Mathematical Problems in Transonic Flow

AbstractWe present an outline of the problem of irrotational compressible flow past an airfoil at speeds that lie somewhere between those of the supersonic flight of the Concorde and the subsonic flight of commercial airlines. The problem is simplified and the important role of modifying the equations with physics terms is examined.

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A hybrid method for transonic flow past multi-element aerofoils

Journal of Fluid Mechanics ◽

10.1017/s0022112086000873 ◽

1986 ◽

Vol 170 ◽

pp. 253-264 ◽

Cited By ~ 2

Author(s):

M. G. Hill ◽

N. Riley

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Compressible Flow ◽

Hybrid Method ◽

Difference Method ◽

Transonic Flow ◽

Potential Flow ◽

Supercritical Flow ◽

Subcritical Flow ◽

Flow Past

A method for calculating transonic potential flow past a multi-element aerofoil configuration is presented. The method is a hybrid method that is based upon a compressible-flow panel method, valid for subcritical flow, and a finite-difference method that is suitable for supercritical flow calculations. The effectiveness of the proposed method is demonstrated, first by application to a single aerofoil and then to a three-element aerofoil.

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Numerical simulation of transonic flow past an F-16A aircraft configuration using CASPER

10.2514/6.2000-125 ◽

2000 ◽

Cited By ~ 1

Author(s):

Yoshiatsu Oki ◽

Takeshi Sakata ◽

Naoki Uchiyama ◽

Takeshi Kaiden ◽

Takeshi Andoh

Keyword(s):

Numerical Simulation ◽

Transonic Flow ◽

Flow Past

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Stability of the Low Reynolds Number Compressible Flow Past a NACA0012 Airfoil

AIAA Journal ◽

10.2514/1.j060792 ◽

2021 ◽

pp. 1-15

Author(s):

Laura Victoria Rolandi ◽

Thierry Jardin ◽

Jérôme Fontane ◽

Jérémie Gressier ◽

Laurent Joly

Keyword(s):

Reynolds Number ◽

Compressible Flow ◽

Low Reynolds Number ◽

Naca0012 Airfoil ◽

Flow Past ◽

Low Reynolds

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A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner–Riesz Multipliers

Zeitschrift für Analysis und ihre Anwendungen ◽

10.4171/zaa/1540 ◽

2015 ◽

Vol 34 (3) ◽

pp. 285-308

Author(s):

Reinhard Farwig ◽

Milan Pokorný

Keyword(s):

Compressible Flow ◽

Flow Past ◽

Rotating Obstacle ◽

Linearized Model ◽

Obstacle Analysis

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Transonic flow past finite wedges

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s030500410002747x ◽

1952 ◽

Vol 48 (1) ◽

pp. 178-187 ◽

Cited By ~ 5

Author(s):

A. G. Mackie ◽

D. C. Pack

Keyword(s):

Incompressible Fluid ◽

Critical Velocity ◽

Speed Of Sound ◽

Compressible Fluid ◽

Transonic Flow ◽

Ideal Gas ◽

Hodograph Method ◽

Subsonic Velocity ◽

Flow Past ◽

Axis Of Symmetry

AbstractThe solution for the flow of an incompressible fluid past an infinitely long wedge with a finite sloping edge (a finite wedge) is generalized by the hodograph method. In the flow thus obtained the axis of symmetry and a sloping edge of the wedge are again part of one streamline. It becomes possible to describe the flow of an ideal gas past a finite wedge if the hypothesis is made that the first singularity on this streamline, along the sloping edge, corresponds to the shoulder of the wedge. For a given wedge, with gradually increasing velocity at infinity upstream, the singularity appears at first at subsonic velocity. Beyond a certain critical velocity at infinity the singularity is always associated with the speed of sound. The hypothesis thus implies that put forward by Maccoll(9) and supported by Busemann(l). A qualitative examination shows that the solution reproduces experimentally known features of the flow of compressible fluid past a finite wedge.

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