Mikhail S. Ivanov

Hysteresis processes in the regular reflection↔Mach reflection transition in steady flows

Abstract Ernst Mach recorded experimentally, in the late 1870s, two different shock-wave reflection configurations and laid the foundations for one of the most exciting and active research field in an area that is generally known as Shock Wave Reflection Phenomena . The first wave reflection, a two-shock wave configuration, is known nowadays as regular reflection , RR, and the second wave reflection, a three-shock wave configuration, was named after Ernst Mach and is called nowadays Mach reflection , MR. A monograph entitled Shock Wave Reflection Phenomena , which was published by Ben-Dor in 1990, summarized the state-of-the-art of the reflection phenomena of shock waves in steady, pseudo-steady and unsteady flows. Intensive analytical, experimental and numerical investigations in the last decade, which were led mainly by Ben-Dors research group and his collaboration with Chpouns, Zeitouns and Ivanovs research groups, shattered the state-of-the-knowledge, as it was presented in Ben-Dor (Shock Wave Reflection Phenomena, Springer, New York, 1991), for the case of steady flows. Skewss and Hornungs research groups joined in later and also contributed to the establishment of the new state-of-the-knowledge of the reflection of shock waves in steady flows. The new state-of-the-knowledge will be presented in this review. Specifically, the hysteresis phenomenon in the RR↔MR transition process, which until the early 1990s was believed not to exist, will be presented and described in detail, in a variety of experimental set-ups and geometries. Analytical, experimental and numerical investigations of the various hysteresis processes will be presented.

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 Modeling of Near-Continuum Flow over a Wedge with Real Gas Effects

Effects of vibrational relaxation and dissociation on the standoff distance of the bow shock wave on a wedge are numerically examined with the use of the kinetic (DSMC method) and continuum (Navier-Stokes equations) approaches. A hypersonic flow around the wedge is computed for Knudsen numbers about 5 x 10 -4 in a wide range of wedge angles both for a monatomic gas (argon) and a diatomic reacting and nonreacting gas (nitrogen). DSMC computations are based on three different real gas effect models. The kinetic and continuum results for the standoff distance are in good agreement for argon and nonreacting nitrogen. The influence of vibration-dissociation coupling on the results of numerical simulations is analyzed. Sensitivity of simulation results to chemical reaction rate constants is also estimated. Numerical simulations show that dissociation is responsible for the nonlinear form of the dependence of the standoff distance on the wedge angle, which qualitatively agrees with available experimental data.

Numerical study of 2D/3D micronozzle flows

Methods for creating thrusters with very low thrust using micronozzles have been actively developed recently. The flow in such nozzles is characterized by low Reynolds numbers and, as a consequence, by high viscous losses. DSMC calculations for flows in plane and three-dimensional micronozzles have been conducted in the present paper. A comparison of DSMC results with available experimental data of the nozzle performance is presented. It is proposed to increase the efficiency of micronozzles by helium injection to the near-wall flow region at the throat. This leads to a significant increase in the gas velocity near the nozzle wall and in the specific impulse.

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.

DSMC Dissociation Model Based on Two-Temperature Chemical Rate Constant

A novel approach to statistical simulation of high-temperature nonequilibrium chemical reactions is described. Vibrationally speciflc dissociation cross sections are sought solving an integral equation whose right side contains a two-temperature reaction rate constant. An approximate stable solution of this equation is found numerically by Tikhonov regularization method. The class of functions to which the solution belongs is deflned on the basis of physical concepts of the form of the sought cross sections as functions of energy. The approach is illustrated by an example of the model of high-temperature dissociation of nitrogen. All stages of model implementation are considered in detail, namely, the mathematical basis, analysis of the model by comparisons with conventional models both at the level of cross sections and at the level of macroscopic reaction rates, and particular applications to computations of near-continuum reacting ∞ows by the Direct Simulation Monte Carlo method.

Accuracy analysis of DSMC chemistry models applied to a normal shock wave

A preliminary validation study of three DSMC chemistry models, two recent and one standard, is presented. First the 2D geometry and numerical approach used to simulate the shock experiments is verified. Next, 2 different vibrational relaxation models are validated by comparison with data for the M=9.3 case where dissociation is small in the nonequilibrium region of the shock. Finally, the 3 DSMC chemistry model results are compared for the M=13.4 case where nonequilbrium dissociation (in the region where the vibrational temperature is greatly different from the rotational and translational temperature) is important. It is shown that the peak vibrational temperature is very sensitive to vibrational favoring in the chemistry model and that the vibrationally-favored KSS model predicts the measured peak quite well.

Hydrogen‐Oxygen Detonation Study by the DSMC Method

The DSMC method was applied to perform a numerical study of detonation in an H2/O2 mixture with detailed chemical kinetics at the molecular level. Collision chemistry models were modified to correctly reproduce the chemical equilibrium in mixtures of polyatomic molecules. The DSMC results on homogeneous constant‐volume adiabatic autoignition of the stoichiometric H2/O2 mixture are in good agreement with the numerical solution of equations of chemical kinetics. The results of the DSMC modeling of a nonstationary detonation wave for different values of pressure yield the velocity of detonation that coincides with the Chapman‐Jouguet velocity. The structure of the detonation wave obtained in the DSMC simulation is in qualitative agreement with the Zeldovich–von Neumann–Doering theory.

DSMC Study of an H2/O 2 Detonation Wave Structure

Direct simulation Monte Carlo (DSMC) method was applied to numerical study of detonation in an H2/O 2 mixture with detailed chemical kinetics on the basis of effective DSMC molecular chemistry models. The results of the DSMC modeling of an unsteady detonation wave initiated by breakdown of a diaphragm between two channels with different pressures yield the velocity of detonation, which coincides with the ChapmanJouguet velocity. The internal structure of the detonation wave obtained in DSMC simulations is in good qualitative agreement with the detonation-wave structure calculated on the basis of the Zeldovich – von Neumann – Doering (ZND) theory. I. Introduction OLECULAR-LEVEL investigations of gas detonation are important both for applications associated with propagation of detonation waves at small scales and for basic research. The molecular-kinetic description of the gas at the level of the distribution functions of molecular velocities and internal states is usually used for rather rarefied gas flows, in particular, in problems of high-altitude aerothermodynamics of space vehicles [1], though it is also applicable for dense flows. The distribution function is sought as the solution of the integrodifferential Boltzmann kinetic equation, which describes the function evolution due to molecular transfer and collisions. The most effective numerical method for solving the Boltzmann equation is currently the Direct Simulation Monte Carlo (DSMC) method [2]. The conventional treatment of the DSMC method is based on considering the gas flow as a set of 10 5 -10 7 particles (each of them represents a large number of gas molecules) and on the principle of

Numerical Investigation of the EXPERT Reentry Vehicle Aerothermodynamics Along the Descent Trajectory

Results of numerical simulations of high-altitude aerothermodynamics of the EXPERT reentry capsule along its descent trajectory are presented. Aerodynamic characteristics for different angles of attack and rolling of the capsule at altitude of 150 down to 20 km are studied. An engineering local bridging method is used in computations. The uncertainty of the engineering method in the transitional regime is determined by comparisons with results obtained by DSMC simulations. I. Introduction During disorbiting, the spacecraft experiences the influence of the atmosphere with significantly varying parameters. To estimate the aerodynamic loads and to predict the landing area, one should know, already at the stage of design, the coefficients of aerodynamic forces and moments of the spacecraft for varying temperature, density, flight velocity, and angles of attack and sideslip for numerous possible descent trajectories. Thousands of various variants have to be computed. At the beginning of descent, at high altitudes where the gas is strongly rarefied, numerical simulations do not involve many difficulties, because theoretical approaches have been developed for simple shapes and the Test Particle Monte Carlo method can be readily used for more complicated shapes. On the other hand, various engineering approaches have been developed for calculating aerodynamic characteristics of various bodies at the final segment of the descent trajectory, in the continuum regime, which are fairly effective. The main problem is the analysis of spacecraft aerodynamics in the transitional regimes between the free-molecular and continuum regimes. The Navier-Stokes equations yield, strictly speaking, incorrect results in the transitional regime and require special modifications for taking into account flow slipping. The Direct Simulation Monte Carlo (DSMC) method provides rather accurate values of aerodynamic characteristics with allowance for physical and chemical processes but requires large amounts of computer memory and performance. Application of the software based on the DSMC method is unreasonably expensive at the initial stage of spacecraft design and trajectory analysis. A possible solution of this problem is the approximate engineering methods. These methods allow calculating aerodynamic characteristics of bodies of arbitrary geometry for multiple variants of free-stream parameters within a reasonable time and then to refine the results at the most important segments of the flight trajectory by the DSMC method. The use of fast approximate engineering methods is the most acceptable approach to solving problems of spacecraft aerodynamics at the stage of conceptual design. The present paper describes the computations of aerodynamics of the EXPERT capsule by an engineering local bridging method at altitudes of 150 down to 20 km with flow parameters corresponding to the expected descent trajectory. The results in the transitional regime are refined by the DSMC method. The errors of the engineering method are studied in detail, and the contribution of various elements of the EXPERT capsule to aerodynamic characteristics is analyzed. II. EXPERT geometry The KHEOPS configuration (Fig. 1) is a blunted pyramidal shape featuring four flaps. The computational model was constructed by the RuSat software system. The total number of panels is approximately 36 thousand. The nose is made in the form of an ellipse with a misalignment of 0.9165. The local radius of the nose part is 0.6 m. The ellipse-cone junction is described by a clothoid. The conical body has a cone angle of 12.5°. The cone is truncated by planes at an angle of 8.35° to the axis of symmetry. Four control flaps are deflected by 20 °.