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The principal aim of the work is development and realization of a computationally efficient method for numerical simulation of turbulent flows with combustion that occur in perspective aircraft combustors. An original combined method is developed. It treats different combustion regimes (in the range from premixed to non-premixed diffusive combustion) without alteration of numerical algorithm. Validation of code for simulation of 3D flows on the basis of unsteady RANS equations for multi-component compressible gas with finite rate chemical reactions is described. "Laminar approximation" and classical presumed PDF approach together with flamelet model with direct calculation of mass fractions and temperature are compared with universal method where PDF approach is used only for calculation of source terms. Application of the developed numerical technology to simulation of model combustor with supersonic flow at the entrance is presented. 2D calculations of this model combustor are considered. Nomenclature i x = i Dekart coordinate i u = i velocity component z = passive admixture fraction (mixtture fraction) N = scalar dissipation rate 2 z   = mixture fraction variance g  = constant in equation for intermittency q = characteristic value of velocity pulsations ω = characteristic frequency of turbulent pulsations k = turbulent kinetic energy ε = turbulent energy dissipation rate θ = heat release rate i Y = mass fraction of component i γ = intermittency factor δ = delta Dirac function p = pressure P, pdf = probability density function (PDF) β1, β2 = assumed beta pdf coefficients t  = kinematic coefficient of turbulent viscosity M = Mach number g S = source term in equation for intermittency Sc = Scmidt number Pr = Prandl number 2 chem t = characteristic chemical time  t = Kolmogorov time scale l t = macroturbulent scale G = mass flow rate per a unit of channel width t = time comb diff c _ = coefficient showing the local input of diffusion combustion, obtained from the comparison of characteristic times of the proceeding processes i SY = averaged in time source term in equations for reacting specie i T = temperature superscripts s = related to the stoihiometric surface value flamelet = related to flamelet library values pdf = values calculated with pdf approach lam = values calculated with quazi-laminar approach cr = critical value (at which flame quenching occures) subscripts O = related to oxydizer flow F = related to fuel flow P = related to products flow t = related to turbulent flow st = related to the stihiometric surface value 0 = corresponds to total parameters w = corresponds to parameters on wall

New quasi-two-dimensional (2.5D) approach to description of three-dimensional (3D) flows in ducts is proposed. It generalizes quasi-one-dimensional (quasi-1D, 1.5D) theories. Calculations are performed in the (x; y) plane, but variable width of duct in the z direction is taken into account. Derivation of 2.5D approximation equations is given. Tests for verification of 2.5D calculations are proposed. Parametrical 2.5D calculations of flow with hydrogen combustion in an elliptical combustor of a high-speed aircraft, investigated within HEXAFLY-INT international project, are described. Optimal scheme of fuel injection is found and explained. For one regime, 2.5D and 3D calculations are compared. The new approach is recommended for use during preliminary design of combustion chambers.

Numerical technology for fast and correct computation of non-stationary viscid gas flows is presented. It consists in the use of explicit numerical scheme with fractional time stepping and “wall law” boundary condition at the solid surfaces. The technology is verified by comparison with the calculation based on the no-slip boundary condition. Using this technology, the physics of supersonic flow in a model duct with combustion of hydrocarbon fuel in pseudoshock is analyzed.

Fast technologies for numerical simulation of high-speed flows in ducts, developed in TsAGI, are described. The examples are presented of the application of experimental data, obtained at T-131 wind tunnel, for validation of the developed numerical technologies: 1) validation of 2.5D and 3D calculations of flow in the elliptic combustor with hydrogen supersonic combustion that was studied within HEXAFLY-INT international project; 2) validation of 2D and 2.5D calculations of flow in high-speed model combustor duct with step-like expansion. Preparation of new series of experiments, oriented on validation of turbulent combustion models, is described.