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Article
Publication date: 3 April 2007

Z.Q. Han, R.W. Lewis and B.C. Liu

The motivation for this work is to establish a model that not only includes the main factors resulting in macrosegregation but also retains simplicity and consistency for…

Abstract

Purpose

The motivation for this work is to establish a model that not only includes the main factors resulting in macrosegregation but also retains simplicity and consistency for the sake of potential application in casting practice.

Design/methodology/approach

A mathematical model for the numerical simulation of thermosolutal convection and macrosegregation in the solidification of multicomponent alloys is developed, in which the coupled macroscopic mass, momentum, energy and species conservation equations are solved. The conservation equations are discretized by using the control volume‐based finite difference method, in which an up‐wind scheme is adopted to deal with the convection term. The alternative direction implicit procedure and a line‐by‐line solver, based on the tri‐diagonal matrix algorithm, are employed to iteratively solve the algebraic equations. The velocity‐pressure coupling is handled by using the SIMPLE algorithm.

Findings

Based on the present study, the liquid flow near the dendritic front is believed to play an important role in large‐scale transport of the solute species. The numerical or experimental results in the literatures on the formation of channel segregation, especially those about the location of the initial flow as well as the morphology of the liquidus front, are well supported by the present investigation.

Research limitations/implications

The modelling is limited to dealing with the thermosolutal convection of two‐dimensional cases. More complicated phenomena (e.g. crystal movement) and 3D geometry should be considered in future research.

Practical implications

The present model can be used to analyze the effects of process parameters on macrosegregation and, with further development, could be applied as a useful tool in casting practice.

Originality/value

The numerical simulation demonstrates the capability of the model to simulate the thermosolutal convection and macrosegregation in alloy solidification. It also shows that the present model has good application potential in the prediction and control of channel segregation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 29 October 2021

Abdelraheem M. Aly and Shreen El-Sapa

The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the…

69

Abstract

Purpose

The purpose of this paper is to work out the magnetic forces on heat/mass transmission in a cavity filled with a nanofluid and wavy porous medium by applying the incompressible smoothed particle hydrodynamics (ISPH) method.

Design/methodology/approach

The cavity is filled by a nanofluid and an undulating layer of a porous medium. The inserted two circular cylinders are rotated around the cavity’s center by a uniform circular velocity. The outer circular cylinder has four gates, and it carries two different boundary conditions. The inner circular cylinder is carrying Th and Ch. The Lagrangian description of the dimensionless regulating equations is solved numerically by the ISPH method.

Findings

The major outcomes of the completed numerical simulations illustrated the significance of the wavy porous layer in declining the nanofluid movements, temperature and concentration in a cavity. The nanofluid movements are declining by an increase in nanoparticle parameter and Hartmann number. The variations on the boundary conditions of an outer circular cylinder are changing the lineaments of heat/mass transfer in a cavity.

Originality/value

The originality of this study is investigating the dual rotations of the cylinders on magnetohydrodynamics thermosolutal convection of a nanofluid in a cavity saturated by two wavy horizontal porous layers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 22 May 2008

Miha Založnik, Shihe Xin and Božidar Šarler

This paper aims to point out the critical problems in numerical verification of solidification simulation codes and the complexity of the verification and to propose and…

Abstract

Purpose

This paper aims to point out the critical problems in numerical verification of solidification simulation codes and the complexity of the verification and to propose and apply a procedure of generalized verification for macrosegregation simulation.

Design/methodology/approach

A partial verification of a finite‐volume computational model of macrosegregation in direct chill (DC) casting of binary aluminum alloys, including the coupled transport phenomena of heat transfer, fluid flow and species transport, is performed. The verification procedure is conducted on numerical test problems, defined as subproblems with respect to the complexity of the physical model, geometry, and boundary conditions. The studied cases are thermal convection with solidification in DC casting, thermal natural convection of a low‐Prandtl‐number liquid metal in a rectangular cavity and 1D directional solidification of a binary Al‐Cu alloy. Grid‐convergence studies, code comparison with an alternative Chebyshev‐collocation method, and comparison with a reference similarity solution are used for verification.

Findings

An excellent ability of the model to accurately resolve the thermal convection in the pertinent range of Prandtl and Rayleigh numbers is shown. Concerns regarding the solution of species transport in the mushy zone remain.

Research limitations/implications

The proposed verification procedure is not completed in its entirety. Further verification of the solutal and thermosolutal convection problems is required.

Originality/value

This paper proposes verification techniques for complex coupled solidification problems involving significant convection in the melt.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 27 June 2008

L. Kaffel Rebaï, A. Mojtabi, M.J. Safi and A.A. Mohamad

The purpose of this paper is to present a numerical and an analytical study of the thermohaline convection with Soret effect in a square enclosure filled with a binary…

Abstract

Purpose

The purpose of this paper is to present a numerical and an analytical study of the thermohaline convection with Soret effect in a square enclosure filled with a binary fluid mixture.

Design/methodology/approach

The horizontal boundaries of the enclosure are impermeable and heated from below while its vertical walls are assumed to be adiabatic and impermeable. The Navier‐Stokes equations under the Boussinesq‐Oberbeck approximation are solved numerically. The results are given for different values of the separation ratio. The critical Rayleigh number at the onset of convection is determined analytically and numerically. The Hopf frequency at the onset of convection is obtained.

Findings

The existence of two stable stationary bifurcation branches is illustrated. Furthermore, it is shown that the existence of stable traveling waves in the transition from one branch to the other depends on the value of the separation ratio. For some values of Rayleigh number, asymmetric flows are observed. A good agreement is found between the numerical solution and analytical analysis.

Originality/value

The present work is the first to consider thermosolutal convection with Soret effect in a square enclosure.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 28 July 2021

Abdeslam Omara, Mouna Touiker and Abderrahim Bourouis

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix…

Abstract

Purpose

This paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.

Design/methodology/approach

The domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.

Findings

The results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, Rk, has practically no effect on Shhot wall, contrary to Nuinterface where a strong increase is observed as Rk is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.

Practical implications

The findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.

Originality/value

The authors believe that the presented results are original and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 March 2005

M. Er‐raki, M. Hasnaoui, A. Amahmid and M. Bourich

Thermodiffusion or Soret effect is a phenomenon that can be encountered in many applications. However only little is known about this phenomenon, particularly in the case…

Abstract

Purpose

Thermodiffusion or Soret effect is a phenomenon that can be encountered in many applications. However only little is known about this phenomenon, particularly in the case of sparsely packed media (i.e. Brinkman media). The aim of this paper is to study numerically and analytically the effect of thermodiffusion on the onset of natural convection in a horizontal Brinkman porous layer with a free‐stress upper boundary.

Design/methodology/approach

The study is performed by solving numerically the governing equations for different combinations of the governing parameters. An analytical solution is also developed in the case of a shallow layer using the approximation of a parallel flow in the core region to predict the critical conditions corresponding to the onset stationary, subcritical and Hopf convection.

Findings

The results obtained show that, in the presence of Soret effect, the numerical and analytical solutions agree well for long enough layers. The thermodiffusion parameter can affect considerably the supercritical and sub‐critical Rayleigh numbers and heat and mass transfer characteristics in the layer. It is also shown that the plane Le‐φ can be divided into three main regions with specific and different behaviours.

Originality/value

The Soret effect can play a stabilizing or a destabilizing role and this, depending on the sign of the separation parameter, φ.

Details

Engineering Computations, vol. 22 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 December 2003

J.M. Zhan and Y.S. Li

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an…

Abstract

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an accurate high‐order difference method. Numerical stability is improved by using fourth‐order accurate upwind‐biased differences to approximate the convection terms. The other terms in the governing differential equations are discretized using fourth‐order central difference. To demonstrate the versatility of the boundary‐fitted coordinate system, natural convection in an eccentric annulus is first simulated. The numerical results are consistent with the experimental results by Kuehn and Goldstein and better than the numerical results by Projahn et al. for eccentric cases. Secondly, the symmetry breaking and overturning states in thermohaline‐driven flows in a two‐dimensional rectangular cavity are simulated first to validate the numerical scheme. The numerical results agree well with those by Dijkstra and Molemaker and Quon and Ghil. Finally, the effect of the Lewis number on the flow system is investigated in detail. Depending on the value of the Lewis number, the flow pattern is either stable and symmetric, periodic and oscillatory, or unsymmetric and random.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 February 2021

Abdelraheem M. Aly and Zehba Raizah

The purpose of this study is to simulate the thermo-solutal convection resulting from a circular cylinder hanging in a rod inside a ∧-shaped cavity.

Abstract

Purpose

The purpose of this study is to simulate the thermo-solutal convection resulting from a circular cylinder hanging in a rod inside a ∧-shaped cavity.

Design/methodology/approach

The two dimensional ∧-shaped cavity is filled by Al2O3-water nanofluid and saturated by three different levels of heterogeneous porous media. An incompressible smoothed particle hydrodynamics (ISPH) method is adopted to solve the governing equations of the present problem. The present simulations have been performed for the alteration of buoyancy ratio (2N2), radius of a circular cylinder (0.05Rc0.3), a height of a rod (0.1Lh0.4), Darcy parameter (103Da105), Lewis number (1Le40), solid volume fraction (0ϕ0.06), porous levels (0η1=η21.5)and various boundary-wall conditions.

Findings

The performed numerical simulations indicated the importance of embedded shapes on the distributions of temperature, concentration and velocity fields inside ∧-shaped cavity. Increasing buoyancy ratio parameter enhances thermo-solutal convection and nanofluid velocity. Adiabatic conditions of the vertical-walls of ∧-shaped cavity augment the distributions of the temperature and concentration. Regardless the Darcy parameter, a homogeneous porous medium gives the lowest values of a nanofluid velocity.

Originality/value

ISPH method is used to simulate thermo-solutal convection of a nanofluid inside a novel ∧-shaped cavity containing a novel embedded shape and heterogeneous porous media.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 25 October 2018

Safae Hasnaoui, Abdelkhalek Amahmid, Abdelghani Raji, Hassen Beji, Mohammed Hasnaoui, Youssef Dahani and Haykel Benhamed

The purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat…

Abstract

Purpose

The purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat generation. The enclosure is heated and salted from its long sides with constant but different temperatures and concentrations. The study focuses on the effects of three main parameters which are, the Soret parameter (Sr = 0 and –0.5), the internal to external Rayleigh numbers ratio 0 ≤ R ≤ 80 and the cavity inclination γ, varied from 0° (vertical position) to 60°. The combined effects of these parameters on fluid flow and heat and mass transfer characteristics are examined for the external Rayleigh number RaE = 105, the Prandtl number Pr = 0.71, the buoyancy ratio N = 1, the Lewis number Le = 2 and the aspect ratio of the cavity A = 2.

Design/methodology/approach

A hybrid lattice Boltzmann-finite difference method (LBM-FD) was used to tackle the problem under consideration. The LBM with the simple relaxation time was used for the fluid flow in the presence of the gravity force, while the temperature and concentration equations were solved separately using an explicit finite-difference technique at the Boltzmann scale.

Findings

The monocellular nature of the flow, obtained for R = 0 is not destroyed by varying the cavity inclination and the Soret parameter but rather by the increase of the parameter R. The Soret parameter and the cavity inclination become perceptible at high values of R. The inclination γ = 60° leads to high mean temperatures compared to the other inclinations. The effect of R on mean concentration is amplified in the presence of Soret effect but limited in the absence of the latter. The negative Soret parameter combined with high internal heat generation and a relatively high inclination is important when the objective is to maintain the fluid at a high concentration of species. The presence of bicellular flow combined with the important elevation undergone by the fluid temperature, makes both the cold and hot walls playing a cooling role with the most important exchanges taking place at the upper part of these walls. The analysis of the mean mass transfer shows that the increase of the inclination may lead to an increase or a decrease of the mass transfer depending on the range of R, in the case of Sr = 0. However, for Sr = −0.5, it is observed that the increase of γ is generally accompanied by a reduction of the mass transfer.

Originality/value

To the best of the authors’ knowledge, the hybrid LBM-FD was not used before to study such a problem. Combined effect of R and inclination may be useful in charging the fluid with species when the objective is to maintain high concentrations in the medium.

Details

Engineering Computations, vol. 35 no. 8
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 27 September 2021

Abdelraheem M. Aly, Noura Alsedais and Hakan F. Oztop

The purpose of this study is to use the incompressible smoothed particle hydrodynamics method to examine the influences of a magnetic field on the double-diffusive…

Abstract

Purpose

The purpose of this study is to use the incompressible smoothed particle hydrodynamics method to examine the influences of a magnetic field on the double-diffusive convection caused by a rotating circular cylinder with paddles within a square cavity filled by a nanofluid.

Design/methodology/approach

The cavity is saturated by two wavy layers of non-Darcy porous media with a variable amplitude parameter. The embedded circular cylinder with paddles carrying T_h and C_h is rotating around the cavity center by a uniform circular velocity.

Findings

The lineaments of nanofluid velocity and convective flow, as well as the mean of Nusselt and Sherwood numbers, are represented below the variations on the frequency parameter, amplitude parameter of the wavy porous layers, Darcy parameter, nanoparticles parameter, Hartmann number and Ryleigh number. The performed simulations showed the role of paddles mounted on circular cylinders for enhancing the transmission of heat and mass within a cavity. The wavy porous layers at the lower Darcy parameter are playing as a blockage for the nanofluid flow within the porous area. Increasing the concentration of the nanoparticles to 6% reduces the maximum flow speed by 8.97% and maximum streamlines |ψ|max by 10.76%. Increasing Hartmann number to 100 reduces the maximum flow speed by 65.83% and |ψ|max by 75.54%.

Originality/value

The novelty of this work is to examine the effects of an inclined magnetic field and rotating novel shape of a circular cylinder with paddles on the transmission of heat/mass in the interior of a nanofluid-filled cavity saturated by undulating porous medium layers.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 32 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

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