Method of Characteristics for Two-Dimensional Supersonic Flow—Graphical and Numerical Procedures

1947 ◽  
Vol 14 (2) ◽  
pp. A154-A162
Author(s):  
Ascher H. Shapiro ◽  
Gilbert M. Edelman
Keyword(s):  
Supersonic Flow ◽  
Numerical Method ◽  
Method Of Characteristics ◽  
Numerical Procedure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Abstract The method of characteristics for two-dimensional supersonic flow is reviewed and summarized. A characteristics chart is presented for use with the graphical procedure of Prandtl and Busemann. A new numerical procedure is described which eliminates graphical operations and which allows of more accurate solutions. To facilitate the numerical method, a table of useful functions is included.

Boundary Layer Closure and Heat Transfer in Constant Base Pressure and Simple Wave Guns

1978 ◽  
Vol 100 (4) ◽  
pp. 690-696 ◽  
Author(s):  
A. D. Anderson ◽  
T. J. Dahm
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Method Of Characteristics ◽  
Simple Wave ◽  
Momentum Equation ◽  
Base Pressure ◽  
Two Dimensional ◽  
The Method Of Characteristics

Solutions of the two-dimensional, unsteady integral momentum equation are obtained via the method of characteristics for two limiting modes of light gas launcher operation, the “constant base pressure gun” and the “simple wave gun”. Example predictions of boundary layer thickness and heat transfer are presented for a particular 1 in. hydrogen gun operated in each of these modes. Results for the constant base pressure gun are also presented in an approximate, more general form.

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.

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