Mathematical modeling of high-speed flow around a blunt body

Mathematics. Physics. Mechanics


Bykov L. V.*, Nikitin P. V.**, Pashkov O. A.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia



Reliable thermal protection of a lander and increasing speeds of atmospheric vehicles lay new higher requirement to the adequacy of elevated heat flow values obtained during the flow simulation of structural elements of aircraft by hypersonic flows.

The paper presents a mathematical model describing the processes of heat and mass exchange, as well as chemical kinetics occurring on the surface of the a blunt cone frontal part of an aircraft during flight in the atmosphere at hypersonic speeds. The model is based on discrete analogues solving of Navier-Stokes equations on an irregular grid, together with convection and diffusion equations for each component of the gas mixture and the equations of turbulence model.

The relevance of this work is stipulated by the necessity of maximum precision of heat and mass exchange parameters prediction on the surface of a hypersonic aircraft. Solution of this problem allows optimization of its trajectory, geometry, weigh and layout parameters at the stage of shape design, and accordingly, determine the requirements for the necessary thermal protection of a lander.

To solve the problem of flow around a blunt body by hypersonic flow we selected a blunt cone with the following parameters: taper — 6°, radius of bluntness — 0.0381 m, incident flow velocity M∞ = 25.0. The static temperature of the gas in the stream: T∞ — 265.86 K, pressure P∞ — 53.85 Pa. Mass concentration of molecules: C (O2) = 0,233, C (N2) = 0,767.

The problem was solved in two-dimensional axisymmetric formulation. Calculation of heat transfer processes on the surface was carried out taking into consideration the catalytic activity of the surface. On solving the problem, we used the discrete analogues of the Navier-Stokes equations for viscous compressible heat-conducting model environment, and the radiative transfer equation.

The results of the simulation of flow around blunt cone are presented and analyzed. The reliability of the results was checked by comparing them with the results of previously published studies.

The proposed mathematical model can be used for solving the gas dynamic and thermal problems for the design of heat-stressed structural elements of hypersonic aircrafts.

This work has been supported by grants № 11-08-00828, № 13-08-01328 a, 14-08-00982 from the Russian Foundation for Basic Research.


mathematical modeling, Navier-Stokes equations, hypersonic vehicle, gas dynamic, heat exchanger, multicomponent flow


  1. Nikitin P.V. Teplovaya zashchita (Thermal protection), Moscow, MAI, 2006, 512 p.
  2. Molchanov A. M., Bykov L.V., Donskikh V. V. Teplovye processy v tehnike, 2012, vol.4, no.11. pp.496-500.
  3. Bykov L.V., Molchanov A.M., Janyshev D.S. Vestnik Moskovskogo aviatsionnogo instituta, 2010, vol.17, no.3, pp. 108-119.
  4. McBride B. J., Gordon S., Reno M. A. Coefficients for Calculating Thermodynamic and Transport Properties of Individual Species, National Aeronautics and Space Administration. Office of Management Scientific and Technical Information Program. 1993.
  5. Modest M. F. The Weighted-Sum-of-Gray-Gases Model for Arbitrary Solution Methods in Radiative Transfer, J. Heat Transfer, 1991, no. 113. pp. 650–656.
  6. Chui E. H., Raithby G. D. Computation of Radiant Heat Transfer on a Non-Orthogonal Mesh Using the Finite-Volume Method , Numerical Heat Transfer, 1993, Part B, no. 23, pp. 269–288.
  7. Hollis B.R., Perkins J.N. Hypervelocity heat-transfer measurements in an expansion tube, AIAA Paper, 1996, pp. 96-2240.
  8. Wood W. A., Eberhardt S. Dual-Code Solution Strategy for Chemically-Reacting Hypersonic Flows, AIAA Paper, 1995, pp. 95-0158.
  9. Widhopf G. F., Wang J. C. T. A TVD Finite-Volume Technique for Nonequilibrium Chemically Reacting Flows, AIAA Paper, 1988, pp. 88-2711.
  10. Menter F. R., Langtry R. B., Likki S. R., Suzen Y. B., Huang P. G. A Correlation-Based Transition Model Using Local Variables: Part I — Model Formulation". (ASME-GT2004-53452), 2004.

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