Solid-liquid Interface Location Research Articles

Experimental and numerical analysis of a phase change material-based shell-and-tube heat exchanger for cold thermal energy storage

This work experimentally and numerically investigates the thermal performance of a vertical shell-and-tube heat exchanger, filled with a biological phase change material (PCM), linked to a water-chiller system for cold thermal energy storage. The system provides the cooling service to a 150 m2 single-family house. An experimental apparatus has been designed to collect the PCM temperature data through the employment of multiple thermocouples located at different heights of the heat exchanger. Starting from the experiment, a comprehensive 3D numerical model of the system has been developed based on the enthalpy-porosity method using COMSOL Multiphysics®. The PCM temperature profiles and the evolution of the solid-liquid interface location at various time instants are used as performance indicators of the model reliability and accuracy. The numerical agreement with the experimental findings is proved using statistical indices, e.g., maximum values of mean absolute error (MAE) and root mean square error (RMSE) equal to 1.18 °C and 1.33 °C, respectively, with regards to central thermocouples. The results reveal that natural convection highly affects the PCM charging/discharging processes, as proved by the PCM liquid fraction, which moves from full to 51 %, between two levels spaced by 0.78 m. The developed 3D model, based on the enthalpy-porosity method, allows to consider boundary conditions variability with both angle and height, which are not usually covered by simplified 2D models. Hence, this model confirms that only 39 % of the PCM mass experiences the complete phase change process, proving that the current design does not allow the PCM to totally exploit the thermal storage potential, thereby making optimization pivotal and challenging.

Numerical study on melting of phase change material in an enclosure subject to Neumann boundary condition in the presence of Rayleigh-Bénard convection

This research study investigated the melting process of a phase change material (PCM), heated from the bottom, under Neumann boundary conditions, in the presence of Rayleigh-Bénard convection. The problem was numerically simulated for a range of domain sizes (1×1−8×8cm2) and heat fluxes (0.5−2W/cm2) using the enthalpy porosity technique, which is mostly applicable in cooling heat exchangers of electronic devices. Scaling analysis and the numerical results were employed to find the relationship between the Nusselt number and the solid-liquid interface location with other dimensionless parameters and develop correlations to predict the Nusselt number and the solid-liquid interface location for this type of melting problem. The results of this research could be used to better understand the heat transfer regimes formed during melting in an enclosure heated from the bottom and predict the Nusselt number and the solid-liquid interface location. It was found that the temperature and Nusselt number fluctuations are initiated in the coarsening subregime when the Rayleigh number was not larger than 106 and thus may not occur for small-sized domains. It can be concluded the coarsening and turbulent subregimes may not occur in small enclosures, while the melting process mostly occurs during turbulent subregiem in large enclosures. The numerical results revealed the fastest advance of heat transfer rate and consequently, solid-liquid interface occur during the formation of Bénard cells when the Rayleigh number was on the order of 104. The Nusselt number and solid-liquid interface location correlations developed in this study were later validated using two new cases of numerical data. The results revealed that these correlations could accurately predict the Nusselt number and solid-liquid interface location.

Melting process modeling of Carreau non-Newtonian phase change material in dual porous vertical concentric cylinders

In this paper a numerical simulation of the melting process of Carreau non-Newtonian phase change material inside two porous vertical concentric cylinders included constant temperatures of the inner and outer walls, represented by Th and Tc, respectively. Half of the void between the two pipes is filled with copper porous media and paraffin wax as a phase change material. The governing equations are converted into a dimensionless form and are solved using the finite element method. The enthalpy porosity theory is applied to simulate the phase change of phase change material while the porous media follow to the Darcy law. Outcomes are shown and compared in terms of the streamline, isotherm, melting fraction and mean Nusselt numbers. The solid liquid interface location and the temperature distribution are predicted to describe the melting process. The effects of the Carreau index, porosity and non-dimensional parameters such as Stefan number, Darcy number, and Rayleigh number are analyzed. Our results indicate a good agreement between this study and the previous investigations. The results show that an increase in Rayleigh number, Stefan number, and Darcy number, increases the melting volume fraction and reduces the melting time. Also, the time of melting non-Newtonian phase change material decreases when Carreau index and porosity decrease.

Analytical modeling and thermal performance analysis of a flat plate latent heat storage unit

The thermal performance of a flat plate latent heat storage unit (LHSU) consisting of parallel flat plate slabs of phase change material (PCM) was investigated with analytical techniques. The approximate analytical expressions of the heat transfer fluid (HTF) transient temperature distribution and the time wise solid-liquid PCM interface location were developed by solving the energy conservation equations and were validated by comparing the present results with fully converged numerical predictions and analytical solutions in published literature. An index of effective latent heat storage ratio, Er, which was defined as the ratio of the actual amount of available latent thermal energy before HTF outlet temperature reaches a specified value to the total latent heat storage capacity, was proposed to evaluate the thermal performance of a LHSU. The effects of geometric parameters and the thermal conductivity of PCM (kp) on Er were investigated. The results show that the analytical model is valid as the Stefan number is less than 0.15. Moreover, Er increases with the rise of the given dimensionless HTF outlet temperature and the enhancement of kp, and decreases linearly with the increase of HTF channel height and PCM slab thickness, with an abrupt change in the derivative of Er at an inflection point. A dimensionless criterion was proposed to help design thermally efficient flat plate LHSU. Additionally, we found that increasing PCM mass by lengthening the PCM slab could significantly improve Er, while thickening the PCM slab would lead to the opposite trend. This investigation provides guidelines for the optimal design of a flat plate LHSU.

Effects of nanoparticles on phase change heat transfer rate in the presence of Rayleigh–Benard convection

This paper experimentally analyzes the effects of nanoparticles on the melting time of Nano-enhanced Phase Change Materials (NePCMs) when Rayleigh-Benard convection is involved. To understand the effects of nanoparticles on the phase change rate reported in many studies, the changes in the parameters affecting the heat transfer are studied. These parameters are identified using scaling analysis on the heat transfer of NePCM in an enclosure heated from the bottom. Al2O3 nanoparticles are dispersed in a PCM (coconut oil) with different concentrations. Several experiments are conducted on these samples to understand whether the effects of nanoparticles on the phase change rate change at different experimental conditions. The results show that the melting rate may increase, decrease or remain unchanged with adding a certain concentration of nanoparticles if the heat transfer conditions change. Adding nanoparticles to a PCM is not recommended in an enclosure heated from the bottom at high Grashof numbers due to the greater Grashof number reduction, although adding nanoparticles to a PCM may reduce the melting time at small Grashof numbers due to the improvement in the thermal conductivity. With the experimental data and scaling analysis, correlations are developed to estimate the effects of nanoparticles on the melting rate and the solid-liquid interface location in the presence of Rayleigh–Benard convection.

Numerical and Experimental Investigation of Phase Change Heat Transfer in the Presence of Rayleigh–Benard Convection

Abstract This research investigates the melting rate of a phase change material (PCM) in the presence of Rayleigh–Benard convection. A scaling analysis is conducted for the first time for such a problem, which is useful to identify the parameters affecting the phase change rate and to develop correlations for the solid–liquid interface location and the Nusselt number. The solid–liquid interface and flow patterns in the liquid region are analyzed for PCM in a rectangular enclosure heated from bottom. Numerical and experimental results both reveal that the number of Benard cells is proportional to the ratio of the length of the rectangular enclosure over the solid–liquid interface location (i.e.,, the liquified region aspect ratio). Their effect on the local heat flux is also analyzed as the local heat flux profile changes with the solid–liquid interface moving upward. The variations of average Nusselt number are obtained in terms of the Stefan number, Fourier number, and Rayleigh number. Eventually, the experimental and numerical data are used to develop correlations for the solid–liquid interface location and average Nusselt number for this type of melting problems.

Revisiting tin melting for phase change model verification

Model verification is necessary before numerical models can be applied to produce meaningful results. For solid-liquid phase change modelling involving convection, pure gallium and tin melting have been widely used as reference for verification. It was later found that contrasting observations have been reported on the flow structure of both metals in the liquid region during the phase change process. Some researchers have reported monocellular while others reported multicellular structures in past works. In this work, tin melting problem was revisited by extending the results to flow structure visualization with Line Integral Convolution (LIC) plots to confirm the flow structure for tin melting thus pure metals in general. Enthalpy-porosity formulation coupled with Finite-Volume Method (FVM) was used to solve the set of governing equations which represented the problem at Prandtl Number = 0.02, Stefan Number = 0.01 and Rayleigh Number = 2.5 x 105. The location of solid-liquid interface and LIC plots at different times were presented. At initial state, the solid-liquid interface was closely similar for all grid sizes but as time progresses, finer grids provided improved solutions as expected. Reasonable fine grid size must be selected for solid-liquid phase change models to ensure complete physics of the problems are captured and eventually yield acceptable numerical results. The LIC plots confirmed that the flow structure is multicellular. Future phase change models referring to pure metal melting problem for verification should obtain similar flow structure to be considered acceptable.

The improved enthalpy-transforming based lattice Boltzmann model for solid-liquid phase change

The phase change process is of significant importance in the application of phase change material (PCM). In this paper, the modified enthalpy-transforming lattice Boltmznan (LB) model is developed to trace the location of solid-liquid interface, using the polynomial enthalpy function. The problems of two-region phase change and phase change by convection are solved to evaluate the presented LB model. The results show that by removing the non-differentiability of linear and hyperbolic-tangent enthalpy functions, the LB model with polynomial scheme can get the temperature distribution more accurately in the problem two-region phase change. Besides, in the problem of phase change by convection, resulted from the variable equivalent heat capacity during phase change, the melting rate of polynomial scheme is between linear scheme and hyperbolic-tangent scheme.

Melting of nano-PCM inside a cylindrical thermal energy storage system: Numerical study with experimental verification

In the current work, the melting process, heat transfer, and energy storage characteristics of a bio-based nano-PCM in a vertical Cylindrical Thermal Energy Storage (C-TES) system are numerically investigated and verified with experimental work. Mathematical models based on non-linear differential equations are developed to study the mass, momentum, and energy transport processes inside the C-TES system. The effects of nanoparticles volume fraction (i.e. ϕ = 0%, 3%, and 5%) and Rayleigh number (i.e. Ranl = 106, 107, and 108) on the melting process are investigated. To compare the numerical results, an experimental setup is developed and transient images are captured to identify the location and shape of solid-liquid interface. To prepare nano-PCM, the copper oxide (CuO) nanoparticles are dispersed into the bio-based coconut oil PCM. The C-TES system is insulated from the bottom, isothermally heated from its lateral walls and the top. Numerically obtained solid-liquid interface locations and melt fractions for base PCM and nano-PCM are compared with experimental analysis and a very good agreement is obtained. The numerical results are further compared with existing numerical and experimental results available in the literature. The work then explains the effects of Rayleigh number and volume fraction of nanoparticles on melt fraction, Nusselt number, and stored energy. The results indicate that adding nanoparticles do not change the patterns of melt fraction, Nusselt number, and energy storage capacity with time compared to the base PCM case. The effects of specific heat capacity of solid nano-PCM, liquid nano-PCM, and latent heat capacity of nano-PCM on energy stored are discussed. The results show that the difference in energy stored with Rayleigh number is less during the beginning of the melting; as melting reaches in the convection dominated regime, a larger difference is observed due to increased melting at larger Rayleigh number.

Nano-PCM filled energy storage system for solar-thermal applications

Abstract In this paper, a nano-PCM filled enclosure, which is a representative geometry of a thermal energy storage (TES) system, is investigated using scale analysis, numerical simulation, and experimental analysis. The enclosure is assumed to be square in shape. It is also assumed that one vertical wall of the enclosure is actively participating in absorbing energy from a source while the remaining walls are insulated. The thermal boundary condition at the active wall is treated as ‘constant heat flux boundary condition’ in this paper. The energy absorbing material, i.e., the nano-PCM, is CuO nanoparticles dispersed in coconut oil PCM. The influence of the volume fraction of nanoparticles ( 0 ≤ φ ≤ 5 % ) is investigated on the flow and thermal fields, heat transfer rate, energy stored and liquid fraction during the melting process of nano-PCM at different values of Rayleigh number based on base PCM ( 10 4 ≤ R a φ = 0 % ≤ 10 8 ). The Rayleigh number is adjusted by adjusting the size of the enclosure (i.e., higher R a represents the larger enclosure). In addition to the isothermal lines and velocity vectors, heatlines are utilized to exhibit the energy flow patterns inside the enclosure during the melting process. Besides the numerical calculations, scale analysis is presented to demonstrate the different stages of melting process of nano-PCM. The detailed scale analysis assists to identify relationship of Nusselt number and solid-liquid interface location as a function of well established dimensionless numbers: Stefan number ( S t e ), Fourier number ( F o ), and Rayleigh number ( R a φ = 0 % ). Finally, an experimental setup is developed to visualize the melting process of nano-PCM inside a prototype enclosure. Experiments are conducted to illustrate the impact of adding nanoparticles into PCM on the melting process. The numerical and experimental results show the significant improvement of the melting process by adding nanoparticles to PCM.

Stefan problems for moving phase change materials and multiple solutions

The traditional Stefan problems concerning solidification or liquidisation phenomena of a phase changing bar are revisited in this paper. Both single and double phase models are taken into consideration while analyzing the problems. The physical phase transition process is permitted to take place under the imposed movement of the material along or reverse directions with a constant speed. Some interesting mathematics are presented, particularly revealing the appearance of multiple solutions for the coefficient which determines the movement of the phase change interface. It is shown that the solid-liquid interface location is enhanced growing relatively faster assisting the phase change process when the semi-infinite slab moves in the direction of melt or freeze. However, the phase change process is expectedly deterred when the bar moves in the opposite direction. When the boundaries are controlled with flux conditions such that the initial position is permitted to release a heat flux inversely proportional to the square root of time, unique interface locations for both the single and two phase models are found up to the Peclet number Pe≤2 corresponding to a solid-liquid interface location factor λ=12. Otherwise solutions are tripled in one phase model and multiple solutions are encountered for the two phase model. For the Stefan problems involving the initial boundary as fixed temperature or heat flux with latent heat a power function of position, explicit phase change solutions appear to be unique for the entire action of the phase change material, no matter whether the single or double phases are considered.

Lattice Boltzmann investigation of the solid-liquid phase change process in a cavity with protruding heater

The solid-liquid phase change process in a cavity with protruding heater is of significant importance to application of phase change material (PCM). In this paper, the phase change lattice Boltzmann (LB) model has been applied and the effects of heater and inclination angle of cavity on phase change process are investigated. The results show that moving the protruding heater is able to change the temperature distribution and location of solid-liquid interface. The phase change process can be accelerated by moving the heater to middle region of cavity. Decreasing the distance between heater and cavity upper wall enhances the flow obstruction, and reduces the heat transferred through upper and right walls of heater. Furthermore, rotating the cavity changes the distance of flow from heater to cavity. Increasing inclination angle from 30° to 45° enhances the heat transfer rate of heater's upper wall and weakens that of heater's right wall.

The quasi-enthalpy based lattice Boltzmann model for solid-liquid phase change

The phase change material (PCM) receives more and more attention for the large amount of latent heat and little temperature variation during phase change. In this paper, a new phase change lattice Boltzmann (LB) model, which is based on the quasi-enthalpy (QE) method, has been developed. The update of temperature is divided into two step, the “prediction” and “consumption (for melting)” or “release (for solidification)”. The problems of one-region phase change, two-region phase change, phase change under constant heat flux and phase change by convection are solved by the present model. All the results are compared with that of analytical solution, integral approximate solution and numerical method. No significant differences can be obtained for all the simulations, which demonstrates that the QE based LB model is able to capture the location of solid-liquid interface and reveal the temperature distribution of PCM accurately.

Investigation of diffusional transport of heat and its enhancement in phase-change thermal energy storage systems

Thermal energy storage in general, and phase-change materials (PCMs) in particular, have been a major topic of research for the last thirty years. Due to their favorable thermo-dynamical characteristics, such as high density, specific heat and latent heat of fusion, PCMs are usually employed as working fluids for thermal storage. However, low thermal conductivities of organic PCMs have posed a continuous challenge in its large scale deployment. This study focuses on experimental and numerical investigation of the melting process of industrial grade paraffin wax inside a semi-cylindrical enclosure with a heating strip attached axially along the center of semi-cylinder. During the first part of the study, the solid-liquid interface location, the liquid flow patterns in the melt pool, and the spatial and temporal variation of PCM temperature were recorded. For numerical simulation of the system, open source library OpenFOAM® was used in order to solve the coupled Navier-Stokes and energy equations in the considered system. It is seen that the enthalpy-porosity technique implemented on OpenFOAM® is reasonably well suited for handling melting/solidification problems and can be employed for system level design. Next, to overcome the inherent thermal limitations of PCM storage material, the study further explored the potential of coupling the existing heat source with copper-water heat pipes, so as to help augment the rate of heat dissipation within the medium by increasing the effective system-level thermal conductivity. Integration of heat pipes led to enhanced transport, and hence, a substantial decrease in the total required melting time. The study provides a framework for designing of large systems with integration of heat pipes with PCM based thermal storage systems.

Numerical Solution of Heat Transfer Process in PCM Storage Using Tau Method

Thermal energy storage units that utilize phase change materials have been widely employed to balance temporary temperature alternations and store energy in many engineering systems. In the present paper, an operational approach is proposed to the Tau method with standard polynomial bases to simulate the phase change problems in latent heat thermal storage systems, that is, the two-dimensional solidification process in rectangular finned storage with a constant end-wall temperature. In order to illustrate the efficiency and accuracy of the present method, the solid-liquid interface location and the temperature distribution of the fin for three test cases with different geometries are obtained and compared to simplified analytical results in the published literature. The results indicate that using a two-dimensional numerical approach can predict the solid-liquid interface location more accurately than the simplified analytical model in all cases, especially at the corners.

Uncertainty Analysis of Solid-Liquid-Vapor Phase Change of a Metal Particle Subject to Nanosecond Laser Heating

The effects of the uncertainties of various parameters, including the laser fluence, diameter of metal powder particles, laser pulse width, and the initial temperature of metal particles on solid-liquid-vapor phase change processes of metal particles under nanosecond laser heating are investigated in this paper. A systematic approach of simulating the phase change with uncertain parameters is presented and a sample-based stochastic model is established in order to investigate the influence of different uncertain parameters on the maximum surface temperature of metal particles, the maximum solid-liquid interface location, maximum liquid-vapor interface location, maximum saturation temperature, and maximum recoil pressure and the time needed to reach the maximum solid-liquid interface location. The results show that the mean value and standard deviation of the laser fluence have dominant effects on all output parameters.

Experimental and numerical studies on melting phase change heat transfer in open-cell metallic foams filled with paraffin

Abstract In the current study, the melting phase change heat transfer in paraffin-saturated in open-celled metallic foams was experimentally and numerically studied. The experiments were conducted with seven high-porosity copper metal foam samples ( ɛ ≥ 90%), and paraffin was applied as the phase-change material (PCM). The wall and inner temperature distribution inside the foam were measured during the melting process. The effects of foam morphology parameters, including porosity and pore density, on the wall temperature and the temperature uniformity inside the foam were investigated. The melting heat transfer is enhanced by the high thermal conductivity foam matrix, although its existence suppresses the local natural convection. A numerical model considering the non-Darcy effect, local natural convection, and thermal non-equilibrium was proposed. The velocity, temperature field, and evolution of the solid–liquid interface location at various times were predicted. The numerically predicted results are in good agreement with the experimental findings. The model as well as the feasibility and necessity of the applied two-equation model were further validated.

Finite element analysis of laser irradiated metal heating and melting processes

Laser technology has shown fast growth due to its demands in material processing and manufacturing. Laser material processing includes various applications like cutting, welding, drilling, cladding and surface treatment. In laser surface treatment, the material properties at the surface are altered through surface alloying and transformation hardening. In this study, an enthalpy-based computational model is developed for analyzing laser heating and melting of metals. The solution to the problem is obtained by using a finite element method and validated by comparing the results with that given by an analytical solution to a limiting case problem. A solution algorithm and a computational code are developed to estimate the temperature distribution, solid-liquid interface location and shape and size of the molten pool. The computational model is validated by comparing results with a limiting case analytical model. The study is conducted to analyze the heating rate, the heat affected zone, and the shape and size of the molten pool using a Gaussian laser beam.

Identification of the heat fluxes and thermal resistance on the ingot-mould surface in continuous casting of metals

Identification of thermal resistance of the gas-gap between the ingot and mould, as well as the heat flux distribution on the phase change from the solid side during continuous casting of metals is the subject of this article. Analysed parameter estimation problems of the steady-state heat conduction belong to the group of inverse problems. The presented work shows the possibility of applying the least square adjustment method with a priori data for the identification of thermal resistance, the interphase location as well the heat flux distribution on the phase change from the solid side and the temperature field within the ingot and mould. The most important feature of the approach is that the unknown thermal resistance of the gas-gap is obtained from the temperature measurements at a number of sensors located in the wall of the mould, and some sensors located in the ingot, by solving the appropriate inverse problem. The validity of the solution of the inverse problem is checked by comparison with the results of direct problem. In this work, a front-tracking method with an automatic mesh generation finite element technique (so called deforming or moving finite-elements) for steady-state equation conduction-advection problems is developed. Such an approach makes it possible to find the exact solid-liquid interface location, because it is the integral part of the solution. Due to the strong convective nature of the problem (casting velocity, thermal parameters) the special up-wind technique is applied.

Studies of the solid–liquid interface location during heated mould continuous casting of metals and alloys

With the industrial implementation of the Ohno continuous casting (OCC) process, many investigations have been carried out on both the fundamental and practical aspects of the process. This paper reviews some of the research, focusing on crucial processing conditions that influence the location of the solidification front in the horizontal Ohno continuous casting system. The effects of the solid–liquid interface position with respect to pure metals, and the liquid + solid (mushy) zone in the case of alloys, on the quality of the cast products have been studied.