A thesis submitted to the Faculty of Engineering and the Built Environment, University of
the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Doctor
of Philosophy.
Johannesburg, May 2017 / Shock{waves (shocks) exist in various shapes; restricted to two dimensions some examples
are planar, cylindrical, parabolic and elliptical. However, most shock{wave research has
been focussed mostly on plane shocks. In this research, the scope is expanded to cylindrical
shock{wave segments where a plane shock can be viewed as a cylindrical shock segment
(referred to as a cylindrical shock) with a large radius of curvature; with this view, the
expectations are that cylindrical and plane shocks behave similarly although with
quantitative di erences.
Whereas plane shocks have constant orientation, constant strength and can be imagined to
extend unbounded, cylindrical shock segments demand that both ends be bound; this leads
to spatial constraints, shock strength varying with respect to radius and shock orientation
being non-constant. Three shock phenomena were investigated: di raction, re
ection and
propagation in converging diverging nozzles. Shock{tube experiments were run for shocks
with a radius of 165 mm and strength between Mach numbers 1.2 and 1.7. Complementing
these were Computational Fluid Dynamics (CFD) and Geometric Shock Dynamics (GSD)
simulations where GSD relies on Whitham's equations.
On shock di raction, cylindrical shocks were shown to behave qualitatively like plane
shocks. Upon encountering a sharp corner, expansion waves propagate along the shock.
However, after re
ecting o the opposite wall they become compression waves and form a
'Mach re
ection (MR)' like con guration on the shock front. A method for calculating the
locus of the expansion waves based on Whitham's theory is presented, which on comparison
with CFD simulations gives good correlation. Comparisons of shock pro les calculated
using Whitham's theory and CFD is also made; it showed good correspondence before the
formation of MR like con gurations after which the pro les di er.
The re
ection of cylindrical shocks was investigated from both an experimental and
numerical perspective. Shock{tube experiments were run for shocks propagating on concave
cylindrical walls with radii of 100 mm, 180 mm, 140 mm and 82 mm, the range was
expanded by use of CFD. An expression for calculating the locus of the MR that forms on
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the shock front was derived which generalises onto plane shocks. Two limits were
recognised, one where shock radius is much greater than wall radius and another where
shock radius is much smaller. The former corresponds to a cylindrical shock on a plane wall
while the latter a plane shock on a cylindrical wall as illustrated by the data gathered.
Cylindrical shock propagation in converging-diverging nozzles was also investigated. In this
case, the phenomena at play are di raction, re
ection and focusing, a combination which
results in a complex evolution of the shock front. Two types of channels were investigated,
one formed from a 3rd order polynomial and another from circular arcs. In both cases, wall
signal were generated on either side of the shock which split the shock{front into three
sections. The decreasing channel cross{section area causes the shock strength to increase
resulting in very weak MR formation on the shock front. Channels from circular walls
exhibit a single peak in the centre line shock strength while that from polynomial pro le
walls results in a double peak. This was then related to type of wall disturbance generated. / MT 2017
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/23544 |
| Date | January 2017 |
| Creators | Ndebele, Bright Bekithemba |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (xxii, 153 leaves), application/pdf, application/pdf |
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