Computation of Chemically Reacting Unsteady One-Dimensional Flows
A mathematical model of one-dimensional chemically reacting flow is presented. The effects of wall friction, heat transfer and gradual area change are inclined in addition to the effects of chemical reaction on the composition and specific heats of gas. The set of quasi-linear hyperbolic partial differential equations obtained are solved by a numerical method of characteristics. The equations for various boundary conditions are also presented.The model was applied to a shock tube in which no chemical reaction took place. The pressure at the closed left end of the shock tube predicted with the model was in very good agreement with the result obtained by Rudinger using a graphical method of characteristics. The model was also applied to a simple quarter-wavelength organ-pipe pulsed combustor. The combustion process was modelled using a simple overall reaction rate equation. The model predicted pressure amplitudes that are in good qualitative agreement with experimental results.
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