An advanced model of fluid dynamics and nonequilibrium vibrational-chemical kinetics in high-temperature viscous flows along the stagnation line is proposed. The present model takes into account detailed state-to-state kinetics and state-dependent transport properties. Fluid dynamics equations are self-consistently coupled to vibrational kinetics, and state-dependent transport terms are properly incorporated in the governing equations. As an example, vibrational kinetics, macroscopic flow parameters, and heat transfer in a N 2 =N mixture are calculated for different flow conditions. A comparison with thermal equilibrium and vibrational frozen flows is presented, showing the important role of detailed kinetics coupled to fluid dynamics. Several models of chemical and vibrational kinetics are assessed and a strong dependence of the flow parameters and surface heat flux on the chemical model is demonstrated. Nomenclature c fr p = mixture frozen specific heat at constant pressure D ij = binary diffusion coefficients D = Fick's diffusion coefficient F = reduced tangential velocity, u=u f = stream function g = dimensionless enthalpy, h=h H M=A j;N = state-specific dissociation rate coefficients h i , h = species and mixture enthalpy per unit mass i, j, k = vibrational quantum number or species indices J i = dimensionless mass diffusion flux J y i = mass diffusion flux normal to the body surface K k;l i;j = rate coefficients for vibrational transitions k f=b r = forward/backward chemical reaction rates l 0 = Chapman-Rubesin parameter M i , M = species and mixture molar mass m i = species molecular mass Ns = total number of species (including vibrational levels) Nv = number of vibrational levels n i , n = species and mixture number density Pr = Prandtl number p = mixture pressure q w = surface heat flux r = local body radius S i , S T = source terms in simplified equations Sc = Schmidt number T = gas temperature u = velocity tangential to the body surface V = auxiliary variable in the Lees-Dorodnitsyn transformation v= velocity normal to the body surface _ W i = dimensionless species source term in the bulk _ W cat i = dimensionless species source term at the wall w = parameters at the body surface _ w i = species source term x, y = Cartesian coordinates x i , y i = species molar and mass fractions = parameters at the boundary-layer edge = first Lees-Dorodnitsyn coordinate = reduced temperature, T=T = thermal conductivity coefficient = shear viscosity coefficient 0 ir , 00 ir = stoichiometric coefficients of reactants and products = second Lees-Dorodnitsyn coordinate i , = species and mixture density
We propose a convenient formulation of elemental transport coefficients in chemically reacting and plasma flows locally approaching thermodynamic equilibrium. A set of transport coefficients for elemental diffusion velocities, heat flux, and electric current is introduced. These coefficients relate the transport fluxes with the electric field and with the spatial gradients of elemental fractions, pressure, and temperature. The proposed formalism based on chemical elements and fully symmetric with the classical transport theory based on chemical species, is particularly suitable to model mixing and demixing phenomena due to diffusion of chemical elements. The aim of this work is threefold: to define a simple and rigorous framework suitable for numerical implementation, to allow order of magnitude estimations and qualitative predictions of elemental transport phenomena, and to gain a deeper insight into the physics of chemically reacting flows near local equilibrium.
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