Alexey N. Kudryavtsev

Transition between regular and Mach reflection of shock waves: new numerical and experimental results

Abstract. New numerical and experimental results on the transition between regular and Mach reflections of steady shock waves are presented. The influence of flow three-dimensionality on transition between steady regular and Mach reflection has been studied in detail both numerically and experimentally. Characteristic features of 3D shock wave configuration, such as peripheral Mach reflection, non-monotonous Mach stem variation in transverse direction, the existence of combined Mach-regular-peripheral Mach shock wave configuration, have been found in the numerical simulations. The application of laser sheet imaging technique in streamwise direction allowed us to confirm all the details of shock wave configuration in the experiments. Close agreement of the numerical and experimental data on Mach stem heights is shown.

Numerical Analysis of Shock Wave Reflection Transition in Steady Flows

Different aspects of the transition between regular and Mach reflections of strong shock waves in steady flows are numerically studied. Two approaches-kinetic (the direct simulation Monte Carlo method) and continuum (Euler equations)-are used to investigate the hysteresis phenomenon in the flow about two symmetrical wedges in two- and three-dimensional statements. The dependence of the final shock wave configuration on initial conditions, the transition from regular to Mach reflection by means of flow perturbations, and three-dimensional effects are examined. The three-dimensionality of the flow is shown to increase the angles of transition from regular to Mach reflection and back and to decrease the Mach stem height

The reflection of asymmetric shock waves in steady flows: a numerical investigation

The theoretical study and experimental investigation of the reflection of asymmetric shock waves in steady flows reported by Li et al. (1999) are complemented by a numerical simulation. All the findings reported in both the theoretical study and the experimental investigation were also evident in the numerical simulation. In addition to weak regular reflection and Mach reflection wave configurations, strong regular reflection and inverse-Mach reflection wave configurations were recorded numerically. The hysteresis phenomenon, which was hypothesized in the course of the theoretical study and then verified in the experimental investigation, was also observed in the numerical simulation.

Numerical Investigation of Shock-Reflection Phenomena in Overexpanded Supersonic Jets

The transition from regular to Mach reflection in a supersonic planar jet operating under overexpanded conditions has been studied numerically. First, inviscid computations are performed by the solution of Euler equations. The results demonstrate that a hysteresis phenomenon is observed as the jet/ambient pressure ratio decreases and increases, causing a change in the angle of incidence of the nozzle-lip shock and, as a consequence, the transition from regular to Mach reflection and back. The angles of forward and backward transitions are close to the theoretical detachment and von Neumann criteria, respectively. Furthermore, turbulent computations (by the use of an improved two-equation model) are conducted to investigate the transition in a more realistic situation

Numerical Study of Backflow for Nozzle Plumes Expanding into Vacuum

This work is prompted by recent experiments on a multiphase (gas/droplets/cooling film) flow expanding from a supersonic nozzle into vacuum. A reverse motion of droplets (in the direction opposite to the flow in the plume core) has been experimentally observed near the nozzle lip. To understand this phenomenon, we have performed a numerical investigation of backflow formation. A hybrid Navier-Stokes/Direct Simulation Monte Carlo approach has been used to simulate the flow in different regimes — from a dense flow inside the nozzle, through very fast expansion near the nozzle lip, to a rarefied, freemolecular flow in the backflow region. A Lagrangian particle algorithm has been employed to trace the droplet motion in the gas flow. It has been shown that the gas backflow constitutes only a small part of the total mass flow rate. As a result, aerodynamic forces are insufficient to turn the droplets around the nozzle lip, and it seems that none of the droplets from the nozzle cannot reach the backflow region. Thus, it can be assumed that all droplets in the backflow originate from the cooling film being destroyed on the nozzle lip. Further, to investigate the viscous expansion flow near the nozzle lip in more detail, a model problem — the flow over a plane wall turning by a large angle (an expansion corner), has been studied using both continuum and kinetic modeling. It has been shown that, due to viscous effects, the flow deviates drastically from the classical Prandtl-Meyer solution. For large deflection angles, the decrease in the flow Mach number and the growth of the flow temperature are observed instead of their increase and fall, respectively. Reasons for such behavior are discussed, and the limits of applicability of the Navier-Stokes solution are analyzed.

Numerical investigation of high speed free shear flow instability and Mach wave radiation

The linear stability theory is used to investigate the emergence, in supersonic free shear flows such as mixing layers and fully expanded plane jets, of supersonically travelling instability waves, which do not vanish in the ambient space. It is shown that, at supersonic convective Mach numbers, the slow and fast supersonic modes in the mixing layer as well as the sinuous supersonic mode in the plane jet should lead to Mach wave radiation. Direct numerical simulations are further used to study nonlinear stages of instability development in high-speed mixing layers and jets. They have shown that the formation of oblique shock waves attached to large-scale structures is observed in free shear flows forced by modes with supersonic phase speeds. The relevance of this phenomenon to the noise generation by high-speed jets is discussed.

Viscous Effects in Steady Reflection of Strong Shock Waves

Regular and Mach reflections of shock waves from the symmetry plane in a steady Mach 4 flow of a monatomic gas have been numerically studied with the use of the continuum (Navier-Stokes) and kinetic (direct simulation Monte Carlo) simulations. Results of the computations demonstrate a prominent effect of flow viscosity and heat conduction in the vicinity of the shock intersection, where the flow parameters depart from the values prescribed by the inviscid theoretical solutions. The reasons for these discrepancies are discussed.

HyCFS, a high-resolution shock capturing code for numerical simulation on hybrid computational clusters

The present paper describes HyCFS code, developed for numerical simulation of compressible high-speed flows on hybrid CPU/GPU (Central Processing Unit / Graphical Processing Unit) computational clusters on the basis of full unsteady Navier-Stokes equations, using modern shock capturing high-order TVD (Total Variation Diminishing) and WENO (Weighted Essentially Non-Oscillatory) schemes on general curvilinear structured grids. We discuss the specific features of hybrid architecture and details of program implementation and present the results of code verification.

Comparison of Different Kinetic and Continuum Models Applied to the Shock‐Wave Structure Problem

Several kinetic and continuum models are used to study the stationary shock‐wave structure problem, which is a classical example of the flow including strong non‐equilibrium phenomena. Simulation results are compared with the experimental measurements.

Viscosity effects on weak shock wave reflection

The effects of flow viscosity on weak shock wave reflection are investigated with the Navier–Stokes and DSMC flow solvers. It is shown that the viscosity plays crucial role in the vicinity of three-shock intersection at the parameters corresponding to the von Neumann reflection of shock waves in steady flow. Instead of a singular triple point, in viscous flow there is a smooth shock transition zone, where one-dimensional shock jump relations cannot be applied.