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introduced. This elementary theory of the shock tube can be described by
a simplified scheme of the physical processes (the assumptions are listed
below). This simplified physical picture of the thermophysical processes in
a shock tube is as follows:
— after the forced rupture of the diaphragm (using a special technical
device), the driver gas in the high pressure chamber expands (compressing
the test gas) into the low pressure chamber filled with the test (driven) gas
under low pressure.
— in the low pressure chamber, a generated shock wave is propagating
in the test gas, and in the high pressure chamber a rarefaction wave is
propagating in the expanding driver gas;
— after the shock wave has reached the end of the pipe, it is reflected
and comes back towards the driver gas;
— then this reflected shock wave is interacting with the contact
discontinuity that separates the driver gas and the test gas, which results in
shock wave partial reflection (in the form of a shock wave or a rarefaction
wave (the criterion identifying these two cases is given below) and partial
refraction and moving (in the form of a shock wave) into the compressed
layer of the driver gas.
Here the following should be noted:
•
if the shock wave interacting with the contact discontinuity escapes
from a denser medium into the less dense one, it is reflected from the
contact discontinuity in the form of a rarefaction waves fan;
•
if the shock wave escapes from a less dense medium into the denser
one, it is reflected in the form of a shock wave.
The course of flow in the aerodynamic shock tube can be conveniently
represented in the form of the so-called
x
−
t
-diagram (Fig. 1). In
x
−
t
-
diagram, area
1
corresponds to the unperturbed initial state of the test
(driven or accelerated) gas, area
2
corresponds to the gas compressed in
the shock wave, areas
3
and
4
are the areas of gas “piston” and unperturbed
initial state of the gas in the high presure chamber before the rarefaction
wave arrival.
The surface denoted by К and separating (between areas
2
and
3
) the
test (driven or accelerated) gas and the driver (accelerating) gas is referred
to as a contact surface (CS) or interface. The gas pressures and the flow
velocities on either side of the CS are equal
(
p
2
=
p
3
, u
2
=
u
3
)
. In the
subsequent instant of time, the shock wave and the rarefaction wave are
reflected from the end walls of the shock tube and begin to interact with
each other.
Experimental and theoretical research into generation and propagation
of the shock waves, rarefaction waves and contact discontinuities in
ISSN 0236-3941. HERALD of the BMSTU. Series “Mechanical Engineering”. 2014. No. 1 5