A Free Boundary Problem in an Unbounded Domain and Subsonic Jet Flows from Divergent Nozzles

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Mathematical Analysis Pub Date : 2024-09-13 DOI:10.1137/23m162301x

Yuanyuan Nie, Chunpeng Wang, Guanming Gai

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Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6337-6360, October 2024.
Abstract. This paper concerns subsonic jet flows from two-dimensional finitely long divergent nozzles with straight solid walls, which are governed by a free boundary problem for a quasilinear elliptic equation. It is assumed that the angle of the nozzle and the location of the inlet are fixed, while the length of the nozzle is free. For a given surrounding pressure and a given incoming mass flux, it is shown that there is a critical number not greater than [math] for the angle of the nozzle such that there exists a unique subsonic jet flow if the angle of the nozzle is less than the critical number. If this critical number is less than [math], then there is not a subsonic jet flow when the angle of the nozzle takes this critical number; furthermore, as the angle of the nozzle tends to this critical number, either the length of the nozzle tends to zero, or a sonic point will occur at the inlet. Moreover, it is shown that the subsonic jet flow tends to a uniform horizontal flow exponentially at the downstream. As to the jet, it is smooth away from the connecting point with the wall of the nozzle, and it connects the wall of the nozzle with [math] regularity for each exponent [math]. Furthermore, the jet is strictly concave to the fluid and tends to a line parallel to the symmetrical axis exponentially.

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无界域中的自由边界问题和来自发散喷嘴的亚音速喷流

SIAM 数学分析期刊》，第 56 卷第 5 期，第 6337-6360 页，2024 年 10 月。摘要本文涉及来自二维有限长发散喷嘴的亚音速喷流，该喷嘴具有笔直的固体壁，受准线性椭圆方程的自由边界问题支配。假设喷嘴的角度和入口的位置是固定的，而喷嘴的长度是自由的。对于给定的周围压力和给定的输入质量通量，可以证明喷嘴角度存在一个不大于 [math] 的临界值，即如果喷嘴角度小于临界值，则存在唯一的亚音速射流。如果该临界值小于[math]，则当喷嘴角度取该临界值时，不存在亚音速射流；此外，当喷嘴角度趋向于该临界值时，要么喷嘴长度趋向于零，要么在入口处出现声波点。此外，亚音速射流在下游以指数形式趋向于均匀水平流。至于射流，它在远离与喷嘴壁连接点的地方是平滑的，在每个指数[math]下，它以[math]规则性连接喷嘴壁。此外，射流严格凹向流体，并以指数方式趋向于平行于对称轴的直线。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.