Low-Prandtl-Number Marangoni Convection Driven by Localized Heating on the Free Surface: Results of Three-Dimensional Direct Simulations

2003 ◽  
pp. 157-175 ◽  
Author(s):  
Thomas Boeck ◽  
Christian Karcher
Keyword(s):  
Free Surface ◽  
Prandtl Number ◽  
Marangoni Convection ◽  
Three Dimensional ◽  
Localized Heating

Bénard–Marangoni convection at low Prandtl number

1999 ◽  
Vol 399 ◽  
pp. 251-275 ◽  
Author(s):  
THOMAS BOECK ◽  
ANDRÉ THESS
Keyword(s):  
Free Surface ◽  
Prandtl Number ◽  
Marangoni Number ◽  
Marangoni Convection ◽  
Three Dimensional ◽  
Bottom Wall ◽  
Liquid Sodium ◽  
Small Scale ◽  
Quiescent State ◽  
Two Dimensional

Surface-tension-driven Bénard convection in low-Prandtl-number fluids is studied by means of direct numerical simulation. The flow is computed in a three-dimensional rectangular domain with periodic boundary conditions in both horizontal directions and either a free-slip or no-slip bottom wall using a pseudospectral Fourier–Chebyshev discretization. Deformations of the free surface are neglected. The smallest possible domain compatible with the hexagonal flow structure at the linear stability threshold is selected. As the Marangoni number is increased from the critical value for instability of the quiescent state to approximately twice this value, the initially stationary hexagonal convection pattern becomes quickly time-dependent and eventually reaches a state of spatio-temporal chaos. No qualitative difference is observed between the zero-Prandtl-number limit and a finite Prandtl number corresponding to liquid sodium. This indicates that the zero-Prandtl-number limit provides a reasonable approximation for the prediction of low-Prandtl-number convection. For a free-slip bottom wall, the flow always remains three-dimensional. For the no-slip wall, two-dimensional solutions are observed in some interval of Marangoni numbers. Beyond the Marangoni number for onset of inertial convection in two-dimensional simulations, the convective flow becomes strongly intermittent because of the interplay of the flywheel effect and three-dimensional instabilities of the two-dimensional rolls. The velocity field in this intermittent regime is characterized by the occurrence of very small vortices at the free surface which form as a result of vortex stretching processes. Similar structures were found with the free-slip bottom at slightly smaller Marangoni number. These observations demonstrate that a high numerical resolution is necessary even at moderate Marangoni numbers in order to properly capture the small-scale dynamics of Marangoni convection at low Prandtl numbers.

Flow Visualization and Pattern Dynamics in Be´nard-Marangoni Convection

2006 ◽  
Author(s):  
Samir Rahal ◽  
Hisao Azuma
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
Surface Deformation ◽  
Marangoni Convection ◽  
Temperature Fields ◽  
Pattern Dynamics ◽  
Free Surface Deformation ◽  
Prandtl Numbers ◽  
Biot Numbers

The aim of this experimental work is to study the pattern dynamics in the Be´nard-Marangoni convection. The free surface deformation fields were visualized by interferometry and the temperature fields by infrared thermography. The influence of the aspect ratio, Rayleigh, Biot and Prandtl numbers, was considered. More dynamics are found to be induced by increasing the Biot number. Conversely, increasing the Prandtl number reduces the dynamics. The deformation magnitude and the wavenumber increase as functions of the gradient of temperature. Two behaviours of the deformation, as a function of Prandtl and Biot numbers, were observed, depending on the value of the gradient of temperature.

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.

scholarly journals Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 821
Author(s):  
Sergey Khrapak ◽  
Alexey Khrapak
Keyword(s):  
Prandtl Number ◽  
Hard Sphere ◽  
Solid Phase ◽  
Freezing Point ◽  
Three Dimensional ◽  
Order Unity ◽  
Strongly Coupled ◽  
Dielectric Fluids ◽  
Weakly Coupled ◽  
Component Plasma

The Prandtl number is evaluated for the three-dimensional hard-sphere and one-component plasma fluids, from the dilute weakly coupled regime up to a dense strongly coupled regime near the fluid-solid phase transition. In both cases, numerical values of order unity are obtained. The Prandtl number increases on approaching the freezing point, where it reaches a quasi-universal value for simple dielectric fluids of about ≃1.7. Relations to two-dimensional fluids are briefly discussed.

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.

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