Numerical Analysis of Turbulent Flow Around Two-Dimensional Bodies Using Non-Orthogonal Body-Fitted Mesh

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Abstract

This paper deals with the numerical simulation of a turbulent flow around two-dimensional bodies by the finite volume method with non-orthogonal body-fitted grid. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of scalar and vector variables. Turbulence is modeled by the k- ε turbulence model and wall functions are used to bridge the solution variables at the near wall cells and the corresponding quantities on the wall. A simplified pressure correction equation is derived and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The numerical procedure is validated by comparing the computed pressure distribution on the surface of NACA 0012 and NACA 4412 hydrofoils for different angles of attack with experimental data. The grid dependency of the solution is studied by varying the number of cells of the C-type structured mesh. The computed lift coefficients of NACA 4412 hydrofoil at different angles of attack are also compared with experimental results to further substantiate the validity of the proposed methodology.

[1] Rhie C.M. (1981): A Numerical Study of the Flow Past an Isolated Airfoil with Separation. – PhD Thesis, Dept. of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign.

[2] Peric M. (1985): A Finite Volume Method for the Prediction of Three-Dimensional Fluid Flow in Complex Ducts. – Ph.D. Thesis, University of London.

[3] Demirdzic I., Gosman A.D., Issa R.I. and Peric M. (1987): A calculation procedure for turbulent flow in complex geometries. – Computers and Fluids, vol.15, pp.251-273.

[4] Karki K.C and Patanker S.V. (1988): Calculation procedure for viscous incompressible flows in complex geometries. – Numerical Heat Transfer, vol.14, pp.295-307.

[5] Majumdar S. (1988): Role of under-relaxation in momentum interpolation for calculation of flow with nonstaggered grids. – Numerical Heat Transfer, Part B, vol.13, pp.125-132.

[6] Choi S.K. (1999): Note on the use of momentum interpolation method for unsteady flows. – Numerical. Heat Transfer, Part A, vol.36, pp.545-550.

[7] Masuko A. and Ogiwara S. (1990): Numerical simulation of viscous flow around practical Hull form. – Fifth International Conference on Numerical Ship Hydrodynamics, pp.211-224.

[8] Yu B., Tao W. and Wei J. (2002): Discussion on momentum interpolation method for collocated grids of incompressible flow. – Numerical Heat Transfer, Part B, vol.42, pp.141-166.

[9] Mulvany N., Tu J.Y., Chen L. and Anderson B. (2004): Assessment of two-equation turbulence modeling for high Reynolds number hydrofoil flow. – International Journal of Numerical Methods in Fluids, vol.45, pp.275-299.

[10] Kuzmin D. and Mierka O. (2006): On the implementation of the k-turbulence model in incompressible flow solvers based on a finite element discretization. – International Conference on Boundary and Interior Layers, Bail 2006, Germany, pp.1-8.

[11] Demirdzic I. (2015): On the discretization of diffusion term in finite-volume continuum mechanics. – Numerical Heat Transfer, Part B, vol.68, pp.1-10.

[12] Martınez J., Piscagliaa F., Montorfanoa A., Onoratia A. and Aithalb S.M. (2017): Influence of momentum interpolation methods on the accuracy and convergence of pressure-velocity coupling algorithms in Open FOAM. – Journal of Computational and Applied Mathematics, vol.309, pp.654-673.

[13] Patanker S.V. (1980): Numerical Heat Transfer and Fluid Flow. – New York: McGraw-Hill.

[14] Demirdzic I. and Peric M. (1990): Finite volume method for prediction of fluid flow in arbitrary shaped domains with moving boundary. – International Journal of Numerical Methods in Fluids, vol.10, pp.771-790.

[15] Peric M. (1990): Analysis of pressure-velocity coupling on non-orthogonal grids. – Numerical Heat Transfer, Part B, vol.17, pp.63-82.

[16] Patanker S.V. and Spalding D.B. (1972): A calculation procedure for heat, mass and momentum transfer in threedimensional parabolic flows. – International Journal of Heat and Mass Transfer, vol.15, pp.1787–1806.

[17] Stone H.L. (1968): Iterative solution of implicit approximations of multidimensional partial differential equations. – SIAM. Journal on Numerical Analysis, vol.5, pp.530-558.

[18] Pinkerton R.M. (1936): Calculated and Measured Pressure Distributions over the Mid Span Section of the NACA 4412 Airfoil. – NACA Report No.563, National Advisory Committee for Aeronautics.

[19] Coles D. and Wadcock (1979): Flying-Hot-Wire Study of Flow Past an NACA 4412 Airfoil at Maximum Lift. – AIAA Journal, vol.17, No.4, pp.321-329.

[20] Kermeen R.W. (1956): Water Tunnel Tests of NACA 4412 and WALCHNER PROFILE 7 Hydrofoils in Noncavitating and Cavitating flows. – California Institute of Technology, Hydrodynamics Laboratory, Report No. 47-5.

[21] Gregory N. and O’Reilly C.L. (1970): Low Speed Aerodynamic Characteristics of NACA 0012 Airfoil Section, Including the Effects of Upper Surface Roughness Simulation Hoarfrost. – National Physical Laboratory, Teddington, England, Aero Report No.1308.

International Journal of Applied Mechanics and Engineering

The Journal of University of Zielona Góra

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CiteScore 2018: 0.4

SCImago Journal Rank (SJR) 2018: 0.163
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