This study predicts the steady state temperature of a turbine wall using heat transfer film coefficients.

1. PARAMETRIC STUDY
OFA
THERMAL LINER
BASED ON RESULTS FROM THE COMPUTER CODE TLINER
BY
JULIO C. BANKS, MSME, P.E.
DECEMBER 1994
Julio C. Banks, PE Page 1 of 31

2. ) ) )
DIe IONSUREALL MPE
P-,
~
~
E--t
......:l
~
~
~
t--t
(f)
......:l
0
u
1500
1400
1300
1200
11 00
1000
900
80'0
-
-
I IE j-
IT I /
~~
~
,~
-
-
~f­
~ I IE' I
~ ~
--....­
~
..--­f-
I­
.---------­
~'­
.-­
- ~V---
l-
I­
-
-
J I
I­
~a-
l-
f-
I I I I I I I I I I I I I I I I I I I I I I I I
2800 '2900 3000 3100 3200 3300 3400 3500 3600 3700 3800
GAS TEMPERATURE (
Julio C. Banks, PE Page 2 of 31

3. 1500
)
1600
A A s
'-' 1400
1300
1200
~
~
0 11 00
u
1000
900
2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800
GAS TEMPERATURE (F)
Julio C. Banks, PE Page 3 of 31

4. )
RA ICTIONS
1600
1500
~ 1400
:21
~
E­
1300
~
~
c:::4
c:::4 1200
~
0
u
1100
1000
2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800
GAS TEMPERATURE (F)
Julio C. Banks, PE Page 4 of 31

5. )
ATU REDICTION
1600
1550
1500
~
~
"--""
§S 1450
~
E-­
1400
1350
1300
1250
1200
1150
I­
/~
/
...
IT-
IE () I /
/
v
/-
T I
i­
/ /V/ /­
/ / V '1'3
-
/ / /Hf
/V V
/i­
-
V //
i­
/
V
4~
~
I
I
I I I I I I I I I I I L I I I II I I I I I I I I I I I I I I I
2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800
GAS TEMPERATURE
Julio C. Banks, PE Page 5 of 31

6. ) ) )
1500
1450
1400
~
~
--- 1350
~
~
~ 1300
~
~
~ 1250
~
~
~ 1200
~
lfJ
:3 1150
o
u
1100
1050
1000
WALL TEMPERATURE PREDICTIONS
~"----~-----~----~----~----~----~----~----~------~--~
!
i-- J -------I----+-J ------,­ ------------1------1----­
lEta 0.751 i _ _ , IIT3 900 FI
---- ! -----,----- -T--- -:- - - - + -. -------1------------I
-------I---J---------------1-----------+------------ -------------------- 810-0- FI
I '
...t'................................... .+........................................................·1···· ······1 ..................."1".................................. ..........-1--..
• I
I
!
I
...............-/--........................................... ···········1··········································....... .j.... .............................)............ ........i
• I I
I ! '
-----1.i _oj - 700 F1
-----J­
i
- - - t - - - - - -----,--- -r ----------- -j -------- -----i
I
! !
!
- - - + - - - - - - - - - - - - 4 + -------------! ----------+-----1
. I
-------1--------+-----1--- -----i----i--------+------ -J ------j-­ --I
2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800
GAS TEMPERATURE
Julio C. Banks, PE Page 6 of 31

7. ---
)
1200
1150
f:2 1100
~
a 1050
~
~
~
~
~
1000
~
~
en 950
~
~
8 900
850
800
) )
WALL TEMPERATURE PREDICTIONS
.lEta = 0,90 I
I .-.-----.---.{..--.--- J ----------j ··-··-····---------l----T
, ; ; : i I ilT3 ~oo FI
, I
.--......-----~-..--....-..--.. ---....-..;-----......--..----.1....------..-------1....----.--------..-J--------..----..---J-- --..-...-..--------i-- ..---....-------..-1---....--....-------....--1.....---..
I I : " I I
I I I IIT3 = 800FI
--t-----------~ ------t---------i------------I----------+­
! I I
------1---------1 ----------1-------------:-------------L------------I--------T-------11;;---:-~-~O FI
---------t------------L---------I--- ----+ -------1-------­
I ! I
!
-----I--------------L--­
I
2800 2900 3000 3100 3200 3300 3400 3500 3600 3700 3800
GAS TEMPERATURE
Julio C. Banks, PE Page 7 of 31

8. File: HEAT.PSD -- Page 1 -- Print At: 4:58:05pm 12-09-94
/ .. Tgas Twall A Twall B Twall C Twall D Twall E Twall F~
3000.0 1192.0 1269.0 1346.0 1078.0 1163.0 1246.0
3200.0 1260.0 1335.0 1411.0 1136.0 1236.0 1300.0
3400.0 1333.0 1408.0 1482.0 1189.0 1269.0 1349.0
3600.0 1413.0 1486.0 1559.0 1230.0 1308.0 1388.0
MORE DATA STUFF
Twall G Twall H Twall I
870.0 962.0 1054.0
886.0 977.0 1069.0
901.0 992.0 1084.0
915.0 1007.0 1098.0
Julio C. Banks, PE Page 8 of 31

9. A Model for Correlating Flat Plate Film Cooling Effectiveness Data for Rows of
Round Holes
by Julio C. Banks, P.E.
The generalized film cooling effectiveness equation, , including decaying thermal diffusivity (a > 0) for  < *,
and constant thermal diffusivity (a = 0) for  > * is implemented here. It should be noted that all film
effectiveness are averages, unless otherwise noted. In the equations shown here, 
= *
Constant parameters
αc 20 deg M 0.5 λρ 3.0 λV 1.0 POD
P
D
= POD 6 Reg 10 10
3

λV
Vc
Vg
= λρ
ρc
ρg
= λV_pen
Vc_pen
Vg_pen
=
0.4585
sin αc 
=
Reg
Wg
Ag






D
μg
= REFD
Reg
0.11 10
5







0.2
0.9811
b
1
3
2
3
5
4
















 C
7.3606
5.5442 sin αc  1 e
0.494 POD
7
4








0.58
1
6.0216 REFD
79.0 1 1.6456 λρ
6




63.7860
4.4284





























λV_pen
0.4585 0.2389 e
0.00296 POD
7


sin αc 
1.341
VR
λV
λV_pen
0.7460
Julio C. Banks, P.E. MathCAD - Eta.xmcd page 1 of 4
Julio C. Banks, PE Page 9 of 31

10. Correlation of Peak Effectiveness Parameter, p
Δηpen if VR 1.0 0 C
3
1 e
C4 λV_pen VR 1( ) 
b
3














0
SED
Se
D
=
π
4
POD
= Se
AHoles
Span
=
SED
π
4
POD
0.1309
ηp SED λρ
b1
 C
1
λV
b2
 e
C2 λV







 Δηpen 0.2086
Correlation of Downstream Effectiveness Parameter,  Λ ηp βref=
Λ C
5
SED M 1 C
6
M
3




1
6

 1.015
Correlation of Turbulent Diffusivity Decay Parameter, a:
a C
7
VR
2
 e
C8 VR
 0.7746
Generalized Film Cooling Effectiveness Equation:
βref βp
βλ
βp






a
= Since
βλ
βp
1.0= due to limited film effectiveness data far
downstream.
Therefore, βref βp=
βref
Λ
ηp






2
23.67 βp βref 23.67 βλ βp β
x
M Se
=
x = distance downstream from coolant hole center.
M = blowing ratio, (W/A)c
/(W/A)g
.
Julio C. Banks, P.E. MathCAD - Eta.xmcd page 2 of 4
Julio C. Banks, PE Page 10 of 31

11. β 200 βλ 23.7
η β( ) if β βλ ηp
e
1
β
βp






a 1







β
βp






1 a
 if β 25 βref ηp
e
β
βref






 ηp
e
1
β
βref






1







β
βref





























η β( ) 0.112
β
1
2
5
10
20
30
40
50
60
70
80
90
100
150
200
250
300
350
400
500
600
700
800
































































 i 1 length β( )
1 10 100 1 10
3

0.01
0.1
1
η βi 
βi
0 100 200 300 400 500 600 700 800
0.05
0.1
0.15
0.2
0.25
η βi 
βi
Julio C. Banks, P.E. MathCAD - Eta.xmcd page 3 of 4
Julio C. Banks, PE Page 11 of 31

12. Superposition of Film Cooling Effectiveness of Multi-rows of Cooling Holes β 200
N = Number of rows of cooling holes, N 2 N 15 i 1 N η
i
η β( )
ησ N( ) η
1
2
N
i
η
i
1
i 1
j
1 η
j
 













ησ 2( ) 0.2106
ε
1
η
1
 k 2 N ε
k
ησ k( )
Film Cooling Effectiveness Build-up, , as a Function of Number of Rows of Cooling Holes
αc 20 ° POD 6 M 0.5 λρ 3 λV 1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
εi
i
ε
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0.112
0.211
0.299
0.377
0.446
0.508
0.563
0.612
0.655
0.694
0.728
0.758
0.785
0.809
0.830

εMean
1
N 1
i
ε
i
ε
i 1

2







N 1
0.565
REFERENCE
Mel R. L'Ecuyer, "A Model for Correlating Flat Plate Film Cooling Effectiveness Data for Rows of Round Holes",
ME-TSPC-TR-85-11. Thermal Science and Propulsion Center School of Mechanical Engineering.
PurdueUniversity, West Lafayette, Indiana, 47907.
Julio C. Banks, P.E. MathCAD - Eta.xmcd page 4 of 4
Julio C. Banks, PE Page 12 of 31

13. A Procedure for Estimating Multi-row Film Cooling Effectiveness
by Julio C. Banks, P.E.
Blowing Parameter: M 1 M
Gc
Gg
= G
W
A
= Subscripts: c = coolant
g = gas path
Max. Angle: α asin
0.5
M






 β 45 deg POD 4 L 2 in X
1
2
L
α 30 deg d 0.125 in Pitch POD d
S
π
4
POD
d S 0.025 in X Pitch λ
X
M S
 η λ α β POD( ) 0.314
λ 20.372
Ac α β POD( )
5
4
cos β( )
4 POD sin atan
tan α( )
sin β( )














for 10 α 80 and 1 β 45 degrees
η λ α β POD( ) AC Ac α β POD( )
eta AC λ 10if
eta 2.5 AC λ
0.426
 otherwise
eta

where λ
X
M S
=
4
π M
X
d






 POD=
Ac α β POD( ) 0.453 η λ α β POD( ) 0.314
ΔX
1
40
Pitch N
L
ΔX
1 i 2 N X
1
d
2
 X
i
X
i 1
ΔX
j 1 N λ
j
1
M S
X
j

0 10 20 30 40 50 60 70 80 90
0.1
0.2
0.3
0.4
0.5
Thermal Film Effectiveness
η λj α β POD 
λj
Julio C. Banks, P.E. Film Cooling.xmcd page 1 of 5
Julio C. Banks, PE Page 13 of 31

14. POD 4 M 1 λa 10 λb
4
π M
POD
2

λb
Pitch
M S( )
=Pitch
M S( )
20.372 λb 20.372 notice that and that
λb does not require equivalent slot height, S
Numerical Solution of the Mean Film Coolant Effectiveness
ηavg
Ac α β POD( ) λa
λa
λb
λη λ α β POD( )



d








λb

ηavg 0.406 or
ηavg
Ac α β POD( )
0.895
Closed-Form Solution of the Mean Film Coolant Effectiveness
ψ
λb
λa
 ηavg
1
ψ
1
4.3554
λa
0.426
ψ
0.574
1 





 Ac α β POD( )
ηavg 0.406 or
ηavg
Ac α β POD( )
0.895
In general λa 10 λb POD( )
4
π M
POD
2
 ψ POD( )
λb POD( )
λa

ηavg α β POD( )
1
ψ POD( )
1
4.3554
λa
0.426
ψ POD( )
0.574
1 





 Ac α β POD( )
Find the pitch to diameter ratio, P/D, to produce a specified target mean film effectiveness
ηtarget 0.45
PODtarget root ηtarget ηavg α β POD( )  POD 
PODtarget 3.7 Pitchtarget PODtarget d Pitchtarget 0.465 in
Julio C. Banks, P.E. Film Cooling.xmcd page 2 of 5
Julio C. Banks, PE Page 14 of 31

15. Superposition of Film Cooling Effectiveness of Multi-rows of Cooling Holes
N = Number of rows of cooling holes, N 2 N 3 i 1 N η
i
ηtarget
ησ N( ) η
1
2
N
i
η
i
1
i 1
j
1 η
j
 












 ησ 2( ) 0.697
ε
1
η
1
 k 2 N ε
k
ησ k( )
Film Cooling Effectiveness Buildup, , as a Function of Number of
Rows of Cooling Holes
1 2 3
0.4
0.5
0.6
0.7
0.8
0.9
εi
i
ε
0.450
0.697
0.834









εMean
1
N 1
i
ε
i
ε
i 1

2







N 1
 εMean 0.67
Length covered by rows of cooling holes
ΔL N 1( ) Pitchtarget ΔL 0.930 in
Julio C. Banks, P.E. Film Cooling.xmcd page 3 of 5
Julio C. Banks, PE Page 15 of 31

16. M 1.000 S 0.025 in AC ε
N
 L 2.000 in η ε
x
1
0 in x
k
x
k 1
Pitchtarget k
2
3
 x
i
0.000
0.465
0.930








in η
0.450
0.697
0.834









eta x( ) 2.5 AC
x ΔL
M S






0.426
 λ x( )
x ΔL
M S

ΔL 0.93 in Δx
Pitchtarget
2
 Δx 0.23 in
NL round N
L ΔL( )
Δx







j N 1 NL
x
j
x
j 1
Δx x
0.00
0.47
0.93
1.16
1.40
1.63
1.86
2.09






















in J 1 NL η
j
eta x
j  J
1
2
3
4
5
6
7
8
 η
J
0.450
0.697
0.834
0.800
0.595
0.501
0.443
0.403

0 1 2 3
0.4
0.5
0.6
0.7
0.8
0.9
Thermal Film Effectiveness
ηJ
xJ
in
ηMean
1
NL 1
i
η
i
η
i 1

2







NL 1

ηMean 0.614 > ηtarget 0.450
Notice that the overall average thermal effectiveness, ηMean, is greater than the  of a single row of holes
Julio C. Banks, P.E. Film Cooling.xmcd page 4 of 5
Julio C. Banks, PE Page 16 of 31

17. Summary
Geometry Specification to Obtain a Target Thermal Effectiveness
Total Stream-Direction length to be film cooled: L 2.00 in
Total Cross-Stream-Direction length to be film cooled: Lcd 3.05 in
No. of Rows in the Gas path Stream direction: N 3
Number of rows of holes in the cross-flow direction: Ncd round
Lcd
Pitch






 Ncd 6
Cooling hole diameter: d 0.125 in
Pitch to Diameter Ratio: PODtarget 3.7
Pitch of the cooling holes: Pitchtarget 0.465 in
Thermal Effectiveness
Thermal Effectiveness of a single row: ηtarget 0.450
Mean Thermal Effectiveness over entire L: ηMean 0.614
Coolant mean temperature is Tcm 800 F
Gas path Film Temperatures
Gas path temperature: Ttg 2150 F F R
Without Film Cooling: Taw Ttg and Tf Taw
Mean Film temperature is Tf Taw ηMean Taw Tcm 
ΔTf Tf Taw
ΔTf 828.6 F i.e., film temperature is now this much lower than
the adiabatic wall temperature.
This drop in film temperature, and the fact that cooling inside the film holes can be substantial (and
not accounted for in this study) would suggest that two rows space at twice the pitch distance in
the gas path stream direction should be sufficient to obtain an adequate drop in wall temperature.
Julio C. Banks, P.E. Film Cooling.xmcd page 5 of 5
Julio C. Banks, PE Page 17 of 31

18. “Procedure for Estimating Multi-row Film Cooling Effectiveness”
White Paper by R. E. Fields
Summary
A search of the published literature for Film Cooling Effectiveness data from multiple
row injection, and for a method to predict the accumulation of film effectiveness using
data from a single row of coolant injection was made.
Only a scant amount of reliable multi-row film cooling data has been reported even
though film cooling has been extensively studied.
The method of nonlinear superposition proposed by J. P. Sellers [1] has been judged
as the best method currently available to estimate the accumulation of film
effectiveness for multiple rows of film coolant injection using data from a single row.
The J. P. Sellers [1] method is recommended to determine the nozzle film cooling
effectiveness for design calculations when data for a specific a single-row
configuration is not available.
The details of the nonlinear superposition method and its application are given below
in the discussion section. A comparison of the results obtained using nonlinear
superposition with the available data from the literature is also provided.
Julio C. Banks, PE Page 18 of 31

19. 2
~"
Discussion
The method of nonlinear superposition as proposed by Sellers [1] for multirow
film coollng injection assumes that the overa11 film effectiveness for several
rows of holes can be estimated using data from a single row of holes. This is
accomplished by assuming that one can simply substitute the film temperature
resulting from the upstream injection of coolant to replace the free stream
adiabatic wall temperature in the local definition of film effectiveness at each
succes~iye downstream injection location. This is illustrated graphically 1n
Figure 1 for the 1nject10n from two rows of f11m holes spaced some distance llX
apart. The film effectiveness downstream of the first injection row is given
by
(1)
and downstream of the second row as
(2)
By using T(1 to replace Tw2 in EQuation (2) the f11 m temperature Tt2 can be
expressed as
(3)
and using Equation (1) to ellmlnate Ttl in Equation (3) gives
Tf2 =llf2Tc2 +( l-11fl ){llfl Tel +( l-T}fl )T81f 1} (4)
Julio C. Banks, PE Page 19 of 31

20. Julio C. Banks, PE Page 20 of 31

21. 4
When fJfL Tel.. fJf2" and Te2 are known then Tf2 can be readily calculated uslng
Equation (4).
It is easil y seen that the method can be extended to en arbi trary number of
injection rows by simply successively repeating the aboye procedure for eech
row in the array. In the case where ~he coolant e)(it temperatures Tel and Tc2
are the same" Equation. (4) reduces to a yery simple expression for the film
effectiveness of the combined rows
(5)
and for N rows EQu6tion (5) can be g~ner61ized to
N i-1
(6)11 = 2T}f1 n(l-T}fj)
1=1 j=O
where [ I1fO= 0
The Equations (6) and (7) are yal1d when the temperature of the coolant
1nj ected from each row 1s et the seme or nearly the same temperature; howeyer
jf the coolant exit temperature of the individual rows are significantly
different, then repeated application of Equation (3) will be required to
determine the additive effects from each row of the fllm injection.
Julio C. Banks, PE Page 21 of 31

22. 5
To use the method of nonlinear superposition described above requires that the
1)f for each row be estimated at all locations where the f11m temperature Tf is
to be assessed. If the 1)f versus distance is not accurately knownJ the
uncertainty in the T)f wi11 be propagated into the estimation of Tf. Since it is
unlikely that single row film effectiveness data is/will be available for all the
configurations considered during the design of a nozzle it becomes necess6ry to
provide a method to estimate fJf for a speciflc configuration with sufficient
. accuracy for design.
A review of the data published in references 2-2 t has led to the
recommepdation . of the following relations' for estimating ."the f11m
effectiveness required to apply the nonlinear superposition method.
x
T)f = Ac for ms <10 (9)
X ]-0.426 x (10)
[T)f =2.5 Ac ms for ms >10
Ac Aerodynamic coverage of the injection row
x Distance downstream of the injection row
m Blowing parameter (PcYc/PQYg) :::. G" /GI- GO' (7!)
s EQUlyalent slot width
Julio C. Banks, PE Page 22 of 31

23. 6
The aerodynamic coverag~ Ac/or the injection from slots and shaped holes can
be assumed to be identical to the maximum geometriC coyerage for properly
designed slots and shaped holes.
The aerodynamic coverage of circular holes; howeyerl 1s not the same as the
geometric coyerage due to tn.~ expans10nJlf th~J·eJ after 1t exits from the hole.
The aerodynamic coverage of the jet from a circular hole is a function of the
blowirrg parameter (mt the surface angle in the streamw1se direction (ex.t and
the angle 1n the tangential direct10n (~). Using the data of references [2-22L
combined with an analytical approximation for the injection processl
a simple
empirical relation h~s been deyeloped to predict the aerodynamic coverage
from the geometric and injection parameters The aerodynamic coverage of
circular holes with a streamwlse pitch to diameter ratio of (P/O), streamwise
angle (cx.t and tangentfal angle (~)I may be estimated with the following
relation
Ac = ( 11 )
tancx.}4 P10 51n {tan- 1(--:-;)
slnp
,:.1·
with 10< ex. <80°
1 <P<45° ­
For circular holes
(' 2)
Julio C. Banks, PE Page 23 of 31
Equation 12 gives the maximum angle, alpha, for a known blowing parameter, M, or it provides the
maximum M for a given angle, alpha.

24. 7
is the recommended relation between the maximum blowing parameter and the
surface angle ex. to Qreyent the film from being blown off the surface.
Because of their empiri cal naturel Equations (11) and (12) must be used with
caution as the lower 11mit of ((, combined and the upper limit of P is
approached. There is very 11ttle data aYailable to check the ya1idlty of these
relations for shallow surface angles 1n combination with a large tangential
component.
The individual row f11m effectiveness and the film accumulation estimated
using nonlinear superposing for up to twenty rows of injection with
. .
aerodynamic coverage (Ac) ranging from 0.1 to 0.7 is presented in Figure 2.
Figure 2b shows only the locus of t~e r:naximum film effectiven~ss achieved
imm~diately downstre~m. of each injection row. The decay of the film
effectiveness between the rows has not been included in Figure 2b. The
cumulative film effectiYenesses of Figure 2b were computed assuming that the
row to row spacing - tJ,x - and the blowing conditions produce a value of
x
ms = 100 for x = A>tl and that the individual row effectiveness for each
aerodynamic coverage value ,decays as shown in Figure 20. Equations (9) and
I
(10) were used to compute the individual row film effectiveness shown in
Figure 2a~ and EQuations (6) and (7) were used to compute the row to row film
accumulation shown 1n Figure 2b.
Julio C. Banks, PE Page 24 of 31

25. 8
(a)
to
(J) 1 ~----------~~~~----~--r-------------~~
w
Z
w
>
t­
u
W .1
LI...
LI...
W
1:
..J
L&... .01
3;
oQ!
LIJ
..J I: : ! I.
AERODYNAM C~
COVERAGE
: 0.7 .
/ .....
p·~.5i
-------- b.3 :
~ .001 &----i----r---r-...,...-,!"""T'""1~---,i--_r_..,.__,.....;_..,....;_.,,__---;--r--ir-T--r-r_n;
(J) 10 100 1(0) l00J0
X!MS
(b)
(J) 1.0
(J)
0.9w
z
w
0.8>
t­ 0.7u
LIJ
LL..
0.6LL.
w
1: 0.5
..J
- 0.4L&...
w
0.3>
t­ 0.2
..J
::J
0.11:
:::J
U 0.0
0 2 4 6 8 10 12 14 16 18 20
ROW NUMBER
Figure 2 IndiYidual and cumulative film effectiveness for multirow injection
Julio C. Banks, PE Page 25 of 31

26. 9
Comparl son of nonlinear superDosition with data
Comparison of experimental data with the prediction is shown in Figure 3.
There is very little reliable data from multirow film alJailable for comparison.
,
To obta~n reliable data requires a meticulously constructed facility and
fastidious data acquisition. The most reliable data found to data in the
literature search for multirow injection is that of SasaKi1 et a1. (2) and Mayle,
et a1. [:3J. The data of Sasaki, et al. is for selJen rows of circular holes at 6 45°
streamwlse angle ( ex. = 45° )., no tangential component ( ~ = 0° ), and P/O = 3.
Using Equation (11) the aerodynamic coverage for thls configuration Ac =0.42.
As easily seen in Figure 3, using 0.42 as the Ac matches the Sasaki, et 81. data
Quite well. The Mayle., et a1. data is for circular holes having (X. =35°., ~ =45°
wi th P10 val ues of both 10 and 14. ~he. aerodynamic COyer8g~ co~puted US} ng
Equation (1 f) for these injection conditions are 0.12 and 0.16 for the P/O of 14
and 101 respectively. Again the agreement between the data and the nonlinear
superposition model as shown in Figure 3 is excellent after 6PPfOximlltely the
6th row. The reason for this is believed to be f11m blow-off 1n the early rows.
Using Equation (12) to estimate the maximum allowable blowing parameter for
the 35° streamwise surface angle gives a blowing parameter of approximately
0.87. To achieve the value of ~s =100 with the injection ge.ometry tested ,by
Mayle, et 81. required 8 blowing parameter of 2.0 and 1.0 for the P/O of 14 and
101 respectiye1y which are aboye the recommended maximums for circu18r
holes.
Julio C. Banks, PE Page 26 of 31

27. 10
1.0
0.9
0.8
(J)
(J)
z
L&J
0.1
LtJ
>-I­
U
L&J
L&.. 0.6
L&..
LtJ
1:
..J
>~
L&..
O.SLtJ
>
....-<t
..J
::J 0.4
1:
::J
u
0.3
0.2
0.1
PREDICTION ­
•
w ~ Shcped _ 0.7
•
Sasaki P10 =3>
(m-O.5, 4SOx (0)
A •
•
"film blown-off
Mayle P/D = 10
(m-I.O,3SOx459)
Mayle P/O =14
(m-2.0, 35OX4SO)
0.0 I---_-_-_-r---,.---,.---r---,.---r--.........,~
o 2 4 6 8 10 12 14 16 18 20
ROW NUMBER
•
A
FIGURE 3 COMPARISON OF MEASURED AND PREDICTED CUMULATIVE FILM EFFECTIVENESS
Julio C. Banks, PE Page 27 of 31

28. 1 1
The final piece of data shown on Figure 3 1S cascade data for three rows of
shaped holes at coverage of 0.7 on the suction slde of the F100 ILC first vane.
No intra-row data was available but the f11m effectiveness immediately down
stream of the third f11m row indicates good agreement, as can be seen in
Figure 3.
f!ut.14
R. E. Field
Inlets and Nozzles
Julio C. Banks, PE Page 28 of 31

29. 12
REFERENCES
J. P. Sellers" "Gaseous Film Coollng wlth Multiple Injection Stations,"
AIAA Joumal" v t" 9" pp2154-2156" December 1963.
2 N. Sosoki" k. Takaloro" T. Kumagai" M. Hamano" ·Film Cooling EffectiYeness
for Injection from Nultirow Holes,,· ASHE J. Engineering Power" y 10 1" pp.
] 01-108" January 1978.
3 R. E. Mayle" F. J. Camarato" "Heat Transfer Inlestiga11on for Multlhole
Aircraft Turbine Blade Coollng,,· AFAPL-tr-37-30" June 1973.
4 C. C. Cowan to S. A. Paul" PW internal correspondence" "Summary of
AESCC Testing o"f Cooling Ponel Configurations,,- June 24,,1987.
5 B. P. Amess to R. R. Sellers" PW internal correspondence" Advanced Film
Hole Concepts Demonstrate 50!C Increase 1n Fllm EffectlYeness,· April 1,
1987.
6 B. P. Amess to R. R. Sellers" PW internal correspondence" Advanced Film
Hole Cascade Results Using PWSOOO First Vane Aerodynamics,," November
7" 1988.
7 S. S. Papel, -Effect on Gaseous Film Coollng of Coolant injection Through
Angled Slots and Normal Holes,,· NASA TN d-299" September 1960.
8 K. K. landiS., -lnnoyatiY~ FUm Cooling Concepts for Advanced Turbines,,"
Quarterly Progress Report No.1" October through December 1983.. FR­
18203-1 ,Janurory 1984
9 K. K. landiS, ·'nnovatiye Film Cooling Concepts for Advanced Turbines,·
Quarterly Progress Report No.2, Janurary through March 1983, FR­
18203-2" June 1984
lOB. Jurban" A. Brown.. -Film Coollng from Two Rows of Holes inclined in the
'~, Streamwise and Spanwise D1rectlons,," ASME 84-GT-286.
Julio C. Banks, PE Page 29 of 31

30. 13
11 G.E. Andrews, MAllkhanlzadeh, F. Bazdini Tehraln, C. I. Hussain, M.S.
Koshkbar Azari, ·Small Diameter Film Cooling Holes: The Influence of
Hole 51ze and Pitch,· presented at the National Heat Transfer Conference,
Pittsburgh, PA., August 9-12, 1987.
12 M. E. Crawford, W. M. Kays, R. J. Moffat, "Full-Coverage Film Cooling,
Part 1: Comparison of Heat Transfer Data for Three Injection Angles,·
ASHE 80-GT-43.
13 H. A. Paradis, '"Fllm Coo11ng of Gas Turbine Blades: A Study of the Effect
of Large Temperature Differences on Film Cooling.Effectiyeness,· ASHE
J. Engineering Power pp 11-20, Janurary 1977.
..
14 J. F. Muska, R. W. Fish, M. Suo, "The Additive Nature of Film Cooling From
Rows of Holes,'" ASHE J. Engineering Power, PP 457-463, October 1976.
15 D. R. Pedersen, E. R. G. Eckert.. R. J. Goldstein, "Film Coollng With large
Density Differences Between the Mainstream and the Secondary Fluid
Measured by the Heat-Moss Transfer Analogy,· ASHE J. Heat Transfer, v99
pp. 620-627, Noyember 1977.~"
16 J. P. Harnett, R. C. Bibkebak, E. R. G. Eckert, .. VElocity Distributions,
Temperature Distributions, EffectiYeness and Heat Transfer for Air
Injected Through a Tangential Slot Into a Turbulent Boundary layer,·
ASHE J. Heat Transfer.. pp. 293-306.. August 1961.
17 . R. J. Goldstein, E. R. G. Eckert, J. W. Romsey, ·Film Coollng with Injection
Through Holes: Adiabatic Wall Temperatures Downstream of 0 Circulor
Hole,· ASHE J. Engineering Power, pp. 384-395, October 1968.
1B R. J. Goldstein, .. Film Cooling,· Advonces in Hell! Tronsfer:. v7pp 321­
379, Academic Press, New Vork, N. V., 1971.
19 J. W. Ramsey, R. J. Goldstein, • Interaction of 8 He~ted Jet with a
Deflecting Stream,· NASA CR-72613, HTL TR No. 92, April 1970.
20 R. Milano to Ilanask, PW 1ntemal correspondence, "Metered Slot Fllm
Effectiveness Oat6.: May 25, 1983
21 W. M. Murray, Jr., PW Experimental Test Department Short Memorandum
.~
Report, ·Film Coollng Results from the Basic Flow Rig 250 13-L,· Report
No. 448B.. April 30,1968.
Julio C. Banks, PE Page 30 of 31

31. 14
22
23
V. L. Streeter.. FllIldl1echonlcs.. McGrew-H111 New YOrk" N.Y., PD 379-416~
1971.
E. Fernandezi private communication with R.E. Fieldl
Aprll 1989.
Julio C. Banks, PE Page 31 of 31