Vikram Shyam

Glenn Research Center, Cleveland, Ohio

Ali Ameri

The Ohio State University, Columbus, Ohio

Comparison of Various Supersonic Turbine

Tip Designs to Minimize Aerodynamic Loss

and Tip Heating

NASA/TM—2012-217607

July 2012

GT2011–46390
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Vikram Shyam

Glenn Research Center, Cleveland, Ohio

Ali Ameri

The Ohio State University, Columbus, Ohio

Comparison of Various Supersonic Turbine

Tip Designs to Minimize Aerodynamic Loss

and Tip Heating

NASA/TM—2012-217607

July 2012

GT2011–46390

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

TURBO EXPO 2011

sponsored by the American Society of Mechanical Engineers (ASME)

Vancouver, British Columbia, Canada, June 6–10, 2011
Acknowledgments

This work was supported by the Fundamental Subsonic Fixed Wing program at the NASA Glenn Research Center and addresses 

the milestone SFW.11.02.003—Develop and validate unsteady Reynolds Averaged Navier Stokes (RANS) and Large Eddy 

Simulations (LES) methods for engine fl ows. We would like to acknowledge the support of Dr. David L. Rigby, Arctic Slope 

Research Company (ASRC), who works at the NASA Glenn Research Center.

Available from

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Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2012-217607 1 

Comparison of Various Supersonic Turbine Tip Designs to 

Minimize Aerodynamic Loss and Tip Heating 

Vikram Shyam 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44130 

Ali Ameri 

The Ohio State University 

Columbus, Ohio 43210 

Abstract 

The rotor tips of axial turbines experience high heat flux 

and are the cause of aerodynamic losses due to tip clearance 

flows, and in the case of supersonic tips, shocks. As stage 

loadings increase, the flow in the tip gap approaches and 

exceeds sonic conditions. This introduces effects such as 

shock-boundary layer interactions and choked flow that are 

not observed for subsonic tip flows that have been studied 

extensively in literature. This work simulates the tip clearance 

flow for a flat tip, a diverging tip gap and several contoured 

tips to assess the possibility of minimizing tip heat flux while 

maintaining a constant massflow from the pressure side to the 

suction side of the rotor, through the tip clearance. The 

Computational Fluid Dynamics (CFD) code GlennHT was 

used for the simulations. Due to the strong favorable pressure 

gradients the simulations assumed laminar conditions in the 

tip gap. The nominal tip gap width to height ratio for this 

study is 6.0. The Reynolds number of the flow is 2.4105

based on nominal tip width and exit velocity. A wavy wall 

design was found to reduce heat flux by 5 percent but suffered 

from an additional 6 percent in aerodynamic loss coefficient. 

Conventional tip recesses are found to perform far worse than 

a flat tip due to severe shock heating. Overall, the baseline flat 

tip was the second best performer. A diverging converging tip 

gap with a hole was found to be the best choice. Average tip 

heat flux was reduced by 37 percent and aerodynamic losses 

were cut by over 6 percent. 

Nomenclature 

δ separation bubble height 

h tip gap height 

h heat transfer coefficient 

k thermal conductivity 

M Mach number 

Nu Nusselt number, hx/k

P pressure 

w tip width 

x distance along tip, with x = 0.0 at the pressure side 

edge 

Y aerodynamic loss coefficient 

Subscripts: 

0 total or stagnation conditions 

1 at inlet to tip gap 

2 at exit from tip gap 

Introduction 

A significant concern in turbine rotors is aerodynamic loss 

due to tip leakage. The pressure distribution set up around the 

rotor blade results in a pressure gradient across the tip gap of 

the rotor. The high pressure gas on the pressure side of the 

blade has a tendency to flow towards the suction side, which is 

at a lower pressure, across the tip. The path of the tip flow 

depends on several parameters such as blade rotational rate, 

blade geometry (tapering, twist, camber, tip gap height, and tip 

contouring) and flow inlet angle. These parameters can be 

reduced to the ratio of tip width to tip gap height, tip inlet 

Mach number and flow direction. No matter what the cause of 

the leakage flow, it results in a drop in efficiency and 

aerodynamic loss. 

A detailed literature review of the basic features of turbine 

tip flow and heat transfer has been conducted by Bunker 

(Ref. 1) and Glezer et al. (Ref. 2). Glezer et al. (Ref. 2) 

describe the primary flow features seen due to tip leakage: the 

pressure side separation bubble on the tip surface and the tip 

leakage vortex. The extent of the bubble and its reattachment 

are contingent on blade thickness, Mach number, Reynolds 

number and tip height (Refs. 2 and 3). For subsonic flows, the 

percentage of inlet flow that constitutes the tip leakage is 

shown to grow linearly with tip gap height. In both References 

1 and 2 the importance of Computational Fluid Dynamics 

(CFD) in tip flow and heat transfer prediction is emphasized 

especially due to the difficulty of conducting experimental 

measurements in a rotating tip gap. O'Dowd et al. (Ref. 4) 

used several techniques to measure the heat transfer 

coefficient and adiabatic wall temperature on a transonic 
NASA/TM—2012-217607 2 

turbine blade tip (Rolls Royce Environmentally Friendly 

Engine). The complexity of measuring accurately the heat flux 

in the tip gap is elaborated on and it is for this reason that CFD 

is of great benefit. Ameri et al. (Ref. 5) simulated the GE-EEE 

(Energy Efficient Engine) high pressure turbine stage and 

studied the tip flow and heat transfer for a smooth tip and for a 

recessed tip. The cavity height of the recess was varied in the 

study to analyze the effect of recess depth on tip heat transfer. 

Two primary vortex structures were observed in the recess. It 

was found that the recess had negligible effect on loss and did 

not improve the heat transfer distribution on the tip as a whole. 

Another study by Ameri et al. (Ref. 6) investigated the effect 

of upstream casing recess on tip leakage and heat transfer and 

found that minimal tip heat transfer occurred for a recess 

height that is almost equal to tip clearance. They concluded 

that the recess has little effect on efficiency. This can be 

explained by approximating the effective tip gap geometry by 

a diverging-converging nozzle. Unless the tip gap height is 

extremely small, the flow will first be expanded and then 

recompressed before exiting to the suction side. Hofer et al. 

(Ref. 7) conducted an experimental study of leakage flow for a 

non-rotating linear turbine cascade. The study looked at the 

impact of cooling in the tip gap for two squealer geometries. 

They considered a full squealer tip and a suction side squealer 

tip and concluded that the suction side squealer resulted in 

higher heat transfer and loss coefficient, 

01 2

01 02

P P

P P Y 

  . This 

is to be expected because at subsonic conditions, the suction 

side squealer tip effectively acts as a converging nozzle that 

accelerates flow through the tip. Hofer et al. (Ref. 7) state that 

neglecting the relative casing motion does not significantly 

alter the results citing previous studies like that of 

Krishnababu et al. (Ref. 8). The latter studied the effect of 

relative casing motion on tip heat transfer and tip leakage 

mass flow for two different tip gap heights. They concluded 

that the effect of relative casing motion is diminished for 

larger tip gap heights due to dominant inviscid effects. In the 

present study, the flow is dominated by inviscid effects owing 

to the high Mach number.

More recently, Wheeler et al. (Ref. 9) conducted a steady 

CFD simulation of tip flow for a transonic turbine rotor using 

the Spalart-Allmaras and the standard k-ε turbulence (with 

wall function) models. They state that at high speeds, the 

choice of turbulence model has little effect on heat transfer 

prediction. Using a quasi-3D approach, they observed a 

quicker reattachment of the separation bubble at higher Mach 

number. They also state that there is a drop in heat transfer 

coefficient due to decreased turbulent mixing at high Mach 

numbers and that the flow is dominated by local pressure 

gradients. As it is pointed out by Wheeler et al. (Ref. 9), high 

speed flow through the tip gap chokes the flow and therefore 

provides an opportunity to move toward higher stage loading 

without added tip losses. 

Shyam et al. (Refs. 10 and 11) performed a threedimensional unsteady simulation of a high pressure turbine 

stage and analyzed the flow in the tip region. The supersonic 

region of the tip was found to exhibit two-dimensional, 

laminar flow. Bands of high and low heat flux were observed 

corresponding to shocks and expansions. The separation 

bubble that forms at the pressure side lip acts as a converging 

diverging nozzle for the flow through the tip gap. The 

reattachment of the separation bubble is accompanied by 

increased heat flux. A throat (minimum available flow area) 

was formed near the tip gap entrance at the location of 

maximum separation bubble height, δ. The pressure ratio 

across the tip was sufficiently high to make the flow sonic at 

the throat. The expanding tip gap (due to the separation bubble 

reattachment) makes the flow supersonic. The flow was 

observed to be over-expanded and goes through a series of 

shocks and expansions before the flow reaches the pressure of 

the suction side. Two regions of tip flow were identified. The 

aft 70 percent of the tip was found to be fully supersonic while 

the leading edge region of the tip was found to be subsonic. 

The work discussed in this paper deals with the aft 

70 percent region where the flow is fully supersonic and 

choked. The flow in this region exhibits two-dimensionality 

and is only unsteady in a quantitative sense. Shyam et al. 

(Ref. 11) show that the unsteadiness results in a “hot spot” in 

the aft 70 percent on the tip caused by radial unsteadiness. 

However, the pattern of heat flux on the tip surface remains 

unchanged. It was suggested in Reference 11 that by 

contouring the tip geometry it would be possible to minimize 

tip heat flux without changing the tip leakage massflow due to 

the tip gap being choked. This study examines 5 different tip 

gap geometries in an attempt to reduce tip heat flux and to 

obtain a flat heat flux profile across the tip without increasing 

aerodynamic losses or tip leakage. The latter is fairly 

straightforward because the tip is choked. The region of the 

blade tip analyzed in this paper is shown in Figure 1. The 

range of width to height ratios is 6.0 to 2.0 for the particular 

geometry of (Refs. 10 and 11). The results of this study are 

applicable to blades experiencing regions of supersonic flow 

across the tip. 

Figure 1.—Extent of supersonic tip study (denoted by red 

arrow). 

w/h~6.5

w/h~2 
NASA/TM—2012-217607 3 

Numerical Setup 

The simulations presented in this paper were performed 

using the Reynolds-Averaged Navier-Stokes code GlennHT 

(Ref. 5). The code has previously been used to study tip heat 

transfer and loss (Refs. 13 and 14). A flat tip was considered 

the baseline case for this exercise. The flow properties were 

obtained from a three-dimensional CFD simulation (Ref. 10). 

The flow in the region of the rotor tip examined shows 

minimal three-dimensionality and the strong pressure gradient 

minimizes the impact of turbulence (Refs. 9 and 11). In this 

study a two-dimensional section of the tip is considered and 

the flow is assumed to be laminar. The results from the 

baseline case were compared to the three-dimensional model 

to ensure that the flow features were qualitatively similar. The 

approximate location of the two-dimensional study with 

respect to the three-dimensional study of (Refs. 10 and 11) is 

shown in Figure 2. It shows a three-dimensional representation 

of a turbine blade and a plane that is representative of flow in 

the aft 70 percent of the tip region. The ratio of tip width to tip 

height is approximately 6.0. In the region of the tip that 

represents a width to height of 2.0 or greater the supersonic 

flow causes a reattachment of the pressure side separation 

bubble. The exit Mach number was approximately 1.18 for all 

simulations to allow for a direct comparison. This also ensures 

that approximately the same massflow passes through the tip 

for the 5 cases considered here (because the tip is choked). 

The solid walls (tip and casing) are modeled as isothermal 

with wall temperature equal to 0.7 times the reference 

temperature. The reference temperature is the tip inlet 

temperature and was obtained from the three-dimensional 

simulation of (Ref. 10) and is consistent with the experiment 

of Tallman et al. (Ref. 12). The casing was assumed to be 

stationary due to the relatively thin boundary layer observed in 

Reference 11. 

Figure 2.—Plane showing shock structure in the tip gap 

from three-dimensional simulation (Ref. 11). 

The simulations were deemed converged when residuals 

achieved the value 10–8 and when tip surface heat flux over 

successive iterations was unchanged. The grids were 

generated using GridPro (Program Development Company) 

and were deemed refined based on previous studies (Refs. 9 

and 11). The grid consists of approximately 70 cells in the tip 

to casing direction and is more refined than the grids used in 

References 9 and 11. The y+ at the first cell off the wall is 

0.01. Five cases are presented here although several more 

geometries were considered. A few of the cases that are not 

presented in detail here are shown in the results section with a 

brief description of why the design was not examined further. 

The results shown here are not intended to be quantitatively 

accurate but serve as a guideline to designing a supersonic tip. 

Case 1: Baseline—Figure 3 shows the grid for the baseline 

case. The grid consists of approximately 81,000 cells with a 

majority of the cells located in the tip gap to resolve the flow. 

The tip gap height is 0.17w, where w is the width of the tip 

and measures 0.2587 in. 

Case 2: Diverging tip gap—Figure 4 shows the grid for this 

case. The tip gap height at the entrance to the tip gap is 0.17w. 

The tip gap height at the tip exit is 0.195w. Approximately 

76000 cells were used for this case. 

Figure 3.—Grid and boundary conditions for case 1 (flat).

Figure 4.—Grid for case 2 (diverging).

w 

Inlet

Exit

Symmetry 

Isothermal

Tip gap 

entrance Tip gap 

exit 

h

Plane showing 

density gradient 
NASA/TM—2012-217607 4 

Figure 5.—Grid for case 3 (wavy wall).

Figure 6.—Dimensions (inches) for case 3 (wavy wall). 

Figure 7.—Grid for case 4 (contoured tip).

Figure 8.—Dimensions (inches) for case 4 (contoured tip).

Figure 9.—Grid for case 5 (contoured tip with hole). 

Figure 10.—Dimensions (inches) for case 5 (contoured tip with 

hole). 

Case 3: Wavy wall—Figure 5 shows the grid for a tip 

contoured as a wavy wall. The grid consists of approximately 

73000 cells. The wavy wall was constructed using a spline 

whose control points are defined as shown in Figure 6. 

Case 4: Separation-Contoured tip—Figure 7 shows the grid 

for the contoured tip that consists of approximately 78000 

cells. The dimensions in inches of the contour are shown in 

Figure 8. The shape at the tip gap entrance was chosen to 

mimic the separation bubble at the pressure side entrance to 

the tip gap. 

Case 5: Separation-Contoured tip with hole—The grid for 

case 5 is shown in Figure 9 and the dimensions in inches for 

the hole location are shown in Figure 10. The grid consists of 

approximately 106000 cells. 

Results and Discussion 

Flow visualization was achieved using Fieldview 

(Intelligent Light). Figure 10 shows the Nusselt number on the 

flat tip surface (case 1). The solid line represents the solution 

using Wilcox’s k-ω turbulence model while the markers 

represent the laminar solution. The results of Figure 10 used a 

wall temperature of 0.9 times the reference temperature to 

make any effects of turbulence more obvious. 
NASA/TM—2012-217607 5 

Figure 11.—Comparison of laminar solution to turbulent 

solution for case 1. 

Figure 12.—Mach number contours for case 1. 

Figure 11 shows that the effect of turbulence is negligible. 

With the exception of a 2 percent difference in the peak heat 

flux at reattachment, the pattern and magnitude of Nusselt 

number on the tip surface are nearly identical for the laminar 

and turbulent solution. 

Figure 12 shows the Mach number contour for the baseline 

case, case 1. At the tip gap entrance the separation bubble 

causes a throat to form. The pressure ratio across the tip gap is 

sufficient to ensure that the flow at the throat is sonic. 

Downstream of the throat the flow expands to supersonic as 

explained in Reference 11. The series of shocks and 

expansions that ensues results in a series of peaks and valleys 

of high and low heat flux on the tip surface. Figure 13 shows 

the Nusselt number, Nu, on the tip for the five cases examined 

here. 

The peaks and valleys are caused by the thickening and 

thinning of the boundary layer as the shocks and expansions 

interact with the boundary layer. The boundary layer itself is 

responsible for the shocks and expansions by causing a change 

in effective flow area. Therefore, if it is possible to design the 

tip in such a way that the boundary layer thickness and the 

effective flow area are approximately constant it would be 

possible to generate a flat heat flux profile on the tip. 

Furthermore, it is desirable to maintain a region of separation 

and a thick boundary layer to minimize the surface heat flux. 

In Figure 13, for case 1, the heat flux peaks at x/w = 0.21. This 

is the region of reattachment where the boundary layer is 

thinnest and the strong (relatively) shock forms due to the 

change in flow geometry. As the boundary layer thickens and 

the shocks decrease in strength the peak values of heat flux are 

Figure 13.—Heat flux on the tip for five tip geometries.

Figure 14.—Comparison of separation bubbles for cases 1 

and 2.

Figure 15.—Mach number contours for case 2. 

reduced and the heat flux profile flattens out. Case 2 is a 

diverging tip gap. The idea was to gradually increase the flow 

area to compensate for boundary layer thickening after the 

first shock (most upstream location). While a thick boundary 

protects the tip surface it narrows the flow area in the tip gap 

and thus creates several shocks and reflections. By diverging 

the tip gap, the hope is to effectively keep the flow area 

constant. This would also extend the separation zone. 

Figure 13 shows that while downstream of the reattachment 

the heat flux profile is indeed “flattened”, the reattachment 

heating is far higher than for the baseline case. 

The reason for this is that the separation bubble has been 

flattened as shown in Figure 14. The reattachment point is also 

shifted downstream. This means that the Mach number and the 

shock heating at reattachment are much higher. The flatter 

separation bubble leads to a thinner boundary layer upon 

reattachment and a smaller “buffer” zone under the separation 

bubble (Fig. 15). This is why between x/w = 0.0 and x/w = 

0.45 the heat flux for case 2 is higher than the heat flux for 

Case 1 

Case 2 

Tip Separation bubble 
NASA/TM—2012-217607 6 

Figure 16.—Mach number contours for case 3. 

case 1. Downstream of x/w = 0.45 the boundary layer thickens 

and the heat flux drops gradually and consistently towards the 

suction side. 

Figure 15 clearly shows that the numerous shocks and 

expansions downstream of reattachment have been eliminated. 

However the region of high Mach number (red color) is still 

present above the separation bubble. The boundary layer (blue 

region) downstream of reattachment (near the tip exit) is much 

thicker for case 2 than for case 1. 

For case 3, the wavy wall was an approximate attempt at 

creating valleys in the tip profile at the shock locations. This 

would cause the effective flow area to remain unchanged. 

However, because the shocks and the boundary layer feed off 

each other, this is a difficult task and the ideal location of the 

peaks and valleys for the tip contour would vary with flow 

conditions. Figure 13 shows that while the heat flux profile is 

somewhat flattened, there is still some fluctuation downstream 

of reattachment. Peak heat flux was also not significantly 

changed. The contouring of the wall does however reduce the 

heat flux between x/w = 0.23 and x/w = 0.41 by significantly 

reducing the shock strength. Peak Mach number in the tip gap 

is also reduced from approximately 1.6 for cases 1 and 2 to 

1.52 for case 3. This can be seen in Figure 16. 

Further improvement to the wavy wall design could be 

beneficial if the design were not so sensitive to the flow. 

Therefore, in case 4 a converging-diverging-converging 

nozzle was attempted. The entrance to the tip gap is contoured 

to follow the separation bubble. The idea is to eliminate 

separation and reattachment or to have a gentle reattachment. 

This objective has clearly been achieved as evidenced from 

Figure 13 between x/w = 0.01 and x/w = 0.31. At the tip gap 

entrance the flow remains attached and the heating in the 

x/w = 0.01 to x/w = 0.31 region is purely due to the free stream 

flow conditions. Unfortunately, the diverging section extends 

too far downstream and the flow has too far to travel through a 

converging section that significantly increases the surface heat 

flux. This is due to the extremely thin boundary layer that 

develops in the absence of a separated region. There are 

pockets of separated flow on the tip that serve to reduce heat 

flux but shock boundary layer interaction compensates for this 

decrease in heat flux. Effectively, the net heat flux 

downstream of x/w = 0.40 is raised with respect to case 1. 

Figure 17 shows density gradient contours for case 4. It is 

interesting to note the ring shaped patterns in the tip gap. 

These “rings” enclose a region of high pressure and low Mach 

number. The upstream half of the rings are compressions and 

similar in structure to bow shocks. The downstream half of the 

rings are expansions. 

Figure 17.—Density gradient contours for case 4. 

Figure 18.—Comparison of separation regions for cases 4 

and 5. 

Figure 19.—Mach number contours in the tip gap for case 5. 

In order to provide the benefits of both the contoured tip gap 

entrance (case 4) and the flat profile downstream of separation 

in case 2 a fifth case (case 5) was simulated that features a 

hole connecting the pressure side of the tip to x/w = 0.37 on 

the tip that is just upstream of the location where heat flux 

from case 4 is seen to exceed the heat flux from case 1. In case 

5, the purpose of the hole is to add blockage to the tip gap and 

to energize the boundary layer downstream of x/w = 0.37. 

Figure 18 shows the separation region upstream of the hole for 

case 5 is markedly larger than in case 4, creating a smooth 

passage for the tip gap flow. Figure 19 shows the Mach 

number contours in the tip gap for case 5. 

Figure 19 shows that the flowpath seen by the tip leakage 

flow is relatively smooth. The shock train is therefore almost 

completely eliminated leading to a lower peak Mach number 

and less loss. It is true that the gas jetting out through the hole 

is hot. However the aim of this study was to see the effect of 

the jet on maintaining the heat flux profile along the tip 

surface. The jet velocity is sufficiently high that it lifts off 

from the surface. Unlike in a film cooling application where 

this is undesirable, the jet lift off ensures that hot gas from the 

hole is not in prolonged contact with the tip surface 

downstream of injection. Future designs could ensure that the 

hole is encased in cooling fluid or the hole could be a cooling 

hole. The density ratio of the jet (ratio of density at jet exit to 

density at throat) is approximately 1.45. The blowing ratio 

(ratio of massflow per unit area at jet exit to massflow per unit 

area at throat) is approximately 0.65. 

 

Separation 

Case 5 

Case 4 
NASA/TM—2012-217607 7 

In either case, it is clear that the objective of energizing the 

boundary layer and creating an extended buffer zone is 

achieved with the exception of the near-hole region. In reality, 

the heat flux downstream of the hole could be expected to lie 

somewhere between that of case 1 and case 5 (shown in 

Fig. 10). The peak shown in Figure 13 will also probably be 

found to be exaggerated should an experiment be done to 

simulate case 5. This is an assumption based on CFD 

predictions of film cooling where CFD shows a sharp increase 

in cooling effectiveness in the near-hole region and a sudden 

drop to near zero effectiveness downstream. Experiments have 

shown that this is in fact not the case (Ref. 15). In case 5, 

upstream of the hole, there is a separation region that was not 

present in case 4. This is due to the blockage created by the 

jet. The net result is a lower heat flux upstream of the jet as 

well. Table 1 shows the cases and the improvement over the 

baseline case with respect to average tip heat flux and loss (by 

measuring entropy generation). 

With the exception of case 5, the baseline case has the least 

aerodynamic loss. Case 3 has lower average heat flux than 

case 1 and has a flatter heat flux profile. Case 5 is the best 

design with the exception of the near hole region. Case 5 

shows a 6.98 percent decrease in loss compared to the baseline 

case. The average heat flux for case 5 is 37.32 percent lower 

than for case 1 while the heat flux from case 3 is only 

5.1 percent lower. As mentioned earlier, case 3 can be greatly 

improved by contouring the wavy wall to compliment the 

shock boundary layer interaction but the contouring would be 

very sensitive to any flow variations. Case 5 however uses the 

tip inlet geometry to form the throat. While there may be some 

fluctuation of heat flux upstream of the hole, there is a 

sufficient heat flux margin for case 5. 

Several other configurations were also simulated that are 

not presented here. Figure 20 shows one such geometry purely 

as a caution for its unsuitability to supersonic tip flows. Over 

670000 cells were used to grid this geometry due to the 

interesting flow visualizations seen here. The geometry is 

similar to a tip recess (also modeled.) The large expansion 

region causes extremely high Mach numbers (maximum Mach 

number is 2.6) and causes the flow to be unsteady due to 

supersonic cavity flow effects. There are severe shocks and 

the heat flux on the surface is several orders of magnitude 

higher than for the flat tip (case 1). Figures 21 and 22 show 

more images of the flow through the recess-like tip gap. The 

contours are of Mach number. Figure 21 shows the subsonic 

region of the flow while Figure 22 shows the supersonic 

region. They are separated for clarity. Other geometries that 

were attempted include several converging tip gap shapes. 

These converging tip gaps are unable to support the pressure 

drop across the tip gap due to the presence of the separation 

bubble (once the flow is sonic at the throat a converging 

downstream section will cause a pressure rise instead of the 

necessary pressure drop that is needed to achieve the suction 

side pressure). A conventional recess tip was also modeled 

and found to perform poorly. 

TABLE 1.—COMPARISON OF 6 TIP GEOMETRIES 

Case tip 

geometry 

Reduction 

tip average 

heat flux 

Peak 

Mach 

number 

Loss 

improvement 

 % % 

1. Flat 0.00 1.65 0.00 

2. Diverging –15.20 1.59 –39.53 

3. Wavy 5.10 1.45 –1.16 

4. Contoured –39.40 1.60 –0.47 

5. Hole+contour 37.32 1.27 6.98 

Recess –120.0 2.50 3.72 

Figure 20.—Density gradient contours in a supersonic tip 

recess.

Figure 21.—Instantaneous Mach number contours in a 

supersonic tip recess (subsonic regime).

Figure 22.—Instantaneous Mach number contours in a 

supersonic tip recess (supersonic regime). 
NASA/TM—2012-217607 8 

Conclusions 

Five different two-dimensional tip geometries were 

simulated using the CFD code GlennHT (Ref. 5). The baseline 

case was a flat tip. Overall, the contoured tip geometry with a 

hole (case 5) had lower aerodynamic loss, lower average heat 

flux and a more flat heat flux profile. The shock-boundary 

layer interaction makes it a challenge to design tip geometry 

for a particular system of shocks. The ideal supersonic tip 

should have a nearly constant boundary layer thickness and a 

thick boundary layer. It has been shown that it is possible to 

manipulate the shock structure in the tip gap by changing the 

tip geometry to achieve this goal. 

Future Work 

In order to build on the results from the simulation of case 5 

an optimizer could be used to contour the aft region of the tip 

to keep the boundary layer thickness fairly constant. It would 

also be interesting to see the effect of turbulence on the 

geometry of case 5 and to replace the pressure side hole with a 

cooling hole. 

References 

1. Bunker, R.S., “A Review of Turbine Blade Tip Heat 

Transfer,” Annals of the New York Academy of 

Science, Vol. 934, pp 64-79, January 2006. 

2. Glezer, B., Harvey, N.W., Camci, C., Bunker, R.S., 

Ameri, A.A., “Turbine Blade Tip Design and Tip 

Clearance Treatment,” notes from von Karman Lecture 

Series 2004, June 2004. 

3. Zhou, C., and Hodson, H., “The Tip Leakage flow of an 

Unshrouded High Pressure Turbine Blade With Tip 

Cooling,” ASME-GT2009-59637, June 2009. 

4. O'Dowd, D., Zhang, Q., Ligrani, P., He, L., Friedrichs, 

S., “Comparison of Heat Transfer Measurement 

Techniques on a Transonic Turbine Blade Tip,” ASMEGT2009-59376, June 2009. 

5. Ameri, A.A., Steinthorsson, E., Rigby, D.L., “Effect of 

Squealer Tip on Rotor Heat Transfer and Efficiency,” 

Journal of Turbomachinery, Vol. 120, pp 753-759, 

October 1998. 

6. Ameri, A.A., Steinthorsson, E., Rigby, D.L., “Effects of 

Tip Clearance and Casing Recess on Heat Transfer and 

Stage Efficiency in Axial Turbines,” Journal of 

Turbomachinery, Vol. 121, pp 683-693, October 1999. 

7. Hofer, T., Arts, T., “Aerodynamic Investigation of the 

Tip Leakage Flow for Blades With Different Tip 

Squealer Geometries at Transonic Conditions,” ASMEGT2009-59909, June 2009. 

8. Krishnababu, S.K., Dawes, W.N., Hodson, H.P., Lock, 

G.D., Hannis, J., Whitney, C., “Aero-Thermal 

Investigations of Tip Leakage Flow in Axial Flow 

Turbines, Part II -Effect of Relative Casing Motion,” 

ASME 2007-GT-27957, May 2007. 

9. Wheeler, A.P.S., Atkins, R., He, L., “Turbine Blade Tip 

Heat Transfer in Low and High Speed Flows,” ASMEGT2009-59404, June 2009. 

10. Shyam, V., Ameri, A., Luk, D.F., and Chen, J.P., “3-D 

Unsteady Simulation of a Modern High Pressure 

Turbine Stage Using Phase Lag Periodicity: Analysis of 

Flow and Heat Transfer,” Journal of Turbomachinery, 

Vol. 133, Iss. 3, July 2011. 

11. Shyam V., Ameri A., Chen J.P., “Analysis of Unsteady 

Tip and Endwall Heat Transfer in a Highly Loaded 

Transonic Turbine Stage,” GT2010-23694, June 2010. 

12. Tallman, J.A., Haldeman, C.W., Dunn, M.G., Tolpadi, 

A.K., and Bergholz, R.F., “Heat Transfer Measurements 

and Predictions for a Modern, High-Pressure, Transonic 

Turbine, Including Endwalls,” ASME-GT2006-90927, 

May 2006. 

13. Ameri, Ali A., “Heat Transfer and Flow on the Tip of a 

Gas Turbine Equipped With a Mean-Camberline Strip,” 

ASME paper 2001-GT-0156, June 2001, NASA/CR—

2001-210764. 

14. Ameri, A.A. and Bunker, R.S., “Heat Transfer and Flow 

on the First Stage Blade Tip of a Power Generation Gas 

Turbine, Part 2: Simulation Results,” ASME paper 99-

GT-283, June, 1999, also NASA/CR-1999-209151, 

April, 1999. 

15. Sinha, A.K., Bogard, D.G., and Crawford, M.E., “FilmCooling Effectiveness Downstream of a Single Row of 

Holes With Variable Density Ratio,” Journal of 

Turbomachinery, Vol. 113, pp 442-449, 1991. 
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4. TITLE AND SUBTITLE

Comparison of Various Supersonic Turbine Tip Designs to Minimize Aerodynamic Loss and 

Tip Heating 

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6. AUTHOR(S)

Shyam, Vikram; Ameri, Ali 

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WBS 561581.02.08.03.21.14.03 

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14. ABSTRACT

The rotor tips of axial turbines experience high heat flux and are the cause of aerodynamic losses due to tip clearance flows, and in the case 

of supersonic tips, shocks. As stage loadings increase, the flow in the tip gap approaches and exceeds sonic conditions. This introduces 

effects such as shock-boundary layer interactions and choked flow that are not observed for subsonic tip flows that have been studied 

extensively in literature. This work simulates the tip clearance flow for a flat tip, a diverging tip gap and several contoured tips to assess the 

possibility of minimizing tip heat flux while maintaining a constant massflow from the pressure side to the suction side of the rotor, through 

the tip clearance. The Computational Fluid Dynamics (CFD) code GlennHT was used for the simulations. Due to the strong favorable 

pressure gradients the simulations assumed laminar conditions in the tip gap. The nominal tip gap width to height ratio for this study is 6.0. 

The Reynolds number of the flow is 2.4×105 based on nominal tip width and exit velocity. A wavy wall design was found to reduce heat 

flux by 5 percent but suffered from an additional 6 percent in aerodynamic loss coefficient. Conventional tip recesses are found to perform 

far worse than a flat tip due to severe shock heating. Overall, the baseline flat tip was the second best performer. A diverging converging tip 

gap with a hole was found to be the best choice. Average tip heat flux was reduced by 37 percent and aerodynamic losses were cut by over 6 

percent. 

15. SUBJECT TERMS

Supersonic heat transfer; Supersonic turbine; Supersonic flow blade tips 

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