Volume-averaging Technique Research Articles

Multiphase flow model of semi solid solidification of novel Al-15Mg2Si-Si composite

In this work, a volume averaging technique based Eulerian multiphase flow CFD (Computational Fluid Dynamics) model is developed to simulate the semi-solid solidification of the cooling slope generated Al-15Mg2Si-4.5Si composite slurry. The four phases considered here are liquid (l), primary solid (Mg2Si), secondary solid (α-Al) and air (a). Whereas latent heat release during solidification is tackled via a temperature correction scheme. The effect of recalescence is also observed in the present solidification model. The simulation findings include shape and size of the α-Al and primary Mg2Si grains, solid fraction, temperature, melt viscosity etc. The developed multiphase flow model of cooling slope casting (semi solid solidification) is applied to a test case having melt pouring temperature (into the slope) of 650°C (923K). The simulation findings are then validated with the help of measurements of microstructural features observed in the experimental (optical) micrographs of the solidified samples.

Simulation of Phase Change Material Absorbers for Passive Cooling of Solar Systems

One of the main challenges that face the reliable use of photovoltaic solar systems in hot arid regions is the prevailing high temperatures during the day. To overcome this issue, Phase Change Materials (PCM) are used for passive cooling providing different options to attain sufficient thermal management solutions for different applications. Passive cooling can be achieved by adjusting a heat sink to the solar PV module. This can be realized by attaching a PCM layer or sensible heat storage to the backside of PV panels. Few studies have reported on simplified modeling and numerical procedures using the apparent heat capacity formulation and volume averaging technique as a robust approach to solving such sophisticated problems with minimal computational efforts, high accuracy, and in a short period of time. However, there is still a need to bridge the large-scale gap between the macroscale within the PCM layer, with a moving melting front, and the length scale of PV modules. Hence, this work focuses on modeling and simulating PCM-Matrix Absorbers (PCM-MA) that consist of fibrous aluminum cellular structure filled with PCM for passive thermal management of PV panels using apparent heat capacity formulation and homogenization based on volume averaging technique. COMSOL Multiphysics FEM software was used for the numerical simulation of the phase change problem by using a Smoothed Heaviside step function to overcome the singularity of PCM challenge that arises with sharp melting temperatures. To validate the proposed model, it has been compared with a benchmark analytical solution for an ice melting problem, i.e., the Stefan problem, in a semi-finite slab, i.e., Neumann’s solution under the same assumptions and boundary conditions. The specific characteristics of phase change and evolution of melting front with time, heat capacity change with the temperature at different times, and with locations along the slab height are presented. As the phase change is modeled to take place over a mushy region, i.e., a narrow temperature interval rather than a sharp melting point, the results show a good coincidence of the heat capacity profile and its peak at different times and locations. The validated model can be used for the optimization of PCM-MA for any specific geographical location and other applications such as the passive cooling of buildings with PCM integrated with the outer envelope. To this end, the results of the simulation in this work are shown to be in agreement with those obtained from the analytical solution.

Functionally-graded foams for volumetric solar receivers

The open volumetric receiver, one of the most important components of a Concentrated Solar Power (CSP) plant, is made up by a ceramic foam on which the concentrated solar radiation impinges. Ceramic foams are employed in volumetric solar receivers because of their high specific surfaces and their operating temperatures higher than those of metal foams. Thermo- fluid-dynamics in the graded ceramic foam of a volumetric solar air receiver for concentrated solar power is investigated numerically. Variable porosities and Pores Per Inch (PPI), according to different power laws, are accounted for. Governing equations are written with the Volume Averaging Technique (VAT) and are solved with the commercial software Comsol Multiphysics. The effects of different porosity and PPI laws, on the fluid velocity, pressure drop and temperatures, under different thermo-fluid-dynamic conditions, are highlighted.

Comparative numerical study of pneumatic conveying of flexible elongated particles through a pipe bend by DEM-CFD

Pneumatic conveying is widely used for the transportation of granular materials, where the flow of a gas is used to drive particles along pipes. While many granular materials comprise of compact and regularly shaped particles, this study aims for the numerical analysis of transport of biomass particles, which are predominantly non-spherical, frequently fiber-like and flexible and yet not broadly addressed. The Discrete Element Method coupled with Computational Fluid Dynamics (DEM-CFD) using a local volume-averaging technique is used as a tool to analyze pneumatic conveying of flexible biomass particles focusing on a pipe bend as relevant domain. The required particle flexibility is incorporated into the DEM by using a bonded particle model. Two different damping coefficients instead of just one are suggested to be used to ensure the same damping ratio at different fiber deformations. A simple technique relying on a smoothing coefficient for the damping forces and moments is proposed to minimize fluctuations and to allow the increase of the used time step in the DEM-CFD simulations. Laboratory tests with wheat straw were performed to determine its mechanical and physical properties. Thereon effects of the particle stiffness, the bond damping, the particle mass flow rate, the particle length and the gas inflow velocity on pneumatic particle transport are numerically analyzed. Obtained results demonstrate that particle trajectories in the vertical pipe section and the pressure drop depend on the particle stiffness. However, the performed comparison with the results obtained using rigid, non-flexible particles suggests that pneumatic conveying of more stiff particles can be achieved by relying on rigid particles without flexible bonds. Additionally, the performed tests using different bond damping values demonstrate the importance of the considered damping ratio for the outcome of the simulations.

A LOCAL THERMAL NONEQUILIBRIUM MODEL FOR COUPLED HEAT AND MASS TRANSFER WITH DISPERSION AND THERMAL DIFFUSION IN POROUS MEDIA

A theoretical model is proposed to predict Darcy-scale mass transport in porous media coupled with nonequilibrium heat transfer and taking into account the thermal diffusion process. A volume-averaging technique was used with approximations leading to a two-equation or two-temperature model for the macroscale energy balance equations. Because of the Soret effect, the concentration deviation with respect to the averaged value is a function of concentration and temperature gradients in the fluid phase, the temperature gradient in the solid phase, and the difference between the two averaged temperatures. The mapping between deviations and averages involves four closure problems for the mass transport equations: problems were solved numerically over a two-dimensional periodic-unit cell for evaluation purposes. The results show that the effective coefficients depend strongly on the thermophysical properties of the medium and the Peclet number. In particular, the effective-Soret coefficient in porous media changes with the Peclet number and the phases' thermal conductivity ratios.

Anisotropic convective heat transfer in open-cell metal foams: Assessment and correlations

Open-cell metal foams are promising materials for heat transfer augmentation, due to their tortuosity and high specific surface area. The volume-averaging technique under the assumption of local thermal non-equilibrium between the solid and fluid phases is often used to model devices equipped with open-cell foams; it requires an accurate knowledge of the interfacial convective heat transfer coefficient. Its dependence on the anisotropy of elongated foam cells is investigated numerically in the present work. Four aluminum foam samples with different porosities and equal PPIs are considered; their geometry is reconstructed by means of x-ray computed tomography. Mass, momentum and energy equations for the fluid phase (air) are solved, while the solid phase is accounted for with a uniform heat flux boundary condition. Interfacial convective heat transfer coefficients and Nusselt numbers are predicted. The dependence of the interfacial heat transfer coefficient in the elongation direction on the effective porosity and fluid inlet velocity is pointed out. The comparison of predicted values with those given by correlations from the open literature shows a good agreement. Finally, correlations for the prediction of Nusselt numbers, accounting for the foam anisotropy, are proposed, which can be useful in the study of metal foams.

A numerical investigation of the effects of metal foam characteristics and heating/cooling conditions on the phase change kinetic of phase change materials embedded in metal foam

Abstract In the last decade, the use of Phase change materials (PCM) as passive thermal energy storage has been widely studied both numerically and experimentally. Despite their advantages, their thermal conductivity is very low, with a large change in volume during the melting and solidification process. One way to increase their poor thermal conductivity is to embed them into open cells metallic foams. In this paper, a numerical study is conducted on the effects of metal foam properties and heating/cooling conditions (cyclic heating and cooling) on the phase change kinetic of PCM embedded in metal foam. Two types of heating condition were studied: constant and sinusoidal heat flux. The mathematical model is based on the volume-averaging technique. The Brinkman–Forchheimer-extended Darcy equation and the local thermal non-equilibrium model that applies a two-energy equation are used. The phase change of PCM is modeled by an enthalpy-porosity method. The numerical results are validated by comparing with experimental data. It is observed from the numerical results that the foam morphology and materials have a significant influence on the melting and solidification of phase change materials. The results also show that the melting time is reduced with sinusoidal heating.

Upscaling of polymer adsorption

This article considers upscaling of polymer adsorption. Input to adsorption values employed in reservoir simulation models are typically obtained from core plug measurements. There are several orders of magnitude in scale difference between core plugs and grid cells in reservoir simulation models, which foster a need for upscaling of the adsorption values.Polymer concentration distribution on the lithofacies scale is investigated in this article. The effect of diffusion on concentration distribution is investigated analytically. The slow diffusion of polymer molecules retards mixing even at the lithofacies scale. We introduce a formula to estimate the redistribution of polymer due to capillary forces in a layered model, and this formula is validated through numerical simulations. From our considerations we conclude that it is questionable to assume a constant polymer concentration in lithofacies models. This impedes applying steady-state upscaling techniques. Such upscaling techniques will over-predict polymer adsorption.Different methods for upscaling adsorption are presented in this paper, and applied to a simplified layered model and to more realistic fine-scale numerical models based on the SPE10 model. These numerical models were populated with adsorption values obtained from published experiments conducted on samples from the Brent sequence modeled in SPE10. Simulations of tertiary polymer flooding on the upscaled models were compared to simulations of the same flooding sequences on the original fine scale models. The tested upscaling methods include a volume averaging technique employed by other authors, and a method were we distribute the adsorption values by the same functional relationship as in the fine scale model. In addition we introduce upscaling methods were we assign zero adsorption to fine scale grid cells with permeability below a given cut-off value. The cut-off value is obtained from a single phase simulation on the fine scale model. In our models the cut-off value methods yield the best match between the coarse scale and fine scale simulation results. The volume averaging technique over-predict the polymer adsorption.Results from both the lithofacies and geomodel scale indicate a tendency to over-predict polymer adsorption, which could lead to conservative estimates for the effect of polymer flooding.

Thermal conduction in open-cell metal foams: Anisotropy and Representative Volume Element

It is well known that the manufacturing process of open-cell foams slightly elongates their struts in one direction, thus making them anisotropic; in turn, anisotropy affects foam characteristics. Furthermore, actual foams can be characterized with reference to a Representative Volume Element (RVE), defined as the cubic sub-volume having the same characteristics as those of the whole foam. An appropriately chosen RVE is very helpful to pass simulation data from a micro-to a macro-scale. The important role played by RVE in characterizing foams performance suggests further research in its determination, in order to reduce computational power and to allow to apply the volume-averaging technique to open-cell foams. In this paper, anisotropy and RVE for the effective thermal conductivity of open-cell metal foams are numerically analyzed. After scanning with Computed Tomography (CT) and postprocessing four open-cell aluminum foams with different porosities and the same Pores Per Inch (PPI) value, their morphologies are investigated in order to evaluate the effects of porosity on cells anisotropy. Foam cell elongation is quantified by an anisotropy ratio. Simulations are performed on CT data with a finite-element method to compute the effective thermal conductivities along three orthogonal directions, and results are compared with data published in the literature. A new correlation between effective thermal conductivity, porosity and direction is presented. The dependence of effective thermal conductivity on cells elongation is also pointed out. RVE sizes for different porosities, directions and inaccuracy thresholds are then investigated. Finally, an existing analytical model is suitably adapted to reliably predict the RVE size with a new correlations which accounts for the directionally-averaged effective thermal conductivity.

CFD simulation to investigate hydrodynamics of oscillating flow in a beta-type Stirling engine

Stirling engines have recently been studied theoretically via two different methods, thermodynamic analysis and CFD simulation. Evidently, second order thermodynamic analysis is simpler and less time consuming than CFD. However CFD considers more details as well as the engine geometry and consequently reflects more details about the flow field and losses phenomena. In this paper, numerical simulation of a typical Stirling engine was conducted by OpenFoam open source software. Dynamic mesh was used to simulate moving pistons and the working fluid was considered compressible. Volume averaging technique was applied to simulate flow in the regenerator as a porous media. The well-established PIMPLE algorithm was used to handle pressure coupling in momentum equation. To investigate the effect of turbulence, a simulation was conducted employing k-ω SST turbulence model and no significant change in the results was observed.

Effects of reservoir heterogeneity on scaling of effective mass transfer coefficient for solute transport

Modeling transport process at large scale requires proper scale-up of subsurface heterogeneity and an understanding of its interaction with the underlying transport mechanisms. A technique based on volume averaging is applied to quantitatively assess the scaling characteristics of effective mass transfer coefficient in heterogeneous reservoir models. The effective mass transfer coefficient represents the combined contribution from diffusion and dispersion to the transport of non-reactive solute particles within a fluid phase. Although treatment of transport problems with the volume averaging technique has been published in the past, application to geological systems exhibiting realistic spatial variability remains a challenge. Previously, the authors developed a new procedure where results from a fine-scale numerical flow simulation reflecting the full physics of the transport process albeit over a sub-volume of the reservoir are integrated with the volume averaging technique to provide effective description of transport properties. The procedure is extended such that spatial averaging is performed at the local-heterogeneity scale.In this paper, the transport of a passive (non-reactive) solute is simulated on multiple reservoir models exhibiting different patterns of heterogeneities, and the scaling behavior of effective mass transfer coefficient (Keff) is examined and compared. One such set of models exhibit power-law (fractal) characteristics, and the variability of dispersion and Keff with scale is in good agreement with analytical expressions described in the literature.This work offers an insight into the impacts of heterogeneity on the scaling of effective transport parameters. A key finding is that spatial heterogeneity models with similar univariate and bivariate statistics may exhibit different scaling characteristics because of the influence of higher order statistics. More mixing is observed in the channelized models with higher-order continuity. It reinforces the notion that the flow response is influenced by the higher-order statistical description of heterogeneity. An important implication is that when scaling-up transport response from lab-scale results to the field scale, it is necessary to account for the scale-up of heterogeneity. Since the characteristics of higher-order multivariate distributions and large-scale heterogeneity are typically not captured in small-scale experiments, a reservoir modeling framework that captures the uncertainty in heterogeneity description should be adopted.

Thermal-Electrochemical Lithium-Ion Battery Simulations on Microstructure and Porous Electrode Scale

Heat production within a battery cell is governed by local fluxes of ions and electrical currents in the microstructure of the battery electrodes. These fluxes are strongly coupled with thermal transport, leading to a fully coupled reaction transport model for batteries. By applying the volume-averaging technique to our thermal-electrochemical microscopic theory the corresponding thermal-electrochemical porous electrode theory can be derived. Implementation of both models in our simulation software BEST allows to compare the results of the homogenized theory with numerically averaged simulations on micro scale. Whereas the numerically averaged results agree very well with the results of porous electrode theory, strong fluctuations around this average (e.g. of the overpotential) are observed in microstructures. Our results raise the question to which extent porous electrode theory can be used to predict degradation phenomena in batteries.

Thermal-Electrochemical Lithium-Ion Battery Simulations on Microstructure and Porous Electrode Scale

Heat production within a battery cell is governed by local fluxes of ions and electrical currents in the microstructure of the battery electrodes. These fluxes on the other hand are strongly coupled with thermal transport, leading to a fully coupled reaction transport model for batteries [1]. It describes ion, charge and heat transport on the length scale of the microscopic active particles that build up an electrode. The implementation of the model in our simulation software BEST [2] allows simulations of transport and reactions in three-dimensionally fully resolved electrode structures. Ion concentration, potential and temperature are obtained in each spatial point of the simulation domain. Thus the dependence of battery performance, heat production and heat distribution in the electrode microstructure can be studied. Due to its geometric complexity this approach is not viable for a simulation on cell scale. To this end effective or homogenized models are commonly employed [3]. By applying the volume-averaging technique to our thermal-electrochemical microscopic theory the corresponding thermal-electrochemical porous electrode theory can be derived [4]. Since volume-averaging neglects the details of the electrode structure it is obvious that ion fluxes and electrical currents cannot be recovered in detail. However, many heat sources of our model depend on the magnitude and distribution of these fluxes (e.g. Joule heating) and are strongly localized on the interfaces between electrolyte and active particles. It is therefore a priory not clear whether upscaled models of this type are at all useful for predictive cell scale simulations if heat production and temperature distribution is of interest. In our contribution we will present the fully coupled thermal battery models for both micro and cell scale. We focus on a simulation study where we compare micro- with equivalent cell scale simulations based on the derived porous electrode theory. Whereas the numerically averaged results agree very well with the results of porous electrode theory, strong fluctuations around this average (e.g. of the overpotential) are observed in microstructures. Especially for the prediction of degradation phenomena, these fluctuations are crucial and cannot be recovered in porous electrode theory. Our results raise the question to which extent porous electrode theory can be used to predict degradation phenomena in batteries. [1] A. Latz and J. Zausch, Journal of Power Sources 196 (2011) 3296. [2] www.itwm.fraunhofer.de/best [3] J. Newman and W. Tiedemann, AIChE 21, (1975) 25. [4] A. Latz, J. Zausch, Multiscale modeling of lithium ion batteries : thermal aspects, Beilstein J. Nanotechnol. 6 (2015) 987–1007. doi:10.3762/bjnano.6.102.

A unified single-field model framework for Volume-Of-Fluid simulations of interfacial species transfer applied to bubbly flows

Most methods for Direct Numerical Simulations of interfacial species transfer across fluid interfaces suffer from poor stability, accuracy and/or the loss of conservativeness or boundedness properties. In the literature this is often attributed to shortcomings in the ‘numerics’. This paper presents a single-field model, termed Continuous Species Transfer (CST) model. The resulting numerical method is virtually void of above problems.In detail we shall set out the model׳s derivation procedure which is based on the Conditional Volume-Averaging technique and thus guides our consistent Finite Volume discretisation practice. The CST method enables the simulation of species transfer in two-phase flows in a realistic range of Henry coefficients and diffusivity ratios in the context of algebraic Volume-Of-Fluid (VOF) interface capturing techniques, given a sufficient resolution of the concentration boundary layer with at least four to five computational cells. Beside setting out the mathematical and numerical foundation of the CST method, we present a sound validation study. The CST method is then applied to the case of interfacial species transfer from single rising bubbles in quiescent liquids. Our method development and numerical simulations have been based on OpenFOAM®, in particular its algebraic VOF solver family interFoam.

Three-dimensional simulation of gas–solid–liquid flows using the DEM–VOF method

Gas–solid–liquid flows are widely found in chemical engineering, e.g. the processes of mixing, wet ball milling, and screw kneading, for which the numerical modeling is now a pressing research topic to help improve the design and investigate operational conditions. On the other hand, computational challenges are posed for existing methods in modeling the interphase interactions and complex boundaries within such three-phase systems. In this paper, an Eulerian–Lagrangian numerical model, specifically the DEM–VOF method, is presented for three-dimensional simulations of gas–solid–liquid flows. The fluid motion is solved by using a computational fluid dynamics (CFD) based approach with gas–liquid interface capturing provided by the volume-of-fluid (VOF) method. The particle phase is tracked by the discrete element method (DEM) as discrete entities. The fluid–particle coupling is achieved by the volume-averaging technique wherein a well-established empirical closure is adopted for the description of hydrodynamic forces. Particularly, the modeling of arbitrary-shaped walls and moving boundaries is addressed via the introduction of signed distance function (SDF) representation and immersed boundary (IB) method, which was proved to be highly efficient for gas–solid–liquid systems interacting with complex geometries. Special attentions when computing fluid–particle interactions near those boundaries are raised and their treatments are also discussed. Various model verifications and validation tests are performed in this study to show the validity and capability of the DEM–VOF method. By comparing with analytical solutions and experimental data, we generally find good agreements from the simulation results, thereby highlighting its potential in accurately modeling complicated gas–solid–liquid flows. To the best of our knowledge, the proposed method is the first report that successfully couples the DEM to a VOF solver with non-trivial wall boundaries.

Scaleup of Effective Mass Transfer in Vapour-Extraction Process Accounting for Field-Scale Reservoir Heterogeneities

Summary Vapour extraction (VAPEX) is a nonthermal process using vapourized solvents, with promising potential to reduce steam consumption in heavy-oil recovery. The key recovery mechanisms are convection and molecular diffusion enhanced by various spreading mechanisms [e.g., capillarity and velocity variations at the micro and macroscale (i.e., dispersion and mixing)]. The efficiency of diffusion/dispersion depends significantly on reservoir heterogeneities, which exhibit a wide range of length scales. This paper demonstrates a procedure for quantifying the scaling characteristics of effective mass transfer accounting for heterogeneities based on the volume-averaging approach. Volume averaging is a mathematical technique used to derive continuum equations at coarse scales given representative transport equations at fine scales. Although treatment of transport problems has been published in the past, application to stochastic geological systems is limited. In the proposed procedure, results from a fine-scale numerical flow simulation reflecting the full physics of VAPEX over a small element of the reservoir are integrated by use of the volume-averaging technique to provide effective description of mass transfer at the coarse scale. Scaling characteristics of effective mass transfer are investigated systematically for different heterogeneity distributions. Results show (1) spatial variability of effective-mass-transfer coefficients increases as a solvent chamber advances through the reservoir; (2) mean and variance of effective-mass transfer vary with length scale in a fashion similar to that of recovery statistics; and (3) variability in effective-mass transfer is a strong nonlinear function of heterogeneity. An original contribution is to provide a general framework for developing scaling relationships of effective mass transfer in VAPEX accounting for reservoir heterogeneities. It also presents an important potential in modelling of other solvent-injection applications. Results demonstrate that effective-mass transfer varies with length scale and heterogeneity; hence, it should be represented properly for accurate prediction of recovery performance in simulations using scaled-up reservoir models.

Simulation of an Aluminum Foam Heat Exchanger Using the Volume Averaging Technique

Open cell metal foams show a high potential for heat transfer applications. In this paper the thermal and hydraulic performance of a metal foam heat exchanger with two tube rows in a staggered layout is studied. Two-dimensional simulations are performed using a bulk model based on the volume averaging technique. A louvered fin heat exchanger with the same tube layout and overall volume is considered as reference case. Velocities range from 1.2 m/s to 3.2 m/s. An experimental validation illustrates the quality of the simulation results. For the same fan power, the 10 ppi and 20 ppi foams show a smaller heat transfer than the louvered fin heat exchanger. This is mainly due to the larger airside heat transfer surface area of the louvered fin heat exchanger (because of the small fin pitch) compared to the foams. 30 and 35 ppi foams, having a specific surface area above 1000 m2/m3, show a better thermal hydraulic performance than the louvered fin design.

Fluid temperature measurements inside metal foam and comparison to Brinkman–Darcy flow convection analysis

Actual air temperatures were locally measured inside commercial aluminum foam cylinder heated at the wall by a constant heat flux, and cooled by forced air flow. The specially-developed experimental technique for such measurements is described in detail, and is shown to produce reasonably good data. Air speeds were in the Darcy regime. The permeability of the foam was directly determined from experimental pressure drop points that were obtained using the same experimental set-up. The experimental air temperatures are compared to their analytical counterparts. The volume-averaged analytical formulation employed the Darcy-extended Brinkman model for momentum, and the non-thermal-equilibrium two-energy-equation model for the temperatures of the solid and the fluid phases inside the foam. The solution steps, which are not new, are summarized. A comparison shows good agreement between the experimental and the analytical air temperatures, given the complexity of the foam’s morphology and the rounding nature of the volume-averaging technique. However, the analysis seems to under-predict the fluid temperature over most of the cross section. The experimental technique can be used for validation of other analytical solutions, numerical models and heat-exchange engineering designs based on metal foam and similar porous media.

Forced convection of air through networks of square rods or cylinders embedded in microchannels

Forced convection of air at near-standard conditions through periodical networks of micrometer square rods or cylinders is investigated. The Navier–Stokes equations subjected to first-order velocity-slip condition, and energy equations for the fluid and solid phases are numerically solved for two-dimensional structures. The flow is created by imposing pressure gradients, and heat is volumetrically generated inside the solid rods. Assuming periodicity in the direction transverse to the pressure gradient, the computational domain consists in long open channels, partially filled with solid rods placed regularly. The various structures considered are then modeled as porous media. For the permeability calculations, both volume averaging technique and multiple scale expansion technique are employed, and the results are favorably compared. The slip effect on permeability is highlighted for Knudsen number of about 0.05. On the other hand, the use of a periodic approach in the flow direction for heat transfer calculations is demonstrated not to be based on realistic assumptions. In addition, the importance of axial heat diffusion in channels of width close to one micrometer is emphasized. The reason is found in the low Peclet numbers typically encountered when the incompressible approximation is invoked. Based on numerical solutions at the microscopic scale, a new macroscopic modeling is suggested. Comparisons between numerical solutions and analytical predictions for various networks of rods are discussed. A very good agreement is shown.

Porous silica matrices infiltrated with PCM for thermal protection purposes

Abstract In this work, numerical and experimental studies are proposed to predict and investigate the thermal absorption characteristics of porous silica infiltrated with phase change materials (PCM) for thermal protection applications. Several types of different solid–liquid phase change composites were introduced into a cylindrical enclosure while it was heated on the left of the enclosure. The numerical simulation was performed using a volume-averaging technique, and a finite volume modelling (FVM) was used to discretise the heat diffusion equation. The phase change process was modelled using the enthalpy–porosity method. The results are portrayed in terms of the temperature distribution and liquid fraction, and the numerical and experimental results showed good agreement. The results indicated that a higher latent heat storage capacity meant a more stable thermal performance of the phase change composite.