Perry L. Johnson

University of Central Florida, Orlando, Florida

Vikram Shyam and Chunill Hah

Glenn Research Center, Cleveland, Ohio

Reynolds-Averaged Navier-Stokes Solutions to

Flat Plate Film Cooling Scenarios

NASA/TM—2011-217025

May 2011
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Perry L. Johnson

University of Central Florida, Orlando, Florida

Vikram Shyam and Chunill Hah

Glenn Research Center, Cleveland, Ohio

Reynolds-Averaged Navier-Stokes Solutions to

Flat Plate Film Cooling Scenarios

NASA/TM—2011-217025

May 2011

National Aeronautics and

Space Administration

Glenn Research Center 

Cleveland, Ohio 44135

Prepared under Contract NNC09ZA01G
Acknowledgments

This work was completed under the support of the Lewis Educational Research Collaborative Internship Program sponsored by 

the Ohio Aerospace Institute. The authors acknowledge Jeffrey Moder for his support with Fluent licensing and 

computer resources as well as Ali Ameri for helpful insight in film cooling Computational Fluid Dynamics

and Dave Rigby for reviewing this manuscript.

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This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2011-217025 1 

Reynolds-Averaged Navier-Stokes Solutions to

Flat Plate Film Cooling Scenarios

Perry L. Johnson

University of Central Florida

Orlando, Florida 32816 

Vikram Shyam and Chunill Hah 

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135 

Abstract

The predictions of several Reynolds-Averaged Navier-Stokes solutions for a baseline film cooling 

geometry are analyzed and compared with experimental data. The Fluent finite volume code was used to 

perform the computations with the realizable k-ε turbulence model. The film hole was angled at 35° to the 

crossflow with a Reynolds number of 17,400. Multiple length-to-diameter ratios (1.75 and 3.5) as well as 

momentum flux ratios (0.125 and 0.5) were simulated with various domains, boundary conditions, and 

grid refinements. The coolant to mainstream density ratio was maintained at 2.0 for all scenarios.

Computational domain and boundary condition variations show the ability to reduce the computational 

cost as compared to previous studies. A number of grid refinement and coarsening variations are 

compared for further insights into the reduction of computational cost. Liberal refinement in the near hole 

region is valuable, especially for higher momentum jets that tend to lift-off and create a recirculating 

flow. A lack of proper refinement in the near hole region can severely diminish the accuracy of the 

solution, even in the far region. The effects of momentum ratio and hole length-to-diameter ratio are also 

discussed.

Nomenclature

D coolant hole nominal diameter, measured at the inlet to the hole, [m]

DR density ratio, c /ρρ ∞ 

I momentum flux ratio, ( ) ( ) 2 2

c U U ∞ ρ ρ

k thermal conductivity, [W/mK] 

L coolant pipe length, [m] 

M mass flux ratio, ( ) ( ) c U U ∞ ρ ρ

p pitch (distance between two neighboring coolant holes), [m] 

P0 operating pressure, [kPa] 

R gas constant for air, [287 J/kg*K]

T temperature, [K]

U mean velocity, [m/s]

U* dimensionless mean velocity

x distance downstream (from the centerline of coolant outlet), [m]

y vertical distance (from the hole exit and adiabatic surface), [m]

z lateral distance (from the centerline of the coolant outlet), [m]
NASA/TM—2011-217025 2 

Greek symbols: 

α angle of hole-axis inclination [°]

η local adiabatic film cooling effectiveness

η laterally-averaged adiabatic film cooling effectiveness

η spatially-averaged adiabatic film cooling effectiveness

θ dimensionless temperature, as in Reference 11 

θ* dimensionless temperature

ρ density [kg/m3

] 

Subscripts: 

aw adiabatic wall

c coolant 

CL centerline

r recovery

∞ crossflow freestream

Introduction

Gas turbine engines, used not only for aero-propulsion but also for land-based electrical power 

generation, operate at higher efficiencies when the firing temperature is increased. Modern engines 

operate well in excess of the allowable temperatures of metal components in the early turbine stages 

downstream of the combustion chamber. To compensate, “coolant” air is bled from the compressor, 

through internal passages, cooling the turbine components before injection into the hot gas path through 

discrete angled film cooling holes. After injection the coolant ideally provides a blanket (or “film”) of 

cooler air on the surface of the components, thus shielding them from the damaging temperatures of the 

hot gas path. As the use of compressor air lowers the performance of the engine, the goal of film cooling 

is to achieve a careful design balance which requires thorough knowledge of the physics involved in the 

interactions of the injected coolant and the hot crossflow.

Film cooling is evaluated primarily by its adiabatic effectiveness, Equation (1), on the downstream 

surface. It is common to compare effectiveness trends along the line directly downstream of the center of 

the hole exit, Equation (2). An alternative measurement is the span-wise averaged effectiveness,

Equation (3), which accounts for the effectiveness on the entire downstream surface.

,exit

(,) (,) r aw

r c

T T xz

x z

T T

− η = − (1) 

( ) ( ,0) CL η =η x x (2) 

(,)

( )

x z dz

x

dz

η

η = ∫

∫ (3) 

In the research laboratory, an easy film cooling model is the use of a flat plate geometry downstream 

of scaled cylindrical holes. Even with this basic geometry, a number of factors can influence the 

effectiveness of the film cooling. Due to large temperature differences, a large density gradient between 

the coolant jet and hot crossflow is present, as quantitatively specified by a density ratio (DR),

Equation (4). Multiplication of the density ratio by a velocity magnitude ratio (VR), Equation (5), the 

blowing ratio, or mass-flux ratio (M) is obtained, Equation (6). A fourth parameter is the momentum-flux 

(I) ratio, Equation (7). Two of these four influential hydrodynamic parameters are independent. 
NASA/TM—2011-217025 3 

c DR

∞

ρ = ρ

(4) 

Uc VR

U∞

= (5) 

( )

( ) c U

M

U ∞

ρ = ρ

(6) 

( )

( )

2

2

c U

I

U ∞

ρ

=

ρ

(7) 

While the VR affects whether the crossflow perceives the injected jet as a blockage or an acceleration, 

M and I have greater success in scaling the results across multiple DR. For example, I usually determines 

closely the trajectory of the jet as it exits the cooling hole (Refs. 1 and 2). Three different regimes for film 

cooling can be defined for simple angle cylindrical holes. First, at low momentum ratios (I <0.3-0.4), the 

coolant jet is deflected immediately toward the wall, providing maximum coverage to the centerline 

downstream of the hole. Once the momentum ratio is increased (0.3-0.4 < I < 0.7-0.8), the jet slightly 

detaches from the downstream surface and penetrates into the crossflow before reattaching further 

downstream. Higher momentum flux ratios (I > 0.7-0.8) results in complete lift-off of the jet and minimal 

film cooling effectiveness downstream. This analysis is based on the experiments of Sinha et al. (Ref. 1) 

and Thole et al. (Ref. 2) at an inclination angle (α) of 35°. 

Geometric parameters can also have great influence on the film cooling flow. The inclination angle of 

a cooling hole is the most obvious geometric parameter. The present study is concerned only with the 

simplest of film cooling hole shapes: a row of stream-wise cylindrical holes. The cylindrical hole was 

naturally the first discrete hole shape studied. Goldstein et al. studied a single cylindrical hole (Ref. 3) and 

a row of cylindrical holes (Ref. 4), reporting adiabatic wall effectiveness. Eriksen and Goldstein (Ref. 5)

studied the heat transfer behind such a row of holes. Goldstein et al. (Ref. 6) began to look at geometric 

and hydrodynamic effects, specifically density ratio and hole length. 

Pedersen et al. (Ref. 7) studied the effect of density ratio in more detail using the heat-mass transfer 

analogy, as did Foster and Lampard (Ref. 8) in their study of cylindrical holes. Pietrzyk et al. (Refs. 9 and 

10) studied the velocity field of the film cooling situation at density ratios of 1.0 and 2.0, considering both 

mean and statistical turbulent data. Sinha et al. (Ref. 1) extended the density ratio study to provide 

adiabatic effectiveness results. Thole et al. (Ref. 2) continued further with mean thermal field 

measurements. As previously mentioned, these two studies bench-marked the trajectory regimes of 

cylindrical film cooling flows. Since the coolant is usually supplied to the hole from a large plenum-like 

area, the exit velocity profile is not fully-developed. Consequently, the length-to-diameter ratio is an 

important parameter when the length of the hole fails to exceed about 5 diameters (Refs. 11 and 12). 

Walters and Leylek (Ref. 13) provided a robust methodology for RANS simulations of film cooling 

flows. Using the standard k-ε turbulence model with a gradient adapted unstructured grid and two-layer 

wall treatment, they compared against the surface data of Sinha et al. (Ref. 1). Azzi and Lakehal (Ref. 14)

and Lakehal (Ref. 15) made anisotropic and turbulent Reynolds number corrections to the k-ε equations, 

showing improvement in the centerline effectiveness predictions of the experiments of (Ref. 1). Recently, 

Large Eddy Simulations (LES), as opposed to RANS, has grown in the field of film cooling research 

(Refs. 16 to 22). RANS, however, remains the workhorse for practical engineering applications due to the 

relative computational ease as compared to LES. In either circumstance, computational domain, boundary 

conditions, and grid resolution are important balances of computational efficiency and solution accuracy.
NASA/TM—2011-217025 4 

The present study investigates the domain, boundary, and resolution considerations using a RANS 

approach in the context of the L/D and I comparisons available in the experimental work of (Refs. 1 and 

2). RANS then can be made a stepping stone to the computationally rigorous LES method, where such 

considerations become even more important. 

Approach

Grid resolution, as in any numerical simulation, is key to the proper computational solution of film 

cooling. Overly coarse grids will lead to gross inaccuracies in the solution while overly fine grids will 

waste time and computational resources. In regions with high gradients in flow properties, finer grids are 

needed to properly resolve the flow, whereas, more uniform regions can be accurately represented by a 

coarser grid. The design of a grid should incorporate the minimum number of cells while still accurately 

capturing the physics of the flow field. This current study investigated a number of different grid 

structures in evaluating the ability of RANS approaches to predict film cooling flows.

Because film cooling from cylindrical holes tends to exhibit a large range of jet trajectories, the current 

study was designed to look at how this may affect the ability of the current RANS approach to predict film 

cooling effectiveness. The highest momentum ratios, with complete detachment, are generally avoided in 

film cooling design. Therefore, the current study simulated two momentum flux ratios at an engine-like 

density ratio of 2.0. The low momentum ratio, with expected full attachment, was 0.125, mirroring the 

experiments of Sinha et al. (Ref. 1) and Thole et al. (Ref. 2). The moderate momentum ratio, I = 0.5, also 

matched experiments from the same investigations. These two studies were performed at different length-todiameter ratios, thus, the current study also needed to reflect this. Sinha et al. used very short holes with

L/D = 1.75, while Thole et al. studied longer holes with L/D = 3.5. With these two variables (momentumflux and length-to-diameter ratios), a total of four cases were defined for the current study. Table 1 

summarizes the test matrix. Table 2 gives the common parameters for all studies.

TABLE 1.—TEST MATRIX

Scope of investigation I = 0.125 I = 0.5

L/D = 1.75 (Sinha et al.) Case 1 Case 2

L/D = 3.5 (Thole et al.) Case 3 Case 4

TABLE 2.—GEOMETRY AND

FLOW CONDITIONS

D 12.7 mm

α 35°

p/D 3.0

U∞ 20 m/s

Tu%∞ 0.2%

T∞ 300 K

Tc 150 K

DR 2.0

M 0.5, 1.0

δ99/D 0.52
NASA/TM—2011-217025 5 

Within each of these four cases, a variety of different grids were tested. First, a basic grid with a thin 

layer of wall refinement was used as a baseline to test boundary condition effects. Type 'a-c' grids fell into 

this category, of which the grid structure near the hole is shown in Figure 1(a). Type 'c' grids used the full 

computational domain of Walters and Leylek (Ref. 13). Type 'b' grids shortened the modeled crossflow by a 

factor of two while type 'a' grids went a step further and shortened the modeled crossflow inlet length, 

replacing its effects with a 1/7 law boundary layer profile (Refs. 14, 15, and 19), Equation (8), with 

experimentally specified boundary layer thickness. In all, this led to a 40 percent reduction in grid cells.

1

7

( ) y Uy U∞

  =     δ (8)

Next, the grid was highly refined in the region near the hole, with regions away from the hole 

generally unaffected. This new refinement gave rise to grids 'd' and 'f', Figure 1(b). The 'f' grids 

encompassed the entire domain of (Ref. 13) while the 'd' grids represented the full domain reduction 

similar to 'a' grids. Following the near-hole refinement in 'd' and 'f' grids, a coarsening was applied to the 

entire flow field to generate grid 'i', Figure 1(c). This coarsening was an attempt to generate similarly 

accurate solutions as grid 'd', but with greatly reduced computation time. Finally, the jet region, as defined 

by the upper 0.5 diameters of the plenum, the coolant hole, and the lower two diameters above the 

crossflow surface, was refined using hanging node adaption. The result of this final grid refinement was 

labeled 'j', Figure 1(d). In hanging node adaption, parent hexahedral cells are split into four children

(a) (b) 

(c) (d)

Figure 1.—Grid topologies used: (a) initial spacing (‘a’, ‘b’, and ‘c’), (b) with near-hole refinement (‘d’ and ‘f’), (c) with 

subsequent total coarsening (‘i’) and (d) with hanging node adaption in the jet region (‘j’).
NASA/TM—2011-217025 6 

hexahedral cells. If the adaption is preformed only for a portion of the grid, the boundary of the adapted 

and non-adapted regions gives rise to hanging nodes, which results from a parent face’s connection with 

four children faces. Extra memory overhead is needed to maintain connectivity, but effective use can 

significantly reduce cell count and computation time. A two-dimensional schematic of a hanging node is 

shown in Figure 2. 

To appreciate the domain reductions involved in changing from the Walters and Leylek grids 'c' and 

'f' to grids 'a' and 'd', the domains are shown side by side in Figure 3 with identical plenum and hole sizes. 

In all, this reduction led to about a grid with about 40 percent of the cells of the full domain. 

Not all cases were run for each grid. Table 3 summarizes the entire spectrum of numerical simulations 

performed in the current study. With four cases and seven grid structures, a total of 19 simulations were 

completed. These solutions enabled comparisons with respect to momentum-flux ratio, length-to-diameter 

ratio, and grid refinement/coarsening. 

Figure 2.—Schematic of a hanging node resulting from the 

hexahedral adaption process (Ref. 23).

(a)

(b)

Figure 3.—Computational domains: (a) reduced grids ‘a’,’d’,’i’,’j’ and (b) full grids ‘c’,’f’.

TABLE 3.—LIST OF GRIDS USED FOR EACH CASE

Grid letter Description Cell count in millions Cases used

a Fully reduced domain 0.21 1,2,3,4

b Partially reduced domain 0.29 1,2

c Full domain of (Ref. 13) 0.50 1,2,3,4

d Grid ‘a’ with near hole refinement 0.77 1,2,3,4

f Grid ‘c’ with near hole refinement 1.31 1,2

i Grid ‘d’ with universal coarsening 0.19 1,2

j Grid ‘i’ with hanging node adaption in jet region 1.03 2
NASA/TM—2011-217025 7 

Numerical Methodology

The numerical domain was established to mirror the experiments of Sinha et al. and Thole et al., the 

important difference between the two experiments being the length of the hole. Some of the grids 

represented the domain used by Walters and Leylek (Ref. 13), which stretched ten diameters above the 

no-slip surface and 20 diameters upstream of the hole. The fully-reduced domain modeled only five 

diameters above the surface and five diameters upstream of the holes. Because a row of holes was being 

modeled, only one-half of the hole needed to be modeled for the steady solution. 

The plenum and crossflow walls were specified with adiabatic no-slip conditions, while symmetry 

planes in the span-wise direction were specified with zero shear and zero heat-flux. The “freestream”

condition was approximated using a symmetry boundary as well. The plenum and crossflow inlets were 

specified by a velocity profile. The near-stagnation plenum was always supplied with a uniform inlet 

velocity profile while the crossflow was given a uniform profile for the long upstream length cases 

('b','c','f') and a 1/7 law velocity profile (Eq. (8)) for the reduced upstream length cases ('a','d','i','j'). A 

pressure-outlet condition controlled the pressure (101.325 kPa) at the crossflow outlet, though the 

absolute pressure was unimportant for the incompressible solution.

Gambit (Ref. 23) grid generation software was used for all grids. The structured hexahedral grids, 

though varying for each case, maintained overall the same structure, with certain refinement or coarsening 

in certain areas. All cases, to varying degrees, maintained refinement near no-slip walls, placing the first 

node with a y+ on the order of unity. 

Fluent’s (Ref. 24) pressure-based incompressible solver with energy equation was used to solve the 

governing equations with the specified boundary conditions. The governing equations were solved in the 

Reynolds-Averaged Navier-Stokes form with the realizable k-ε turbulence model to achieve closure.

Though modeled as incompressible with respect to pressure, the ideal-gas relation was used with nominal 

pressure to relate density to temperature, Equation (9). This relationship allowed for the creating of a 

density ratio of 2.0 as previously discussed. 

P0

RT ρ = (9)

Near the walls, Fluent’s enhanced wall treatment (two-layer model) was used for improved accuracy 

over standard wall-functions. Discretization was accomplished with a second-order upwind scheme for 

the convective terms and central differencing scheme for the diffusive terms. The SIMPLE segregated 

algorithm was used to deal with pressure/velocity coupling. For a given iteration, the three momentum 

(velocity) equations were solved sequentially, followed by a pressure-correction continuity equation. 

After the fluxes were updated based on these new solutions, scalar values such as temperature and 

turbulence quantities were updated. Convergence was dictated by three criteria: scaled residuals below 

10–6, iterative convergence of local surface temperature monitors, and global conservation errors for mass 

and energy more than three orders of magnitude below the overall mass and energy flows. The aggression 

of the solution convergence process was dictated by relaxation factors for each of the equations. These 

relaxation parameters were started low to avoid divergence, then increased as the solution began 

successfully converging toward lower scaled residuals. For detail on the above techniques, the reader is 

referred to the Fluent User's Guide.
NASA/TM—2011-217025 8 

Results and Discussion

Validation With Previous Studies: Grid Effects

Each of the four cases are first compared against their respective experimental results from

Sinha et al. (Ref. 1) or Thole et al. (Ref. 2). Case 1 was the low momentum ratio for the short holes in 

Reference 1. Figure 4 compares the experimental results of centerline effectiveness with the various 

numerical solutions from the current investigation. The results from the unstructured, adaptive grid of 

Walters and Leylek (Ref. 13) as well as the structured grid of Azzi and Lakehal (Ref. 14) are shown 

alongside the present results. In general the present results over-predict the centerline effectiveness, as 

would be expected based on previous knowledge of the turbulent anisotropy of the film cooling flow. 

Cases 'a', 'b', and 'c' produced effectiveness values identical to one another, indicating that the domain 

reductions had no effect on the surface conditions predicted by the solver. Grids 'd' and 'f', however, 

slightly deviate from the first three with slightly lower effectiveness near the hole but slightly higher 

effectiveness 5 to 15 diameters downstream. Other grid coarsening and refinement still failed to closely 

predict the experimental results, as one might expect given the assumptions of the turbulence models.

Figure 5 presents the span-wise averaged effectiveness trends with downstream distance for the same 

case. Numerical solutions here show under-prediction of the effectiveness, further reinforcing the underprediction of the lateral spreading as the cause for over prediction of centerline effectiveness.

The under-prediction of lateral spreading is clearly shown in Figure 6, where effectiveness is shown 

in the spanwise direction. Over-prediction of effectiveness at the centerline is balanced by underprediction of effectiveness at the mid-span. The overall effect, referring back to Figure 5, is a slight 

under-prediction of laterally-averaged effectiveness.

Figure 4.—Centerline effectiveness for Case 1: L/D = 1.75, I = 0.125.
NASA/TM—2011-217025 9 

Figure 5.—Laterally-averaged effectiveness for Case 1: L/D = 1.75, I = 0.125.

Figure 6.—Local effectiveness in the span-wise direction for Case 1: L/D = 1.75, I = 0.125.
NASA/TM—2011-217025 10

Case 2 results are compared in Figures 7 to 9 against the higher momentum ratio (I = 0.5) from

(Ref. 1). The experimental centerline results in Figure 7 suggest a lift-off and reattachment regime, 

yielding far lower effectiveness values near the hole. The 'a', 'b', and 'c' grids (again, agreeing with one 

another) fail to predict any sort of jet lift-off. The grid refinement in the near-hole region (grids 'd' and 'f') 

do capture the jet lift-off region. The lift-off is still captured, even with the coarsening of grid 'i' down to 

under 200,000 cells. The failure to predict the near hole lift-off (grids 'a', 'b', 'c') is detrimental to the rest 

of the prediction downstream. The correct prediction, however, does not need great resolution in the main 

body of flow, just in the region near the exit lip of the hole. There is still an overall over-prediction of 

centerline effectiveness for the refined numerical solutions, indicating the under-prediction of lateral 

spreading still applies at the higher momentum ratio. The original grids ('a', 'b', and 'c') show an underprediction of centerline effectiveness at most x/D. The trends suggest that the separation of the jet is 

delayed by a coarse grid in the region of the jet exit. This exaggerates the effect of the lift-off and fails to 

capture a noticeable reattachment. Therefore, the coarseness in the region of the hole exit throws off the 

rest of the solution downstream. 

Figure 7.—Centerline effectiveness for Case 2: L/D = 1.75, I = 0.5.

Figure 8.—Laterally averaged effectiveness for Case 2: L/D = 1.75, I = 0.5.
NASA/TM—2011-217025 11

Figure 9.—Local effectiveness in the span-wise direction for Case 2: L/D = 1.75, I = 0.5.

Case 2 laterally averaged results in Figure 8 again show an under-prediction compared to the 

experiments, reiterating the lack of lateral spreading. The trend of the effectiveness with x/D is matched 

much closer by the refined grids. The near hole resolution greatly effects the solution at all x/D. Again, the 

general coarsening in grid 'i' confirms that the extra refinement needed in near the hole can be balanced by a

coarser mainstream, yielding similar solutions with significant reduction in computational cells.

Figure 9 compares lateral spreading predictions from the current simulations with the experimental 

data from Sinha et al. Again, there is obvious lack of lateral spreading. The higher effectiveness at the 

centerline is balanced by lower effectiveness near the mid-span. As in the case with the lower momentum 

ratio, the net result is slight under-prediction of laterally-averaged results. In general, the current 

simulations are able to capture the trends of effectiveness values fairly accurately, though the quantitative 

values may not be correct.

Cases 3 and 4 correspond to the temperature field measurements of Thole et al. (Ref. 2). For Case 3 

validation, temperature profiles in the wall normal direction are compared at three different downstream 

distances in Figure 10. Near the hole, a slight over-prediction of jet trajectory seems to be apparent in the 

profiles. The refined grid at the hole exit captures the shape of the profiles much more closely than the 

original grids. 

Case 4, with higher momentum ratio, provides a better chance for comparison. Figure 11 shows the 

temperature profiles in the wall normal direction for the same x/D locations as above. It is clear from these 

profiles that the under-prediction seen in Case 2 effectiveness plots is due to a significant over-prediction of 

the jet trajectory. This is not a feature of the turbulence model, however, as the refinement in the near hole 

region corrects the disagreement and leads to much closer agreement in effectiveness and jet trajectory. 

Figure 12 presents the contours of temperature throughout the flow. Here, the trajectory differences are quite 

clear. Even the refined grid projects a slightly higher trajectory than the experimental results, but this could 

be attributable to the turbulence model. Still, as in all previous results, it is worth reiterating that, trajectory 

aside, the jet core temperature is over-predicted, perhaps as a consequence of the turbulent model 

assumption of isotropic eddy diffusivity or constant turbulent Prandtl number (Ref. 15).

 
NASA/TM—2011-217025 12

Figure 10.—Wall normal nondimensional temperature profiles for Case 3: L/D = 3.5, I = 0.125.

Figure 11.—Wall normal nondimensional temperature profiles for Case 4: L/D = 3.5, I = 0.5.
NASA/TM—2011-217025 13

Figure 12.—Center-plane non-dimensional temperature contours for Case 4: L/D = 3.5, I = 0.5.

Momentum Ratio Effects

For the remainder of the paper, grid 'd' results will be used to compare between cases, as this grid 

yielded the best results and most accurately reflects the behavior of the turbulence model. Figure 13 

compares centerline effectiveness results for Cases 1 and 2, corresponding to the shorter length holes with 

two different momentum ratios. It is obvious that the lift-off occurring in the higher momentum ratio 

yields a much lower effectiveness in the near hole region. Upon reattachment, however, the higher 

momentum jet approaches and overtakes the low momentum jet in effectiveness around x/D = 15 in the 

experiment and x/D = 23 in the numerical solution. In the far field, the higher momentum ratio yields 

slightly better effectiveness, despite near hole lift-off, as shown by both experimental and numerical 

evidence. The common theme is over-prediction of centerline results.

The corresponding laterally averaged results for Cases 1 and 2 are compared in Figure 14. Here, the 

low momentum jet gives rise to a monotonically decreasing effectiveness, as in the centerline. The higher 

momentum jet, however, appears to monotonically increase in effectiveness within the first 15 diameters.

It is clearly flattening out, however, and if the results were extended further, would be shown to decrease. 

Again, it appears as though, despite beginning much lower near the hole, the effectiveness of the high 

momentum jet is overtaking the low momentum jet somewhere downstream of 15 diameters.
NASA/TM—2011-217025 14

Figure 13.—Centerline effectiveness comparison for L/D = 1.75 at I = 0.125 versus 0.5.

Laterally Averaged Effectiveness

Figure 14.—Laterally averaged effectiveness comparison for L/D = 1.75 at I = 0.125 versus 0.5.
NASA/TM—2011-217025 15

Figure 15.—Wall normal nondimensional temperature profiles for L/D = 3.5 at I = 0.125 versus 0.5.

Cases 3 and 4, with longer holes corresponding to the experiments of Thole et al. (Ref. 2), present 

another chance to investigate the effects of momentum ratio. Wall normal temperature profiles are 

presented in Figure 15. At both momentum ratios, the numerical solution tends to slightly over-predict the 

jet trajectory. Despite the higher mass flux rate, the higher momentum jet does not show higher jet core 

dimensionless temperatures than the lower momentum jet, with the slight exception of the experimental 

results at the further downstream point. This is perhaps due to increased entrainment of hot crossflow 

fluid into the jet of higher momentum balancing out the higher mass flow rate of coolant. The higher 

momentum jet does eventually overcome this and overtake the low momentum jet further downstream, as 

shown in previous results. 

Length-to-Diameter Ratio Effects

Besides varying the momentum ratio, the scope of the current study also allows for a brief discussion 

of length-to-diameter ratio. Cases 1 and 2 correspond to the shorter hole lengths of Sinha et al.

(L/D = 1.75), whereas Cases 3 and 4 have longer hole lengths, those of Thole et al. (L/D = 3.5). Hole 

length effects can be compared at low momentum ratios between Cases 1 and 3 and high momentum 

ratios between Cases 2 and 4.

Shorter holes give the coolant flow less time to develop inside the tube before injection into the 

crossflow. Due to the inclination angle of the jet, the coolant flowing into the hole from the plenum 

separates from the trailing edge of the hole inlet, unable to complete the 145° turning angle. Figure 16 

shows this separation region for the higher momentum ratio case. This separation is not mirrored on the 

leading edge side of the coolant hole. This jetting effect produces higher velocities toward the leading 

edge and lower velocities in the trailing edge region, as shown in Figure 17. If the hole is long enough, 

the jetting effect attenuates and has little effect on the injection velocity profile. A shorter hole length will 

not provide the means for the jet to develop as such inside the hole. The hole exit profile, then, yields 

higher velocities at the leading edge. This can be seen as a higher effective inclination angle at the 

injection; the flow enters the hole from the plenum traveling roughly normal to the crossflow and the hole 

is not long enough to completely turn the coolant hole before injection. The higher effective inclination 

leads to lower effectiveness values, as discussed by (Refs. 11 and 12).
NASA/TM—2011-217025 16

Figure 16.—Velocity vectors, colored by velocity magnitude, showing flow 

separation at the trailing edge of the coolant hole inlet at I = 0.5.

Figure 17.—Velocity vectors, colored by velocity magnitude, showing the jetting effect of the 

coolant inside the short hole (L/D = 1.75) at I = 0.5.
NASA/TM—2011-217025 17

Figures 18 and 19 compare centerline and laterally-averaged effectiveness values downstream of the 

low momentum jets. The two hole lengths provide the same effectiveness curve. The effects of hole 

length is thus negligible at low momentum ratios from the viewpoint of these simulations. The coolant 

flow moves slowly enough that the hole quickly turns the coolant flow and there is not a significant 

difference between a hole of length 1.75 diameters and one twice as long. The flow at the exit of the 

1.75 diameter hole may not be fully developed in the strict sense, but it is developed enough such that 

adding additional length to the hole does not significantly change the downstream effectiveness of the jet. 

Figure 18.—Centerline effectiveness for I = 0.125 at L/D = 1.75 versus 3.5.

Figure 19.—Laterally Averaged effectiveness for I = 0.125 at L/D = 1.75 versus 3.5.
NASA/TM—2011-217025 18

For the same two cases, Figure 20 shows wall normal temperature profiles at the selected downstream 

locations. Again, the change in the length of the hole results in no distinguishable difference in the 

temperature profiles.

When the momentum of the jet is increased, however, length to diameter ratio plays a larger role. 

Figures 21 and 22 show the effectiveness curves for the higher momentum jet (I = 0.5). There is now a 

clear difference in the effectiveness of the jet. As suspected by the above analysis, the longer hole leads to 

higher effectiveness values. The matching of laterally-averaged effectiveness between Case 4 and the 

Sinha et al. results is mere coincidence. The two results are from two different holes lengths. The proper 

comparison with Sinha et al. is Case 2. The inclusion of Thole et al. results in these curves is achieved by 

taking the asymptotic values from the wall normal profiles and plotting the three points to get a rough feel 

for the effectiveness predicted by those experiments.

Figure 20.—Wall normal dimensionless temperature profiles for I = 0.125 at L/D = 1.75 versus 3.5.

Figure 21.—Centerline effectiveness trends for I = 0.5 at L/D = 1.75 versus 3.5.
NASA/TM—2011-217025 19

Figure 22.—Laterally averaged effectiveness trends for I = 0.5 at L/D = 1.75 versus 3.5.

Figure 23.—Wall normal dimensionless temperature profiles for I = 0.5 at L/D = 1.75 versus 3.5.

This situation is further confirmed in Figure 23, where the wall normal temperature profiles are 

compared. The proper comparison with experimental data is Case 4. The shorter hole results show a 

minimum temperature (maximum non-dimensional temperature) at higher wall normal distances than the 

longer hole results. This indicates a higher trajectory of the coolant jet, as expected.
NASA/TM—2011-217025 20

Conclusions

1. The domain of Walters and Leylek (Ref. 13), which is typical of RANS film cooling simulations, can 

be dramatically reduced in both the wall normal and upstream directions. The reduction in upstream 

crossflow length can be safely compensated for by the application of a 1/7 law boundary layer profile 

with appropriate thickness. The current case showed a 60 percent reduction in cell count with these 

considerations. 

2. The grid refinement in the area near the trailing edge of the hole exit is crucial to the prediction of 

high momentum coolant jets. The RANS equations (with k-ε turbulence model) have trouble 

predicting the nature of recirculation in the under-side of the detached jet without ample grid points 

clustered near the lip. This restriction does not lead to a dramatic increase in cell count if balanced by 

the view that a coarser grid can be used in the crossflow. In all, a grid count under 200,000 produced 

results indistinguishable from the finest grid used in this study.

3. The errant nature of the k-ε model’s isotropic assumption cannot be corrected by grid refinement. The 

universal under-prediction of lateral spreading, manifested in over-prediction of centerline 

effectiveness and wall normal contours in conjunction with under-prediction of laterally-averaged 

effectiveness, is an artifact of the turbulence model and not of discretization error.

4. Experimental trends with respect to momentum ratio and length-to-diameter ratio can be matched 

well with the RANS results. Higher momentum jets and shorter holes diminish the film cooling 

effectiveness by increasing the trajectory of the jet above the cooled surface.

5. The results of this study serve as further motivation for the use of LES in attempting to more 

accurately resolve the behavior of the film cooling jet. The observations of this study serve as a guide 

to the development of an LES film cooling approach for obtaining time-accurate solutions while 

resolving the larger scales of turbulence.

References

1. Sinha, A.K., Bogard, D.G., and Crawford, M.E., 1991, “Film Cooling Effectiveness Downstream of a 

Single Row of Holes With Variable Density Ratio,” ASME Journal of Turbomachinery, 113, 

pp. 442–449. 

2. Thole, K., Sinha, A., Bogard, D.G., and Crawford, M.E., 1992, “Mean Temperature Measurements of 

Jets With a Crossflow for Gas Turbine Film Cooling Application,” Rotating Machinery Transport 

Phenomena, J.H. Kim and W.J. Yang, eds., Hemisphere Pub. Corp., New York. 

3. Goldstein, R.J., Eckert, E.R.G., and Ramsey, J.W., 1968, “Film Cooling with Injection Through 

Holes: Adiabatic Wall Temperatures Downstream of a Circular Hole,” ASME Journal of Engineering 

for Power, 90, pp. 384–395. 

4. Goldstein, R.J., Eckert, E.R.G., Eriksen, V.L., and Ramsey, J.W., 1970, “Film Cooling Following 

Injection Through Inclined Circular Tubes,” Israel Journal of Technology, 8, pp. 145–154. 

5. Eriksen, V.L., and Goldstein, R.J., 1974, “Heat Transfer and Film Cooling Following Injection 

Through Inclined Circular Tubes,” ASME Journal of Heat Transfer, 96, pp. 239–245. 

6. Goldstein, R.J., Eckert, E.R.G., and Burggraf, F., 1974, “Effects of Hole Geometry and Density on 

Three-Dimensional Film Cooling,” International Journal of Heat and Mass Transfer, 17, pp. 595–607. 

7. Pedersen, D.R., Eckert, E.R.G., and Goldstein, R.J., 1977, “Film Cooling with Large Density 

Differences Between the Mainstream and the Secondary Fluid Measured by the Heat-Mass Transfer 

Analogy,” ASME Journal of Heat Transfer, 99, pp. 620–627. 

8. Foster, N.W., and Lampard, D., 1980, “The Flow and Film Cooling Effectiveness Following Injection 

Through a Row of Holes,” ASME Journal of Engineering and Power, 102, pp. 584–588. 

9. Pietrzyk, J.R., Bogard, D.G., and Crawford, M.E., 1989, “Hydrodynamic Measurements of Jets in 

Crossflow for Gas Turbine Film Cooling Applications,” ASME Journal of Turbomachinery, 111, 

pp. 139–145. 
NASA/TM—2011-217025 21

10. Pietrzyk, J.R., Bogard, D.G., and Crawford, M.E., 1990, “Effects of Density Ratio on the 

Hydrodynamics of Film Cooling,” ASME Journal of Turbomachinery, 112, pp. 57–62. 

11. Burd, S.W., Kaszeta, R.W., and Simon, T.W., 1996, “Measurements in Film Cooling Flows: Hole 

L/D and Turbulence Intensity Effects,” ASME Journal of Turbomachinery, 120,

pp. 791–798. 

12. Lutum, E. and Johnson, B.V., 1999, “Influence of Hole Length to Diameter Ratio on Film Cooling 

With Cylindrical Holes,” ASME Journal of Turbomachinery, 121, pp. 233–242. 

13. Walters, D.K., and Leylek, J.H., 2000, “A Detailed Analysis of Film-Cooling Physics: Part I – 

Streamwise Injection With Cylindrical Holes,” ASME Journal of Turbomachinery, 122, pp. 102–112. 

14. Azzi, A., and Lakehal, D., 2002, “Perspectives in Modeling Film Cooling of Turbine Blades by 

Transcending Conventional Two-Equation Turbulence Models,” ASME Journal of Turbomachinery, 

124, pp. 472–484. 

15. Lakehal, D., 2002, “Near-Wall Modeling of Turbulent Convective Heat Transport in Film Cooling of 

Turbine Blades With the Aid of Direct Numerical Simulation Data,” ASME Journal of 

Turbomachinery, 124, pp. 485–498. 

16. Acharya, S., Tyagi, M., and Hoda, A., 2001, “Flow and Heat Transfer Predictions for Film Cooling,” 

Heat transfer in gas turbine systems, Ann. N.Y. Acad. Sci., 934, pp. 110–125. 

17. Tyagi, M., and Acharya, S., 2003, “Large Eddy Simulation of Film Cooling Flow From an Inclined 

Cylindrical Jet,” J. Fluid Mech, 125, pp. 734–742. 

18. Peet, Y.V., and Lele, S.K., 2008, “Near Field of Film Cooling Jet Issued Into a Flat Plate Boundary 

Layer: LES Study,” GT2008-50420, Proceedings of ASME Turbo Expo 2008, Berlin, Germany. 

19. Leedom, D.H., and Acharya, S., 2008, “Large Eddy Simulations of Film Cooling Flow Fields From 

Cylindrical and Shaped Holes,” Proceedings of ASME Turbo Expo 2008, Berlin, Germany, GT2008-

51009. 

20. Renze, P., Schroder, W., Meinke, M., 2008, “Large-Eddy Simulation of Film Cooling Flows at 

Density Gradients,” International Journal of Heat and Fluid Flow, 29, pp. 18–34. 

21. Renze, P., Schroder, W., and Meinke, M., 2008, “Large-Eddy Simulation of Film Cooling Flow 

Ejected in a Shallow Cavity,” Proceedings of the ASME Turbo Expo 2008, Berlin, Germany, 

GT2008-50120. 

22. Rozati, A., and Tafti, D.K., 2008, “Large Eddy Simulations of Leading Edge Film Cooling: Analysis 

of Flow Structures, Effectiveness, and Heat Transfer Coefficient,” International Journal of Heat and 

Fluid Flow, 29, pp. 1–17. 

23. Gambit, 2008, “Gambit Version 2.3.16,” USA, ANSYS Inc. 

24. Fluent, 2008, “Fluent Version 6.3.26,” USA, ANSYS Inc. 
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Reynolds-Averaged Navier-Stokes Solutions to Flat Plate Film Cooling Scenarios 

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14. ABSTRACT

The predictions of several Reynolds-Averaged Navier-Stokes solutions for a baseline film cooling geometry are analyzed and compared 

with experimental data. The Fluent finite volume code was used to perform the computations with the realizable k-ε turbulence model. The 

film hole was angled at 35° to the crossflow with a Reynolds number of 17,400. Multiple length-to-diameter ratios (1.75 and 3.5) as well as 

momentum flux ratios (0.125 and 0.5) were simulated with various domains, boundary conditions, and grid refinements. The coolant to 

mainstream density ratio was maintained at 2.0 for all scenarios. Computational domain and boundary condition variations show the ability 

to reduce the computational cost as compared to previous studies. A number of grid refinement and coarsening variations are compared for 

further insights into the reduction of computational cost. Liberal refinement in the near hole region is valuable, especially for higher 

momentum jets that tend to lift-off and create a recirculating flow. A lack of proper refinement in the near hole region can severely diminish 

the accuracy of the solution, even in the far region. The effects of momentum ratio and hole length-to-diameter ratio are also discussed.

15. SUBJECT TERMS

Film cooling; Turbulence model; Heat transfer 

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