Yevgeniy A. Bondar

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.

Comparison of direct simulation Monte Carlo chemistry and vibrational models applied to oxygen shock measurements

Validation of three direct simulation Monte Carlo chemistry models—total collision energy, Quantum Kinetic, and Kuznetsov state specific (KSS)—is conducted through the comparison of calculated vibrational temperatures of molecular oxygen with measured values inside a normal shock wave. First, the 2D geometry and numerical approach used to simulate the shock experiments is verified. Next, two 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 and with newly obtained thermal rates. Finally, the three chemistry model results are compared for M = 9.3 and 13.4 in the region where the vibrational temperature is greatly different from the rotational and translational temperature, and thus nonequilibrium dissociation is important. It is shown that the peak vibrational temperature is very sensitive to the initial nonequilibrium rate of reaction in the chemistry model and that the vibrationally favored KSS model is much closer to the measured peak, but the post-peak behavior indicates that some details of the model still need improvement.

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.

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.

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

DSMC Modeling of the Detonation Wave Structure in Narrow Channels

RANSITIONAL and near-continuum flows are important for numerous promising applications, in particular, in the development of microand nanoelectromechanical systems (MEMS and NEMS) and low-thrust engines for aerospace applications. A more profound understanding of the nature of flows in such engineering systems is an urgent problem of today’s fluid mechanics and also molecular physics [1, 2]. A principally novel aspect of this field is the development of micro-devices capable of performing mechanical work with the use of chemically induced heat release. As the efficiency of conventional devices, such as internal combustion engines, rapidly decreases with a decrease in their size because of higher heat loss, a reasonable direction of MEMS and NEMS evolution seems to be the use of detonation waves at the microscopic scale for accelerating combustion processes and increasing the heat-release rate [3, 4]. This requires better understanding of physical and chemical processes associated with propagation of detonation waves at small scales. There is a significant current effort in this direction; in particular, the beginning of activities aimed at creating a microscopic test facility (shock tube 10 μm in diameter) was announced [4]. Some recent publications also deal with microdetonics – processes that occur during detonation of microscopic amounts of explosives. Interesting results were obtained in experimental research of propagation of detonation waves in capillary tubes (V.I. Manzhalei, Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 1992-1999); in particular, Manzhalei found that detonation waves under such conditions can propagate with velocities that are only 0.45-0.6 of the Chapman-Jouguet velocity. It should be noted that propagation of detonation waves in thin capillary tubes is important for explosion safety problems. Numerical simulations can become a really indispensable tool for solving problems of detonation at small scales. There are two different approaches, kinetic and continuum, to the gas flow modeling. In the first approach, the gas is considered at a level of the molecular velocity distribution function which can be determined as the solution of the kinetic Boltzmann equation; in the second approach, the gas or liquid is presented as a continuum whose motion is determined by the laws of conservation of mass, momentum, and energy. Flows whose geometric scales are typical of MEMS are near-continuum or transitional, which necessitates allowance for rarefaction effects, because the mean free path of molecules λ cannot be considered as negligibly small, as compared with the characteristic length scale L of the flow. Though the kinetic approach can be used to describe gas flows in all regimes, its application in practice for modeling a rather dense gas is impossible because of tremendous computational resources needed for that. The most effective numerical method for solving the Boltzmann equation is currently the Direct Simulation Monte Carlo (DSMC) method [5]. It allows computations of steady flows with Knudsen numbers Kn=λ /L=0.001 for twodimensional problems and Kn=0.005 for three-dimensional problems, i.e., up to the continuum flow regime [6, 7]. The DSMC method is well suited for modeling flows with nonequilibrium chemical reactions. Collision models of various chemical processes (vibrational and electron excitation and relaxation, dissociation, recombination, ionization, etc.) can be implemented directly into the collision algorithm. Nevertheless, the DSMC method can be hardly applied to compute unsteady flows because of considerable statistical fluctuations arising if averaging over a sufficiently large time period cannot be performed, which is the case with unsteady flows. Solving such problems is impossible without parallel computational technologies and without using advanced multiprocessor computers. The continuum approach is usually much less expensive, which is a strong argument for using the latter. It is applicable, however, for low Knudsen numbers only. For Knudsen numbers Kn ~ 10 -2 and higher, the continuum approach has

Numerical simulations of nonequilibrium flows over rounded models at reentry speeds

Chih-Yung Wen⇤ Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong Heriberto Saldivar Massimi† Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan 70101 Yen-Sen Chen‡ National Space Organization, Hsinchu Science Park, Hsinchu, Taiwan 30078 Shen-Min Liang§ Department of Computer Application Engineering, Far East University, Taiwan 744 Yevgeniy A. Bondar¶ and Mikhail S. Ivanov k Khristianovich Institute of Theoretical and Applied Mechanics SB RAS, Novosibirsk, Russia 630090

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.

Numerical study of non-equilibrium gas flows with shock waves by using the Navier–Stokes equations in the two-temperature approximation

Validation of various models of vibration-dissociation coupling for simulating high-enthalpy non-equilibrium gas flows of binary mixtures of oxygen O2/O and nitrogen N2/N is discussed. Numerical simulations are based on the Navier–Stokes equations in the two-temperature approximation. The rate of VT-exchange is computed by a modification of the Landau–Teller formula, which was derived from the kinetic Boltzmann equation. The dissociation rate is calculated by different two-temperature models: β-model, Marrone–Treanor, Macheret–Fridman, Kuznetsov, and Park models. Numerical results are compared with available experimental measurements.