| Summary: | There have been numerous studies on the steady state transition criteria between regular reflection (RR) and
Mach reflection (MR) of shock waves for a stationary, two-dimensional (2D) wedge in a steady supersonic free
stream since the original shock wave reflection research by Ernst Mach in 1878. The steady, 2D transition
criteria between RR and MR are well established. There has been little done to consider the dynamic effect
of rapid wedge rotation on RR $ MR transition.
This thesis presents the results of an investigation of the effect of rapid wedge rotation on transition
between 2D regular and Mach reflection in the weak and strong-reflection ranges, with experiment and com-
putational fluid dynamics. A novel facility was designed to rotate a pair of large aspect ratio wedges in a 450
mm × 450 mm supersonic wind tunnel at wedge rotation speeds up to 11000 deg/s resulting in wedge tip
speeds approximately 3.3 % of the free stream acoustic speed. Steady state, baseline experiments, in which
the wedges were rotated very gradually, were also completed. High-speed images and measurements are pre-
sented for the steady and dynamic experiments. Numerical solution of the inviscid governing flow equations
was used to model the steady case and to mimic the experimental motion in the dynamic experiments. The
two-dimensional, Euler CFD code was developed at the University of the Witwatersrand.
Steady state experiments were completed in the weak and strong-reflection ranges and transition measure-
ments were compared to 2D steady, theoretical values and Euler computations. There was close agreement
between theoretical, computational and experimental transition for the steady case, with the following ex-
ception. Due to the levels of free stream noise in the supersonic wind tunnel, incidence-induced hysteresis
was not observed in the strong-reflection region and transition occurred at the von Neumann condition for
increasing and decreasing incidence. In the ideal case, RR ! MR transition occurs at the detachment
condition and the reverse transition occurs at the von Neumann condition. Therefore, there is discrepancy
between steady theory/CFD and experiment for RR ! MR transition in the strong-reflection range only,
which is consistent with observations in other facilities with sufficient levels of free stream noise.
Dynamic RR ! MR Transition : Rapid wedge rotation did generate a measurable dynamic effect on RR
! MR transition. This thesis presents the first experimental evidence of RR ! MR reflection transition beyond the steady detachment condition in the weak and strong-reflection ranges. In all instances, there
was good agreement between experiment and 2D CFD, including dynamic RR ! MR transition in the
strong-reflection region. The agreement between the experiment, in which small perturbations are always
present in the free stream, and the CFD, in which the free stream is without perturbations, implies that
RR ! MR transition in the strong-reflection region becomes insensitive to free stream noise above a certain
critical rotation speed. Due to the close agreement between CFD and experiment, the Euler code was also
applied to scenarios beyond the limits of the current facility to explore the influence of variables in the
parameter space, viz. rotation speed, initial incidence and rotation centre. CFD was also used to investigate
the dynamic transition mechanism over a limited number of simulations. For dynamic RR ! MR transition,
a distinction is drawn between the sonic, length scale and detachment conditions. The point at which the
flow downstream of the reflection point goes sonic is not necessarily the point at which the wedge length
scale, from the wedge trailing edge expansion, is communicated to the reflection point. There is evidence to
support that the RR ! MR transition criteria for the rapidly rotating wedge is neither the sonic or length
scale conditions, but rather the condition at which the reflected wave can no longer satisfy the boundary
condition at the reflection point. Dynamic simulations showed that RR could be maintained with a length
scale present at the reflection point. Other dynamic simulations showed, for the first time, that transition
to MR was possible without the wedge length scale being communicated to the reflection point.
Dynamic MR ! RR transition : Rapid wedge rotation generated a measurable effect on MR ! RR
transition. The first experimental evidence of MR ! RR transition below the steady von Neumann condition
is presented. Once again, there was good agreement between experiment and 2D CFD. CFD was used to
investigate the sensitivity of transition to rotation speed, initial incidence and rotation centre in the strong
and weak-reflection ranges. Due to impulsive wedge start and rapid wedge rotation, there are very marked
dynamic effects on the variation of Mach stem height with wedge incidence and the deviation from the
steady transition conditions is significant. The MR ! RR transition was found to be dependent on the
initial condition and the transient variation of Mach stem height with wedge incidence.
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