Transonic Potential Flows in A Convergent--Divergent Approximate Nozzle

TL;DR

This paper proves the existence, uniqueness, and stability of certain transonic flows in a model of a convergent-divergent nozzle, using advanced mathematical techniques for mixed-type equations.

Contribution

It establishes the mathematical foundation for stable transonic flows in an approximate nozzle model, extending understanding of flow behavior under perturbations.

Findings

Transonic flows are stable under perturbations at the nozzle entry.

Existence and uniqueness of solutions are proven for the model.

Flow regularity is established in a Riemannian manifold setting.

Abstract

In this paper we prove existence, uniqueness and regularity of certain perturbed (subsonic--supersonic) transonic potential flows in a two-dimensional Riemannian manifold with "convergent-divergent" metric, which is an approximate model of the de Laval nozzle in aerodynamics. The result indicates that transonic flows obtained by quasi-one-dimensional flow model in fluid dynamics are stable with respect to the perturbation of the velocity potential function at the entry (i.e., tangential velocity along the entry) of the nozzle. The proof is based upon linear theory of elliptic-hyperbolic mixed type equations in physical space and a nonlinear iteration method.