Apparent Heat Capacity Research Articles

Numerical simulation and experimental validation of the oleogel formation from grape seed oil and beeswax

This study focuses on numerical modeling of the oleogelation process using grape seed oil and beeswax and its validation using experimental approach. The main goal is to investigate how the cooling rate affects this process. The necessary physical and thermal properties of the oleogel for modeling were determined through experiments. Additionally, differential scanning calorimetry was used to characterize phase transitions. The apparent heat capacity method was applied in the numerical modeling to simulate the phase change process, and the energy equation was solved using the finite element method. The numerical model demonstrated a maximum relative error of 5.4%, indicating a strong agreement between the numerical results and experimental data. After validating the numerical model, five different cooling rates were investigated. The findings showed that oleogelation begins near the bottom boundary of the setup and then propagates toward the center. Furthermore, the fraction of the total time required for the phase change to complete varied between 0.35 and 0.04 as the cooling rate decreased. This indicates that slower cooling rates provide more time for heat transfer, allowing for more thorough gelation and completing the phase transition in a smaller fraction of the total time. The proposed model can save time and costs while delivering accurate data on creating a beneficial oleogel.

Comparison of Different Numerical Models for Solidification of Paraffin-Based PCMs and Evaluation of the Effect of Variable Mushy Zone Constant

The impact of the mushy zone parameter (Amushy) and the chosen numerical model during the solidification of a commercial paraffin-type phase change material (PCM) in a vertical cylinder under T-history conditions was examined through numerical simulations. The cooling process was modeled using three methods implemented in the CFD software ANSYS Fluent 2020 R2: the enthalpy–porosity method, the apparent heat capacity (AHC) method, and a new model proposed by the authors which incorporates heat capacity directly into ANSYS Fluent. To accurately define the boundary conditions, radiative heat transfer between surfaces was taken into account. Furthermore, the influence of the mushy zone parameter on the simulation accuracy and solidification rate was investigated, with the parameter being treated as a function of the liquid fraction. The results indicate that the proposed model aligns closely with experimental data regarding cooling temperature, offering better predictions compared to the other models. It was observed that temperature varies with time but not with position, suggesting that this model more effectively satisfies the lumped system condition—an essential characteristic of the T-history experiment—compared to the other methods. Additionally, the analysis showed that a higher mushy zone parameter enhances the accuracy of simulations and predicts a shorter solidification time; approximately 11% for the E-p and 7% for the AHC model. Using a variable mushy zone parameter based on the liquid fraction also produced similar results, resulting in an increased solidification rate.

Characteristics of OP35E-based phase-change emulsion and its potential applications in thermal management

ABSTRACT A phase-change emulsion was prepared using OP35E (melting peak at 36.58 ℃) as the phase-change material and Span60-PEG600 blend as a compound emulsifier. This phase-change emulsion exhibited low viscosity, low subcooling, low electrical conductivity, high heat capacity, non-corrosiveness, and high stability.The viscosity, subcooling, electrical conductivity, and pH value of the emulsion were 2.67 mPa∙s, 1.03°C, 99.3 us/cm, and 7.80, respectively. No phase separation occurred after the emulsion was left to stand for 1 month. The volume average particle size increased by only 0.14 μm, Neither agglomeration nor stratification of the emulsion occurred after 400 high/low-temperature cycles. The electrical conductivity and pH value of the emulsion were determined to be 150.5 µs/cm and 7.23, respectively, indicating small variations. In the 60-day static corrosion test, the emulsion exhibited low corrosiveness to 304 stainless steel, T2 copper, and H62 brass, with corrosion amounts of 0.240 g/m2, 0.719 g/m2, and 1.438 g/m2, respectively.The melting peak of the emulsion occurred at the temperature of 35.45°C, and the enthalpy of melting was 35.28 J/g. The maximum apparent specific heat capacity of emulsion is 9.94 J/(g∙K), which is more than twice that of conventional coolants such as water and ethylene glycol. In conclusion, the OP35E-based phase-change emulsion has a high heat storage capacity and exhibits great potential application in lithium battery thermal management systems.

Study on the Influence of Laser Power on the Heat–Flow Multi-Field Coupling of Laser Cladding Incoloy 926 on Stainless Steel Surface

In order to explore the influence of laser power on the evolution of molten pool and convective heat transfer of laser cladding Incoloy 926 on stainless steel surface, a three-dimensional thermal fluid multi-field coupled laser cladding numerical model was established in this paper. The variation of latent heat during solid-liquid phase transformation was treated by apparent heat capacity method. The change in the gas–liquid interface was tracked using the mesh growth method in real time. The instantaneous evolution of temperature field and velocity flow field of laser cladding Incoloy 926 on a stainless steel surface under different laser power was discussed. The solidification characteristic parameters of the cladding layer were calculated based on the temperature-time variation curves at different nodes. The mechanism of the impact of laser power on the microstructure of the cladding layer was revealed. The experiment of laser cladding Incoloy 926 on 316L surface was carried out under different laser power. Combined with the numerical simulation results, the effects of laser power on the geometrical morphology, microstructure and element distribution of the cladding layer were compared and analyzed. The results show that with the increase in laser power, the peak temperature and flow velocity of the molten pool surface both increase significantly. The thermal influence of the molten pool center on the edge is enhanced. The temperature gradient, solidification rate, and cooling rate increased gradually. The microstructure parameters (G/R) are relatively small when the laser power is 1000 W. In the experimental range, the dilution rate and wetting angle of the cladding layer both increase with the increase in laser power. When the laser power is 1000 W, the alloying elements of the cladding layer are more evenly distributed and the microstructure is finer. The experimental results are in good agreement with the simulation results.

Investigations on the heat transfer performance of phase change material (PCM)-based heat sink with triply periodic minimal surfaces (TPMS)

During the operational process of electronic components, excessive heat generation results in significant temperature elevation. This elevated temperature poses a significant risk to their service life. Regarding the issue of efficient thermal management of electronic devices in enclosed spaces experiencing high heat flow, a thermal management scheme for electronic equipment using TPMS and a PCM-based heat sink is proposed. The apparent heat capacity method is employed to simulate the melting process of the PCM-based heat sink. The effects of structural parameters w1, w3, and C of TPMS structures on the heat transfer characteristics (including base temperature, liquid fraction, average cell temperature, and average heat transfer coefficient) of the PCM-based heat sink during the melting process are discussed. A temperature testing platform is established. Experimental research is performed to investigate the effect of TPMS structures with two different printing prototypes (Sample 1, and Sample 2) on the heat sink during the intermittent cycle. The results indicate that increasing the parameters C and w1 significantly improves the average heat transfer coefficient (HTC) of the heat sink. When C increases from 0.3 to 0.7, the average HTC increases from 307 W/(m2·K) to 358 W/(m2·K). When w1 increases from 1 to 3, the average HTC increases from 284.5 W/(m2·K) to 321.3 W/(m2·K). Sample 1, possessing superior thermal conductivity, exhibits better heat transfer performance. When the temperature achieves a stable periodic variation, the base temperature of Sample 1 stabilizes within the range of 310 K-340 K. And Sample 2 stabilizes within the range of 315 K-350 K.

Thermal modeling of porous medium integrated in PCM and its application in passive thermal management of electric vehicle battery pack

The integration of a composite of porous medium with phase change material (PCM) offers significant advantages in thermal management systems, enhancing heat transfer efficiency and addressing various thermal regulation challenges. This approach utilizes the PCM's latent heat absorption and the enhanced thermal conductivity provided by the porous medium, resulting in optimized system performance. Its applicability spans across electronics cooling and building insulation systems. However, predicting the thermal behavior of this composite material is challenging, necessitating computational tools to anticipate its response under different conditions and evaluate its influence on cooling strategies. The objective of this study is to create a computational tool specifically tailored to evaluate constitutive parameters of this composite material, thereby providing a comprehensive description of its thermal behavior. To achieve this goal, the multiscale homogenization principle is employed to assess the composite's effective thermophysical material properties using the representative volume element approach. The repeating unit cell of the aluminum lattice is incorporated into the PCM to define a representative volume element. The finite element method (FEM) is utilized to solve the three-dimensional homogenization problem, yielding an orthotropic effective thermal conductivity due to the inherent symmetry of the repeating material cell. Moreover, the study leverages the apparent heat capacity method to effectively manage the phase transitions within the PCM domain, utilizing smooth and temperature-dependent functions to accurately describe the thermophysical properties of the PCM. Integrating the composite into battery pack thermal management, this study thoroughly examines thermal dynamics by comparing outcomes with and without PCM integration. The transient thermal problem is accurately tackled using the FEM, employing the evaluated effective constitutive parameters of the homogenized composite to minimize computational effort. The results indicate a notable decline in the highest temperatures of the battery pack, leading to a reduction of about 14 °C at the specific moment when the phase change material fully transitions into its liquid form. The obtained results emphasize the effectiveness and practical feasibility of the proposed thermal management strategy. The modeling approach presented provides a robust tool with significant efficiency in reducing computational time for analyzing the thermal behavior of large models, as the utilization of the homogenization technique notably decreases the computational time.

Experimental and numerical investigations on the intermittent heat transfer performance of phase change material (PCM)-based heat sink with triply periodic minimal surfaces (TPMS)

The excessive heat generated during the operation of electronic components leads to significant temperature increases, posing a significant risk to their service life. For the problem of efficient thermal management of electronic devices in confined spaces experiencing high heat flow, a scheme using triply periodic minimal surfaces and a phase change material-based active–passive cooling heat sink is proposed to control the temperature of electronic equipment. The apparent heat capacity method is employed to simulate the intermittent process of the phase change material-based heat sink. The optimization based on Box-Behnken Design and Nondominated Sorting Genetic Algorithm II is analyzed to obtain an improved triply periodic minimal surface structure. The effect of thermal performance (including base temperature, liquid fraction, and Grashof number) of an intermittent heat sink based on an improved structure is discussed. Visualization and temperature testing platforms are established. Through visualization experiments, the internal temperature and liquid fraction distribution of the heat sink are obtained, and the simulation results are in good agreement with the test results. The results show that the base temperature, liquid fraction, and Grashof number achieve a steady periodic variation during the intermittent process. Specifically, the base temperature remains stable in the range of 314 K to 340 K, the liquid fraction stabilizes between 0.8 and 1.0, and the Grashof number stabilizes between 100 and 1000. At the heating power of 30 W or below, the base temperature of the heat sink exhibits a steady periodic variation. At the heating power of 40 W, the maximum base temperature of the heat sink exceeds 370 K.

Transient thermal 2D FEM analysis of SiC MOSFET in short-circuit operation including high-temperature material laws and phase transition of aluminum source electrode

Understanding the electrothermal behavior of SiC MOSFET power devices under extreme operation conditions, such as short circuits, is crucial for their application certification. However, simulating short circuits in electronic components is challenging due to the necessity of a comprehensive thermal and electrical Multiphysics model that incorporates material laws and respects elevated temperatures with broad ranges. It is also needed to model the melting of the topside Al electrode. The paper presents for the first time a 2D electrothermal FEM that simulates the thermodynamic behavior of SiC MOSFET at high temperatures transistors under short-circuit conditions, including wide-range temperature-dependent material property laws. This work models the Al phase transition by considering the apparent heat capacity method and including the latent heat absorbed during the Al solid-liquid phase change (PC). The geometric accuracy of this study provides significant added values compared to existing 1D models. It was deduced that including the temperature-dependent material laws highly impacted the results. The rise in SiC junction temperature led to a delay in the onset of Al melting. It also impacted the progression manner of the Al melting process after the formation of new melting fronts.

Level-set topology optimization of heat sinks with phase-change material

Phase-change materials (PCMs) excel in storing significant thermal energy through the latent heat of fusion during phase changes. However, they often suffer from low thermal conductivity, requiring the incorporation of materials with higher thermal conductivity to overcome this limitation. In this study, we employ the level-set method to topologically optimize the distribution of both PCM and high thermal conductivity materials within heat sinks.The heat transfer process is modeled as an unsteady diffusion problem, with PCM integrated using the apparent heat capacity method. The finite element method, implemented using FEniCS, is utilized to compute the temperature distribution at each time step. The optimization problem is solved using ParaLeSTO, a modular topology optimization software written in C++, seamlessly interfacing with FEniCS through its Python interface.To compute boundary point sensitivities for level-set topology optimization, the discrete adjoint method is employed, combining a perturbation scheme with automatic differentiation. The proposed methodology is first applied to a two-dimensional example of temperature oscillation minimization with a heat flux boundary condition, drawn from existing literature. Subsequently, a two-dimensional example with multiple volumetric heat sources is studied, followed by an extension to a three-dimensional design domain.Comparisons with optimized designs without PCM, serving as a reference, highlight the superior thermal performance of heat sink designs with PCM. The results showcase a maximum temperature reduction of up to 42%, a mean temperature reduction of up to 42%, and a temperature variance reduction of up to 94%. This research contributes to heat sink design by offering discrete solutions that significantly improve thermal performance as compared to designs without PCM. Its impact extends to addressing crucial challenges in thermal management across various applications, including automotive cooling systems, aerospace components, and consumer electronics.

CFD simulation of solid/liquid phase change in commercial PCMs using the slPCMlib library

Modelling the solidification and melting behavior of phase change materials (PCMs) can present several challenges, including non-isothermal phase change, multi-step transitions, complex enthalpy-temperature relations and convective heat transfer. To tackle these challenges, this study proposes a novel numerical method based on real experimental data for modelling complex phase change behavior of commercial PCMs in Ansys Fluent CFD software. The phase transition of PCMs is simulated with the apparent heat capacity (AHC) method, which is implemented as a User-Defined Function (UDF). Heat convection is simulated with the Boussinesq approximation. The method is validated by comparing to the Ansys Fluent built-in Solidification and Melting (S&M) model for the case of piecewise constant heat capacity. The results show that AHC method provides excellent agreement with S&M model for a piecewise constant heat capacity model. In addition, the AHC method solves convergence problems even for narrow phase change temperature ranges when a smooth heat capacity function is assumed. Finally, the AHC model is also tested on a set of commercial PCMs exhibiting complex phase change behavior. Temperature dependent specific heat capacities are determined from heat capacity data provided by PCM manufacturing companies and are imported as cubic Hermite spline functions from the solid-liquid phase change material library slPCMlib available at https://slpcmlib.ait.ac.at/. From the presented case study and tested PCMs it can be concluded that the AHC method is numerically robust when used with sufficiently smooth heat capacity functions, and it can be recommended for the analysis of heat transfer with PCMs showing a complex phase change behavior.

Kinetic glass transition in granular gases and nonlinear molecular fluids.

In this paper, we investigate, both analytically and numerically, the emergence of a kinetic glass transition in two different model systems: a uniformly heated granular gas and a molecular fluid with nonlinear drag. Despite the profound differences between these two physical systems, their behavior in thermal cycles share strong similarities, which stem from the relaxation time diverging algebraically at low temperatures for both systems. When the driving intensity--for the granular gas-or the bath temperature-for the molecular fluid-is decreased to sufficiently low values, the kinetic temperature of both systems becomes "frozen" at a value that depends on the cooling rate through a power law with the same exponent. Interestingly, this frozen glassy state is universal in the following sense: for a suitable rescaling of the relevant variables, its velocity distribution function becomes independent of the cooling rate. Upon reheating, i.e., when either the driving intensity or the bath temperature is increased from this frozen state, hysteresis cycles arise and the apparent heat capacity displays a maximum. The numerical results obtained from the simulations are well described by a perturbative approach.

A viscoelastic-viscoplastic thermo-mechanical model for polymers under hypervelocity impact

In hypervelocity impact (HVI) events, the thermo-mechanical behaviors of polymer materials are significantly influenced by viscous effects, thereby affecting energy absorption and shielding performance. A viscoelastic-viscoplastic thermo-mechanical model was newly developed to simulate the mechanical behavior and heat generation of polymer materials under HVI. The viscoelastic-viscoplastic constitutive equation and the Mie-Grüneisen equation of state (EOS) were applied to describe the deviatoric deformation and strongly nonlinear volumetric compression behavior. Moreover, the heat generation was calculated considering contributions from plastic work, irreversible entropy increase, and viscous dissipation which was not considered in the previous HVI numerical model. The temperature increase was calculated through adopting the apparent heat capacity method. The model was coded and seamlessly integrated into the LS-DYNA program through a user-defined material subroutine. Additionally, the FEM-SPH adaptive method was adopted to accurately simulate the fragmentation which always accompanies in the HVI event, wherein the finite element method (FEM) handles contact and deformation behavior, while the smoothed particle hydrodynamics (SPH) method addresses the formation and motion of debris clouds. Ultra-high molecular weight polyethylene (UHMWPE) was selected as the sample material, and its model parameters were calibrated based on the data from quasi-static and dynamic experiments. Good effectiveness and accuracy have been validated through comparing the simulation results and experimental results from the literatures. A noteworthy feature is that the model has the capability to capture the temperature distribution and various energy components induced by the impact, including viscous dissipation, plastic work, and residual energy. Finally, a comparison was made to explore the influence of viscosity on the impact response of UHMWPE plates. The analysis results indicate that material viscosity significantly improves energy absorption capabilities and overall shielding performance.

Mathematical modeling of apparent specific heat capacity of channel catfish with different microwave heating time

AbstractChannel catfish fillets with different microwave heating times were evaluated by differential scanning calorimetry and low‐field nuclear magnetic resonance to build suitable modeling of apparent specific heat capacity (Cp) ranging from −60 to 90°C (except the obvious phase change region from −20 to 20°C). The content of bound water (Wb), immobilized water (Wi), and free water (Wf) were weighted and calculated. According to non‐linear fitting of experimental data, the obtained empirical equation of Cp, temperature (T), Wb, Wi, and Wf of samples was:. The equation was in good correlation (R2 > 0.95) with the experiment data and could provide a basis for improvement of processing parameters.

Quantification of geometrical errors and thermal effects during wire EDM of thin wall structures—A numerical study

Machining thin-walled structures with a high aspect ratio using Wire EDM can lead to geometrical errors, primarily of two types; overcut error due to kerf formation and thermal deformation of the entire wall section. To understand the driving mechanisms behind these errors three distinct numerical models were developed. Initially, a model based on a moving heat source was created, employing the apparent heat capacity approach to predict kerf width and the associated overcut error. These insights were then utilized to formulate a transient temperature distribution model with a redesigned geometry, considering time-dependent evolution of the kerf and corresponding changes in the material properties of the sub-domains. Finally, a thermo-mechanical coupled model was developed to predict geometrical errors caused by the deflection of the wall, considering the varying stiffness of the part. A series of experiments were conducted to gain insight into the effect of the designed wall thickness on wall deflection. For the selected design profile and machine parameters, the model predicts a 62.4% reduction in thickness and a corresponding over-cut error of 188μm. Similarly, the model predicts wall deformation in the range of 6μm to 312μm for various wall thickness levels and these findings were validated with experimental observations.

DEVELOPMENT OF TECHNIQUES AND EXPERIMENTAL INSTALLATIONS FOR DETERMINING THE HEAT CAPACITY OF IRON ORE MATERIALS

One of the most important thermophysical pellets characteristics is considered — their heat capacity, which affects the technological production process of iron ore pellets at the stage of their heat treatment in a layer on a conveyor belt. Since the physical heat capacity of materials is determined by the enthalpy value, the mixing method is used to measure the latter, which is implemented on an installation with an adiabatic calorimeter. The research object is Kachkanar pellets of different basicity. The average values of the pellets enthalpy and their physical heat capacity, taking into account changes in the phase and chemical composition of the material, are presented in the interpolation equations form. The temperature dependences of the apparent heat capacity of pellets of various basicity at different heating rates were determined using a newly created experimental setup that allows determining the complex of thermophysical characteristics. Estimates of the enthalpy change and the dependence of the apparent heat capacity on temperature for fluxed and unfluxed concentrates of Sokolovsko-Sarbaysky mining and processing plant were carried out on an experimental installation using the method of quantitative thermal analysis. The presented methods for determining the enthalpy and heat capacity of iron ore pellets and concentrates, as well as the designs created for the implementation of these methods can be used to determine the heat capacities of various materials of metallurgical production and to optimize the operating parameters of their heat treatment.

Transient thermal behavior of clay walls integrated with phase change materials

There are several advantages of using phase change materials (PCMs) in building walls for creating energy-efficient structures. Incorporating PCMs into clay walls with the hope of improving their thermal characteristics under transient boundary conditions is the major goal of this study. Numerical simulations are performed utilizing the finite element method and the apparent heat capacity formulation to predict the melting and solidification behavior of PCM-integrated walls. By introducing a 2 cm thick layer of PCM with a typical melting temperature of 32 °C into the middle of a clay wall, the results demonstrate a significant reduction of approximately 57 % in heat flow on the inner surface. Furthermore, compared to a standard clay wall without PCM, this integration extended the time lag by about 5.5 h.

Multi-objective optimization of a metal hydride reactor coupled with phase change materials for fast hydrogen sorption time

Recently, the utilization of phase change materials (PCM) for the heat storage/recovery of the metal hydride's reaction heat has received increasing attention. However, the poor heat management process makes hydrogen sorption very slow during heat recycling. In this work, the H2 charging/discharging performance of a metal hydride tank (MHT) filled with LaNi5 and equipped with a paraffin-based (RT35) PCM finned jacket as a passive heat management medium is numerically investigated. Using a two-dimensional mathematical model validated with our in-house experiments, the effects of design parameters such as PCM thermophysical properties and the fin size on hydrogen charging/discharging times of the MHT are investigated systematically. The results showed that the PCM's melting point and apparent heat capacity have a conflicting impact on the hydrogen sorption times, i.e., the low melting point and high specific heat capacity reduce the H2 charging time. In contrast, the hydrogen discharging time follows the opposite trend. As a result, a multi-objective optimization was conducted to simultaneously minimize the H2 charging/discharging times using the thermal properties and size of the PCM. The optimum solutions selected from the Pareto front show that the PCM melting point should be around 42–43 °C for fixed hydrogen ab/desorption pressures of 10/1.5 bar. Moreover, the comparison between the MHT-PCM using the optimized PCM and reference PCM showed that the former reduced the hydrogen charging/discharging times by 48.6 % and 4 %, respectively. At the same time, the hydrogen storage efficiency of the optimal design is 100 % as compared to 96 % for the reference design. Besides, among the practical PCMs, inorganic PCMs (salt hydrates and eutectics) display favorable hydrogen charging time below 3000 s at the expense of hydrogen discharging time (above 7000 s) in our case study.

The cytisine-enriched poly(3-hydroxybutyrate) fibers for sustained-release dosage form

The polymeric cytisine-enriched fibers based on poly(3-hydroxybutyrate) were obtained using electrospinning method. The biocompatibility study, advanced thermal analysis and release of cytisine from the poly(3-hydroxybutyrate) fibers were carried out. The nanofibers' morphology was evaluated by scanning electron microscopy. The formation and description of phases during the thermal processes of fibers by the advanced thermal analysis were examined. The new quantitative thermal analysis of polymeric fibers with cytisine phases based on vibrational, solid and liquid heat capacities was presented. The apparent heat capacity of fibers was measured using the standard differential scanning calorimetry. The quantitative analysis allowed for the study of the glass transition and melting/crystallization process. The mobile amorphous fraction, degree of crystallinity and rigid amorphous fraction were determined depending on the thermal history of semicrystalline polymeric fibers. Furthermore, the cytisine dissolution behaviour was studied. It was observed that the kinetic of the release from polymeric nanofiber is delayed than for the marketed product. The immunosafety of the tested polymeric nanofibers with cytisine was confirmed by the Food and Drug Agency Guidance as well as the European Medicines Agency. The polymeric matrix with cytisine seems to be a promising candidate for the prolonged release formulation.

Thermo-fluid performance enhancement in a long double-tube latent heat thermal energy storage system

Thermodynamic analysis and flow rate optimization for the long double-tube latent heat thermal energy storage systems (LHTESS) are performed. Computer modeling is carried out using created software and is based on a developed 3D non-steady non-linear coupled thermo-fluid mathematical model that combines the apparent heat capacity method and finite volume method for the sodium nitrate (NaNO3) phase change materials (PCM) and for the Syltherm800 heat transfer fluid (HTF). The mathematical model and numerical algorithm are verified through comparison with experimental data. It is found that the laminar flow of HTF ensures the uniform temperature in PCM and in HTF and this temperature is equal to the PCM melting temperature. It is proved that the PCM and HTF average temperatures along the LHTESS can be equalized using spatial and temporal velocity variations of the HTF. Mutual impact of the heat transfer and fluid mechanics parameters in the long double-tube LHTESS was studied by correlation between Nusselt numbers and Reynolds numbers. The optimal HTF flow rate parameters were analyzed based on the non-equilibrium thermodynamics method. It is discovered that the laminar regime 0 < Re < 2000 and the turbulent regime 12000<Re<15000 are the most optimal for long double-tube LHTESS of the described geometry.

Consistent description of phase-change processes in substances with density contrast: A finite volume based approach

Phase-change is an important phenomenon and usually it causes a concomitant change in the density of the underlying materials. As applications of phase-change grow, it is important to develop numerical tools that can model this phase-change behaviour accurately; many efforts have improved the ability of numerical algorithms to do so; however, with materials in which phase-change causes significant change in density, these approaches are inadequate in predicting the phase-change interface or the temperature profiles during this process. To address these limitations, we present a “moving mesh” method that explicitly accounts for volumetric expansion during the melting (or, evaporation) process by introducing liquidus or vapour cells at appropriate locations adjacent to the interface. This moving mesh approach is used in conjunction with the apparent heat capacity method implemented through a finite volume scheme to represent the one-dimensional propagation of the melting (or, vapour) front during heating. This new algorithm has been validated for the Stefan's analytical solution, in addition to verifying the conservation of energy principle. We subsequently use our approach to investigate phase-change phenomena for a host of materials with a large gamut of density contrasts between the various phases, and compare the results to those obtained using a fixed-grid approach. The moving mesh method forecasts an early commencement of melting (or, evaporation) at a given position, a comparatively rapid movement of the front, and a larger volume fraction of the molten (or, vapour) phase, for substances that expand upon phase change, while the opposite is observed for the melting of ice, considered as a special case in this study. We hope that the proposed scheme will be adopted in addressing phase-change problems involving significant density contrasts.