Two Models for Cavity Flow—A Theoretical Summary and Applications

1968 ◽  
Vol 90 (2) ◽  
pp. 269-274 ◽  
Author(s):  
R. L. Street ◽  
B. E. Larock
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Nonlinear Theory ◽  
Cavity Length ◽  
Cavity Flow ◽  
Two Dimensional ◽  
Circular Arc ◽  
Blunt Nose

A summary is given of two-dimensional, steady-state, nonlinear theory for two finite-cavity models and their solutions. Two applications are described. First, the influence of the foil’s depth of submersion below a free surface on cavity length and foil performance is described. Second, the effect of a blunt nose on a circular-arc hydrofoil is examined.

Wakes of Developed Cavities

1977 ◽  
Vol 21 (04) ◽  
pp. 225-238
Author(s):  
Jean-Marie Michel
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Drag Coefficient ◽  
Cavity Length ◽  
Lift Coefficient ◽  
Cavity Flow ◽  
Numerical Results ◽  
Two Dimensional ◽  
Flow Configuration ◽  
Wake Model

A linearized wake model with a momentum defect is presented for the two-dimensional cavity flow around a base-vented foil which is placed in a free-surface channel. The numerical results show that, for a given cavity underpressureσ, the boundary conditions on the wake of the cavity have repercussions on the cavity length and the lift coefficient, whereas the drag coefficient is not modified. Similar features can be expected whenever the flow configuration is made strongly asymmetric by the external boundaries, especially by a free surface.

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.

A multimodal method for liquid sloshing in a two-dimensional circular tank

2010 ◽  
Vol 665 ◽  
pp. 457-479 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Analytical Form ◽  
The Body ◽  
Liquid Sloshing ◽  
Two Dimensional ◽  
Surface Conditions ◽  
Natural Modes ◽  
Body Boundary ◽  
Multimodal Method

Two-dimensional forced liquid sloshing in a circular tank is studied by the multimodal method which uses an expansion in terms of the natural modes of free oscillations in the unforced tank. Incompressible inviscid liquid, irrotational flow and linear free-surface conditions are assumed. Accurate natural sloshing modes are constructed in an analytical form. Based on these modes, the ‘multimodal’ velocity potential of both steady-state and transient forced liquid motions exactly satisfies the body-boundary condition, captures the corner-point behaviour between the mean free surface and the tank wall and accurately approximates the free-surface conditions. The constructed multimodal solution provides an accurate description of the linear forced liquid sloshing. Surface wave elevations and hydrodynamic loads are compared with known experimental and nonlinear computational fluid dynamics results. The linear multimodal sloshing solution demonstrates good agreement in transient conditions of small duration, but fails in steady-state nearly-resonant conditions. Importance of the free-surface nonlinearity with increasing tank filling is explained.

Experiments on Circular-Arc and Flat-Plate Hydrofoils

1958 ◽  
Vol 2 (01) ◽  
pp. 34-67
Author(s):  
Blaine R. Parkin
Keyword(s):  
Flat Plate ◽  
High Speed ◽  
Cavity Flow ◽  
Hydrodynamic Characteristics ◽  
Water Tunnel ◽  
Pitching Moment ◽  
Two Dimensional ◽  
Circular Arc ◽  
Wide Range ◽  
Good Agreement

An investigation in the High-Speed Water Tunnel of the two-dimensional hydrodynamic characteristics of sharp-edged hydrofoils is described. The lift, drag, and pitching moment were measured in cavitating and noncavitating flows for flat-plate and circular-arc profiles. The theory of Wu for the forces on sharp-edged profiles in full-cavity flow and the experimental results showed good agreement over a wide range of attack angles.

A Nonlinear Theory of Sloshing in Rectangular Tanks

1974 ◽  
Vol 18 (04) ◽  
pp. 224-241 ◽  
Author(s):  
Odd M. Faltinsen
Keyword(s):  
Steady State ◽  
Power Series ◽  
Boundary Value Problem ◽  
Nonlinear Theory ◽  
Reasonable Agreement ◽  
Steady State Solution ◽  
State Solution ◽  
Two Dimensional ◽  
The Stability ◽  
Theory And Experiment

A two-dimensional, rigid, rectangular, open tank without baffles is forced to oscillate harmonically with small amplitudes of sway or roll oscillation in the vicinity of the lowest natural frequency for the fluid inside the tank. The breadth of the tank is 0(1) and the depth of the fluid is either 0(1) or in-finite. The excitation is 0(ε) and the response is 0(ε1/3). A nonlinear, inviscid boundary-value problem of potential flow is formulated and the steady-state solution is found as a power series in ε1/3 correctly to 0(ε). Comparison between theory and experiment shows reasonable agreement. The stability of the steady-state solution has been studied.

Two-Dimensional Base-Vented Hydrofoils Near a Free Surface: Influence of the Ventilation Number

1975 ◽  
Vol 97 (4) ◽  
pp. 465-473 ◽  
Author(s):  
A. Rowe ◽  
J. M. Michel
Keyword(s):  
Free Surface ◽  
Asymptotic Expansions ◽  
Constant Coefficient ◽  
Cavity Length ◽  
Matched Asymptotic Expansions ◽  
Two Dimensional ◽  
Drag Coefficients ◽  
Lift And Drag ◽  
Limiting Values

The method of matched asymptotic expansions is used to analyze the flow around a base-vented lifting foil with rounded nose beneath a free surface. The foil is defined numerically. Results concerning the lift and drag coefficients and the limiting values of incidences without cavitation are compared with experiments. The relation between the cavity length and the ventilation number at several depths of submergence is given in the case of a symmetrical wedge: it agrees with the experimental one except by a nearly constant coefficient.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

scholarly journals New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

2017 ◽  
Vol 376 (2111) ◽  
pp. 20170220 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Free Surface ◽  
Gravity Waves ◽  
Water Waves ◽  
Two Dimensional ◽  
Physical Plane ◽  
Theme Issue ◽  
Nonlinear Water Waves ◽  
Dimensional Gravity ◽  
Irrotational Motion ◽  
Exact Relations

Steady two-dimensional surface capillary–gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained. This article is part of the theme issue ‘Nonlinear water waves’.

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