شبیه‌سازی عددی جریان غیرلزج در رژیم ماوراء صوت بروش بدون شبکه با اعمال اثرات گاز داغ

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار، گروه مهندسی مکانیک، دانشگاه شهید مدنی آذربایجان، تبریز، ایران

2 دانشجوی کارشناسی ارشد، گروه مهندسی مکانیک، دانشگاه شهید مدنی آذربایجان، تبریز، ایران

چکیده

در این تحقیق برای حل جریان غیر لزج ماوراء صوت از روش بدون شبکه مبتنی بر روش کمترین مربعات خطا و سری تیلور استفاده شده است. بمنظور پایدارسازی حل و جلوگیری از نوسانات ناخواسته خصوصاً در همسایگی موج ضربه­ای از جملات مشتقات مرتبه دوم و چهارم به عنوان استهلاک مصنوعی استفاده شده است. در این تحقیق فرض شده است که واکنش های شیمیایی صورت گرفته در اثر بالا رفتن دما به صورت تعادلی بوده و از نمودارهای استخراج شده برای تخمین نسبت گرمای ویژه استفاده گردیده است. برای گسسته سازی زمانی معادلات حاکم از روش صریح چهار مرحله ای رانگ-کوتا استفاده شده و برای تسریع همگرائی از روش هموارسازی مانده ها و گام زمانی محلی استفاده شده است. نتایج حاصل از حل با روش بدون شبکه با نتایج روش حجم کنترل با توزیع نقاط یکسان مقایسه شده است و مقایسه ها نشان میدهد که استفاده از روش بدون شبکه در مقایسه با روش حجم محدود دارای همگرایی بهتر و زمان محاسباتی کمتری است. همچنین استفاده از مدل گاز واقعی و اثرات گاز داغ به جای استفاده از مدل گاز ایده آل منجر به محل دقیق موج ضربه­ای می شود و توزیع دما و فشار پشت موج ضربه ای با واقعیت تطابق بهتری دارد.

کلیدواژه‌ها


[1] Anderson J.D., Hypersonic and High Temperature Gas Dynamic, second ed., McGrawHill, New York, 2006.
[2] Tannehill J.C., Mugge P.H., Improved curve fits for the thermodynamics properties of equilibrium air suitable for numerical computation using Time-Depend or Shock-Capture  method, NASA-CR-178411, 1974.
[2] Johnston I.A., Simulation Of Flow around Hypersonic Blunt-Nosed Vehicles for the Calibration of Air Data System, A thesis submitted for the degree of Doctor of Philosophy, University of Queensland , 1999.
[2] Hashemi M.Y., Jahangirian A., Simulation of high-speed flows by an unstructured grid implicit method including real gas effects, Int. J. Numer. Meth. Fluids, Vol.56, pp. 1281–1287, 2008.
[3] Lohner R., Onate E., A General Advancing Front Technique for Filling Space with Arbitrary Objects, International Journal for numerical methods in Engineering, Vol.64, No.12, pp. 1977-1991, 2004.
[4] Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P., Meshless methods: An overview and recent developments, Comput, Methods Appl. Mech. Eng., Vol.139, pp.3-47, 1996.
[5] Gingold R.A., Monaghan J.J., Smoothed Particle Hydrodynamics: Theory and Application to Nonspherical Stars, Monthly Notices of the Royal Astronomical Society, Vol.181, pp.275-389, 1977.
[6]Lesoinne M., Kaila, V., Meshless aeroelastic simulations of aircraft with large control surface deflections, AIAA paper 2005-1089, AIAA 43rd Aerospace Sciences Meeting and Exhibit, Reno, January 2005.
[7] Atluri S.N., Kim H.G., Cho J.Y., A critical assessment of the truly meshless local petrov-galerkin (mlpg) and local boundary integral equation (lbie) methods, Computational Mechanics, Vol.24, pp.348-372, 1999.
[8] Lin H., Atluri S.N., The meshless local petrov-galerkin (mlpg) method for solving incompressible navier-stokes equations, CMES, Vol.2, No.2, pp.117-142, 2001.
[9] Kansa E.J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-i, Computers Math. Applic., Vol.19, pp.127-145, 1990.
[10] Kansa E.J., Multiquadrics-a scattered data approximation scheme with applications to computational fluid-dynamics-ii, Computers Math. Applic., Vol.19, pp.147-161, 1990.
[11] Mavriplis D.J., Revisiting the least-squares procedure for gradient construction on unstructured meshes, AIAA paper 2003-3986, AIAA 16th Computational Fluid Dynamics Conference, Orlando, FL, June 2003.
[12] Batina J.T., A gridless euler/navier-stokes solution algorithm for complex aircraft applications, AIAA paper 1993-0333, AIAA 31st Aerospace Sciences Meeting and Exhibit, Reno, NV, January 1993.
[13] Liu J., Su S., A potentially gridless solution method for the compressible euler/navier-stokes equations”, AIAA paper 1996-0526, AIAA 34th Aerospace Sciences Meeting and Exhibit, Reno, NV, January, 1996.
[14] Onate E., Idelsohn S., A mesh-free finite point method for advective-diffusive transport and fluid flow problems, Computational Mechanics, Vol.212, pp.83-292, 1998.
[15] Lohner R., Sacco C., Orlate E., Idelsohn S., A finite point method for compressible flow, Int. J. Numer. Meth. Eng., Vol.53, pp.1765-1779, 2002.  
[16] Ramesh V., Deshpande S.M., Euler computations on arbitrary grids using lskum, In N. Satofuka, editor, Computational Fluid Dynamics 2000: Proceedings of the First International Conference on Computational Fluid Dynamics, pp. 783-784, Springer-Verlag, 2000.
[17] Harish G., Pavanakumar M., Store separation dynamics using grid-free Euler solver, AIAA paper 2006-3650, AIAA 24th Applied Aerodynamics Conference, San Francisco, CA, June 2006.
[18] Morinishi K., Effective accuracy and conservation consistency of gridless type solver, In N. Satofuka, editor, Computational Fluid Dynamics 2000: Proceedings of the First International Conference on Computational Fluid Dynamics, pp. 325-330. Springer-Verlag, 2000.
[19] Balasubramanyam S., Rao S.V.R., A grid-free upwind relaxation scheme for inviscid compressible flows, International Journal for Numerical Methods in Fluids, Vol.51, pp.159-196, 2006.
[20] Katz A., Jameson A. A Meshless Volume Scheme, 19th AIAA computational Fluid Dynamics Conference, AIAA paper 2009-3534, 2009.
[21] Katz A., Jameson A., A Comparison of Various Meshless Schemes Within Unified Algorithm, 47th AIAA aerospace sciences meeting and exhibit, AIAA paper 2009-0596, 2009.
[22] Hashemi M.Y., Jahangirian A., An efficient implicit mesh-less method for compressible flow calculations, Int. J. Numer. Meth. Fluids, Vol.67, pp. 754–770, 2011.
[23] Hashemi Y., Jahangirian  A., Implicit fully mesh-less method for compressible viscous flow calculations, Journal of Computational and Applied Mathematics, Vol.235, pp. 4687–4700, 2011.
[24] Hlsenrath J., Klein M., Tables of Thermodynamics Properties of Air in Chemical Equilibrium Including Second  Virial Correction  From 1500 to 15000K, Arnold Engineering Development Center Report No. Aedc-Tr-65 - 68, 1965.
[25] Lou H, Baum J.D., Lohner R., A Hybrid Cartesian grid and gridless method for compressible flows, Journal of Computational Physics, Vol.214, pp. 618-632, 2006.
[26] Hoffmann K.A., Chiang S.T., Computational Fluid Dynamics for Engineers, Vol.1, second ed., Engineering Education System, 1993.
[27] Jameson A., Analysis and Design of Numerical Schemes for Gas Dynamics, Journal of Computational Fluid Dynamics, Vol.4, pp. 171-215, 1995.
[28] Jameson A., Schmidt W., Turkel, E., Numerical Solution of Euler Equations by Finite Volume Methods Using Rung-Kutta Time Stepping Schemes,  AIAA paper 81-1259, 1981.
[29] Jahangirian A., Hadidoolabi M., Unstructured Moving grids for Implicit Calculation of Unsteady Compressible Viscos Flows, International Journal for numerical methods in Fluids, Vol.47, No.10, pp. 1107-1113, 2005.
[30] Mavriplis D.J., Jameson A., Martinelli L., Multigrid solution of the Navier–Stokes equations on the triangular meshes, In:27th sciences meeting, Reno, Nevada, USA,  AIAA paper, pp. 9–12, 1989.
[31] Holmes D.G., Inviscid 2D solution on Unstructured, Adaptive Grids, Numerical Methods for Flows in Turbomachinery, Von Karman Institute for Fluid Dynamics Lecture Series (VKI-LS) 1989–06, 1989.
[32] Ambrosio A., Wortman A., Stagnation Point Shock Detachment Distance for Flow around Spheres and Cylinders, Journal of the Aerospace Sciences, Vol.29, No.7, pp. 875-875, 1962.
[33] Billig F.S., Shock-Wave Shapes around Spherical and Cylindrical-Nosed Bodies, Journal of Spacecraft and Rockets, Vol.4, No.6, pp. 822–823, 1967.
[34] Ramezani A., Some Innovations in Numerical Simulation of Inviscid Three Dimensional Flow with Moving Boundaries, A thesis submitted for the degree of Doctor of Philosophy, Sharif University of Technlogy , 2009.
[35] Mavriplis D.J., Jameson A., Multigrid Solution of the Two-Dimensional  Euler Equations on Unstructured Triangular Meshes, AIAA paper 1987-0353, AIAA 25th Aerospace Sciences Meeting and Exhibit, Reno. Drikakis D., Tsangaris S. On the Accuracy and Eficiency of CFD Methods in Real Gas Hypersonic, International Journal for Numerical Methods, Vol.16, pp. 759-775, 1993.