A Schwarz-Christoffel Method for Generating Two-Dimensional Flow Grids

A new coordinate generation technique, developed by Davis for external flows, is extended to allow for accurate grid generation for a variety of complex internal flow configurations. The approach is based on numerical integration of the Schwarz-Christoffel transformation for polygonal surfaces. It is shown to be second-order accurate with mesh size due to analytic treatment of boundary singularities. The method is flexible enough to allow for treatment of severe internal geometries, for a high degree of control of mesh spacing, and for generation of either orthogonal or nonorthogonal grids. In addition, this technique directly provides the two-dimensional incompressible potential flow solution for internal flows, as well as a simple expression for calculating the grid metric coefficients. Sample cases include symmetric and asymmetric channel, diffuser, and cascade flows.

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The aerodynamic theory of sails. I. Two-dimensional sails

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1961.0086 ◽

1961 ◽

Vol 261 (1306) ◽

pp. 402-422 ◽

Cited By ~ 55

Keyword(s):

Lift Coefficient ◽

Linear Equations ◽

Three Dimensional ◽

Angle Of Incidence ◽

Two Dimensional ◽

Inviscid Incompressible Fluid ◽

Two Dimensional Flow ◽

Linearized Theory ◽

High Degree ◽

Additional Equation

This paper deals with the preliminaries essential for any theoretical investigation of three-dimensional sails—namely, with the two-dimensional flow of inviscid incompressible fluid past an infinitely-long flexible inelastic membrane. If the distance between the luff and the leach of the two-dimensional sail is c , and if the length of the material of the sail between luff and leach is ( c + l ), then the problem is to determine the flow when the angle of incidence α between the chord of the sail and the wind, and the ratio l / c are both prescribed; especially, we need to know the shape of, the loading on, and the tension in, the sail. The aerodynamic theory follows the lines of the conventional linearized theory of rigid aerofoils; but in the case of a sail, there is an additional equation to be satisfied which expresses the static equilibrium of each element of the sail. The resulting fundamental integral equation—the sail equation—is consequently quite different from those of aerofoil theory, and it is not susceptible to established methods of solution. The most striking result is the theoretical possibility of more than one shape of sail for given values of α and l / c ; but there appears to be no difficulty in choosing the shape which occurs in reality. The simplest result for these realistic shapes is that the lift coefficient of a sail exceeds that of a rigid flat plate (for which l / c = 0) by an amount approximately equal to 0.636 ( l / c ) ½ . It seems very doubtful whether analytical solutions of the sail equation will be found, but a method is developed in this paper which comes to the next best thing; namely, an explicit expression, as a matrix quotient, which gives numerical values to a high degree of accuracy at so many chord-wise points. The method should have wide application to other types of linear equations.

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The Prediction of Turbulent, Supersonic, Two-Dimensional, Boundary-Layer Flows

Aeronautical Quarterly ◽

10.1017/s0001925900005825 ◽

1971 ◽

Vol 22 (3) ◽

pp. 274-294 ◽

Cited By ~ 1

Author(s):

S. Sivasegaram ◽

J. H. Whitelaw

Keyword(s):

Experimental Data ◽

Turbulent Energy ◽

Two Dimensional ◽

Boundary Layer Flows ◽

Adiabatic Wall ◽

Mean Velocity ◽

Wide Range ◽

Two Dimensional Flow ◽

Dimensional Boundary ◽

Flow Configurations

SummaryThe prediction procedures of Bradshaw and Ferriss and Spalding and Patankar are compared with a wide range of experimental data obtained in turbulent, supersonic, two-dimensional flow. Both procedures are shown to result in satisfactory predictions of mean velocity profiles and wall shear stress in adiabatic-wall situations: in addition, the procedure of Spalding and Patankar is shown to be satisfactory in heat transfer situations. The Bradshaw and Ferriss procedure employs a turbulent energy hypothesis in contrast to the mixing-length assumptions used in the present version of the Spalding and Patankar procedure. The close agreement between the predictions of the two procedures indicates a lack of experimental data obtained in flow configurations with suddenly imposed or relaxed pressure gradients.

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Rotational compressible inverse design method for two-dimensional, internal flow configurations

AIAA Journal ◽

10.2514/3.11364 ◽

1993 ◽

Vol 31 (3) ◽

pp. 551-558 ◽

Cited By ~ 9

Author(s):

V. Dedoussis ◽

P. Chaviaropoulos ◽

K. D. Papailiou

Keyword(s):

Design Method ◽

Internal Flow ◽

Inverse Design ◽

Two Dimensional ◽

Flow Configurations ◽

Inverse Design Method

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A Method for Validating Two-Dimensional Flow Configurations in Particle Streak Velocimetry

Journal of Fluids Engineering ◽

10.1115/1.483279 ◽

2000 ◽

Vol 122 (2) ◽

pp. 438-439 ◽

Cited By ~ 3

Author(s):

Y. M. Gbamele´ ◽

P. Desevaux ◽

J.-P. Prenel

Keyword(s):

Density Distribution ◽

Flow Visualization ◽

Laser Light ◽

Two Dimensional ◽

Visualization Technique ◽

Power Density Distribution ◽

Two Dimensional Flow ◽

Particle Streak Velocimetry ◽

Qualitative Technique ◽

Flow Configurations

A polychromatic flow visualization technique for Particle Streak Velocimetry (PSV) is described. The method uses several adjoining laser light sheets of different wavelengths with a homogeneous power density distribution. This method allows us to make sure of the 2-D and 3-D nature of flows and to improve the frames quality processed in PSV. The feasibility study of this qualitative technique is established on a hydrodynamic flow. [S0098-2202(00)02402-0]

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