The Effects of Gravity and Surface Tension Gradients on Cellular Convection in Fluid Layers With Parabolic Temperature Profiles

1970 ◽  
Vol 92 (3) ◽  
pp. 351-358 ◽  
Author(s):  
Walter R. Debler ◽  
Louis W. Wolf
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Critical Rayleigh Number ◽  
Numerical Procedure ◽  
Surface Boundary ◽  
Thermal Boundary Conditions ◽  
Free Surface Boundary Condition ◽  
Fluid Layers ◽  
Surface Boundary Condition

The effects of surface tension and buoyancy on the convection stability of fluid layers with a mean parabolic temperature distribution is examined. A variety of free-surface, thermal boundary conditions are used. Quantitative values for the effect on the critical Rayleigh number of the free-surface boundary condition, fluid depth, and physical properties are given. The role of the mean temperature profile is also discussed. The results should be of value in judging experiments where a free surface is used to enhance the flow visualization. The numerical procedure used to find the eigenvalues was effective and easily altered to obtain results for similar stability problems.

scholarly journals A note on solitary waves with variable surface tension in water of infinite depth

2006 ◽  
Vol 48 (2) ◽  
pp. 225-235 ◽  
Author(s):  
E. Özuğurlu ◽  
J.-M. Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Solitary Waves ◽  
Surface Boundary ◽  
Two Dimensional ◽  
Infinite Depth ◽  
Free Surface Boundary Condition ◽  
Variable Surface ◽  
Dimensional Gravity ◽  
Surface Boundary Condition

AbstractTwo-dimensional gravity-capillary solitary waves propagating at the surface of a fluid of infinite depth are considered. The effects of gravity and of variable surface tension are included in the free-surface boundary condition. The numerical results extend the constant surface tension results of Vanden-Broeck and Dias to situations where the surface tension varies along the free surface.

SPLASH Free-Surface Flow Code Methodology for Hydrodynamic Design and Analysis of IACC Yachts

1993 ◽  
Author(s):  
Bruce S. Rosen ◽  
Joseph P. Laiosa ◽  
Warren H. Davis ◽  
David Stavetski
Keyword(s):  
Free Surface ◽  
High Performance ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Surface Boundary ◽  
Induced Drag ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
America’S Cup ◽  
Areas Of Interest

A unique free-surface flow methodology and its application to design and analysis of IACC yachts are discussed. Numerical aspects of the inviscid panel code and details of the free-surface boundary condition are included, along with enhancements developed specifically for the '92 America's Cup defense. Extensive code validation using wind tunnel and towing tank experimental data address several areas of interest to the yacht designer. Lift and induced drag at zero Froude number are studied via a series of isolated fin/bulb/winglet appendages. An isolated surface piercing foil is used to evaluate simple lift/free­surface interactions. For complete IACC yacht models, upright wave resistance is investigated, as well as lift and induced drag at heel and yaw. The excellent correlation obtained for these cases demonstrates the value of this linear free-surface methodology for use in designing high performance sailing yachts.

Coupled Dynamic Analysis of a Moored Spar Platform in Time Domain

2010 ◽  
Author(s):  
M. D. Yang ◽  
B. Teng
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Dynamic Analysis ◽  
Time Domain ◽  
Surface Boundary ◽  
Spar Platform ◽  
Mooring Lines ◽  
Coupled Dynamic Analysis ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

A time-domain simulation method is developed for the coupled dynamic analysis of a spar platform with mooring lines. For the hydrodynamic loads, a time domain second order method is developed. In this approach, Taylor series expansions are applied to the body surface boundary condition and the free surface boundary condition, and Stokes perturbation procedure is then used to establish corresponding boundary value problems with time-independent boundaries. A higher order boundary element method is developed to calculate the velocity potential of the resulting flow field at each time step. The free-surface boundary condition is satisfied to the second order by 4th order Adams-Bashforth-Moultn method. An artificial damping layer is adopted on the free surface to avoid the wave reflection. For the mooring-line dynamics, a geometrically nonlinear finite element method using isoparametric cable element based on the total Lagrangian formulation is developed. In the coupled dynamic analysis, the motion equation for the hull and dynamic equations for mooring lines are solved simultaneously using Newmark method. Numerical results including motions and tensions in the mooring lines are presented.

scholarly journals Free-Surface Effects on Interaction of Multiple Ships Moving at Different Speeds

2019 ◽  
Vol 63 (4) ◽  
pp. 251-267 ◽  
Author(s):  
Zhi-Ming Yuan ◽  
Liang Li ◽  
Ronald W. Yeung
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Present Article ◽  
Hydrodynamic Interaction ◽  
Surface Effects ◽  
Superposition Method ◽  
Surface Boundary ◽  
Gravitational Acceleration ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition

Ships often have to pass each other in proximity in harbor areas and waterways in dense shipping-traffic environment. Hydrodynamic interaction occurs when a ship is overtaking (or being overtaken) or encountering other ships. Such an interactive effect could be magnified in confined waterways, e.g., shallow and narrow rivers. Since Yeung published his initial work on ship interaction in shallow water, progress on unsteady interaction among multiple ships has been slow, though steady, over the following decades. With some exceptions, nearly all the published studies on ship-to-ship problem neglected free-surface effects, and a rigid-wall condition has often been applied on the water surface as the boundary condition. When the speed of the ships is low, this assumption is reasonably accurate as the hydrodynamic interaction is mainly induced by near-field disturbances. However, in many maneuvering operations, the encountering or overtaking speeds are actually moderately high (Froude number Fn > 0.2, where <inline-graphic xlink:href="josr10180089inf1.tif"/>, U is ship speed, g is the gravitational acceleration, and L is the ship length), especially when the lateral separation between ships is the order of ship length. Here, the far-field effects arising from ship waves can be important. The hydrodynamic interaction model must take into account the surface-wave effects. Classical potential-flow formulation is only able to deal with the boundary value problem when there is only one speed involved in the free-surface boundary condition. For multiple ships traveling with different speeds, it is not possible to express the free-surface boundary condition by a single velocity potential. Instead, a superposition method can be applied to account for the velocity field induced by each vessel with its own and unique speed. The main objective of the present article is to propose a rational superposition method to handle the unsteady free-surface boundary condition containing two or more speed terms, and validate its feasibility in predicting the hydrodynamic behavior in ship encountering. The methodology used in the present article is a three-dimensional boundary-element method based on a Rankine-type (infinite-space) source function, initially introduced by Bai and Yeung. The numerical simulations are conducted by using an in-house‐developed multibody hydrodynamic interaction program “MHydro.” Waves generated and forces (or moments) are calculated when ships are encountering or passing each other. Published model-test results are used to validate our calculations, and very good agreement has been observed. The numerical results show that free-surface effects need to be taken into account for Fn > 0.2.

Earthquake-induced sloshing in a rigid circular tank

1991 ◽  
Vol 18 (6) ◽  
pp. 904-915 ◽  
Author(s):  
Michael Isaacson ◽  
Kesavan Subbiah
Keyword(s):  
Free Surface ◽  
Response Spectra ◽  
Simple Extension ◽  
Inviscid Fluid ◽  
Surface Boundary ◽  
Hydrodynamic Damping ◽  
Free Surface Boundary Condition ◽  
Surface Boundary Condition ◽  
Time Domain Response ◽  
The Time Domain

The present paper describes the sloshing of a liquid in a rigid circular cylindrical tank subjected both to harmonic and to irregular base motion. Initially, the boundary value problem for the case of an inviscid fluid and a harmonic base motion is solved on the basis of linearized potential flow theory. The case of energy dissipation of a real fluid is then treated by a simple extension to this, which involves an assumption of dissipation at the free surface and a corresponding modification to the free surface boundary condition. In order to treat earthquake-induced motions, this solution is then extended to (i) the stochastic response to a base motion which describes a stationary random process; (ii) the time-domain response to a specified base acceleration record; and (iii) a simplified method of estimating maximum forces using a modal analysis and involving earthquake response spectra. The estimation of hydrodynamic damping is briefly considered, and example applications are provided. Key words: added mass, cylinders, damping, earthquakes, hydrodynamics, sloshing.

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