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Methods that use spatial gradients of enthalpy to evaluate effective specific heats and capture latent heat effects in phase change problems have been used successfully in finite element formulations based on linear interpolation. In view of the greater geometrical flexibility and efficiency of biquadratic isoparametric elements, it is of interest to assess the use of the methods with these elements. In comparisons with an accurate semi‐analytic solution for a test problem, it is shown that the enthalpy gradient methods with quadratic interpolation are prone to error. A new procedure is proposed that uses bilinear sub‐elements for enthalpy, formed by subdivision of the biquadratic temperature elements. This is shown to be accurate and robust, for phase change intervals as small as 0.02°C.

During the thermal processing of thin films in which low intensity line heat sources are used, extended processing times are often required to reach steady state (˜15 sec). In addition, the melting of the film may occur some time after processing has begun, and therefore there is no initial melting condition within the film. In such cases, computer simulations may become very time consuming, and the development of an efficient computational method which incorporates the initial formation of the melt during processing is necessary. A general technique was developed to accurately model two‐dimensional heat conduction in a multilayer film structure with one‐dimensional phase change in one of the thin films. These conditions frequently exist in thin film thermal processing when the thermal gradient through the thickness of the melting film can be considered negligible. The method involves an implicit formulation of the modified enthalpy method. The solid/liquid interface energy‐balance equation is taken into account which allows the exact location of the interface to be tracked within a control volume. A comparison is made between the explicit and implicit modified methods to test efficiency and accuracy. The implicit method is then applied to the zone‐melting recrystallization of a silicon thin film in a multilayer structure.

The Fay and Riddell (F–R) formula is an empirical equation for estimating the stagnation-point heat flux on noncatalytic and fully catalytic surfaces, based on an assumption of equilibrium. Because of its simplicity, the F–R has been used extensively for reentry flight design as well as ground test facility applications. This study aims to investigate the uncertainties of the F-R formula by considering velocity gradient, chemical species at the boundary layer edge, and the thermochemical nonequilibrium (NEQ) behind the shock layer under various hypersonic NEQ flow environments.

The stagnation-point heat flux calculated with the F–R formula was evaluated by comparison with thermochemical NEQ calculations and existing flight experimental values.

The comparisons showed that the F–R underestimated the noncatalytic heat flux, because of the chemical composition at the surface. However, for fully catalytic heat flux, the F–R results were similar to values of surface heat flux from thermochemical NEQ calculations, because the F–R formula overestimates the diffusive heat flux. When compared with the surface heat flux results obtained from flight experimental data, the F–R overestimated the fully catalytic heat flux. The error was 50% at most.

The results provided guidelines for the F–R calculations under hypersonic flight conditions and for determining the approximate error range for noncatalytic and fully catalytic surfaces.

In the present work, a numerical method, based on the well established enthalpy technique, is developed to simulate the growth of binary alloy equiaxed dendrites in presence of melt convection. The paper aims to discuss these issues.

The principle of volume-averaging is used to formulate the governing equations (mass, momentum, energy and species conservation) which are solved using a coupled explicit-implicit method. The velocity and pressure fields are obtained using a fully implicit finite volume approach whereas the energy and species conservation equations are solved explicitly to obtain the enthalpy and solute concentration fields. As a model problem, simulation of the growth of a single crystal in a two-dimensional cavity filled with an undercooled melt is performed.

Comparison of the simulation results with available solutions obtained using level set method and the phase field method shows good agreement. The effects of melt flow on dendrite growth rate and solute distribution along the solid-liquid interface are studied. A faster growth rate of the upstream dendrite arm in case of binary alloys is observed, which can be attributed to the enhanced heat transfer due to convection as well as lower solute pile-up at the solid-liquid interface. Subsequently, the influence of thermal and solutal Peclet number and undercooling on the dendrite tip velocity is investigated.

As the present enthalpy based microscopic solidification model with melt convection is based on a framework similar to popularly used enthalpy models at the macroscopic scale, it lays the foundation to develop effective multiscale solidification.

The homographic approximation, in which the Heaviside step function is replaced by a continuous smooth curve, is applied to the enthalpy method for heat transfer problems with isothermal phase change. Both the finite difference and finite element implementations, based on the basic enthalpy, the apparent heat capacity and the source term formulations, are considered. A 1‐D Stefan problem of melting a solid is used as a test problem. The accuracy of the numerical solutions is measured globally using L2 error norms and comparison is made between the solutions using homographic approximation and those using linear approximation. The advantages of using homographic approximation are examined.

This paper aims to propose a semi-analytical benchmarking framework for enthalpy-based methods used in problems involving phase change with latent heat. The benchmark is based on a class of semi-analytical solutions of spatially symmetric Stefan problems in an arbitrary spatial dimension. Via a public repository this study provides a finite element numerical code based on the FEniCS computational platform, which can be used to test and compare any method of choice with the (semi-)analytical solutions. As a particular demonstration, this paper uses the benchmark to test several standard temperature-based implementations of the enthalpy method and assesses their accuracy and stability with respect to the discretization parameters.

The class of spatially symmetric semi-analytical self-similar solutions to the Stefan problem is found for an arbitrary spatial dimension, connecting some of the known results in a unified manner, while providing the solutions’ existence and uniqueness. For two chosen standard semi-implicit temperature-based enthalpy methods, the numerical error assessment of the implementations is carried out in the finite element formulation of the problem. This paper compares the numerical approximations to the semi-analytical solutions and analyzes the influence of discretization parameters, as well as their interdependence. This study also compares accuracy of these methods with other traditional approach based on time-explicit treatment of the effective heat capacity with and without iterative correction.

This study shows that the quantitative comparison between the semi-analytical and numerical solutions of the symmetric Stefan problems can serve as a robust tool for identifying the optimal values of discretization parameters, both in terms of accuracy and stability. Moreover, this study concludes that, from the performance point of view, both of the semi-implicit implementations studied are equivalent, for optimal choice of discretization parameters, they outperform the effective heat capacity method with iterative correction in terms of accuracy, but, by contrast, they lose stability for subcritical thickness of the mushy region.

The proposed benchmark provides a versatile, accessible test bed for computational methods approximating multidimensional phase change problems. The supplemented numerical code can be directly used to test any method of choice against the semi-analytical solutions.

While the solutions of the symmetric Stefan problems for individual spatial dimensions can be found scattered across the literature, the unifying perspective on their derivation presented here has, to the best of the authors’ knowledge, been missing. The unified formulation in a general dimension can be used for the systematic construction of well-posed, reliable and genuinely multidimensional benchmark experiments.

The purpose of this paper is to develop a coupled lattice Boltzmann model for the simulation of the freezing process in unsaturated porous media.

In the developed model, the porous structure with complexity and disorder was generated by using a stochastic growth method, and then the Shan-Chen multiphase model and enthalpy-based phase change model were coupled by introducing a freezing interface force to describe the variation of phase interface. The pore size of porous media in freezing process was considered as an influential factor to phase transition temperature, and the variation of the interfacial force formed with phase change on the interface was described.

The larger porosity (0.2 and 0.8) will enlarge the unfrozen area from 42 mm to 70 mm, and the rest space of porous medium was occupied by the solid particles. The larger specific surface area (0.168 and 0.315) has a more fluctuated volume fraction distribution.

The concept of interfacial force was first introduced in the solid–liquid phase transition to describe the freezing process of frozen soil, enabling the formulation of a distribution equation based on enthalpy to depict the changes in the water film. The increased interfacial force serves to diminish ice formation and effectively absorb air during the freezing process. A greater surface area enhances the ability to counteract liquid migration.

This paper sets out to present developments of a numerical model of squeeze casting process.

The entire process is modelled using the finite element method. The mould filling, associated thermal and thermomechanical equations are discretized using the Galerkin method. The front in the filling analysis is followed using volume of fluid method and the advection equation is discretized using the Taylor Galerkin method. The coupling between mould filling and the thermal problem is achieved by solving the thermal equation explicitly at the end of each time step of the Navier Stokes and advection equations, which allows one to consider the actual position of the front of the filling material. The thermomechanical problem is defined as elasto‐visco‐plastic described in a Lagrangian frame and is solved in the staggered mode. A parallel version of the thermomechanical program is presented. A microstructural solidification model is applied.

During mould filling a quasi‐static Arbitrary Lagrangian Eulerian (ALE) is applied and the resulting temperatures distribution is used as the initial condition for the cooling phase. During mould filling the applied pressure can be used as a control for steering the distribution of the solidified fractions.

The presented model can be used in engineering practice. The industrial examples are shown.

The quasi‐static ALE approach was found to be applicable to model the industrial SQC processes. It was found that the staggered scheme of the solution of the thermomechanical problem could parallelize using a multifrontal parallel solver.

This paper aims to establish a lattice Boltzmann (LB) method for solid-liquid phase transition (SLPT) from the pore scale to the representative elementary volume (REV) scale. By applying this method, detailed information about heat transfer and phase change processes within the pores can be obtained, while also enabling the calculation of larger-scale SLPT problems, such as shell-and-tube phase change heat storage systems.

Three-dimensional (3D) pore-scale enthalpy-based LB model is developed. The computational input parameters at the REV scale are derived from calculations at the pore scale, ensuring consistency between the two scales. The approaches to reconstruct the 3D porous structure and determine the REV of metal foam were discussed. The implementation of conjugate heat transfer between the solid matrix and the solid−liquid phase change material (SLPCM) for the proposed model is developed. A simple REV-scale LB model under the local thermal nonequilibrium condition is presented. The method of bridging the gap between the pore-scale and REV-scale enthalpy-based LB models by the REV is given.

This coupled method facilitates detailed simulations of flow, heat transfer and phase change within pores. The approach holds promise for multiscale calculations in latent heat storage devices with porous structures. The SLPT of the heat sinks for electronic device thermal control was simulated as a case, demonstrating the efficiency of the present models in designing and optimizing SLPT devices.

A coupled pore-scale and REV-scale LB method as a numerical tool for investigating phase change in porous materials was developed. This innovative approach allows for the capture of details within pores while addressing computations over a large domain. The LB method for simulating SLPT from the pore scale to the REV scale was given. The proposed method addresses the conjugate heat transfer between the SLPCM and the solid matrix in the enthalpy-based LB model.

A two‐dimensional, macroscopic, stationary, finite element model is presented for both laser remelting and laser cladding of material surfaces. It considers, in addition to the heat transfer, the important fluid motion in the melt pool and the deformation of the liquid—gas interface. The velocity field in the melt is driven by thermocapillary forces for laser remelting, but also by forces due to powder injection for laser cladding. For a given velocity field within the liquid region, the stationary enthalpy (or Stefan) equation is solved. An efficient scheme allows the LU decomposition of the finite element matrix to be performed only once at the first iteration. Then, the velocity is updated using the Q₁—P₀ element with penalty methods for treating both the incompressibility condition and the slip boundary conditions. Numerical results for three different processing speeds for both laser remelting and laser cladding demonstrate the efficiency and robustness of the numerical approach. The influence of the thermocapillary and powder injection forces on the fluid motion and subsequently on the melt pool shape is seen to be important. This kind of calculations is thus necessary in order to predict with precision the temperature gradients across the solidification interface, which are essential data for microstructure calculations.