Abstract
In this paper, a new algorithm is developed to solve a two dimensional supersonic flow around a wedge-shaped airfoil. The MacCormack predictor-corrector method is utilized to develop a solution. To further investigate the flow properties, a numerical algorithm written in C++ has been compiled so that it may be compared to commercial softwares. The developed algorithm is compiled and run with the initial conditions of a free stream Mach number of 2 while the wedge angle is set at 15º. The compiled program revealed that the flow velocities increased without bound. Adjustment of this condition was achieved by adding artificial dissipation. The addition of dissipation term into the code resulted stable output and the presence of a shock. Same case was also simulated with ANSYS Fluent and CFL3D softwares using second order discretization.
Keywords
References
- Jameson, A., Baker, T. (1987). Improvements to the aircraft Euler method. Proceedings of the 25th AIAA Aerospace Sciences Meeting; Reno, USA.
- Beam, R.M., Warming, R.F., (1976). An implicit finite-difference algorithm for hyperbplic systems in conservation law form. J. Of Comp. Physics, 22(1), 87-110.
- Beam, R.M., Warming, R.F., (1978). An implicit factored scheme fort he compressible Navier-Stokes equations. AIAA Journal, 16(4), 393-402.
- Degani, A.T., Fox, G.C. (1994). Derivation of the Beam and Warming algorithm for compressible Navier-Stokes equations. NPAC Technical Report SCCS 675.
- Durran, D.R. (2010). Numerical methods for fluid dynamics. Springer.
- Ganzha, V.G., Vorozhtsov, E.V. (1996). Computer aided analysis of difference schemes for partial differential equations. Wiley.
- Jameson, A., Schmidt, W., Turkel, E. (1981). Numerical solution of the Euler equations by finite volüme methods using Runge-Kutta time stepping schemes. AIAA Paper 1259.
- Konangi, S., Palakurthi, N.K., Ghia, U. (2016). Von Neuman stability analysis of a segregated pressure-based solution scheme for one-dimensional and two-dimensional flow equations. J. of Fluids Eng., 138(10):101401.
- Laney, C.B. (1998). Computational gas synamics. Cambridge Universiy press, New York.
- Lax, P.D., Wendroff, B. (1960). Systems of conservation laws. Comm. Pure Appl. Math, 13, 217-237.
- Leveque, R.J. (1992). Numerical methods of conservation laws. Springer, 2nd edition.
- MacCormack, R.W. (1969). The effect of viscosity in hypervelocity impact cratering. AIAA, 69-354, American Institute of Aeronautics and Astrophysics, Cincinnati.
- MacCormack, R.W. (1982). A numerical method for solving the equations of compressible viscous flow. AIAA J., 20(9), 1275-1281.
- Strikwerda, J.C. (2004). Finite difference schemes and partial differential equations. Society for industrial and applied mathematics, Philadelphia, 2nd edition.
- Von Neuman, J. Richtmyer, R.D. (1950). A method fort he numerical calculation of hydrodynamic shocks. J. Appl. Phys., 21(3), 232-237.
Abstract
Bu makalede, kama şeklindeki bir kanat profili etrafındaki iki boyutlu süpersonik akışı çözmek için yeni bir algoritma geliştirilir. Çözümü geliştirmek için MacCormack kestirici-düzeltici yönteminden fayda sağlanır. Akış özelliklerini daha detaylı incelemek için C++ yazılım dilinde bir sayısal algoritma derlenmiş ve böylece ticari yazılımlar ile kıyas yapılması sağlanmıştır. Başlangıç şartları olarak serbest akım Mach sayısı 2 ve kama açısı 15º olacak şekilde geliştirilen algoritma derlenmiş ve çalıştırılmıştır. Derlenen programın açığa çıkardığı sonuç ile akış hızlarının sınırsız şekilde arttığı gözlemlenmiştir. Bu durumun düzeltilmesi ise algoritmaya suni dağılım terimi eklenerek yapılmıştır. Suni dağılım teriminin geliştirilen koda eklenmesi ile sonuç istikrarlı olmuş ve beklenen şokun gözlemlenmesine neden olmştur. Aynı durum ayrıca ANSYS Fluent ve CFL3D yazılımları ile ikinci derecede kesikli hale getirilerek de simüle edilmiştir.
Keywords
References
- Jameson, A., Baker, T. (1987). Improvements to the aircraft Euler method. Proceedings of the 25th AIAA Aerospace Sciences Meeting; Reno, USA.
- Beam, R.M., Warming, R.F., (1976). An implicit finite-difference algorithm for hyperbplic systems in conservation law form. J. Of Comp. Physics, 22(1), 87-110.
- Beam, R.M., Warming, R.F., (1978). An implicit factored scheme fort he compressible Navier-Stokes equations. AIAA Journal, 16(4), 393-402.
- Degani, A.T., Fox, G.C. (1994). Derivation of the Beam and Warming algorithm for compressible Navier-Stokes equations. NPAC Technical Report SCCS 675.
- Durran, D.R. (2010). Numerical methods for fluid dynamics. Springer.
- Ganzha, V.G., Vorozhtsov, E.V. (1996). Computer aided analysis of difference schemes for partial differential equations. Wiley.
- Jameson, A., Schmidt, W., Turkel, E. (1981). Numerical solution of the Euler equations by finite volüme methods using Runge-Kutta time stepping schemes. AIAA Paper 1259.
- Konangi, S., Palakurthi, N.K., Ghia, U. (2016). Von Neuman stability analysis of a segregated pressure-based solution scheme for one-dimensional and two-dimensional flow equations. J. of Fluids Eng., 138(10):101401.
- Laney, C.B. (1998). Computational gas synamics. Cambridge Universiy press, New York.
- Lax, P.D., Wendroff, B. (1960). Systems of conservation laws. Comm. Pure Appl. Math, 13, 217-237.
- Leveque, R.J. (1992). Numerical methods of conservation laws. Springer, 2nd edition.
- MacCormack, R.W. (1969). The effect of viscosity in hypervelocity impact cratering. AIAA, 69-354, American Institute of Aeronautics and Astrophysics, Cincinnati.
- MacCormack, R.W. (1982). A numerical method for solving the equations of compressible viscous flow. AIAA J., 20(9), 1275-1281.
- Strikwerda, J.C. (2004). Finite difference schemes and partial differential equations. Society for industrial and applied mathematics, Philadelphia, 2nd edition.
- Von Neuman, J. Richtmyer, R.D. (1950). A method fort he numerical calculation of hydrodynamic shocks. J. Appl. Phys., 21(3), 232-237.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | April 15, 2020 |
| Published in Issue | Year 2020 Issue: 18 |
