The transition between the Regular Reflection (RR) and Mach Reflection (MR) phenomenon impacts the design of the supersonic and hypersonic air-breathing vehicles. The aim of this paper is to numerically investigate the dynamic transition from RR to MR of unsteady supersonic flow over a two-dimensional wedge, whose trailing edge moves along the x-direction upstream with a velocity, V(t) at a free-stream Mach number of M∞ = 3. The simulation is conducted using the unsteady compressible inviscid flow solver, which is implemented in OpenFOAM®, the open-source CFD tool. Further, the wedge motion is applied by moving the mesh boundary, performing the Arbitrary Lagrangian-Eulerian (ALE) technique. In addition, the sonic and the detachment criteria are used to define the dynamic transition from RR to MR during the increase of the wedge angle. Different reduced frequencies, κ, in the range of [0.1–2] for the moving wedge are applied to study the lag in the dynamic transition from the steady-state condition. The results show that the critical value of κ = 0.4 distinguishes between the rapid and gradual lag in the transition from RR to MR. In addition, the transition from RR to MR occurs above the Dual Solution Domain (DSD), since the shock is curved downstream during the rapid motion of the wedge.

No abstract

The shock wave boundary layer interaction (SW-BLI) phenomenon over transonic and supersonic airfoils captured the attention of aerospace engineers, due to its disastrous effect on the aerodynamic performance of these vehicles. Thus, the scientific community numerically and experimentally investigated several active and passive flow control elements to reduce the effect of the phenomenon, such as vortex generator, cavity, and bump. They focused on designing and optimizing the shape and location of the bump control element. However, the transit movement of the bump from the state of a clean airfoil to the state of an airfoil with a bump needs more investigation, especially the dynamics of the shock system. Thus, it is preferred to start with simple geometry, such as a flat plate, to fully understand the flow behavior with a morphing bump. In this paper, the shock dynamics due to the movement of a bump over a flat plate flying at supersonic speed are numerically investigated. The bump is located at the impingement position of the shock wave and is moved at different speeds. This study determines the suitable speed that achieves the minimum entropy change, which is the representation parameter of the transition period. The two-dimensional unsteady Navier-Stokes equations are solved using OpenFOAM to simulate the flow field variables, while the motion of the bump is tracked using the Arbitrary Lagrangian-Eulerian (ALE) technique. The results show that a spatial lag on the shock system from the steady-state solution occurs due to the movement of the bump. Further, the spatial lag increases with the increase in the bump’s speed. This causes a high increase in the flow parameters and consequently the total entropy changes on the bump surface. Generally, it is common to move the bump over the longest possible time to approximate a quasi-steady flow during the motion. However, this causes a deviation in the flow parameters between the final time of transition and the steady-state case of bump existence. Thus, it is concluded that the optimal non-dimensional time for a morphing bump in a supersonic flow of Mach number of 2.9 is 2, which is different than the longest time of 10.

The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach Reflection (MR) and Regular Reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the x-direction with a velocity, V(t) at a free-stream Mach number of. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. Further, the Arbitrary Lagrangian-Eulerian (ALE) technique is applied to deform the mesh during the wedge motion. The dynamic transition from MR to RR is defined by two criteria, the sonic and the Von-Neumann. Moreover, the lag in the dynamic transition from the steady-state condition is studied using various reduced frequencies, κ, in the range of [0.1–2]. The lag effect in the shock system is remarkable at the high values of the reduced frequency, κ = 1.5 and 2.0. Furthermore, because the shock is bent upstream during the fast motion of the wedge, the transition from MR to RR happens below the Dual Solution Domain (DSD).