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Keywords: finite element method, Theta method, implicit scheme, streamline-upwind/Petrov-Galerkin method, compressible Navier-stokes equation, Sutherland law, ideal gas law, shock-capturing term.

Summary

The objective of this paper is an analysis of a body in a compressible viscous flow using the finite element method. Generally, it is assumed that the fluid is incompressible when a fluid flow is analyzed, but fluid is compressive in many actual cases. As an example of an actual flow, there is a sonic flow. The sonic flow is classified by its Mach number. The Mach number is expressed by the ratio of the relative velocity of the fluid flow and the acoustic velocity. When the Mach number of the flow is higher than 0.3, the compressible effect cannot be disregarded. Therefore, it is necessary for compressibility to analyze the fluid more accurately and widely.

The basic equation to consider compressibility is the compressible Navier-Stokes equation. The ideal gas equation is applied to solve pressure and to analyze a pressure field around a body. The Sutherland equation is used to represent the temperature dependence of µ. As a spatial discritization, the finite element method using the streamline-upwind / Petrov-Galerkin (SUPG) method is applied. As a temporal discritization, the Theta method including an implicit scheme is applied. The shock-capturing term is employed to suppress numerical oscillation.

In the numerical studies, the compressible viscous flows using two shape types for the body are analyzed and the occurrence of shock wave are compared. As case 1, the shape of body is set as a cylinder. As case 2, the shape of body is set as NACA0020. The Reynolds number is set to 10000. The Mach number M_infinity is set to 0.3. The free-stream parameters are taken to be rho=1.0, u₁=1.0, u₂=0.0, theta=1.0. The free-stream value of total specific energy e is calculated using these free-stream parameter. The value of the parameters are Theta=0.9, Delta t=0.0001 and epsilon=1.0.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 94 PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by: Paper 156 An Analysis of Compressible Viscous Flows around a Body using the Finite Element Method S. Nasu and M. Kawahara Department of Civil Engineering, Chuo University, Tokyo, Japan doi:10.4203/ccp.94.156 purchase the full-text of this paper Full Bibliographic Reference for this paper S. Nasu, M. Kawahara, "An Analysis of Compressible Viscous Flows around a Body using the Finite Element Method", in , (Editors), "Proceedings of the Seventh International Conference on Engineering Computational Technology", Civil-Comp Press, Stirlingshire, UK, Paper 156, 2010. doi:10.4203/ccp.94.156 Keywords: finite element method, Theta method, implicit scheme, streamline-upwind/Petrov-Galerkin method, compressible Navier-stokes equation, Sutherland law, ideal gas law, shock-capturing term. Summary The objective of this paper is an analysis of a body in a compressible viscous flow using the finite element method. Generally, it is assumed that the fluid is incompressible when a fluid flow is analyzed, but fluid is compressive in many actual cases. As an example of an actual flow, there is a sonic flow. The sonic flow is classified by its Mach number. The Mach number is expressed by the ratio of the relative velocity of the fluid flow and the acoustic velocity. When the Mach number of the flow is higher than 0.3, the compressible effect cannot be disregarded. Therefore, it is necessary for compressibility to analyze the fluid more accurately and widely. The basic equation to consider compressibility is the compressible Navier-Stokes equation. The ideal gas equation is applied to solve pressure and to analyze a pressure field around a body. The Sutherland equation is used to represent the temperature dependence of µ. As a spatial discritization, the finite element method using the streamline-upwind / Petrov-Galerkin (SUPG) method is applied. As a temporal discritization, the Theta method including an implicit scheme is applied. The shock-capturing term is employed to suppress numerical oscillation. In the numerical studies, the compressible viscous flows using two shape types for the body are analyzed and the occurrence of shock wave are compared. As case 1, the shape of body is set as a cylinder. As case 2, the shape of body is set as NACA0020. The Reynolds number is set to 10000. The Mach number M_infinity is set to 0.3. The free-stream parameters are taken to be rho=1.0, u₁=1.0, u₂=0.0, theta=1.0. The free-stream value of total specific energy e is calculated using these free-stream parameter. The value of the parameters are Theta=0.9, Delta t=0.0001 and epsilon=1.0. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £125 +P&P)
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