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.

Force and Moment Measurements of Supercavitating Hydrofoils of Finite Span With Comparison to Theory

1975 ◽  
Vol 97 (4) ◽  
pp. 453-462
Author(s):  
P. Leehey ◽  
T. S. Stellinger
Keyword(s):  
Aspect Ratio ◽  
Asymptotic Expansions ◽  
Cavity Length ◽  
Large Aspect Ratio ◽  
Drag Coefficients ◽  
Finite Span ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Lift And Drag ◽  
Good Agreement

Measurements were made of lift, drag, and moment coefficients, and cavity length for aspect ratio 3 and 5 supercavitating hydrofoils of elliptical planform. These measurements are compared with theoretical predictions obtained from matching asymptotic expansions for large aspect ratio. Good agreement was obtained for lift and drag coefficients for angles of attack from 10 deg to 15 deg and for a wide range of cavity lengths. Theoretical moment coefficients were too large indicating the need for lifting surface corrections.

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.

scholarly journals Two-dimensional resonators with small openings

1982 ◽  
Vol 24 (1) ◽  
pp. 2-27 ◽  
Author(s):  
G. R. Bigg ◽  
E. O. Tuck
Keyword(s):  
Natural Frequency ◽  
Asymptotic Expansions ◽  
Velocity Potential ◽  
Low Frequency ◽  
Matched Asymptotic Expansions ◽  
Two Dimensional ◽  
Acoustic Response ◽  
Closed Cavity ◽  
Small Opening

AbstractThe acoustic response of a two-dimensional nearly-closed cavity to an excitation through a small opening is examined, using the method of matched asymptotic expansions. The Helmholtz mode of vibration is discussed using a low-frequency expansion of the velocity potential in the cavity interior. The variation in frequency and magnitude of the resonator response is explored, both for the Helmholtz and the natural-frequency modes.

A free-streamline model of the two-dimensional sail

1970 ◽  
Vol 42 (3) ◽  
pp. 433-446 ◽  
Author(s):  
J. P. Dugan
Keyword(s):  
Two Dimensional ◽  
Drag Coefficients ◽  
The Moment ◽  
Lift And Drag

The two-dimensional sail is considered in a free-streamline model to complement the oft-considered airfoil model which is limited to small angles of attack. The shape of the sail, the lift and drag coefficients, and the moment are obtained for various angles of attack and states of tension.

Flow along a horizontal plate near a free surface

1993 ◽  
Vol 252 ◽  
pp. 399-418
Author(s):  
Milan Hofman
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flat Plate ◽  
Viscous Liquid ◽  
Gravity Waves ◽  
Asymptotic Expansions ◽  
Small Amplitude ◽  
Surface Effect ◽  
Matched Asymptotic Expansions ◽  
Horizontal Plate

The problem of flow along a horizontal semi-infinite flat plate moving in its own plane through a viscous liquid just below the free surface is considered. The method of matched asymptotic expansions is used to analyse the interaction between the free surface and the boundary layer formed on the plate. It is found that, due to viscosity, small-amplitude gravity waves on the free surface can be formed. The formulae for the resistance of the plate containing the free-surface effect and for the lift, appearing as a new phenomenon, are derived.

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.

The evolution of stress intensity factors in the propagation of two dimensional cracks

2000 ◽  
Vol 11 (5) ◽  
pp. 453-471 ◽  
Author(s):  
AVNER FRIEDMAN ◽  
BEI HU ◽  
JUAN J. L. VELAZQUEZ
Keyword(s):  
Stress Intensity ◽  
Elastic Medium ◽  
Plane Strain ◽  
Asymptotic Expansions ◽  
Stress Intensity Factors ◽  
Matched Asymptotic Expansions ◽  
Two Dimensional ◽  
Intensity Factors ◽  
Plane Strain Deformation ◽  
Isotropic Elastic Medium

The aim of this paper is to describe a technique based on matched asymptotic expansions that allows us to derive the variation of the stress intensity factors in a homogeneous isotropic elastic medium under plane strain deformation. The case of antiplane shearing is also considered.

Matched asymptotics for two-dimensional planing hydrofoils with spoilers

1998 ◽  
Vol 358 ◽  
pp. 259-281 ◽  
Author(s):  
G. M. FRIDMAN
Keyword(s):  
Asymptotic Solution ◽  
Flat Plate ◽  
Linear Theory ◽  
Asymptotic Expansions ◽  
Flow Problem ◽  
Matched Asymptotic Expansions ◽  
Asymptotic Solutions ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Matched Asymptotics

The purpose of the paper is to demonstrate the effectiveness of the matched asymptotic expansions (MAE) method for the planing flow problem. The matched asymptotics, taking into account the flow nonlinearities in those regions where they are most pronounced (i.e. in the vicinity of the edges), are shown to significantly extend the range where the linear theory gives good results. Two model problems are used: the planing flat plate with a spoiler on the trailing edge and the curved planing foil. Asymptotic solutions obtained by the MAE method are compared with those obtained using linear and exact nonlinear theories. Based on the results, the asymptotic solution to the planing problem under the gravity is proposed.

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.

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