scholarly journals Convection in a mushy layer along a vertical heated wall

2021 ◽  
Vol 926 ◽  
Author(s):  
S. Boury ◽  
C.R. Meyer ◽  
G.M. Vasil ◽  
A.J. Wells
Keyword(s):  
Boundary Layer ◽  
Numerical Study ◽  
Heated Wall ◽  
Solid Matrix ◽  
Mushy Region ◽  
Mushy Layer ◽  
Icy Moons ◽  
Vertical Boundary ◽  
Theoretical Predictions ◽  
Region Ii

Motivated by the mushy zones of sea ice, volcanoes and icy moons of the outer solar system, we perform a theoretical and numerical study of boundary-layer convection along a vertical heated wall in a bounded ideal mushy region. The mush is comprised of a porous and reactive binary alloy with a mixture of saline liquid in a solid matrix, and is studied in the near-eutectic approximation. Here, we demonstrate the existence of four regions and study their behaviour asymptotically. Starting from the bottom of the wall, the four regions are (i) an isotropic corner region; (ii) a buoyancy dominated vertical boundary layer; (iii) an isotropic connection region; and (iv) a horizontal boundary layer at the top boundary with strong gradients of pressure and buoyancy. Scalings from numerical simulations are consistent with the theoretical predictions. Close to the heated wall, the convection in the mushy layer is similar to a rising buoyant plume abruptly stopped at the top, leading to increased pressure and temperature in the upper region, whose impact is discussed as an efficient melting mechanism.

Weak convection, liquid inclusions and the formation of chimneys in mushy layers

1999 ◽  
Vol 388 ◽  
pp. 197-215 ◽  
Author(s):  
T. P. SCHULZE ◽  
M. GRAE WORSTER
Keyword(s):  
Solid Fraction ◽  
Stokes Equations ◽  
Numerical Study ◽  
Solidification Rate ◽  
Mushy Region ◽  
Mushy Layer ◽  
Liquid Region ◽  
Interfacial Conditions ◽  
Buoyancy Driven Convection ◽  
Steady Convection

We present a numerical study of steady convection in a two-dimensional mushy layer during solidification of a binary mixture at a constant speed V. The mushy layer is modelled as a reactive porous medium whose permeability is a function of the local solid fraction. The flow in the liquid region above the mushy layer is modelled using the Stokes equations (i.e. the Prandtl number is taken to be infinite). The calculations follow the development of buoyancy-driven convection as the flow amplitude is increased to the level where the solid fraction is driven to zero at some point within the mushy region. We show that this event cannot occur before the local buoyancy-driven volume flux exceeds the solidification rate V. Further increases in the flow amplitude lead to the formation of a region with negative solid fraction, indicating the need to switch from the Darcy approximation to the Stokes flow approximation. These regions ultimately become what are known as chimneys. We exhibit solutions which give the detailed structure of the temperature, solute, flow and solid fraction fields within the mushy layer. A key finding of the numerics is that these fledgling chimneys emerge from the interior of the mushy layer, rather than eating their way down from the top of the layer, as the amplitude of the steady convection is increased. We discuss some qualitative features of the resulting liquid inclusions and, in the light of these, reassess the interfacial conditions between mushy and liquid regions.

scholarly journals Development of Depth-Limited Wave Boundary Layers over a Smooth Bottom

2020 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Hitoshi Tanaka ◽  
Nguyen Xuan Tinh ◽  
Xiping Yu ◽  
Guangwei Liu
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Wave Motion ◽  
Numerical Study ◽  
Experiment Data ◽  
Tidal Motion ◽  
Long Period ◽  
Simulation Results ◽  
Wave Boundary

A theoretical and numerical study is carried out to investigate the transformation of the wave boundary layer from non-depth-limited (wave-like boundary layer) to depth-limited one (current-like boundary layer) over a smooth bottom. A long period of wave motion is not sufficient to induce depth-limited properties, although it has simply been assumed in various situations under long waves, such as tsunami and tidal currents. Four criteria are obtained theoretically for recognizing the inception of the depth-limited condition under waves. To validate the theoretical criteria, numerical simulation results using a turbulence model as well as laboratory experiment data are employed. In addition, typical field situations induced by tidal motion and tsunami are discussed to show the usefulness of the proposed criteria.

Interactions between steady and oscillatory convection in mushy layers

2010 ◽  
Vol 645 ◽  
pp. 411-434 ◽  
Author(s):  
PETER GUBA ◽  
M. GRAE WORSTER
Keyword(s):  
Standing Waves ◽  
Mushy Layer ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Mushy Layers ◽  
Theoretical Predictions ◽  
Convection Patterns ◽  
The Stability ◽  
Nonlinear Solutions ◽  
Steady Convection

We study nonlinear, two-dimensional convection in a mushy layer during solidification of a binary mixture. We consider a particular limit in which the onset of oscillatory convection just precedes the onset of steady overturning convection, at a prescribed aspect ratio of convection patterns. This asymptotic limit allows us to determine nonlinear solutions analytically. The results provide a complete description of the stability of and transitions between steady and oscillatory convection as functions of the Rayleigh number and the compositional ratio. Of particular focus are the effects of the basic-state asymmetries and non-uniformity in the permeability of the mushy layer, which give rise to abrupt (hysteretic) transitions in the system. We find that the transition between travelling and standing waves, as well as that between standing waves and steady convection, can be hysteretic. The relevance of our theoretical predictions to recent experiments on directionally solidifying mushy layers is also discussed.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

scholarly journals Free Convective MHD Flow Past a Vertical Cone with Variable Heat and Mass Flux

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
J. Prakash ◽  
S. Gouse Mohiddin ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Mass Flux ◽  
Numerical Study ◽  
Convection Boundary Layer ◽  
Vertical Cone ◽  
Local Skin ◽  
Surface Mass ◽  
Flow Past ◽  
Power Law Exponent

A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to qwx=xm and qw*(x)=xm, respectively, where x denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent (m), surface mass flux power-law exponent (n), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

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