Procedure to Validate Direct Numerical Simulations of Wall- Bounded Turbulence Including Finite-Rate Reactions

cp = specific heat at constant pressure, J= kg K cv = specific heat at constant volume, J= kg K E = total energy, J=m Ev = vibrational energy, J=m h = specific enthalpy, J=kg h = heat of formation, J=kg Keq = Equilibrium constant kB = Boltzmann’s constant, 1:381 10 23 J=K kb = backward reaction coefficient kf = forward reaction coefficient M = molecular weight, kg=mole NA = Avogadro’s number, 6:022 10 mole 1 p = pressure [ s s R̂=Ms T], Pa q = heat flux [ @T=@xj ], J= m s Sij = Strain rate tensor [ 1 2 @ui=@xj @uj=@xi ], s 1 T = translational temperature, K u = velocity, m=s v = diffusion velocity, m=s v = average thermal velocity, m=s w = production rate, kg= m s x = spatial coordinate along streamwise direction, m y = spatial coordinate along wall-normal direction for twodimensional flows, m z = spatial coordinate along wall-normal direction for three-dimensional turbulent flows, m = heat capacity ratio or catalytic recombination coefficient R̂ = universal gas constant, 8.314 J= mole K v = vibrational temperature, K = mixture thermal conductivity, J= K m s = mixture viscosity, kg= m s = density, kg=m ij = shear stress tensor (2 Sij 23 ijSkk), Pa