| Summary: | A thesis submitted to the Faculty of Engineering and the Built Environment, University of
the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor
of Philosophy.
Johannesburg, January 2018 === The diffraction of shock waves has been explored in many contexts in which either the
shock wave is plane and the confi ning volume has complex geometry or where the shock
wave has some non-plane geometry, typically something like spherical since this is the
approximate shape of the waves generated by blasts. However, these studies have not
considered more complex initial wave shapes or exit geometries. This study therefore
addresses this de ciency in two ways.
The dynamic conical shock wave was originally proposed as a mechanism for the initiation
of fusion whereby the focusing of the shock wave near the axis of symmetry would produce
the high temperatures and pressures required. This was explored numerically and
theoretically, as no experimental method was considered viable, and it was found that the
regular re
ection of a shock wave de ned by conical wave geometry is not stable and will
revert to an irregular re
ection pattern at the axis. Three primary geometries were
identi ed distinguished by the number of irregular re
ections formed and in
uenced by the
induced vortical
ow. The current study used a developed experimental apparatus to study
conical shock waves and an additional, new re
ection pattern, named the von Neumann
type (vN-type) for the similarity to the von Neumann re
ection of weak plane waves, was
identi ed. In addition, instability of the conical shear layer present as a result of the
irregular re
ection at the axis of the shock wave was identi ed experimentally which
resembles the Kelvin-Helmholtz instability previously only studied in two-dimensional
con gurations of compressible
ow. Dynamic bending of the central jet from the re
ection
axis was also tested as a function of upstream occlusion in the shock tube and this suggests
possible future work in compressible jet actuation.
The current study also considered the diffraction of plane shock waves at the inclined or
curved exits of shock tubes, which are more general examples of duct interaction of the sort
that might be found in engines or ventilation systems. This was done experimentally using
novel, open test sections for a conventional shock tube and for a limited number of
computational cases. These
ows are characteristically different from the diffraction of
shock waves from tubes of complex cross-section studied to date where the exit plane is still
normal to the direction of travel of the wave. This is because the shock wave still undergoes
simultaneous diffraction at all points around the edge of the tube in such a case while in
this study the wave diffracts at different times around the tube periphery. This affects the
strength of both the emerging incident wave and the diffraction and thus an atypical
formation of the jet and vortex takes place.
In the case of the inclined plane exit of the shock tube, two primary phenomena were noted:
de
ection of the jet and change of the jet cone angle; and variations in the vortex diffraction
behaviour. For the former effect a large inclination of the exit from the normal increased the
spread of the jet and the inclination away from the tube axis. Also, a system of secondary
shock waves forms in the jet due to the expansion fans formed at the diffraction edge,
typical of under expanded jets but becomes weaker as exit surface inclination increases. The
second effect noted is of the increased curvature as a function of time after diffraction for
higher inclinations, due to the much stronger induced velocities for the portion of the vortex
shed on the obtuse upstream edge. The vortex loop also loses coherence with increasing
inclination because of the weak vortex shedding at the downstream edge of the tube.
The results for the curved exit are similar although the effects are not as extreme since the
limiting diffraction angles are lower than for the extreme plane cases due to the
characteristics of circular geometry. In the extreme case of part of the shock tube exit being
tangent to the exit surface, the vortex again does not form a closed loop but rather
terminates in the exit surface. This was particularly tested here with a plane section at the
tangent point. However, the secondary re
ection of the diffracted shock wave due to the
curvature of the surface toward the diffracted wave, which tends to disrupt the vortex,
means that an internal diffraction with a fully closed tube would result in a short-lived
vortex loop.
In both of the latter cases the vortex loop, or arch if it cannot close into a loop, is part of
the physical mechanism whereby a jet
ow exiting a pipe adjusts to being a di use
ow
along the exit surface. This is accomplished by the spreading of the sheet of vorticity, which
is the boundary layer in the pipe and the jet boundary outside of it, by the origination of
turbulence in the breakdown of the vortex arch or loop.
The diffraction of shock waves from non-orthogonal apertures demonstrates features
previously unidenti ed and suggests complex
ow patterns which simpli ed
two-dimensional analysis cannot describe. === MT 2018
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