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National Advisory Committee for Aeronautics, Report - Unsteady Oblique Interaction of a Shock Wave with a Plane Disturbance

The unsteady one-dimensional interaction of normal shock
waves and disturbances, such as sound waves or other shock
waves, has been studied quite thoroughly (an example is
Kantrowitz’ paper on shock stability, ref. 1). The steady
interaction between normal shock waves and plane Mach
waves has been treated by Adams (ref. 2).

The general class of unsteady flow problems is currently
of increasing interest, in connection particularly with sta-
bility of high—speed aerodynamic and combustion processes.
The effect of a shock passing through a flow field (or vice
verse) is likely to be important in many applications. For ex-
ample, ahot-wire anemometer intended to measure thefluctuat—
ing field of turbulencein asupersonic streamwill actuallymeas-
ure the turbulence as modified by passage through the nearly
steady bow shock of the probe.

Considering, for simplicity, that the flow interacting with
a normal shock is a nonviscous field of Weak disturbance, it
may usually be considered irrotational and isentropic (such
as produced by a moving slender body) and therefore can be
imagined to be composed of a suitable array of sound waves.
Another possible type of weak nonviscous disturbance would
be a stationary, incompressible flow of variable vorticity
(turbulence which is convected rapidly past the point of
observation is commonly thought of in this way).

Either of these two types of flow may be represented as a
linear combination of plane waves (each wave either a sound
wave or a rotational wave, depending on the type of flow
to be represented) of various amplitudes, wave lengths,
and orientations. Thus, if the interactive eifect of a. shock
and each constituent wave may be found by a linear analysis,
the complete problem may in principle be solved by linear
combination of the resulting flow fields behind the shock.
The interaction between a turbulent field and a wind-tunnel
screen or contraction, or both, has been successfully carried
out in references 3 through 5 by this method.