Three-dimensional Stokes flow caused by a translating–rotating sphere bisected by a free surface bounding a semi-infinite micropolar fluid

2008 ◽  
Vol 31 (10) ◽  
pp. 1233-1256
Author(s):  
M. S. Faltas ◽  
E. I. Saad
Keyword(s):  
Free Surface ◽  
Stokes Flow ◽  
Micropolar Fluid ◽  
Three Dimensional ◽  
Rotating Sphere

Two-dimensional bubbles in slow viscous flows

1968 ◽  
Vol 33 (3) ◽  
pp. 475-493 ◽  
Author(s):  
S. Richardson
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Cross Section ◽  
Stokes Flow ◽  
Function Theory ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Bubble Surface ◽  
Two Dimensional ◽  
Elliptical Cross

The representation of a biharmonic function in terms of analytic functions is used to transform a problem of two-dimensional Stokes flow into a boundary-value problem in analytic function theory. The relevant conditions to be satisfied at a free surface, where there is a given surface tension, are derived.A method for dealing with the difficulties of such a free surface is demonstrated by obtaining solutions for a two-dimensional, in viscid bubble in (a) a shear flow, and (b) a pure straining motion. In both cases the bubble is found to have an elliptical cross-section.The solutions obtained can be shown to be unique only if certain restrictive assumptions are made, and if these are relaxed the same methods may give further solutions. Experiments on three-dimensional inviscid bubbles (Rumscheidt & Mason 1961; Taylor 1934) demonstrate that angular points appear in the bubble surface, and an analysis is presented to show that such a discontinuity in a two-dimensional free surface is necessarily a genuine cusp and the nature of the flow about such a point is examined.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

Three-dimensional numerical model for open-channels with free-surface variations

2003 ◽  
Vol 41 (1) ◽  
pp. 110-112
Author(s):  
ZhixiaN. Cao ◽  
Rodney Day ◽  
Sarah Liriano
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Three Dimensional ◽  
Open Channels

Base-Vented Hydrofoils of Finite Span Under a Free Surface: An Experimental Investigation

1984 ◽  
Vol 28 (02) ◽  
pp. 90-106
Author(s):  
Jacques Verron ◽  
Jean-Marie Michel
Keyword(s):  
Experimental Investigation ◽  
Free Surface ◽  
Flow Rate ◽  
Cavity Length ◽  
Three Dimensional ◽  
Leading Edge ◽  
Pulsation Frequency ◽  
Cavity Pressure ◽  
Air Flow Rate ◽  
Cavity Configuration

Experimental results are given concerning the behavior of the flow around three-dimensional base-vented hydrofoils with wetted upper side. The influence of planform is given particular consideration so that the sections of the foils are simple wedges with rounded noses. Results concern cavity configuration, the relation between the air flow rate and cavity pressure, leading-edge cavitation, cavity length, pulsation frequency, and force coefficients.

Thermocapillary Convection With Undeformable Curved Surfaces in Open Cylinders

2001 ◽  
Author(s):  
Bok-Cheol Sim ◽  
Abdelfattah Zebib
Keyword(s):  
Free Surface ◽  
Critical Frequency ◽  
Thermocapillary Convection ◽  
Three Dimensional ◽  
Quantitative Agreement ◽  
Fluid Volume ◽  
Uniform Heat Flux ◽  
Free Surfaces ◽  
Space Experiments ◽  
Steady Convection

Abstract Thermocapillary convection driven by a uniform heat flux in an open cylindrical container of unit aspect ratio is investigated by two- and three-dimensional numerical simulations. The undeformable free surface is either flat or curved as determined by the fluid volume (V ≤ 1) and the Young-Laplace equation. Convection is steady and axisymmetric at sufficiently low values of the Reynolds number (Re) with either flat or curved interfaces. Only steady convection is possible in strictly axisymmetric computations. Transition to oscillatory three-dimensional motions occurs as Re increases beyond a critical value dependent on Pr and V. With a flat free surface (V = 1), two-lobed pulsating waves are found on the free surface and prevail with increasing Re. While the critical Re increases with increasing Pr, the critical frequency decreases. In the case of a concave surface, four azimuthal waves are found rotating clockwise on the surface. The critical Re decreases with increasing fluid volume, and the critical frequency is found to increase. The numerical results with either flat or curved free surfaces are in good quantitative agreement with space experiments.

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