Three dimensional steady subsonic Euler flows in bounded nozzles

We consider the problem of steady Euler flows in a torus. We show that in the absence of a direction of symmetry the solution for the vorticity contains δ-function singularities at the rational surfaces of the torus. We study the effect of a small but finite viscosity on these singularities. The solutions near a rational surface contain cat's eyes or islands, well known in the classical theory of critical layers. When the islands are small, their widths can be computed by a boundary-layer analysis. We show that the islands at neighbouring rational surfaces generally overlap. Thus, steady toroidal flows exhibit a tendency towards Beltramization.

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Wavelet-based regularization of the Galerkin truncated three-dimensional incompressible Euler flows

Physical Review E ◽

10.1103/physreve.96.063119 ◽

2017 ◽

Vol 96 (6) ◽

Author(s):

Marie Farge ◽

Naoya Okamoto ◽

Kai Schneider ◽

Katsunori Yoshimatsu

Keyword(s):

Three Dimensional ◽

Euler Flows ◽

Incompressible Euler

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Singularities in Three-Dimensional Compressible Euler Flows with Vorticity

Theoretical and Computational Fluid Dynamics ◽

10.1007/s001620050071 ◽

1998 ◽

Vol 10 (1-4) ◽

pp. 385-391 ◽

Cited By ~ 7

Author(s):

J.T. Stuart

Keyword(s):

Three Dimensional ◽

Compressible Euler ◽

Euler Flows

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Atmospheric Reentry Dynamics of Conic Objects

Mathematical Problems in Engineering ◽

10.1155/2009/859678 ◽

2009 ◽

Vol 2009 ◽

pp. 1-14 ◽

Cited By ~ 2

Author(s):

J. P. Saldia ◽

A. Cimino ◽

W. Schulz ◽

S. Elaskar ◽

A. Costa

Keyword(s):

Euler Equations ◽

Degrees Of Freedom ◽

Three Dimensional ◽

Aerodynamic Coefficients ◽

Conical Body ◽

Six Degrees Of Freedom ◽

Atmospheric Reentry ◽

Variation Diminishing ◽

Euler Flows ◽

Key Issues

One of the key issues in a reentry risk analysis is the calculation of the aerodynamic coefficients. This paper presents a methodology to obtain these coefficients and couple it to a code that computes re-entry trajectories considering six degrees of freedom. To evaluate the different flight conditions encountered during the natural re-entry of conical objects, the Euler Equations for gasdynamics flows are used. A new scheme TVD (Total Variation Diminishing) is incorporated to a finite volume unstructured cell-centred formulation, for application to three-dimensional Euler flows. Finally, numerical results are obtained for a conical body at different attack angles and Mach. With these results, the calculation of the trajectories during atmospheric re-entry is completed.

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