Dmitry Khotyanovsky

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 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.

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.

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.

Effects of Viscosity on Steady Reflection of Weak Shock Waves

The viscosity effects on weak shock wave reflection are investigated with the Navier– Stokes and DSMC flow solvers. It is shown that the viscosity plays a crucial role in the vicinity of three-shock intersection. 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. At the parameters corresponding to the von Neumann reflection, when no inviscid three-shock solution exists, the three-shock configuration is also observed. The existence of a viscous zone in the region of shock-wave interaction allows a continuous transition from the parameters behind the Mach stem to the parameters behind the reflected shock, which is impossible in the three-shock theory. I. Background and motivation Many interesting phenomena that occur in oblique shock wave reflection have been discovered in the past. The main feature herein is the existence of two possible configurations of shocks, regular and irregular. Regular reflection consists of the incident shock wave and the reflected shock wave with supersonic flow behind the reflected shock. Irregular reflection, which is in most cases called Mach reflection due to E. Mach who first discovered this phenomenon, is a complex shock wave pattern that combines the incident and reflected shock waves and the Mach stem. A contact discontinuity (slip surface) emanates from the triple point due to inequality of entropy in the flow passing through the incident and reflected shocks and the flow passing through the Mach stem. Classical theoretical methods such as shock polar analysis and the three-shock theory based on Rankine–Hugoniot jump conditions across the oblique shocks were developed by J. von Neumann to describe the shock wave configurations at various flow parameters and to predict transitions between different types of shock wave interaction. These theoretical methods predict well most of the features of shock wave interaction. Steady shock wave reflection is very important in aerodynamics and has been extensively studied in recent years with an emphasis on strong shock waves (for flow Mach numbers higher than 2.2 in air). For supersonic civil aviation, however, the lower Mach number range is of greatest interest. Regular and irregular interactions of different types are inherent in such critical phenomena as off-design inlet flows, inlet starting, and flow stalling. Interactions and reflections of weak shock waves are typical for supersonic inlet flows at low and moderate Mach numbers (M=1-2). There are many problems of irregular shock reflections in steady flows which are not yet investigated. One of the most exciting phenomena that occurs in irregular reflection of weak shock waves is a shock wave reflection in the range of flow parameters where the von Neumann’s three-shock theory does not produce any solution whereas the experiments reveal 1 a three-shock structure similar to the Mach reflection pattern. This inconsistency is referred to as the von Neumann paradox, and the observed reflection pattern is called the von Neumann reflection (vNR). Inviscid numerical simulations

Numerical study of the interaction of the N-wave with the plate leading edge in the supersonic stream

The results of three-dimensional numerical simulations of the interaction of the plane N-wave propagating at an angle to the free stream in the transverse direction with the sharp and blunted leading edges of the plate in a supersonic flow are presented. Interaction of the N-wave with a weak shock attached to the leading edge of the sharp plate causes corrugation of the shock wave surface that propagates downstream. A steady pressure perturbation is also formed that propagates inside the boundary layer in the transverse direction at an angle close to the Mach angle. This perturbation causes curving of the streamlines in the boundary layer and generation of a quasi-steady vorticity disturbance. In the case of the N-wave impinging on the leading edge of the blunted plate there is a large subsonic zone behind the bow shock where the pronounced oblique directivity of the disturbance transmitted through the shock is declined. Nevertheless, local disturbances of the flow parameters are observed in the boundary ...

Numerical study of the viscous heat-conducting gas flow in a long shock tube

The results of numerical simulations of the propagation of the shock wave in a cylindrical shock tube of large length are presented. The results of the numerical computations agree well with the experimental data of Duff. The effects of viscous friction and heat conduction cause significant difference of the shock wave velocity from its inviscid theoretical value. The results of the computations at the considered flow parameters show that the shock wave and the contact surface, starting from a certain moment of time, propagate with equal speeds.

DNS of surface roughness effects on laminar–turbulent transition in a supersonic boundary layer

The effects of the distributed surface roughness on mean flow distortion and generation of flow instabilities in a supersonic boundary layer at Mach number 2 are studied with the direct numerical simulation. Roughness elements cause distortions of the mean flow field and flow unsteadiness in their wake. Farther downstream, growth of the fluctuations contained in the streamwise vortices and the interaction of the adjacent vortices lead to a breakup of the boundary layer manifesting the beginning of the laminar–turbulent transition.

A comparative study of accuracy of shock capturing schemes for simulation of shock/acoustic wave interactions

We simulate transmission of a small-amplitude disturbance wave through a shock wave. Results of our numerical experiments performed with different high-order shock-capturing schemes show that the capability of a scheme to correctly predict the amplification of the disturbances crucially depends on the Riemann solver used in evaluation of numerical fluxes. Incorrectly high amplification rates are produced by the solvers resolving shock waves sharply, with no interior points in numerical profiles of steady shock waves. In particular, both the exact Riemann solver and the popular Roe flux difference splitting demonstrate such unphysical behavior. A possible explanation of such behavior is proposed. More dissipative solvers, such as the global Lax–Friedrichs splitting, produce transmission coefficients close to the predictions of linear theory.