0.8
0.6
0
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
1
3.50E-03 3.00E-03 2.50E-03 2.00E-03 1.50E-03
6.00E-03 5.50E-03
1.2
5.00E-03 4.50E-03 4.00E-03
y/ca
6.00E-03 5.50E-03
1.2
0 -2.5
-3
-3.5
-4
-4.5
-5
-5.5
0 -2.5
-3
z/ca
Figure e : Contours of vw
Figure 3.69 : Turbulence stress contours for x/ca=2.831 w/ double trip strip
-3.5
-4
-4.5
-5
z/ca
Figure f : Contours of uw
-5.5
114 k/U
2
∞
1.0E-02 9.6E-03 9.2E-03
1.4
8.8E-03 8.3E-03 7.9E-03
1.2
7.5E-03 7.1E-03 6.7E-03
1
5.13E-04
6.3E-03
y/ca
5.9E-03 4.64E-03
5.5E-03
0.8
5.0E-03 4.6E-03 4.2E-03
0.6
3.8E-03 3.4E-03
2.16E-03 9.25E-04
3.0E-03
0.4
3.40E-03
2.6E-03 2.2E-03 1.8E-03
9.18E-03
1.3E-03
0.2
9.3E-04
1.00E-02
9.18E-03
1.00E-02
5.1E-04
2.58E-03 1.0E-04
-2
-2.5
-3
-3.5
-4
z/ca Figure 3.70 : TKE contours at x/ca=2.062 highlighting repeatability of the facility Color contours were taken first, and contour lines were taken after varying tip gap heights and blade boundary layer trips.
115
blade region near leading edge of blade
Inflow
blade
tip gap tip leakage vortex
blade counter-rotating vortex generated by separation of flow laving tip gap from endwall
tip gap
Figure 3.71 : Sketch illustrating flow pattern observed in the linear compresor cascade. Shown are the tip leakage vortex and a counter rotating vortex. The tip leakage vortex is seen to convect across the lower endwall pushing the counter rotating vortex with it.
region at about half chord of blade
