Abstract
The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t > 0 in the (x, t) plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Döring (ZND) combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the corresponding Riemann solution may be transformed into a weak deflagration coalescing with the pre-compression shock wave after perturbation. Moreover, in some cases, although no combustion wave exists in the corresponding Riemann solution, the combustion wave may occur after perturbation, which shows the instability of the unburnt gases.
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Project supported by the National Natural Science Foundation of China (No. 10971130), the Shanghai Leading Academic Discipline Project (No. J50101), the Shanghai Municipal Education Commission of Scientific Research Innovation Project (No. 11ZZ84), and the Graduate Innovation Foundation of Shanghai University
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Liu, Yj., Sheng, Wc. Generalized Riemann problem for gas dynamic combustion. Appl. Math. Mech.-Engl. Ed. 32, 1079–1090 (2011). https://doi.org/10.1007/s10483-011-1482-6
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DOI: https://doi.org/10.1007/s10483-011-1482-6