Incident Shock Wave Interaction with an Axisymmetric Cone Body Placed in Shock Tube

This work presents a numerical simulation of the interaction of an incident shock wave propagates from the left to the right with a cone placed in a tube at shock. The Mathematical model is based on a non stationary, viscous and axisymmetric flow. The Discretization of the Navier-stokes equations is carried out by the finite volume method in the integral form along with the Flux Vector Splitting method of Van Leer. Here, adequate combination of time stepping parameter, CFL coefficient and mesh size level is selected to ensure numerical convergence. The numerical simulation considers a shock tube filled with air. The incident shock wave propagates to the right with a determined Mach number and crosses the cone by leaving behind it a stationary detached shock wave in front of the nose cone. This type of interaction is observed according to the time of flow.

• Rabah Haoui

• Supersonic flow
• viscous flow
• finite volume
• cone body

[1] A.H. Shapiro, The Dynamics and Thermodynamics of Compressible fluid flow, The Ronald Press Company, New York, Volume II, 1954, pp.
664.
[2] H. Schlichting, Boundary-layer theory, 7th edition, McGraw-Hill, New
York, 1979.
[3] Goudjo, J.A. Désidéri, a finite volume scheme to resolution an
axisymmetric Euler equations (Un schéma de volumes finis décentré pour la résolution des équations d-Euler en axisymétrique), Research
report INRIA 1005, 1989.
[4] R. Haoui, "Effect of mesh size on the viscous flow parameters of an
axisymmetric nozzle," International Journal of Aeronautical and space
Sciences, vol.12(2), 2011, pp. 127-133.
[5] K. A. Hoffmann, Computational fluid dynamics for engineers, Volume
II. Chapter 14, Engineering Education system, Wichita, USA, pp.202-
235, 1995.
[6] B. Van Leer, "Flux Vector Splitting for the Euler Equations," Lecture
Notes in Physics. 170, 1982, pp. 507-512.
[7] J.H. Ferziger & all, Computational Methods for Fluid Dynamics,
Chapter 8, Springer-Verlag, Berlin Heidelberg, New York, 2002,
pp.217-259,.
[8] R. Haoui, "Physico-chemical state of the air at the stagnation point
during the atmospheric reentry of a spacecraft," Acta astronautica,
vol.68, 2011, pp.1660-1668.
[9] R. Haoui, A. Gahmousse, D. Zeitoun, "Condition of convergence
applied to an axisymmetric reactive flow," 16th CFM, no.738, Nice,
France, 2003
[10] R. Haoui, “Finite volumes analysis of a supersonic non-equilibrium flow
around the axisymmetric blunt body,” International Journal of
Aeronautical and space Sciences, vol.11(2), 2010, pp. 59-68.