Subsonic divided gas flow in an infinitely long branching channel

Cheng, Jianfeng; Du, Lili

doi:10.1090/tran/7403

Subsonic divided gas flow in an infinitely long branching channel
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by Jianfeng Cheng and Lili Du PDF

Trans. Amer. Math. Soc. 371 (2019), 1859-1885 Request permission

Abstract:

This paper deals with the compressible subsonic flows in an infinitely long asymmetric branching channel with two exhaust ducts. The flow satisfies the slip boundary conditions on the nozzle walls, and the total mass flux is prescribed in the inlet of the nozzle. We first established the existence of smooth subsonic irrotational flows through the branching channel for given sufficiently small total mass flux in the inlet. Several results on uniqueness are also obtained. In particular, imposing the location of the branching point on the nose of the channel, the uniqueness and the asymptotic behavior of the subsonic flow in upstream and downstream are shown, provided that the total mass flux is less than some critical value. Due to the asymmetric geometrics, the location of the branching point of the fluids has to be considered here. Of particular interest, it is observed that the location of the branching point on the nozzle wall is monotonic and continuously dependent on the ratio of the mass fluxes in the two exhaust ducts, and the branching point is the unique stagnation point in the fluid field and its closure. Finally, as a direct application, some results on subsonic-sonic divided flows are established.

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