Multi-valued solutions of steady-state supersonic flow. Part 1. Linear analysis

1976 ◽  
Vol 75 (4) ◽  
pp. 751-764 ◽  
Author(s):  
L. F. Henderson ◽  
J. D. Atkinson
Keyword(s):  
Supersonic Flow ◽  
Wave Equations ◽  
Subsonic Flow ◽  
Equations Of Motion ◽  
Point Sources ◽  
Physical Situation ◽  
Perfect Gas ◽  
Flat Plates ◽  
Scale Line ◽  
Flow Part

The shock wave equations for a perfect gas often provide more than one solution to a problem. In an attempt to find out which solution appears in a given physical situation, we present a linearized analysis of the equations of motion of a flow field with a shock boundary. It is found that a solution will be stable when there is supersonic flow downstream of the shock, and asymptotically unstable when there is subsonic flow downstream of it. It is interesting that both flows are found to be stable against disturbances of the d'Alembert type which grow from point sources; it is only when larger-scale line sources are considered that one can discriminate between the stabilities of the two types of flow. The results are applicable to supersonic flow over flat plates at incidence, to wedges, and to some cases of regular reflexion, diffraction and refraction of shocks.

Axially-symmetrical supersonic flow near the centre of an expansion

1950 ◽  
Vol 2 (2) ◽  
pp. 127-142 ◽  
Author(s):  
N.H. Johannesen ◽  
R.E. Meyer
Keyword(s):  
Approximate Solution ◽  
Supersonic Flow ◽  
Conventional Method ◽  
Velocity Gradient ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Initial Curvature ◽  
Boundary Wall

SummaryWhen a uniform, two-dimensional supersonic flow expands suddenly round a corner in a wall it forms a pattern known as a Prandtl-Meyer expansion or centred simple wave. If the flow is two-dimensional but not initially uniform, or if it is axially-symmetrical, the expansion is still centred, but is not a simple wave. An approximate solution is given in this paper for the isentropic, irrotational, steady two-dimensional or axially-symmetrical flow of a perfect gas in the neighbourhood of the centre of such an expansion. The solution is designed to replace the conventional method of characteristics in such a region.The main application is to a jet issuing from a nozzle that discharges into a container with a pressure lower than that in the nozzle; in particular, a formula is derived for the initial curvature, at the lip of the nozzle, of the boundary of the jet. The solution also applies to the flow near an edge in a boundary wall, and a formula is derived for the velocity gradient on the wall immediately downstream of the edge.

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part I: Subsonic Flow

2009 ◽  
Vol 83 (2) ◽  
pp. 269-292 ◽  
Author(s):  
Jeffrey M. Bergthorson ◽  
Michael B. Johnson ◽  
Aristides M. Bonanos ◽  
Michael Slessor ◽  
Wei-Jen Su ◽  
...  
Keyword(s):  
Shear Flow ◽  
Subsonic Flow ◽  
Molecular Mixing ◽  
Flow Part

Classical electrodynamics of spinning particles

1984 ◽  
Vol 62 (10) ◽  
pp. 943-947
Author(s):  
Bruce Hoeneisen
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Wave Equations ◽  
Dipole Moments ◽  
Equations Of Motion ◽  
Radiation Reaction ◽  
Classical Electrodynamics ◽  
Electric Dipole Moments ◽  
Gauge Invariant ◽  
Intrinsic Angular Momentum

We consider particles with mass, charge, intrinsic magnetic and electric dipole moments, and intrinsic angular momentum in interaction with a classical electromagnetic field. From this action we derive the equations of motion of the position and intrinsic angular momentum of the particle including the radiation reaction, the wave equations of the fields, the current density, and the energy-momentum and angular momentum of the system. The theory is covariant with respect to the general Lorentz group, is gauge invariant, and contains no divergent integrals.

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