Comparison between Finite Volume Method (FVM) Based on Inviscid and Viscous Flow with Experimental and Fluent Results
Applied and Computational Mathematics
Volume 4, Issue 1-1, January 2015, Pages: 12-17
Received: Jan. 4, 2015; Accepted: Jan. 26, 2015; Published: Feb. 9, 2015
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Abobaker Mohammed Alakashi, Department of Aeronautic, University Tun Hussein Onn Malaysia, Johor, Malaysia
Bambang Basuno, Department of Aeronautic, University Tun Hussein Onn Malaysia, Johor, Malaysia
Hasan Taher. M. Elkamel, Department of Aeronautic, University Tun Hussein Onn Malaysia, Johor, Malaysia
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The Finite Volume Method (FVM) is currently the most popular method in CFD. The main reason is that it can resolve some of the difficulties that the other methods have. Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems [1]. Finite volume method can be classified into three groups: (1) Cell-centered scheme, (2) Cell-vertex scheme with overlapping control volumes and (3), Cell-vertex scheme with dual control volumes [2]. The present work used Finite volume based Cell Cell-centered. This approach used the grid cell identical to its control volume. While in view of a manner the grid cells in this work can be defined numerically, it can follow as a structured grid based on Elliptic grid generation PDEs [3]. Computer code had been developed by using a cell centered Finite volume scheme combined with structured grid approach. The computer codes applied for the case of compressible flow past through an airfoil NACA 0012, in which the flow problem can be treated as purely inviscid flow or as the flow with viscous effect but considered to be as a laminar flow. The comparison result presented in term of pressure coefficient Cp for different angle of attack using available experimental result and the result provided by Fluent software. In term for the case of flow problem treated as an inviscid flow, both the developed computer code and Fluent software produce the result closed to the experimental result. However if the developed computer code as well as fluent software treated the flow problem to include the viscous effect by considering them as a laminar flow both are slightly deviate with the experimental results. Strictly speaking the present developed computer code give a similar result as the experimental result, which both showing that this type of airfoil having a sensitive effect to the angle of attack. A small change of angle of attack will produce a significant change to the location of shock will occurred.
Finite Volume Method, Cell Cell-Centered scheme, Navier-Stokes, Euler Equation
To cite this article
Abobaker Mohammed Alakashi, Bambang Basuno, Hasan Taher. M. Elkamel, Comparison between Finite Volume Method (FVM) Based on Inviscid and Viscous Flow with Experimental and Fluent Results, Applied and Computational Mathematics. Special Issue: New Orientations in Applied and Computational Mathematics. Vol. 4, No. 1-1, 2015, pp. 12-17. doi: 10.11648/j.acm.s.2015040101.13
LeVeque, Randall J. Finite volume methods for hyperbolic problems. Vol. 31. Cambridge university press, 2002
J. Blazek, ‘Computational Fluid Dynamics Principles and Applications’ 2nd Ed.Switzerland, 2001
K. A. Hoffman and S.T .Chiang, Computational-Fluid-Dynamics Volume I, Engineering Education System, USA, 2000.
J. D. Anderson, Jr, Computational Fluid Dynamics, the basics with applications, McGraw-Hill, 1995.
J.C. Tannehill, D.A. Anderson. D. A, and R.H. Pletcher , Computational Fluid Mechanics and Heat Transfer, 2nd Ed., Taylor & Francis, New York, 1997.
J. H. Ferziger, and M. Perić, Computational Methods for Fluid Dynamics, Springer, 1996.
Causon, D. M., C. G. Mingham, and L. Qian. Introductory Finite Volume Methods for PDEs. Bookboon, 2011.
RabahHaoui, Effect of Mesh Size on the Viscous Flow Parameters of an Axisymmetric Nozzle.,”World Academy of Science, Engineering and Technology 59, 2011.
Thompson, Joe F., Bharat K. Soni, and Nigel P. Weatherill, eds. Handbook of grid generation. CRC press, 2010.
T. Cebeci, and A.M.O. Smith, Analysis of Turbulence Boundary Layers, London: Academic Press, 1974.
H. Sclichting, and K, Gertsen, Boundary layer theory. 8th Revised and Enlarged Edition, Germany: Springer, pp.392-400 2000.
Sorenson, Reese L. "A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation." NASA Technical Memorandum 81198 (1980): 1-58.
Morton, Keith W., and David Francis Mayers. Numerical solution of partial differential equations: an introduction. Cambridge university press, 2005.
T.D. Taylor, “Numerical Method for Predicting Subsonic, Transonic, and Supersonic Flow”, France, Tech. Rep. AGARD-AG-187, 1974.
D.G. Korn, “Computation of Shock Free Transonic Flow for Airfoil Design”, AEC Research and Development Report, New York, Courant Inst. of Mathematics and Science, NYO-1480-125, 1969
C. Kroll, M. Aftosmis, and D. Gaitonde, “An Examination of Several High Resolution Schemes Applied to Complex Problems in High Speed Flows”, Final Report Wright Laboratory, Ohio, AD-A250 814, 1992.
A. Arias, O. Falcinelli, N.J. Fico, and S. Elaskar, “Finite Volume Simulation of a Flow Over a Naca 0012 Using Jameson, Maccormack, Shu and Tvd Esquemes”, Mechanical Computational, vol. 16, Córdoba, pp. 3097-3116, 2007.
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