numerical simulation for film cooling technique with inlet boundary conditions perturbation

7/30/2019 Numerical Simulation for Film Cooling Technique With Inlet Boundary Conditions Perturbation

1/14

International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976

6340(Print), ISSN 0976 6359(Online) Volume 3, Issue 2, May-August (2012), IAEME

559

NUMERICAL SIMULATION FOR FILM COOLING TECHNIQUE

WITH INLET BOUNDARY CONDITIONS PERTURBATION

B. Bounegta1, R. Dizene

2and M. Abdelkarim

1

1Sciences and Technology University of Bechar-Algeria

2Sciences and Technology, Houari Boumediene University of, Algiers-Algeria

Corresponding author Email: [email protected]

ABSTRACT

Large Eddy Simulation approach of flow field and film cooling effectiveness is performed using the

Fluent Computational Fluid Dynamics code and carried out by using the LES turbulence model. This

simulation of mean velocity and turbulent kinetic energy fields are presented for lateral jet in crossflow

at injection angle of 35. The blowing ratio is 5.0=R

M . The flow obtained in such a periodic domain

is described, focusing on information relevant to estimation of mass/momentum/energy fluxes through

the plate. LES results underline the potential of the approach for industrial use.

Keywords: Large eddy simulation, Film cooling, interaction jet, turbulent jet.

1. INTRODUCTIONFilm cooling is a significant cooling technique and applied widely for turbine blade. The interaction of

jets with crossflow generates complex flow fields which exist in a variety of industrial applications.

Gas turbines are used for aircraft propulsion, in land-based power generation and in industrial

applications. The thermal efficiency and power output of a gas turbine rise with increasing turbine inlet

temperature. In modern gas turbines, inlet temperature can reach 2000 K which exceeds the melting

point of the blade and vane materials. Therefore, gas turbine elements must be cooled [1, 4] see Fig. 1

and Fig. 2.

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING ANDTECHNOLOGY (IJMET)

ISSN 0976 6340 (Print)

ISSN 0976 6359 (Online)

Volume 3, Issue 2, May-August (2012), pp. 559-572

IAEME: www.iaeme.com/ijmet.html

Journal Impact Factor (2012): 3.8071 (Calculated by GISI)

www.jifactor.com

IJMET

I A E M E


2/14



560

Figure 1. Physical coordinatessystem

Figure 2. Schematic of the Mixing of control volumes

The interaction of the jets with crossflow has been investigated in numerous experimental studies [5,

6]. Measurements of turbulent mean flow properties can be found in refs. [7]. numerous computational

studies of the generic problem of turbulent jets in crossflow are also reported in the literature [8].

Numerical simulation is an important method to study the transverse jet-crossflow. Many recent, Tyagi

and Acharya employed a Large Eddy Simulation (LES) scheme to investigate the detailed coherent

flow structures of film cooling. Numerical simulation can provide ideal boundary conditions but may

fail to accurately predict the flow separation and correct physics [9].

Both 2D and 3D cases are considered with a double hole jet geometries. The results of this paper can

serve as a reference for future experimental validation and technical implementation to real gas turbine

applications.

2. COMPUTATIONAL MODELWith the development of grid technique and computational methods, many researches have

investigated the characteristics of the flow field in film-cooled turbine by solving the Navier-Stokes

equations.

Filtering the Navier-Stokes equations, one obtains

( ) (1)0=

+

i

i

uxt


3/14



561

( ) ( ) (2)j

ij

ij

ij

j

ji

j

i

xx

p

xxuu

xu

t

=

+

here ij is the stress tensor due to molecular viscosity defined by

(3)3

2ij

l

l

i

j

j

i

ijx

u

x

u

x

u

+

=

and ij is the subgrid-scale stress defined by

(4)jijiij uuuu =

The numerical scheme is used to solve the 3D Reynolds-Averaged Navier-Stokes (RANS) equation on

general structured non orthogonal multi-block grids.

2.1 Numerical approach used in Large Eddy SimulationsThe LES solver uses a finite-volume discretization of the fully compressible multi-species (variable

heat capacities) Navier-Stokes equations. It is able to handle fully unstructured/structured/hybrid

meshes. Higher order temporal and spatial schemes [10-11] offer reliable unsteady solutions for

complex geometries as encountered in the field of aeronautical gas turbine.

In LES, large eddies are resolved directly, while small eddies are modeled. Large eddy simulation

(LES) thus falls between DNS and RANS in terms of the fraction of the resolved scales. The rationale

behind LES can be summarized as follows:

Momentum, mass, energy, and other passive scalars are transported mostly by large eddies. Large eddies are more problem-dependent. They are dictated by the geometries and boundary

conditions of the flow involved.

Small eddies are less dependent on the geometry, tend to be more isotropic, and areconsequently more universal.

The chance of finding a universal turbulence model is much higher for small eddies.Resolving only the large eddies allows one to use much coarser mesh and larger times-step sizes in

LES than in DNS. However, LES still requires substantially finer meshes than those typically used for

RANS calculations. In addition, LES has to be run for a sufficiently long flow-time to obtain stable

statistics of the flow being modeled. As a result, the computational cost involved with LES is


4/14



562

normally orders of magnitudes higher than that for steady RANS calculations in terms of memory

(RAM) and CPU time. Therefore, high-performance computing (e.g., parallel computing) is a

necessity for LES, especially for industrial applications.

2.1.1 LES closures for turbulent stresses

The concept of LES introduces the notion of spatial filtering to be applied to the set of governing

equations used to simulate turbulent reacting flows [12]. Resulting from this operation are unclosed

terms issued from non linear character of the Navier-Stokes equations, sub-grid scale (SGS) models

need to be supplied to mimic the turbulent scale effects on the solved field [12, 13].

Generally, compared to RANS, the LES approach requires refined high-quality numerical meshes and

small time steps, and as a consequence, significant amount of computer time. Due to considerable

progress in computational sciences and hardware in recent years, LES is becoming feasible for

increasingly complex systems, including complex geometries and complex flow physics. LES shows

all the features of emerging technology for modeling design and optimization in industrial applications.

The calculation with Large Eddy Simulation where the unsteady Navier Stokes equations are solved

for and the dynamics of the large scales resolved correctly. Only the dynamics of the small scales are

generally geometry independent and are well represented by eddy viscosity gradient approximations.

Thus LES predictions are expected to provide better agreement than the RANS prediction.

The large eddy simulation approach (LES) is intermediate between DNS, where all fluctuations are

resolved, and the statistical simulations based on RANS, where only the mean flow is resolved. In

LES severe Reynolds number restrictions of DNS are bypassed by directly simulating the large scales

(GS) only and supplying the effect of the missing small scales (SGS) by a so-called sub-grid model

see Table 1. This obtained by filtering the Navier-Stokes equations in space, in order to eliminate the

flow fluctuations smaller then the filter size. In this way, the new unknowns of the problem become

the filtered flow variables. Like for RANS, due to the non-linearity of original problem, the new

equations contain additional unknown terms, the so-called sub-grid scale (SGS) terms, representing

the effect of the eliminated small scales on filtered equations. In order to close the problem, these

terms must be modeled, but, due to the fact that small unresolved scales are often simpler nature thatthe inhomogeneous large motions, since they do not significantly depend on the large scale motion,

rather simple closure models may work well for many applications. Another advantage of this method

is the possibility of directly simulating the largest scales, which are usually more interesting from the

engineering point of view. Computationally, LES clearly is less demanding than DNS, but in general

much more expensive than RANS. The reason is that, independent by the problem to be solved, LES

always requires fully three dimensional and time-dependant calculations even for flows which are two


5/14

International Journal of

6340(Print), ISSN 0976

or one dimensional in the mean. M

time to obtain stable and significan

the analysis of complex three-dim

fails. The utilization of LES for en

interest in this method has largely i

The commercial software FLUEN

simulation models were built accor

above one million and enough to

simulation model of zero pressure g

2.2 Filtered Navier-Stokes Equati

The governing equations employed

equations in either Fourier (wave

process effectively filters out the e

used in the computations. The re

.

A filtered variable (denoted by an o

( ) ( ) ( ) '','=D

dxxxGxx

Where D is the fluid domain, aneddies.

The finite-volume discretization its

Where is the volume of a comp

( ) 'x,0

x',1',

VxxG

Research is primarily focused on

Significant effort is devoted to wal

near-wall turbulence. Applications

equilibrium turbulent flows in com

2.3 Subgrid-Scale Models

echanical Engineering and Technology (IJMET

359(Online) Volume 3, Issue 2, May-August (20

563

reover LES, like DNS, needs to be carried out for l

t statistics. For these reasons, LES should provide

ensional and time-dependent problems where RA

ineering problem is not yet very expensive, but in r

creased [11, 14].

T 6.3 was applied for the numerical simulation

ding to the experiment models. The cell number o

obtain grid-independent result. Figure 1 shows th

radients as example [15, 16].

ons

for LES are obtained by filtering the time-depende

-number) space or configuration (physical) spac

dies whose scales are smaller than the filter width

ulting equations thus govern the dynamics of la

ver bar) is defined by

(5)

G is the filter function that determines the scale

lf implicitly provides the filtering operation:

tational cell. The filter function, ),( 'xxG , implied h

(6)

large eddy simulation with application to wall-

l-layer modeling, especially on zonal hybrid RANS

include transitional flows (bypass transition due to

lex geometries.

), ISSN 0976

2), IAEME

ong periods of

best results for

NS frequently

ecent years the

research. The

each model is

e mesh of the

t Navier-Stokes

. The filtering

or grid spacing

ge eddies [14].

of the resolved

ere is then

bounded flows.

/LES models of

akes), and non


6/14



564

The subgrid-scale stresses resulting from the filtering operation are unknown, and require modelling.

The subgrid-scale turbulence models in FLUENT employ the Boussinesq hypothesis as in the RANS

models, computing subgrid-scale turbulent stresses from

ijtijkkij S 231 = (7)

Where t is the subgrid-scale turbulent viscosity. The isotropic part of the subgrid-scale stresses kk is

not modeled, but added to the filtered static pressure term. ijS is the rate-of-strain tensor for the

resolved scale defined by:

+

=

i

j

j

iij

x

u

x

uS

2

1(8)

For compressible flows, it is convenient to introduce the density-weighted (or Favre) filtering

operator:

= (9)

The Favre Filtered Navier-Stokes equation takes the same form as Equation. The compressible form

of the subgrid stress tensor is defined as:

jijiij uuuuT += (10)

This term is split into its isotropic and deviatoric parts

32143421

isotropic

ijll

deviatoric

ijllijij TTTT 3

1

3

1+= (11)

The deviatoric part of the subgrid-scale stress tensor is modeled using the compressible form of the

Smagorinsky model:

( )ijiiijtijllij TT = 231 (12)

As for incompressible flows, the term involving llT can be added to the filtered pressure or simply

neglected indeed, this term can be re-written as pMT sgsll2.= where sgsM is the subgrid Mach

number. This subgrid Mach number can be expected to be small when the turbulent Mach number of

the flow is small.


7/14



565

FLUENT offers four models for t : the Smagorinsky-Lilly model, the dynamic Smagorinsky-Lilly

model, the WALE model, and the dynamic kinetic energy subgrid-scale model.

Subgrid-scale turbulent flux of a scalar, , is modeled using s subgrid-scale turbulent Prandtl number

by:

jt

tj

xq

=

(13)

where jq is the subgrid-scale flux.

Smagorinsky-Lilly Model

This simple model was first proposed by Smagorinsky. In the Smagorinsky-Lilly model, the eddy-

viscosity is modeled by

SLst2. = (14)

sL is the mixing length for subgrid scales and ijij SSS .2= In FLUENT, sL is computed using:

= 31

,min VCdL ss (15)

where is the von Krmn constant, dis the distance to the closest wall, sC is the Smagorinsky

constant, and Vis the volume of the computational cell. .

Lilly derived a value of 0.17 for sC for homogeneous isotropic turbulence in the inertial subrange.

However, this value was found to cause excessive damping of large-scale fluctuations in the presence

of mean shear and in transitional flows as near solid boundary, and has to be reduced in such regions.

In short, sC is not a universal constant, which is the most serious shortcoming of this simple model.

Nonetheless, sC value of around 0.1 has been found to yield the best results for a wide range of flows,

and is the default value in FLUENT.

2.4 Inlet Boundary Conditions for the LES Model

No Perturbations

The stochastic components of the flow at the velocity-specified inlet boundaries are neglected if the

No Perturbations option is used. In such cases, individual instantaneous velocity components are

simply set equal to their mean velocity counterparts. This option is suitable only when the level of

turbulence at the inflow boundaries is negligible or does not play a major role in the accuracy of the

overall solution [15].


8/14



566

3. RESULTS AND DISCUSSION

The results are presented with the following structure. First the mean flow flied and the turbulent

transport of the jet-crossflow interaction is discussed. Next the findings are compared with

experimental data and numerical simulations to show the quality of the computational method.

Figure .3 shows the spreading of jets in the lateral direction at various locations =dx/ -9, 0, 5, 10,

15, 20 and 25 for the jet simulation. This result of the bound vortices being confound in a smaller

space, inducing a large v component of velocity and thus aiding the spread of the jet. Therefore

upstream the two interact; reducing significantly the effect of the boundary layer thickness will

produce the well known horseshoe vortex. The vorticity associated with the wake side of the jet will

produce a pair of bound vortices.

Figure 3. Profiles of multiple jet v-velocity at various stations for = 35 and 5.0=RV .

Figure .4(a) and (b): In this section the film cooling effectiveness is presented as two-dimensional

contour plots. Figure .4(b): the film cooling effectiveness LES solution is qualitatively similar to Azzi

simulation case [7], but it is very better distribution and more spread in lateral direction.


9/14



567

(a) Simulation Azzi (2001)

(b) Simulation LES model

Figure 4. Compared film cooling effectiveness at the velocity ratio 0.5 in the (a) and (b).

Figure .5 shows five different x-planes =dx/ 0, 3.5, 5, 10, 15. These planes along with the blade

surface are colored by the temperature. One can observe the presence of a pair of counter rotating

vortices. Which is asymmetric and the center of the vortex is moving away from the blade surface. It

is clearly that the solution is highly asymmetric for the film cooling problem. LES solutions capture

the fluid thermal characteristics of the flow.

Figure 5. Temperature distribution (at x/d= 0, 3.5, 5, 10, 15) and stream lines shows asymmetry in theLES solution.

Figure .6(a) and (b) shows qualitative comparison of the temperature distribution on the blade surface

for RaNS and DES solution respectively. Figure .6(c) plots the normalized temperature line contoursfor the same DES solution qualitatively. Figure clearly shows that maximum cooling takes place in a

very small region just beyond the trailing edge of the hole which is similar to the experimental resultsobtained by Sinha et al. [5, 15].

(a) Study RANS solution (b) Time averaged DES solution

(c) Temperature contour lines DES time averaged solution

Figure 6. Comparison of temperature distribution for RANS and DES solution on the flat plate.

(Sagar Kapadia (2003)).


10/14



568

Figure .7(a) shows qualitative of temperature distribution on the blade surface for the time LES

solution (simulation). Figure .7(b) plots the normalized temperature line contours for LES solution

qualitatively.

(a) Time LES solution

(b) Temperature contour lines LES time averaged solution

Figure 7. Temperature distribution for LES solution on the flat plate.

Figure 8. Shows the qualitative and quantitative distributions velocity magnitude (a) - calculated and

(b)- measured.

(a) Calculated velocity magnitude LES model (b) Measured velocity magnitude (Gustafsson, 2006)

Figure 8. Compared LES model with experimental data

Figure 9, Figure 10 and Figure 11 shows the blade temperature contours at 0/ =dy and Normal to the

mid plane at 0/ =dz , and film cooling effectiveness.


11/14



569

(a) Blade temperature contours at 0/ =dy

(b) Normal to the mid plane at 0/ =dz

Figure 9. Temperature contours on the planes (a) and (b) show downstream spread of the cooling

effect.

(a) Simulation Azzi (2001)

(b) Simulation LES model

Figure 10. Compared film cooling effectiveness in the (a) and (b)


12/14



570

0/ =Dx 5.3/ =Dx

10/ =Dx

15/ =Dx

Figure 11. Temperature contour at various stations for time-averaged LES solution

4. CONCLUSIONS

A method is presented to perform Large-Eddy Simulations of interaction of jet in cross-flow.

In this study conjugate heat transfer in turbulent flow over turbine blades has been simulated and

studied using the computational fluid dynamics code FLUENT in order to calculate temperatures and

velocities fields.LES calculations resolve the energy equation carrying structures and only model the small-scale

fluctuations which are generally isotropic in nature. In general, LES results require greater

computational effort but show improvements over RANS, and the following observations are noted: LES prediction of the mean velocities, turbulence and cooling effectiveness are in excellent

agreement with Sumanta Acharya (2009) measured data. In this study we have modified andused a dynamic model for the Wale coefficient. No ad hoc corrections are needed for

obtaining good agreement.

These results indicate that an SGS model is not needed for an accurate simulation of thiscase. As discussed earlier, the grid resolution in the near wall has to be very fine to resolvethe small energy-producing structures there. So that to resolve the near wall region, the fine

grid LES has effectively approached the RANS in the near wall limit.

Note that the LES turbulence statistics were computed for the resolved velocity field only. Asa result, the LES Reynolds stress profile with the SGS model should be lower than the RANSsolution because the SGS contribution was not included.

As the Les grid resolution in the crossflow plane approaches the RANS resolution, it isinteresting to see the effect of the SGS model on the turbulence solution. The simulation wasperformed using the finer LES grid. The use of the SGS model makes essentially no

difference in the mean streamwise velocity solution. Small differences are also observed in

the turbulent velocity fluctuations.

REFERENCES

1. Jovanovic, M.B., De Lange, H.C., van Steenhoven, A. (2008), Effect of Hole imperfection on

Adiabatic Film Cooling Effectiveness. Int. J. of heat and Fluid Flow29, pp377-388.


13/14



571

2. Acharya S. (2009), Film Cooling Simulation and Control. Int. Symp. On Heat Transfer in Gas

Turbine Systems, Antalia Turkey.

3. Radhouane A. et al.(2009), Effet de la variation de la temprature de deux jeux inclins sur leurdispersion au sein d'un coulement transversal de temprature constante. Proceeding ICHMT

International convective heat and mass transfer, Tunisia, 26/04-01/05/20094. Mangesh, K. and Yavuzkurt S. (2009), Calculation of gas turbine blade temperatures using an

iterative conjugate heat transfer approach. Heat Transfer in Gas Turbine Systems, Antalya, Turkey.5. Sagar, K., Subrata, R. Heidmann, J.(2003), Detached Eddy Simulation Of Turbine Blade Cooling.36th Thermophysics Conference. AIAA-2003-3632. Orlando, Florida.6. Gustafson K.M., Gunnar Johansson T. (2006), Numerical simulation of effusion cooling with

comparisons to experimental data. Progres in Computational Fluid Dynamics, Vol. 6, Nos. 1/2/3.7. AZZI A.(2001), Investigation Numrique du Refroidissement par Film Appliqu aux Aubes des

turbines Gaz. Thse de Doctorat d'tat, USTO Algrie.8. Acharya, S. (2009), Film cooling Simulation and control, Turbine-09, Antalya, Turkey, August.

9. Kalghatgi, P. and Acharya, S. (2009), LES of Film Cooling Over Rough Surfaces, Turbine-09,

Antalya, Turkey, August.10. Leedom, D. and Acharya, S. (2009a), LES of Cylindrical Hole Film-Cooling: Plenum Effects,

submitted for publication.11. Renze, P., Schroder, W., and Meinke, M. (2008), Large-Eddy Simulation of Film Cooling Flows

at Density Gradients."International Journal of Heat and Fluid Flow, 29: 18-34.12. Lamarque N. (2007), Schmas numriques et conditions limites pour la simulation aux grandes

chelles de la combustion diphasique dans les foyers dhlicoptre. Thse de Doctorat, , Institut

national polytechnique de TOULOUSE.13. Knost, D. G. (2003), Predictions and Measurements of Film-Cooling on the Endwall of a First

Stage Vane. Master of Science in Mechanical Engineering,. Virginia Polytechnic Institute and State

University, USA.14. Trong T. Bui, A (2000), Parallel, finite-Volume Algorithm for Large-Eddy Simulation of

Turbulent flows. Computers and Fluids,. 29: 877-915.

15. FLUENT, ANSYS Inc. FLUENT 6.3 Documentation, 2006.16. 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. J. Turbomachinery 113, , pp 442-449.

Nomenclature

a : Thermal diffusivity ( )sm2

pC : Specific heat of fluid ( )KkgJ

D : Diameter ( )m

RD : Density ratio

E: Empirical constant (= 9.793)

k: Turbulent kinetic energy ( )22 sm

sgsk : Subgrid-scale kinetic energy

sL : Mixing length for subgrid scales

RM : Blowing ratio

sgsM : Subgrid Mach number

P : Pressure 2mN


14/14



572

rP : Prandtl number

trP : Turbulent Prandtl number (0.85 at the wall)

jq : Subgrid-scale flux

.

q : Wall heat flux

S: Source term

ijS : Rate-of-strain tensor

pT : Temperature at the cell adjacent to wall ( )K

wT : Temperature at the wall ( )K

u : Streamwise velocity component ( )sm

v : Spanwise velocity component ( )sm

V : Volume of the computational cell.

w : Lateral velocity

zyx ,, : coordinates

py : Distance from point to the wall

Greek symbols

: Jet issuing angle

: Boundary layer

: Von Krmn constant (= 0.4187)

: Adiabatic film cooling effectiveness

: Heat conductivity ( )KmW

: Dynamic viscosity of the fluid ( )smkg

: Kinematic viscosity of fluid ( )sm2

: Density of fluid 3mkg

: Stress tensor 2smkg

ij : Subgrid-scale stress

Subscripts

aw : Adiabatic wall

J: Jet flow (coolant)

numerical simulation for film cooling technique with inlet boundary conditions perturbation

Documents