Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 21, No. 4 (November 2008) 397-406   

PDF URL: http://www.ije.ir/Vol21/No4/A/6-940.pdf  
downloaded Downloaded: 121   viewed Viewed: 2312

  APPLICATION OF THE SCHWARZ-CHRISTOFFEL TRANSFORMATION IN SOLVING TWO-DIMENSIONAL TURBULENT FLOWS IN COMPLEX GEOMETRIES
 
 
R. Moosavi

Department of Mechanical Engineering, Yasouj University
P.O. Box 75914, Yasouj, Iran
rmoosavi81@gmail.com


S. A. Gandjalikhan Nassab*

Department of Mechanical Engineering, Shahid Bahonar University
P.O. Box 76169-133, Kerman, Iran
ganjali2000@yahoo.com

* Corresponding Author
 
 
( Received: March 12, 2008 – Accepted in Revised Form: May 09, 2008 )
 
 

Abstract    In this paper, two-dimensional turbulent flows in different and complex geometries are simulated by using an accurate grid generation method. In order to analyze the fluid flow, numerical solution of the continuity and Navier-Stokes equations are solved using CFD techniques. Considering the complexity of the physical geometry, conformal mapping is used to generate an orthogonal grid by means of the Schwarz-Christoffel transformation. The standard k-ε turbulence model is employed to simulate the mean turbulent flow field, using a linear low-Re k-ε model for near wall region. The governing equations are transformed in the computational domain and the discretized forms of these equations are obtained by the control volume method. Finite difference forms of the governing equations are solved in the computational plane and the SIMPLE algorithm is used for the pressure-velocity coupling. The important part of the present work is based on the numerical integration of Schwraz-Christoffel transformation in grid generation for simulating fluid flow in different complex geometries. To validate the computational results, the theoareticil data is compared with that of theoretical results achieved by other investigators, which are in reasonable agreement

 

Keywords    Schwarz-Christoffel Transformation, Grid Generation, Turbulent Flow

 

References   

1. Thompson, J. F., Warsi, Z. U. A. and Mastin, C. W., “Boundary-Fitted Coordinate System for Numerical Solution of Partial Differential Equations”, A Review, Journal of Computational Physics, Vol. 47, (1982), 1-108.

2. Sridhar, K. P. and Davis, R. T., “A Schwarz-Christoffel Method of Generating Two-Dimensional flow Grids”, Journal of Fluid Engineering, Vol. 197, (1985), 330-337.

3. Moayeri, M. S. and Taghdiri, M. A., “Boundary Conforming Orthogonal Grids for Internal flow Problems”, Iranian Journal of Science and Technology, Vol. 17, No. 3, (1993), 191-201.

4. Milne-Thomson, L. M., “Theoretical Hydrodynamics”, 4th Edition, Macmillan, New York, U.S.A., (1960).

5. Mansouri, S. H., Hosseini Sarvari, S. M., Keshavarz, A. and Rahnama, M., “An Analytical Numerical Method for Grid Generation by Mathematica”, Proc. of 26th Annual Iranian Mathematics Conference, Shahid Bahonar University of Kerman, Kerman, Iran, Vol. 1, (1995), 251-258.

6. Mansouri, S. H., Mehrabian, M. A. and Hosseini Sarvari, S. M., “Simulation of Ideal External and Internal flows with Arbitrary Boundaries using Schwarz-Christoffel Transformation”, Int. Journal of Eng., Trans. A, Vol. 17, No. 4, (2004), 405-414.

7. Chowdhury, S. J. and Ahmadi, G., “A Thermohydrodynamically Consistent Rate Dependent Model for Turbulence-Part II. Computational Results”, Int. Journal of Non-Linear Mechanics, Vol. 27, No. 4, (1992), 705-718.

8. Yap, C. R., “Turbulent Heat and Momentum Transfer in Recirculation and Impinging Flows”, Ph.D. Thesis, Faculty of Technology, University of Manchester, Manchester, U.K., (1987).

9. Raisee, M. and Hejazi, S. H., “Application of Linear and Non-Linear Low-Re k-ε Models in Two Dimensional Predictions of Convective Heat Transfer in Passages with Sudden Contractions”, Int. Journal of Heat and Fluid Flow, Vol. 28, (2007), 429-440.

10. Patankar, S. V. and Spalding, B. D., “A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows”, Int. Journal of Heat and Mass Transfer, Vol. 15, (1972), 1787-1806.

11. Yilmaz, I. and Oztop, H. F., “Turbulence Forced Convection Heat Transfer Over Double Forward Facing Step Flow”, Int. Communication in Heat and Mass Transfer, Vol. 33, (2006), 508-517.

12. Le, H., Moin, P. and Kim, J., “Direct Numerical Simulation of Turbulent flow Over a Backward-Facing Step”, J. Fluid Mech., Vol. 330, (1997), 349-374.

13. Kim, J., Kline, S. J. and Johnston, J. P., “Investigation of Separation and Reattachment of a Turbulent Shear Layer: Flow Over a Backward Facing Step”, Report MD-37, Thermo-Science Division, Dept. of Mech. Engng, Stanford University, Stanford, CA, U.S.A., (1978).


Download PDF 



International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir