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The model of double diffusive convection in a bidisperse porous medium was examined. Brinkman effects and slip were allowed to be used in macropores. In the micropores, only the Darcy effects are held. In equilibrium, the concentration of solutes is thought to be a linear function of temperature. We performed both a linear and a nonlinear stability analysis, with a particular emphasis on the impact of slip boundary conditions on the system's instability and stability. After deciding when the instability started, we determined the critical Rayleigh number as a function of the slip coefficient. Numerical findings for stability/instability thresholds were also presented.

The fractional of a time derivative for the incompressible smoothed particle hydrodynamics (ISPH) method is adopted to handle thermal radiation on thermosolutal convection in a porous cavity barred by nanoencapsulated phase change materials (NEPCMs). A novel work on the rotational velocities of two rods during thermosolutal convection of NEPCMs within a novel cavity of two connected circular cylinders is introduced. The management of heat-mass transfer and velocity magnitude inside distinct designed materials below various boundary conditions carries improvements for energy efficiency. The physical factors are thermal radiation [Formula: see text], Fusion temperature [Formula: see text], Rayleigh number [Formula: see text], hot source length [Formula: see text], Darcy number [Formula: see text], and fractional order parameter [Formula: see text]. This study reported the role of thermal/solutal conditions in varying the dual convection flow and heat capacity contour. The lower Da provides an elevated porous resistance which decelerates the nanofluid velocity. The fusion temperature alters a heat capacity contour.

The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The main governing parameters of the problem are the Rayleigh, the Hartmann, the Soret, the Dufour and the Lewis numbers, the buoyancy ratio, the enclosure aspect ratio, and the normalized porosity of the porous medium. An asymptotic parallel flow approximation is applied to determine the onset of subcritical nonlinear convection. In addition, a linear stability analysis is performed to predict explicitly the thresholds for the onset of stationary, overstable and oscillatory convection, and the Hopf bifurcation as functions of the governing parameters. The combined effect of a magnetic field, Soret and Dufour parameters have a noticeable influence on the intensity of the convective flow, the heat and mass transfer rates, and the thresholds of linear convection. It is found that the imposition of a magnetic field delays the onset of convection and its intensification can lead to the total suppression of the convective currents. The heat transfer rate increases with the Dufour number and decreases with the Soret number and vice versa for the mass transfer rate.

Different from other alloys, the observation in this work on the dendritic mushy zone shows that the freckles are formed in two different regions before and after peritectic reaction in directional solidification of Sn–Ni peritectic alloys. In addition, the experimental results demonstrate that the dendritic morphology is influenced by the temperature gradient zone melting and Gibbs–Thomson effects. A new Rayleigh number (RaP) is proposed in consideration of both effects and peritectic reaction. The prediction of RaP confirms the freckle formation in two regions during peritectic solidification. Besides, heavier thermosolutal convection in samples with larger diameter is also demonstrated.

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.

In this paper, we study the problem of thermosolutal convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from above or below. This problem is studied under the effects of Soret and slip boundary conditions. Both linear and nonlinear stability analyses are employed. When the layer is heated from below and salted from above, the boundaries exhibit great concordance, resulting in a very narrow region of probable subcritical instabilities. This proves that linear analysis is reliable enough to forecast the beginning of convective motion. The Chebyshev collocation technique and QZ algorithm have been used to solve systems of linear and nonlinear theories. For thermal convection in a dissolved salt field with a complex viscoelastic fluid of the Navier–Stokes–Voigt type, instability boundaries are computed. When the convection is of the oscillatory type, the Kelvin–Voigt parameter is observed to play a crucial role in functioning as a stabilizing agent. This effect's quantitative size is shown.

International audience; Experiments of directional solidification of TiAl cylindrical samples were conducted within the frame of the ESA GRADECET project. The experiments were performed in the ESA "Large Diameter Centrifuge" using a furnace with a well defined thermal protocol. The furnace was mounted in the centrifuge and free to tilt in such a way that the total apparent gravity (sum of terrestrial gravity and centrifugal acceleration) was aligned to the cylinder centerline. Several centrifugation levels were investigated besides to one reference case out of the centrifuge. In this work, we present 3D numerical simulations of these experiments paying special attention in the liquid thermosolutal buoyancy convection and aluminum macrosegregation. The numerical model accounts for the non-inertial accelerations that appear in the rotating reference frame (centrifugal and Coriolis), motionless solid, the-mosolutal Boussinesq approximation and an infinitely fast microscopic diffusion model between the phases to depict the solid growth. The results showed that the Coriolis acceleration entirely modifies the liquid flow regime during solidification leading to a 3D aluminum segregation pattern with respect to the case solidified under normal terrestrial gravity conditions. Additionally the magnitude of aluminum segregation increases with the level of centrifu-* Corresponding author

In the present paper, a numerical investigation was performed to assess the effect of the rheological behavior of non-Newtonian fluids on Rayleigh–Benard thermosolutal convection instabilities within shallow and finite aspect ratio enclosures. Neumann and Dirichlet thermal and solutal boundary condition types were applied on the horizontal walls of the enclosure. Using the Boussinesq approximation, the momentum, energy, and species transport equations were numerically solved using a finite difference method. Performing a nonlinear asymptotic analysis, a bistability convective phenomenon was discovered, which was induced by the combined fluid shear-thinning and aiding thermosolutal convection effects. Therefore, bistability convection was the main focus in the current study using the more practical constitutive Carreau–Yasuda viscosity model, which is valid from zero to infinite shear rates. Also, the combined effects of the rheology parameters and double diffusive bistability convection were studied. For aiding flow, the shear-thinning and the slower diffusing solute effects were counteracting and, as a result, two steady-state finite amplitude solutions were found to exist for the same values of the governing parameters, which indicated and demonstrated evidence for the existence of bistability convective flows. For opposing flows, the shear-thinning effect strengthened subcritical flows, which sustained well below the threshold of Newtonian thermosolutal convection. Thus, bistability convection did not exist for opposing flows, as both the shear-thinning and the slower diffusing component effects favored subcritical convection.

In this paper, three-dimensional thermosolutal natural convection and entropy generation in a cubic cavity filled with a non-Newtonian Carreau-Yasuda fluid has been simulated by Lattice Boltzmann Method (LBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 104 and 105), the Buoyancy ratio (N = -1, 0.1, 1), the Lewis number (Le = 0.5, 2.5, 10, 100, and 1000), power-law indexes (n = 0.5, 1, and 1.5), Carreau number (Cu = 0.01, 0.1, 1, 10 and 100), and Carreau-Yasuda parameter (m = 0.1, 0.5, and 1). Results indicate that the rise of Rayleigh number enhances heat and mass transfer for various studied parameters. The increase in power-law index provokes heat and mass transfer to drop gradually. However, the effect of power-law index on heat and mass transfer rises steadily as Rayleigh number rises. The enhancement of Carreau number decreases heat and mass transfer, but; the increases in the Carreau-Yasuda parameter augments heat and mass transfer significantly. The augmentation of the buoyancy ratio number enhances heat and mass transfer. It was found that mass transfer increases as Lewis number augments. The augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the power-law index provokes various irreversibilities to drop significantly. The enhancement of the buoyancy ratio causes the summation entropy generations to increase considerably. The rise of Carreau number and Carreau-Yasuda parameter decreases and increases the total irreversibilities; respectively.

An investigation of the stability of an micropolar nanofluid overlying a sparsely packed porous medium and implanted in a parallel conduit is reviewed. Linear and also nonlinear terms are incorporated for the study. A Darcy-Brinkman-Forchheimer drag force model is deployed. To evaluate nanoscale effects the Buongiorno model is employed. The equations for mass, momentum, angular momentum, energy and nanoparticle species conservation with correlated wall conditions are non-dimensionalized. Modified diffusivity ratio and Lewis number stable the system, the micropolar parameters concentration Rayleigh number destable system for stationary convection. Concentration Rayleigh number, micropolar parameters stabilize and Lewis number destabilizes the system for oscillatory convection. Applications of the study include micro/nano-fluidic devices, nano-doped energy systems and packed beds in chemical engineering.

The objective of the current paper is to investigate the thermosolutal flow along with heat and mass dissipation rates in an upright porous annular space subjected to discrete heating and salting along the vertical boundaries with insulated and impermeable horizontal boundaries. To solve the model equations, an implicit finite difference scheme with over relaxation technique has been implemented. The numerical predictions focus specifically on the effect of buoyancy ratio, Lewis number, Darcy number and source-sink arrangements on fluid flow behavior, thermal and solutal characteristics, average Nusselt and Sherwood numbers. The simulations were performed for an extensive range of dimensionless parameters (−10 ≤ N ≤ 10, 0.1 ≤ Le ≤ 1, 10−5 ≤ Da ≤ 10−1) by considering two different types of source-sink arrangements and found that the flow circulation strength is maximum with in-line arrangement of source and sink compared to alternative arrangement. Also, we found that in case-I, regardless of Lewis number, the maximum heat and mass dissipation rates takes place through top source during opposing flow, and through bottom source for aided flow. However, in case-II arrangement, irrespective to type of flow, the greater amount of heat and mass transport is found through the bottom source at the inner cylinder compared to top source placed at outer cylinder.

Embedded the thermal and solutal buoyancy into the momentum conservation equation as an additional force term using the Boussinesq approximation, a 2D CA-FVM model is extended to simulate the dendritic growth with thermosolutal convection. The model is firstly validated by comparison of numerical predictions with the benchmark test of Rayleigh – Benard convection and the analytical solutions of the stagnant film model for the free dendritic growth with thermosolutal convection, and good agreements between the numerical results with analytical solutions are obtained. Later, numerical simulations for both the equiaxed and columnar dendritic growth of Fe-0.82wt%C binary alloy with thermosolutal convection are performed. The results show that, for the equiaxed dendritic growth in an undercooled melt, the dendrite tip growth rapidly decreases from the high velocity to a relative low steady-state value. With the further growth of dendrite, the thermosolutal convection induced by the solute rejection and latent heat release is enhanced and four vortexes are developed between the dendrite arms. Thus, the asymmetries of the dendrite morphology, temperature and solute profiles are intensified. For the columnar dendritic growth with thermosolutal convection under the unidirectional solidification process, the thermosolutal convection transports the rejected solute downward and makes the solute enrich at the interdendritic region. The thermosolutal convection facilitates the upstream dendritic growth, but inhibits the downstream dendritic growth. Moreover, with the increase of deflection angle of gravity, the advection on the top region and the clock-wise vortex flow at the interdendritic region intensified, and finally the columnar dendrite morphology becomes more asymmetrical.

Using a perturbation method, we solve asymptotically the nonlinear partial differential equations that govern double-diffusive convection (with heat and solute diffusing) in a two-dimensional rectangular domain near a critical point in parameter space where the linearized operator has a quadruple-zero eigenvalue. The asymptotic solution near this codimension-four point is found to depend on two slow-time-dependent amplitudes governed by two nonlinearly-coupled Van der Pol–Duffing equations. Through numerical approximation of the 3-dimensional Poincare map in the four-dimensional state space of the amplitude equations, we detect and analyze the bifurcations of the amplitude equations as the thermal Rayleigh number, R T , is increased (for R S ≪ R T , the solute Rayleigh number) with all other parameters fixed. The bifurcations observed include: Hopf, pitchfork and Neimark–Sacker bifurcations of limit cycles, symmetric and asymmetric saddle–node bifurcations of 2-tori, and reverse torus-doubling cascades. In addition, chaotic solutions are found numerically to emerge via two different types of routes: (1) a route involving a homoclinic explosion in the Poincare map and; (2) type-I intermittency routes near saddle–node bifurcations of 2-tori. The homoclinic explosion occurs when two unstable 2-tori form homoclinic connections with a saddle limit cycle, thereby creating a homoclinic butterfly in the Poincare map that leads to a discrete Lorenz-like attractor.

The main purpose of our investigation is to show the impact of pertinent parameters; such Lewis and porous thermal Rayleigh numbers as well as the buoyancy and the aspect ratios; on the double-diffusive convection phenomena which occur within a porous annulus; found between a cold (and less concentric) outer circular cylinder and a hot (and concentric) inner one, to come out with global correlations which predict the mean transfer rates in such annulus. To do so, the physical model for the momentum conservation equation is made using the Brinkman extension of the classical Darcy equation. The set of coupled equations is solved using the finite volume method and the SIMPLER algorithm. Summarizing the numerical predictions, global correlations of overall transfer within the porous annulus as a function of the governing studied parameters are set forth which predict within ±2% the numerical results. These correlations may count as a complement to previous researches done in the case a Newtonian-fluid annulus. It is to note that the validity of the computing code used was ascertained by comparing our results with the experimental data and numerical ones already available in the literature.

A numerical investigation of Soret and Dufour effects on heat and mass transfer in a Salt Gradient Solar Pond (SGSP) and its storage efficiency under meteorological conditions of Tangier (Morocco) is presented. This SGSP consists of an open square cavity filled with a saline solution. Its vertical and bottom walls are adiabatic and impermeable. Transfers are described by the Navier-Stokes, thermal energy and diffusion equations which are solved with a finite volume scheme and the Gauss method. The link between the pressure and velocity fields is carried out by the SIMPLE algorithm. The numerical model, developed in Fortran 95 language, is satisfactorily validated by comparisons with previously published numerical and experimental studies. Results show that the Dufour effect on thermosolutal convection in a SGSP is more relevant than the Soret effect. Nevertheless, increasing the value of the Dufour coefficient from 0 to 0.8 improves heat and mass transfer in the SGSP. Therefore, the amount of the thermal energy accumulated in the storage zone is reduced by about 5.56 %. In addition, the heat losses through the SGSP free surface are improved by around 8.53 %.

In this study, the bifurcation phenomenon and the existence of dual asymmetry solutions of double-diffusive convection driven by an internal thermal and solutal source in a horizontal cavity have been investigated systematically. The problem is solved by the SIMPLE algorithm with the QUICK scheme in a non-uniform staggered grid system. The Rayleigh numbers, 200 ≤ Ra ≤ 106, buoyancy ratios, −20 ≤ Nc ≤ 20, Soret numbers, 0 ≤ Sr ≤ 0.8, and Dufour numbers, 0 ≤ Df ≤ 0.8, are considered in this study. Different streamlines for the onset and evolution of static bifurcation are tracked. The paper aims to determine the critical Rayleigh numbers and buoyancy ratios for the onset of symmetry-breaking through bifurcation diagrams based on the vortex length. The results indicate that increasing buoyancy can destabilize the symmetric system. The strong couple diffusion effect delays the onset of bifurcation flow. A pair of asymmetric modes can be obtained under different initial conditions.

The present study simulates the 3D unsteady double-diffusive natural convection subject to opposing thermal and solutal buoyancy forces (N

The unsteady double-diffusive natural convection flow in a rectangular enclosure filled with soft rocks which are subjected to humid air, including water vapor absorption and thermoelasticity, is studied numerically. The high order compact finite difference schemes are adopted for better simulation of this problem, and a Darcy–Brinkman–Forchheimer extended model combined with the absorption and thermoelasticity effects is introduced. The effects of the thermal and solutal Rayleigh numbers, hygroscopicity, Darcy numbers and thermoelasticity on the flow are investigated in detail. Results are presented in the form of streamlines and isolines of temperature and mass fraction as well as the plots of average Nusselt and Sherwood numbers over the walls under different conditions. The flow structure develops from conduction-dominated to steady convection-dominated as increasing Rayleigh number or increasing buoyancy ratio as well as increasing Darcy numbers. The thermoelasticity effects of soft rocks play an important role in the analysis of thermal convection flow by the change of temperature and permeability, while the water vapor absorption effects may have a slight effect on the flow in the beginning and vanish with the absorption effects becoming weak. Nevertheless, the effect may significant reduce the mechanical strength properties of soft rocks.

Thermosolutal convection with reaction in a porous media of Darcy type is studied using the energy method. The effect of the reaction terms on the temperature and salt Rayleigh numbers are presented graphically. Furthermore, nonlinear energy stability boundaries for different values of the reaction terms are compared with the linear instability boundaries obtained by Pritchard and Richardson (2007).

Thermosolutal convection inevitably occurs during the solidification of alloys owing to the nonuniform distribution of temperature and/or solute concentration, and this can drastically alter the resulting solidification microstructures. In this study, we present a large-scale simulation scheme for the phase-field lattice Boltzmann model, which can express dendrite growth upon considering the solute, heat transport, and liquid flow. A multiple mesh and time step method was employed to reduce computational costs, where different mesh sizes and time steps are used to solve the phase-field equation, the advection–diffusion equations of heat and solute, and the lattice Boltzmann equations for fluid flow. Furthermore, we implemented parallel computations using multiple graphics processing units (GPUs) to accelerate the large-scale simulation. Through the application of the multiple mesh and time step method, the computation was accelerated by approximately one hundred times compared to the case using a constant mesh and time step for all equations. Moreover, we confirmed that the developed parallel-GPU computation combined with the multiple mesh and time step method could achieve good acceleration and scaling through increasing the number of GPUs. We also confirmed that the developed method could simulate multiple dendrite growth with thermosolutal convection.

We describe a mathematical model of double-diffusive (thermosolutal) convection in a saturated porous layer, when the solubility of the solute depends on the temperature, and the porosity and permeability of the porous medium evolve through dissolution and precipitation. We present the results of linear and weakly nonlinear stability analyses and explore the longer-term development of the system numerically. When the solutal concentration gradient is destabilising, the dynamics are somewhat similar to those previously found for single-species convection (Ritchie & Pritchard, J. Fluid Mech., vol. 673, 2011, pp. 286–317), including the occurrence of subcritical instabilities driven by a reaction–diffusion mechanism. However, when the solutal concentration gradient is stabilising and the thermal gradient is destabilising, novel dynamics emerge. These include a vertical segregation of circulation cells and porosity perturbations near the onset of convection, and over longer time scales the formation of a low-permeability region in the middle of the layer, pierced by occasional high-permeability channels. Under these conditions, convection may die away to nearly zero for extended periods before resuming vigorously in localised regions at later times.

The present study deals with effect of Hall currents on thermal convection of ferromagnetic fluids in porous medium. The combined effect of solute gradient, medium permeability, magnetic field and Hall currents on the thermal stability has been investigated. It is found that Hall currents destabilize the system. The magnetic field and solute gradient have stabilizing effect on the convection. The medium permeability has conditional effect on the stability. The principle of exchange of stabilities (PES) is not satisfied under these conditions. In the absence of magnetic field and solute gradient, PES is valid.

In this study, we investigated numerically two- and three-dimensional convective heat and mass transfer in a horizontal rectangular enclosure filled with heterogeneous porous media. The main goal is to underline the limitation of the widely used classical parallel flow assumption. The considered configuration is Cartesian. The horizontal and vertical walls are submitted to different mass and heat transfer. The Darcy model and the Boussinesq approximation are considered. The governing parameters which control the problem are the Darcy-Rayleigh number, Rt, the buoyancy ratio, N, the enclosure aspect ratio, A, the local permeability ratio, Kr and the Lewis number (fixed to ten in the present study). The obtained results with two-dimensional (2D) and three-dimensional (3D) approaches are compared to underline similarities and differences. We demonstrate the limit validity of 2D solution and the transition to 3D solutions when the convective forces or the domain permeable heterogeneity increases. The flow intensity, heat and mass transfer increases with the domain permeable heterogeneity.

International audience; Freckles are common defects in industrial casting. They result from thermosolutal convection due to buoyancy forces generated from density variations in the liquid. The present paper proposes a numerical analysis for the formation of channel segregation using the three-dimensional (3D) cellular automaton (CA)—finite element (FE) model. The model integrates kinetics laws for the nucleation and growth of a microstructure with the solution of the conservation equations for the casting, while introducing an intermediate modeling scale for a direct representation of the envelope of the dendritic grains. Directional solidification of a cuboid cell is studied. Its geometry, the alloy chosen as well as the process parameters are inspired from experimental observations recently reported in the literature. Snapshots of the convective pattern, the solute distribution, and the morphology of the growth front are qualitatively compared. Similitudes are found when considering the coupled 3D CAFE simulations. Limitations of the model to reach direct simulation of the experiments are discussed.

A two-phase model based on the double-diffusive approach is used to perform a numerical study of natural convection of alumina-water nanofluids in differentially heated vertical slender cavities. In the mathematical formulation, Brownian diffusion and thermophoresis are assumed to be the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum and energy for the nanofluid, and continuity for the nanoparticles is solved through a computational code relying on the SIMPLE-C algorithm for the pressure-velocity coupling. The effective thermal conductivity and dynamic viscosity of the nanofluid, and the coefficient of thermophoretic diffusion of the suspended solid phase, are evaluated using three empirical correlations based on a high number of experimental data available from diverse sources, and validated by way of literature data different from those used in generating the...

Double-diffusive systems, such as thermosolutal convection, in which the density depends on two components that diffuse at different rates, are prone to both steady and oscillatory instabilities. Such systems can evolve into layered states, in which both components, and also the density, adopt a “staircase” profile. Turbulent transport is enhanced significantly in the layered state. Here we exploit an analogy between magnetic buoyancy and thermosolutal convection in order to demonstrate the phenomenon of magnetic layering. We examine the long-term nonlinear evolution of a vertically stratified horizontal magnetic field in the so-called “diffusive regime,” where an oscillatory linear instability operates. Motivated astrophysically, we consider the case where the viscous and magnetic diffusivities are much smaller than the thermal diffusivity. We demonstrate that diffusive layering can occur even for subadiabatic temperature gradients. Magnetic layering may be relevant for stellar radiative zones, with implications for the turbulent transport of heat, magnetic field, and chemical elements.

International audience; A comparative study among solidification experiments for three selected alloys (Sn-3 wt.%Pb, Sn-6.5 wt.%Pb and Sn-10 wt.%Pb) was conducted on a benchmark experiment model under the same experimental conditions. The goal of this paper is to analyze the effect of variation in concentration on the solidification process with respect to different aspects: thermal, dynamic, structure, and morphology of segregation. Experimental results consist of instantaneous temperature maps provided by a lattice of 50 thermocouples welded on the large crucible side and post-mortem characterizations of the samples, such as X-ray imaging, solute local composition and metallography. Measurement of the instantaneous temperature field and numerical computation of liquid solid interface evolution allows us to evaluate the effect of variation in concentration on thermosolutal convection behavior. Experimental results show that an increase in concentration greatly enhances the mechanism of the columnar-to-equiaxed transition (CET) and leads to refinement of the equiaxed structure. However, a significant effect of solutal element (lead) stratification is observed, which can slow down thermosolutal convection, in particular for large concentrations. Especially, without any stirring lead segregation which likely occurs during the melting phase may suppress natural convection. Furthermore, lead stratification is significantly reduced when electromagnetic stirring is opposed to natural convection before the solidification phase begins.

A numerical model is built for the solidification of a binary alloy with thermosolutal convection under centrifugal condition. The model is based on the macroscopic transport equations derived using the volume-averaging method. New formulations are derived for a non-linear phase diagram and temperature-dependent thermophysical properties. Simulations are performed to substantiate experiments with TiAl alloys carried out on ESA’s Large Diameter Centrifuge (LDC) using different angular velocities, ω. These experiments comprise a region of transient columnar growth of β-Ti dendrites under decreasing temperature gradient and increasing growth velocity followed by the columnar-to-equiaxed transition (CET). The simulation results show that CET is triggered by a sudden drop of the temperature gradient ahead of the advancing solidification front being a consequence of a sudden change of the flow pattern. We show that the flow pattern driven by density inversion changes abruptly once the permeability of the columnar structure increases above some critical value. This promotes the Rayleigh–Benard instability and the development of local convection cells along with an extended region of very low temperature gradient. The intensity and asymmetry of the flow in the local convection cells increase with increasing ω. The results show that a mushy zone developing in transient conditions and with gradually increasing permeability can significantly alter the flow pattern even in centrifugal conditions with a dominant contribution from Coriolis forces.

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.

The thermosolutal convection can alter segregation pattern, change dendrite morphology and even cause freckles formation in alloy solidification. In this work, the multiphase-field model was coupled with lattice Boltzmann method to simulate the dendrite growth under melt convection in superalloy solidification. In the isothermal solidification simulations, zero and normal gravitational accelerations were applied to investigate the effects of gravity on the dendrite morphology and the magnitude of melt flow. The solute distribution of each alloy component along with the dendrite tip velocity during solidification was obtained, and the natural convection has been confirmed to affect the microsegregation pattern and the dendrite growth velocity. In the directional solidification simulations, two typical temperature gradients were applied, and the dendrite morphology and fluid velocity in the mushy zone during solidification were analyzed. It is found that the freckles will form when the average fluid velocity in the mushy zone exceeds the withdraw velocity.

Abstract The influence of the melt flow on the solidification structure is bilateral. The flow plays an important role in the solidification pattern, via the heat transfer, grain distribution, and segregations. On the other hand, the crystal structure, columnar or equiaxed, impacts the flow, via the thermosolutal convection, the drag force applied by the crystals on the melt flow, etc. As the aim of this research was to further explore the solidification–flow interaction, experiments were conducted in a cast cell (95 * 95 * 30 mm3), in which an ammonium chloride–water solution (between 27 and 31 wt pct NH4Cl) was observed as it solidified. The kinetic energy (KE) of the flow and the average flow velocity were calculated throughout the process. Measurements of the volume extension of the mush in the cell and the velocity of the solid front were also taken during the solidification experiment. During the mainly columnar experiments (8 cm liquid height) the flow KE continuously decreased over time. However, during the later series of experiments at higher liquid height (9.5 cm), the flow KE evolution presented a strong peak shortly after the start of solidification. This increase in the total flow KE correlated with the presence of falling equiaxed crystals. Generally, a clear correlation between the strength of the flow and the occurrence of equiaxed crystals was evident. The analysis of the results strongly suggests a fragmentation origin of equiaxed crystals appearing in the melt. The transition from purely columnar growth to a strongly equiaxed rain (CET) was found to be triggered by (a) the magnitude of the coupling between the flow intensity driven by the equiaxed crystals, and (b) the release and transport of the fragments by the same flow recirculating within the mushy zone. Graphical Abstract Coupling mechanism at the origin of CET: 1-2 strong flow running through the mush transporting out dendrite fragments (white dots); 3-4 equiaxed growth and drag of the downward flow. If the vortex is sufficiently stable, the horizontal configuration can lead to freckle appearing; a) vertical solidification front; b) horizontal solidification front.

A transient two-dimensional ISPH method based on the time-fractional derivative was applied for emulating thermosolutal convection of the nano-encapsulated phase change material (NEPCM) embedded in an annulus between an inner wavy shape and outer hexagonal-shaped cavity. The impacts of a magnetic field and double rotations amongst an inner wavy shape and outer hexagonal-shaped cavity on the heat and mass transmission of NEPCM in an annulus have been conducted. Effects of a time parameter τ (0.01 − 1), frequency parameter ω (1 − 7), fractional time derivative α (0.95 − 1), Darcy parameter Da (10−2 − 10−4), Hartmann number Ha (0 − 100), fusion temperature θf (0.05 − 0.8), and Rayleigh number Ra (103 − 105) on the contours of temperature, heat capacity, concentration, and velocity field as well as profiles of Nu ¯ and Sh ¯ are investigated. The main findings signaled that the double rotations plays effectively in speed up the nanofluid movements, and changing the features of temperature, concentration, and heat capacity inside an annulus. An augmentation in a frequency parameter boosts the nanofluid speed by 128.57%. A decline in α from 1 to 0.95 enhances the maximum nanofluid velocity by 13.73%. The nanofluid movements within an annulus are reduced according to an increase in Ha and a decrease in Da. The power in the Rayleigh number enhances the nanofluid movements within an annulus.

A numerical model is developed to simulate the temperature field, the thermosolutal convection, the solute segregation and the growth interface morphology during the growth of ZnTe crystal from Te rich solution by the temperature gradient solution growth (TGSG) technique. Effects of the temperature gradient on the transport phenomena, the growth interface morphology and the growth rate are examined. The influences of the latent heat and the thermal conductivity of ZnTe crystal on the transport phenomena and the growth interface are also discussed. We find that the mass transfer of ZnTe in the solution is very slow because of the low diffusion coefficient and the lack of mixing in the lower part of the solution. During the growth, dilute solution with high density and low growth temperature accumulates in the central region of the growth interface, making the growth interface change into two distinct parts. The inner part is very concave, while the outer part is relatively flat. Growth conditions in front of the two parts of the growth interface are different. The crystalline quality of the inner part of the ingot is predicted to be worse than that of the outer part. High temperature gradient can significantly increase the growth rate, and avoid the diffusion controlled growth to some extent.

International audience; A special case that stands out in thermosolutal convection is that for which the thermal and solutal convection forces are equal and generate opposite effects (N = -1). This antagonistic effect between the two buoyancy forces is expected to generate unpredictable and unique behaviors when combined with thermodiffusion and internal heating phenomena. The present numerical study is dedicated to this particular case considering a binary mixture confined in a vertical rectangular cavity with an aspect ratio A = 2. The lattice Boltzmann method with multiple relaxation time is used to analyze the effect of the control parameters which are the Soret parameter (Sr = -0.5, 0 and 0.5), and the internal to external Rayleigh numbers ratio (0

An analysis of thermosolutal convection and entropy generation considering Soret and Dufour effects inside an inclined rectangular enclosure attached with porous wall has been investigated. The physical parameters are in the ranges such as buoyancy ratio (-10 ≤ N ≤ 10), permeability (10−9 ≤ Da ≤ 10−1) and thickness (0 ≤ d ≤ 1.0) of porous wall, enclosure inclination angle (0° ≤ Φ ≤ 90°), Soret number (0 ≤ Sr ≤ 1.5) and Dufour number (0 ≤ Du ≤ 1.5). Heatlines and masslines taking Soret and Dufour effects into account are obtained as effective tools that visualizes the heat and species transported paths. Results demonstrate that Soret number has mild impact on heat transfer rate and promotes moisture transportation, while increasing Dufour number could boot heat transfer rate and reduce moisture transfer rate. Furthermore, increasing Soret numbers enhances entropy generation induced by heat transfer and fluid friction, while entropy generation induced by fluid friction, heat and moisture transfer is dropped with stronger Dufour effect. Present work can benefit the heat and moisture transfer performance and entropy generation minimization of thermal storage wall system.

Under a NASA (National Aeronautics and Space Agency)-ESA (European Space Agency) collaborative research project, MICAST (Microstructure formation in casting of technical alloys under a diffusive and magnetically controlled convection conditions), three Al-7 wt% Si samples (MICAST-6, MICAST-7 and MICAST2-12) were directionally solidified aboard the International Space Station (ISS) to determine the effect of mitigating convection on the primary dendrite array morphology. MICAST-6 was processed with a step-increase in the growth speed from 5 to 50 µm s−1, MICAST-7 with a step-decrease from 20 to 10 µm s−1, and MICAST2-12 with constant speed of 40 µm s−1. Nearest-neighbor primary dendrite arm spacings and primary dendrite trunk diameters were measured on transverse sections taken at approximately 5 mm intervals along the length of the MICAST samples. In MICAST samples, especially in the steady-state growth regime, the observed primary dendrite nearest-neighbor spacings show a good agreement with predictions from the Hunt-Lu numerical model. The maximum to minimum (highest 10% to lowest 10%) nearest-neighbor spacing ratio in MICAST samples is 2.10 ± 0.27 in agreement with Hunt-Lu model, which assumes pure diffusive transport. Trunk diameters in MICAST samples also agree well with predictions from a coarsening based model. The terrestrial-grown equivalent samples, on the other hand, display smaller nearest-neighbor spacing, and larger primary dendrite trunk diameters than those predicted from the models. Thermosolutal convection appears to increase the dendrite tip radius, causing the trunk diameter to increase, while simultaneously reducing the primary dendrite spacing. This requires verification-experiments involving directional solidification followed by rapid quenching of the liquid-solid interface in metallic alloys in a low gravity environment. The International Space Station currently does not have on-board hardware to conduct such experiments.

Hypoeutectic Al-7 wt .% Si alloys were directionally solidified vertically downward in cylindrical molds that incorporated an abrupt cross-section decrease (9.5 mm to 3.2 mm diameter) which, after 5 cm, reverted back to 9.5 mm diameter in a Bridgman furnace; two constant growth speeds and thermal gradients were investigated. Thermosolutal convection and cross-section-change-induced shrinkage flow effects on macrosegregation were investigated. Dendrite clustering and extensive radial macrosegregation was seen, particularly in the larger cross-sections, before contraction and after expansion, this more evident at the lower growth speed. This alloy shows positive longitudinal macrosegregation near cross-section decrease followed by negative macrosegregation right after it; the extent of macrosegregation, however, decreases with increasing growth speed. Primary dendrite steepling intensified as solidification proceeded into the narrower section and negative longitudinal macrosegregation was seen on the re-entrant shelves at expansion. A two-dimensional model accounting for both shrinkage and thermo-solutal convection was used to simulate solidification and the resulting mushy-zone steepling and macrosegregation. The experimentally observed longitudinal and radial macrosegregation associated with the cross-section changes during directional solidification of an Al–7Si alloy is well captured by the numerical simulations.

In the current study, the evolutions of channel segregations in several alloy systems, such as the typically used model alloys (e.g., Ga-In, Sn-Pb, Sn-Bi, Al-Cu, and Ni-based superalloy) and some special steels, are numerically simulated in a cavity solidified unidirectionally. The simulations are based on a modified continuum macrosegregation model with an extension to the multicomponent systems. The results of model alloys and steels indicate that when the thermosolutal convection is strong enough, flow instability occurs, which in turn destabilizes the mushy zone. Subsequently, the channel segregation forms with the continuous interaction between solidification and flow. The formation behavior and severity of channel segregations in various systems are different owing to their distinct melt convection strengths and solidification natures. In the current simulations, channels are apparent for model alloys with high content of solutes, whereas they are slight in some special steels, such as 27SiMn steel, and totally disappear in carbon steels. These occurrence features of channel segregation in simulations of steels are consistent with the analyses by a modified Rayleigh number associated with alloying elements, and both outcomes are well supported by the fully sectioned steel ingots in experiments.

This paper deals with thermosolutal convection in an inclined enclosure inserted with heat-generating porous blocks under the influence of magnetic field. The general Brinkman-extended Darcy model is adopted to formulate the fluid flow in the enclosure. An extensive series of numerical simulations is investigated in the range of parameters 0 ≤ Ha ≤ 150, 103 ≤ Ra ≤ 107, −10.0 ≤ N ≤ 10.0, 10−9 ≤ Da ≤ 10−1, 0.1 ≤ Kr ≤ 10 and −90° ≤ Φ ≤ 90°. Streamline, isotherms, isoconcentrations and masslines are produced to illustrate the fluid, heat and moisture flow structures. It is founded that overall Nusselt number is an increasing function of Ra, N, Da and Kr in the vertical enclosure, while decreasing with Ha. The permeability and thermal conductivity of porous blocks have no significant effect on moisture transfer rate. The Nusselt and Sherwood curves for different inclination angle are presented to be parabolic, and the maximum are near at Ф = −10° and 30°, respectively. In addition, correlations of the overall Nusselt and Sherwood numbers depending on thermal Rayleigh number, buoyancy ratio, Hartmann number and inclination angle have been obtained, which are beneficial to determine heat and moisture transfer rates in electrical devices.

International audience; Solidification of alloys in a thermal gradient usually involves the generation of flows by thermal or thermosolutal convection. We experimentally study their effects on the dynamics of a solidification interface by inducing a controlled sweeping flow in a directional solidification device. Flow is induced in the sample from an external thermosiphon. Downstream inclination of microstructures and downstream sidebranch development are observed. However, the major outcome is the evidence of large scale travelling waves on the solidification interface. They are induced by the coupling between solidification and flow and yield repetitive striations of the solid phase. Two waves are observed and characterized.

In order to investigate the effect of natural convection in columnar to equiaxed transition (CET), Al-3.0wt.%Cu and Al-3.0wt.%Cu-5.5wt.%Si alloys ingots were obtained during the transient horizontal directional solidification (THDS). Aiming to analyze the effect of superheat in the formation of the macrostructure in ternary Al-Cu-Si alloy, the experiments were conducted with three superheat temperatures above the liquidus temperature of the ternary alloy. A water-cooled solidification experimental device was used. Continuous temperature measurements were made during solidification at different positions in the casting and the data were automatically acquired. Thermal analysis has been applied to determine the thermal parameters such as growth rate (VL), cooling rate (TR) and temperature gradient (GL), whose values have been interrelated with the CET. The observation of the macrostructures has indicated that the resulting thermosolutal convection combined with superheat seem to favor the transition, which did not occur in a single plane, for all ingots obtained, i.e., it has been seen in a range of positions in ingots. The addition of Si element in binary Al-Cu alloy anticipates the CET. A comparison with experimental results for CET occurrence in different growth directions has been carried out.