Ye. A. Bondar

Direct Monte Carlo simulation of high-temperature chemical reactions in air

A novel approach to modeling high-temperature nonequilibrium dissociation in air at a level of molecular collisions is proposed. Information on the energy dependence of the specific reaction cross sections, which is necessary for such modeling, is determined numerically from available macroscopic information on the dependence of the reaction rate constant on translational and vibrational temperatures. The results of Direct Simulation Monte Carlo (DSMC) computations show that the proposed model yields a correct reaction rate in vibrational-translational nonequilibrium. The use of the new model in DSMC computations of high-altitude aerothermodynamics results in obtaining a noticeably different flow structure and a higher heat flux, as compared to that predicted by standard DSMC models (such as the total collision energy model).

Development and testing of a numerical simulation method for thermally nonequilibrium dissociating flows in ANSYS Fluent

Various issues of numerical simulation of supersonic gas flows with allowance for thermochemical nonequilibrium on the basis of fluid dynamic equations in the two-temperature approximation are discussed. The computational tool for modeling flows with thermochemical nonequilibrium is the commercial software package ANSYS Fluent with an additional userdefined open-code module. A comparative analysis of results obtained by various models of vibration-dissociation coupling in binary gas mixtures of nitrogen and oxygen is performed. Results of numerical simulations are compared with available experimental data.

Study of the shock wave structure by regularized Grad’s set of equations

In this work, we continue to study the possibility of applying moment equations for strongly nonequilibrium flows by an example of the problem of the shock wave structure in a monatomic gas in a wide range of Mach numbers for various models of molecular interaction. The object of the study is the so-called regularized 13-moment Grad’s system (R13). First time, both linear and nonlinear versions of this system of equations were considered for the problem at such wide range of parameters. The Godunov method with increased accuracy is used as a numerical tool for solving the R13 system. The numerical results for the R13 system are analyzed by using data obtained by the Direct Simulation Monte Carlo (DSMC) method, experimental data, and analytical results. As a whole, the R13 system provides an adequate description of the shock wave structure in a wide range of Mach numbers. For Mach numbers around 2, good agreement with experimental and DSMC results is observed for both linear and nonlinear versions of the s...

Different variants of R13 moment equations applied to the shock-wave structure

Various versions of the regularized 13-moment system (R13) are applied to the problem of the shock wave structure in a monatomic Maxwell gas for Mach numbers up to M = 10. Numerical solutions are compared to direct simulation Monte Carlo results computed by the SMILE++ software system, in order to identify applicability and limitations of the variants. Over time, several versions of the R13 equations were presented, which differ in non-linear contributions for high-order moments but agree in asymptotic expansion to the third order in the Knudsen number. All variants describe typical subsonic microflows well, for which the non-linear contributions only play a minor role. The challenge of the present study is to determine the real boundaries of applicability of each variant of the moment equations as applied to non-equilibrium supersonic flows, depending on the Mach number and local Knudsen number.

Numerical study of shock wave entry and propagation in a microchannel

The entry of a shock wave with the Mach number Mis = 2.03 into a microchannel and its further propagation is numerically studied with the use of kinetic and continuum approaches. Numerical simulations on the basis of the Navier — Stokes equations and the Direct Simulation Monte Carlo method are performed for different Knudsen numbers Kn = 8·10−3 and 8·10−2 based on the microchannel half-height. At the Knudsen number Kn = 8·10−3, amplification of the shock wave after its entry into the microchannel is observed. Further downstream, the shock wave is attenuated, which is in qualitative agreement with experimental data. It is demonstrated that results predicted by a quasi-one-dimensional model (which ignores viscosity and heat conduction) of shock wave propagation over a channel with an abrupt change in the area agrees with results of numerical simulations on the basis of the Euler equations. In both cases, shock wave acceleration (amplification) after its entry into the microchannel is observed. At the Knudsen number Kn = 8·10−2, the influence of the entrance shape on shock wave propagation over the microchannel is examined. Intense attenuation of the shock wave is observed in three cases: channel with sudden contraction, junction of two channels with an additional thin separating plate, and rounded junction in the form of a sector with an angle of 90° (quarter of a circumference). It is shown that the microchannel entrance shape can affect further propagation of the shock wave. The wave has the highest velocity in the case with a rounded entrance.

Study of the shock wave structure by regularized Grad's set of equations

This study is devoted to the analysis of applicability of moment equations to the shock wave structure problem in a wide range of Mach numbers. A modification of original Grads 13-moment set of equations, so-called regularized Grads set of equations (R13), is taken as a mathematical model. The numerical method for this set is formulated as a variant of the explicit high-order Godunov scheme with linear reconstruction of flow parameters. The degree of applicability of moment equations is determined by comparisons with Direct Simulation Monte Carlo (DSMC) predictions. Numerical results for hard sphere molecules show that the R13 set of equations describes well the internal structure of the shock wave in a wide range of Mach numbers. Nevertheless, R13 set significantly overpredicts the overall temperature overshoot (about 3 times for M=8), which is apparently related to nonlinearity of the dependence of the product of the transverse temperature component and density on normalized density.

Rarefaction effects in hypersonic flow about a blunted leading edge

The rarefaction effects in the problem of hypersonic flow around a profile with blunted leading edge are studied in the flow regimes when the edge bluntness radius is comparable with the mean free path in the free stream. The flow around a cylindrically blunted thick plate at zero incidence was modelled numerically in the transitional regime by using the direct simulation Monte Carlo method, the finite-difference solution of the kinetic equation of the relaxation type (the ellipsoidal statistical model), and the solution of the Navier — Stokes equations. It is shown that for the Knudsen numbers in terms of the bluntness radius below 0.1, the Navier — Stokes equations can be applied successfully for viscous flow description behind the shock wave provided that the initial rarefaction effects are taken into account via the slip and temperature jump boundary conditions on the plate surface. For Knudsen number of about 0.5, the rarefaction effects are more appreciable; in particular, a substantial anisotropy of the distribution function takes place, but the Navier — Stokes equations yield, as before, a qualitatively correct result. The initial stage of the boundary layer development in the edge vicinity has been studied. In the considered range of Knudsen numbers, the entropy layer near the edge is comparable with the boundary layer thickness. As the distance from the leading edge increases one observes the absorption of the entropy layer by the boundary layer. In the studied parameter range, the interaction between the boundary and entropy layers leads to a flow stability increase.

The Analysis of Different Variants of R13 Equations Applied to the Shock-Wave Structure

This paper studies the applicability of various versions of the regularized 13-moment system (R13) as applied to the problem of the shock wave structure in a monatomic Maxwell gas in a wide range of Mach numbers (1.0<M<8.0). Over time, several versions of the R13 equations were presented, which differ in non-linear contributions for high-order moments. The challenge of this study is to determine the range of applicability of each variant of the moment equations as applied to non-equilibrium supersonic flows, depending on the Mach number and local Knudsen number. Numerical results obtained for the R13 system are compared to DSMC data computed by the SMILE++ software system.

Modeling of the Plume of an ATON-Hall Thruster

A particle approach was applied to simulate numerically the ATON thruster plume flow. Comparison with ground-based facility experimental data was performed. The facility effects were assessed using two different techniques for the plume-background gas interaction, Particle-in-Cell/Monte Carlo collisions method and Particle-in-Cell/Direct Simulation Monte Carlo method. The importance of modeling the plume-background gas interaction was shown by a comparison of the computational results obtained using these two methods with total ion current measurements. ATON thruster plume expansion under space vacuum conditions was also simulated by the Particle-in-Cell/Monte Carlo collisions method.

DIRECT STATISTICAL MONTE CARLO SIMULATION OF THE SHOCK-WAVE STRUCTURE IN DISSOCIATING GAS *

The applicability of a new model in terms of the description of real gas effects in the Direct Simulation Monte Carlo method is analysed. The model is used in a numerical study of the internal structure of the front of a strong shock wave and relaxation zone behind the front for conditions corresponding to spacecraft entry into the Martian atmosphere. The influence of the free-stream parameters on relaxation of various energy modes of molecules in the wave front and in the relaxation region is considered. The effect of chemical reactions on the flow structure is studied. A detailed analysis of flow nonequilibrium is performed at the level of the velocity distribution function and population of rotational and vibrational levels of molecules.