Proceedings of Global Power and Propulsion Society ISSN-Nr: 2504-4400

Beijing Conference 2019 16th – 18th September, 2019

www.gpps.global

This work is licensed under Attribution 4.0 International (CC BY 4.0) See: https://creativecommons.org/licenses/by/4.0/legalcode

GPPS-BJ-2019-0109

ANALYSIS OF FLOW CHARACTERISTICS AND OVERALL COOLING EFFECTIVENESS OF ULTRA-HIGH IMPINGEMENT DISTANCE HEAT

SHIELD

Zhou Jianjun Shenyang Aero-engine Institute of Aero Engine

Corporation of China Shenyang, China

Xie Long Northwest University of Technology

2810164922@qq.com Xi’an, China

Liu Cunliang Northwest University of

Technology

liucunliang@nwpu.edu.cn Shenyang, China

ABSTRACT

Computational investigations is reported on a flat plate

subjected to combined impingement and film cooling.

Conjugate heat transfer and 3-D steady RANS approach with

the k-ω SST turbulence model were used for analysis of the

impingement and film cooling plates. The flow dynamic

features of impinging jets and the coolant-mainstream

interaction in presence of heat shield are described. The

discharge coefficients are presented at blowing ratio M = 0.2

to 0.8 and Reynolds number Re 9300 to 75000 respectively.

A comparison between the conventional heat shield and

ultra-high impingement distance heat shield shows that the

discharge coefficients values for the new heat shield are

higher. The value of overall cooling effectiveness for the new

heat shield is lower than the conventional structure at low

blowing ratio, but at high blowing ratio, the values of overall

cooling effectiveness for both the heat shields are almost

equal. As the blowing ratio is increased from 0.2 to 0.8, the

overall effectiveness values show an increasing trend for

both the heat shields.

INTRODUCTION

An afterburner is a key component for the modern

engines. The thrust augmentation provides by afterburning or

reheating is critical for takeoff, maneuverability and

acceleration. Therefore, there has been ongoing demand of

higher temperature ratio to meet the goal of maximum thrust.

As a consequence, the afterburner outlet temperature for

recent high-performance engines exceeds 2200K (Stephen,

1960), which is far beyond the melting point of the

afterburner cylinder.

The original flat-plate heat shield is a housing for

enclosing the afterburner tube and receiving the coolant from

the compressor for delivery along the tube, which is

composed of several cylindrical cylinders. The cooling air

can flow out from the joint between the cylinders, forming a

film on the hot gas side wall and protect the surface from the

hot exhaust gas (Stephen, 1960; Gérard et al, 1991). This

structure has a low film cooling effectiveness so that requires

a large quantity of cooling air to protect the wall.

(Donald et al, 1986) and (Howard et al, 1990) proposed

a new structure of the liner that contains a plurality of double

wall elements. Each element is generally annular and extends

from a first axial part to a second axial part. The second axial

part is placed inwardly towards the geometric center line of

the afterburner duct, and both the two axial part have holes

attached. This structure includes both impingement and film

cooling techniques, which makes full use of cooling air.

However, it is complicated and difficult to process and

maintain.

Later, the transverse corrugated heat shield has been

proposed. The wave axis of the latitudinal corrugated liner is

parallel to the streamwise direction. This structure can

effectively absorb the radial high frequency oscillation

energy of 1000-2000HZ, which is mostly used in the turbojet

afterburner. There remains a recirculation zone between its

peaks and troughs, which can make full use of the cooling air

and enhance heat transfer. (Zhang et al, 2000) analyzed the

temperature distribution of the transverse corrugated liner

under experimental and numerical simulation conditions.

2

Concluded that along the flow direction, the temperature of

the wave wall gradually increases and has a certain range of

temperature fluctuations. (Qu et al, 2016) analyzed the

influence of blowing ratio, corrugation wavelength and

corrugation amplitude on the cooling efficiency of the

transvers corrugated heat shield. The results show that with

the increase of the blowing ratio, the average adiabatic film

cooling effectiveness increases, and there is an optimal

blowing ratio M=0.2. Both the corrugation wavelength and

the corrugation amplitude have a little influence on the

average adiabatic film cooling effectiveness.

Today’s turbofan afterburner with low frequency energy

of 100-500HZ has a large radial dimension. Therefore it is

better to use the longitudinal ripple heat shield that can

absorb the low frequency oscillation energy. The wave axis

of longitudinal ripple heat shield is perpendicular to the

streamwise direction. (Funazaki, 2001) came up with a

longitudinal corrugated heat shield with certain range of hole

diameter and hole pitch, which only drill holes in the

downstream waves. They show that this structure can make

the distribution of cold air more uniform and reduce the

consumption of cold air. (Thomas, 1993) proposed a

corrugated wall with uniformly hole and introduced a low

cost manufacturing method for making the combustor liners.

They show that this kind of structure can effectively reduce

the radial temperature gradient and thermal stress, thus

improving the fatigue stress. Also, more complex studies

such as the influence of the cooling channel dimensionless

height, corrugated wall dimensionless height and

aerodynamic parameters on film cooling effectiveness have

been conducted, the results show that the distribution of

overall cooling effectiveness in the direction of streamwise is

uneven, so there is a hidden danger of excessive thermal

stress. (Nathan et al, 2016) used either crossflow,

impingement, or a combination of both to supply the film

cooling to investigate overall film cooling and impingement

cooling effectiveness. The results show that the heat transfer

coefficient generally increases with streamwise development,

and increase with increasing blowing ratio. (Li et al, 2018)

proposed a method to improve full-coverage effusion cooling

effectiveness by varying the cooling arrangements and wall

thickness. They found that adding impingement and pins to

film cooling, and decreasing wall thickness increase the

cooling efficiency significantly. (Sneha et al, 2018) provided

spatially-resolved distributions of adiabatic cooling

effectiveness for effusion surface and spatially-resolved

distributions of surface Nusselt numbers impingement

surface.

During the development of heat shield, its aerodynamic

parameters, cooling effectiveness and coolant consumption

have always been improved. However, its temperature non-

uniformity restricts its development. The author proposed a

impingement/film cooling apparatus with ultra-high

impingement distance, the distance from the impingement

surface to the effusion surface is 20 cH d . The porous heat

shield with an ultra-high impingement distance can

effectively limit the oscillating combustion of the afterburner

by generating the gas damping and turbulence. It also can

effectively improve the uniformity of discharge coefficient

and overall cooling effectiveness while maintaining a

relatively high level of overall cooling effectiveness.

ANALYSIS

Discharge Coefficient

The discharge coefficient of the orifice is defined as the

ratio of actual mass flow rate to that which should be pass

through the cross-sectional area (Huning, 2008). It can be

written in the form

d

id

mC

m

(1)

The ideal mass flow rate can be calculated:

2 1

* 2 21 * * *

1 1 1

2 1m

1 R

k k k

i

p pkp A

k T p p

(2)

Discharge coefficients CD of hole are impacted by

several different factors: Reynolds Number, length to

diameter ratio, cross flow at inlet and outlet, pressure ratio

(Huning, 2008). The inlet or outlet approaching flow inclined

to the orifice axis caused by crossflow is accompanied by

flow loss, which decreases the discharge coefficient. Rohde

et al (Rohde et al, 1969) experimentally investigated the

discharge coefficient with cross-flow near the entrance of

orifice. They considered the ratio of velocity head of the

orifice jet to the velocity head of the main flow as a function

of the discharge coefficient

* *= p pjet crop p

(3)

(Gritsch et al, 1998a; Gritsch et al, 2001) considered the

influence of both entry and exit crossflow near the holes on

the discharge coefficient. They plotted the discharge

coefficient vs the ratio of jet to internal or external flux

momentum. The formulas are:

2

2

2

2

jet

c

jet

g

u

jet inCr

u

u

jet extCr

u

I

I

(4)

The result shows that the discharge coefficient increases

with the increased in either jet inCrI or jet extCrI . The results

also indicated that the discharge coefficient with crossflow is

lower than that without crossflow at the low momentum flux

3

ratio. The influence of crossflow on the discharge coefficient

can be neglected when the momentum flux ratio exceed 2.

NUMERICAL SIMULATION APPROACH

Combined impingement and film cooling Geometries

The impingement and film holes are staggered

arrangement as shown in Fig. 1. As shown in Fig. 2, to

guarantee the complete development of the mainstream, the

test plate is extended for 30 cd on the upstream. To

eliminate the impact of back flow, the test is extended for 40

cd on the downstream. The length of cH is 20 cd for the

ultra-high impingement distance model (model 1) and 5 dc

for the conventional impingement distance model (model 2).

The length of cL is 200 mm. The value of Φ and b are

fixed. The hole number of the jet impingement holes and

film holes was shown in Fig. 3.

The jet hole pitch are the same in the X and Y directions

for both impingement holes and film holes, which can be

determined by:

2

2

4

4

4

4

st f sp f f f f st f sp f

f f f

st c sp c c c c st c sp c

c c c

A n n X Y b d n n

X Y db

A n n X Y b d n n

X Y d

(5)

Fig. 1 Schematic of the cooling pattern

Fig. 2 Geometry parameters of the computational model

Fig. 3 The number of impingement an film holes

Fig. 4 Boundary conditions of the computational domain

Boundary Condition and Numerical Approach The periodic boundary condition is assigned to the

sidewalls in Y direction as shown in Fig. 4. The top and

bottom of the effusion wall are set as couple wall. The

impingement wall is adiabatic wall. The mass inlet boundary

is applied at the inlet of mainstream and coolant. The

mainstream Reynolds number from 9300 to 75000 is

calculated based on the parameters of hot gas inlet. The mass

flux of coolant depends on both of the blowing ratio

f f g gM u u from 0.2 to 1 or the mainstream

Reynolds number. The variables in blowing ratio depend on

the aperture area of film holes and the parameters of coolant

inlet. The fluid is ideal gas, and its specific heat and thermal

conductivity depend on temperature. The fluid dynamic

viscosity is determined by Sutherland’s formula. The

commercial CFD software ANSYS Fluent 16.0 was

employed in solving the steady RANS equations. The SST k-ω turbulence model was applied, because the previous

numerical computation research (Dees, et al, 2012; Mensch

et al, 2014; Panda et al, 2012; Ramachandran et al, 2015;

Zhou et al, 2016; Dyson et al, 2014; Zhao et al, 2016)

indicated that better simulation results can be obtained by

4

using the SST k-ω turbulence model. The criteria of

convergence is that the residual value of energy is below 10-

9. As shown in Fig. 5, the value of y+ of the first cell layer on

the target wall was less then 1. To validate the numerical

model, the numerical results were compared with experiment

data, as shown in Fig. 6(Qu, et al, 2017).

Fig. 5 The value of Y+ on the target wall

Fig. 6 Laterally averaged overall cooling effectiveness

Grid Independence

Fig.7 grid of fluid and solid domains

The structured grids were used for discreting fluid and

solid domain and O-type grids were applied on all the holes,

which were generated by ANSYS ICEM as shown in Fig. 7.

(Deng et al, 2016) has demonstrated that the grid

number of solid domain has little influence on the simulation

result of conjugated heat transfer model. Thus the mesh

generation method of solid domain is similar to that of fluid

domain. Three different number of grids were generated to

validate the independence of the grid with the method of

“Grid Convergence Index” described in (Ji et al, 2008). The

three employed fluid domain grids have 7.8 million cells,

10.9 million cells,15.6 million cells, respectively. The values

of cooling effectiveness for gird 2 and gird 3 are almost

equal, so the gird 2 was employed for the computation of the

conjugate model.

RESULT AND DISCUSSION

Effect of Reynolds number on flow characteristic of impingement hole

The case 1 has a larger level of discharge coefficient

than case 2 as shown in Fig. 9. This is mainly due to the vena

contracta of the impingement hole. The impingement holes

has a small ratio of length to diameterc c

l d . To

investigate the vena contracta, it was represented by the

velocity contour. The number of contour levels was eight for

each Reynolds number. The smallest cross-sectional area of

high velocity region was applied to represent the vena

contracta as shown in Fig. 8. Increasing the Reynolds

number from 9300 to 42000 cause a large separation at the

hole entrance and the flow cannot reattach to the hole

sidewall, which reduces the vena-contracta area and actual mass flow rate. The line 2 and line 3 as shown in Fig. 8 are

almost coincide, which means that the Reynolds number

from 42000 to 75000 has less influence on vena contracta.

Fig. 9 also shows that the discharge coefficient of the

downstream hole is larger than that of the upstream hole.

This is due to the end of coolant plenum is closed and the

coolant will flow back, which reduces the intensity of

entrance crossflow.

Fig. 8 vena contracta

5

Fig. 9 The discharge coefficient of impingement holes for Re = 9300, 42000, 75000, M = 0.3

Effect of Reynolds number on flow characteristic of effusion hole

Fig. 10 The discharge coefficient of film holes for Re = 9300, 42000, 75000, M = 0.3

The ratio of length to diameter of film hole is 0.75,

which is a short hole too. Fig. 10 shows that the discharge coefficient of the

upstream effusion holes is negative (use the value of zero to

represent) at Reynolds number Re = 9300. This is due to the

pressure of the front-end of chamber in X direction is lower

than the mainstream pressure. The impingement flow cannot

eject through the effusion hole, and even the mainstream

pour back into the chamber.

Fig. 10 also shows that the discharge coefficient of the

downstream holes is higher than that of upstream holes. This

is due to the outflow at upstream thickens the downstream

boundary layer. The thick boundary layer reduces the flow

area and accelerates the velocity of the mainstream as shown

in Fig.8. According to the principle of mass conservation,

when the density is assumed to be constant, the increase of

velocity can reduce the pressuregp , therefore increases the

pressure ratio. Another reason is the film accumulation at the

downstream provides the protection for downstream holes.

The large low velocity region near the outlet of film holes

reduces the influence of the mainstream crossflow, resulting

in larger exit cross-sectional area compared with the

upstream film hole as shown in Fig. 12.

Fig. 11 Velocity contour for center plane of film holes

Fig. 12 Comparison of upstream and downstream hole cross-sectional area (left: upstream; right:

downstream)

Effect of blowing ratio on discharge coefficient of film hole

Fig. 13 The relation between discharge coefficient and blowing ratio for film holes

6

Fig. 14 The pressure ratio of film holes inlet and mainstream under different blowing ratio

Fig.11 shows the effect of blowing ratio on discharge

coefficient of film holes. With the increases of blowing ratio,

the discharge coefficient increase. This is because of the

enhanced suction of the film hole by the increased pressure

ratio, which causes more penetration into the mainstream.

For the case1 in Fig. 13, there are some holes with a

discharge coefficient of negative (use the value of zero to

represent). This is due to the pressure ratio of these holes is

less than 1 as shown in Fig. 14 and the insufficient pressure

cannot eject the impingement flow in chamber through the

film holes.

The impact of impingement distance on discharge coefficient of impingement holes

Fig. 15 Flow characteristic of impingement gap

Fig. 16 vena contracta of film hole

Fig. 17 Discharge coefficient of high impingement distance model and low impingement distance

model.

Fig. 15 shows a complex interaction between the

impingement jet and effusion jet air feed. There remains a

reverse flow in the impingement gap. The interaction of jet-

impacting flow causes a upwash flow. The upwash flow will

reattach to the impingement surface and form a crossflow.

The effect of the crossflow on the exit cross-section area

highly depends on the impingement distance. For the high-

impingement-distance chamber, there remains a larger

momentum loss for the upwash, and the larger the

momentum loss of upwash, the smaller the momentum of

crossflow. This means that for the higher impingement

distance chamber, the exit cross-section area of impingement

holes is larger as shown in Fig. 16. Therefore, the level of

discharge coefficient for model 1 (high-impingement-

distance gap) is larger by a factor of 0.02, compared to the

model2 (low-impingement-distance gap) as shown in Fig. 17.

The effect of impingement gap on discharge coefficient of film holes

Fig. 18 shows that the difference between model 1 and

model 2 is smaller at low blowing ratio M=0.2. With the

increased of blowing ratio, the difference becomes larger.

And for the most of film holes, the discharge coefficient of

model 1 is larger than model 2 at blowing ratio M=0.8. This

is due to the vortex near the effusion wall in chamber is

enhanced by the increase of blowing ratio, which washes

7

away the impingement jet that should have blown into the

film holes as shown in Fig. 19. And for model 2, the intensity

of the vortex is larger due to the low impingement distance,

which will cause less entrance than model 1.

From Fig. 18, we can also see that the distribution of

discharge coefficient is more uneven for model 2. This is due

to the impingement jet cannot be fully developed in small

space for model 2, which resulting in uneven inlet condition

for each hole.

Fig. 18 Discharge coefficient of the third row of film holes of model 1 and model 2 at the blowing ratio

of 0.2 and 0.8.

Fig. 19 The vortex in impingement gap with short impingement distance

The impact of impingement distance on overall cooling effectiveness

Overall cooling effectiveness is defined as follows:

g w

g c

T T

T T

(6)

Model 1

Model 2

Fig. 20 Contour of overall cooling effectiveness on interaction surface where the coolant interacts with

the mainstream (for M = 0.6)

Fig. 21 Laterally averaged overall cooling effectiveness

Fig. 20 show that as the impingement distance decreases

from 20d to 5d, the overall cooling effectiveness is

improved. The regions of high overall cooling effectiveness

are concentrated near the impingement area. For the model 2,

the spot area with high overall cooling effectiveness is more

obvious and thus generates a higher gradient of temperature.

The larger thermal stress caused by higher temperature

gradient will reduce the thermodynamic efficiency and the

service life of model 2. The Fig. 21 shows that with the impingement distance

decreases from 20d to 5d, the overall cooling effectiveness

increases by approximately 0.1. The difference of overall

cooling effectiveness φ between model 1 and model 2 is

smaller with the increase of blowing ratio. This is due to the

stronger impingement cooling at larger blowing ratio reduces

the influence of impingement distance. The Fig.18 also

shows that the difference of overall cooling effectiveness φ

between model 1 and model 2 is smaller at large fx d .

This is due to the accumulated film at the downstream is the

main factor affecting the cooling effectiveness.

8

CONCLUSION

Numerical study was applied to investigate the flow

characteristic and overall cooling effectiveness of

laminated configuration with high impingement distance.

This paper also compared the uniformity of temperature and

discharge coefficient of high and low-impingement-distance

heat shield.

Some conclusions are summary as follows:

Due to the short ratio of length to diameter c cl d of

impingement holes, with the increase of Reynolds number

from 9300 to 42000, the discharge coefficient decreases.

When the Reynolds number increases from 42000 to 75000,

the influence of Reynolds number decreases, thus the

increase of discharge coefficient mainly depends on the

pressure ratio. Due to the influence of crossflow in coolant

plenum, the discharge coefficient of the downstream

impingement hole is larger than that of the upstream hole.

The increase of Reynolds number of films holes has less

impact on the discharge coefficient at the hole number from

20 to 75 due to the higher difference of pressure ratio. The

mainstream crossflow at the exit of film holes is weakened

by the accumulation of film.

The discharge coefficient of impingement holes

increases with the increase of blowing ratio.

The discharge coefficient of film holes increases with

the increase of blowing ratio. At blowing ratio M=0.8, the

discharge coefficient value is on approximately the same

level, due to the overall increase in pressure ratio.

The overall cooling effectiveness increases with the

increase of blowing ratio. Because of the accumulation of

film at downstream, the overall cooling effectiveness is

larger at downstream.

The impingement-hole discharge coefficient of high

impingement model is larger than that of low impingement

model. And for the most of film holes, the discharge

coefficient of high impingement model is larger than that of

low impingement model.

The overall cooling effectiveness of conventional heat

shield is larger than that of ultra-high impingement distance

heat shield. But the overall cooling effectiveness of

conventional heat shield is poor and the temperature

gradient of model 2 is larger, which will reduce the

thermodynamic efficiency and the service life.

ACKNOWLEDGMENTS

The authors acknowledge gratefully the financial

support from the National Natural Science Foundation of

China (Grant No. 51776173) and the Fundamental Research

Funds for the Central Universities (Grant No.

3102017gx06006).

NOMENCLATURE

φ overall cooling effectiveness

l length of the hole

dc diameter of impingement hole, mm

df diameter of effusion hole, mm

Hc impingement distance, mm

Lc the length of test plate, mm

CD discharge coefficient (actual mass flow rate/ideal

mass flow rate)

m actual mass flow rate

idm

ideal mass flow rate

θ the ratio of velocity head of the orifice jet to the

velocity head of the main flow

p pressure

p* total pressure

I momentum flux ratio

M blowing ratio, c c g gU / U

Re

reynolds number based on hydraulic diameter of hot

gas inlet g g gU D /

δc Impingement wall thickness

δf film wall thickness

Φ porosity of impingement wall

X streamwise coordinate , m

Y coordinate normal to the test surface, m

Z spanwise direction, m

b aperture area ratio of film hole to impingement hole

n Holes number

Greek symbols

φ Overall cooling effectiveness

density, 3

kg m

molecular viscosity, 2Ns m

Subscripts

intCr crossflow at the hole entrance

extCr crossflow at the hole exit

g hot gas

c coolant

f film

1 entrance

2 exit

st streamwise direction

sp spanwise direction

id ideal

jet jet gas

cro crossflow

st-c streamwise direction of impingement wall

sp-c spanwise direction of impingement wall

st-f streamwise direction of effusion wall

sp-f spanwise direction of effusion wall

References [1] Critsch M, Schulz A, Wittig S, 2001, “Effect of

Crossflow on the discharge coefficient of Film Cooling

Holes With Varying Angles of Inclination and

Orientation”. Journal of Turbomachinery, 2001, 123:

781-787.

9

[2] Critsch M, Schulz A, Wittig S. 1998, “Method for

Correlating Discharge of Film-Cooling Holes”. AIAA

Journal, 1998, 36(6): 976-980.

[3] Dees, J. E., Bogard, D. G., Ledezma, G. A., Laskowski,

G. M., Tolpadi, A. K., 2012, “Experimental

Measurements and Computational Predictions for an

Internally Cooled Simulated Turbine Vane”, ASME

Journal of Turbomachinery, Vol. 134, pp. 061003-1-9. [4] Deng, Q., Zhou, W., Feng, Z, 2016, “Conjugate Heat

Transfer Analysis for Laminated Cooling Effectiveness:

Part B: Effects of Film Hole Incline Angle”, ASME

Paper No. GT2016-57256.

[5] Donald N. Burr, 1986, “Gas Turbine Engine Combustor

Splash Ring Construction”. United States Patent:

4566280,1986-01-28.

[6] Dyson, T. E., Bogard, D. G., Bradshaw, S. D., 2014,

“Evaluation of CFD Simulations of Film Cooling

Performance on a Turbine Vane Including Conjugate

Heat Transfer Effects”, International Journal of Heat

and Fluid Flow, Vol. 50, pp. 279-286.

[7] Gérard E. A. Jourdain, Saintry Sur Seine, Marc G.

Loubet, 1991, “Heat Protective Lining for an

Afterburner or Transition Duct of a Turbojet engine”,

United States Patent:5060034.

[8] Howard L. Foltz, Westchester, Ohio, 1990 “Combustor Liner Cooling Arrangement”. United States Patent:

4896510, 1990-01-30.

[9] Huan Zhang, Hui-Ping TAN, Hong Liu, 2000, “Flow

Field Calculation and Buckling Analysis for

Afterburner”, Journal of Combustion Science and

Technology, Vol. 6, PP.107-110

[10] Huning M, 2008 “Comparison of Discharge Coefficient

Measurements and Correlations for Several Orifice with

Cross-flow and Roation Around Several Axes”. ASME

GT2008 – 50976, 2008.

[11] Ji Pei, Shouqi Yuan, Wenjie Wang, 2008, Procedure for

Estimation and Reporting of Uncertainty Due to

Discretization in CFD Applications. ASME-Journal of

Fluid Engineering. Vol. 130, pp: 078001-1-4.

[12] K. Funazaki, Japan, 2001, “Studies on Cooling Air

Ejected Over a Corrugated Wall: Its Aerodynamic

Behavior and Film Effectiveness ”, Iwate University, Morioka, ASME01-GT-143.

[13] Li-Hong QU, Jing-Zhou Zhang, Xiao-Ming Tan, 2016,

“Numerical Investigation of Film Cooling

Characteristics for Effusion Holes on a Transverse

Ripple Heat Shield”, Journal of Engineering

Thermophysics, Vol,37, pp: 1532-1537.

[14] Mensch, A., Thole, K. A., Craven, B. A., 2014,

“Conjugate Heat Transfer Measurements and

Predictions of a Blade Endwall with a Thermal Barrier

Coating”, ASME Journal of Turbomachinery, Vol. 136,

pp. 121003-1-11.

[15] Nathan Rogers+ , Zhong Ren+ , Warren Buzzard+ ,

2016,“Effect of Double Wall Cooling Configuration and

Conditions on Performance of Full Coverage Effusion

Cooling”, ASME Paper No. GT2016-56515.

[16] Panda, R. K., Prasad, B.V. S. S. S., 2012, “Conjugate

Heat Transfer from a Flat Plate with Combined

Impingement and Film Cooling”, ASME Paper No.

GT2012-68830.

[17] Qu Li-hong, Zhang Jing-zhou, Tan Xiao-ming, 2017,

“Improvement on Film cooling effectiveness by a

combined slot-effusion scheme”. Applied Thermal

Engineering, 126(2017), 379-392.

[18] Ramachandran, S. G., Shih, I. P., 2015, “Biot Number

Analogy for Design of Experiments in Turbine Cooling”, ASME Journal of Turbomachinery, Vol. 137,

pp. 0610021-14.

[19] Rohde J E, Richards H T, Metzger G W, 1969,

“Discharge Coefficient for Thick Plate Orifices with

Approach Flow Perpendicular and Inclined to the

Orifice Axis”. NASA TN D – 5467, 1969.

[20] S. Stephen Papell, 1960, Effect on Gaseous Film

Cooling of Coolant Injection Through Angled Slots and

Normal Holes[R]. NASA Report NASA – TN – D -299.

[21] Sneha Reddy Vanga+ , Zhong Ren+ , Austin J Click#,

2018, “Double Wall Cooling of a Full Coverage

Effusion Plate with Main Flow Pressure Gradient,

Including Internal Impingement Array Cooling”, ASME

Paper No. GT2018-77036.

[22] Thomas G. Wakeman, Alan Walker, Harvey M. Maclin,

1993, “Gas Turbine Engine Multi-Hole Film Cooled

Combustor Liner and Method of Manufacture, United States Patent:5181379, 1993-1-26.

[23] Weihong Li , Xunfeng Lu, Xueying Li, 2018, “On

Improving Full-Coverage Effusion Cooling Efficiency

by Varying Cooling Arrangement and Wall Thickness in

Double Wall Cooling Application”, ASME Paper No.

GT2018-77230.

[24] Zhao Liu, Xing Yang, Jun Li. 2016, “Effect of Bleed

Position and Bleed Angle om Impingement Cooling of a

Spherical-Dimpled Surface ”,ASME Paper No.

GT2016-57540

[25] Zhou, W., Deng, Q., Feng, Z., 2016, “Conjugate Heat

Transfer Analysis for Laminated Cooling Effectiveness,

Part A: Effects of Surface Vurvature”, ASME Paper No.

GT2016-57243.

10