Analysis of gas-dynamic processes and development of model of flows in hypersonic shock tube

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PROCESS MODELING
ANALYSIS OF GAS-DYNAMIC PROCESSES AND DEVELOPMENT
OF MODEL OF FLOWS IN HYPERSONIC SHOCK TUBE
V.V. Kuzenov , M.A. Kotov
Ishlinskii Institute for Problems in Mechanics of the RAS,
Moscow, Russian Federation
e-mail:
The paper considers the simplified one-dimensional mathematical models of
the processes, which describe both formation and propagation of shock waves,
rarefaction waves, and contact discontinuities in shock tubes. These models are based
on the quasi-one-dimensional equations of radiation gas dynamics. Experimental and
theoretical studies of both the formation and propagation of shock waves, rarefaction
waves and contact discontinuities using shock tubes have always been of significant
interest and they are currently being developed. It results from the fact that the shock
tubes are the most convenient tool of laboratory research in such contemporary fields
of modern science and technology as aerophysics and chemical kinetics, gas dynamics
and molecular physics. The flows of a multicomponent gas proves to be important
for many modern technological and power facilities as well as in hypersonic aircraft.
The multicomponent gas undergoes chemical conversions, oscillatory, and electron
excitation. A relatively simple instrument for creating non-equilibrium processes in
the gases is a shock wave propagating in a tube of a circular or rectangular cross-
section. This cross-section geometry allows simplifying the gas-dynamic flow pattern
in the working section.
Keywords: shock tube, gas dynamics equations, nonlinear quasimonotonous compact
difference scheme, Runge–Kutta multistep method
The problem statement. The aim of the paper is to examine the
processes of formation and propagation of shock waves (SW), rarefaction
waves and contact discontinuities in shock tubes using simplified one-
dimensional mathematical models.
One of the important tasks is to develop numerical methods and a
computational model code to describe unsteady one-dimensional radiation-
magnetogasodynamic processes in different types of shock tubes.
Description of processes occurring in shock tubes. The shock tubes
that generate shock waves have the following principle of operation (Fig. 1):
the shock wave is generated in the tube containing a test (driven) gas when
a “piston” of some kind is moving at a hypersonic speed. The shock tube, in
which a compressed air is used for generating shock waves, operates in the
most effective way when the ratio of the velocity of a sound in the working
gas ( CR — driver gas) to the velocity of sound in the test gas (CSt — driven
gas) is sufficiently high (CR/CSt 1). The heating of the driver gas in
a shock tube with an electric discharge, solid or gaseous substances may
be accompanied by a remarkable increase of the ratio mentioned above.
This is related to the fact that the gas temperature can increase from 2 кK
(without gas heating) up to 20 кK (with gas heating), which results in the
ISSN 0236-3941. HERALD of the BMSTU. Series “Mechanical Engineering”. 2014. No. 1 3