G. P. Oblapenko

Reaction and internal energy relaxation rates in viscous thermochemically non-equilibrium gas flows

In the present paper, reaction and energy relaxation rates as well as the normal stress are studied for viscous gas flows with vibrational and chemical non-equilibrium. Using the modified Chapman-Enskog method, multi-temperature models based on the Treanor and Boltzmann vibrational distributions are developed for the general case taking into account all kinds of vibrational energy transitions, exchange reactions, dissociation, and recombination. Integral equations specifying the first-order corrections to the normal mean stress and reaction rates are derived, as well as approximate systems of linear equations for their numerical computation. Generalized thermodynamic driving forces associated with all non-equilibrium processes are introduced. It is shown that normal stresses and rates of non-equilibrium processes can be expressed in terms of the same driving forces; the symmetry of kinetic coefficients in these expressions is proven. The developed general model is applied to a particular case of a pure N2...

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.

Mutual effect of vibrational relaxation and chemical reactions in viscous multitemperature flows.

We study coupling of vibrational relaxation and chemical reactions in nonequilibrium viscous multitemperature flows. A general theoretical model is proposed on the basis of the Chapman-Enskog method modified for strongly nonequilibrium reacting flows; the model differs from models commonly used in computational fluid dynamics since it is able to capture additional cross-coupling terms arising in viscous flow due to compressibility and mutual influence of all nonequilibrium processes occurring in a mixture. The set of fluid dynamic equations is derived starting from the Boltzmann equation; the relaxation terms in these equations are described using the kinetic transport theory formalism. Reaction and relaxation rates depend on the distribution function and thus differ in the zero-order and first-order approximations of the Chapman-Enskog method. An algorithm for the calculation of multitemperature reaction and relaxation rates in both inviscid and viscous flows is proposed for the harmonic oscillator model. This algorithm is applied to estimate the mutual effect of vibrational relaxation and dissociation in binary mixtures of N(2) and N, and O(2) and O, under various nonequilibrium conditions. It is shown that modification of the Landau-Teller expression for the VT relaxation term works rather well in nitrogen, whereas it fails to predict correctly the relaxation rate in oxygen at high temperatures. In oxygen (in contrast to nitrogen), the first-order cross effects of dissociation and VT relaxation are found to be significant. A method for calculation of vibrational relaxation time based on the kinetic theory definition is suggested. Two-temperature dissociation rate coefficients are calculated in the zero- and first-order approximations and compared to other models.

State-to-state models of vibrational relaxation in Direct Simulation Monte Carlo (DSMC)

In the present work, the application of state-to-state models of vibrational energy exchanges to the Direct Simulation Monte Carlo (DSMC) is considered. A state-to-state model for VT transitions of vibrational energy in nitrogen and oxygen, based on the application of the inverse Laplace transform to results of quasiclassical trajectory calculations (QCT) of vibrational energy transitions, along with the Forced Harmonic Oscillator (FHO) state-to-state model is implemented in DSMC code and applied to flows around blunt bodies. Comparisons are made with the widely used Larsen–Borgnakke model and the influence of multi-quantum VT transitions is assessed.

Vibration-dissociation coupling in multi-temperature viscous gas flows

Vibrational and chemical relaxation rates are studied in viscous multi-temperature flows of binary mixtures with strong thermo-chemical non-equilibrium. Cross-coupling effects between dissociation reactions and slow VT relaxation are investigated, and viscous corrections accounting for these effects are computed for flows behind strong shock waves and in nozzles. The applicability of simplified relaxation models, such as the Landau–Teller equation for vibrational relaxation and the Treanor–Marrone and Park models for dissociation reactions is analyzed, along with the necessity of accounting for viscous effects in simulations of non-equilibrium reacting flows.

Inverse Laplace transform as a tool for calculation of state-specific cross sections of inelastic collisions

In the present work we study the cross sections of VV (vibration-vibration), VT (vibration-translation) energy exchanges and state-specific dissociation reactions in N2 and O2 molecules. Applying the inverse Laplace transform to approximations for state-resolved rate coefficients obtained by quasi-classical trajectory calculations we derive analytical expressions for the cross sections. The results are analyzed in a wide range of energies and vibrational levels. It is shown that cross sections of VV transitions increase almost linearly with the energy of the colliding particles. VT exchanges and dissociation reactions manifest threshold behaviour, and their cross sections are non-monotonic. The dissociation threshold is considerably shifted towards the low energy region for high vibrational states. Using the hard sphere model for the dissociation cross section results in significant inaccuracy. The results of our work can be applied in non-equilibrium fluid dynamics while simulating rarefied gas flows usi...

Low-Cost Robotic Set-Up for Pursuit Problems

Abstract In the paper two robotic set-ups illustrating pursuing problems are presented. Both set ups are made of LEGO Mindstorms NXT set and use advance programming tools. Using the presented set ups allows teachers to include low cost robotic projects into science and engineering education.