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Research Papers

Control of Tip Leakage in a High-Pressure Turbine Cascade Using Tip Blowing PUBLIC ACCESS

[+] Author and Article Information
Ralph J. Volino

Fellow ASME
Mechanical Engineering Department,
United States Naval Academy,
Annapolis, MD 21402
e-mail: volino@usna.edu

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 27, 2016; final manuscript received November 6, 2016; published online February 7, 2017. Editor: Kenneth Hall.

J. Turbomach 139(6), 061008 (Feb 07, 2017) (12 pages) Paper No: TURBO-16-1176; doi: 10.1115/1.4035509 History: Received July 27, 2016; Revised November 06, 2016

Blowing from the tip of a turbine blade was studied experimentally to determine if total pressure loss could be reduced. Experiments were done with a linear cascade in a low-speed wind tunnel. Total pressure drop through the blade row and secondary velocity fields in the passage between two blades were measured. Cases were documented with various blowing hole configurations on flat and squealer tipped blades. Blowing normal to the tip was not helpful and in some cases increased losses. Blowing from the bottom of a squealer cavity provided little benefit. With a flat tip, blowing from holes located near and inclined toward the pressure side generally reduced total pressure drop by reducing the effect of the tip leakage vortex. Holes near the axial location of maximum loading were most helpful, while holes closer to the leading and trailing edges were not as effective. Higher jet velocity resulted in larger total pressure drop reduction. With a tip gap of 1.5% of axial chord, jets with a velocity 1.5 times the cascade inlet velocity had a significant effect. A total pressure drop reduction of the order 20% was possible using a jet mass flow of about 0.4% of the main flow. Jets were most effective with smaller tip gaps, as they were more able to counter the leakage flow.

Tip leakage, through the gaps between the tips of unshrouded turbine blades on a rotor and the turbine casing, can account for about 1/3 of the total losses in a turbine stage [1]. The leakage, which is caused by the pressure difference between the pressure and suction sides of the blade, unloads the tip region of the airfoil, since the leaking fluid is not exerting a force on the blade. After exiting the tip gap, the leaking fluid rolls up into the tip leakage vortex, which persists into downstream stages, further complicating the flow and leading to additional losses.

Reducing the tip gap size would reduce losses and improve efficiency, but some clearance is necessary to allow for thermal expansion and prevent rubbing between the blades and casing. Various methods of reducing leakage by changing the tip geometry have been used in practice as described by Bunker [2]. Squealer tips (e.g., see Booth et al. [1] and Ameri et al. [3]) are commonly used to both reduce leakage and reduce the contact area if rubbing occurs. Winglets as described by Coull et al. [4], Zhou et al. [5], and O'Dowd et al. [6] provide another means to reduce leakage and can be used in combination with squealer cavities. Shrouded airfoils are another alternative. Shrouds and winglets, however, must be cooled and add extra weight, which is not desirable. Other conceivable methods of flow control include the use of plasma actuators (e.g., see Saddoughi et al. [7] and Ashrafi et al. [8]) and blowing from the tip or casing.

Tip blowing could utilize cooling air. High-pressure turbine airfoils are typically cooled, and film cooling is often employed on the blade tips. Cooling air might be directed to counter the leakage flow. Many studies have considered tip heat transfer, but fewer have investigated the aerodynamic effects of tip film cooling. Dey and Camci [9] conducted an experimental study with blowing from a row of holes in a blade tip. The holes were inclined toward the pressure side. They saw little effect on the leakage flow or losses. Rao and Camci [10,11] used the same facility with higher jet mass flow rates. They reported a reduction in total pressure loss, but the jet velocities required appear to be higher than achievable in an engine. Niu and Zang [12] conducted a numerical study of blowing from the tip. They used rows of holes inclined toward the pressure side. Holes closest to the pressure side produced the best results, reducing tip leakage and losses, but also increasing the strength of the passage vortex. The mass flow rates used in the simulations indicate jet velocities higher than achievable in an engine. Mercan et al. [13] did experiments with blowing from a row of holes along the camber line of a blade with a flat tip. The holes were directed normal to the tip. They observed a reduction in tip leakage and associated losses around the tip leakage vortex and a slight increase in the size of the passage vortex. Blowing from the holes in the upstream part of the tip was more effective than blowing from the holes near the trailing edge. Hofer and Arts [14] considered blades with squealer rims and blowing from normal holes in the base of the squealer cavity and holes on the pressure surface of the blade near the tip. They saw only marginal changes in losses with blowing. Hohlfeld et al. [15] conducted a numerical study and indicated that blowing from the base of a small tip cavity helped to reduce leakage flow if the tip gap was small. Zhou and Hodson [16] considered film cooling from ten normal holes on the tips of flat and squealer tip blades. The cooling flow helped to reduce losses in the flat tip cases, particularly when the tip gap was small. With squealer tips, cooling had less effect and in some cases increased losses. Zhou et al. [5] and O'Dowd et al. [6] studied the effect of cooling with winglet tips, finding that cooling flow caused a small increase and small decrease in the aerodynamic losses in the respective studies. In a study of transonic tip flows, Wheeler and Saleh [17] found that tip blowing resulted in a small reduction in losses for a flat tipped blade, but provided no benefit with a squealer tip. Chen et al. [18] presented numerical simulations for cases with different hole locations, angles, and flow rates. Some cases showed a reduction in losses, but it appears that the required jet velocities were higher than obtainable under engine conditions. Wang et al. [19] did numerical simulations for cases with blowing from the tip of a blade with a partial squealer cavity. They showed improved cooling with no change in losses.

The studies to date show some consistencies. Blowing from the tip appears to provide more benefit with flat tips than with squealer tips. The benefits are higher with smaller tip gaps. There are also some open questions, however. Some studies showed improvement with jets directed normal to the tip, while others only showed benefits with inclined jets. Some indicated significant changes in losses, while in other cases the changes were small. The velocity and mass flow of cooling air required also varied, with some studies showing changes in the leakage flow only with very high jet velocities, and others showing improvement with velocities achievable under engine conditions.

The present study considered blowing from the tip of a high-pressure turbine blade with the intent of reducing total pressure drop through the blade row. Jet locations, size, inclination angle, and velocity were all varied on both flat tip and squealer tip blades. Experiments were done in a linear cascade in a low-speed wind tunnel. Conditions were set to match baseline cases in Volino [20] without tip blowing. Documentation includes total pressure drop measurements and instantaneous velocity fields in the passage acquired with particle image velocimetry (PIV).

Experiments were conducted in a closed-loop wind tunnel with a seven blade linear cascade in one corner of the loop, as shown in Fig. 1. A tailboard was positioned to produce periodicity. The airfoils were two–dimensional, and the shape was the general electric E3 (energy efficient engine), high-pressure turbine, stage 1 rotor blade tip cross section [21,22]. Details are provided in Table 1 and in Ref. [20]. Blades were used with flat tips and with squealer tips. The squealer rim was 2.54 mm thick (0.019Cx) and extended all the way around the blade, as shown in Fig. 2. The squealer cavity was 5 mm deep (0.038Cx). The cascade blades had a high aspect ratio (span/Cx) of 4.8. This aspect ratio was much higher than in the E3 design, which had a span approximately equal to Cx. The large span was chosen to simplify the flow by ensuring that the boundary layers on the two endwalls would not merge. Since the span in the experiments was not representative of engine conditions, Cx is used below as the normalizing quantity for the tip gap size. The tip gap was 0.015Cx in cases presented below unless otherwise noted. Conditions of the endwall boundary layer measured just upstream of the blades are presented in Table 2.

A coarse grid located upstream of the cascade produced 4% background freestream turbulence at the inlet plane of the cascade with integral length scale of 0.15Cx in the streamwise component and 0.04Cx in the cross stream component. More details of the freestream turbulence are available in Refs. [23,24].

Previous work in the facility, described by Volino [20,25] and Volino et al. [23,24], showed that wakes generated upstream of the cascade caused a nearly uniform rise in total pressure drop across the flow field. Wakes did not change the flow structure significantly. To simplify the experiments in the present study, wakes were only included in a few cases, and these cases confirmed that the wakes did not greatly change the flow structure or the effect of the flow control techniques employed. Only cases without wakes are reported below.

The rotation of the blades relative to the endwall was not modeled in the stationary cascade. The effect of relative motion on the leakage flow is not necessarily large, as indicated in studies such as Srinivasan and Goldstein [26] and Krishnababu et al. [27], although others such as Palafox et al. [28] have noted important effects.

Data were acquired mainly at Re = 30,000 based on inlet velocity and axial chord with a few comparison cases at Re = 60,000. The Reynolds number was low compared to engine conditions, but was limited by the facility. The study still captured many of the important features of endwall and tip leakage flows, including the important vortices.

To produce tip blowing, each blade consisted of a 605 mm long main section, attached to the lower endwall, and a removable 30 mm long tip. The main section had a 12.7 mm diameter spanwise hole through the center of the blade at about the midchord. This hole was supplied with compressed air through a fitting at the bottom of the cascade. Air exiting the hole entered the tip, which was hollow, as shown in Fig. 2. Holes for jets passed through the top of the tip, which was 11.5 mm thick. The supply air for the jets was metered through solenoid valves before entering the blades. The velocity through the solenoids was sonic in all the cases, and the mass flow rate was calibrated against the supply pressure. The average jet velocity exiting the tip was computed by dividing the total mass flow rate by the total cross-sectional area of all the jet holes.

In an engine, the jets would be supplied by the cooling air in the blade, and the available pressure would allow a maximum jet velocity of about 1.5 times the inlet main flow velocity to the blade row, depending on the local static pressure at different locations on the tip (see Green et al. [29] for tip pressure measurements on a typical airfoil). Considering the higher density of the cooling air, a blowing ratio, B = ρjetVjet/ρiUi, of 2 might be achieved. In the present experiments, the jet and mainflow temperatures and densities were equal, so B = Vjet/Ui. In most cases, B was set between 1 and 2. It should be noted that only the average B is known for each case, since all the jets on the blade tip were fed from a common plenum and the individual jet velocities could not be measured.

Measurements.

Total pressure coefficients were documented using a pitot tube upstream of the cascade for the inlet stagnation pressure and velocity, and a Kiel probe traversed 0.1Cx downstream of the cascade. Pressure difference was measured using a pressure transducer (0–500 Pa range Validyne transducer). Pressure readings were acquired at a 10 kHz sampling rate over a 10 s period and averaged. A traverse was located in the wind tunnel downstream of the cascade to move the probe. The flow blockage caused by the traverse was checked [30] and found to result in less than 2% variation in wind tunnel velocity when the traverse was moved, when it was located at least 2Cx downstream of the cascade. The Kiel probe was traversed through a grid across 2.2 blade spacings and extending from z = 0.01 to 1.1Cx from the endwall (plane 3 in Fig. 3). The grid spacing in both directions was 0.038Cx. The uncertainty in the total pressure coefficient, ψ, was 6% of the maximum ψ = 3.3 measured. The total pressure coefficient used in this study is related to the total pressure loss, but it is an approximation since the upstream total pressure was measured at a single point in the freestream. The pressure drop associated with the flow control jets themselves could be included in the average value of ψ for a passage, but was not significant in the present study due to the low total mass flow rate of the jets (approximately 0.3% of the main flow). The contribution of the jet pressure loss to the average ψ would be about 0.01, which was within the measurement uncertainty.

Velocity fields were measured using PIV. Image pairs were acquired using a 250 mJ, 8 ns pulse yttrium aluminium garnet laser (Quantel CFR 400) and 4 megapixel camera (TSI PowerView Plus with Nikkor micro 55 mm lens). The time delay between the images in each pair was 55 μs. The flow was seeded with olive oil particles using an atomizer (TSI 930706). For all the cases and image planes considered, 1000 image pairs were acquired. Velocity vectors were computed from the images using tsi insight 4 g software with a recursive grid (64 × 64 pixels with 50% overlap in both passes). This processing resulted in 0.01Cx spacing between computed velocity vectors as shown in the figures. The uncertainty in the velocities in the measurement planes was 0.06 m/s. The uncertainty in the vorticity or swirl strength computed from the velocities had a maximum of 25% for local values and was 3% for values averaged over the full field of view. All the uncertainties are based on a 95% confidence interval. PIV data were acquired in planes 1 and 2 shown in Fig. 3, which were normal to the main flow in the passage between blades B3 and B4 at the trailing edges of the pressure and suction side blades, respectively. The laser sheet entered through the top endwall, and the camera was located inside the wind tunnel, downstream of the cascade.

Exploratory Cases.

A series of initial experiments were conducted to reduce the parameter space for more detailed testing. Total pressure drop surveys were made for cases with blowing from only the center blade in the cascade using jet holes of diameter d/Cx = 0.038. Total pressure drop was area-averaged pitchwise across one blade spacing and spanwise from z = 0 to 1.1Cx and from z = 0 to 0.6Cx. Averaging was done for the passages on each side of the blade with blowing. Results from these initial cases are described briefly next, but are not presented in detail.

A squealer tip blade was considered first, with a single hole directed normal to the tip, located along the camber line at x/Cx = 0.23. With very high jet velocities (B > 10), the spatially averaged total pressure drop in the controlled passage (on the suction side of the controlled blade) was reduced, but it was increased in the pressure side passage. Regions of high ψ indicated that with very high B, a significant amount of air was being injected into the pressure side passage. With lower B, the jet had little effect.

Next, a row of 11 normal holes spaced evenly along the camber line from leading to trailing edge was tried with the squealer tip blade. With B = 1.6 and 2.1, the jets increased the total pressure drop through the controlled passage by up to about 35%.

The squealer cavity was then filled with modeling clay, with a single normal hole extending through the clay from the now flat tip to the original hole at x/Cx = 0.23. Next, a single hole inclined at about 30 deg to the tip surface and directed toward the pressure side of the blade was put through the clay to the original hole at x/Cx = 0.23. The length-to-diameter ratio of the inclined section of the hole was about 2. With B = 2.2, blowing from either the normal or inclined hole had little effect on the total pressure drop. The carving of holes through the clay was not precision machining, but was accepted as a way to assess several geometries without the need to manufacture multiple blade tips. More carefully made holes, as described below, were used after the initial reduction of the parameter space.

The flat tip was next tried with nine normal holes spaced along the camber line with B = 1.6. The holes were pushed through the clay to the nine most centered holes previously drilled at the base of the squealer cavity (holes 1 and 11 not used). The jets increased the total pressure drop by about 9%. Next, the same nine holes were changed to inclined holes. Each hole was inclined toward the pressure side at as shallow an angle as possible with respect to the blade tip. With B = 1, the jets had no measurable effect. As B was increased to 1.2, 1.6, and 2.1, the average total pressure drop in the controlled passage was reduced by about 4%, 11%, and 14%, respectively. The nine-hole geometry was also tried with the tip gap increased to 0.038Cx. With the larger tip gap, blowing with B = 1.6 and 2.1 increased the total pressure drop.

To better test inclined holes, a new squealer blade tip shown in Fig. 4 was made with a 3D printer. It included 11 holes inclined toward the pressure side and positioned such that air leaving in the direction of each hole would just clear the pressure side squealer rim. The five most upstream holes were inclined at 45 deg to the base of the squealer cavity and had a length-to-diameter ratio of 3.3. The next three holes were also inclined at 45 deg, but had lower length-to-diameter ratios due to the limitation of the lower blade thickness toward the trailing edge. The thin trailing edge required that the most downstream three holes be at steeper angles. Blowing from all the 11 holes with B = 1.4 increased total pressure drop. Total pressure drop also increased with B = 2.2, but not by as much as with B = 1.4. Cases were then done with blowing from only the upstream seven holes. With B = 2.2, the pressure drop associated with the tip leakage vortex was significantly reduced, but the pressure drop associated with the passage vortex went up. Overall, there was little change from the case with no blowing. The effects of blowing increased slightly with B when it was varied from 1.1 to 3.3.

A squealer tip with a central rib, shown in Fig. 5, was printed to move the jets closer to the endwall. The rib followed the camber line, was 7 mm (0.05Cx) wide, and had the same height as the squealer rim. Holes inclined at 45 deg to the tip exited the pressure side of the rib. The length-to-diameter ratio of the holes ranged from about 4 where the blade was thickest to about 1.2 where the blade was thinnest. With B = 1.1 and 2.2, the jets had little effect.

Since it appeared that jets directed counter to the leakage flow could be effective, a blade tip with holes on the pressure surface near the tip was made in an attempt to block air from entering the tip gap. The tip, had a squealer cavity and ten holes in a line on the pressure surface, centered 0.07Cx from the tip. The holes were inclined at 60 deg to the pressure surface and 30 deg to the endwall. With B = 2.2, the average total pressure drop increased by 17%. With B = 1.1, the effect was still detrimental, but not as large.

The results described above confirm some of the observations reported in the literature. Blowing from normal holes on a flat tip or at the base of a squealer cavity was not helpful at any jet velocity achievable in an engine and can be detrimental if a large amount of air from multiple holes simply adds to the leakage flow. Jets from holes on the pressure side near the tip were also not helpful. Blowing from a squealer tip with holes inclined toward the pressure side can produce some positive effects if the blowing ratio is sufficiently high, but the overall benefit tends to be small. Holes near the trailing edge were not helpful since they could not be inclined sufficiently due to the thickness of the blade. Blowing from a flat tip with inclined holes (albeit with relatively short length-to-diameter ratios in the cases described above) provides some benefit if the blowing ratio is high enough. Essentially, it appears that jets can be effective if they provide enough momentum to counter the leakage flow. Jets normal to the tip do not provide momentum in the required direction. With a squealer, jets may change direction or diffuse within the cavity instead of directly opposing the leakage flow. With a large tip gap, there may be too much leakage flow momentum for the jets to counter. Ineffective jets can add mass flow to the leakage and increase total pressure drop.

The next cases considered the effect of hole size and jet velocity for a flat tip with inclined holes. The squealer cavity of Fig. 4 was filled in with clay, and the upstream seven holes were extended through the clay with various diameters (all the diameters equal for a given test). The spatially averaged total pressure drop coefficient ψ was normalized on its value for the B = 0 case and is shown in Fig. 6. Open symbols are for the pressure side (uncontrolled) passage of the blade with blowing, and filled symbols are for the controlled passage. Smaller holes used less mass flow at a given B, but the larger holes generally produced lower ψ, which is consistent with their providing more momentum to counter the tip leakage. With no apparent advantage of using smaller holes, all the subsequent tests were done with d/Cx = 0.038.

The final exploratory cases considered jet angle. Blade tips were 3D printed with flat tips and seven holes, as shown in Fig. 7. Tips were made with 45 deg holes and with 30 deg holes. Results are shown in Fig. 8. The jets produced only a small reduction in ψ at B = 1, but provided more benefit at larger B. The lower jet angle (providing more momentum directly counter to the leakage flow) produced better results, particularly as blowing ratio was increased.

Blowing From Inclined Holes on a Flat Tip.

Guided by the results above, all the subsequent cases included blowing from a flat tip with holes of diameter d/Cx = 0.038, directed toward the pressure side and inclined at 30 deg to the tip surface. A set of blade tips with seven holes, as shown in Fig. 7, were printed and installed on the five center blades in the cascade. The downstream edge of each hole was 2 mm (0.015Cx) from the pressure side of the tip. The axial locations of the holes are given in Table 3. Individual holes were blocked by covering them with thin tape so that the effectiveness of various hole combinations could be tested. All the five blades were the same in any given test to maintain periodicity in the cascade.

Figure 9 shows average total pressure drop as a function of B for various jet hole combinations. Averaging was across one blade pitch and from z = 0 to 1.1Cx (the full spanwise measurement region) for Fig. 8(a), and from z = 0 to 0.6Cx (the region most influenced by the endwall flow) for Fig. 8(b). Blowing from single holes was not as effective as from multiple holes. The cases with both holes 3 and 4 active were among those with the lowest pressure drop. The use of more holes, in addition to holes 3 and 4, did not improve the results significantly. The absence of either hole 3 or 4 resulted in at least somewhat higher pressure drop. If a blade span equal to the axial chord is assumed for the purpose of computing the mass flow rate through the passage, the total jet mass flow rate utilizing two holes is 0.29% of the main flow with B = 1 (0.57% with B = 2).

The importance of holes 3 and 4 may be explained by Fig. 10, which shows the pressure distribution on the surface of the blade. Pressure taps were located on the blade at the midspan (open symbols) and 0.32Cx from the tip (filled symbols). Maximum loading was at x/Cx ≈ 0.25, corresponding to the location of jet hole 3. This suggests that blowing near or just downstream of the maximum loading location may be most effective. The midspan results in Fig. 10 show no variation with tip blowing. The pressure taps at z = 0.32Cx are too far from the tip to show large variation from those at midspan, but the loading is lower near the tip, as expected. The tip loading increases with the jet blowing ratio, indicating along with the total pressure results of Fig. 9, that the jets reduce the tip leakage flow.

To test if more jet holes near the maximum loading location might be beneficial, a set of blade tips with nine closely spaced holes, shown in Fig. 11, were made. The tips included holes at locations 2–5 of Table 3, and additional holes halfway between these holes. Total pressure results using these tips are shown in Fig. 12 and compared to holes 3–4 results from Fig. 9. The additional holes did not provide a large benefit, so cases using the tips of Fig. 7 with holes 3 and 4 active are the focus of the discussion below.

Figure 13 shows the total pressure drop contours for the cases using holes 3 and 4. A single passage is shown, with the endwall at the top of the plots and the suction and pressure sides on the left and right, respectively. The strip along the entire span at y/Cx = 0 is due to the wake of blade B4. The orange peak near the endwall is due to the tip leakage vortex. The secondary peak below it is due to the passage vortex. As the blowing ratio is increased, the tip leakage vortex peak is weakened. Figure 14 shows pitchwise-averaged ψ as a function of distance from the endwall. The highest peak at z/Cx = 0.1 is due to the leakage vortex and is greatly reduced as jet velocity increases. The passage vortex peak at z/Cx = 0.3 is less affected. It increases slightly between B = 0 and 1, in agreement with some of the observations in the literature mentioned above, then decreases at higher B. For z/Cx > 0.4, the jet effect is small, and beyond z/Cx = 0.6, the jets appear to have no effect. The value of ψ is essentially constant for z/Cx > 0.8, indicating that this region is unaffected by the endwall secondary flow. Area-averaged values of ψ are given in Table 4.

The total pressure surveys acquired in plane 3 of Fig. 3 at x = 0.1Cx downstream of the trailing edges do not necessarily represent mixed out losses due to the proximity to the blade row. Data were acquired in another plane, 0.7Cx downstream of the trailing edges, and ψ contours are presented in Fig. 15. Comparing to Fig. 13, the wakes of the blades are clearly wider, but ψ has lower magnitude at the downstream station (note that the color range in Fig. 15 is half that in Fig. 13). The peaks associated with the vortices are still clear, but they are again spread over a larger area and the maximum magnitudes are lower. Pitchwise-averaged results for the cases of Fig. 15 are shown in Fig. 16. There is a peak very near the endwall that was not visible at the upstream location in Fig. 14. The near wall peak may have been present upstream, but since the endwall boundary layer grows in the streamwise direction, it may be more possible to resolve it in the measurement at the downstream location. As at the upstream location, the tip leakage vortex peak is most affected by the jets. The passage vortex peak increases slightly as B is increased from 0 to 1, then drops at higher B. For z/Cx < 0.4, the values in Fig. 16 are lower than in Fig. 14. This is reversed for 0.4 < z/Cx < 1, as the region affected by the secondary flow spreads in the spanwise direction. The area-averaged values in Table 4 show somewhat lower values at the downstream location. This is counterintuitive since losses must increase. The difference must be due to measurement uncertainty and the spread of the area of secondary flow effects outside the measurement region.

The flowfield responsible for the total pressure drop is shown in Fig. 17. The left column in the figure shows the velocity vectors in plane 1 of Fig. 3, and the right column shows the vectors in plane 2. Superimposed on the velocity vectors are contours of the dimensionless swirl strength. The swirl strength, λ, is the part of the vorticity due to rotation (as opposed to shear). It is defined as the imaginary part of the complex eigenvalue of the local velocity gradient tensor and was used in the present study in a two-dimensional form as explained by Hutchins et al. [31]. By definition, λ is always positive, but a sign can be assigned based on the local vorticity to show the direction of rotation. Positive swirl indicates counterclockwise rotation in the view of the figures in this paper, which are looking downstream through the cascade. The suction side of the passage corresponds to yn/Cx = 0, and the pressure side is located at yn/Cx ≈ 0.4. For plane 1, the pressure side is on the pressure surface as shown in Fig. 3. For plane 2, the pressure side is downstream of the pressure surface trailing edge in the flow direction. The tip leakage vortex appears as the blue area of clockwise rotation in the upper left corner of plane 1 for the B = 0 case. Below it, the red region of counterclockwise rotation is the passage vortex. With B = 1, the leakage vortex in plane 1 is slightly smaller but its intensity is as strong as in the case with no blowing. As B is increased to 1.5, however, the leakage vortex is clearly smaller and weaker, and with B = 2, it is no longer visible. The reduction in tip leakage vortex strength in plane 1 is consistent with the lower total pressure drop shown in Figs. 1316 and Table 4. The passage vortex remains in about the same position in plane 1 at all the blowing ratios. This position is farther from the suction surface than in cases with no tip gap and no tip leakage shown by Volino [25]. This is again consistent with the total pressure drop, which shows the leakage vortex is present, albeit weakened, even with B = 2.

In plane 2 in Fig. 17, the leakage vortex is clear, and its size and strength do not appear to change as blowing ratio is increased. This is somewhat surprising, since both planes 1 and 2 are downstream of the jet injection locations at holes 3 and 4. The vortex still clearly forms, but perhaps the jets divert the leakage flow to a more downstream location, delaying the formation of the vortex, as observed by Niu and Zang [12], and this delay results in lower total pressure drop.

The time-averaged turbulence quantities associated with the velocity fields of Fig. 17 are shown in Figs. 18 and 19. The rms pitchwise fluctuating velocity, the rms spanwise fluctuating velocity, and the Reynolds shear stress in the plane are shown in the three columns. Each row is for a different jet blowing ratio. In Fig. 18, the result from plane 1 shows the high turbulence associated with the leakage flow. As the blowing ratio is increased, the peak turbulence levels are reduced to about half those at B = 0. The turbulent shear stress, which is highest in the high shear region around the leakage vortex, is reduced to near zero when B = 2. This is consistent with the absence of the leakage vortex in Fig. 17 for this case. In plane 2 (Fig. 19), the peak turbulence quantities are lower than in plane 1, but they are spread over a larger area, consistent with the spread of the vortices in Fig. 17 and the spread of the high total pressure drop regions between Figs. 13 and 15. The turbulence levels in Fig. 19 decrease as the blowing ratio increases. Blowing does not reduce the turbulence as much in plane 2 as in plane 1, consistent with the still visible leakage vortex in plane 2 of Fig. 17 at all the blowing ratios. The total pressure drop results from the integrated effect of the turbulence and shear acting upstream. The delay of the appearance of the leakage vortex and the subsequent reduction in turbulence, particularly in plane 1, are consistent with the reduction in total pressure drop shown in Figs. 1316.

Effect of Reynolds Number.

Total pressure surveys in the planes 0.1Cx and 0.7Cx downstream of the trailing edges were made for cases with blowing from holes 3 and 4 with the Reynolds number increased to 60,000. Total pressure drop contours are shown in Figs. 20 and 21. Pitchwise-averaged values are shown in Figs. 22 and 23. Area-averaged values are given in Table 4. Comparing to Figs. 1316, the blade wakes far from the endwall are thinner and have lower total pressure drop at the high Reynolds number due to the thinner boundary layers on the blades. The endwall boundary layer should also be thinner at high Re, which results in a weaker passage vortex and lower associated pressure drop. The tip leakage vortex peaks, however, are slightly higher at Re = 60,000. Thinner endwall boundary layers may result in higher mass flow through the tip gap, resulting in a stronger leakage vortex and higher total pressure drop. Figure 24 shows the area-averaged total pressure drop for each case normalized on the result for the B = 0 case at the same Reynolds number. The jets are not quite as effective at reducing the total pressure drop at Re = 60,000, presumably because the leakage flow is stronger, so the jets cannot counter it as effectively. Results are shown for blowing from holes 3 and 4 and from holes 3–5. The addition of hole 5 blowing does not significantly change the results at either Reynolds number, as shown in Fig. 9 for the Re = 30,000 cases.

Effect of Tip Gap Size.

Cases were documented with the tip gap increased to 0.02Cx and with the gap reduced to roughly 0.01Cx. Total pressure contours from the location 0.1Cx downstream of the trailing edges are shown in Fig. 25, and area-averaged values are given in Table 5. Comparing the large and small tip gap cases with the 0.015Cx gap cases of Fig. 13 and Table 4, for z/Cx > 0.3 there is little change as tip gap size or blowing ratio is varied. The passage vortex peak does not change greatly. The tip leakage vortex peak, however, is roughly proportional to the tip gap size. Figure 26 shows area-averaged total pressure drop coefficients normalized using the ψ values for the cases with the same tip gap and B = 0. Blowing reduces the total pressure drop in all the cases, but the percentage reduction is smaller when the tip gap is large. As mentioned above, this may be because the jets are not able to fully counter the stronger leakage flow with the larger tip gap. The velocity fields and swirl strength in planes 1 and 2 are shown in Fig. 27. In agreement with the total pressure results, the leakage vortex is stronger in both planes 1 and 2 with larger gap size. Blowing reduces the strength of the vortex with all the tip gaps, particularly in plane 1. To quantify the leakage vortex strength, the area, Av, occupied by the vortex in the measurement plane was identified as the region near the suction surface and endwall where the swirl strength was below a threshold (λCx/Ui < −1). The average dimensionless swirl strength in this region was then multiplied by Av. The results for the cases of Figs. 17 and 27 are presented in Table 6 and Fig. 28. In plane 1, both the magnitude of the average swirl strength and the area occupied by the tip leakage vortex increase with the tip gap size. As blowing ratio is increased, the mean swirl strength does not change greatly, but the vortex area is clearly reduced. In plane 2, the mean swirl strength does not change much with tip gap size, but the vortex area increases as the gap becomes larger. Changing the blowing ratio does not have as clear an effect as in plane 1.

Experiments were performed in a linear cascade to determine if blowing from the tip could be used to reduce total pressure drop through the blade row. Various jet numbers, locations, inclination angles, diameters, and velocities were considered on flat and squealer tip blades. With a tip gap of 0.015Cx, blowing from holes normal to the tip was not effective. Blowing from the pressure surface near the tip was also unhelpful. In general, blowing that did not help tended to increase total pressure drop by adding to the leakage flow. Blowing from holes inclined toward the pressure side reduced total pressure drop in some cases. With a squealer tip, the effects were small. With a flat tip, significant effects were possible. Blowing from locations near the location of maximum loading appeared to be most effective. The jets appeared to delay the formation of the tip leakage vortex to a location farther downstream and reduce the turbulence levels in the passage. With a jet blowing ratio of 1.5, which was equivalent to a jet mass flow rate of about 0.4% of the main flow through the passage, total pressure drop was reduced by about 20%. At higher Reynolds numbers, overall total pressure drop was lower due to the thinner boundary layers on all the surfaces, but the loss due to the tip leakage vortex was slightly higher and the flow control jets were somewhat less effective. The leakage vortex strength and the total pressure drop increased, and the jets were less effective with larger tip gaps. For the cases considered, tip blowing provided a significant benefit with a low cost in terms of jet mass flow. The effect on film cooling of jets in the configurations tested was not considered and needs assessment.

The support of the Naval Academy Technical Support Department Shop and Fluids Laboratory was greatly appreciated.

This work was sponsored by the National Aeronautics and Space Administration (NASA) under cooperative Agreement No. NNC11IA11I. The grant monitor was Dr. David Ashpis of the NASA Glenn Research Center.

  • Av =

    cross-sectional area of tip leakage vortex in measurement plane

  • B =

    Vjet/Ui, blowing ratio

  • Cp =

    (PT − P)/(ρiUi2/2), pressure coefficient

  • Cx =

    axial chord length

  • d =

    jet hole diameter

  • H =

    shape factor, displacement thickness/momentum thickness

  • P =

    local static pressure

  • PT =

    upstream stagnation pressure

  • PTe =

    downstream stagnation pressure

  • Re =

    UiCx/ν, inlet Reynolds number

  • Reθ =

    Uiθ/ν, momentum thickness Reynolds number

  • Ui =

    inlet freestream velocity

  • Vjet =

    average jet velocity

  • v′ =

    rms fluctuating pitchwise velocity

  • w′ =

    rms fluctuating spanwise velocity

  • x =

    axial coordinate

  • xn =

    local streamwise coordinate

  • y =

    pitchwise coordinate

  • yn =

    coordinate normal to local streamwise direction and to spanwise direction, distance from suction surface

  • z =

    spanwise coordinate, distance from the endwall

  • δ99.5 =

    boundary layer thickness

  • θ =

    momentum thickness

  • λ =

    swirl strength

  • ν =

    kinematic viscosity

  • ρi =

    main flow density

  • ρjet =

    jet density

  • ψ =

    (PT − PTe)/(ρiUi2/2), total pressure coefficient

  • ψο =

    total pressure coefficient for B = 0 case

Booth, T. C. , Dodge, P. R. , and Hepworth, H. K. , 1982, “ Rotor-Tip Leakage—Part I: Basic Methodology,” ASME J. Eng. Power, 104(1), pp. 154–161. [CrossRef]
Bunker, R. S. , 2006, “ Axial Turbine Blade Tips: Function, Design, and Durability,” AIAA J. Propul. Power, 22(2), pp. 271–285. [CrossRef]
Ameri, A. A. , Steinthorsson, E. , and Rigby, D. L. , 1998, “ Effect of Squealer Tip on Rotor Heat Transfer and Efficiency,” ASME J. Turbomach., 120(4), pp. 753–759. [CrossRef]
Coull, J. D. , Atkins, N. R. , and Hodson, H. H. , 2014, “ High Efficiency Cavity Winglets for High Pressure Turbines,” ASME Paper No. GT2014-25261.
Zhou, C. , Hodson, H. , Tibbott, I. , and Stokes, M. , 2013, “ Effects of Winglet Geometry on the Aerodynamic Performance of Tip Leakage Flow in a Turbine Cascade,” ASME J. Turbomach., 135(5), p. 051009. [CrossRef]
O'Dowd, D. O. , Zhang, Q. Q. , He, L. L. , Cheong, B. Y. , and Tibbott, I. I. , 2012, “ Aerothermal Performance of a Cooled Winglet at Engine Representative Mach and Reynolds Numbers,” ASME J. Turbomach., 135(1), p. 011041. [CrossRef]
Saddoughi, S. , Bennett, G. , Boespflug, M. , Puterbaugh, S. L. , and Wadia, A. R. , 2014, “ Experimental Investigation of Tip Clearance Flow in a Transonic Compressor With and Without Plasma Actuators,” ASME J. Turbomach., 137(4), p. 041008. [CrossRef]
Ashrafi, F. , Michaud, M. , and Vo, H. D. , 2016, “ Delay of Rotating Stall in a Compressor Using Plasma Actuators,” ASME J. Turbomach., 138(9), p. 091009. [CrossRef]
Dey, D. , and Camci, C. , 2000, “ Development of Turbine Tip Clearance Flow Downstream of a Rotor Blade With Coolant Injection From a Tip Trench,” 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery: (ISROMAC-8), Honolulu, HI, Mar. 26–30, pp. 572–579.
Rao, N. M. , and Camci, C. , 2004, “ Axial Turbine Tip Desensitization by Injection From a Tip Trench—Part 1: Effect of Injection Mass Flow Rate,” ASME Paper No. GT2004-53256.
Rao, N. M. , and Camci, C. , 2004, “ Axial Turbine Tip Desensitization by Injection From a Tip Trench—Part 2: Leakage Flow Sensitivity to Injection Location,” ASME Paper No. GT2004-53258.
Niu, M. , and Zang, S. , 2009, “ Numerical Investigation of Active Tip-Clearance Control Through Tip Cooling Injection in an Axial Turbine Cascade,” J. Therm. Sci., 18(4), pp. 306–312. [CrossRef]
Mercan, B. , Ostovan, Y. , Dočan, E. , and Uzol, O. , 2012, “ Experimental Investigation of the Effects of Waveform Tip Injection in a Low Pressure Turbine Cascade,” ASME Paper No. GT2012-69316.
Hofer, T. , and Arts, T. , 2009, “ Aerodynamic Investigation of the Tip Leakage Flow for Blades With Different Tip Squealer Geometries at Transonic Conditions,” ASME Paper No. GT2009-59909.
Hohlfeld, E. M. , Christophel, J. R. , Couch, E. L. , and Thole, K. A. , 2005, “ Predictions of Cooling From Dirt Purge Holes Along the Tip of a Turbine Blade,” Int. J. Turbo Jet Engines, 22(3), pp. 139–152. [CrossRef]
Zhou, C. , and Hodson, H. , 2011, “ Tip Leakage Flow of an Unshrouded High Pressure Turbine Blade With Tip Cooling,” ASME J. Turbomach., 133(4), p. 041028. [CrossRef]
Wheeler, A. P. S. , and Saleh, Z. , 2013, “ Effect of Cooling Injection on Transonic Tip Flows,” AIAA J. Propul. Power, 29(6), pp. 1374–1381. [CrossRef]
Chen, S. , Zhou, Z. , Cui, T. , Wang, J. , and Wang, S. , 2014, “ Effects of Tip Injection on Tip Clearance Flow in a Low-Pressure Turbine Stator Cascade,” ASME Paper No. GT2014-25185.
Wang, Z. , Zhang, Q. , Liu, Y. , and He, L. , 2015, “ Impact of Cooling Injection on Transonic Over-Tip Leakage Flow and Squealer Aerothermal Design Optimization,” ASME J. Eng. Gas Turbines Power, 137(6), p. 062603. [CrossRef]
Volino, R. J. , 2014, “ Effects of Endwall Boundary Layer Thickness and Blade Tip Geometry on Flow Through High Pressure Turbine Passages,” ASME Paper No. GT2014-27013.
Halila, E. E. , Lenahan, D. T. , and Thomas, T. T. , 1982, “ Energy Efficient Engine High Pressure Turbine Test Hardware Detailed Design Report,” Report No. NASA CR-167955.
Timko, L. P. , 1984, “ Energy Efficient Engine High Pressure Turbine Component Test Performance Report,” Report No. NASA CR-168289.
Volino, R. J. , Galvin, C. D. , and Ibrahim, M. B. , 2013, “ Effects of Periodic Unsteadiness on Secondary Flows in High Pressure Turbine Passages,” ASME Paper No. GT2013-95881.
Volino, R. J. , Galvin, C. D. , and Brownell, C. J. , 2014, “ Effects of Unsteady Wakes on Flow Through High Pressure Turbine Passages With and Without Tip Gaps,” ASME Paper No. GT2014-27006.
Volino, R. J. , 2015, “ Experiments With a New Ribbed Blade Tip and Endwall Geometry on a High Pressure Turbine Blade,” ASME Paper No. GT2015-44065.
Srinivasan, V. , and Goldstein, R. J. , 2003, “ Effect of Endwall Motion on Blade Tip Heat Transfer,” ASME J. Turbomach., 125(2), pp. 267–273. [CrossRef]
Krishnababu, S. K. , Dawes, W. N. , Hodson, H. P. , Lock, G. D. , Hannis, J. , and Whitney, C. , 2009, “ Aerothermal Investigations of Tip Leakage Flow in Axial Flow Turbines—Part II: Effect of Relative Casing Motion,” ASME J. Turbomach., 131(1), p. 011007. [CrossRef]
Palafox, P. , Oldfield, M. L. G. , LaGraff, J. E. , and Jones, T. V. , 2008, “ PIV Maps of Tip Leakage and Secondary Flow Fields on a Low-Speed Turbine Blade Cascade With Moving End Wall,” ASME J. Turbomach., 130(1), p. 011001. [CrossRef]
Green, B. R. , Barter, J. W. , Haldeman, C. W. , and Dunn, M. G. , 2004, “ Averaged and Time-Dependent Aerodynamics of a High Pressure Turbine Blade Tip Cavity and Stationary Shroud: Comparison of Computational and Experimental Results,” ASME J. Turbomach., 127(4), pp. 736–746. [CrossRef]
Volino, R. J. , 2010, “ Separated Flow Measurements on a Highly Loaded Low-Pressure Turbine Airfoil,” ASME J. Turbomach., 132(1), p. 011007. [CrossRef]
Hutchins, N. , Hambleton, W. T. , and Marusic, I. , 2005, “ Inclined Cross-Stream Stereo Particle Image Velocimetry Measurements in Turbulent Boundary Layers,” J. Fluid Mech., 541, pp. 21–54. [CrossRef]
Copyright © 2017 by ASME
View article in PDF format.

References

Booth, T. C. , Dodge, P. R. , and Hepworth, H. K. , 1982, “ Rotor-Tip Leakage—Part I: Basic Methodology,” ASME J. Eng. Power, 104(1), pp. 154–161. [CrossRef]
Bunker, R. S. , 2006, “ Axial Turbine Blade Tips: Function, Design, and Durability,” AIAA J. Propul. Power, 22(2), pp. 271–285. [CrossRef]
Ameri, A. A. , Steinthorsson, E. , and Rigby, D. L. , 1998, “ Effect of Squealer Tip on Rotor Heat Transfer and Efficiency,” ASME J. Turbomach., 120(4), pp. 753–759. [CrossRef]
Coull, J. D. , Atkins, N. R. , and Hodson, H. H. , 2014, “ High Efficiency Cavity Winglets for High Pressure Turbines,” ASME Paper No. GT2014-25261.
Zhou, C. , Hodson, H. , Tibbott, I. , and Stokes, M. , 2013, “ Effects of Winglet Geometry on the Aerodynamic Performance of Tip Leakage Flow in a Turbine Cascade,” ASME J. Turbomach., 135(5), p. 051009. [CrossRef]
O'Dowd, D. O. , Zhang, Q. Q. , He, L. L. , Cheong, B. Y. , and Tibbott, I. I. , 2012, “ Aerothermal Performance of a Cooled Winglet at Engine Representative Mach and Reynolds Numbers,” ASME J. Turbomach., 135(1), p. 011041. [CrossRef]
Saddoughi, S. , Bennett, G. , Boespflug, M. , Puterbaugh, S. L. , and Wadia, A. R. , 2014, “ Experimental Investigation of Tip Clearance Flow in a Transonic Compressor With and Without Plasma Actuators,” ASME J. Turbomach., 137(4), p. 041008. [CrossRef]
Ashrafi, F. , Michaud, M. , and Vo, H. D. , 2016, “ Delay of Rotating Stall in a Compressor Using Plasma Actuators,” ASME J. Turbomach., 138(9), p. 091009. [CrossRef]
Dey, D. , and Camci, C. , 2000, “ Development of Turbine Tip Clearance Flow Downstream of a Rotor Blade With Coolant Injection From a Tip Trench,” 8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery: (ISROMAC-8), Honolulu, HI, Mar. 26–30, pp. 572–579.
Rao, N. M. , and Camci, C. , 2004, “ Axial Turbine Tip Desensitization by Injection From a Tip Trench—Part 1: Effect of Injection Mass Flow Rate,” ASME Paper No. GT2004-53256.
Rao, N. M. , and Camci, C. , 2004, “ Axial Turbine Tip Desensitization by Injection From a Tip Trench—Part 2: Leakage Flow Sensitivity to Injection Location,” ASME Paper No. GT2004-53258.
Niu, M. , and Zang, S. , 2009, “ Numerical Investigation of Active Tip-Clearance Control Through Tip Cooling Injection in an Axial Turbine Cascade,” J. Therm. Sci., 18(4), pp. 306–312. [CrossRef]
Mercan, B. , Ostovan, Y. , Dočan, E. , and Uzol, O. , 2012, “ Experimental Investigation of the Effects of Waveform Tip Injection in a Low Pressure Turbine Cascade,” ASME Paper No. GT2012-69316.
Hofer, T. , and Arts, T. , 2009, “ Aerodynamic Investigation of the Tip Leakage Flow for Blades With Different Tip Squealer Geometries at Transonic Conditions,” ASME Paper No. GT2009-59909.
Hohlfeld, E. M. , Christophel, J. R. , Couch, E. L. , and Thole, K. A. , 2005, “ Predictions of Cooling From Dirt Purge Holes Along the Tip of a Turbine Blade,” Int. J. Turbo Jet Engines, 22(3), pp. 139–152. [CrossRef]
Zhou, C. , and Hodson, H. , 2011, “ Tip Leakage Flow of an Unshrouded High Pressure Turbine Blade With Tip Cooling,” ASME J. Turbomach., 133(4), p. 041028. [CrossRef]
Wheeler, A. P. S. , and Saleh, Z. , 2013, “ Effect of Cooling Injection on Transonic Tip Flows,” AIAA J. Propul. Power, 29(6), pp. 1374–1381. [CrossRef]
Chen, S. , Zhou, Z. , Cui, T. , Wang, J. , and Wang, S. , 2014, “ Effects of Tip Injection on Tip Clearance Flow in a Low-Pressure Turbine Stator Cascade,” ASME Paper No. GT2014-25185.
Wang, Z. , Zhang, Q. , Liu, Y. , and He, L. , 2015, “ Impact of Cooling Injection on Transonic Over-Tip Leakage Flow and Squealer Aerothermal Design Optimization,” ASME J. Eng. Gas Turbines Power, 137(6), p. 062603. [CrossRef]
Volino, R. J. , 2014, “ Effects of Endwall Boundary Layer Thickness and Blade Tip Geometry on Flow Through High Pressure Turbine Passages,” ASME Paper No. GT2014-27013.
Halila, E. E. , Lenahan, D. T. , and Thomas, T. T. , 1982, “ Energy Efficient Engine High Pressure Turbine Test Hardware Detailed Design Report,” Report No. NASA CR-167955.
Timko, L. P. , 1984, “ Energy Efficient Engine High Pressure Turbine Component Test Performance Report,” Report No. NASA CR-168289.
Volino, R. J. , Galvin, C. D. , and Ibrahim, M. B. , 2013, “ Effects of Periodic Unsteadiness on Secondary Flows in High Pressure Turbine Passages,” ASME Paper No. GT2013-95881.
Volino, R. J. , Galvin, C. D. , and Brownell, C. J. , 2014, “ Effects of Unsteady Wakes on Flow Through High Pressure Turbine Passages With and Without Tip Gaps,” ASME Paper No. GT2014-27006.
Volino, R. J. , 2015, “ Experiments With a New Ribbed Blade Tip and Endwall Geometry on a High Pressure Turbine Blade,” ASME Paper No. GT2015-44065.
Srinivasan, V. , and Goldstein, R. J. , 2003, “ Effect of Endwall Motion on Blade Tip Heat Transfer,” ASME J. Turbomach., 125(2), pp. 267–273. [CrossRef]
Krishnababu, S. K. , Dawes, W. N. , Hodson, H. P. , Lock, G. D. , Hannis, J. , and Whitney, C. , 2009, “ Aerothermal Investigations of Tip Leakage Flow in Axial Flow Turbines—Part II: Effect of Relative Casing Motion,” ASME J. Turbomach., 131(1), p. 011007. [CrossRef]
Palafox, P. , Oldfield, M. L. G. , LaGraff, J. E. , and Jones, T. V. , 2008, “ PIV Maps of Tip Leakage and Secondary Flow Fields on a Low-Speed Turbine Blade Cascade With Moving End Wall,” ASME J. Turbomach., 130(1), p. 011001. [CrossRef]
Green, B. R. , Barter, J. W. , Haldeman, C. W. , and Dunn, M. G. , 2004, “ Averaged and Time-Dependent Aerodynamics of a High Pressure Turbine Blade Tip Cavity and Stationary Shroud: Comparison of Computational and Experimental Results,” ASME J. Turbomach., 127(4), pp. 736–746. [CrossRef]
Volino, R. J. , 2010, “ Separated Flow Measurements on a Highly Loaded Low-Pressure Turbine Airfoil,” ASME J. Turbomach., 132(1), p. 011007. [CrossRef]
Hutchins, N. , Hambleton, W. T. , and Marusic, I. , 2005, “ Inclined Cross-Stream Stereo Particle Image Velocimetry Measurements in Turbulent Boundary Layers,” J. Fluid Mech., 541, pp. 21–54. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic of linear cascade

Grahic Jump Location
Fig. 2

Squealer tip: (a) top view showing squealer cavity and (b) bottom view showing internal cavity for jet supply air

Grahic Jump Location
Fig. 3

Measurement planes for PIV and total pressure

Grahic Jump Location
Fig. 4

Squealer tip with 11 inclined holes

Grahic Jump Location
Fig. 5

Squealer tip with central rib and ten inclined holes

Grahic Jump Location
Fig. 6

Area-averaged (0 < z/Cx < 1.1) total pressure coefficient normalized on B = 0 value for flat tip with seven 45 deg inclined holes of indicated diameters. Open symbols—uncontrolled passage and solid symbols—controlled passage. Note: All the figures for Re = 30,000, 30 deg inclined holes of d/Cx = 0.038, 0.015Cx tip gap unless otherwise noted.

Grahic Jump Location
Fig. 7

Flat tip with seven inclined holes

Grahic Jump Location
Fig. 8

Area-averaged (0 < z/Cx < 1.1) total pressure coefficient normalized on B = 0 value for flat tip with seven inclined holes of indicated angles; open symbols—uncontrolled passage and solid symbols—controlled passage

Grahic Jump Location
Fig. 9

Area-averaged total pressure coefficient normalized on B = 0 value with blowing from indicated holes: (a) average over 0 < z/Cx < 1.1 and (b) average over 0 < z/Cx < 0.6

Grahic Jump Location
Fig. 10

Pressure profiles on blades, blowing from holes 3 to 4; open symbols—midspan and solid symbols—0.32Cx from tip

Grahic Jump Location
Fig. 11

Flat tip with nine inclined holes

Grahic Jump Location
Fig. 12

Area-averaged (0 < z/Cx < 0.6) total pressure coefficient normalized on B = 0 value with blowing from indicated holes

Grahic Jump Location
Fig. 13

ψ contours 0.1Cx downstream of trailing edges: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2. Note: All the figures here and below for blowing from holes 3 and 4 of Fig. 7 and Table 3.

Grahic Jump Location
Fig. 14

Pitchwise-averaged ψ for contours of Fig. 13

Grahic Jump Location
Fig. 15

ψ contours 0.7Cx downstream of trailing edges: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2

Grahic Jump Location
Fig. 16

Pitchwise-averaged ψ for contours of Fig. 15

Grahic Jump Location
Fig. 17

Velocity vectors and λCx/Ui contours: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2

Grahic Jump Location
Fig. 18

Turbulence quantities in plane 1: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2

Grahic Jump Location
Fig. 19

Turbulence quantities in plane 2: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2

Grahic Jump Location
Fig. 20

ψ contours 0.1Cx downstream of trailing edges, Re = 60,000: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2

Grahic Jump Location
Fig. 21

ψ contours 0.7Cx downstream of trailing edges, Re = 60,000: (a) B = 0, (b) B = 1, (c) B = 1.5, and (d) B = 2

Grahic Jump Location
Fig. 22

Pitchwise-averaged ψ for contours of Fig. 20

Grahic Jump Location
Fig. 23

Pitchwise-averaged ψ for contours of Fig. 21

Grahic Jump Location
Fig. 24

Area-averaged (0 < z/Cx < 0.6) total pressure coefficient normalized on B = 0 value at Re = 30,000 (solid symbols) and Re = 60,000 (open symbols)

Grahic Jump Location
Fig. 25

ψ contours 0.1Cx downstream of trailing edges: (a) 0.01Cx gap, B = 0, (b) 0.01Cx gap, B = 1.5, (c) 0.02Cx gap, B = 0, and (d) 0.02Cx gap, B = 1.5

Grahic Jump Location
Fig. 26

Area-averaged (0 < z/Cx < 0.6) total pressure coefficient normalized on B = 0 value for different tip gaps

Grahic Jump Location
Fig. 27

Velocity vectors and λCx/Ui contours: (a) 0.01Cx gap, B = 0, (b) 0.01Cx gap, B = 1.5, (c) 0.02Cx gap, B = 0, and (d) 0.02Cx gap, B = 1.5

Grahic Jump Location
Fig. 28

Tip leakage vortex strength as a function of tip gap size for cases with and without blowing in planes 1 and 2

Tables

Table Grahic Jump Location
Table 1 Cascade parameters
Table Grahic Jump Location
Table 2 Inlet endwall boundary layer parameters
Table Grahic Jump Location
Table 3 Jet holes of Fig. 7 axial locations
Table Grahic Jump Location
Table 4 Spatially averaged total pressure drop coefficient, ψ, in x = 0.1Cx and x = 0.7Cx planes (for Figs. 13, 15, 20, and 21)
Table Grahic Jump Location
Table 5 Spatially averaged total pressure drop coefficient, ψ, in x = 0.1Cx plane and Re = 30,000 for tip gaps of Fig. 25
Table Grahic Jump Location
Table 6 Tip leakage vortex average dimensionless swirl strength, cross-sectional area, and product of swirl and area for cases of Figs. 17 and 27

Errata

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