A.A. Ameri

AYT Corporation, Brook Park, Ohio

E. Steinthorsson

Institute for Computational Mechanics in Propulsion, Cleveland, Ohio

David L. Rigby

NYMA, Inc., Brook Park, Ohio

Effects of Tip Clearance and Casing Recess

on Heat Transfer and Stage Efficiency

in Axial Turbines

NASA/CR—1998-208514

August 1998

ICOMP–98–04

NI STITUTE FOR COMPUTATIONAL MECHAN CI S

RP NI OPULS OI N

ICOMP

Lewis Research Center

Ohio Aerospace Institute
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A.A. Ameri

AYT Corporation, Brook Park, Ohio

E. Steinthorsson

Institute for Computational Mechanics in Propulsion, Cleveland, Ohio

David L. Rigby

NYMA, Inc., Brook Park, Ohio

Effects of Tip Clearance and Casing Recess

on Heat Transfer and Stage Efficiency

in Axial Turbines

NASA/CR—1998-208514

August 1998

National Aeronautics and

Space Administration

Lewis Research Center

Prepared under Contract NAS3–27571

ICOMP–98–04

NI STITUTE FOR COMPUTATIONAL MECHAN CI S

RP NI OPULS OI N

ICOMP

Lewis Research Center

Ohio Aerospace Institute

Prepared for the

Turbo Expo ‘98

sponsored by the International Gas Turbine Institute

of the American Society of Mechanical Engineers

Stockholm, Sweden, June 2–5, 1998
Acknowledgments

This work was sponsored by the Smart Green Engine Project managed at NASA Lewis Research Center by

Mr. Kestutis Civinskas. The authors wish to express their gratitude to Dr. Raymond Gaugler, chief of the

Turbine Branch, Mr. Ned Hannum chief of the Turbomachinery and Propulsion Systems Division as well as to

Dr. Louis Povinelli chief scientist of the Turbomachinery and Propulsion Systems Division of

NASA Lewis Research Center and Director of ICOMP for their support and encouragement of this work.

As always we had the benefit of helpful suggestions offered by Mr. Robert Boyle of NASA Lewis Research Center.

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

Available from

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Trade names or manufacturers’ names are used in this report for

identification only. This usage does not constitute an official

endorsement, either expressed or implied, by the National

Aeronautics and Space Administration.
1

ABSTRACT

Calculations were performed to assess the effect of the tip

leakage flow on the rate of heat transfer to blade, blade tip and

casing. The effect on exit angle and efficiency was also examined.

Passage geometries with and without casing recess were

considered. The geometry and the flow conditions of the GE-E3

first stage turbine, which represents a modern gas turbine blade

were used for the analysis. Clearance heights of 0%, 1%, 1.5%

and 3% of the passage height were considered. For the two largest

clearance heights considered, different recess depths were

studied. There was an increase in the thermal load on all the heat

transfer surfaces considered due to enlargement of the clearance

gap. Introduction of recessed casing resulted in a drop in the rate

of heat transfer on the pressure side but the picture on the suction

side was found to be more complex for the smaller tip clearance

height considered. For the larger tip clearance height the effect of

casing recess was an orderly reduction in the suction side heat

transfer as the casing recess height was increased. There was a

marked reduction of heat load and peak values on the blade tip

upon introduction of casing recess, however only a small

reduction was observed on the casing itself. It was reconfirmed

that there is a linear relationship between the efficiency and the

tip gap height. It was also observed that the recess casing has a

small effect on the efficiency but can have a moderating effect on

the flow underturning at smaller tip clearances.

NOMENCLATURE

A inlet area

C axial chord

Cp constant pressure specific heat

d distance upstream of the leading edge expressed as a

 percent of the axial chord.

G clearance height, expressed as percent of the annulus

 height (see Fig. 1)

h heat transfer coefficient- wall heat flux/(T0-Tw)

k thermal conductivity or kinetic energy of turbulence/

N rotation rate

Pr Prandtl number=

R recess depth (see Fig. 1) or gas constant for air

Re Reynolds number

T temperature/

Tu turbulence intensity

V total velocity/

friction velocity,

X distance measured from the leading edge (see Fig.1)

y normal distance from wall

dimensionless distance from a wall,

mass flow rate

specific heat ratio

viscosity

wall shear stress

density

Subscripts

t total conditions

w wall

0 total inlet condition

1 base case (see Fig. 14)

RT0

( ) μCp ⁄ k

T0

2k

3

-----     ⁄ V

RT0

v

* τw ( )ρ⁄

y

+ y+ y

v

*

ν = ----

m ̇

γ

μ

τw

ρ

ω ( ) 2πNC RT0 ⁄ ( )

 EFFECTS OF TIP CLEARANCE AND CASING RECESS ON HEAT TRANSFER AND

STAGE EFFICIENCY IN AXIAL TURBINES

A. A. Ameri

 AYT Corporation, Brook Park, Ohio, USA

E. Steinthorsson

Institute for Computational Mechanics in Propulsion (ICOMP)

NASA Lewis Research Center, Cleveland, Ohio, USA

David L. Rigby

NYMA, Inc. NASA Lewis Group, Cleveland, Ohio, USA

NASA/CR 1998-208514
2

INTRODUCTION

The tip clearance is responsible for a significant portion of

losses in turbines. Much attention is being paid to reduction in

losses due to the tip clearance flows since other sources of loss

are not as amenable to manipulation as the tip clearance losses.

Blade tips are also susceptible to burnouts and oxidation due to

the large thermal loading on and near the blade tips. Losses and

heat load in the tip region increase as the tip gap widens. This

increase in losses and the increased heat load is particularly

deleterious to the operation of engines under certain periods of

operation, such as during take off when the clearance gap is

wider. The tip clearance also widens as the engine gets older.

Tip and casing treatments are used to improve the

efficiency and reduce the tip heat transfer. Among the various

treatments used for the blade tip are the use of squealer type

blades, the most widely used among them being the double

squealer tip which is simply a recess in the blade tip. Ameri et

al. (1997) simulated the flow and heat transfer due to tip recess

and showed that the effect on efficiency was insignificant and

also the heat transfer issues were not ameliorated by the tip

recess. An experimental study performed by Kaiser and Bindon

(1997) showed that for their 1 1/2 stage turbine, the recessed tip

had a negative effect on the efficiency. Neither the numerical

conclusions of Ameri et. al nor those of Kaiser and Bindon were

in agreement with the popular belief that the tip recess increases

the efficiency by reducing the tip clearance flow.

Another method employed to reduce the tip clearance

losses is the use of the casing recess. In this work in addition to

the examination of the effect of the clearance height we examine

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

its influence on efficiency. There is some experimental work

available in the open literature, namely that of Haas and Kofsky

(1979), which addresses the effect of the casing recess on the

efficiency for a small turbine. Their experiments show that the

maximum efficiency is achieved using a casing recess at level

with the tip of the blade. There is also one numerical study

R G

d

C

X

Fig. 1 Sketch of the geometry near the tip and the nomenclature

(Briley et al. 1991) of turbine blade flow that does include tip

clearance and casing recess, however their effects are not separated.

The task of calculation of the heat transfer and particularly

efficiency in terms of absolute magnitudes is a formidable one

especially for complex flow passages such as the flow passage at

hand. A comparative study is however possible if special care is

taken to retain as much similarity between the grid distribution for

the cases considered as possible.

In the section to follow we will give a brief description of the

numerical method used in the simulations. Next the flow field near

the tip and the recess will be discussed and salient features pointed

out. Then we will present the heat transfer results which include

the blade surface near the tip, the tip and casing heat transfer. Next

we will present the results of the calculations of the exit angle.

Finally we will present the results of the calculations of efficiency

for a range of gap heights and casing recesses and close by

presenting a summary and the conclusions.

COMPUTATIONAL METHOD

The simulations in this study were performed using a multiblock computer code called TRAF3D.MB (Steinthorsson et al.

1993). This code is a general purpose flow solver designed for

simulations of flows in complicated geometries. The TRAF3D.MB

code solves the full compressible Reynolds averaged, NavierStokes 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. 1996,1997a and Ameri et al. 1997) employs the

k-ω turbulence model developed by Wilcox (1994a,1994b) with

subsequent 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 for turbulent Prandtl number, Prt

 is used. A

constant value for Pr=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 AND THE GRID

Figure 1 shows a sketch of the problem and the definitions of

some of the variables used in the study. As tabulated in Table 1,

four gap clearances of G=0%, 1%, 1.5% and 3% of the passage

height are used. The 0% and 1% cases are run without casing

recess. For the two wider gaps, the recess heights are varied. For

the 1.5% gap case there are two sets of calculations for d, namely

d=15% and 25% of the chord. For the 3% gap d=25% of the chord

is used.

The blade chosen for this study is a generic modern gas

turbine rotor blade, the General Electric E3 (Energy Efficient

Engine) design which is detailed in two NASA reports (Halila et

al., 1982 and Timko, 1982). The rotor blades have a constant axial

chord length of 2.87 cm. and an aspect ratio of 1.39. Figure 2(a)

shows the blade geometry and the basic features of the grid, The

insets (b) and (c) show the details of the grid on the tip and on the

casing showing the recess geometry. The grid is generated using a

commercially available computer program called GridProTM. The

grid topology is quite complex and the grid for a geometry with tip

Cp

TABLE 1. Summary of cases

G d R/G

0 --- 0. (no casing recess)

1. --- 0.(no casing recess)

1.5 --- 0.(no casing recess)

1.5 15% 0.5, 1. (level), 1.5

1.5 25% 0.5, 1. (level), 1.5

3 --- 0.(no casing recess)

3 25% 1/3, 2/3, 1. (level)

NASA/CR 1998-208514
3

clearance and casing recess consists of 310 blocks. Once the grid

is generated, for reasons of computational efficiency, the blocks

are merged to produce fewer number of blocks namely 29 blocks

for runs with casing recess and 26 blocks for runs without casing

recess. This was done using the Method of Weakest Descent as

described in Rigby et al. (1997b) and Rigby (1996). In order to

keep the grids for the many cases considered in this work as

similar as possible we have assured that the general topology is

the same for all the cases considered. Therefore after the first grid

was generated, the grids for the remaining similar cases could be

generated rather quickly. The viscous grid is generated by

embedding grid lines where needed. We have required that the

stretching ratio not to 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 specified such that the distance in wall units, (y+)

is less than unity. This is verified and the distribution of y+ on and

near the tip will be given in the results section. One attractive

feature of the generated grid is that as shown in Fig. 2(b) the

viscous grid wraps around the blade instead of extending into the

free stream. This feature of the grid improves the convergence of

the solution. Near the edge of the blade, in the tip region (Fig.

2(b)) better refinement of the grid might be required for more

accurate results, however since we are making relative

comparisons extreme measures are avoided. In spite of the

above, the total number of grid points is typically around 1.3

million. 59-65 grid points are used radially within the tip

clearance. 33 grid points are used to resolve the boundary layers

on the blade. This does not include the “inviscid” blade to blade

grid which is also quite fine. At the inlet patch the number of grid

points is 85 in the pitchwise and 97 in the spanwise direction.

RUN CONDITIONS

The run conditions are provided in Table 2. The manner in

which the boundary conditions are imposed both for the flow and

turbulence variables are as given in Ameri et al. (1997). However

for the sake of completeness the inlet boundary conditions are

given in Figs. 3(a) and (b). The swirl angle in Fig. 3(a) was

specified as per measurements of Timko(1982). The inlet total

temperature and pressure were specified by the use of the law of

the wall through the specification of the inlet boundary layer

thickness at the hub and the casing. For the turbulence quantities,

an inlet turbulence intensity of 8% and a length scale of 1% of

axial chord was used. These values were estimated and believed

to be representative of the conditions existing at the inlet of the

blade row.

RESULTS AND DISCUSSION

General Remarks

All the cases presented herein have been converged to better

than 0.01% mass flow error. The residual for all the cases

dropped 6 to 7 orders of magnitude. The heat transfer and

efficiency results have been checked for convergence by

comparing solutions after consecutive runs of 300 iterations. The

present calculations match the experimental mass flow rate to

within 0.5% percent. As described earlier, in order to achieve

accurate resolution of heat transfer on surfaces, the grid was

generated to result in dimensionless distance of the first cell

center off the walls to be below unity. Figure 4 shows a typical

distribution of dimensionless wall distance on and near the tip. It

can be seen that the goal has been met.

Clearance gaps chosen for the study of recessed casing are

relatively wide since tip clearance effects are stronger for larger

(a)

(b) (c)

TABLE 2. Run conditions

Absolute press. ratio across the blade row 0.44

Reynolds number (based on inlet relative

conditions) and blade chord.

200,000

Inlet Mach number (relative) 0.38

Dimensionless rotation rate, ω 0.0254

Twall/Ttotal at inlet 0.7

Fig. 2 GE, E3 first stage rotor blade. (a) Overall grid. (b) details

of the tip grid near the edge and (c) details of the casing grid

NASA/CR 1998-208514
4

(a)

Fig. 4 Distribution of on and near the blade tip. G=3% y

+

Fig. 5 (a) Streamline patterns for (a) G=1.5%, R/G=1. at

d=15% and (b) G=3% and R/G=1., d=25%

gaps and the effect of recessed casing are expected to be more

pronounced as was shown by Haas and Kofsky (1979).

Flow Field

Figure 5 shows streamline patterns for a 1.5% clearance gap

and those for a 3% clearance gap. Both cases possess a casing

recess upstream. In the two figures the edge vortex, suction side

tip vortex and the larger structure which appears to be a

horseshoe vortex are present. The low momentum fluid behind

the recess also appears to be joining this larger structure in both

of the cases. The larger tip clearance gives rise to a larger tip

vortex by virtue of its larger mass flow rate through the tip. The

above mentioned structures enhance the heat transfer to the blade

and will be discussed further in subsequent sections. Figure 6(a)

shows the region behind the casing recess. The arrows in this

figure and in all subsequent ones are projections of the relative

velocity vectors onto the viewing area. A distinct recirculation

zone (blockage) can be discerned behind the recess. Figures 6(b)

and (c) show the flow relative to the blade at a radial location mid

gap of the tip clearance for the G=1.5% without and with a

casing recess upstream, respectively. The modification of the

flow over the tip downstream of the recess as compared to the no

recess case is quite obvious from the two figures. In particular

the larger secondary flow due to reduced fluid momentum behind

the casing recess is quite apparent. The relative reduction in the

magnitude of the velocity over the tip for the recessed case is

also apparent from the two vector plots.

Further observations with the regards to the flow structure

will be made in connection with heat transfer in the ensuing

sections.

Heat Transfer

The present computational method has been applied to a

variety of turbine heat transfer problems by using an algebraic

turbulence model (Ameri and Steinthorsson 1995, 1996). The

present turbulence model was tested against the heat transfer

Recess

(b)

0.2

0.3

0.2

0.4

0.3

0.2 0.3 0.2 0.1

0.4

0.3

Recess

65.0 70.0 75.0 80.0

Inlet absolute angle (degress)

0.0

0.2

0.4

0.6

0.8

1.0

(R−Rhub)/(Rtip−Rhub)

Measured, Timko(1982)

Present

(a)

0.60 0.70 0.80 0.90 1.00 1.10

Pt/Pt0, Tt/Tt0

0.80

0.85

0.90

0.95

(R−Rhub)/(Rcasing−Rhub)

Pt/Pt0

Tt/Tt0

(b)

Fig. 3 (a) Inlet absolute swirl angle and (b) inlet total temperature

and total pressure

NASA/CR 1998-208514
5

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.

(1997). Very good comparison using the current method for blade

surface heat transfer with experimental data was achieved by

Garg and Rigby (1998). Heat transfer results for internal flows

can be found in Rigby et al. (1996, 1997a).

The rate of heat transfer is presented in terms of Stanton

number defined as:

(1)

where h is the heat transfer coefficient based on the absolute inlet

total temperature. is the constant pressure specific heat

(assumed a constant), is the mass flow rate and A is the inlet

area. The ratio of is very much a constant for the cases

considered.

Blade Heat Transfer. Figure 7 shows the rate of heat transfer at

the mid-span. By referring to this figure and specifically the

magnitude of the rate of heat transfer at the stagnation point an

appreciation can be gained for the magnitude of the rate of heat

transfer shown elsewhere on the blade.

Figure 8 shows the blade heat transfer rate at two locations of

90 and 95% passage height. On the pressure side, the effect of

increase in tip clearance height is to increase the blade heat

transfer near the tip. Also discernible is the increase in heat

transfer as the tip itself is approached due to sink effect.

St h

( ) m ̇ ⁄ A inletCp

= ----------------------------------

Cp

m ̇

m ̇ /A

(c)

(b)

(a)

-1.0 -0.5 0.0 0.5 1.0

Pressure side X/C Suction side

0.0

2.0

4.0

6.0

8.0

10.0

Stx1000

Fig. 7 Mid span blade heat transfer

Fig.6 Velocity vectors at (a) behind the casing recess

showing the recirculation zone, and radial location mid gap

of the tip clearance, G=1.5% for, (b) no casing recess and (c)

level recess at d=0.15

-1.0 -0.5 0.0 0.5 1.0

Pressure side X/C Suction side

0.0

2.0

4.0

6.0

8.0

10.0

Stx1000

G=1.5%, R/G=0, @90% (Rcasing-Rhub)

G=1.5%, R/G=0, @95%

G=3.0%, R/G=0, @90% 

G=3.0%, R/G=0, @95% 

G=3.0%, R/G=1, @90%

G=3.0%, R/G=1, @95%

Fig. 8 Heat transfer near the tip as affected by the tip clearance

height and casing recess

NASA/CR 1998-208514
6

Introduction of a casing recess causes a drop in the pressure side

heat transfer.

The heat transfer on the suction side is more complex. Shown

in Fig. 9 is the suction side heat transfer contours near the tip for a

number of cases. The contour plots are provided for two gap

clearances of 1.5% and 3% and for a range of casing recess heights

as needed. Figures 9(a) and 9(e) show that the effect of doubling

the gap height on the suction side heat transfer is to enlarge the

area on the blade influenced by the tip vortex flow, thus raising the

suction side heat transfer load. The peak heat transfer for the

smaller tip clearance is larger. This could be attributed to the effect

2

3

4

5 6 7

3

4

5 6

6

1.5% gap, R/G=0. (a)

3

3

4

4

5 6

7 8

(c) 1.5% gap, R/G=1., d=25%

6

6

4 5

6 7

6

5

4

3

3

8 9

(d) 1.5% gap, R/G=1., d=15%

6

5

4 3

3

6

(e) 3% gap, R/G=0.

2

3 3

4

5

6

6

7

6

(h) 3% gap, R/G=1, d=25%

6

7

4 5

7 7

6

5

4

3

3

(b) 1.5% gap, R/G=0.5, d=15%

3

4 3

6

4

5

5 7

(f) 3% gap, R/G=.33, d=25%

4 5 6 6

3 7

(g) 3.% gap, R/G=.66, d=25%

Fig. 9 Near tip suction side heat transfer.(1000x Stanton no.)

(a)

L.E.

(b)

T.E.

Fig. 10 Velocity vectors near the tip on the blade suction side

for (a) G=1.5%, R/G=1. and d=15% and (b) G=3%, R/G=1.

NASA/CR 1998-208514
7

8

10 9

7

6

5

6

5

4

3

11 9

7

6

5

4

6

5

4

No Recess.

G=1%

G=1.5%

G=3.% 9

7

7

6

5

5

6

4

(a)

(b)

0.0 0.2 0.4 0.6 0.8 1.0

X/Chord

4.0

5.0

6.0

7.0

8.0

9.0

Stantonx1000

1.0% tip clearance

1.5% 

3.0% 

Fig. 11 (a) Contours of 1000xStanton number over the blade

tip for three gap widths and (b) line plot of the average tip heat

transfer as a function of the axial distance

of the secondary flow that runs across the passage toward the

blade suction side. In Fig. 10(a) the velocity vectors at a location

near the crown of the blade for the G=1.5%, R/G=1. and d=15%

are shown. The effect of the crossflow on the suction side of the

blade is obvious from the figure. The “hot spots” near the tip in

Figs. 9(b), 9(c) and 9(d) are attributable to this effect. The tip

clearance flow on the other hand in Fig. 10(b) dominates the

suction side of the blade. The 3% tip clearance cases all have the

tip vortex dominant flows on the suction side. There is a gradual

reduction of the heat loading on the suction side as the casing

recess height is increased.

Tip Heat Transfer. Tip Heat transfer will be presented in the

form of contour plots of Stanton number accompanied by a line

plot representing the average rate of heat transfer on the blade tip

as a function of axial distance.

Figure 11 shows the rate of heat transfer as measured by

Stanton number on the tip of the blade for three gap clearances.

The line plot shows the increasing tip clearance gap to elevate

the rate of heat transfer over the upstream portion of the blade

but have the opposite effect on the downstream portion. Near the

trailing edge the heat transfer is mostly dominated by the size

and the extent of the separation bubble.

In Fig. 12, the flow over the blade tip at three locations

along the blade for the case of 3% tip clearance is presented. The

separation of the flow upon entering in the gap is evident from

that figure. The locations of flow reattachment in the planes

considered have been marked with white arrows. The tip flow at

the location farthest downstream on the blade shows that the hot

gas from the core does not come in contact with the tip surface.

Examination of the tip flow for smaller gaps (not shown to

conserve space) revealed that the location on the tip where the

flow does not reattach moves downstream as the gap narrows.

Therefore the larger the gap size the larger the portion of the

blade where the flow is unattached leading to smaller heat

transfer rates in the downstream portion of the blade tip. Further

discussion of the effect of the tip clearance height on the blade

tip will be given at the end of this section.

To investigate the effect of casing recess on the tip heat

transfer two gap clearances of 1.5% and 3% were considered.

Figures 13(a) and (b) show the effect of casing recess upstream

of the blade row for G=1.5%. A range of R/G values from 0 to

1.5 was considered. The casing recess was placed at 25% chord

upstream. The contour plots show the local effect of the

upstream recess on the blade tip heat transfer. Looking at the

peak heat transfer it can be seen that the recess on the casing

reduces the peak level of heat transfer and in general the larger

the recess the smaller is the peak heat transfer. The line plot at

the bottom shows the integrated average of the tip heat transfer

over the blade tip. The line plots show a decreasing level of tip

heat transfer as a function of casing recess depth. A different set

of calculations was run for the recess placed at 15% chord

upstream of the blade row. Figure 14 shows the results of those

runs. The line plot in Fig. 14(b) clearly shows that the effect on

the tip heat transfer is larger in this case (d=15%) as compared to

the case of d=25% as one would expect intuitively.

Figure 15 shows the variation of the tip heat transfer as a

function of recess depth for the larger 3% tip clearance. A range

Fig. 12 Velocity vectors showing flow through the tip clearance at

three locations. Observed flow reattachment is marked by the

arrow.

NASA/CR 1998-208514
8

of recess depths is chosen namely, R/G’s of 0, 1/3, 2/3 and 1, the

latter being even with the blade tip. The reduction of the tip heat

transfer is again apparent from that figure, however in this case it

appears to be confined mainly to the forward portion. The reason

is that for this large clearance gap the gas flows relatively

unimpeded over the aft portion of the tip and is less affected by

the presence of a casing recess upstream of the blade.

Figure 16 shows plots of relative total temperature, relative

velocity magnitude, turbulence intensity and kinetic energy of

turbulence for the 1.5% clearance and no upstream recess (base

Fig. 13 (a) Contours of 1000xStanton

number over the blade tip and (b) line plots

of average tip heat transfer. d=25%,

G=1.5%

Fig. 14 (a) Contours of 1000xStanton

number over the blade tip and (b) line plots

of average tip heat transfer. d=15%,

G=1.5%

0.0 0.2 0.4 0.6 0.8 1.0

X/Chord

R/G=0, No recess

R/G=0.5

R/G=1, (level)

R/G=1.5

0.0 0.2 0.4 0.6 0.8 1.0

X/Chord

R/G=0, No recess

R/G=0.33

R/G=0.66

R/G=1. (level)

Fig. 15 (a) Contours of 1000xStanton

number over the blade tip and (b) line

plots of average tip heat transfer. d=25%,

G=3.0%

0.0 0.2 0.4 0.6 0.8 1.0

X/Chord

4.0

5.0

6.0

7.0

8.0

9.0

Stantonx1000

R/G=0, No recess

R/G=0.5

R/G=1, (level)

R/G=1.5

9 8 7 6

5

4

3

5

4

4

5

6

7

5

4

3

8 9

9 8 7 6

5

4

5

4

6

11 9

7

6

5

4

6

5

4

9 8 7

6

5

4

6

5

4

9

6

5

4

5

7

3

9

6

5

4

5

7

3

11 9

7

6

5

4

6

5

4

d=15%

G=1.5%

(a)

R/G=0

R/G=0.5

R/G=1

R/G=1.5

9

7

7

6

5

5

6

4

7

9 8

6

5

4

3

7

7

9 8 7

6

7

5

4

3

7

9 8 7

6 6

7

6

4 5

3

R/G=0

R/G=0.5

d=25%

G=1.5%

R/G=1

R/G=1.5

d=25%

G=3.0%

R/G=0

R/G=0.33

R/G=1.

R/G=0.66

(a) (a)

(b) (b) (b)

case). Figures 17 and 18 show the ratios of the same quantities

for G=1.5%, R/G=1 and G=3%, R/G=0 cases to the

corresponding quantities of the base case. The purpose of those

figures is to aid in determining the cause of change in tip heat

transfer by the presence of a recess or by an increase in tip

clearance. Referring to Figs. 16, 17 and 18, judging by the levels

of turbulence intensity it is likely that the tip flows are all fully

turbulent. The drop in heat transfer for the case in Fig. 17

(corresponding to Fig. 14, R/G=1) appears to be due to the

reduction in the total temperature as well as the flow velocity. In

NASA/CR 1998-208514
9

1.07

0.90

0.97

0.97

1.00

1.04

0.95

1.00

0.50

0.70

0.80

0.90 0.95

1.00

1.05

1.20

0.80

0.80

1.00

1.00

1.20

0.80

0.80

0.95

1.25

1.15

1.05

1.05 0.95

1.20

1.00

0.90

0.85

Tt/Tt1

V/V1

Tu/Tu1

k/k1

G=1.5%

R/G=1.

d=15%

Fig. 17 Ratios of relative total

temperature, velocity magnitude, turbulence

intensity and kinetic energy of turbulence at

mid gap, G=1.5%, R/G=1., d=15%.

0.83

0.84

0.86

0.87

0.88

0.85

0.82

0.25

0.30

0.30 0.35 0.45

0.55

0.65

0.75

0.80

0.50

Tt1

V1

6.00E-02

6.00E-02

4.00E-02

6.00E-02

1.00E-01

2.00E-01

5.00E-02

6.00E-03

4.00E-03

5.00E-03

4.00E-03

6.00E-03

8.00E-03

9.00E-03

1.00E-02

1 40E 0

Tu1

k1

G=1.5%

R/G=0.

fact if one assumes a relationship of wall heat flux proportional

to velocity ratio to a 0.8 power which is commonly done for a

turbulent boundary layer flow, it appears as though most of the

drop in heat transfer on the tip can be accounted for by the

velocity drop. The same can be said for the 3% clearance where

the increase in the tip heat transfer in the attached flow regions is

associated with an increase in velocity.

Casing Heat Transfer. Information on the casing heat transfer

can be used for cooling of the casing to alleviate “hot spots” or

for the purposes of active control of tip clearance. Since the grid

rotates at the blade rotation rate, there is no unsteady effect due

to rotation which is not accounted for in the calculations.

Figure 19 shows the effect of tip gap height on the

circumferentially averaged casing heat transfer. The casing heat

transfer as should be expected (Epstein et al, 1985) drops by a

large factor (~5) along the axial direction. It is also shown that

the casing heat transfer is markedly affected by the tip clearance

gap. The trend is shown to be an increase in heat transfer as the

gap widens. The change in the level of heat transfer on the

casing is initiated near the blade leading edge and persists past

the trailing edge of the blade.

Casing heat transfer is also expected to be influenced by the

presence of the recess on the casing. Figure 20 shows the effect

of casing recess on the casing heat transfer. The dip on the heat

transfer curve corresponds to a location just downstream of the

recess where the casing is in the recirculating flow region. There

is some reduction on the rate of heat transfer on the casing due to

the presence of the recess however it appears to be slight.

Tip Mass Flow

Figure 21(a) is a plot of mass flow rate through the tip

clearance normalized by inlet mass flow rate. There is a linear

relationship between the mass flow through the clearance and

Fig. 16 Relative total temperature,

velocity magnitude, turbulence intensity

and kinetic energy of turbulence at mid

gap, G=1.5%, R/G=0.

1.25

1.20

1.10

1.00

1.10

1.05

1.15

1.80

1.60

1.50

1.40

1.30

1.20

1.10

1.40

0.60

0.80

1.00

0.60

0.70 0.85

0.65

0.50

0.80

0.80

0.50

0.50

1.30

1.00 1.20

0.50

0.80

Tt/Tt1

V/V1

Tu/Tu1

k/k1

G=3%

R/G=0.

Fig. 18 Ratios of relative total temperature, velocity magnitude, turbulence intensity and kinetic energy of

turbulence at mid gap, G=3%, R/G=0.

NASA/CR 1998-208514
10

the tip clearance height. Figure 21(b) shows the mass flow rate

through the tip gap as the upstream recess is introduced. The case

of 1.5% tip clearance shows an increase in the mass flow rate as

recess is introduced initially but shows a reduction thereafter.

The mass flow rate is normalized by the tip mass flow rate

without the casing recess which is quite small for the G=1.5%

case and therefore the variations in the mass flow due to the

presence of the casing recess are quite small. For the 3%

clearance the effect of clearance height is more uniform. The

reduction in velocity in the tip region of Fig. 17 is due to

blockage of the flow coming from the inlet. The fact that the

mass flow rate does not change greatly suggests that the flow

-0.5 0.0 0.5 1.0 1.5

X/C

0.0

5.0

10.0

Stanton x 1000

No Recess

d=15%, R/G=1. 

d=25%, R/G=1.

-0.5 0.0 0.5 1.0 1.5

X/C

No Recess

d=25%, R/G=1. 

(a) (b)

G=1.5% G=3%

Fig. 20 Casing heat transfer as affected by the presence of the

recess. (a) 1.5% and (b) 3% clearance

Fig. 19 Circumferentially averaged heat transfer on the casing

as affected by the tip clearance height

through the tip clearance is mainly due to the pressure difference

across the blade.

Exit Angle

An important variable in the design of turbine stages is the exit

angle. It is known that as the gap widens the unguided flow

through the clearance increases and therefore it causes the flow to

enter the next set of blades at an angle other than the intended

design angle. Figure 22 shows the pitchwise averaged exit angles

at two axial locations for the clearance heights considered with and

without casing recess. The solid lines are for cases without casing

recess. All the runs having the same tip clearance height are

represented with the same symbol for the purposes of easy

identification. The intended design values at hub, mean and tip are

taken from (Timko, 1982) and are also included.

The exit angle associated with zero clearance is represented

by a thick solid line without symbols. The no clearance case is

overturned near the casing (as near the hub) due to secondary

flows. On the other hand, cases with tip clearance have various

degrees of underturning proportional to the tip clearance height

due to the suction side tip vortex. In Fig. 22(a), the no clearance

case has formed a maximum turning limit for all the other cases

considered. Addition of a recess has a worsening effect for the

case of large tip clearance but has an obvious moderating effect

for the lower tip clearance height.

Efficiency

In a previous paper Ameri et al. (1997) presented a method to

compute the adiabatic efficiency as a by-product of the heat

transfer calculations. The expression used for the calculation of

the adiabatic efficiency is:

(2)

In the above formula and signify the mass averaged,

absolute total temperature and pressure. The subscripts and

η

T′

in T′ex –

T′

in 1

p'

ex

p′

in

----------

     ( )γ γ – 1 ⁄

–

= -----------------------------------------------------------------

T′ P′

in ex

-0.5 0.0 0.5 1.0 1.5

X/C

0.0

5.0

10.0

Stanton x 1000

1.0% Clearance

1.5%

3.0%

0.0 1.0 2.0 3.0

Tip clearance height (G)

0.0

5.0

10.0

15.0

% inlet mass flow rate

0.0 0.5 1.0 1.5

R/G

0.980

0.990

1.000

1.010

Tip mass flow ratio x 100

G=1.5%, d=15%

G=1.5%, d=25%

G=3.0%, d=25%

(a) (b)

Fig. 21 (a) Tip clearance mass flow rate normalized by the inlet mass

flow rate vs. tip clearance height. (b) Tip clearance mass flow rate

normalized by the tip mass flow rate without recess vs. recess depth

NASA/CR 1998-208514
11

signify the integration locations inlet and outlet of the

computational domain and is the specific heat ratio. Since the

calculations are done with a wall boundary condition other than

adiabatic, the exit total temperature is corrected for the heat

transfer. Further details can be found in Ameri et al (1997).

For the present set of calculations, the integration planes are

located at 50% chord upstream of the blade and 100% chord

downstream of the blade. The exit location was selected

relatively far downstream to allow for mixing to take place and

therefore allow for the differences in efficiency to become

apparent. Figure 23 shows the effect of the height of the tip

clearance gap on the adiabatic efficiency without the presence of

the casing recess. The calculations were performed for the case

of no tip clearance as well as 1, 1.5 and 3% tip clearance cases.

The solid line is a best fit to the calculations. The variation of

efficiency with gap height is seen to be linear with a slope of

~1.5 point per percent gap clearance. Both the linearity and the

magnitude of the slope agree with the general rule of thumb

exercised by designers. The open symbols are calculated from a

γ

0.0 1.0 2.0 3.0 4.0 5.0

100 x G/Span

88.0

90.0

92.0

94.0

96.0

Efficiency

Present calculations

Best fit to calculations

Correlation, Hong & Groh 1966

Fig. 23 Adiabatic efficiency as affected by the tip clearance height

graphic correlation put forth by Hong and Groh (1966) as

reproduced in NASA SP-290 edited by Glassman(1994). The

graphical correlation expresses the efficiency as a fraction of

efficiency with no clearance. The no clearance value is obtained by

extrapolation. The variation of efficiency as shown in Fig. 23

provides confidence in the results of the calculations. The

efficiencies calculated suggest that the losses associated with the tip

clearance are approximately 20, 30 and 45 percent of the total

losses for the case of 1%, 1.5% and 3% clearance, respectively.

This is in agreement with the work of Boyle et al. (1985) and

confirms the suggestion made elsewhere that measures taken to

reduce the losses due to tip leakage can have a significant effect on

the total losses especially when operating with relatively wide tip

clearance.

The magnitudes of efficiency calculated here were changed

slightly by the presence of the recessed casing. Table 3 shows the

calculated efficiency for the 1.5% tip clearance cases considered.

For the 1.5% clearance gap the magnitude of the efficiency without

the recess was calculated to be 92.06%. For d=15% at R/G=0.5 the

magnitude of the efficiency rose to 92.24% which although is a

0.2% increase, it constitutes 8% of the losses due to tip clearance.

For the d=25% the efficiency rose to 92.29% or 9.5% of the tip

clearance losses at R/G=1. For the d=15% case the value of

efficiency for R/G=1 appears to be anomalous although no reason

for this drop in efficiency was found. More points might be

required to capture the highs and lows of this relationship.

Table 4 contains the efficiency values for the 3% tip clearance

cases. The efficiency reaches a maximum of 90.28% or an increase

of 0.2% compared to the no recess condition. This is an increase

equivalent to recovering 4.5% of the losses due to the tip clearance.

A trend can be inferred from the table where there is an

intermediate value of casing recess height for which the efficiency

reaches a peak. Further increase in the recess height leads to losses

in the flow that can offset the gains otherwise attained.

SUMMARY AND CONCLUSIONS

In this paper, results are presented from three-dimensional

simulations of flow and heat transfer in an unshrouded turbine rotor

passage with and without casing recess. Casing recess is a

configuration often found in turbine blade passages. For the

purposes of the calculations a generic modern gas turbine blade

namely that of first stage rotor of GE-E3

 turbine was selected. A

multi-block grid was generated to discretize the flow field.

Clearance heights of 0%, 1%, 1.5% and 3% of the passage height

?90.0 ?70.0 ?50.0

Exit angle (degrees)

0.0

0.2

0.4

0.6

0.8

1.0

(Radius?Rhub)/Span

G=0.0%, R/G=0.

G=1.0%, R/G=0.

G=1.5%, R/G=0.

G=1.5% ,R/G=1., d=15%

G=1.5%, R/G=1., d=25%

G=3.0%, R/G=0.

G=3.0%, R/G=1., d=25%

Design

-90.0 -70.0 -50.0 -30.0 -10.0

Exit angle (degrees)

0.0

0.2

0.4

0.6

0.8

1.0

(Radius-Rhub)/Span

G=0.0%, R/G=0.

G=1.0%, R/G=0.

G=1.5%, R/G=0.

G=1.5%, R/G=1., d=15%

G=1.5%, R/G=1., d=25%

G=3.0%, R/G=0.

G=3.0%, R/G=1., d=25%

Design

(a)

(b)

10% Chord

100% Chord

Fig. 22 Exit angle at (a) 10% chord and (b) 100% chord

downstream of the blade row

NASA/CR—1998-208514
12

were considered. For the two largest clearance heights considered,

different recess depths were studied.

There was an increase in the thermal load on all the heat

transfer surfaces considered due to enlargement of the clearance

gap.

Introduction of recessed casing resulted in a drop in the rate of

heat transfer on the pressure side but the picture on the suction side

was found to be more complex for the smaller tip clearance height

considered. For the larger tip clearance height the effect of casing

recess was a reduction in the suction side heat transfer.

There was a marked reduction of heat load and peak values on

the blade tip upon introduction of casing recess, however only a

small reduction was observed on the casing itself.

It was reconfirmed that there is a linear relationship between the

efficiency and the tip gap height. It was also observed that the casing

recess has a small effect on the efficiency.

It was also observed that the recessed casing can have a

moderating effect on the flow underturning at smaller tip clearances.

ACKNOWLEDGEMENT

This work was sponsored by the Smart Green Engine Project

managed at NASA Lewis Research Center by Mr. Kestutis

Civinskas. The authors wish to express their gratitude to Dr.

Raymond Gaugler, chief of the Turbine Branch, Mr. Ned Hannum

chief of the Turbomachinery and Propulsion Systems Division as

well as to Dr. Louis Povinelli chief scientist of the Turbomachinery

and Propulsion Systems Division of NASA Lewis Research Center

and Director of ICOMP for their support and encouragement of this

work. As always we had the benefit of helpful suggestions offered

by Mr. Robert Boyle of NASA Lewis Research Center. Some of the

computations were performed on the CRAY-C90 of NAS at NASA

Ames Research Center.

REFERENCES

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

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

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

Turbine Rotor Blade Tip and Shroud Heat Transfer,” IGTI 96-GT189.

Ameri, Ali A., and Steinthorsson, E., Rigby, David L., 1997,

“Effect of Squealer Tip on Rotor Heat Transfer and Efficiency,”

ASME 97-GT-128. To be published in the journal of

Turbomachinery.

Boyle, Robert J., Haas, Jeffrey E. and Katsanis, Theodore,

1985, “Comparison Between Measured Turbine Stage Performance

and the Predicted Performance Using Quasi-3D Flow and

Boundary Layer Analyses,” J. of Propulsion and Power, Vol.1

no.3, pp 242-251.

Briley, W. R., Roscoe, D. V., Gilbeling, H. J., Buggeln, R. C.

and Sabnis, J. S., 1991, “Computation of Flow Past a Turbine

Blade With and Without Tip Clearance,” IGTI paper 91-GT-56.

Epstein, A. H., Guenette, G. R., Norton, R. J. G. and Cao

Yuzhang, 1985, “Time Resolved Measurements of a Turbine

Rotor Stationary Tip Casing Pressure and Heat Transfer Field,”

AIAA paper 85-1220.

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

Film-Cooled Blade-Effect of Hole Physics”, accepted for

presentation at the International Gas Turbine Institute

Conference and Exposition, June, 1998, Stockholm. Sweden.

Glassman, Arthur, J., Turbine Design and Application,

NASA SP-290, 1994.

Haas, Jeffrey, F. and Kofsky, Milton, G., 1979, “Effect of

Rotor Tip Clearance and Configuration on Overall Performance

of a 12.77- Centimeter Tip Diameter Axial-Flow Turbine,”

NASA, TM 79025.

Halila, E. E. and Lenahan, D. T., and Thomas, T.T., 1982,

“Energy Efficient Engine, High Pressure Turbine Test Hardware

Detailed Design Report,”, NASA CR-167955.

Hong, Yong S, and Groh, F. G., “Axial Turbine Loss

Analysis and Efficiency Prediction Method.”, Rep. D4-3220,

Boeing Co., Mar. 11, 1966.

Kaiser, I. and Bindon, P. J., 1997, “The Effect of Tip

Clearance on the Development of Loss Behind a Rotor and a

Subsequent Nozzle,” IGTI paper 97-GT-53.

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 Steinthorsson E., 1997a,

“Numerical Prediction of Heat Transfer in a Channel with Ribs

and Bleed,” IGTI paper 97-GT-431.

Rigby, D. L., Steinthorsson, E., Coirier, W. J., 1997b,

“Automatic Block Merging Using the Method of Weakest

Descent,” AIAA Paper 97-0197.

Rigby, D. L., 1996 “Method of Weakest Descent for

Automatic Block Merging,” 15th Int. Conf. on Num. Methods in

Fluid Dynamics, Monterey, CA, June 1996.

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

“Internal Passage Heat Transfer Prediction Using Multiblock

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

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.

Timko, L.P., 1982, “Energy Efficient Engine High Pressure

Turbine Component Test Performance Report,” NASA CR168289.

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.

TABLE 3. Efficiency, G=1.5%

R/G=0 R/G=0.5 R/G=1. R/G=1.5

d=15% 92.06 92.24 91.85 92.16

d=25% 92.06 92.07 92.29 92.04

TABLE 4. Efficiency, G=3%

R/G=0 R/G=1/3 R/G=2/3 R/G=1.

d=25% 90.09 90.28 90.15 90.03

NASA/CR 1998-208514
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E–11287

18

A03

Effects of Tip Clearance and Casing Recess on Heat Transfer and

Stage Efficiency in Axial Turbines

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

Gas turbine; Heat transfer; Efficiency; Casing recess; Tip clearance

WU–523–26–13–00

NAS3–27571

Unclassified -Unlimited

Subject Categories: 34 and 07 Distribution: Nonstandard

NASA CR—1998-208514

ICOMP–98–04

Institute for Computational Mechanics in Propulsion

22800 Cedar Point Road

Cleveland, Ohio 44142

Prepared for the Turbo Expo 98 sponsored by the International Gas Turbine Institute of the American Society of Mechanical Engineers, Stockholm, Sweden, June 2–5, 1998. A.A. Ameri, AYT Corporation, Brook Park, Ohio; E. Steinthorsson,

Institute for Computational Mechanics in Propulsion, Cleveland, Ohio; and David L. Rigby, NYMA, Inc., 2001 Aerospace

Parkway, Brook Park, Ohio. Responsible person, A.A. Ameri, organization code 5820, (216) 433–8346.

Calculations were performed to assess the effect of the tip leakage flow on the rate of heat transfer to blade, blade tip and

casing. The effect on exit angle and efficiency was also examined. Passage geometries with and without casing recess

were considered. The geometry and the flow conditions of the GE-E3 first stage turbine, which represents a modern gas

turbine blade were used for the analysis. Clearance heights of 0%, 1%, 1.5% and 3% of the passage height were considered. For the two largest clearance heights considered, different recess depths were studied. There was an increase in the

thermal load on all the heat transfer surfaces considered due to enlargement of the clearance gap. Introduction of recessed

casing resulted in a drop in the rate of heat transfer on the pressure side but the picture on the suction side was found to be

more complex for the smaller tip clearance height considered. For the larger tip clearance height the effect of casing recess

was an orderly reduction in the suction side heat transfer as the casing recess height was increased. There was a marked

reduction of heat load and peak values on the blade tip upon introduction of casing recess, however only a small reduction

was observed on the casing itself. It was reconfirmed that there is a linear relationship between the efficiency and the tip

gap height. It was also observed that the recess casing has a small effect on the efficiency but can have a moderating effect

on the flow underturning at smaller tip clearances.