PHYSICAL REVIEW E 104, 055101 (2021) Dynamic effects in transition from regular to Mach reflection in steady supersonic flows Rohtash Goyal , * A. Sameen , † T. Jayachandran , ‡ and G. Rajesh § Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India (Received 7 August 2021; accepted 18 October 2021; published 9 November 2021) The effect of rapid wedge rotation on the transition from regular (RR) to Mach reflection (MR) is investigated. This unsteady shock reflection transition is compared with the steady-state transition. The dependence of various flow features such as the unsteady Mach stem height, position of the reflection point, and shock angle at the reflection or triple point on the wedge angle for a fixed Mach number is compared at various rotation rates. The study is further extended to compare the dynamic effects for various Mach numbers in the strong shock reflection domain at higher wedge speeds. Transition lines corresponding to different rotation speeds are obtained similar to the detachment transition line in steady cases. It is found that the pivot point has only marginal effect on the transition point, but it substantially affects the Mach stem growth and the movement of the reflection point, specifically at higher Mach numbers. The location of the transition from the inlet also depends on the pivot point and the rate of rotation. DOI: 10.1103/PhysRevE.104.055101 I. INTRODUCTION Shock wave reflection is one of the interesting and impor- tant phenomena in high-speed flows. Shock wave reflections are observed in nozzle flows, supersonic inlets, and vari- ous other applications and are broadly classified into regular reflection (RR) and irregular reflection (IR) [1]. The most common type of irregular reflection observed in steady flows is a simple Mach reflection (SMR), also known as a Mach reflection (MR). There are clear, distinct features for RR and MR, best described with the help of a schematic diagram, as shown in Figs. 1(a) and 1(b). Regular reflection is a two-shock structure in which an incident shock wave (i) and a reflected shock wave (r ) meet at the reflection point R as shown in Fig. 1(a). In the RR, the reflected shock wave induces an equal and opposite flow deflection to the one induced by the incident shock wave [2,3]. On the other hand, an MR is a three shock structure, consisting of an incident shock wave, a reflected shock wave, and a Mach stem (m) with a slipstream (s), intersecting at the triple point T as shown in Fig. 1(b). In the MR, the net flow deflection near the triple point induced by the incident and the reflected shock wave is equal to the flow deflection induced by the Mach stem [2,3]. The slipstream acts as a contact surface, and the pressure across it near the triple point is uniform. Apart from the standard solution of an IR, which is the MR, various nonstandard solutions such as von Neumann reflection (vNR) [4,5], Guderely reflection (GR) [6,7], and Vaislev reflection (VR) [8] which are collectively known as weak-Mach reflections (WMR) [9] exist and are not so common in steady flows. * ae18s007@smail.iitm.ac.in † Corresponding author: sameen@ae.iitm.ac.in ‡ t_jayachandran@iitm.ac.in § rajesh@ae.iitm.ac.in These shock structures transit into one another depend- ing on various parameters, a phenomenon known as shock wave transition [10]. The shock wave transitions commonly occurring in the steady flows are regular to Mach reflection (henceforth indicated as RR → MR) and Mach to regular re- flection (MR → RR). It is important to identify the transition point because the transition leads to a significant change in the flow properties [11]. Azevedo and Liu [12] showed the significant influence of the subsonic region behind the Mach stem in acoustic pressure levels after the transition to MR, which could have been otherwise supersonic in an RR. Hence, the identification of the transition point in physical and param- eter spaces is important in designing supersonic vehicles and engine inlets. The steady-state RR ↔ MR transition has been a contin- ued interest since the pioneering work of von Neumann [2]. A detachment condition for the transition RR → MR and the von Neumann condition for the transition MR → RR were introduced by von Neumann [2,3]. These criteria were not in complete agreement with the experimental results obtained for a wide range of Mach numbers and wedge angles [13]. The transition criteria also depend on the domain where the reflec- tions happen. The shock reflections were classified into two domains [14], a weak shock reflection domain and a strong shock reflection domain based on a critical free stream Mach numbers M 0C = 2.47 for monoatomic gas and M 0C = 2.2 for diatomic gas. The flow downstream of the reflected shock is subsonic in a weak shock reflection domain, whereas it is supersonic in a strong shock reflection domain. A length scale criterion for RR → MR transition was also proposed, and it was postulated that, for a finite length scale (a Mach stem) to exist in an MR, there must be a communication of pressure signals to the reflection point through the expansion fan, which can only happen when the flow downstream of the reflection point is sonic, also known as the sonic criterion for RR → MR transition [15]. There have been several studies to 2470-0045/2021/104(5)/055101(13) 055101-1 ©2021 American Physical Society