Complex dynamics in a stratified lid-driven square cavity flow

2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Complex Dynamics ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Stable Temperature ◽  
Wide Range ◽  
Side Walls ◽  
Steady State Solutions

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

Upwelling of a stratified fluid in a rotating annulus: steady state. Part 2. Numerical solutions

1973 ◽  
Vol 59 (2) ◽  
pp. 337-368 ◽  
Author(s):  
J. S. Allen
Keyword(s):  
Steady State ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Rotational Frequency ◽  
Navier Stokes ◽  
Rossby Number ◽  
Navier Stokes Equations ◽  
Finite Difference Approximations ◽  
Side Walls ◽  
Steady State Solutions

Numerical solutions of finite-difference approximations to the Navier–Stokes equations have been obtained for the axisymmetric motion of a Boussinesq liquid in a rigidly bounded rotating annulus. For most of the cases studied, a temperature difference is maintained between the top and bottom surfaces such that essentially a basic stable density stratification is imposed on the fluid. The side walls are thermally insulated and the motion is driven by a differential rotation of the top surface. Approximate steady-state solutions are obtained for various values of the Rossby number ε and the stratification parameter S = N2/Ω2, where N is the Brunt–Väisälä frequency and Ω is the rotational frequency. The changes in the flow field with the variation of these parameters is studied. Particular attention is given to an investigation of the meridional, or up welling, circulation and its dependence on the stratification parameter. The effects on the flow of different boundary conditions, such as an applied stress driving, specified temperature at the side walls and an applied heat flux at the top and bottom surfaces, are also investigated.

Optimization of the Heat and Mass Transfer Processes in a Mechanism of Polycrystalline Silicon Production by the Bridgeman’s Technique

2010 ◽  
Vol 5 (2) ◽  
pp. 75-84
Author(s):  
Elena M. Smirnova ◽  
Vladimir N. Popov
Keyword(s):  
Stokes Equations ◽  
Crystallization Front ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Nonuniform Heating ◽  
Navier Stokes Equations ◽  
Convective Flows ◽  
Mass Transfer Processes ◽  
Side Walls ◽  
Convective Diffusion Equation

The distribution of incoherent impurities in the melt for the polycrystalline silicone production by the Bridgeman’s technique was studied with the aid of 3D numerical simulation. Under study was the influence of the phase transition configuration on the distribution of the displaced substance near the crystallization front under the conditions of azimuthnonuniform heating of crucible side walls. The flow in the liquid is described by Navier-Stokes equations in the Boussinesq approximation, the distribution of the dissolved substance concentration is found from the solution of the convective diffusion equation. The obtained results show that the nonuniform heating of the melt changes the structure of convective flows; in the case of flat or convex crystallization front, these flows promote the displacement of the dissolved admixture toward the crucible walls. The processes were considered within the range of parameters following the real temperatures in a growth furnace and the melt, crucible size and shape

Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts

1992 ◽  
Vol 114 (4) ◽  
pp. 936-943 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Published Data ◽  
Circular Duct ◽  
Uniform Wall Temperature ◽  
Wide Range

This paper numerically investigates the effects of buoyancy on fully developed laminar flow in a curved duct with an elliptic cross section. The flow of Newtonian fluids is assumed steady in terms of Boussinesq approximation. The curved elliptic duct is subjected to thermal boundary conditions of axially uniform heat flux and peripherally uniform wall temperature. The numerically generated boundary-fitted coordinate system is applied to discretize the solution domain of the elliptic duct, and the Navier-Stokes equations and the energy equation, including the curvature ratio, are solved by use of the control volume-based finite difference method. The solution covers a wide range of curvature ratios, and Dean and Grashof numbers. The results presented are displayed graphically and in tabular form to illustrate the buoyancy effect. It is further shown that buoyancy acts to increase both the Nusselt number and the friction factor and changes the distribution of the velocity and the temperature. The results for the curved circular duct with and without buoyancy are compared with the data available in the open literature for all cases. Also compared with the published data are the results of laminar flow in a curved elliptic duct, and very good agreement is obtained.

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Murat Manguoglu ◽  
Ahmed H. Sameh ◽  
Faisal Saied ◽  
Tayfun E. Tezduyar ◽  
Sunil Sathe
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Handling Time ◽  
Navier Stokes ◽  
Preconditioning Techniques ◽  
Navier Stokes Equations ◽  
Nonsymmetric Linear Systems ◽  
Steady State Solutions

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Modeling Of The Alloying Substances Distribution In The Melt During Pulsed Induction Heating Of The Substrate

2017 ◽  
Vol 12 (2) ◽  
pp. 111-118
Author(s):  
Vladimir Popov
Keyword(s):  
Induction Heating ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Empirical Formulas ◽  
Metal Solidification ◽  
Navier Stokes Equations ◽  
High Frequency Electromagnetic Field ◽  
Melting And Solidification

Under study is the applicability of the high-frequency electromagnetic field impulse for metal heating and melting with a view to its subsequent alloying. The processes of heating, phase transition, heat and mass transfer in the molten metal, solidification of the melt are considered with the aid the proposed mathematical model. The substrate surface is covered with a layer of alloying substances. The distribution of the electromagnetic energy in the metal is described by empirical formulas. Melting and solidification of the metal is considered at the Stephan’s approximation. The flow in the liquid is described by the Navier – Stokes equations in the Boussinesq approximation. According to the results of numerical experiments, the flow structure in the melt and distribution of the alloying substances was evaluated versus the characteristics of induction heating

ON THE EXISTENCE AND UNIQUENESS OF TWO‐FLUID CHANNEL FLOWS

2005 ◽  
Vol 9 (1) ◽  
pp. 67-78 ◽  
Author(s):  
J. Socolowsky
Keyword(s):  
Stokes Equations ◽  
Channel Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Parameters ◽  
Free Boundary Value Problems ◽  
Fluid Channel ◽  
Density Ratios ◽  
Steady State Solutions ◽  
Two Fluid

iscous two‐fluid channel flows arise in different kinds of coating technologies. The corresponding mathematical models represent two‐dimensional free boundary value problems for the Navier‐Stokes equations. In this paper the solvability of the related stationary problems is discussed and computational results are presented. Furthermore, it is shown that depending on the flow parameters like viscosity or density ratios and on the fluxes there can happen nonexistence of steady‐state solutions. For other parameter sets the solution is even unique. Dvieju, tekančiu kanale, klampiu skysčiu srauto uždavinys iškyla taikant ivairias skirtingu rušiu paviršiu padengimo technologijas. Atitinkamas matematinis modelis išreiškiamas dvimačiu kraštiniu uždaviniu su laisvu paviršiumi Navje-Stokso lygtims. Straipsnyje nagrinejamas santykinai stacionaraus uždavinio išsprendžiamumas ir pateikiami skaičiavimo rezultatai. Be to parodoma, kad priklausomai nuo sroves parametru kaip ir nuo klampumo ir tankio santykio stacionarus sprendiniai gali neegzistuoti. Su kitais parametrais egzistuoja tiksliai vienas sprendinys.

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