Proceedings of International Conference on Engineering and Information Technology

Sep. 17-19, 2012, Toronto, Canada

* Corresponding author. Tel.: +4917620235271

Germany; E-mail: drsattar@uotechnology.edu.iq

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Comparison of RANS Turbulence Models and LES in CFD Simulation using OpenFOAM

Sattar Al-Jabair Assist. Prof. in Mech. Eng. Dept., University of Technology, Baghdad, Iraq

Abstract A separated flow in a three-dimensional wavy channel is simulated numerically using open source program

OpenFOAM, in order to comparison and evaluation the turbulence models. This study included seven RANS-based turbulence models (standard k- , Realizable k-, RNG k-, Launder Sharma k-, Lam Bremhorst k-, nonlinear k- Shih, Menter SST k-) and one model of large eddy simulation (one equation model). All computational work is carried out using open source software: pre-processing GAMBIT software for geometry and meshing, OpenFOAM CFD solver, and Paraview post-processing for visualization. In all simulation wall function are used, with three values of Reynolds number 3000, 6000 and 10000 based on inlet bulk velocity and hydraulic diameter of inlet wavy channel at amplitude wave length ratio (a/) equal 0.25. Keywords: RANS, LES, Turbulence modeling, OpenFOAM source code.

Nomenclature

a Wave amplitude (m) DH Hydraulic diameter (m) p Pressure drop (Pa) L Length (m) Re Reynolds number

Greek Symbols Dynamic viscosity [kg/m.s]

Subscripts i, j, k x ,y, z

Refer to coordinates location in X, Y , Z

s, e Start and end t Time

Notations CFD Computational fluid dynamics DNS Direct numerical simulation LES Large eddy simulation RAS Reynolds Averaged stresses RANS Reynolds Averaged Navier-Stokes

Non-dimensional Numbers Re Reynolds number y+ Dimensionless distance

1. Introduction

A correct prediction of a separated flow remains one of the main challenges in the computational fluid dynamics (CFD), especially in the turbulence modeling. The computational prediction of flow separation of a turbulent boundary layer from a wavy surface is a process of primary concern. The fluid flow becomes detached from the surface and instead takes the form of eddies and vortices. Due to wavy surface shape the flow separation occurs, it is a challenging computational

problem and experiments indicate that the flow in the recirculation zone is complex and strongly time-dependent. However, the physical phenomena that arise are a subject of interest for many engineering components and systems. Streamlined car bodies, low-pressure turbine blades and highly loaded aircraft wings, wave generation on liquid surfaces or liquid surface instability and compact heat exchanger are some examples of where flow separation can have significant influence of the ability of the device in question to perform electively. There are many literature about wavy surface included the flow field and heat transfer phenomena [1-6], but not refer to powerful of turbulence model for this case, so one of goals for this study is achieve that.

A number of studies and experiments have been carried out in the discussed problem. In measurements of wall shear stress and pressure forces the works under leading of Hanratty are classical [7], and [8]. The mostly cited data of velocity components were proved by LDV measurements by Hudson [9], and [10]. The configuration of his experiments was later used in DNS simulations of Maass and Schumann [11], Cherukat et. al. [12] and Yoon et. al. [13]. The latter reference was used to verify my results in the location of separation and reattachment points.

Wavy channel flow is a three-dimensional simulated numerically using open source program OpenFOAM. In order to comparison and evaluation the turbulence models. This study included seven RAS turbulence

models (standard k- , Realizable k-, RNG k-, Launder Sharma k-, Lam Bremhorst k-, nonlinear k- Shih, Menter SST k-) and one model of large eddy simulation (one equation model). All the governing equations of theses turbulence models are shown in the references [4, 15, 16, 17, and 18].

The main flow features evaluated is the shape and position of the flow separation. Most of the models tested

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have problems describing the complex dynamics of flow separation in these particular cases. Turbulent ows uctuate on a broad range of time and length scales. This makes the simulation of such ows difficult and it is often necessary to model the turbulence in some way.

The main objective of this study is to evaluate the tested RANS-models prediction of the flow over the wavy surface. We mainly evaluate the results with respect to the location and shape of the separation zone and the velocity, pressure and Reynolds stress distribution in the near the wall. Also, one of the purposes of this project is to use open-source CFD software instead of commercial software for the simulations. This type of software is advantageous for smaller companies to use, as the cost of commercial CFD package licenses can be prohibitive. Moreover it is very important in the academic life especially for researchers, to understand the differential equations formulation and increase their Innovation and development in numerical modeling for any physical problem.

2. Problem Formulation

In this study, ow in a symmetric wavy-wall

channel was analysed. The working uid (air) was assumed to be Newtonian uid with constant uid properties, and the ow was considered to be turbulent according to Reynolds number values, incompressible, unsteady and three-dimensional. As will be seen in Fig. 1, the shape of the low wavy-wall prole in the region xs xxe is given as

y(x)=-Ly-a sin[(x-xs)/Ly ]

where (xs) and (xe) are the start and end points of the

wavy-wall channel, respectively, and (a) is the amplitude

of the wavy surface. The channel mean height (Ly) is set

equal to the wave length (); whereas four complete

wave cycles were proven convenient in representing the

channel length to eliminate the effect of periodicity on the

flow fields in the channel inlet and outlet. The no-slip

boundary condition is employed at the wall, whereas the

periodic boundary conditions are applied in the

streamwise direction. Table (1) shows the boundary

conditions in the inlet region. In all calculation, Simulation results applied for Re=3000, 6000, 10000, (a/) =0.25,

and seven turbulence models.

Fig. (1) Computational domain in this study for (a/) =0.25, dimensions in cm.

3. Theory dna Turbulence Models

The Reynolds Averaged Navier-Stokes (RANS) equation is:

(

)

( )

( )

Where - is called Reynolds Stresses, the term

(

)

Must be modeled using turbulence models.

Turbulence models are required to predict the

Reynolds stresses and scalar transport terms in order to

close the system of expanded time-averaged RANS

equations (continuity, momentum, and scalar transport

equations). Seven RANS-based turbulence models with

one model of LES are used in order to investigate which

the best for turbulent flow in corrugated channels flow.

This section describes some of the commonly used

turbulence models, and then presents relevant details

regarding the specific turbulence models used in this

project.

All the turbulence models in this study are based on variances of the Reynolds averaged Navier-Stokes (RANS) equations, in which average values for turbulent fluctuations are used for modelling the turbulence. Several variations of the k- model have been made, as well as low-Reynolds numbers modifications of it as in (Launder Sharma k-, Lam Bremhorst k-, and nonlinear k- Shih). The high Reynolds number models listed use log-law type wall functions as a (standard k- , Realizable k-, and RNG k-). The low Reynolds number models calculate flow to the wall, and with these models, it is important for the y+ value to be approximately 1, whereas with high-Reynolds models, y+ should range from approximately 30-60 to 300-400 in the log layer. Also large eddy simulations (LES) were developed to extend the simulation of unsteady flows.

The desired result of an LES computation is to obtain

a DNS equivalent solution for the large-scale turbulence on a much coarser grid than is required for DNS. An LES simulation requires: A grid fine enough to discretize the small nearly isotropic scales of the turbulence, A low dissipation numerical scheme, A filter function to determine the division of the turbulent spectrum into grid realized and subgrid regions, and A sub-grid turbulence model. A true LES simulation is more than a high Reynolds number computation run without a turbulence model. Although the resulting solution from such a simulation may resemble turbulent flow, the resulting solution will most likely not represent an equivalent DNS solution. Two things are required to close the modelled LES equations: The sub-grid turbulent kinetic energy ksgs, and the sub-grid eddy viscosity sgs, [14].

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4. CFD OpenFOAM

OpenFoam (Open Field Operation and

Manipulation) is an open source computational fluid dynamics program produced by OpenCFD Ltd. Its origins come from the late 1980 at Imperial College (London) when a group of people decided to develop a powerful tool to be able to run flexible general simulations. It was released open source in 2004 under the GNU General Public License. OpenFoam is written in C++ and it is used an object oriented approach which makes the code to be understandable and permits the user to implement its own files in order to adapt it to each specific case. Basically, OpenFoam is a library used to create executable, known as applications, in order to solve the case the user is working with. There are two kinds of applications: solvers, that are to solve cases; and utilities, that are designed for data transformation.

There is a variety of commercial CFD software

available such as Fluent, Ansys CFX, ACE, as well as a wide range of suitable hardware and associated costs, depending on the complexity of the mesh and size of the calculations. Commercial CFD packages can cost up to about $20000 (US Dollars) per year for licenses,

maintenance, and support. Complicated

transient cases with fine meshes will require more powerful computer processors and RAM than simpler cases with rough meshes. A typical engineering workstation (i.e. 32 GB processing RAM with quad processors) at a cost of approximately $3000-$5000 (US Dollars), or a combination of several processors running in parallel, is probably the minimum investment needed to get started.

Results presentation included the OpenFOAM

for the CFD calculations with pisoFoam solver (Transient solver for incompressible flow), paraView for visualization, along with other useful scientific and mathematics related software. Calculations for this project were carried out for approximately one million cells.

5. Results and Discussion 5.1 Grid Independency

Several grids have been tested for the case of

LES, k- , and Menter SST k- turbulence models. Table

(2) shows the Separation point for five grids used. It can

Table (1) Values used in this project for turbulence intensity I, kinetic energy k, dissipation , and frequency . * [15] , ** [4, 19]

Inlet area = 2*10

-2 m

2 *I = 0.16 * Re

-1/8 k = 1.5*(I*U) **

0.75 1.5

, 0.07 = / k

U [m/s]

Reynolds number (Re)

Intensity ( I) (/)

kinetic energy (k) (/)

Dissipation ()

(/)

frequency ()

1.44 3000 0.0588 0.0107 0.0827 7.7289

2.89 6000 0.0539 0.0363 0.5167 14.234

4.82 10000 0.0505 0.0871 1.9206 22.050

Table (3) The (x/) location of separation and reattachment points for validation test for (a/)=0.05, Lx=2 and Re=6760.

Turbulence

Models Separation point Diff % Reattachment point Diff %

1 DNS [13] 0.14 0.0 0.62 0.0

2 k- 0.13982 -0.1285 0.64112 3.4064 3 Realizable k- 0.13794 -1.4714 0.61984 -0.0258 4 RNG k- 0.14143 1.0214 0.63186 1.9129 5 Menter SST k- 0.13845 -1.1071 0.66998 8.0612 6 Launder Sharma k- 0.13647 -2.5214 0.70132 13.1161 7 Lam Bremhorst k- 0.13548 -3.2285 0.70067 13.0112 8 Nonlinear Shih k- 0.1419 1.3571 0.65021 4.87258 9 LES 0.14010 0.0714 0.62021 0.03387

Table (2) Results of grid independency according to the (x/) location of separation point.

Grid Size k- Menter SST k- LES

500 000 0.13891 0.13777 0.14000

750 000 0.13898 0.13822 0.14008

1000 000 0.13982 0.13845 0.14010

1250 000 0.13981 0.13846 0.14009

1300 000 0.13982 0.13845 0.14010

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Standard k- Realizable k- RNG k- Lam Bremhorst k- Launder Sharma k- Non Linear KE Shih Menter SST k-

Standard k- Realizable k- RNG k- Lam Bremhorst k- Launder Sharma k- Non Linear KE Shih Menter SST k-

be see that, a little difference between the last two

sets of grid results and the grid of 1 000 000 is used in

all subsequent calculation of this study to decrease the

time cost of the solution convergence, without

effecting in the solution accuracy.

5.2 Comparison with DNS data

In order to validate the results the rst run was

done with ow characteristics that are the same as those

used by Yoon et. al. [13]. Table (3) shows the

comparison results with [13] according to the separation

and reattachment points for case (a/) =0.05, (Lx=2 )

and Re=6760. The table shows reasonable agreement

for the matching data, the best turbulence models for

separation point are LES, standard k- , RNG k-, Menter

SST k-, Realizable k-, Nonlinear Shih k-, Launder

Sharma k-, Lam Bremhorst k-, respectively. While for

reattachment point the best turbulence models are LES,

Realizable k-, RNG k-, standard k- , Nonlinear Shih k-

, Menter SST k-, Lam Bremhorst k-, Launder Sharma

k-, respectively.

5.3 Results

Calculations were performed for several Reynolds

numbers from a low value up to 10000, for Re = 3000, 6000 and 10000. This set provides a representative sampling of the developing flow in a wavy passage in the regime where transition to an oscillatory state takes place. Fig. (2) shows the Axial Velocity profiles at Re=10000 , z/Lz=0.5 for different turbulence models at two locations (A) at x/Lx=0.542 (3rd divergent region) and, (B) x/Lx=0.64 (3rd convergent region). In Fig. (2A) we can be seen the acceleration of the velocity magnitude in the center of the channel to developed the core flow and the position of reverse flow near the walls to developed the recirculating flow. The max. and min. axial velocity in the core flow occurred by using Lam Bremhorst k-, and standard k- turbulence models respectively. While the max. and min. axial reverse velocity occurred by using Launder Sharma k-, and standard k- turbulence models respectively. From the figure we deduction there are two vortices near the both wavy walls.

Streamwise vortices appear near wavy wall produce the outward uid motion carrying the low speed uid lumps toward the high speed ow region and in opposite way the wall-ward uid motion feeding the high speed uid lumps toward the low speed ow region. These motions have a signicant effect on the momentum transfer around the vortices. These vortices are generated with larger population within the up-slope region. In Fig. (2B) the core flow are strong due to change in the area of the channel where the max. axial velocity happened by using Bremhorst k-, and Nonlinear Shih k- turbulence models respectively. Fig. (3) shows the Axial pressure profiles at Re=10000, y/Ly=0.5, and z/Lz=0.5 for different turbulence models. The large pressure drop occurred in the first wave due to change in area of the channel suddenly, after that the pressure drop is constant nearly in the other waves. The max. and min. pressure drop during the channel happened by using Nonlinear Shih k- and standard k- turbulence models respectively.

(A)

(B) Fig. (2) Axial velocity profiles at Re=10000 , z/Lz=0.5 for

different turbulence models A. x/Lx=0.542 (3rd divergent region) B. x/Lx=0.64 (3rd convergent region)

Fig. (3) Axial pressure profiles at Re=10000, y/Ly=0.5, and z/Lz=0.5 for different turbulence models.

Table (4) shows the comparison between turbulence models according to max. and min. values of flow properties (velocity vector, velocity components, kinetic energy, dissipation rate, Reynolds stress magnitude, omega and wall shear stress) at Re=3000. The values are the same nearly. The max. and min. values of these parameters for all turbulence models are show in table in red color. Table (5) represented the (x/) location of separation and reattachment points for (a/) =0.25, and Re=6000 in all waves region.

Fig. (4) represents the transient results for Large

eddy simulation case, (z/Lz)=0.5, and Re=6000. In this case we can see the growth of vortices with time moreover to the vortices movement in the channel. At first the vortices are begin in upper tip of wavy wall (time=32min) and then become more large from that in

A B

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the previous time, where are moving in the axial direction till it go out of the channel or colloid with opposite wavy wall and finish. This sequence are periodical in all simulation until reach to steady state solution. The periodic and oscillatory cases of generated vortices are show in velocity component in y-direction moreover to the movement of vortices in the channel. Finally the Sub-grid eddy viscosity transient results are presents in the figure as shown in the right side.

6. Conclusion

The present study has presented the comparison of the selected turbulence models RANS and LES in using for simulation of turbulent flow in wavy channels.

The major outcome of this study is recommended the open source software to use with high efficiency according to the results, where there is good matching with the results of DNS, moreover to save in cost. Also this type of software has wide range for development in numerical modeling for any physical problem.

The separation and attachment points were used to compare the results of these models of turbulence with the DNS. From the results it has been shown that all of RANS and LES models predict the location of separation point well especially LES, k- , and RNG k- but for attachment point the best models are LES, Realizable k-, and RNG k- model. This conclusion is consistent with expectation regarding to field of use of the selected models.

References

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Experiments in a high-amplitude Kinoshita

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McCoy, A. (2009). Mass exchange in a shallow

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(1990). Flow Near Sloped Bank in Curved

Channel. Journal of Hydraulic Engineering.

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Cambridge: University Press.

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Structures in Fluids, Plasmas and Nonlinear

Media.

[7] Zilker D.P., Cook G.W. and Hanratty T.J.:

Influence of the amplitude of a solid wavy wall

on a turbulent flow. Part 1. Non-separated

flows, J. Fluid Mech., 82, 1977, 29-51.

[8] Zilker D.P. and Hanratty T.J.: Influence of the

amplitude of a solid wavy wall on a turbulent

flow. Part 2. Separated flows, J. Fluid Mech.,90,

1979, 257-271.

[9] Hudson J.D.: The effect of a wavy boundary on

turbulent flow, Ph.D. Thesis, University of

Illinois, Urbana, IL, 1993.

[10] Hudson J.D., Dykhno L. and Hanratty T.J.:

Turbulence production in flow over a wavy

wall, Exper. Fluids,20 , 1996, 257

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simulation of separated turbulent flow over

wavy boundary, In: Hirschel E.H. (Ed.): Flow

simulation with high performance computers,

Notes on numerical fluid mechanics, 52 , 1996,

227-241.

[12] Cherukat P., Na Y., Hanratty T.J. and

McLaughlin J.B.: Direct numerical simulation

of a fully developed turbulent flow over a wavy

wall, Theoret. Comput. Fluid Dynamics, 11,

1998, 109-134.

[13] Yoon H.S., El-Samni O.A., Huynh A.T., Chun

H.H., Kim H.J., Pham A.H. and Park I.R.:

Effect of wave amplitude on turbulent flow in a

wavy channel by direct numerical simulation,

Ocean Engineering, 36 , 2009, 697-707.

[14] Pierre S., Large eddy simulation for

incompressible flows, An introduction, second

edition, 2010.

[15] CFD Online.www.cfd-online.com/wiki/

Turbulence_intensity , accessed May 2012.

[16] Hjertager, Bjrn H. Turbulence Theory and Modelling, Lecture Notes, Aalborg University Esbjerg, Denmark (2005).

[17] Hjertager, Bjrn H. Computational Analysis of Fluid Flow Processes, Lecture Notes, Aalborg University Esbjerg, Denmark (2007).

[18] Versteeg, H K; Malalasekera, W.An Introduction to Computational Fluid Dynamics,

The Finite Volume Method, Second edition, Pearson Education Limited, Essex, England

(2007).

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http://openfoam.cfd-online.com/cgi-bin/forum

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1598-1605.

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Table (5) The (x/) location of separation and reattachment points for (a/)=0.25, and Re=6000.

Turbulence Models Section A Section B Section C Section D Section E

1 k- 1.063 1.464

1.878 2.578

2.864 3.596

3.896 4.583

4.882 5.805

2 Realizable k- 1.140 1.421

1.902 2.522

2.899 3.576

3.903 4.577

4.890 5.797

3 RNG k- 1.115 1.433

1.933 2.534

2.768 3.566

3.867 4.580

4.888 5.801

4 Menter SST k- 1.077 1.468

1.888 2.588

2.888 3.599

3.892 4.588

4.885 5.808

5 Launder Sharma k- 1.045 1.394

1.765 2.501

2.793 3.511

3.866 4.590

4.891 5.794

6 Lam Bremhorst k- 1.055 1.414

1.783 2.522

2.725 3.525

3.879 4.593

4.893 5.789

7 Nonlinear Shih k- 1.043 1.409

1.780 2.528

2.713 3.527

3.882 4.588

4.889 5.793

8 LES 1.072 1.467

1.894 2.579

2.871 3.592

3.893 4.585

4.880 5.809

A B C D E

Table (4) Comparison between turbulence models according to max. and min. values of flow properties at Re=3000.

Turbulence

Models U

(/) (/) Ux

(/) Uy

(/) Uz

(2/2) k

(2/3)

(/2)

)

(/2)

x

1 k- 4.0583 0.0000

4.0581 -0.7827

1.3922 -1.3931

0.5893 -0.5903

0.5027 0.0043

1375 0.0671

0.5805 0.0050

---- 0.0416 -0.1674

2 Realizable

k- 4.3438 0.0000

4.3438 -0.8445

1.4043 -1.4043

0.5698 -0.5702

0.4800 0.0000

1294 0.0238

0.5600 0.0000

---- 0.0408 -0.1651

3 RNG k- 4.2317 0.0000

4.2316 -0.8265

1.4027 -1.4015

0.6085 -0.6097

0.4884 0.0033

1319 0.0682

0.5640 0.0039

---- 0.0407 -0.1655

4 Menter SST k- 4.2167 0.0000

4.2163 -0.8673

1.3780 -1.3760

0.5543 -0.5549

0.2500 0.0000

---- 0.3000 0.0000

1x105

0.770 0.0421 -0.1520

5 Launder

Sharma k- 4.2961 0.0000

4.2960 -0.8780

1.3694 -1.3567

0.5741 -0.5816

0.7500 0.0000

2143 0.0002

0.8600 0.0000

---- 0.0402 -0.1249

6 Lam Bremhorst

k- 4.3629 0.0000

4.3628 -0.8860

1.3881 -1.3877

0.5564 -0.5554

0.1100 0.0000

2345 0.0120

0.0228 0.0000

---- 0.0425 -0.1502

7 Nonlinear Shih

k- 4.2424 0.0000

4.2054 -0.8860

1.3566 -1.3443

0.5564 -0.5554

0.1400 0.0000

2224 0.0370

0.0264 0.0000

---- 0.0411 -0.1498

8 LES 4.1422 0.0000

4.3628 -0.8860

1.3881 -1.3877

0.5564 -0.5554

0.1100 0.0000

2113 0.0240

0.0228 0.0000

---- 0.0421 -0.1502

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Time (min)

Velocity Magnitude

( / ) Velocity component in y-direction

( / ) Sub-grid eddy viscosity

( 2/ 2)

32

58

95

191

436

500

Fig. (4) Transient results for LES case, z/Lz=0.5, and Re=6000.