A.A. Ameri

AYT Corporation, Brook Park, Ohio

R.S. Bunker

General Electric Corporation, Schenectady, New York

Heat Transfer and Flow on the First Stage Blade

Tip of a Power Generation Gas Turbine

Part 2: Simulation Results

NASA/CR—1999-209151

April 1999

ASME 99–GT–283
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A.A. Ameri

AYT Corporation, Brook Park, Ohio

R.S. Bunker

General Electric Corporation, Schenectady, New York

Heat Transfer and Flow on the First Stage Blade

Tip of a Power Generation Gas Turbine

Part 2: Simulation Results

NASA/CR—1999-209151

April 1999

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Contract NAS3–98106

Prepared for the

44th Gas Turbine and Aeroengine Congress, Exposition, and Users' Symposium

sponsored by the International Gas Turbine Institute of

the American Society of Mechanical Engineers

Indianapolis, Indiana, June 7–10, 1999

ASME 99–GT–283
Acknowledgments

This work was sponsored by the Smart Green Engine Project managed at NASA Glenn Research Center (formerly

NASA Lewis Research Center) by Mr. Kestutis Civinskas. Helpful suggestions offered to the first author by his

colleagues Mr. Robert Boyle, Dr. David Rigby, and Dr. Erlendur Steinthorsson are hereby acknowledged. Some of

the computations were performed on the CRAY–C90 of NAS at NASA Ames Research Center.

Available from

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1

ABSTRACT

A combined experimental and computational study has been

performed to investigate the detailed distribution of convective

heat transfer coefficients on the first stage blade tip surface for a

geometry typical of large power generation turbines(>100MW).

This paper is concerned with the numerical prediction of the tip

surface heat transfer. Good comparison with the experimental

measured distribution was achieved through accurate modeling of

the most important features of the blade passage and heating

arrangement as well as the details of experimental rig likely to

affect the tip heat transfer. A sharp edge and a radiused edge tip

were considered. The results using the radiused edge tip agreed

better with the experimental data. This improved agreement was

attributed to the absence of edge separation on the tip of the

radiused edge blade.

NOMENCLATURE

Cp constant pressure specific heat

h heat transfer coefficient

Pr Prandtl number

R gas constant

Re Reynolds number

T temperature/

Tu turbulence intensity

V magnitude of the velocity/(R T0) 1/2

dimensionless distance from a wall,

specific heat ratio

Subscripts

t total conditions

0 total inlet condition

T0

y

+ y+ y

v

*

ν = ----

γ

INTRODUCTION

Blade tips are susceptible to burnout and oxidation due to

high thermal loading associated with flow through blade tip gaps.

Efficient internal or film cooling schemes are necessary to protect

the blade against damage. The design of such schemes requires

detailed knowledge of heating patterns on and near the tip which

could be gained by predictive methods. The quality of the

predictive method can only be assessed through comparison with

relevant experimental data. In the absence of comprehensive data

on tip heat transfer, in order to validate computations relating to

tip and casing treatments and their effects on heat transfer, the

available data on various aspects not directly related to the blade

tip heat transfer have been relied upon. For example, for the

assessment of the effect of tip recess on the tip heat transfer and

efficiency, Ameri et al. (1998a) used the data of Metzger et

al.(1989) for modeled tip recess to verify the applicability of the

numerical scheme and especially the turbulence model.

Numerical prediction of the effect of the casing recess on the

blade and tip heat transfer and efficiency (Ameri et al. 1998b)

was deemed reliable on the basis of the good experiences of the

past with the numerical scheme and favorable comparison of the

calculated efficiency as a function of tip clearance height with

experimental correlations.

There are in fact some heat transfer data available on blade

tips but are limited to discrete point measurements on locations

mainly along the mean camber line of the tip of rotating blades

(Dunn et al. 1984a,1984b and Dunn and Kim, 1992). The data do

provide a useful check on the numerical prediction of heat

transfer as was done by Ameri and Steinthorsson (1995, 1996).

As the variation of the rate of heat transfer on the tip can be large,

the complete map of the tip heat transfer would of course be more

useful and agreement with such data more reassuring.

The complete measured heat transfer map of the blade tip as

presented in part 1 of this paper provides the valuable test case

which can engender confidence in the numerical solutions. The

 Heat Transfer and Flow on the First Stage Blade Tip of a Power Generation Gas Turbine

Part 2: Simulation Results

A. A. Ameri

 AYT Corporation, Brook Park, OH, USA

R. S. Bunker

General Electric Corp. R & D Center

Schenectady, NY, USA

NASA/CR—1999-209151
2

results reported in this paper constitute the first reported direct

comparison between the experimental and numerical calculation

of blade tip heat transfer. It is also the first time a computation on

a radiused edge tip is presented.

The paper is organized as follows: In the ensuing section a

brief description of the experimental setup will be provided.

Following this the numerical method used in the simulations will

be described. Subsequently the results of the numerical

simulations will be presented and finally a summary and the

conclusions of the work will be presented.

THE EXPERIMENTAL SETUP

The experimental setup and conditions will be briefly

discussed in this section. A detailed description can be found in

part 1 of this paper.

Figure 1 shows the definition of the airfoils and the shroud.

The blade profiles are typical of a large power generation turbine.

The cascade is linear and the span is 10.16cm. As can be seen the

shroud contains a step or a recess ahead of the blades to model a

similar feature found in an actual turbine shroud. The tip

clearance varies from 1.27 to 2.79 mm. However in this paper we

will exclusively address the nominal gap width of 2.03 mm.

Figure 2 shows the design of the actual two passage blade

cascade.

The experiments were conducted using two types of blade

tips namely, a sharp edged tip and a radiused tip with a radius of

2.54 mm around the perimeter of the tip. The measurements were

taken on the tip of the middle blade. The adjacent blades are

simulated by the use of contoured walls. A splitter plate was

placed ahead of the blade to help force equal mass flow rate in the

two passages.

Table I lists the run conditions for the cascade and input to

the numerical simulations. Our calculations were limited to the

5% turbulence intensity.

THE COMPUTATIONAL METHOD

The simulations in this study were performed using a multiblock computer code called LeRC-HT, previously known as

TRAF3D.MB(Steinthorsson et al. 1993) which is based on a

single block code designed by Arnone et al. (1991). This code is

a general purpose flow solver designed for simulations of flows in

complicated geometries. The code solves the full compressible

Reynolds-averaged, Navier-Stokes equations using a multi-stage

Runge-Kutta based multigrid method. It uses the finite volume

method to discretize the equations. The code uses central

differencing together with artificial dissipation to discretize the

convective terms. The overall accuracy of the code is second

order. The present version of the code (Rigby et al. 1996, 1997

and Ameri et al. 1998a) employs the k-ω turbulence model

developed by Wilcox (1994a,1994b) with modifications by

Menter (1993). The model integrates to the walls and no wall

functions are used. For heat transfer a constant value of 0.9

turbulent Prandtl number, Prt is used. A constant value for

Prandtl number (Pr) equal to 0.72 is used. Viscosity is a function

of temperature through a 0.7 power law (Schlichting, 1979) and

 is taken to be a constant.

GEOMETRY MODELING AND THE GRIDS

Two types of modeling were utilized for the present problem.

Cp

13.37 cm

44.9 

65.75 

5.19 cm

12.45 cm

2 mm Tip

3.43 cm Shroud

LE TE

Fig. 1 Airfoil and shroud definition

splitter plate turbulence bars

turbulence grids

Fig. 2 The cascade

TABLE 1. Run Conditions

Pressure ratio across the blade row 0.69

Exit Reynolds number 2.57E6

Inlet Mach number 0.30

Turbulence intensity 5% and (9%)

Inlet angle 44.9 deg.

NASA/CR—1999-209151
3

(a) Modeling of the flow using a periodic blade cascade as shown

in Fig. 3 and (b) modeling using the complete flow path including

the splitter plate. For both of the above the casing recess is

included. Details of the casing recess can be seen more closely in

Fig. 4(b). The casing recess also extended over the splitter plate

as was the case in the experiment. Sharp and radiused edged tips

were used. Figure 5 shows a radiused edge blade. The same grid

topology was used with the radiused and the sharp edge grid. The

grid is generated using a commercially available computer

program called GridProTM. The sharp edge case was run with the

side walls modeled using slip and no slip boundary conditions. It

was decided that since the heat transfer and pressure results did

not differ significantly the slip boundary condition for the side

walls be used for the radiused edge case in order to conserve

CPU time. The model in Figure 3 consisted of 1.2 million cells.

The model of Fig. 4, it consisted of 1.4 or 1.8 million cells

depending on whether slip or no-slip side walls were used. The

viscous grid is generated by embedding grid lines where needed,

including the grid around the splitter. The stretching ratio did not

exceed 1.25 for the viscous grid away from the no-slip surfaces.

The distance to the first cell center adjacent to solid wall is such

that the distance in wall units, (y+) is near or below unity. To

resolve the boundary layers 33-35 grid points are used. This does

not include the “inviscid” blade to blade grid which is also quite

fine. Within the tip 65-69 grid point are used in the spanwise

direction. At the inlet patch the number of grid points is 85 in the

pitchwise and 97 in the spanwise direction.

RESULTS AND DISCUSSION

General Remarks

All the cases presented herein have been converged to better

than 0.002% mass flow error between the inlet and the exit of the

computational domain. The residual for all the cases dropped 6 to

7 orders of magnitude. Typically 2000 fine grid iterations with

two levels of multigrid were necessary for convergence. The heat

transfer results have been checked for convergence by comparing

solutions after consecutive runs of 300 iterations.

(a)

Fig. 3 Overall grid using periodic flow assumption.

Fig. 4 Modeling the complete passage. (a) Overall geometry

and grid. (b) Close up near the leading edge

Fig. 5 Radiused edge tip and the surface grid

(b)

casing recess

NASA/CR—1999-209151
4

A number of calculations were made to help determine the

proper way of modeling the geometry. The choices were a linear

cascade with periodic boundary conditions and modeling the

channels as in the experimental rig. The results as relates to the

pressure distribution is presented in the next section. The heat

transfer results are presented in the subsequent section.

Pressure Distribution

As described in Part 1, the experimental blade passage

consists of one blade with variable clearance and two shaped

walls representing the adjacent blades. It might be expected that

any similarity to a periodic flow in the two passages is quickly

lost as one approaches the tips of the blade since the flow passes

over only the center blade. Figure 6 shows the pressure

distribution at the midspan and near the tip of the blade for an

experimental run for which the tip gap is closed. The numerical

prediction in that figure is done using a periodic setup as in Fig.

3. The calculated midspan pressure distribution matches the

characteristics of the experimental measurements leading to the

conclusion that the midspan flow is quite periodic. Near the tip

the agreement between the experimental and the numerical

results is lost. This indicates that the assumption of periodic flow

is not a realistic option for calculation of quantities in the endwall

region.

Figure 7 shows the calculated near tip pressure distribution

for periodic and complete passage simulations. The agreement

with the near tip pressure distribution appears to improve

considerably by accounting for the side walls and the splitter

plate. Figure 8 shows the pressure distribution on the tip of the

blade. The pressure tap locations are near the edge of the blade as

shown on the insets. The agreement appears to be good. As

expected the agreement with the results obtained using periodic

boundary conditions was quite bad and is not shown here. Good

agreement with the measured data was also obtained, as shown in

Fig. 9, for the blade tip pressure when a radiused tip blade is

used.

0.0 0.2 0.4 0.6 0.8 1.0

Normalized Airfoil Axial Distance

1.0

1.2

1.4

1.6

1.8

2.0

Total Pressure/Local Static Pressure

Sharp Tip Calculated

Radiused Tip Calculated

Sharp Tip Periodic Calculated

Near Tip Exp. Data 

0.0 0.2 0.4 0.6 0.8 1.0

Normalized Airfoil Axial Distance

1.00

1.20

1.40

1.60

1.80

Total Pressure/Local Static Pressure

Calculated P/S

Calculated S/S

Data P/S

Data S/S

Fig. 6 Blade pressure distribution data and computed pressure

distribution using periodic conditions.

Fig. 8 Blade tip surface pressure distribution with sharpedged tip and the baseline clearance(2.03 mm).

0.0 0.2 0.4 0.6 0.8 1.0

Normalized Axial Distance

1.0

1.5

2.0

2.5

Total Pressure/Local Static Pressure

Calculated P/S

Calculated S/S

Data P/S

Data S/S

Fig. 9 Blade tip surface pressure distribution with round-edged

tip and the baseline clearance(2.03 mm).

0.0 0.2 0.4 0.6 0.8 1.0

Normalized Airfoil Axial Distance

1.0

1.4

1.8

2.2

Total Pressure/Local Static Pressure

Midspan, No Gap, Data

Near-Tip, No Gap, Data

Midspan, No Gap, Calculated

Near-Tip, No Gap, Claculated

Midspan, With Gap, Calculated

Fig. 7 Near tip pressure distribution data and computed pressure

distribution using the complete passage and periodic cascade.

NASA/CR—1999-209151
5

Figures 11 and 12 show the measured and computed heat

transfer coefficient for the sharp edge tip and radiused edged

cases. For the sharp edge case, it might be said that the general

agreement is good. The largest relative difference between the

experimental and calculated values is in the area of the ‘sweet

spot’ (see part 1) where the error reaches 30%. However the

agreement is good elsewhere and is generally below 15-20% of

the measured value. In addition, the region of high heat transfer

rate which was marked as area (4) in the part 1 of this paper

corresponding to the high entry loss region is captured. The

experimental measurements show the highest heat transfer rate

under the present conditions to take place in the trailing edge

region. This is backed up by the numerical calculation.

Figure 12 shows experimental and calculated tip heat transfer

for the radiused edge blade. The agreement in this case is much

improved over the sharp edge case above, and is consistently

better than 15% over the entire tip. Apparently the prediction is

helped by rounding of the edges which eliminates the separation

and reattachment on the blade tip. Figures 13(a) and (b) show the

flow streamlines over the tip of the blade with the sharp and

radiused edges. The separation vortex is present everywhere along

the pressure side of the sharp edge blade tip and becomes quite

large starting from the maximum loss region. On the other hand

the flow over radiused edge tip is quite smooth and there is no sign

of any vortical structures present on the blade tip.

The agreement between the calculations and the measured

results is quite good, especially if one considers the fact that the

flow over the tip is also influenced by the upstream casing recess.

The analysis performed lead us to the conclusion that the

experimental data do not lend themselves to predictions using

periodic modeling of the flow and at least the side walls need to

be incorporated in the computational domain. A run without the

splitter plate was not attempted but it is safe to assume that the

existence of the splitter is necessary as it was in the experiments

to help with equalizing the flow rate between the two channels.

Heat Transfer

The present computational method has been applied to a

variety of turbine heat transfer problems both using an algebraic

turbulence model (Ameri and Steinthorsson 1995, 1996) and as

with the present calculations using a low Reynolds number twoequation model. The present turbulence model was tested against

the heat transfer data of Metzger et. al. (1989) for flow over a

cavity to show suitability of the model for blade tip recess flows

in Ameri et al. (1998a). Very good comparison using the current

method for blade surface heat transfer with experimental data

was achieved by Garg and Rigby (1998).

The rate of heat transfer is presented in terms of the heat

transfer coefficient which is defined as:

(1)

Tinlet is the inlet total temperature and Twall is the wall

temperature. Twall was determined from the experimental

measurements and found to be 1.06 times the inlet total

temperature. The heat transfer coefficient was calculated on the

blade tip in the gridded area shown in Fig. 10a where a constant

temperature boundary condition is imposed. A constant

temperature boundary condition results in a much faster

convergence than a constant heat flux boundary condition.

Although the experiment was run using a constant heat flux

boundary condition, it is expected and was found to be true that

the constant heat flux and constant temperature boundary

condition yield similar results in the present fully turbulent flow

regime. Also the assumption of constant wall boundary condition

is justifiable on the grounds that the experimental variation in the

wall temperature was quite small. An effectively adiabatic

boundary condition was imposed on all the other surfaces. The

experimental measuring area is shown in Fig. 10b. The areas are

quite equivalent with the exception of the trailing edge where the

computational heated area extends further back on the blade.

The definition of heat transfer coefficient in equation (1) was

chosen to be consistent with the experimental data. Use of

adiabatic wall temperature instead of inlet total temperature leads

to a more general definition. The present definition is more

convenient computationally as it does not require the calculation

of adiabatic wall temperature. In the present study the

experimental variables are matched as much as possible to make

the comparison and thus the conclusions valid.

Both the sharp edge and radiused edge cases with the tip gap

of 2.03 mm and a 5% turbulence intensity at the inlet were

studied. A very thin boundary layer thickness of 0.1% of the

passage height was imposed at the inlet to the computational

domain. Also a turbulence intensity of 10% with a length scale of

1% of blade chord were imposed at the inlet. This yielded a

turbulence intensity of 4% at the inlet to the blade cascade.

h Qwall

Twall Tinlet ( ) – = -------------------------------------

(a)

(b)

HEATED AREA

Fig. 10 Heat transfer blade tip (a) computational domain and

(b) measuring area

NASA/CR—1999-209151
6

Fig. 11 Sharp edge blade tip heat transfer coefficient for

2.03 mm clearance and Tu=5%. (W/m2/K), (a) Measured

and (b) calculated

900

1000

800

1200 1000 900

800

700

600

(a)

800

900

700

900

1100

1300

1500

1700

1000

1100

(b)

800

700

900

1200

1000

1200

1400 1600

1500

(b)

700

900

800

1000

1400 1200

1000

900

800

700

600

(a)

Figures 14(a) and 14(b) show the magnitude of the velocity

over the blade tip at the mid gap location. The relative magnitude

of the velocity between the two cases and the respective tip heat

transfer rates are well correlated. This is especially true

downstream of the mid chord. Ameri et al. (1998b) showed that

the most influential factor in raising the rate of tip heat transfer is

the magnitude of the velocity. This was shown by noting the

change in the magnitude of the velocity as well as the turbulence

intensity and the total temperature as the gap was widened.

SUMMARY AND CONCLUSIONS

In this paper the numerical prediction and comparison with

the experimental data of tip heat transfer for a blade representing

a first stage blade of a large power generation turbine was

undertaken. The casing, upstream of the blade tip was recessed. It

was found that for the calculation of blade tip heat transfer for the

present experimental model of the tip, assumption of periodic

flow was invalid and the entire passage had to be modeled. It was

found that a good representation of the tip heat transfer can be

made by our numerical method consisting of a cell centered finite

volume scheme and a k-ω low Reynolds number turbulence

model. The numerical results for the radiused edge blade agreed

better with the experimental data. This could be due to the

Fig. 12 Radiused edge blade tip heat transfer coefficient for

2.03 mm clearance and Tu=5%. (W/m2/K), (a) Measured

and (b) calculated

(b)

(a)

Fig. 13 Flow streamlines over the blade tip for (a) sharp

edge blade and (b) radiused edge blade.

NASA/CR—1999-209151
7

absence of separation on the blade tip for the radiused edge

blade.

REFERENCES

Ameri, Ali A., and Steinthorsson, E., 1995, “Prediction of

Unshrouded Rotor Blade Tip Heat Transfer,” ASME 95-GT-142.

Ameri, Ali A., and Steinthorsson, E., 1996, “Analysis of Gas

Turbine Rotor Blade Tip and Shroud Heat Transfer,” IGTI 96-

GT-189.

Ameri, Ali A., and Steinthorsson, E., Rigby, David L.,

1998a, “Effect of Squealer Tip on Rotor Heat Transfer and

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

Ameri, A. A., Steinthorsson, E. and Rigby, D. L. 1998b,

“Effects of Tip Clearance and Casing Recess on Heat Transfer

and Stage Efficiency in Axial Turbines,” ASME paper 98-GT369., to published in the Journal of Turbomachinery.

Arnone, A., liou, M.S., and Povinelli, L. A., 1991,

“Multigrid Calculation of Three Dimensional Viscous Cascade

Flows”, AIAA Paper 91-3238.

Dunn, M. G., Kim, J. 1992, “Time-Averaged Heat Flux and

Surface Pressure Measurements on the Vanes and Blades of the

SSME Fuel Side Turbine and Comparison with Prediction for a

Two Stage Turbine,” Journal of Turbomachinery, Vol. 116, pp.

14-22

Dunn, M.G., Rae, W.J. and Holt, J.L. 1984a, “Time

Measurement and Analyses of Heat Flux Data in a Turbine Stage:

Part I- Description of Experimental Apparatus and Data

Analysis,”, ASME Transactions, Journal of Turbomachinery, Vol.

106, No. 1, pp. 229-233.

Dunn, M.G., Rae, W.J. and Holt, J.L. 1984b, “Time

Measurement and Analyses of Heat Flux Data in a Turbine Stage:

Part II- Discussion of Results and Comparison with Predictions,”,

ASME Transactions, Journal of Turbomachinery, Vol. 106, No. 1,

pp. 234-240.

Garg, Vijay, K. and Rigby, David L., “Heat Transfer on a

Film-Cooled Blade-Effect of Hole Physics”, ASME 98-GT-404.

Menter, Florian R., 1993, “Zonal Two-Equation k-ω

Turbulence Models for Aerodynamic Flows,” AIAA-93-2906.

Metzger, D. E., Bunker, R. S. and Chyu, M. K., 1989,

“Cavity Heat Transfer on a Transverse Grooved Wall in a Narrow

Channel”, J. of Heat Transfer, Vol. 111, pp. 73-79.

Rigby David, L., Ameri Ali, A. and Steinthorrson E., 1996,

“Internal Passage Heat Transfer Prediction Using Multiblock

Grids and k-ω Turbulence Model,” IGTI paper 96-GT-188.

Rigby, D. L., Ameri A., A. and Steinthorrson E., 1997,

“Numerical Prediction of Heat Transfer in a Channel with Ribs

and Bleed,” ASME 97-GT-431.

Schlichting, H. Boundary Layer Theory. McGraw-Hill, New

York, seventh ed. pp. 312-313.

Steinthorsson, E., Liou, M. S., and Povinelli, L.A., 1993,

“Development of an Explicit Multiblock/Multigrid Flow Solver

for Viscous Flows in Complex Geometries,” AIAA-93-2380.

Wilcox, D. C., 1994a, Turbulence Modeling for CFD, DCW

industries, Inc. La Canada, CA.

Wilcox, D. C., 1994b, “Simulation of Transition with a TwoEquation Turbulence Model,” AIAA Journal, Vol. 32, No.2, pp.

247-255.

Fig.14 Magnitude of the velocity (V), at the mid gap height of

the blade tip for (a) sharp edge blade and (b) for the radiused

edge blade.

(a)

0.4

0.8

(b)

0.4

1.0

NASA/CR—1999-209151
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13

A03

Heat Transfer and Flow on the First Stage Blade Tip of a Power

Generation Gas Turbine

Part 2: Simulation Results

A.A. Ameri and R.S. Bunker

Gas turbine; Blade tip; Heat transfer; Numerical simulation

WU–523–26–13–00

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NAS3–98106

AYT Corporation

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Unclassified -Unlimited

Subject Categories: 02 and 34 Distribution: Nonstandard

Prepared for the 44th Gas Turbine and Aeroengine Congress, Exposition, and Users' Symposium sponsored by the International Gas Turbine Institute of the American Society of Mechanical Engineers, Indianapolis, Indiana, June 7–10, 1999.

A.A. Ameri, AYT Corporation, 2001 Aerospace Parkway, Brook Park, Ohio 44142; R.S. Bunker, General Electric Corporation, R&D Center, Schenectady, New York. Project Manager, R. Gaugler, NASA Glenn Research Center, organization code

5820, (216) 433–5882.

A combined experimental and computational study has been performed to investigate the detailed distribution of convective heat transfer coefficients on the first stage blade tip surface for a geometry typical of large power generation turbines

(>100MW). This paper is concerned with the numerical prediction of the tip surface heat transfer. Good comparison with

the experimental measured distribution was achieved through accurate modeling of the most important features of the

blade passage and heating arrangement as well as the details of experimental rig likely to affect the tip heat transfer. A

sharp edge and a radiused edge tip were considered. The results using the radiused edge tip agreed better with the experimental data. This improved agreement was attributed to the absence of edge separation on the tip of the radiused edge

blade.