State-to-State Simulation of Nonequilibrium Nitrogen Stagnation-Line Flows: Fluid Dynamics and Vibrational Kinetics

Abstract

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

Different Approaches for Modelling of Heat Transfer in Non-Equilibrium Reacting Gas Flows

“…Such an approach is not completely self-consistent, since the flow parameters and transport terms remain uncoupled, but it makes possible to take into account the influence of the state-to-state kinetics on the flow parameters and heat transfer near the wall. Recently, a similar N 2 /N flow was studied in Orsini et al (2008) within a more rigorous model incorporating the accurate kinetic theory transport algorithms directly into the boundary layer equations. In this paper, the accurate set of the fluid dynamic equations was solved, and the results are compared to those obtained within the simplified formulation of the problem.…”

State-to-State Kinetic Theory Approach for Transport and Relaxation Processes in Viscous Reacting Gas Flows

“…Evaluation of the state-dependent transport coefficients in the flows behind shock waves, in nozzles and in a boundary layer has been done using the approximate way: first, macroscopic parameters were found from simplified fluid-dynamics equations and then implemented to the accurate kinetic theory transport algorithms (see [1]). Self-consistent approach based on the direct implementation of the state-to-state transport kinetic theory algorithms to the CFD code was performed, for the first time, in [5,6] for a viscous flow of a binary mixture near a body surface. The comparison of the results obtained in the frame of simplified and self-consistent approaches showed a noticeable difference.…”

Role of State-to-State Kinetics in Determining Transport Coefficients for Hypersonic Flow Simulations

“…A justification for this more general state kinetic approach for transport coefficients for given sets of flow conditions was provided in earlier work, see for example [14,15].…”