The existence of compressible subsonic impinging jet flow in an arbitrary nozzle

The main purpose of this paper is to show the well-posedness theory of two-dimensional symmetric compressible subsonic impinging jet flow. More precisely, for any given atmospheric pressure, we show that there exists a critical value, such that if the incoming mass flux is less than the critical value, then there exists a smooth symmetric compressible subsonic impinging jet flow, and the free boundary of the flow detaches smoothly from the end points of the nozzle. Moreover, the asymptotic behavior at the far field and the positivity of horizontal velocity of the flow are also obtained. On the other hand, under the star-shaped condition on the given nozzle, we will get the uniqueness of compressible subsonic impinging jet flow. Finally, we show that the vertical velocity of the flow is positive under the monotonous hypothesis on the upper nozzle wall.

Keywords

arbitrary nozzle, impinging jet, free boundary, subsonic, existence, uniqueness

2010 Mathematics Subject Classification

35J25, 35Q31, 76G25

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This work is supported in part by the Teacher Development Scientific Research Staring Foundation of Chengdu University of Technology (No. 10912-KYQD2020-08411).

Received 3 November 2019

Accepted 5 January 2021

Published 11 November 2021