The quasi-one-dimensional equations of uid motion are coupled with the equations for nite-rate chemistry to model high-speed engine ow elds. The model was developed for rapid vehicle design and optimization, where a wide range of engine inlet conditions may be encountered. Incorporating the timescales of fuel mixing and ignition are crucial for accurate prediction of combustor performance, especially for nonhydrogen fuels and off-design conditions (where equilibrium assumptions are invalid). The effects of area change, friction, mass injection, fuel mixing, and heat transfer to the combustor walls are included. The resulting model is compared to experimental results for hydrogen-fueled scramjet engines to demonstrate the ability to predict wall pressure pro les and fuel ignition point. Application to a rocket-based combined-cycle engine and a hydrocarbon scramjet missile engine are discussed. The model presented predicts peak pressure and fuel ignition accurately, as well as ow eld pressures in regions where boundary-layer separation is not present.
Nomenclaturehydraulic diameter, m f st = stoichiometric fuel/air ratio g = gravitational acceleration, m/s 2 h = enthalpy per unit mass, J/kg I sp = speci c impulse, s L = length, m M = Mach number M W = molecular weight, kg/kmol M W = mixture molecular weight, kg/kmol P m = mass ow rate, kg/s P w = wetted perimeter, m Pr = Prandtl number p = pressure, N/m 2 P Q = heat-transfer rate, J/s R u = universal gas constant, J/(kmol-K) T = temperature, K; thrust, N U = velocity, m/s V = volume, m 3 X = mole fraction x = axial coordinate, m N x = nondimensional axial coordinate Y = mass fraction°= ratio of speci c heats 1x = control volume increment of x " = ratio of gas injection velocity to freestream velocitý = ef ciency ½ = density, kg/m 3 . Associate Fellow AIAA. Á = equivalence ratio P ! = molar production rate, kmol/(s-m 3 ) Subscripts added = species added for mass/fuel injection aw = adiabatic wall comb = combustor e = end eff = effective f = total fuel available i = i th species inj = injection mix = mixing o = total or stagnation conditions r = available for reaction s = start st = stoichiometric conditions w = wall x; 1x = control volume descriptors 1 = freestream conditions Superscripts 00 = per unit area 000 = per unit volume ¤ = evaluated at the reference temperature
