Steven J. Schneider

Glenn Research Center, Cleveland, Ohio

Analysis of Turbine Blade Relative Cooling Flow 

Factor Used in the Subroutine Coolit Based on

Film Cooling Correlations

NASA/TM—2015-218738

June 2015
NASA STI Program . . . in Profi le

Since its founding, NASA has been dedicated 

to the advancement of aeronautics and space science. 

The NASA Scientifi c and Technical Information (STI) 

Program plays a key part in helping NASA maintain 

this important role.

The NASA STI Program operates under the auspices 

of the Agency Chief Information Offi cer. It collects, 

organizes, provides for archiving, and disseminates 

NASA’s STI. The NASA STI Program provides access 

to the NASA Technical Report Server—Registered 

(NTRS Reg) and NASA Technical Report Server—

Public (NTRS) thus providing one of the largest 

collections of aeronautical and space science STI in 

the world. Results are published in both non-NASA 

channels and by NASA in the NASA STI Report 

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of 

completed research or a major signifi cant phase 

of research that present the results of NASA 

programs and include extensive data or theoretical 

analysis. Includes compilations of signifi cant 

scientifi c and technical data and information 

deemed to be of continuing reference value. 

NASA counter-part of peer-reviewed formal 

professional papers, but has less stringent 

limitations on manuscript length and extent of 

graphic presentations.

• TECHNICAL MEMORANDUM. Scientifi c 

and technical fi ndings that are preliminary or of 

specialized interest, e.g., “quick-release” reports, 

working papers, and bibliographies that contain 

minimal annotation. Does not contain extensive 

analysis.

• CONTRACTOR REPORT. Scientifi c and 

technical fi ndings by NASA-sponsored 

contractors and grantees.

• CONFERENCE PUBLICATION. Collected 

papers from scientifi c and technical 

conferences, symposia, seminars, or other 

meetings sponsored or co-sponsored by NASA.

• SPECIAL PUBLICATION. Scientifi c, 

technical, or historical information from 

NASA programs, projects, and missions, often 

concerned with subjects having substantial 

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientifi c and 

technical material pertinent to NASA’s mission.

For more information about the NASA STI 

program, see the following:

• Access the NASA STI program home page at 

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI 

Information Desk at 757-864-6500

• Telephone the NASA STI Information Desk at

 757-864-9658

• Write to:

NASA STI Program

 Mail Stop 148

 NASA Langley Research Center

 Hampton, VA 23681-2199
Steven J. Schneider

Glenn Research Center, Cleveland, Ohio

Analysis of Turbine Blade Relative Cooling Flow 

Factor Used in the Subroutine Coolit Based on

Film Cooling Correlations

NASA/TM—2015-218738

June 2015

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

Level of Review: This material has been technically reviewed by technical management. 

NASA STI Program

Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681-2199

National Technical Information Service

5285 Port Royal Road

Springfi eld, VA 22161

703-605-6000

This report is available in electronic form at http://www.sti.nasa.gov/ and http://ntrs.nasa.gov/
NASA/TM—2015-218738 1 

Analysis of Turbine Blade Relative Cooling Flow Factor Used in the 

Subroutine Coolit Based on Film Cooling Correlations 

Steven J. Schneider 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

Heat transfer correlations of data on flat plates are used to explore the parameters in the Coolit 

program used for calculating the quantity of cooling air for controlling turbine blade temperature. 

Correlations for both convection and film cooling are explored for their relevance to predicting blade 

temperature as a function of a total cooling flow which is split between external film and internal 

convection flows. Similar trends to those in Coolit are predicted as a function of the percent of the total 

cooling flow that is in the film. The exceptions are that no film or 100 percent convection is predicted to 

not be able to control blade temperature, while leaving less than 25 percent of the cooling flow in the 

convection path results in nearing a limit on convection cooling as predicted by a thermal effectiveness 

parameter not presently used in Coolit. 

Nomenclature 

Description Units Example 

A flow area m2

 varies 

a sonic velocity m/s varies 

B distance between blades m 0.02 

C1 convection from combustion gas W/m2

 varies 

C2 convection to cooling air W/m2

 varies 

Dc cooling passage width m varies 

Dh hydraulic diameter of cooling passage m varies 

FAC relative cooling flow factor in Coolit1

 varies 

h convective heat transfer coefficient W/m2

 K varies 

H height of blades m 0.05 

kc thermal conductivity of cooling air W/m K 0.0553 

kg thermal conductivity of combustion gas W/m K 0.164 

L length of blade in flow direction m 0.05 

m momentum ratio (cUc/gUg) varies 

Mc cooling flow Mach number 0.3 

Mg combustion flow Mach number 0.6 

mc  mass flow of cooling air kg/s varies 

mg  mass flow of combustion gas kg/s varies 

ms  mass flow in film cooling layer kg/s varies 

mtot  total mass flow kg/s varies 
NASA/TM—2015-218738 2 

P pressure kPa varies 

Ptc cooling flow inlet total pressure kPa 3040 

Ptg combustion gas inlet total pressure kPa 3040 

Pr Prandtl Number varies 

RecDh Reynolds No. based hydraulic diameter varies 

Regx Reynolds No. based on axial distance varies 

Res Reynolds No. based on slot height varies 

s film cooling slot height m varies 

Ttc cooling flow inlet total temperature K 880 

Ttg combustion gas total temperature K 2280 

Taw adiabatic wall temperature of blade K varies 

Tw wall temperature K varies 

U uniform velocity m/s varies 

x axial distance from cooling slot m varies 

 fraction of cooling flow in convection varies 

c specific heat ratio of cooling gas 1.4 

g specific heat ratio of combustion gas 1.25 

ηx film-cooling effectiveness varies 

conv thermal effectiveness of convection (Eq. (3)) varies 

c viscosity of cooling air kg/m/s 3.89e-5 

g viscosity of combustion gas kg/m/s 7.41e-5 

 density of gas kg/m3

 varies 

 cooling effectiveness of wall (Eq. (2)) varies 

Subscripts: 

c pertaining to cooling flow 

g pertaining to combustion flow 

i pertaining to coolant inlet 

o pertaining to coolant outlet 

s pertaining to static flow conditions 

t pertaining to total flow conditions 

x pertaining to axial position along blade 

Analytic Procedure 

A methodology based on a combination of film cooling and internal convection cooling is used to 

check the relative cooling flow factors in the Coolit (Ref. 1) subroutine which is used for estimating 

turbine cooling flow requirements. The relative cooling flow factor (FAC) is chosen during a Coolit 

analysis to estimate dimensionless cooling as a function of desired blade temperature using the following 

equations. 

1.25

1

0.022 FAC 





 







 

 

g

c

m

m



 (1) 
NASA/TM—2015-218738 3 

The cooling effectiveness  is defined by the following equation, which gives a relationship between 

combustion gas temperature, cooling gas temperature, and desired wall temperature. 

tg tc

tg w

T T

T T



   (2) 

Equation (1) is a curve fit to data (Ref. 2) for a full coverage film cooled vane where FAC = 1 is assumed 

in Coolit. 

There is also a thermal effectiveness parameter (Ref. 3) conv that is monitored in this analysis and 

may be useful to monitor in Coolit as well. It is a measure of how close the wall temperature is to the 

coolant temperature at the outlet of the internal convection path. It is calculated as a cooling performance 

indicator in this analysis. It is defined as follows 

wo tci

tco tci

T T

T T

n 

 conv  (3) 

Convection Cooling Only Case 

The internal convection only case is analyzed using Figure 1. 

Convective heat transfer per unit area (C2) inside the blade is modeled by empirical data in the form 

of heat transfer coefficients (h) in fully turbulent pipe flow (RecDh>2300), which is easy to achieve in 

blade passages, but should always be checked. Correlations in the form of Nusselt Numbers are used to 

model specific data sets. 

0.8 0.4 0.023Re Pr cD c c

c h

Dh h k

h D Nu   (4) 

where 

c c

c h

cDh A

m D

   Re (5) 

and 

sc c

c c c M

m a A

   (6) 

and 

c

c h H D

A D

  2 (7) 

The convective heat transfer per unit area inside the blade is then 

       T   x T x

D

k C x h T x T x cD c w tc

h

c c w tc h     0.8 0.4

2 0.023 Re Pr (8) 
NASA/TM—2015-218738 4 

Convective heat transfer per unit area (C1) outside the blade is modeled by correlations of turbulent flow 

over a flat plate at constant temperature. The local Nusselt Number correlation is as follows for turbulent 

flow with Reynolds Numbers 5105<Regx<107,which can be difficult to achieve near the leading edge of 

the blade, but is used here with that caveat. 

0.8 1 3 0.0292Re Pr gx g

g

g

gx k

h x

Nu   (9) 

where 

g

sg g

gx

U x



 Re  (10) 

and 

g

g

g a

M

U  (11) 

The convective heat transfer per unit area on the outside of the blade is then a function of axial position as 

follows. 

       T T   x

x

k

C x h x T T x gx g tg w

g  g tg  w   0.8 1/ 3

1 0.0292 Re Pr (12) 

Neglecting axial conduction C1(x) = C2(x) and for simplicity assuming zero wall thickness leads to the 

following equation for wall temperature as a function of axial position. 

 

 

0.8 1 3 0.8 0.4

0.8 1 3 0.8 0.4

0.0292 Re Pr 0.023 Re Pr

0.0292 Re Pr 0.023 Re Pr

cD c

h

c gx g

g

cD c tc

h

c gx g tg

g

w

h

h

D

k

x

k

T x

D

k T

x

k

T x





 (13) 

The blade length (L) is then divided into N increments of x = L/N and integrated numerically with 

the flow of heat across the wall increasing the coolant flow temperature (Ttc) as a function of axial 

position (x), but with the combustion gas temperature (Ttg) remaining unchanged. Heat flows in from both 

sides of the blade into the ith increment of x according to the following equation. 

    i i tc tc

c pc

i x T T

H x

m C

C    1 2 1

 (14) 

Substituting for C1(x) and solving for Ttci+1 the increase in cooling temperature flow is obtained. 

  T T   x

x

k

m C

H x T T gx g tg w

g

c pc

tc tc i i     

0.8 1 3 0.0292 Re Pr 2

1  (15) 
NASA/TM—2015-218738 5 

These equations are then numerically integrated for heat flux C1(x), coolant flow temperature Ttc(x), 

and wall temperature Tw(x). 

Film and Convection Cooling Case 

The external film cooling using slot cooling and internal convection cooling case is analyzed using 

the Figure 2 schematic shown below. Only the flow downstream of the slot is modeled. The leading edge 

is not modeled. Since a row of holes is typically used on a turbine blade, it would have to be converted to 

an equivalent slot width for use with the slot correlations. In this case only the fraction  of the total 

coolant flow mc  flows through the blade and the remainder fraction 1- is used for film cooling. 

Convective heat transfer per unit area (C2) inside the blade is again modeled by empirical data in the 

form of heat transfer coefficients (h) in fully turbulent pipe flow using Equations (4) and (8). 

where the Reynolds Number is now 

c c

c h

cDh A

am D

   Re (16) 

and the convection coolant flow area is 

sc c

c c c M

am a A

   (17) 

Convective heat transfer per unit area (C1) outside the blade is modeled by correlations of turbulent film 

cooling, which alters heat transfer by both a velocity and temperature change near the wall. Correlations 

(Ref. 4) have been developed to account for both effects. 

Dealing with the velocity first, a momentum ratio of the coolant flow to hot gas flow is defined as 

follows 

sg g

sc c

U

U

m



  (18) 

Values of this parameter separate flow regimes identified as boundary layer and wall jet regimes in film 

cooling analyses. 

Boundary Layer Flow Regime 

The boundary layer regime is estimated to occur between 0.5<m<1.3 with the following correlation 

0.7

0.069 Re 



 



   s

x

k

h x

Nu s

g

g

gx (19) 

where the Reynolds Number based on slot width s is defined as follows 

c

sc c s

U s



 Re  (20) 
NASA/TM—2015-218738 6 

The convective heat transfer per unit area on the outside of the blade as a function of axial position is then 

as follows. 

        T   x T x

s

x

x

k

C x h x T x T x s aw w

g

g aw w   

 



   

0.7

1 0 (21) .069 Re

Neglecting axial conduction C1(x) = C2(x) and for simplicity assuming zero wall thickness leads to the 

following equation for wall temperature as a function of axial position. 

 

   

0.8 0.4

0.7

0.8 0.4

0.7

0.069 Re 0.023 Re Pr

0.069 Re 0.023 Re Pr

D c

h

c s

g

D c tc

h

c s aw

g

w

h

h

D

k

s

x

x

k

T x

D

k T x

s

x

x

k

T x

  

 





  

 





 (22) 

The effect of temperature change due to film cooling near the wall is taken into account by defining the 

adiabatic wall temperature Taw used in Equations (21) and (22) in lieu of using the total gas temperature 

Ttg. The adiabatic wall temperature Taw is obtained from correlations of the film-cooling effectiveness 

parameter x as follows. 

 

tg tc

tg aw x

x T T

T T



   (23) 

Different correlations (Ref. 4) exist for the near slot region and the region far downstream of the slot. The 

near slot region is defined by 0<x/s<150 with the following correlation 

0.15 0.3

0.6 Re 

















 



 



  



g

c x s

m

ms

x (24) 

Data for this correlation was also limited to 0.5<m<1.3, 0.8<sc/sg<2.5, and 0.0019<s<0.0064 m. The far 

downstream correlation defined by x/s150 is given by the following correlation. 

0.2 0.8

3.68 Re 

















 



 



  



g

c x s ms

x (25) 

Wall Jet Regime 

The wall jet regime is estimated to occur at m1.3 with the following correlation 

0.44

0.8 Nu 0.10Re 



 



   s

x

k

h x

s

g

g

gx (26) 

 
NASA/TM—2015-218738 7 

The convective heat transfer per unit area on the outside of the blade as a function of axial position 

for this case is then as follows. 

        T   x T x

s

x

x

k

C x h x T x T x s aw w

g

g aw w   

 



   

0.44

0.8

1 0 (27) .10 Re

Again, neglecting axial conduction C1(x) = C2(x) and for simplicity assuming zero wall thickness leads to 

the following equation for wall temperature as a function of axial position. 

 

   

0.8 0.4

0.44

0.8

0.8 0.4

0.44

0.8

0.10 Re 0.023 Re Pr

0.10 Re 0.023 Re Pr

D c

h

c s

g

D c tc

h

c s aw

g

w

h

h

D

k

s

x

x

k

T x

D

k T x

s

x

x

k

T x

  

 





  

 





 (28) 

Again, the effect of temperature change due to film cooling near the wall is taken into account by defining 

the adiabatic wall temperature Taw used in Equations (27) and (28) in lieu of using the total gas 

temperature Ttg. The adiabatic wall temperature Taw is obtained from correlations of the film-cooling 

effectiveness parameter x defined by Equation (23). Different correlations (Ref. 4) exist for different 

flow regimes as follows 

For the regime defined by 0<x/s<150 and 1.3<m<4 and x/ms<8 

nx  1.0 (29) 

For the flow regime defined by 0<x/s<150 and 1.3<m<4 and 8<x/ms<11 

1

0.6 0.05







 



   

ms

x x (30) 

For the regime defined by 0<x/s<150 and 1.3<m<4 and x/ms>11 

  0.2

0.15 0.3

0.7 Re  



















 



 



   m

s

x

g

c x s (31) 

For the far downstream regime x/s150 the correlation given by Equation (25) is used again. 

The blade length (L) is again divided into N increments of x = L/N and the equations are integrated 

numerically with the flow of heat across the wall increasing the coolant flow temperature (Ttc) as a 

function of axial position (x), and the adiabatic wall temperature Taw also varying with (x). Heat flows in 

from both sides of the blade into the ith increment of x according to Equation (14). In the boundary layer 

regime between 0.5<m<1.3 substituting Equation (21) for C1(x) and solving for Ttci+1 the increase in 

cooling temperature flow is obtained. 

  T   x T x

s

x

x

k

m C

H x T T s aw w c

c pc

tc tc i i   

 



    

0.7

0.069 Re 2

1  (32) 

 
NASA/TM—2015-218738 8 

The wall jet regime at m1.3 substitutes Equation (27) for C1(x) and solving for Ttci+1 the increase in 

cooling flow temperature is obtained. 

  T   x T x

s

x

x

k

m C

H x T T s aw w c

c pc

tc tc i i   

 



    

0.44

0.8 0.10 Re 2

1  (33) 

These equations are then numerically integrated for heat flux C1(x), coolant flow temperature Ttc(x), 

adiabatic wall temperature Taw(x), and wall temperature Tw(x). 

Solution Procedure 

These equations are integrated over 0<X<L for the example parameters given in the nomenclature 

section and the results are given in Figures 3 through 9. Both an excel spreadsheet and a Fortran program 

given in Appendix A with an example input file in Appendix B are provided. Note that the balance of heat 

flux can be changed by varying the flow Mach Numbers. For these calculations the hot combustion flow 

has a Mach Number Mg = 0.6, whereas the cold coolant flow has a Mach Number of Mc = 0.3. A 

summary of the results and a comparison of the Coolit assumptions is given in Table 1 with further 

discussion below. 

Figure 3(a) shows cooling flow outlet temperature Ttco which decreases as cooling flow increases. It 

also shows the wall inlet and outlet temperatures, Twi and Two, respectively, which remain above 1750 K. 

This calculation says that pipe flow type convection cooling by itself cannot reduce the wall temperature 

much below 1750 K when the combustion temperature is 2280 K. The use of fin type structures inside the 

blade can enhance the cooling, but that is not analyzed here. Figure 3(b) plots the parameters conv, , and 

FAC from Equations (3), (2), and (1), respectively. The desired value of  for a 1400 K wall temperature 

with 2280 K combustion temperature and 880 K cooling flow temperature is  = 0.626, which is never 

reached in this calculation. The current use of FAC = 2 in Coolit estimates that there is only a factor of 2 

difference between the cooling flow required for a blade with convection cooling only vs. a blade with a 

full coverage film. Unless there are significant coolant enhancement features inside the blade, this could 

grossly underestimate cooling requirements with convection only. Figure 3(c) gives the wall temperature 

profiles as a function of axial position at dimensionless cooling flow rates of 0.1, 0.2, and 0.4. If the 

combustion gas temperature is reduced to 1680 K, then the 1400 K wall temperature is possible as shown 

in Figure 4 where  = 0.349, mc mg  /  = 0.033, FAC = 3.27, and conv = 0.322. 

In order to compare the film cooling analysis of Equations (16) to (33) with the 100 percent 

convection cooling analysis of Equations (4) to (15), a film cooling analysis with 98 percent convection 

and 2 percent film cooling is given in Figure 5 at 2280 K combustion temperature for comparison with 

Figure 3. There are some slight differences, but the wall temperature remains above 1750 K in agreement 

with that of Figure 3. Also, when the combustion gas temperature is reduced to Tg = 1680 K in Figure 6, 

the film cooling prediction is mc mg  /  = 0.023, FAC = 2.28, and conv = 0.445. These numbers are at least 

comparable to those of Figure 4, in spite of the fact that this is a gross extrapolation of the film coolant 

data in that the slot dimensions are three orders of magnitude smaller than those used in the data 

correlations. 

The 75 percent convection 25 percent film cooling case at Tg = 2280 K is shown in Figure 7. The 

effect of the film cooling effectiveness parameter x is shown by adiabatic wall temperature at the inlet 

(x = 0) and outlet (x = L) of the cooling passage, Tawi and Tawo, respectively in Figure 7(a). This reduction 

in temperature from 2280 K significantly reduces the heat flux and resulting wall temperature. The 

1400 K wall temperature Two is reached with mc mg  /  = 0.059 as shown in Figure 7(a) and FAC = 1.40 as 

shown in Figure 7(b). They are listed in Table 1. This case is in good agreement with the Coolit 

prediction of mc mg  /  = 0.054 calculated by Equation (1) for FAC = 1.3 given in Coolit. The thermal 
NASA/TM—2015-218738 9 

effectiveness parameter conv calculated using Equation (3), however, is only 0.166 whereas in 

Reference 3, where it is defined, only data above 0.5 is referenced. This indicates that the cooling flow for 

this case may be used more effectively. The calculated wall temperature for different mass flow ratios 

mc mg  /  is shown as a function of axial position along the blade in Figure 7(c). It shows that when one 

correlation is handed off to another as x increases the transition is not always smooth. 

The 50 percent convection 50 percent film cooling case at 2280 K is shown in Figure 8. In this case 

the 1400 K wall temperature is reached with mc mg  /  = 0.032 and FAC = 0.766 as shown in the 

Figures 8(a) and (b) and listed in Table 1. This compares with the Coolit prediction of mc mg  /  = 0.050 

for FAC = 1.2 used in Coolit. Since Coolit is anchored in full coverage film coolant data from Reference 

2 where FAC = 1.0, this film coolant data where FAC<1.0, suggests that a thick high velocity film leads 

to lower coolant massflow requirements indicating that it is more effective in cooling the blade than the 

full coverage film injected through a perforated surface. The thermal effectiveness parameter conv = 

0.408, calculated using Equation (3) is still low for this case when compared to those reported in 

Reference 3 (conv0.5). 

The 25 percent convection 75 percent film cooling case at 2280 K is shown in Figure 9. In this case 

the 1400 K wall temperature is reached with mc mg  /  = 0.023 and FAC = 0.550 as shown in the 

Figures 9(a) and (b) and listed in Table 1. This compares with the Coolit prediction of mc mg  /  = 0.046 

for FAC = 1.1 used in Coolit. Again, since Coolit is anchored in full coverage film coolant data from 

Reference 2 where FAC = 1.0, this film coolant data where FAC<1.0, suggests that a thick high velocity 

film leads to lower coolant massflow requirements than the full coverage film injected through a 

perforated surface. The thermal effectiveness parameter conv = 0.803, calculated using Equation (3) is 

comparable to those reported in Reference 3 (conv0.5) in this case. 

Conclusions 

The use of flat plate film and convection cooling correlations predicts the trends currently employed 

for cooling analysis in Coolit, but should be considered optimistic due to their ideal nature, since injecting 

the film through a row of holes rather than a slot would increase turbulent heat transfer as would the 

positive pressure gradients within the blades due to their thinning of the boundary layers. The baseline in 

Coolit (FAC = 1.0) is the data set obtained in a full coverage film cascade experiment. The use of flat 

plate film correlations, perhaps optimistically, predicts that a thick uniform film introduced through a row 

of holes can reduce heat transfer (FAC<1.0) below that of the full coverage film introduced through holes 

distributed evenly over the whole surface. A detailed cascade experiment would be needed to prove this, 

however. This analysis does show that care must be taken in the Coolit assumptions when assuming that a 

blade is cooled by convection only in that overheating is possible. Also, at the opposite extreme, 

assuming that the bulk of the cooling flow is diverted from convection within the blade to a film cooling 

layer on the blade could lead to overheating of the convection coolant. An additional parameter not 

presently monitored in Coolit is the thermal effectiveness parameter given by Equation (3). This 

parameter matches the heat flux into the blade with the rise in temperature of the convection cooling 

within the blade. It would be wise to monitor this parameter in a Coolit analysis to show that excess 

cooling is not being employed for a given cooling configuration. 

 
NASA/TM—2015-218738 10 

TABLE 1.—FOLLOWING AN EXAMPLE IN REFERENCE 4, RESULTS FOR 3040 KPA, 2280 K 

COMBUSTION FLOW WITH 880 K COOLING FLOW TO ACHIEVE 1400 K WALL TEMPERATURE, 

 i.e.,  = 0.626 WITH RESULTS USING COOLIT IN PARENTHESES 

100% convection cooled 75% convection 

25% film 

50% convection 

50% film 

25% convection 

75% film 

mc mg  /  Not possible (0.084) 0.059 (0.054) 0.032 (0.050) 0.023 (0.046) 

FAC Not possible (2.0) 1.4 (1.3) 0.766 (1.2) 0.550 (1.1) 

conv Not possible 0.166 0.408 0.803 
NASA/TM—2015-218738 11 
NASA/TM—2015-218738 12 
NASA/TM—2015-218738 13 
NASA/TM—2015-218738 14 
NASA/TM—2015-218738 15 
NASA/TM—2015-218738 16 
NASA/TM—2015-218738 17 
NASA/TM—2015-218738 18 
NASA/TM—2015-218738 19 

Appendix A.—Fortran Source Code 

      PROGRAM MAIN   !Turbine Blade Cooling Flow Calculation

      CHARACTER*80 INPUTFILE, OUTPUTFILE

!     Kase=1 is Convection Cooled Only, KASE=2 is Film Cooled and Convection Cooled

      REAL KC,MUC,MWC,KG,MUG,MWG,LEN,MOMR,MASSR,MACHG,MACHC,MG,MC,MTOT,MS

      REAL MASSRI,MASSRF

      DIMENSION TW(100)

      DOUBLE PRECISION ETAX,REGX,TWI,TAWX,TTC,C1,C2,A,B,TW

      NAMELIST/INPT1/KASE,PTG,TTG,KG,MWG,GAMG,MACHG,MUG

      NAMELIST/INPT2/PTC,TTC,KC,MWC,GAMC,MACHC,MUC

      NAMELIST/INPT3/RBAR,LEN,WID,HT,ALPHA,MASSRI,MASSRF,DMASSR,N,NPRINT

!     DATA PTC,TTC,KC,MUC/3040.,880.,0.0553,3.89E‐5/

!     DATA MWC,GAMC,MACHC/28.95,1.4,0.6/

!     DATA PTG,TTG,KG/3040.,2280.,0.164/

!     DATA MUG,MWG,GAMG,MACHG/7.41E‐5,27.76,1.25,0.6/

!     DATA RBAR,LEN,WID,HT/8314.,0.05,0.02,0.05/

!     DATA MASSR,N,NPRINT/0.108,1000,10/

!     DATA KASE,ALPHA/2,0.85/

      WRITE(*,*)

      WRITE(*,'(a)') ' HTBLD'

      WRITE(*,'(a,$)') '  Enter HTBLD input data file: '

      READ(*,'(a)') inputfile

      WRITE(*,'(a,$)') ' Enter HTBLD output data file: '

      READ(*,'(a)') outputfile

      open(5,file=inputfile,status='unknown',form='formatted')

      open(6,file=outputfile,status='unknown',form='formatted')

      READ(5,INPT1)

      READ(5,INPT2)

      READ(5,INPT3)

      NBET=N/NPRINT

      TSG=TTG/(1.+(GAMG‐1.)/2.*MACHG*MACHG)

      TSC=TTC/(1.+(GAMC‐1.)/2.*MACHC*MACHC)

      UG=MACHG*SQRT(GAMG*RBAR/MWG*TSG)

      UC=MACHC*SQRT(GAMC*RBAR/MWC*TSC)

      VELR=UC/UG

      RHOTG=PTG/RBAR*MWG/TTG*1000.

      RHOTC=PTC/RBAR*MWC/TTC*1000.

      CPC=GAMC*RBAR/MWC/(GAMC‐1.)

      CPG=GAMG*RBAR/MWG/(GAMG‐1.)

      RHOSG=RHOTG/(TTG/TSG)**(1./(GAMG‐1.))

      RHOSC=RHOTC/(TTC/TSC)**(1./(GAMC‐1.))

      DENSR=RHOSC/RHOSG

      PSG=PTG/(TTG/TSG)**(GAMG/(GAMG‐1.))

      PSC=PTC/(TTC/TSC)**(GAMC/(GAMC‐1.))

      AG=HT*WID

      MG=RHOSG*UG*AG

      IM=(MASSRF‐MASSRI)/DMASSR+2
NASA/TM—2015-218738 20 

      MASSR=MASSRI

      TTCI=TTC

      DO 300 II=1,IM

      MC=MASSR*MG

      RHOSGUG=RHOSG*UG

      RHOSCUC=RHOSC*UC

      MOMR=RHOSCUC/RHOSGUG

      PRG=MUG*CPG/KG

      RHOSCUC=MOMR*RHOSGUG

      AC=MC/RHOSCUC

      IF(KASE.EQ.2)AC=ALPHA*MC/RHOSCUC

      DC=AC/HT

      MTOT=MC+MG

      PRC=MUC*CPC/KC

      DX=LEN/REAL(N)

      DH=2.0*AC/(HT+DC)

      RECDH=MC*DH/AC/MUC

      IF(KASE.EQ.2)RECDH=ALPHA*MC*DH/AC/MUC

      MS=MC*(1.‐ALPHA)

      US=UC

      AS=MS/RHOSC/US

      S=AS/HT

      ALPHAMC=ALPHA*MC

      RES=RHOSC*US*S/MUC

      X=DX

      TTC=TTCI

      DO 200 J=1,NPRINT

      DO 100 I=1,NBET

      IF(KASE.EQ.1)GO TO 90

      XOS=X/S

      XOMS=X/MOMR/S

      IF(MOMR.GT.1.3)GO TO 91

      ETAX=0.6*(1./XOMS)**0.3*(RES*MOMR*MUC/MUG)**0.15

      IF(MOMR.LE.1.3)GO TO 92

   91 IF(XOS.LE.150.0.AND.XOMS.LE.8.0)ETAX=1.0

      IF(XOS.LE.150.0.AND.XOMS.GT.8.0)ETAX=1./(0.6+0.05*XOMS)

      IF(XOS.LE.150.0.AND.XOMS.GE.11.)ETAX=0.7*XOS**(‐0.3)*(RES*MUC/MUG)**0.15*MOMR**(‐0.2)

   92 IF(XOS.GT.150.)ETAX=3.68*(1./XOMS)**0.8*(RES*MUC/MUG)**0.2

      IF(ETAX.GT.1.)ETAX=1.

      TAWX=TTG‐ETAX*(TTG‐TTCI)

      IF(J.EQ.1.AND.I.EQ.NBET)TAWXI=TAWX

   90 REGX=RHOSG*UG*X/MUG

      IF(KASE.EQ.1)A=0.0292*KG/X*REGX**0.8*PRG**(1./3.)

      IF(KASE.EQ.2.AND.MOMR.LE.1.3)A=0.069*KG/X*(RES*X/S)**0.7

      IF(KASE.EQ.2.AND.MOMR.GT.1.3)A=0.1*RES**0.8*KG/X*XOS**0.44

      B=0.023*KC/DH*RECDH**0.8*PRC**0.4

      IF(KASE.EQ.1)TWI=(A*TTG+B*TTC)/(A+B)

      IF(KASE.EQ.2)TWI=(A*TAWX+B*TTC)/(A+B)
NASA/TM—2015-218738 21 

      IF(KASE.EQ.1)C1=A*(TTG‐TWI)

      IF(KASE.EQ.2)C1=A*(TAWX‐TWI)

      C2=B*(TWI‐TTC)

      TTCOLD=TTC

      IF(KASE.EQ.1)TTC=TTC+2.0*C1*HT*DX/MC/CPC

      IF(KASE.EQ.2)TTC=TTC+2.0*C1*HT*DX/ALPHA/MC/CPC

      XOLD=X

  100 X=X+DX

  200 TW(J)=TWI

      TTCO=TTC

      ETACONV=(TTCO‐TTCI)/(TWI‐TTCI)

      PHI=(TTG‐TWI)/(TTG‐TTCI)

      FAC=MASSR/0.022/(PHI/(1.‐PHI))**1.25

      WRITE(6,30)MASSR,ETACONV,PHI,FAC,TAWXI,TAWX,TTCO,(TW(IJ),IJ=1,NPRINT)

  300 MASSR=MASSR+DMASSR

   30 FORMAT(1X,4F8.4,13F8.1)

      close(5)

      close(6)

      STOP

      END
 
NASA/TM—2015-218738 23 

Appendix B.—Namelist Input for 75 Percent Convection Cooling Case 

NAMELISTS

$INPT1

KASE=2  

PTG=3040.

TTG=2280.

KG=0.164

MWG=27.76

GAMG=1.25

MACHG=0.6

MUG=7.41E‐05

$END

$INPT2

PTC=3040.

TTC=880.

KC=0.0553

MWC=28.95

GAMC=1.4

MACHC=0.3

MUC=3.89E‐05

$END

$INPT3

RBAR=8314.

LEN=0.05

WID=0.02

HT=0.05

ALPHA=0.75

MASSRI=0.01

MASSRF=0.06

DMASSR=0.001  

N=1000  

NPRINT=10

$END

 
NASA/TM—2015-218738 24 

References 

1. Gauntner, J.W., Algorithm for Calculating Turbine Cooling Flow and the Resulting Decrease in 

Turbine Efficiency, NASA-TM-81453, February 1980. 

2. Livingood, J.N.B., Ellerbrock, H.H., and Kaufman, A., 1971 NASA Turbine Cooling Research Status 

Report, Figure 23 of NASA-TMX-2384, September 1971. 

3. Esgar, J.B., Colladay, R.S., and Kaufman, A., An Analysis of the Capabilities and Limitations of 

Turbine Air Cooling Methods, NASA-TND-5992, September 1970. 

4. Lefebvre, A.H., Gas Turbine Combustion, Chapter 8. Heat Transfer, Taylor and Francis Publishers, 1983.