Direct Calculations of One-, Two-, and Three-Dimensional Detonations by the CESE Method

The present paper reports one-, two-, and threedimensional numerical simulation of propagating detonations. We solve the Euler equations for chemically reacting flows with the space-time CESE method. The stiff source terms in the species equations are treated by a volumetric integration over a space-time region as an integral part of the space-time flux conservation. The classical ZND solution is used for code validation as well as the initial condition in the simulations. One-dimensional results include a piston problem and an instability problem. Two-dimensional cases include planar detonation waves and an oblique detonation over a ramp. Three-dimensional results include planar detonations in square ducts of various sizes. For H2/air mixtures at various equivalence ratios, the cell size of the calculated soot trace compares well with experimental data. For the same flow conditions, the cell sizes of two-dimensional calculations are generally 30 to 40% less than that in three-dimensional ones. Moreover, both the amplitude and the frequency of the peak pressures in the calculated three-dimensional detonations are much higher than that in the twodimensional results. Similarly, the frequency and amplitudes of the calculated two-dimensional pressure peaks are higher than that of the galloping one-dimensional detonations. While oneand two-dimensional simulations provide qualitative features of propagating detonations, one has to resort to three-dimensional simulations to obtain realistic flow structures of a detonation wave.

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