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.

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.

Focusing effects in two-dimensional, supersonic flow

1949 ◽  
Vol 242 (844) ◽  
pp. 153-171 ◽  
Keyword(s):  
Method Of Characteristics ◽  
Inverse Transformation ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Geometrical Method ◽  
Independent Variables ◽  
Flow Problems ◽  
Sonic Line ◽  
Hodograph Transformation ◽  
Line Patterns

The steady, supersonic, irrotational, isentropic, two-dimensional, shock-free flow of a perfect gas is investigated by a new, geometrical, method based on the use of characteristic co-ordinates. Some of the results apply also to more general problems of compressible flow involving two independent variables (§1). The method is applied in particular to the treatment of the non-linear, non-analytic features. The variation in magnitude of discontinuities of the velocity gradient is determined as a function of the Mach number in § 4. The reflexion at the sonic line of such discontinuities is treated in § 7. The isingularities of the field of flow are discussed in §§ 5 to 5.4; Craggs’s (1948) results are extended to the case when the velocity components are not analytic functions of position, and to the case in which both the hodograph transformation and the inverse transformation are singular.. Examples are given of singularities that occur in familiar flow problems, but have not hitherto been described (§§ 5.3, 5.4). Some properties are established of the geometry in the large of Mach line patterns; these properties are useful for the prediction of limit lines (§ 5.2). The problem of the start of an oblique shockwave in the middle of the flow is briefly reviewed in §6. In the appendix it is shown that the conventional method of characteristics for the numerical treat­ ment of two-dimensional, isentropic, irrotational, steady, supersonic flows must be modified near a branch line if a loss of accuracy is to be avoided.

Computational Analysis of the Transonic Flow Field of Two-Dimensional Minimum Length Nozzles

1991 ◽  
Vol 113 (3) ◽  
pp. 479-488 ◽  
Author(s):  
B. M. Argrow ◽  
G. Emanuel
Keyword(s):  
Supersonic Flow ◽  
Flow Field ◽  
Method Of Characteristics ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Minimum Length ◽  
Two Dimensional ◽  
Sonic Line ◽  
Inlet Geometry ◽  
Straight Sonic Line

The method of characteristics is used to generate supersonic wall contours for two-dimensional, straight sonic line (SSL) and curved sonic line (CSL) minimum length nozzles for exit Mach numbers of two, four and six. These contours are combined with subsonic inlets to determine the influence of the inlet geometry on the sonic-line shape, its location, and on the supersonic flow field. A modified version of the VNAP2 code is used to compute the inviscid and laminar flow fields for Reynolds numbers of 1,170, 11,700, and 23,400. Supersonic flow field phenomena, including boundary-layer separation and oblique shock waves, are observed to be a result of the inlet geometry. The sonic-line assumptions made for the SSL prove to be superior to those of the CSL.

The development of weak waves in the steady two-dimensional flow of a gas with vibrational relaxation past a thin wedge

1975 ◽  
Vol 69 (1) ◽  
pp. 109-128 ◽  
Author(s):  
R. P. Hornby ◽  
N. H. Johannesen
Keyword(s):  
Supersonic Flow ◽  
Shock Tube ◽  
Small Angle ◽  
Vibrational Relaxation ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Wave Decay ◽  
Two Dimensional Flow ◽  
Thin Wedge

The method of characteristics is used to calculate the supersonic flow past a wedge of small angle with non-equilibrium effects. The wave decay and development distances are presented in a concise similarity form which permits accurate extrapolation to very weak waves. The numerical solutions are compared with shock-tube flows of CO2 and N2O.

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.

Modeling and Simulation of Supersonic Flow in 2D Nozzle Using MacCormack’s and Upwind Methods

2014 ◽  
Vol 1016 ◽  
pp. 569-573
Author(s):  
Mohsen Chegeni ◽  
Marzieh Ehterami ◽  
Mustafa Hadi Doolabi ◽  
Mohamad Saleh Soltaninezhad
Keyword(s):  
Supersonic Flow ◽  
Method Of Characteristics ◽  
Splitting Method ◽  
Nozzle Geometry ◽  
Two Dimensional ◽  
Characteristics Method ◽  
Upwind Methods ◽  
Cfd Method ◽  
Volume Method ◽  
The Ideal

In this work, two-dimensional inviscid supersonic flow in nozzle has been investigated using CFD schemes and characteristics method. The employed scheme is MacCormack’s finite volume method. Our own code CHARMAC, was written using MATLAB environment. Standard boundary conditions and the grid parameters were considered to solve the problem. Before analyzing the flow by CFD method, we obtained the ideal nozzle geometry using the method of characteristics for a 2D divergent Nozzle. Using 2D nozzle flow relations, an optimal throat area is found. At the end we compare the results with the advection upstream splitting Method (Ausm) and Fluent.

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