Kudryavtsev A. Khotyanovsky D.
Numerical study of the viscous heat-conducting gas flow in a long shock tube
Reporter: Khotyanovsky D.
The results of numerical simulations of the propagation of the shock wave in a cylindrical shock tube of large length are presented. The computations are based on the Navier–Stokes model in axisymmetric formulation. Flow parameters correspond to the conditions of the experiment [1]: internal diameter of the tube is 28.575 mm, the tube length from the diaphragm to the right boundary of the computational domain is 7.5 m. Wall temperature is considered constant and equals 300 K. Argon was used as both driver and driven gas. The computations were performed with the boundary conditions of velocity slip and temperature jump. The pressure on the right from the diaphragm was fixed and equaled to p0 = 66.66 Pa, the initial pressure ratio was varied. At flow parameters considered herein (low ratio of the tube diameter to its length, small initial pressure) gasdynamic characteristics of the flow are largely governed by viscous effects: Reynolds number based on initial values of the speed of sound and flow viscosity equals Re0 = 431 in this case. The results of the numerical computations agree well with the experimental data [1]. The effects of viscous
friction and heat conduction cause significant difference of the shock wave velocity from its inviscid theoretical value. The results of the computations show that, at the considered flow parameters, the shock wave and the contact surface, starting from a certain moment of time, propagate with equal speeds. At large distances downstream along the shock tube, the shock wave degenerates into a weak pressure disturbance driven from behind by the contact discontinuity and propagating at subsonic speed.
[1] Duff R.E. Shock‐Tube Performance at Low Initial Pressure // Physics of Fluids. 1959, v. 2, n. 2, pp. 207–216.
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