scholarly journals Linearized planing-surface theory with surface tension. Part I: Smooth detachment

1982 ◽  
Vol 23 (3) ◽  
pp. 241-258 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Surface Pressure ◽  
Leading Edge ◽  
Surface Slope ◽  
Surface Theory ◽  
Surface Pressure Distribution ◽  
Jump Discontinuities ◽  
Impulsive Pressure

AbstractIn the absence of surface tension, the problem of determining a travelling surface pressure distribution that displaces a portion of the free surface in a prescribed manner has been solved by several authors, and this “planing-surface” problem is reasonably well understood. The effect of inclusion of surface tension is to change, in a dramatic way, the singularity in the integral equation that describes the problem. It is now necessary in general to allow for isolated impulsive pressure, as well as a smooth distribution over the wetted length. Such pressure points generate jump discontinuities in free-surface slope. Numerical results are obtained here for a class of problems in which there is a single impulse located at the leading edge of the planing surface and detachment with continuous slope at the trailing edge. These results do not appear to approach the classical results in the limit as the surface tension approaches zero, a paradox that is resolved in Part II, which follows.

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.

Generalisation of the Condition for Waviness in the Pressure Distribution on a Cambered Plate

1963 ◽  
Vol 67 (632) ◽  
pp. 529-530 ◽  
Author(s):  
E. Angus Boyd
Keyword(s):  
Pressure Distribution ◽  
Surface Pressure ◽  
Leading Edge ◽  
Metal Plate ◽  
Two Dimensional ◽  
Striking Result ◽  
Surface Pressure Distribution

Recently some data from tests done on a cambered plate have been published. The shape of metal plate aerofoil tested matched that taken up by a flexible two-dimensional sail. The most striking result in the rneasurements was the waviness present near the leading edge in the upper surface pressure distribution. To find the theoretical conditions under which such a waviness would occur a parabolic skeleton aerofoil was investigated, as this shape differed little from the actual aerofoil tested.

Spreading and instability of a viscous fluid sheet

1990 ◽  
Vol 211 ◽  
pp. 373-392 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Related Problem ◽  
Numerical Solutions ◽  
Thin Sheet ◽  
Leading Edge ◽  
Small Disturbance ◽  
Inclined Plane ◽  
Moving Contact Line ◽  
Moving Contact

Experiments by Huppert (1982) have demonstrated that a finite volume of fluid placed on an inclined plane will elongate into a thin sheet of fluid as it slides down the plane. If the fluid is initially placed uniformly across the plane, the sheet retains its two-dimensionality for some time, but when it has become sufficiently long and thin, the leading edge develops a spanwise instability. A similarity solution for this motion was derived by Huppert, without taking account of the edge regions where surface tension is important. When these regions are examined, it is found that the conditions at the edges can be satisfied, but only when the singularity associated with the moving contact line is removed. When the sheet is sufficiently elongated, the profile of the free surface shows an upward bulge near the leading edge. It is suggested that the observed instability of the shape of the leading edge is a result of the dynamics of the fluid in this bulge. The related problem of a ridge of fluid sliding down the plane is examined and found to be linearly unstable. The spanwise lengthscale of this instability is, however, dependent on the width of the channel occupied by the fluid, which is at variance with the observed nature of the instability. Preliminary numerical solutions for the nonlinear development of a small disturbance to the position of a straight leading edge show the incipient development of a finger of fluid with a width that does not depend on the channel size, in accordance with the observations.

Unsteady Linearized Lifting-Surface Theory in the Presence of a Free Surface

1987 ◽  
Vol 31 (03) ◽  
pp. 151-163
Author(s):  
J. Leclerc ◽  
P. Salaun
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Unknown Function ◽  
Pressure Difference ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Thin Structures ◽  
Surface Theory ◽  
Lifting Surface ◽  
The Right

A new lifting-surface theory is developed for the computation of three-dimensional hydrodynamic pressures on thin structures in the presence of a free surface. Two interesting cases are treated: the steady case and the supercritical unsteady case. The theory is linearized and the problem is reduced to the solution of an integral equation where the unknown function is the pressure difference between the elements of the structure and the right-hand side the angle of attack. Forces and moments are presented in both the steady and unsteady cases. This theory allows the analysis of flutter and the study of steady drag and of the turn of ships.

Experimental investigation of flowfield over an iced aerofoil

2016 ◽  
Vol 120 (1227) ◽  
pp. 735-756 ◽  
Author(s):  
M.D. Manshadi ◽  
M.K. Esfeh
Keyword(s):  
Shear Layer ◽  
Surface Pressure ◽  
Low Frequency ◽  
Leading Edge ◽  
Velocity Fluctuations ◽  
Surface Pressure Distribution ◽  
Unsteady Separation ◽  
Flow Features ◽  
Velocity Spectra ◽  
Naca 0015

ABSTRACTWind-tunnel measurements were used to study the characteristics of the unsteady separation bubbles on a NACA 0015 aerofoil with simulated two-dimensional leading-edge glaze ice accretions. The unsteadiness present in the iced-aerofoil flowfield was determined using measurements of the time-dependent aerofoil surface pressure distribution at Reynolds number of 1.0 × 106. Additionally, the unsteady flow features were investigated through the power spectrum of the stream-wise velocity fluctuations using a hot-wire anemometry. The results showed that the highest value of root-mean-square fluctuation of the surface pressure consistently occurred upstream of the mean shear-layer reattachment location. Spectral analysis of stream-wise velocity fluctuations near reattachment location revealed evidence of the regular frequency at Strouhal numbers of 0.5-0.63. Moreover, the low-frequency oscillations associated with shear-layer flapping was also identified in the wake velocity spectra on the order of 10 Hz that resulted in Strouhal numbers of 0.0186-021.

Supersonic Flow over Thin Symmetrical Wings with Given Surface Pressure Distribution

1952 ◽  
Vol 3 (4) ◽  
pp. 263-279 ◽  
Author(s):  
F. A. Goldsworthy
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Integral Equation ◽  
Supersonic Flow ◽  
Pressure Distribution ◽  
Surface Pressure ◽  
Integral Equation Method ◽  
Normal Velocity ◽  
Vertical Derivative ◽  
Surface Pressure Distribution

SummaryThe inverse problem of determining the supersonic flow past a thin symmetrical wing at zero incidence with given surface pressure distribution is solved for wings of arbitrary plan form. Expressions are obtained for the vertical derivative of the potential on the wing surface from which, using the linearised boundary condition of zero normal velocity at the surface, the profile of the wing can be designed. The integral equation method adopted by J. C. Evvard and extended by G. N. Ward is used. The analysis cannot be applied to pointed wings, whose leading edges are subsonic. The results in Part I are completely general and are applied to specific problems in Part II.

Potential flow solution for a yawed surface-piercing plate

1991 ◽  
Vol 226 ◽  
pp. 291-317 ◽  
Author(s):  
Hongbo Xü
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Surface Condition ◽  
Leading Edge ◽  
Radiation Condition ◽  
Lateral Force ◽  
Vertical Surface ◽  
Analytical Investigation ◽  
Surface Boundary ◽  
Kutta Condition

This paper presents the results of an analytical investigation of the steady translation of a vertical surface-piercing plate at a small angle of attack. This problem is the antisymmetric equivalent of the symmetric thin-ship problem solved by Michell. The linearized boundary-value problem is transformed into an integral equation of the first kind by the method of Green functions. The Kelvin–Havelock Green function is used to satisfy the linearized free-surface boundary condition and radiation condition. A pressure Kutta condition is imposed at the trailing edge. Effective algorithms are developed to evaluate the hypersingular kernel without recourse to numerical integration. The resulting integral equation is solved by a collocation method with a refined scheme of discretization. After establishing the convergence of the present algorithm, computations are carried out for a surface-piercing rectangular plate of aspect ratio 0.5. The integrated lateral-force and yaw-moment coefficients show good agreement with experimental data. Other parameters of the flow such as pressure distributions, drag, strength of leading-edge singularity and free-surface profiles on the plate are also presented. The incompatibility between the pressure Kutta condition and the linearized free-surface condition does not affect the global solution.

scholarly journals Gridless Determination of Aerodynamic Loads Using Lagrangian Particle Tracks

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Christoph Mertens ◽  
José L. Costa Fernández ◽  
Andrea Sciacchitano ◽  
Bas W. Van Oudheusden ◽  
Jurij Sodja
Keyword(s):  
Surface Pressure ◽  
Lift Force ◽  
Leading Edge ◽  
Integrated Approach ◽  
Force Balance ◽  
Lagrangian Particle ◽  
Flow Measurements ◽  
Aerodynamic Loads ◽  
Flexible Wing ◽  
Surface Pressure Distribution

The aerodynamic loads on a flexible wing in terms of the surface pressure distribution and the lift force along the span are determined experimentally based on non-intrusive Lagrangian particle tracking (LPT) measurements. As the flexible wing deforms under the aerodynamic loads, its deformed shape is first reconstructed based on structural LPT measurements conducted together with the flow measurements in an integrated approach. Based on the reconstructed wing shape, flow tracers data are collected along surface normals to evaluate the surface pressure, as well as along elliptic paths around the wing to determine the circulation. The lift force is calculated from the surface pressure by integrating the pressure difference along the chord, as well as from the circulation using the Kutta-Joukowski theorem. The circulation-based lift results are in very good agreement with reference measurements from a force balance, with differences in the total lift force on the wing of less than 5%. The lift estimation based on the extrapolated surface pressure is consistently lower than the circulation-based lift, by about 10%, due to the limited accuracy of the pressure extrapolation near the leading edge region, where a considerable fraction of the lift is generated.

The stress singularity in surfactant-driven thin-film flows. Part 1. Viscous effects

1998 ◽  
Vol 372 ◽  
pp. 273-300 ◽  
Author(s):  
O. E. JENSEN ◽  
D. HALPERN
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Free Surface ◽  
Surface Diffusion ◽  
Fluid Layer ◽  
Stress Singularity ◽  
Leading Edge ◽  
Return Flow ◽  
Viscous Effects ◽  
Stick Slip

The leading edge of a localized, insoluble surfactant monolayer, advancing under the action of surface-tension gradients over the free surface of a thin, viscous, fluid layer, behaves locally like a rigid plate. Since lubrication theory fails to capture the integrable stress singularity at the monolayer tip, so overestimating the monolayer length, we investigate the quasi-steady two-dimensional Stokes flow near the tip, assuming that surface tension or gravity keeps the free surface locally at. Wiener–Hopf and matched-eigenfunction methods are used to compute the ‘stick-slip’ flow when the singularity is present; a boundary-element method is used to explore the nonlinear regularizing effects of weak ‘contaminant’ surfactant or surface diffusion. In the limit in which gravity strongly suppresses film deformations, a spreading monolayer drives an unsteady return flow (governed by a nonlinear diffusion equation) beneath most of the monolayer, and a series of weak vortices in the fluid ahead of the tip. As contaminant or surface diffusion increase in strength, they smooth the tip singularity over short lengthscales, eliminate the local stress maximum and ultimately destroy the vortices. The theory is readily extended to cases in which the film deforms freely over long lengthscales. Limitations of conventional thin-film approximations are discussed.

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