Numerical simulation of combustion processes

Abstract

In this paper, we propose a numerical method for solving the problem of the propagation and combustion of a methane jet in an axisymmetric satellite air flow. Within the framework of the modified turbulence model and the Arrhenius law, mathematical and numerical models of the problem of a turbulent axisymmetric methane jet in an infinite cocurrent air flow at a finite reaction rate have been developed. By introducing functions and generalized Schwab-Zel'dovich functions, as well as the stream function, ten differential equations for the conservation of substances are represented by differential equations equivalent to them. The equations of the turbulent boundary layer of a multicomponent gas for an axisymmetric jet are transformed with the transition to dimensionless variables and the introduction of a stream function. The dimensionless equations of the turbulent boundary layer of reacting gases in von Mises coordinates are used for modeling. For the numerical solution of the combustion problem according to the Arrhenius law, an implicit finite-difference scheme was used, which provides the second order of approximation accuracy in longitudinal and transverse coordinates. This made it possible to significantly reduce the calculation time as a result of using a large calculation step for the longitudinal coordinate. In connection with the nonlinearity of the equations of conservation and transfer of substances, an iterative process was organized. Some results of the computational experiment are presented. Comparison of the results of calculating the change in the temperature of the axial flow according to the turbulence models modified by k − ε and Prandtl with experimental data. The adequacy of the results was verified by the implementation of the laws of conservation of mass, momentum and total enthalpy, as well as by comparing the results with experimental data from other authors with the largest 5% deviation. This means that the previously presented algorithm and calculation program can be used for practical purposes. The results obtained with both turbulence models were compared with experimental data. Analyzing the results, one can notice that the k − ε model coincides more qualitatively with the experiment than the Prandtl turbulence model.