Search

The two-temperature model of local thermal nonequilibrium (LTNE) is utilized to investigate a weakly nonlinear stability of thermosolutal convection in an Oldroyd-B fluid-saturated anisotropic porous layer. The anisotropies in permeability, thermal conductivities of the porous medium, and solutal diffusivity are accounted for by second-order tensors with their principal directions coinciding with the horizontal and vertical coordinate axes. A modified Darcy–Oldroyd model is employed to describe the flow in a porous medium bounded by impermeable plane walls with uniform and unequal temperatures as well as solute concentrations. The cubic-Landau equations are derived in the neighborhood of stationary and oscillatory onset using a modified perturbation approach and the stability of bifurcating equilibrium solutions is discussed. The advantage is taken to present some additional results on the linear instability aspects as well. It is manifested that the solutal anisotropy parameter also plays a decisive role on the instability characteristics of the system. It is found that the stationary bifurcating solution transforms from supercritical to subcritical while the oscillatory bifurcating solution transforms from supercritical to subcritical and revert to supercritical. The Nusselt and Sherwood numbers are used to examine the influence of LTNE and viscoelastic parameters on heat and mass transfer, respectively. The results of Maxwell fluid are outlined as a particular case from this study.

A full three-dimensional (3D) numerical simulation of solidification was carried out for a benchmark experiment on a binary Sn-10 wt. %Pb alloy. The experiment process involves a melting stage, a first holding stage at constant temperature with electromagnetic stirring, setting a mean horizontal temperature difference (second holding stage), and finally solidification stage by decreasing the temperature under a imposed horizontal temperature gradient. The numerical model is applied only to investigate the solidification stage and compared with the measured temperature fields and macrosegregation obtained from the postmortem analysis. A columnar numerical model based on a two-phase volume-averaged approach is used for the numerical simulation, accounting for thermosolutal convection and assuming perfect microscopic mixing (lever rule) in the mushy zone. It demonstrates that such a model is able to predict stratification in the solute from the liquid phase and mushy zone during the solidification. The effect of the sedimentation on macrosegregations and channel segregation or freckles which develop during the solidification stage is also predicted by the model and compared with experimental data. Emphasis is given to the main factors that have a direct effect on the development and morphology of segregated channels, namely, the remelting phenomenon, dendrite fragmentation, and the solidification front instabilities.

Numerical solutions for thermosolutal convection in a vertical concentric cavity partly filled with a porous medium are presented in this paper. The cavity is subject to pre-selected horizontal temperature and concentration gradients. The general Brinkman-Forchheimer-extended Darcy model is adopted to formulate the fluid flow through the porous matrix in the cavity. The effects of the controlling parameters on the flow patterns and heat and mass transfer behavior are thoroughly documented. Different flow structures are produced in the course of the computations, which respond to the geometric parameters, fluid nature, thermofluid dynamic parameters and porous matrix characteristics. The collection of numerical results elucidates that the double diffusion zone varies and, besides it is strongly dependent on the coupling between the Prandtl and Lewis numbers. Moreover, the variations of the Sherwood number show the presence of an extended range of double diffusion phenomena within the conditions pertinent to Darcian flow at Da=10−5. It has been discovered that a partly porous annular cavity is more efficient than a fully porous annular cavity. This aspect may have a beneficial impact on engineering applications in the areas of filtration and thermal insulation.

The solidification of a dilute alloy (bismuth-tin) under Bridgman crystal growth conditions is investigated. Computations are performed in two dimensions with a uniform grid. The simulation includes the species concentration, temperature and flow fields, as well as conduction in the ampoule. Fully transient simulations have been performed, with no simplifying steady state approximations. Results are obtained under microgravity conditions for pure bismuth, and for Bi-0.1 at.% Sn and Bi-1.0 at.% Sn alloys, and compared with experimental results obtained from crystals grown in the microgravity environment of space. For the Bi-1.0 at.% Sn case the results indicate that a secondary convective cell, driven by solutal gradients, forms near the interface. The magnitude of the velocities in this cell increases with time, causing increasing solute segregation at the solid/liquid interface. Finally, a comparison between model predictions and results obtained from a space experiment is reported. The concentration-dependence of the alloy melting temperature is incorporated in the model for this case. Satisfactory correspondence is obtained between the predicted and experimental results in terms of solute concentrations in the solidified crystal.

A numerical study is made of double-diffusive convection in a square cavity with a sliding top lid in the presence of combined vertical temperature and concentration gradients. The bottom lid and other two walls are kept fixed. The side walls are adiabatic and impermeable to solute while the top and bottom lids are kept at constant but distinct temperature and concentration. The governing unsteady Navier–Stokes equations combined with the heat and mass transport equations are solved numerically through a finite volume method on a staggered grid system using QUICK scheme for convective terms. The resulting equations are then solved by an implicit, time-marching, pressure correction-based algorithm. The flow configuration is classified into four cases depending on positive/negative values of thermal Grashof number and solutal Grashof number. A detailed comparison of the four flow configurations is made in this paper. In conclusion, these four flow configurations can be brought to either stably or unstably stratified field. Furthermore, the possibility of salt-fingering and double-diffusive instability in the absence of the top lid motion is explored and the effect of the lid motion is clearly exhibited. The dependence of the average rates of heat and mass transfer from the top and bottom lids on the flow parameters is also investigated in the presence of top lid motion.

The paper explores the potential of a recently developed special front tracking method in the identification of the interface between columnar and equiaxed structures formed during a binary alloy solidification, driven by thermosolutal convection. The method, based on theoretical and experimental dendrite tip kinetics, is capable of directly distinguishing between the columnar mush and the undercooled liquid/equiaxed region developing ahead of the dendrite tip curve. A new numerical model and its computational algorithm are proposed, where the classical Eulerian volume averaged description of the transport processes is coupled with the Lagrangian front tracking method on a fixed control-volume grid. Having thus distinguished zones of different dendrite structures, distinct simulation models are used within each of the zones, e.g., the Darcy’s porous medium model in the stationary dendrite region, and a model of slurry with floating dendrites in the equiaxed part of the mush. The calculated temperature and solute concentration fields are compared with the relevant results of the classical enthalpy-porosity model, for an example problem of Pb-48 wt % Sn alloy solidification driven by diffusion and thermosolutal convection. And a good match with both solutions is exhibited. A preliminary validation study is also presented by comparing the available experimental data with the model predictions. Possible reasons for some observed discrepancies between the calculations and the experimental findings are discussed. Finally, the proposed front tracking approach is used to address the question of the impact of dendrites floating in the liquid on the flow pattern and macrosegregation in the solidifying alloy.

The onset of thermosolutal convection in a fluid-saturated porous medium in the presence of a horizontal pressure gradient and the Soret effect under the two-temperature model of local thermal nonequilibrium (LTNE) is investigated. The Darcy model with the time-dependent velocity term in the momentum equation is employed together with the Oberbeck–Boussinesq approximation. The eighth-order eigenvalue differential equation obtained by employing linear stability analysis is solved using Galerkin's method of weighted residuals (GMWR) and also analytically. The onset of convection instills through oscillatory rather than stationary mode, and the critical stability parameters for the same are determined. The horizontal pressure gradient reinforces together with the solute concentration gradient and the scaled interphase heat transfer coefficient in evidencing mixed behavior on the criterion for the onset of oscillatory convection. Besides, the similarities and differences between the results of thermal and thermosolutal LTNE porous mixed convection are discerned.

Development of the solid–liquid interface, distribution of the particle concentration field, as well as the development of thermosolutal convection during solidification of colloidal suspensions in a differentially heated cavity are investigated. The numerical model is based on the one-fluid mixture approach combined with the single-domain enthalpy porosity model for phase change, and it is implemented in fluent software package. The linear dependence of the liquidus and solidus temperatures with the concentration of the nanoparticles was assumed. A colloidal suspension consisting of water and copper or alumina nanoparticles were considered. In the current investigation, the nanoparticle size selected was 5 and 2 nm. The suspension was solidified unidirectionally inside a square differentially heated cavity that was cooled from the left side. It was found that the solid–liquid interface changed its morphology from a planar shape to a dendritic one as the solidification process proceeds in time, due to the constitutional supercooling that resulted from the increased concentration of particles at the solid–liquid interface rejected from the crystalline phase. Initially, the flow consisted of two vortices rotating in opposite directions. However, at later times, only one counter clockwise rotating cell survived. Changing the material of the particle to alumina resulted in crystallized phase with a higher concentration of particles. If it is compared to that of the solid phase resulted from freezing the copper–water colloidal suspension. Decreasing the segregation coefficient destabilizes the solid–liquid interface and increases the intensity of the convection cell with respect to that of the case of no particle rejection. At slow freezing rates, the resulting crystal phase consisted of lower particle content compared to the case of higher freezing rate.

The transient transport of momentum, energy, and species during solidification of a Pb-19 percent Sn alloy is numerically simulated with and without magnetic damping. The system is contained in an axisymmetric, annular mold, which is cooled along its outer vertical wall. Since thermosolutal convection accompanies solidification and is responsible for final macrosegregation patterns, application of a steady magnetic field, which is parallel to the axis of the mold, has the potential to reduce macrosegregation by damping buoyancy-driven flow during solidification. Results show that, during early stages of solidification, the magnetic field significantly affects thermally driven flow in the melt, as well as interactions between thermally and solutally driven flows. However, interdendritic flows and macrosegregation patterns are not significantly altered by moderate magnetic fields. Scaling analysis reveals that extremely strong fields would be required to effectively dampen convection patterns that contribute to macrosegregation. 40 refs., 13 figs., 1 tab.

Thermosolutal convection driven by opposed thermal and solutal buoyancy forces is experimentally investigated, by employing an electrochemical system in a low aspect ratio enclosure. In certain parametric ranges, it is observed that both the current and the temperature fluctuate. Criteria associated with the solutal Grashof number, and buoyancy and aspect ratios have been correlated to classify the characteristics of mass and heat transfer processes and various flow regimes, and a new length scale is suggested. The unsteady transport phenomena are found to depend on the Lewis number, Grashof number, and buoyancy and aspect ratios.