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the shock tube shows that there are deviations from an idealized one-
dimensional gas flow. For example, in most studied cases, the speed of
the shock wave and the contact surface speed are practically equal. This
similarity of the speed values of the CS and the shock wave results from
the CS acceleration, which, in its turn, is associated with the formation of
a boundary layer (which decelerates the shock wave) on the walls of the
aerodynamic shock tubes.
This effect can be explained as follows: the speed of the shock wave
front appears to be lower and the CS speed to be higher than the one-
dimensional theory predicts, which in its turn, is connected with the fact
that the gas piston (the CS plays its role) pushing the shock wave is not
completely impenetrable: the mass flux discharging into the front expands
from the shock-compressed area into the wall boundary layer, and thus the
mass concentrated between the shock wave front and the contact surface
remains constant.
This effect is the most appreciable when condition
L
R
1
is satisfied
(where
L, R
are the shock tube length and the radius), as well as when
the initial pressure of the test (driven or accelerated) gas decreases [1]. In
this case, the dynamic boundary layer “displaces” most effectively the gas
flow moving along the tube axis from the area which is adjacent to the
tube wall. This effect of flow displacement can be taken into account (in
a first approximation) by the use of boundary layer approximate equations
and gas dynamics quasi-one-dimensional equations.
An important factor, which misrepresent the one-dimensional gas flow
in a shock tube, is the duration of the diaphragm rupture (the time of
the diaphragm opening that depends on the material of the diaphragm
and the pressure value in the high-pressure chamber); it ranges from 100 to
1000
μ
s. The gas flow pattern after the rupture of the diaphragm central part
corresponds to the discharge of the pulse gas jet into the low pressure area.
The disturbances (of the shock wave or of the compression wave) caused
by the expanding jet in the test (driven or accelerated) gas, are reflected
from the walls of the shock tube and create spatial stream uniformities in
the flow structure. These uniformities result in deviation from the idealized
one-dimensional gas flow pattern.
It is also important that the contact boundary surface (separating the
driver gas from the test gas) is unstable and in the course of time acquires
an irregular spatial (bell-shaped) shape. The gases remaining on different
sides of the contact boundary may mix, which results in the nonuniformity
(non-one-dimensionality) of a gas flow stream in the shock tube.
It should be noted that the proposed computing algorithms for the
numerical modeling of aerothermophysical characteristics of the shock
6 ISSN 0236-3941. HERALD of the BMSTU. Series “Mechanical Engineering”. 2014. No. 1