Ali Ameri

The Ohio State University, Columbus, Ohio

Vikram Shyam

Glenn Research Center, Cleveland, Ohio

David Rigby

Vantage Partners, LLC, Brook Park, Ohio 

Phillip Poinsatte

Glenn Research Center, Cleveland, Ohio

Douglas Thurman 

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Erlendur Steinthorsson

A & E Consulting, Inc., Pepper Pike, Ohio 

Development of the Glenn Heat-Transfer (Glenn-HT) 

Computer Code to Enable Time-Filtered Navier-Stokes 

(TFNS) Simulations and Application to Film Cooling 

on a Flat Plate Through Long Cooling Tubes

NASA/TM—2014-218098

April 2014
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Ali Ameri

The Ohio State University, Columbus, Ohio

Vikram Shyam

Glenn Research Center, Cleveland, Ohio

David Rigby

Vantage Partners, LLC, Brook Park, Ohio 

Phillip Poinsatte

Glenn Research Center, Cleveland, Ohio

Douglas Thurman 

U.S. Army Research Laboratory, Glenn Research Center, Cleveland, Ohio

Erlendur Steinthorsson

A & E Consulting, Inc., Pepper Pike, Ohio 

Development of the Glenn Heat-Transfer (Glenn-HT) 

Computer Code to Enable Time-Filtered Navier-Stokes 

(TFNS) Simulations and Application to Film Cooling 

on a Flat Plate Through Long Cooling Tubes

NASA/TM—2014-218098

April 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors would like to acknowledge the support of the NASA Fundamental Aeronautics Program’s Fixed Wing project, 

under whose funding this work was performed.

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Space Administration.

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—2014-218098 1

Development of the Glenn-Heat-Transfer (Glenn-HT) Computer 

Code to Enable Time-Filtered Navier Stokes (TFNS) Simulations

and Application to Film Cooling on a Flat Plate 

Through Long Cooling Tubes

Ali Ameri

The Ohio State University

Columbus, Ohio 43210

Vikram Shyam

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

David Rigby

Vantage Partners, LLC

Brook Park, Ohio 44142

Phillip Poinsatte

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Douglas Thurman

U.S. Army Research Laboratory

Glenn Research Center

Cleveland, Ohio 44135

Erlendur Steinthorsson

A & E Consulting, Inc.

Pepper Pike, Ohio 44124

Abstract

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) 

formulation for turbomachinery-related flows has enabled improved engine component designs. RANS

methodology has limitations that are related to its inability to accurately describe the spectrum of flow 

phenomena encountered in engines. Examples of flows that are difficult to compute accurately with 

RANS include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of 

streams, and separated flows. Large eddy simulation (LES) can improve accuracy but at a considerably 

higher cost. In recent years, hybrid schemes that take advantage of both unsteady RANS and LES have 

been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS) 

method applied to compressible flows. The method developed by Shih and Liu was implemented in the 

Glenn-Heat-Transfer (Glenn-HT) code and applied to film-cooling flows. In this report the method and its 

implementation is briefly described. The film effectiveness results obtained for film cooling from a row of 

30° holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and two blowing 

ratios of 0.5 and 1.0 are shown. Flow features under those conditions are also described. 
NASA/TM—2014-218098 2

1.0 Introduction

High operating pressure ratios as well as increased turbine inlet total temperatures are expected to be 

the hallmarks of NASA’s N+3 engines. Cooling of blades with film cooling is an effective means of 

insulating blades from hot combustion gases and is thus expected to continue to be an important method

for cooling unless materials are developed that can tolerate much higher temperatures. Currently, the 

cooling air used for high-pressure turbine cooling comprises approximately 15 percent of the mass flow 

through the core. This use of cooling air is a loss to the efficiency of the engine and needs to be 

minimized.

For film-cooling flows in the higher blowing ratio M range (M > 1.0) Reynolds-averaged NavierStokes (RANS) analysis does not produce accurate solutions (Ref. 1). Argument is made that RANS 

models are not adequate for film-cooling flows as the unsteady interactions and mixing of the main

stream and cooling stream play an important role that are not accounted for by such models. In recent 

years attempts have been made to model film-cooling flows using large eddy simulation (LES) and 

detached eddy simulation (DES). Some of these attempts have resulted in computations of cooling 

effectiveness but others have used LES to shed light on the physics of film cooling. Guo et al. (Ref. 2)

used LES to study the effect of low blowing ratios (0.1 and 0.48) for respective 90° and 30° inclined 

angles. Their purpose was to investigate the turbulent flow structure and the vortex dynamics for gas 

turbine blade film cooling. Their work concluded that turbulent flow downstream of the cooling holes is 

highly anisotropic and also that LES is well suited for such simulations. Tyagi and Acharya (Ref. 3)

studied film-cooling physics for a blowing ratio of 0.5 and a short tube with a 1.75 length-to-diameter 

ratio. They showed good agreement with experimental measurements for velocity distributions

downstream of the hole and described the physical features of the flow resulting from the film-cooling

flow. More recently, Fujimoto (Ref. 4) used surface-adjusted octree hexahedral meshes to perform LES 

computations of film-cooling effectiveness. Fujimoto compared his results and the results of a multiblock 

LES computation with the experimental data of Sinha et al. (Ref. 5) and reported good agreement with the 

experimental data for a range of blowing ratios.

Computations have been performed on turbine blades to determine both the heat transfer coefficient 

and the film effectiveness for film cooling using DES, which uses a combined RANS and LES for the 

blade surface downstream of an internally ribbed slot. One example is the work of Martini et al. (Ref. 6)

which ascribes great advantage to using DES over modeling using RANS methods.

In their earlier LES work for film-cooling flows, Peet and Lele (Ref. 7) used a combination of 

computational fluid dynamics (CFD) codes—an incompressible method for the plenum and the pipe, and 

a compressible method for the cross stream and the interaction zone. They computed turbulence statistics 

and effectiveness of the film cooling for a low-blowing-ratio (M = 0.5) case. One of the issues often 

confronted when computing film-cooling flows concerns the effect of the plenum. Plenum modeling and 

related assumptions are sources of uncertainty. The plenum is often included in the numerical model but 

the incompressible flow within the plenum reduces the convergence rate of the numerical schemes. This 

limitation has little to do with engine conditions and is encountered as experimental setups use plena for 

film cooling. To model the flow realistically the plena have to be included in the computations.

To eliminate the uncertainty associated with using plena, a new film-cooling experiment has been 

designed, which uses very long film-cooling pipes with length-to-diameter ratios greater than 20 (Ref. 8). 

This leads to fully developed flow in the pipe and thus requires no further characterization of the pipe 

flow. In addition, other confounding conditions such as the effect of the plenum exit and pipe length do 

not enter the experiment or affect computational results.

The work reported herein utilized the experimental conditions described in (Ref. 8) and conducted a 

numerical study employing a time-filtered Navier-Stokes (TFNS) method. The resulting film-cooling 

effectiveness distributions were compared to the data reported in Reference 8. The filtering of equations is

performed on timescales rather than length scales of turbulence using an algebraic Reynolds stress model 

as the subfilter model. The underlying model is described by Liu and Shih (Ref. 9) and is further 

elucidated in References 10 to 12. The subfilter model in the present work does not use wall functions in 
NASA/TM—2014-218098 3

contrast to what was done with TFNS (or earlier versions of the model). Instead it uses a model version 

that is integrated all the way to the wall (Ref. 13). This was necessary since the previous uses of TFNS 

were for combustion computations, so near-wall flows and heat transfer were not emphasized.

1.1 Description of Work

Flow over a flat plate and temperature distribution downstream of film-cooling holes at a 30°

inclination and two blowing ratios of 0.5 and 1.0 for a single nominal density ratio DR of unity were 

simulated. The range of momentum ratios is thus the same as the blowing ratios. Earlier computations 

(Ref. 1) performed at a blowing ratio of M = 2 showed the inadequacy of the k-ω turbulence model 

(Ref. 14) at high blowing ratios. In this study, several turbulence models within the Glenn-Heat-Transfer 

(Glenn-HT) code (Ref. 15) were used for an intermediate blowing ratio of unity. A commercial code CFX 

and the models within it (shear stress transport (SST) and k-ε) were also applied and verified that results 

are highly dependent on the choice of turbulence model, which is not acceptable.

Elements of the work performed to enable simulation of film cooling using TFNS are as follows:

(1) Programming and testing of required routines to simulate unsteady flows, including routines to 

allow long-term averaging of flow quantities, Reynolds stresses, and relevant unsteady boundary 

conditions.

(2) Programming the low Reynolds number k-ε and algebraic Reynolds stress model (ARSM) and

verifying that they both worked for turbulent flow heat transfer on a plate.

(3) Programming and testing of the SST model.

(4) Programming and testing of individual numerical probes, rakes, or a plane of rakes to allow 

tracking of the flow variables. 

(5) Implementing the TFNS elements (based on the low-Reynolds-number ARSM into the GlennHT code).

(6) Modeling of the long-piped film-cooling-hole geometry.

(7) Researching and implementing methods to allow efficient domain dicing and subsequent 

multiprocess simulations.

(8) Simulating film-cooling flow using RANS and unsteady Reynolds-averaged Navier-Stokes 

(URANS).

(9) Simulating film-cooling effectiveness using TFNS.

The numerical work was tied to an experimental campaign to measure the flow field and surface film 

effectiveness resulting from film cooling. Computations attempted to simulate and predict those 

experiments. The experimental campaign results are presented by Shyam et al. in Reference 8. In this 

report, the numerical work performed to achieve better agreement with the experimental data presented 

by Shyam et al. is described and evaluated in detail. The improved ability to simulate film-cooling flows 

is demonstrated and the need for additional refinements is discussed.

1.2 Experiment Setup and Conditions

A 30× engine scale test facility was used to interrogate the highly complex three-dimensional flow 

field associated with detached flows to resolve the shear layer and wake regions. A schematic of the test 

flow and geometry are shown in Figure 1. Experiments were carried out in an open-loop tunnel with a 

temperature-controlled coolant loop. The tunnel consisted of an aluminum bellmouth, flow-conditioning 

screens, 8.2-in.- (20.82-cm-) wide by 0.75 in.- (1.91-cm-) thick square acrylic sections, the test section on 

the tunnel floor, and a lid directly above for either viewing or actuator support. Air was drawn from the 

room and passed through flow-conditioning sections prior to the test section entry.
NASA/TM—2014-218098 4

Figure 1.—Schematic of the tunnel setup and the cooling airflow with the long pipes (from Ref. 8).

Airflow was provided by a 7-hp (5220-W) fan. The free-stream velocity was 29.86 ft/s (9.1 m/s) and 

the Reynolds number was 11 000, based on free-stream velocity and coolant hole diameter (d). The test 

section is a square section of cross section measuring 8.00 by 8.00 in. (20.32 by 20.32 cm) by 34.00 in.

(86.36 cm) in length (L). The free-stream turbulence intensity (Tu) at the inlet of the test section measured 

approximately 1.5 percent without a grid and 4 percent with a square grid (not used in the simulations). 

The boundary layer thickness was 1.27 cm at x/d = –0.5, and was taken to be the vertical distance from 

the wall at which the velocity is equal to 99 percent of the free-stream velocity.

Pressurized supply air provided coolant flow through a heat exchanger that consisted of a copper tube 

coiled inside in an ice water tank. The coolant was fed through a manifold to three separate flow meters 

then to acrylic tubes with L/d = 20 connected to each cooling hole. The separate cooling tubes provided 

an opportunity to model the cooling flow in each hole as fully developed.

The test section consisted of a flat acrylic plate with three 0.75-in.- (1.9-cm-) diameter holes inclined 

at 30°. The holes were spaced at three times the hole diameter. 

To determine the tunnel flow rate, a total pressure probe was placed upstream of the test section and 

static pressure taps were placed on the sidewalls. Free-stream temperature was measured with an openball thermocouple located upstream of the holes near the total pressure probe. Coolant temperature was 

measured with open-ball thermocouples inside the coolant tubes. Temperature survey data was taken 
NASA/TM—2014-218098 5

along the centerline plane of the tunnel and at several cross sectional planes with a small open ball type E 

thermocouple probe attached to an actuator above the test section. The adiabatic wall temperature was 

determined from the thermocouple probe surveys with the probe located near the floor of the test section. 

Various hotwire probes were used to obtain the three-dimensional velocity components and turbulent 

stresses along the centerline and at several streamwise planes.

Infrared (IR) thermography was used to obtain the adiabatic film-cooling effectiveness. Further 

details and extensive data may be found in Shyam et al. (Ref. 8).

1.3 Time-Filtered Navier-Stokes Analysis

The unsteady approach called time-filtered Navier-Stokes (TFNS), also referred to as “partially 

resolved Navier-Stokes (PRNS) or very large eddy simulations” (Refs. 9 to 13), was used for this work. 

The method was developed for the simulation of large turbulent eddies and requires only relatively coarse 

grid resolution as is often used in RANS simulations. The method is based on the concept of temporal 

filtering of Navier-Stokes equations. This purportedly avoids grid dependence issues associated with LES 

such as the direct connection between the filter size and the grid resolution. In TFNS the larger timescales 

(or lower frequencies) of the turbulence are directly calculated and the effects of the unresolved 

turbulence timescales are modeled by a dynamic equation system. Contents of both resolved and 

unresolved turbulence are regulated by a filtering control parameter (FCP), which is related to the width 

of the temporal filter. The method as utilized in this work solves the flow all the way to the wall and 

avoids the use of wall functions.

The basic TFNS equations and its subfilter model presented by Liu and Shih (Ref. 9) are grid 

invariant, that is, they do not have grid spacing as a parameter in their formulations. It is therefore 

possible to achieve a grid-independent numerical solution for a fixed FCP. Another distinction is that 

TFNS enables performance of URANS, very large eddy simulations (VLES), LES, and even Direct 

Numerical Simulations (DNS) in a unified way through the judicious selection of the value of FCP, and

the appropriately refined grid. It should be noted that the TFNS approach is not a variant of the hybrid 

RANS/LES (Refs. 16 to 19). There is no enforced transition between the perceived RANS and LES 

domains.

The subfilter model was constructed to use a more general relationship between the unresolved 

turbulent stresses and the resolved turbulent flow field. Shih and Liu (Ref. 11) used rational mechanics 

analysis and obtained a general constitutive relationship for the Reynolds stresses. In addition to the 

dissipative and diffusive effects accounted for through the eddy viscosity, the subfilter model accounts for 

the effects of anisotropy and rotation. Source terms introduced in the momentum equation sustain the 

turbulent fluctuations in the calculated flow field. One important outcome using this constitutive 

relationship described by Shih and Liu (Ref. 20) is the ability of TFNS to sustain turbulent fluctuations

for a turbulent pipe flow in the lower range of applicable Reynolds numbers while the k-ε variant was not 

able to sustain a turbulent flow contrary to the observed physical behavior. The model adopted for TFNS 

simulations in the Glenn-HT code employs this unique feature of the nonlinear subfilter model.

A detailed description of the TFNS equations and the subfilter model developed by Shih and Liu

(Ref. 11) follows in the next section.

1.3.1 Formulation

The formulation follows steps described in Reference 9. The additional formulation needed to 

implement the model without the use of wall functions is summarized from the literature and will be

provided below. 

Using a homogeneous temporal filter G(t – tʹ), the large timescale turbulence variable φ and its 

density-weighted variable φ

 can be defined as
NASA/TM—2014-218098 6

(t x t x G t t dt ,, , i i ) ( ) ( ) ρφ φ = φ − φ= ′ ′′ ρ ∫  (1)

where the integral is over the entire time domain and G satisfies the normalization condition

G t t dt ( − = ′ ′ ) 1 ∫ .

There are several such temporal filters available, the simplest one is the top hat filter:

( ) 1 , if 2

0 , otherwise

T T t t

Gt t  ∆ − ≤∆ ′ − = ′ 



(2)

where ΔT is the width of the top hat filter. Using this filter, the left part of Equation (1) becomes

( ) ( )

/2

/2

1 , ,

T

T

t

i i

T t

t x t x dt

+∆

−∆

φ= φ ′ ′ ∆ ∫ (3)

Equation (3) suggests that φ and φ

 become the exact Reynolds-averaged quantity and Favre-averaged 

quantity, respectively when ΔT → ∞. On the contrary, they will become the instantaneous turbulent 

quantity as ΔT → 0. For a finite ΔT, they represent the quantities of large timescale turbulence.

Performing the filtering operation defined by Equation (1) on the Navier-Stokes equations, a set of 

exact, basic equations for the resolved, large timescale turbulence ( φ and φ

 ) are obtained:

( ) ( ) , , , , ,

2 2

3 i i j i ij j ij ij kk t j j

u uu p s s

  ρ + ρ =− −τ + μ − δ μ         (4)

( ) ( ), ( , , )   , ,

2 2

3 i i kk i i ij ij kk ii i t i e u e T ps q s s s s Q   ρ +ρ =κ + − + μ − μ +    

    (5)

, ( ), 0, t i i ρ + ρ = =ρ u p RT  (6)

( )  τ ≡ρ − ≡ρ − ij i j i j i i i u u uu q ue ue , ( )     (7)

where sij = (uij + uji)/2. The operators (...),t and (...),i represent the temporal and spatial derivatives, 

respectively. The density, velocity, temperature, pressure, internal energy per unit mass, and the heating

rate are represented by ρ, ui, T, p, e, and Ԛ, respectively. The viscosity and kinematic viscosity are given 

by μ and ν, κ is the heat conductivity of the fluid, and R is the universal gas constant. The extra terms

created by the process of time-filtering nonlinear Navier-Stokes equations, τij and qi represent the effects 

of unresolved, small time-scale turbulence—the unresolved turbulent stresses and heat fluxes. The 

following was proposed to model the unresolved turbulent stresses τij:

( ) ( )

( )

3

1 3 3 2

4

2 2

5 5 3

1 2 3

3

2 3

ij T ij ij kk ij kk ik kj ik kj

ik kj ik kj ik km mj kl lm mk ij s ij ij kk

k f s s Af s s

k A f s s s s II s s

τ =− μ −δ + δ τ − ρ ω −ω

ε

+ ρ ω − ω +ω ω −ω ω δ + −δ     ε

     

         

(8)
NASA/TM—2014-218098 7

where k and ε are the turbulence kinetic energy and dissipation rate defined in Equations (17) and (18)

( ) ( ) ( ) , , , , 2 , 2 , 2 . ij i j j i ij i j j i s kk mm kl lk s u u    = + ω= − = −  u u II s s s s      The model coefficients Cμ, A3, and A5

are constrained by the realizability condition and the rapid distortion theory limit. They are not arbitrary 

but formulated in Reference 21:

2

22 *

3 5 2 4 ** * * * * *

2 3

1.0

1 1.6 , , 7 4.0 0.5 1.5

4

s

t

s

k AC S

CA A k k k SS A U S

μ

μ

  −     ε μ = = = +Ω Ω + +Ω ρ ε ε ε

(9)

in which

( ) ** *

* *

* 3

1 6 cos , arccos 6 , 3 ( )

ij jk ki

s

SS S

A W W

S = φ φ= = (10)

( ) ( ) 2 2 * * * * ** * * 1 ,, , 3

U S ij ij ij ij ij ij ij kk = + Ω = Ω = ωω = − δ S SS S s s   (11)

Also,

( )

T

k k C f μ μ

+ νε

μ =ρ

ε

(12)

The coefficients f1, f3, and f5 are functions of ΔT/T, that is, the ratio of the temporal filter width to the 

global timescale of the turbulent flow of interest, where the global timescale T can be considered as the 

maximum integral timescale in the entire domain. These functions must have the following property: 

0 if 0

1 if 1 

T

T

i

T

T f T

T

 ∆

 →   ∆    =    ∆  → 

(13)

This lets the unresolved turbulent stresses τij vanish when the filter width ΔT vanishes, and τij approaches

the Reynolds-averaged stresses as ΔT increases towards the global timescale T. 

All fi have the same form in the TFNS model as

2

2 1, 3, 5 T TT

i f i T TT

     ∆ ∆∆ ≈− =           (14)

The ratio ΔT/T is used to set the FCP. For example, FCP = 0.30, using ΔT/T = 0.16 is intending to 

directly resolve those turbulence scales that are responsible for about 70 percent of the total turbulent 

kinetic energy and model the rest of the unresolved turbulence scales that contain about 30 percent of the 

total turbulent kinetic energy. An FCP of 0.3 was used in these computations.

1.3.1.1 Modeling of Unresolved Turbulent Heat Fluxes 

A common practice in modeling unresolved turbulent heat fluxes q ue ue i ii ≡ρ − (   ) is to employ the 

following isotropic model:
NASA/TM—2014-218098 8

i Ti , q e = −κ  (15)

The simplest form that considers the effects of strain and rotation should be

i T i T ij ij j , 1 2, ( ) k

q e cs c e = −κ − κ + ω

ε    (16)

The expanded relationship resulted in unstable numerics and thus only one term was retained. 

1.3.1.2 Transport Equations for Subscale k-ε

To complete the proposed model for τij, k, and ε, the unresolved turbulent kinetic energy and its 

dissipation rate is needed. The exact transport equations can be derived from Navier-Stokes equations, 

and contain several higher order of unclosed terms due to the temporal filtering operation. The first step in 

the derivation procedure is to establish the transport equation for τij, followed by a tracing operation to 

establish the equation for τii (which is ρk ), and this leads to the transport equation for k.

In the current implementation a low Reynolds number version of the equations is used to allow direct 

solution in the near-wall regions without the use of wall functions. The damping functions used are from 

References 21 and 22. The equations and the damping functions are as follows:

( ) i T ij ij

ii i

k k uk s

tx x x

∂∂ ∂ ∂  

ρ + ρ = μ+μ − τ −ρε   ∂∂ ∂ ∂  

  (17)

A model transport equation for the dissipation rate ε was constructed by the analogy to Equation (17) as

( )

2

22 3

1 1 , , Ti T ij ij j j

ii i

Cf C u C f s s s

tx x x k k

εε ε ε ε

∂ ∂ ∂ ∂ε   ε ρ ε μμ ρε+ ρ ε= μ+μ − τ − +   ∂∂ ∂ ∂   + υε ρ     (18)

where Cε1 = 1.45, Cε2 = 1.92, and Cε3 = 1.0; while keeping in mind that they can be further constructed as 

functions of the local subscale turbulence quantities (Ref. 14):

5

1

1 exp i

i

i

fμ a R

=

    = −       ∑ (19)

5

1

1

1 exp i

i

i

fε a R

=

    =− −  ′

    ∑ (20)

( ) 2

2 1 0.22exp 36 t f R ε =− − (21)

also

3/2 k k( ) R + υε = υε

(22)

and 

2

t

k R ρ = με

(23)

The coefficients are given in Table I.
NASA/TM—2014-218098 9

TABLE I.—COEFFICIENTS FOR EQUATIONS (19) AND (20)

1 2 3 4 5

ai 3.3×103 –6.0×10–5 6.6×10–7 –3.6×10–9 8.4×10–12

i a′ 2.53×10–3 –5.7×10–5 6.55×10–7 –3.6×10–9 8.3×10–12

Low-Reynolds-number terms that do not use wall distance were deemed more appropriate for the 

class of flows of interest in this work, which involve separated boundary layers. Note the wall distance 

does not appear in the model terms.

2.0 Film-Cooling Flow Computations

The numerical scheme and the turbulence model were implemented in the Glenn-HT code (Ref. 15), a 

multiblock-structured grid N–S solver. The computer code uses a four-stage multistage Runge-Kutta 

scheme with fourth-order artificial dissipation with eigenvalue scaling. The added model, in its steady 

form, was applied to flow over a flat plate and the resulting wall friction and heat transfer from an 

adiabatic wall and a heated wall, respectively, were computed and found to be in good agreement with 

correlations.

Subsequent film-cooling flow computation simulations were conducted in accordance with

experimental conditions. Geometric scaling was performed to raise the flow Mach number and to

maintain the Reynolds number based on the film-cooling hole. The density ratio of the flow was held to 

near unity by adjusting the total temperature at the hole inlet. Even though blowing ratios of 0.5, 1.0, 1.5,

and 2.0 were computed, only ratios of 0.5 and 1.0 are discussed in this report. The computational domain 

extended 12 diameters upstream and 16 diameters downstream of the cooling hole. Spacing between the 

holes was equal to three hole diameters in the experiment. For the computations, a period of 3 diameters 

was similarly imposed. However, it was understood that due to flow unsteadiness, imposition of 

periodicity is a simplification that is done to reduce computation resource requirements. The free-stream 

boundary condition was placed at five diameters from the wall where an exit boundary condition was 

specified. An exit boundary condition was also specified at the outlet on the domain.

The Tu (1.5 percent as measured) and a turbulence length scale were specified at the inlet. No 

particular handling of the inlet boundary condition to include unsteadiness for our TFNS computations 

was performed. Also, the grid upstream of the hole region was not as well refined as in the vicinity of the 

hole. This causes the incoming flow to be steady. Cases where the grid is refined in the inlet region and

inclusion of unsteady boundary condition should be considered as a follow-on to this work. This will 

involve modifications to the inlet boundary condition briefly mentioned in this report.

A number of grid blocks were assigned to individual CPUs in a way that allowed balanced parallel 

computing. To reduce communications overhead, smaller blocks were further consolidated before 

implementing grouping. Initially, 120 groups (CPUs) were used by refining blocking. It was possible to 

increase that number to 1200 for improved parallel capability. The grid itself contained approximately 

8 million cells. Particular attention was paid to grid refinement in areas near the no-slip walls and the 

cooling hole outlet and downstream of the cooling hole with wall shear-stress-scaled grid spacing of 

Δx+ < 300, Δy+ < 3, Δz+ < 200. Grid cells in the film-cooling flow core were constructed to be uniform 

and nearly cubic in shape. Figure 2 shows the grid topology. Figure 2(a) shows the computational domain 

with multiple blocks; Figure 2(b), the grid along the symmetry plane; and Figure 2(c) and Figure 2(d),

closeup views of the grid near the cooling hole.
NASA/TM—2014-218098 10

Figure 2.—Grid topology. (a) Computational domain with multiple blocks. (b) Grid along symmetry plane. (c) Closeup 

view of grid along symmetry plane near hole exit. (d) Top view of surface grid in hole.

2.1 RANS and URANS Analysis

As previously mentioned, film-cooling effectiveness prediction accuracy suffers greatly when RANS 

is used and the blowing ratio is relatively high (>~1). RANS and URANS computations were performed 

to assess their performance in predicting the film-cooling effectiveness before TFNS computations were 

performed. Figure 3 shows the experimental measurements of the laterally averaged effectiveness of film 

cooling downstream of the hole and predictions using a variety of models available in Glenn-HT code and

the commercial code. Computations were performed for a blowing ratio M = 1 and density ratio DR = 1. 

The effectiveness data were obtained using thermocouples and documented in Reference 8. Results were 

obtained on a once-coarsened version of the grid shown in Figure 2 using both RANS and URANS

versions of the model described earlier. In addition, the low-Reynolds-number SST model developed by 

Langtry and Sjolander (Ref. 23) was used and implemented in the code for this work. For the runs with 

CFX commercial code, two turbulence models, namely, Menter’s SST and the standard k-ε model were 

utilized (Ref. 24).
NASA/TM—2014-218098 11

Figure 3.—Measured and computed laterally averaged effectiveness downstream of 

film-cooling holes.

Effectiveness is defined as one of the following:

η = (T∞ – Taw)/(T∞ – Tc) (24)

or

η1 = (Tr – Taw)/(Tr – Tc) (25)

The results above are for η and show a large variance and dependence on the chosen turbulence models. 

T∞ refers to the inlet total temperature, Taw is the adiabatic wall temperature, Tc is the coolant temperature,

and Tr is the recovery temperature (adiabatic wall temperature) between the holes in a region not affected 

by film cooling as was the case in the experimental measurements. 

2.2 TFNS Solutions

Two sets of computations using the TFNS method—a density ratio of unity (DR = 1) and the blowing 

ratios of 0.5 and 1.0—are presented in the following sections. As mentioned previously, the FCP for the 

TFNS was set to 0.3. The dimensionless time step was set to 0.005 and the CFL to 3.0 with residual 

smoothing turned on. Other important parameters for computations are the second- and fourth-order 

artificial dissipation terms coefficients used along with the second-order central scheme (Ref. 15). 

Those coefficients were κ2 = 0.125 and κ4 = 0.001. The value of the second-order dissipation was not 

critical as the flow was wholly subsonic, but a smaller value of the fourth-order dissipation coefficient of 

κ4 = 0.0005 produced nonphysical wiggles in the solution and thus κ4 was selected as the lowest safe 

value that produced smooth solutions.

2.2.1 Blowing Ratio of 0.5

Figure 4 plots spanwise-vorticity contours, which show the development of vortical structures

downstream of the cooling hole. Shedding occurs because of coolant interaction with the mainstream 

flow. Tyagi and Acharya (Ref. 3) asserted that the observed vortical structures in film-cooling flow are 

related to the development, evolution, growth, and transport of the hairpin vortices.
NASA/TM—2014-218098 12

Figure 4.—Initiation of rib vortices and convection downstream.

Figure 5.—Q-criterion isosurfaces of Q* = 0.1 at M = 0.5 and DR = 1.0. (a) Overview of the domain. (b) Near-hole view.

Figure 5 shows isosurface presentation of the dimensionless quantity Q* = 0.1, of the Q-criterion 

(Ref. 25) defined as 0.5 (ωiωi – Sij Sij) where the positive values represent locations in the flow where the

vorticity dominates the strain. The isosurfaces are colored by the nondimensional temperature 1 – η, thus 

the blue regions show cooling air and the red regions are at free-stream conditions. The cooling air with 

the higher density propagates downstream with periodic mixing patterns and appears first at a location 

slightly upstream of the hole and stays periodic some distance downstream before it starts to become

random. The patterns indicate definite rib vortices that form around the film column and convect 

downstream. These ribs appear to be quite regular and are likely to be of the Kelvin-Helmholtz instability 

wave type. Hairpin vortices are seen further downstream of the rib vortices as shown in Figure 5. The 

coherent vortical structures persist for several hole diameters downstream of the hole and then break up. 

This may coincide with the rapid deterioration in effectiveness seen in Figure 6, particularly in the 

spanwise direction shown as a well-defined narrowing of the color bands.

Figure 7 shows the computed time-averaged film effectiveness contours for this case and the 

experimental measurements using IR thermography from Reference 8.

The differences between the distribution of the surface effectiveness generated by CFD and that 

produced by IR thermography may be attributable to an inconsistency between the measured 

(experimental) and computed upstream boundary conditions. A recent LES study by Ziefle and Kleiser 

(Ref. 26) discussed the effect of the unsteady cross-stream inlet condition on the cooling effectiveness. 

Figure 8 shows this difference clearly. According to Ziefle and Kleiser, effectiveness contours produced
NASA/TM—2014-218098 13

Figure 6.—Computed instantaneous effectiveness contours for M = 0.5 and DR = 1.0.

Figure 7.—Time-averaged film effectiveness contours for M = 0.5 and DR = 1.0. (a) Computed. (b) Experimental 

(from Ref. 8).

Figure 8.—Comparison of the film effectiveness η contour distributions (from Ref. 26). (a) With unsteady 

cross stream. (b) Without unsteady cross stream.
NASA/TM—2014-218098 14

Figure 9.—Centerline film effectiveness contours for M = 0.5 and DR = 1.0. (a) Measured. (b) Computed.

by their own LES computations were three tailed, similar to Figure 7(a), when steady crossflow was 

established upstream (Figure 8(a)), as is the case with our TFNS computations. Contours were pointed in 

the downstream direction (Figure 8(b)) when realistic unsteady crossflow was set up upstream. As 

described earlier, the experimental measurements of effectiveness were made with an unsteady upstream 

condition characterized by a Tu of 1.5 percent. Therefore suitable unsteady inlet boundary condition is 

needed to allow for simulation of realistic film-cooling flows and to be able to directly compare to the 

experimental data in Reference 8. Johnson and Shyam (Ref. 27) used a recycling and rescaling method to 

model a more realistic inlet boundary to the film-cooling jet and they saw some improvement to the 

physical structures but not a significant improvement in effectiveness prediction. A more effective

approach to obtaining improved simulations could be the synthetic eddy modeling (SEM) devised by 

Jarrin et al. (Ref. 28) applied to the mainstream flow.

Figure 9(a) shows the measured dimensionless quantity of film effectiveness along the center plane of 

the film-cooling hole, and Figure 9(b) shows the computed contour lines for the same domain. The 

measured quantities were taken using thermocouples (Ref. 8). The computational contours of 

effectiveness (η1) are not as diffused as the measured ones. Note that the values of effectiveness 

calculated from the thermocouple data do not approach zero above the jet in the free stream while the 

computed results in Figure 9(b) did as expected. Effectiveness is based on tunnel inlet total temperature as 

shown in Equation (22), and is zero upstream of the hole. Correcting for that discrepancy enhances the 

agreement with the experimental data but the main discrepancy appears to be caused by not accounting 

for the crossflow unsteadiness in the computations. Ziefle and Kleiser show the effect of the crossflow 

unsteadiness. Figure 10(a) shows the contours of effectiveness in the presence of crossflow unsteadiness 

while Figure 10(b) shows the contours in the absence of such unsteadiness. It is clear that the cross-stream 

turbulence enhances breakup of the cooling jet and promotes its dissipation. The differences between the 

measurements in Figure 9(a) and computations in Figure 9(b) are likely similarly attributable to the effect

of the crossflow unsteadiness.

Figure 11 and Figure 12 show the respective spanwise-averaged and the centerline values of filmcooling effectiveness for M = 0.5 and DR = 1.0. The green line shows effectiveness from IR thermography 

for a case with higher Tu (4 percent). The results from IR thermography for low turbulence are within the 

error bands of the thermocouple data. Spanwise-averaged effectiveness (η1), plotted as the red line in 

Figure 11, appears to overpredict the measured data. The discussion by Ziefle and Kleiser on the effect of 
NASA/TM—2014-218098 15

Figure 10.—Film effectiveness contours through the centerline of the film-cooling hole 

from Reference 26. (a) With unsteady cross stream. (b) Without unsteady cross 

stream.

Figure 11.—Spanwise-averaged film effectiveness for M = 0.5 and DR = 1.0.

Figure 12.—Centerline film effectiveness for M = 0.5 and DR = 1.0.
NASA/TM—2014-218098 16

the neglected cross-stream unsteadiness applies here. In addition, LES computations performed by Tyagi 

and Acharya for the blowing ratio of 0.5 for the 35° short hole pipe, produced high effectiveness similar 

to what is shown in Figure 11. Tyagi and Acharya applied random fluctuations using a Gaussian 

distribution with its variance taken from the kinetic energy of turbulence. Thus no coherence existed in 

the incoming flow. This type of specification dies out rapidly and does not result in unsteady free stream. 

This similarity suggests that the presence of an unsteady inlet boundary condition may be crucial to 

agreement with the experimental data. Note that the CFD results show that a relatively high level of 

cooling effectiveness is maintained much further downstream of the hole than the experiment, and is 

consistent with the contours shown in Figure 9.

2.2.2 Blowing Ratio of 1.0

Figure 13 shows isosurfaces of the Q* for the case of M = 1 and DR = 1. The level of Q* was held at 

0.1 to allow for comparison with the M = 0.5 computation. The horseshoe vortex appears to have been 

initiated at the leading edge of the cooling hole. Figure 13(a) shows a better formed horseshoe vortex

compared to the M = 0.5 case. The initial mixing region between the two streams seems to have more of 

an axial vorticity character than the previous case where it had more of the ring-type character. Ring 

vortices are also present in the near-hole region, and the rings and vortex filaments show a higher level of 

mixing than previously observed for the lower blowing case. The ring vortices appear to be organized,

survive for some distance, and dissipate toward the end of the domain.

Figure 14(a) shows cooling effectiveness contours on the plate surface from IR thermography for a

free-stream Tu of 1.5 percent. The maximum effectiveness downstream of the hole is approximately 0.45 

and occurs at approximately 2.5 diameters downstream of the hole trailing edge. In addition, the contours 

appear to be aligned with the flow direction indicating that there is uniform cooling that seems to extend 

downstream and does not drop off as quickly as for M = 0.5. The coverage appears to extend to y/d = ±1

and the coverage shown by the CFD results in Figure 14(b) is narrower than the experimental data. The 

difference between experimental and computed contours is most pronounced near the hole. The low 

values of effectiveness downstream of the hole in Figure 14(b) are due to a lack of mixing of the free 

stream and the cooling flows, and is an indication of jet lift-off. Again, for this case, absence of 

unsteadiness in the free stream is a likely reason for the differences in effectiveness. 

Figure 15 shows the local effectiveness at a plane located at z/d = 0.0 based on thermocouple surveys. 

Notice in the region between x/d = 0.5 to 2.0 an area of relatively lower effectiveness appears. The 

computed contours, while showing similar behavior, have a wider lift-off zone and narrower height of the 

jet as they protrude into the free stream. This can be attributed to the neglected effect of the unsteady 

cross stream discussed in relation to Figure 9 and Figure 10.

Figure 13.—Q-criterion isosurfaces of Q* = 0.1 at M = 1.0 and DR = 1.0. (a) Overview of the domain. (b) Near-hole view.
NASA/TM—2014-218098 17

Figure 14.—Film-cooling effectiveness contours downstream of hole for M = 1.0, DR = 1.0, and Tu = 1.5 percent. (a) 

Measured. (b) Computed.

Figure 15.—Centerline film effectiveness contours at M = 1.0 and DR = 1.0. (a) From thermocouple survey 

Tu = 1.5 percent (b) Computed contours.

Figure 16 and Figure 17 show spanwise-averaged and centerline effectiveness for M = 1.0, DR = 1.0,

and Tu = 1.5. Computed results start out with a dropoff in the span-averaged effectiveness from excessive 

jet lift-off as shown in Figure 16. Jet reattachment, not seen in the experiment, causes a rise in the 

centerline effectiveness (Figure 17). This is one of the most important phenomena in the simulation of 

film cooling and is resolved by including the effect of inlet unsteadiness into simulations.
NASA/TM—2014-218098 18

Figure 16.—Spanwise-averaged film effectiveness for M = 1.0, DR = 1.0, and Tu = 1.5.

Figure 17.—Centerline film effectiveness for M = 1.0, DR = 1.0, and Tu = 1.5.

3.0 Conclusions

The time-filtered Navier-Stokes (TFNS) method was implemented in the Glenn-Heat Transfer 

(Glenn-HT) code and analyses of a flat plate cooled by long holes inclined at 30° to the free stream were

conducted to obtain both steady and unsteady flow solutions. The data were provided by an 

accompanying experiment. Results showed that steady solutions are highly dependent on the turbulence 

model used. To reduce this dependence, the unsteady TFNS analysis was used. The purpose is to allow 

resolution of larger unsteady flow structures believed to be mainly responsible for the breakup of the filmcooling stream. Features such as Kelvin Helmholtz structures resulting from the interaction of the two 

streams and vortical structures associated with hairpin vortices can be observed in the simulated flows. 

Good agreement was not achieved when the film effectiveness distributions obtained from the

computations were compared to the experimental IR thermography. Based on the literature for the 

blowing ratio of 0.5, it was concluded that achieving a successful agreement between the computational 
NASA/TM—2014-218098 19

results and the experimental data requires matching of the free-stream turbulence, which the Glenn-HT 

code is not equipped to do at this time. Results of the TFNS computations, however, are consistent with 

computations performed in the literature without the effect of free stream.

4.0 Future Work

Computations in this report show the importance of accurate representation of the inlet boundary 

conditions and explain why future work should include implementation of suitable boundary conditions. 

The inlet boundary for each experiment also needs to be well characterized including the Reynolds 

stresses for use with improved boundary specifications.

Periodic boundary conditions at the spanwise boundaries impose correlated turbulence, which is not 

accurate and leads to the interaction between neighboring holes that are not being modeled accurately,

especially in the downstream region. Future work could simulate a row of three holes with a symmetry 

boundary condition imposed on the spanwise boundaries. 

NASA/TM—2014-218098 21

Appendix—Symbols list

d diameter

DR density ratio

e internal energy per unit mass

G time filter defined in Equation (2)

k turbulence kinetic energy

L length

M blowing ratio

p pressure

Ԛ heating rate

qi heat fluxes

R universal gas constant

T temperature

t time

Tu free-stream turbulence intensity

u velocity

x streamwise coordinate measured from hole trailing edge

y spanwise coordinate 

z normal to the plate coordinate

ΔT temporal filter width

ε turbulence dissipation rate

η effectiveness defined in Equation (24)

η1 effectiveness defined in Equation (25)

ĸ thermal conductivity

μ viscosity

ν kinematic viscosity

ρ density

τij unresolved turbulent stresses

φ turbulence variable 

ω specific dissipation rate

(...),t temporal derivative

(...),i spatial derivative

Subscripts

T turbulent value

aw adiabatic wall 

c coolant 

r recovery

∞ inlet total

Superscripts

time filtered value

~ density weighted value
NASA/TM—2014-218098 22

References

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Ratio. NASA/TM—2009-215517, 2009. http://ntrs.nasa.gov

2. Guo, X.; Schröder, W.; and Meinke, M.: Large-Eddy Simulations of Film Cooling Flows. Comput. 

Fluids, vol. 35, 2006, pp. 587–606. 

3. Tyagi, M.; and Acharya, S.: Large Eddy Simulation of Film Cooling Flow From an Inclined 

Cylindrical Jet. Trans. ASME, J. Turbomach., vol. 125, 2003, pp. 734‒742.

4. Fujimoto, S.: Large Eddy Simulation of Film Cooling Flows Using Octree Hexahedral Meshes. 

GT2012‒70090, 2012.

5. Sinha, A.K.; Bogard, D.G.; and Crawford, M.E.: Film-Cooling Effectiveness Downstream of a 

Single Row of Holes With Variable Density Ratio. Trans. ASME, J. Turbomach., vol. 113, 1991, 

pp. 442‒449. 

6. Martini, P., et al.: Detached Eddy Simulation of Film Cooling Performance on the Trailing Edge 

Cutback of Gas Turbine Airfoils. Trans. ASME, J. Turbomach., vol. 128, no. 2, 2006, pp. 292‒299. 

7. Peet, Y.; and Lele, S.K.: Computational Framework for Coupling Compressible and Low Mach 

Number Codes. AIAA J., vol. 46, no. 8, 2008, pp. 1990‒2001.

8. Shyam, V., et al.: Long Hole Film Cooling Dataset for CFD Development, Part 1: Infrared 

Thermography and Thermocouple Surveys. NASA/TM—2013-218086-PART1, 2013.

http://ntrs.nasa.gov

9. Liu, N.-S.; and Shih, T.-H.: Turbulence Modeling for Very Large-Eddy Simulation. AIAA J., 

vol. 44, no. 4, 2006, pp. 687‒697.

10. Shih, T.-H.; and Liu, N.-S.: Modeling of Internal Reacting Flows and External Static Stall Flows 

Using RANS and PRNS. Flow, Turbulence and Combustion, vol. 81, 2008, pp. 279‒299.

11. Shih, T.H.; and Liu, N.S.: A Nonlinear Dynamic Subscale Model for PRNS/VLES of Internal 

Combustor Flows. AIAA‒2009‒0467, 2009.

12. Liu, Nan-Suey; Wey, Thomas; and Shih, Tsan-Hsing: Time-Filtered Navier-Stokes Approach and 

Emulation of Turbulence-Chemistry Interaction. AIAA 2013‒0707, 2013.

13. Shih, Tsan-Hsing, et al.: Modeling of Turbulent Swirling Flows. NASA TM‒113112, 1997.

http://ntrs.nasa.gov

14. Wilcox, D.C.: Simulation of Transition With a Two-Equation Turbulence Model. AIAA J., vol. 32, 

no. 2, 1994, pp. 274‒255. 

15. Steinthorsson, E.; Liou, M.S.; and Povinelli, L.A.: Development of an Explicit Multiblock/Multigrid 

Flow Solver for Viscous Flows in Complex Geometries. AIAA‒93‒2380 (NASA TM‒106356), 

1993.

16. Davidson, L.; and Peng, S.H.: Hybrid LES‒RANS Modeling: A One-Equation SGS Model 

Combined With a κ–ω Model for Predicting Recalculating Flows. Int. J. Numer. Meth. Fl., vol. 43, 

2003, pp. 1003‒1018.

17. Larsson, J.; Lien, F.S.; and Yee, E.: The Artificial Buffer Layer and the Effect of Forcing in Hybrid 

LES/RANS. Internat. J. Heat Fluid Flow, vol. 28, 2007, pp. 1443‒1459.

18. Spalart, P.R.; Jou, W.H.; and Allmaras, S.R.: Comments on the Feasibility of LES for Wings and on 

a Hybrid RANS/LES Approach. Advances in DNS/LES, Greyden Press, Dayton, OH, 1997.

19. Fasel, H.F.; von Terzi, D.A.; and Sandberg, R.D.: A Methodology for Simulating Compressible 

Turbulent Flows. J. App. Mech., vol. 73, pp. 405‒412. 

20. Shih, Tsan-Hsing; and Liu, Nan-Suey: Assessment of a Partially Resolved Numerical Simulation 

(PRNS) Approach in the National Combustor Code (NCC) for Turbulent Non-Reacting and 

Reacting Flows. NASA/TM—2008-215418, 2008. http://ntrs.nasa.gov

21. Shih, Tsan-Hsing, et al.: Modeling of Turbulent Swirling Flows. NASA TM‒113112, 1997.

http://ntrs.nasa.gov

22. Shih, T-S; Chen, K-H; and Liu N-S: A Non-Linear k‒ε Model for Turbulent Shear Flows. AIAA 

98‒3983, 1998.
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23. Langtry, R.B.; and Sjolander, S.A.: Prediction of Transition for Attached and Separated Shear 

Layers in Turbomachinery. AIAA 2002‒3641, 2002.

24. ANSYS CFX Reference Guide. Release 13, 2010. 

http://www1.ansys.com/customer/content/documentation/130/cfx_ref.pdf Accessed Nov. 25, 2013.

25. Hunt, J.C.R.; Wray, A.; and Moin, P.: Eddies, Stream, and Convergence Zones in Turbulent Flows. 

Center for Turbulence Research Report CTR‒S88, 1988.

26. Ziefle, J.; and Kleiser, L.: Numerical Investigation of a Film-Cooling Flow Structure: Effect of 

Crossflow Turbulence. J. Turbomach., vol. 135, no. 4, 2013, pp. 041001—041001‒12. 

27. Johnson, P.L.; and Shyam, V.: Large Eddy Simulation of a Film Cooling Flow Injected From an 

Inclined Discrete Cylindrical Hole Into a Crossflow With Zero-Pressure Gradient Turbulent 

Boundary Layer. NASA/TM—2012-217695, 2012. http://ntrs.nasa.gov

28. Jarrin, N., et al.: A Synthetic-Eddy Method for Generating Inflow Conditions for LES. Internat. J. 

Heat Fluid Flow, vol. 27, 2006, pp. 585‒593.
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Development of the Glenn Heat-Transfer (Glenn-HT) Computer Code to Enable

Time-Filtered Navier-Stokes (TFNS) Simulations and Application to Film Cooling on a

Flat Plate Through Long Cooling Tubes

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14. ABSTRACT

Computational fluid dynamics (CFD) analysis using Reynolds-averaged Navier-Stokes (RANS) formulation for turbomachinery-related

flows has enabled improved engine component designs. RANS methodology has limitations that are related to its inability to accurately

describe the spectrum of flow phenomena encountered in engines. Examples of flows that are difficult to compute accurately with RANS

include phenomena such as laminar/turbulent transition, turbulent mixing due to mixing of streams, and separated flows. Large eddy

simulation (LES) can improve accuracy but at a considerably higher cost. In recent years, hybrid schemes that take advantage of both

unsteady RANS and LES have been proposed. This study investigated an alternative scheme, the time-filtered Navier-Stokes (TFNS)

method applied to compressible flows. The method developed by Shih and Liu was implemented in the Glenn Heat-Transfer (Glenn-HT)

code and applied to film cooling flows. In this report the method and its implementation is briefly described. The film effectiveness results

obtained for film cooling from a row of 30° holes with a pitch of 3.0 diameters emitting air at a nominal density ratio of unity and four

blowing ratios of 0.5, 1.0, 1.5 and 2.0 are shown. Flow features under those conditions are also described.

15. SUBJECT TERMS

Filming cooling; Infrared; Heat transfer; Turbomachinery; Computational fluid dynamics; Large eddy simulation; Time-filtered NavierStokes; Turbulent flow; Turbulence models; Navier-Stokes

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