Nomenclature C = molar concentration, mol=m cp;k = specific heat at constant pressure for species k, J= kg K D = injector diameter, m Dk = diffusion coefficient for species k, m =s E = total energy per unit mass, J=kg f = frequency, 1=s H = total enthalpy per unit mass, J=kg h = enthalpy per unit mass, J=kg hk = enthalpy per unit mass for species k, J=kg H j = subgrid-scale total enthalpy flux vector, J= m s h = subgrid-scale species mass fraction-enthalpy correlation, J=kg J = jet-to-crossflow momentum flux ratio k = turbulent kinetic energy, m=s k = subgrid-scale kinetic energy, m=s M = Mach number m = mass flow rate, kg=s Mw = molecular weight, kg=mol p = static pressure, Pa Prt = turbulent Prandtl number pt = total pressure, Pa qj = heat flux vector, J= m s q j = subgrid-scale energy diffusion due to species diffusion, J= m s R = mixture’s gas constant, J= kg K Rk = gas constant for species k, J= kg K ReD = Reynolds number based on D rs = spatial correlation coefficient rts = time–space correlation coefficient Sij = rate of strain tensor, 1=s Sct = turbulent Schmidt number T = static temperature, K t = time, s Tt = total temperature, K T = subgrid-scale mixture gas constant-temperature correlation, J=kg T = reference temperature, K U = velocity magnitude, m=s u, v, w = velocity components in x, y, and z directions, m=s Uc = convection velocity, m=s ui = velocity component in xi direction, m=s Vj;k = species diffusion velocity vector for species k, m=s x, y, z = streamwise, transverse, and spanwise direction distances in Cartesian coordinates, m xi = Cartesian coordinates, m Yk = mass fraction for species k Y j;k = subgrid-scale species diffusion vector, kg= m s = specific heat ratio hf;k = standard heat of formation at T , J=kg in = mean boundary-layer thickness at inlet, m m = mixing efficiency sgs j;k = subgrid-scale species mass fraction-diffusion velocity correlation, kg= m s = mixture’s thermal conductivity, J= m K s = mixture’s molecular viscosity, kg= m s t = subgrid-scale eddy viscosity, m =s = density, kg=m ij = viscous stress tensor, Pa sgs j = subgrid-scale viscous work, J= m s sgs ij = subgrid-scale stress tensor, Pa ’ = local equivalence ratio