Two-Dimensional, Steady, Cavity Flow About Slender Bodies in Channels of Finite Breadth

1957 ◽  
Vol 24 (2) ◽  
pp. 170-176
Author(s):  
Hirsh Cohen ◽  
Robert Gilbert
Keyword(s):  
Cavity Length ◽  
Solid Wall ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Integral Equation Formulation ◽  
Slender Bodies ◽  
Linearized Theory ◽  
Finite Breadth ◽  
Arbitrary Body ◽  
Cavity Width

Abstract The steady, cavitating flow past slender symmetrical bodies placed in a solid-wall channel is studied by means of the linearized theory of Tulin. The free-boundary condition is linearized and boundary conditions are applied on the line of symmetry of the flow in analogy with thin-air-foil theory. A singular integral equation formulation of the boundary-value problem is obtained and can be solved to yield expressions for cavity length, maximum cavity width, and drag coefficient as functions of the cavitation number and the channel breadth. These expressions are given for an arbitrary body and evaluated for the case of a wedge.

Steady Performance of a Flexible Hydrofoil Near a Free Surface

1990 ◽  
Vol 34 (04) ◽  
pp. 302-310
Author(s):  
Salwa M. Rashad ◽  
Theodore Green
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Cavity Length ◽  
Leading Edge ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Deformation Characteristics ◽  
Flow Depth ◽  
Lift And Drag ◽  
The Galerkin Method

A linearized cavity-flow theory is used to develop a mathematical model to study the steady characteristics of a flexible hydrofoil near a free surface. The Galerkin method is employed to account for the mutual interaction between the fluid and structure forces. Cheng and Rott's method [1]2 is used to derive general expressions for the deformation characteristics in steady flow of an arbitrarily shaped hydrofoil, with a clamped trailing edge and free leading edge. From the analysis it is possible to determine the lift and drag coefficients, cavity length, and the foil steady deformation for any given specific foil shape, cavitation number, angle of attack, flow depth/chord ratio and rigidity. Sample numerical results are given, and the effects of flexibility and the proximity of the free surface are discussed. Chordwise flexibility tends to increase drag and decrease lift coefficients. This effect is more serious near the free surface. A slight increase of the thickness near the leading edge diminishes the flexibility effects.

The Role of Eigensolutions in Nonlinear Inverse Cavity-Flow Theory

1988 ◽  
Vol 110 (3) ◽  
pp. 315-324
Author(s):  
B. R. Parkin
Keyword(s):  
Inverse Problem ◽  
Free Surface ◽  
Direct Problem ◽  
Cavity Flow ◽  
Cavitation Number ◽  
The Novel ◽  
Cavity Shape ◽  
Linearized Theory ◽  
Exact Point

The method of Levi Civita is applied to an isolated fully cavitating body at zero cavitation number and adapted to the solution of the inverse problem in which one prescribes the pressure distribution on the wetted surface and then calculates the shape. The novel feature of this work is the finding that the exact theory admits the existence of a “point drag” function or eigensolution. While this fact is of no particular importance in the classical direct problem, we already know from the linearized theory that the eigensolution plays an important role. In the present discussion, the basic properties of the exact “point-drag” solution are explored under the simplest of conditions. In this way, complications which arise from non-zero cavitation numbers, free surface effects, or cascade interactions are avoided. The effects of this simple eigensolution on hydrodynamic forces and cavity shape are discussed. Finally, we give a tentative example of how this eigensolution might be used in the design process.

Symmetric, Rotational, Supercavitating Flow About a Slender Wedge

1964 ◽  
Vol 86 (3) ◽  
pp. 569-575 ◽  
Author(s):  
R. L. Street
Keyword(s):  
Drag Coefficient ◽  
Cavity Length ◽  
Rotational Flow ◽  
Drag Coefficients ◽  
Irrotational Flow ◽  
Supercavitating Flow ◽  
Slender Bodies ◽  
Linearized Theory

Two approximations to the linearized theory for supercavitating flow about slender bodies are applied to the case of a symmetric, rotational flow about a slender wedge. Both approximations produce relationships for the cavity length and drag coefficients; one approximation also gives certain nonunique solutions not encountered in the corresponding irrotational flow. The presence of rotation is shown to create significant changes in the length of the trailing cavity, but small changes in the drag coefficient.

The Hydrofoil with Finite Cavity in a Solid-Wall Channel

1971 ◽  
Vol 15 (02) ◽  
pp. 125-140
Author(s):  
Steven H. Schot
Keyword(s):  
Cavity Length ◽  
Solid Wall ◽  
Lift Coefficient ◽  
Cavitation Number ◽  
Channel Width ◽  
Width Ratio ◽  
Third Order ◽  
Choked Flow ◽  
Method Of Solution ◽  
Correction Terms

The asymmetrical fully cavitating linearized flow about an arbitrarily shaped slender hydrofoil placed anywhere in a solid-wall channel is considered as a doubly connected region problem. The method of solution involves conformal mapping and a generalization of the Plemeli formulas to doubly periodic functions. The velocity field is expressed in terms of Jacobi's that a functions with the nome q of these functions related directly to the cavity-length/channel-width ratio. Explicit results are obtained for a fully cavitating flat plate at small angles of attack in a midchannel position. For small q, simple wall effect correction terms are obtained for the cavity length and the lift coefficient as a function of cavitation number. These correction terms are correct up to and including third order in q and require no quadratures. For large values of the cavity-length/channel-width ratio (q close to unity) the asymptotic choked flow solution is used to compute the blockage cavitation number and the lift coefficient for the choked flow.

The Linearized Theory of a Supercavitating Hydrofoil With a Jet Flap

1964 ◽  
Vol 86 (4) ◽  
pp. 851-858 ◽  
Author(s):  
Hung-Ta Ho
Keyword(s):  
Theoretical Analysis ◽  
Momentum Flux ◽  
Vortex Sheet ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Pitching Moment ◽  
Cavity Shape ◽  
Small Deflection ◽  
Small Incidence ◽  
Linearized Theory

A theoretical analysis is carried out for the steady cavity flow about thin hydrofoil sections at small incidence α, at the trailing edge of which a thin jet emerges at a small deflection τ. The flow is assumed to be inviscid and incompressible and the cavitation number is taken to be zero. The jet is assumed so thin that it can be considered as a vortex sheet across which the velocity is discontinuous. For the case of a flat plate, expressions have been obtained for lift, drag, pressure distribution, pitching moment, the jet shape, and the cavity shape. Numerical calculations are made for a number of jet momentum-flux coefficients CJ lying between 0.01 and 5.

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