Simulation of Transient Compressible Turbulent Reactive Flows

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Abstract
A simulation procedure capable of handling transient compressible flows involving combustion is presented. The method uses the velocity components and pressure as primary flow variables. The differential equations governing the flow are discretized by integration over control volumes. The integration is performed by application of up-wind differencing in a staggered grid system. The solution procedure is an extension of the SIMPLE-algorithm accounting for compressibility effects. Turbulence is treated by solving the equations of kinetic energy of turbulence and of dissipation rate of kinetic energy of turbulence. The combustion model incorporates solution of balance equations for the mixture fraction and the mass fraction of fuel. The rate of combustion in the latter equation is modelled according to the “eddy-dissipation model” of Magnussen and Hjertager. A validation calculation of the classical shock-tube problem is performed and good agreement between analytical solution and computed predictions is found. Flame acceleration by repeated obstacles is also modelled, and comparisons with large-scale and small-scale experimental data are encouraging.

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