The compressible shear layer of a Mach Reflection
Date
2016-10-11
Authors
Hall, Russell Edward
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Abstract
The Mach Re
ection occurring in pseudo-steady
ows has been studied for well over a century.
A Mach Re
ection consists of incident and re
ected shocks, a Mach stem and a shear layer.
Three Shock Theory proposed by von Neumann in the 1940's shows good agreement to
experimental data in the strong shock domain (Ms > 2) however, poor agreement is obtained
in the weak shock domain (Ms < 1:5).
A pseudo-steady Single Mach Re
ection (SMR) was studied in a large scale facility for a
single wedge angle, a complimentary study was undertaken in a conventional shock tube over
a wide range of wedge angles. The Mach numbers used were in the range 1:27 Ms 1:59
and the wedge angles 25 w 38 . A shadowgraph
ow visualisation system was used in
conjunction with a single shot camera to obtain high resolution images. Various shock angles
were measured as well as the triple point trajectory from the leading edge of the wedge.
As expected, poor agreement to Three Shock Theory was obtained in the current (Ms; w)
domain.
The spread angle of the shear layer was measured from the triple point. An oblique shock
analysis was used to obtain the theoretical velocity and density ratio across the shear layer
as well as other properties such as shear velocity ( U) and convective Mach number (Mc).
The analysis revealed that the e ect of compressibility on the growth of the shear layer was
negligible. The spread angle increased with increasing incident shock strength and wedge
angle. A comparison to the theoretical models of Papamoschou and Rikanati et al. showed
good agreement for some wedge angles and intermediate Mach numbers. Recommendations
for future work include increasing the Mach number and wedge angle range as well as the
implementation of di erent
ow visualisation setups.
Description
A dissertation 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 Master
of Science in Engineering.
Johannesburg, May 2016