533.6.011.5 Modeling supersonic flow around blunted cones, taking into account the curvature discontinuity along the generatrix of the solid

Bulgakov V. N. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Kotenev V. P. (Bauman Moscow State Technical University/JSC MIC NPO Mashinostroyenia), Sapozhnikov D. A. (JSC MIC NPO Mashinostroyenia/МГТУ им.Н.Э.Баумана)

SUPERSONIC FLOW, CURVATURE DISCONTINUITY ALONG A GENERATRIX OF A SOLID, GENETIC ALGORITHM


doi: 10.18698/2309-3684-2017-2-8193


The article presents an analytical expression for calculating pressure on the surface of blunted cones in a supersonic gas flow, taking into account the curvature discontinuity along the generatrix. We used a genetic algorithm and multi-stage functional optimisation methods for the least-squares method to determine free parameters of the expression. We compare the results obtained to the rigorous numerical solution to the inviscid problem. The comparison shows that it is possible to use the analytical expression for pressure distribution over a surface in a wide Mach number range for various cone halfangles. The expression proposed accounts for the curvature discontinuity along the generatrix at the point where the sphere is tangent to the conical surface, unlike the expressions found in previously published works.


[1] Mayer C.S.J., Laible A.C., Fasel H.F. AIAA Journal, 2011, vol. 49, no. 1, pp. 67–86.
[2] Gauer M., Paull A. Journal of Spacecraft and Rockets, May-June 2008, vol. 45, no. 3, pp. 459–471.
[3] Tissera Sh., Drikakis D. Journal of Spacecraft and Rockets, vol. 47, no. 4, July-August 2010, pp. 563–570.
[4] Dimitrienko Yu.I., Kotenev V.P., Zakharov A.A. Metod lentochnykh adaptivnykh setok dlya chislennogo modelirovaniya v gazovoy dinamike [Ribbonshaped adaptive mesh method for numerical simulations in gas dynamics]. Moscow, FIZMATLIT Publ., 2011, 296 p.
[5] Dimitrienko Yu.I., Koryakov M.N., Zakharov A.A. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2015, no. 8, pp. 75–91.
[6] Ericsson L.E. AIAA Journal, 1971, vol. 9, no. 2, pp. 297–304.
[7] Sarantsev A.I. Uchenye zapiski TsAGI — TsAGI Science Journal, 1991, vol. XXII, no. 1, pp. 82–88.
[8] Kotenev V.P. Matematicheskoe modelirovanie — Mathematical Models and Computer Simulations, 2014, vol. 26, no. 9, pp. 141–148.
[9] Kotenev V.P., Sysenko V.A. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1 (1), pp. 68–81.
[10] Kotenev V.P. Vestnik MGTU im. N.E. Baumana. Spets. vyp. “Matematicheskoe modelirovanie” — Herald of the Bauman Moscow State Technical University. Special edition on mathematical modeling, 2011, pp. 150–153.
[11] Kotenev V.P., Bulgakov V.N., Ozhgibisova Yu.S. Matematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2016, no. 3 (11), pp. 33–52.
[12] Dimitrienko Yu.I., Zakharov A.A., Koryakov M.N., Syzdykov E.K. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie — Proceedings of Higher Educational Institutions. Маchine Building, 2014, no. 3, pp. 23–34.
[13] Lunev V.V. Techenie realnykh gazov s bolshimi skorostyami [High-speed flows in real gases]. Moscow, FIZMATLIT Publ., 2007, 759 p.
[14] Krasnov N.F. Osnovy aerodinamicheskogo rascheta. Aerodinamika tel vrashcheniya, nesushchikh i upravlyayushchikh poverkhnostey. Aerodinamika letatelnykh apparatov [Foundations of aerodynamic computations. Aerodynamics of solids of revolutions, lifting surfaces and control surfaces. Aerodynamics of aircraft]. Moscow, Vysshaya Shkola Publ., 1981, 496 p.
[15] Lyubimov A.N., Rusanov V.V. Techeniya gaza okolo tupykh tel. V 2 tomakh. Tom 2. [Gas flows in the vicinity of blunted shapes. In 2 vols. Vol. 2]. Moscow, Nauka Publ., 1970, 379 p.
[16] Panteleev A.A. Metaevristicheskie algoritmy poiska globalnogo ekstremuma [Metaheuristic algorithms for locating the global extremum]. Moscow, MAI-PRINT Publ., 2009, 159 p.
[17] Kovalenko V.V. Metod rascheta nevyazkogo sverkhzvukovogo obtekaniya fyuzelyazhey i krylev i ikh komponovok [Computation method for inviscid supersonic flow around aircraft bodies and wings and their layouts]. Trudy TsAGI — TsAGI Proceedings, 1975, no. 1699.


Bulgakov V.N., Kotenev V.P., Sapozhnikov D.A. Modeling supersonic flow around blunted cones, taking into account the curvature discontinuity along the generatrix of the solid. Маthematical Modeling and Coтputational Methods, 2017, №2 (14), pp. 81-93



Download article

Количество скачиваний: 559