Investigation of mixing and burning processes in supersonic flows is one of the key trends in construction of effective engines for high-speed propulsion systems. Current research is aimed to development of mathematical model and computational algorithms of supersonic mixing and burning.

RANS approach with classical Spalart-Allmaras (SA) turbulence model supplemented with diffusion model is used. Specific heat coefficient depends from temperature in the polynomial form. Laminar and turbulent heat transfer coefficients are calculated using Reynolds analogy. Diffusion coefficient is obtained from viscosity coefficients and Schmidt numbers. Detailed kinetics mechanism consists of 22 reversible reactions between 9 components. Three reactions from kinetics set are also pressure-dependent.

Reynolds averaged Navier-Stokes equation system analogue for compressible multicomponent gas, closed with SA turbulence model equation is solved. Parallel realization of hybrid GMRES-LU-SGS method is used for equation system solution. Time integration is carried out with explicit-implicit method. Chemical kinetics equation system is solved with Gear method.

Processes of parallel hydrogen injection in vitiated air supersonic flow and further mixing, ignition and flame stabilization in model Burrows-Kurkov combustor are investigated for validation of computational algorithm. Calculations were performed in 2D and 3D statements. Combustor geometry is given in [1]. Hydrogen flow has velocity, corresponding to Mach number , vitiated air flow – corresponding to Mach number . Other flow parameters are given in [2]. Combustor walls are made of copper and able to warm up. Inflow boundary condition for vitiated air stream is set as parameters profiles, obtained from gas flow through 1m long rectangular channel problem solution. For hydrogen inflow boundary condition is specific mass flow rate. Outflow boundary condition is hybrid, depending from local Mach number.

Problem was solved in 2D and 3D cases, that showed similar, but not identical results. Minor quantity differences can be explained by presence of side boundary layers in 3D case. Profiles of main parameters such as Pitot pressure, total temperature, static temperature and Mach number were analyzed in two planes: near the splitter end and near the combustor exit. Additionally, molar fractions of components were investigated near the combustor exit. Obtained results have good agreement with experimental [1] and computational [2] data. Total temperature and static temperature profiles correspond experimental data even better than calculations from [2].

It can be stated that model is functioning correctly and can be used for reacting supersonic flows modelling.

Calculations are carried out on “MVS – 10P” cluster of JSCC RAS.

References

1. Burrows M.C., Kurkov A.P. Analytical and Experimental Study of Supersonic Combustion of Hydrogen in a Vitiated Airstream // NASA-TM-X-2828, September 1973.
2. Edwards, J.R., J.A. Boles, and R.A. Baurle. 2012. Large-eddy/ Reynolds-averaged Navier-Stokes simulation of a supersonic reacting wall jet. Combustion and Flame 159: 1127­–1138.