Experimental investigation of tripping between regular and Mach reflection in the dual-solution domain

Summary

Experiments were conducted in the Mach 4.0 Ludwieg tube facility at the California Institute of Technology. First, the hysteresis phenomenon, first proposed by [1] is explored. Second, tripping from regular reflection to Mach reflection by depositing laser energy onto one of the wedges is considered. These experimental results are compared with numerical computations and theoretical estimates.

A double wedge model was constructed with the lower wedge being fixed and the upper wedge being adjustable. This asymmetric configuration was chosen for simplicity and follows the work of [2] and [3].

Computationally, the hysteresis phenomenon is easy to demonstrate. However, experimentally, due to tunnel noise, the hysteresis phenomenon is more difficult to show and the maximum angle to which regular reflection can be maintained is reduced. This angle is a qualitative measure of the quietness of the tunnel.

In order to demonstrate the hysteresis phenomenon, the upper adjustable wedge was set so that the shock angles are well below the von Neumann condition, and therefore only regular reflection is possible. As the upper wedge angle is increased into the dual solutions domain, at some point a sudden transition to Mach reflection with a finite Mach stem height occurs. Further increase of the upper wedge angle causes the Mach stem to grow further. If the upper wedge angle is then decreased, the Mach stem height is decreased continuously until it reaches zero at the von Neumann condition and regular reflection is restored.

Experiments were conducted moving the upper wedge at different speeds to study the effect of the wedge speed on transition. It was found experimentally, that if the wedge was moved quickly, regular reflection could be maintained further into the dual-solution domain. This is believed to be due to the fact that the wedge spends less time at any given angle so that the chance of a sufficiently strong disturbance occurring is smaller.

By depositing laser energy on the lower wedge a small blast wave is created. This disturbance can be compared to the disturbance from a solid particle impacting the wedge. Using high-speed cinematography we can capture the disturbance to the incident shock. Soon after the disturbance is introduced, a small Mach stem is formed and grows to its steady-state height. This growth rate is compared with theoretical calculations.

The importance of energy deposition location is also discussed. If the energy is deposited far downstream on the wedge, it has to be very strong to reach the incident shock; however, if the energy is deposited far upstream, it also has to be very strong, because it will weaken before it reaches the reflection point. Therefore, there is an optimum location, in terms of minimum energy required to cause transition from regular to Mach reflection. This is also explored computationally, and for downstream locations, a theoretical estimate of the energy required is presented.