Numerical study of cell morphology effects on convective heat transfer in reticulated ceramics

Understanding the influence of foam morphology on the heat transport mechanism is an essential task for the design engineers. The assessment of foam thermal properties was performed using experimental techniques or simulation approaches such as Finite Elements analysis and/or computational fluid dynamics and was, up to now, mainly focused on describing the influence of some average parameters, such as cell size and porosity. Recent numerical analysis have instead demonstrated that local cell morphological structures can strongly influence thermal conduction in ceramic foams. Therefore, in the present work, the effect of morphological characteristics, namely ligament radius, cell inclination angle and ligament tapering, on the convective heat transfer of ceramic foams were studied. The approach used is Computational Fluid Dynamics (CFD) and foam geometries were schematically represented with tetrakaydecahedra geometries. The numerical simulations, performed with ANSYS/Fluent on different tetrakaydecahedra geometries, aimed at evaluating pressure drop and heat exchange through the foam. A heat exchanger efficiency parameter was defined and then evaluated for the different foam geometries at several air flow velocities. Results show the influence of the different morphological parameters and, in particular, that the heat exchanger efficiency of the foams decreases when increasing the air flow velocity.     

Coupled radiation and flow modeling in ceramic foam volumetric solar air receivers

Ceramic foams are promising materials for the absorber of volumetric solar air receivers in concentrated solar thermal power (CSP) receivers. The macroscopic temperature distribution in the volumetric solar air receiver is crucial to guarantee that volumetric solar air receivers work steadily, safely and above all, efficiently. This study analyzes the temperature distribution of the fluid and solid phases in volumetric solar air receivers. The pressure drop in the ceramic foams and the interfacial heat transfer between the flowing fluid and solid are included in the model. The radiative heat transfers due to concentrated solar radiation absorption by the ceramic foam and the radiation transport in the media were modeled with the P₁ approximation. The energy fields of the fluid and solid phases were obtained using the local thermal non-equilibrium model (LTNE). Comparison of the macroscopic model with experimental results shows that the macroscopic model can be used to predict the performance of solar air receivers. Sensitivity studies were conducted to analyze the effects of velocity, porosity, mean cell size and the thermal conductivity of the solid phase on the temperature fields. The results illustrate that the thermal non-equilibrium phenomena are locally important, and the mean cell size has a dominant effect on the temperature field.     

基于能量流的塔式太阳能热发电吸热器动态建模

塔式太阳能热发电空气吸热器的最大热应力与其温度变化率成正比,吸热器出口空气温度的动态特性影响塔式光热系统的功率特性。结合热电比拟理论,采用对流换热系数和Rosseland辐射传递方程描述传热过程,建立塔式太阳能热发电系统中碳化硅泡沫陶瓷吸热体的能量流模型。通过剖析空气吸热器工作过程的传热特性,得出平均能流密度、吸热体厚度、平均孔径对出口空气温度、吸热体温度的影响,为该类空气吸热器的设计提供了理论依据。     

Theoretical and numerical investigation of flow stability in porous materials applied as volumetric solar receivers

This article reports results of a theoretical analysis as well as a numerical study investigating the occurrence of flow instabilities in porous materials applied as volumetric solar receivers. After a short introduction into the technology of volumetric solar receivers, which are aimed to supply heat for a steam turbine process to generate electricity, the general requirements of materials applied as solar volumetric receivers are reviewed. Finally, the main methods and results of the two studies are reported. In the theoretical analysis it is shown that heat conductivity as well as permeability properties of the porous materials have significant influence on the probability of the occurrence of flow instabilities. The numerical study has been performed to investigate the occurrence of unstable flow in heated ceramic foam materials. In the simulations a constant heat flow of radiation, that is absorbed in a defined volume, and constant permeability coefficients are assumed. Boundary conditions similar to those of the 10 MW Solucar Solar project have been chosen. In a three dimensional, heterogeneous two phase heat transfer model it was possible to simulate local overheating of the porous structure. The parameters heat conductivity, turbulent permeability coefficient and radial dispersion coefficient have been varied systematically. Consequently, for a heat flux density of 1 MW/m² a parameter chart could be generated, showing the possible occurrence of “unstable” or “stable” thermal and fluid mechanical behaviour. These numerical results are beneficial for the design of optimized materials for volumetric receivers.     

Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

One dimensional thermal analysis of silicon carbide ceramic foam used for solar air receiver

Using air as heat transfer fluid for electricity generation offers some significant advantages for the development of Concentrated Solar Power (CSP): high conversion efficiency, low environmental impact and being used in deserts or other areas scarce of water resources. Silicon carbide ceramic foams have the characteristics of light weight, high strength, large specific surface areas, high porosity and excellent thermal shock resistance performance which make them particularly fit for absorber material in CSP. In this paper, thermal performance of silicon carbide ceramic foam as solar air receiver is investigated analytically based on the one dimensional physical model. The analytical results show that the air flow resistance increases obviously with increasing air outlet temperature, the air flow resistance while the air outlet temperature is equal to 1000 °C is nearly 3 times the one while the air outlet temperature is equal to 20 °C with air velocity range is between one and six meters per second. The results of one dimensional analysis of flow and heat transfer process of ceramic foams suggest that there exists an input solar energy flux limit for the unpressurized system, which will lead to limit the power capacity and the outlet air temperature enhancement.     

Performance of a double pass solar air collector

Double pass counter flow solar air collector with porous material in the second air passage is one of the important and attractive design improvement that has been proposed to improve the thermal performance. This paper presents theoretical and experimental analysis of double pass solar air collector with and without porous material. A mathematical model has been developed based on volumetric heat transfer coefficient. Effects of various parameters on the thermal performance and pressure drop characteristics have been discussed. Comparison of results reveals that the thermal efficiency of double pass solar air collector with porous absorbing material is 20-25% and 30-35% higher than that of double pass solar air collector without porous absorbing material and single pass collector respectively.     

Heat transfer performance analysis of a solar flat-plate collector with an integrated metal foam porous structure filled with paraffin

The analysis of energy storage process of a solar flat-plate collector with an integrated aluminum foam porous structure filled with paraffin as the phase-change medium is reported in this paper. The momentum conservation of liquid paraffin is modeled with Darcy’s law with the Brinkman–Forchheimer’s extension, while heat transfer between the metal foams and paraffin in solid and liquid phases is modeled with a two-temperature model. It is shown that the assumption of the local thermal equilibrium between the metal foams and paraffin invoked in previous studies is inappropriate in predicting the heat transfer behavior, whereas the two-temperature model proposed in this work without this assumption can more realistically predict the real-world phase-change heat transfer process in the solar collector. In particular, the numerical results indicate that the heat transfer performance can be significantly improved by using the aluminum foams filled with paraffin.     

泡沫铝通道内瞬态流动的平均换热系数

针对泡沫铝金属填充矩形通道内的对流换热开展了瞬态实验研究,分析了泡沫铝孔径(孔隙率)、流体流量(流速)等关键参数的影响。为了有效地处理实验数据,重新定义并推导了平均换热系数的计算公式,得到了泡沫铝通道内流动的平均换热系数,并引入了基于渗透率的雷诺数和达西数,确定了相关换热、流动准则数关系。实验研究表明,流速的增大有利于对流换热的强化:而平均换热系数对泡沫金属孔径较敏感;对于低孔隙率泡沫金属,渗透率成为影响换热强度的主要因素,相同或接近的孔隙率下,孔径越大,渗透率和达西数越大,越有利于换热,且压损减小。     

Comparison and Analysis of Heat Transfer in Aluminum Foam Using Local Thermal Equilibrium or Nonequilibrium Model

Aluminum foams are favorable in modern thermal engineering applications because of the high thermal conductivity and the large specific surface area. The present study aims to investigate an application of porous aluminum foam by using the local thermal equilibrium (LTE) and local thermal nonequilibrium (LTNE) heat transfer models. Three-dimensional simulations of laminar flow (porous foam zone), turbulent flow (open zone), and heat transfer are performed by a computational fluid dynamics approach. In addition, the Forchheimer extended Darcy's law is employed to evaluate the fluid characteristics. By comparing and analyzing the average and local Nusselt numbers, it is found that the LTNE and LTE models can reach the same Nusselt numbers inside the aluminum foam when the air velocity is high, meaning that the aluminum foam is in a thermal equilibrium state. Besides, a high interfacial heat transfer coefficient is required for the aluminum foam to reach a thermal equilibrium state as the height of the aluminum foam is reduced. This study suggests that the LTE model can be applied to predict the thermal performance at high fluid velocities or for the case with a large height.     

Numerical and experimental study of forced convection in graphite foams of different configurations

Forced convection heat transfer in a channel with different configurations of graphite foams is experimentally and numerically studied in this paper. The physical properties of graphite foams such as the porosity, pore diameter, density, permeability and Forchheimer coefficient are determined experimentally. The local temperatures at the surface of the heat source and the pressure drops across different configurations of graphite foams are measured. In the numerical simulations, the Navier–Stokes and Brinkman–Forchheimer equations are used to model the fluid flow in the open and porous regions, respectively. The local thermal non-equilibrium model is adopted in the energy equations to evaluate the solid and fluid temperatures. Comparisons are made between the experimental and simulation results. The results showed that the solid block foam has the best heat transfer performance at the expense of high pressure drop. However, the proposed configurations can achieve relatively good enhancement of heat transfer at moderate pressure drop.     

High efficiency solar air heater

This article presents an analysis for a novel type of solar air heater. The main idea is to minimize heat losses from the front cover of the collector and to maximize heat extraction from the absorber. This can be done by forcing air to flow over the front glass cover (preheat the air) before passing through the absorber. Hence, this design needs an extra cover to form a counter-flow heat exchanger. Porous media forms an extensive area for heat transfer, where the volumetric heat transfer coefficient is very high. Hence, using a porous absorber will enhance heat transfer from the absorber to the airstream. In the design of this type of collector, which combines double air passage and porous media, care should be taken to minimize pressure drop. However, the thermal efficiency of this type of collector is significantly higher than the thermal efficiency of conventional air heaters. The thermal efficiency of the suggested collector exceeds 75% under normal operating conditions. The pressure drop is not so significant if high porous medium is used and careful design of U-return section is considered.     

Microtomography-Based Simulation of Transport through Open-Cell Metal Foams

Important heat transfer parameters of aluminum foams of varying pore sizes are investigated through CT-scanning at 20 micron resolution. Small sub-samples from the resulting images are processed to generate feature-preserving, finite-volume meshes of high quality. All three foam samples exhibit similar volumetric porosity (in the range ～91–93%), and thereby a similar thermal conductivity. Effective tortuosity for conduction along the coordinate directions is also calculated. Permeability simulations in the Darcy flow regime with air and water show that the foam permeability is isotropic and is of the order of 10^?7 m². The convective heat transfer results computed for this range of Reynolds numbers exhibit a dependence on the linear porosity, even though the corresponding volumetric porosity is the same for all the samples considered.     

Performance of Forced Convection Heat Transfer in Porous Media Based on Gibson–Ashby Constitutive Model

A novel simulation model is developed for predicting the performance of forced convection heat transfer in the porous metal foam. Based on the physical geometry of the Gibson-Ashby constitutive model, the theoretical model proposed is able to predict the mechanical behaviors and thermal physical properties of porous materials simultaneously. The theoretical predictions of the overall heat transfer coefficient and pressure drop were compared with available experimental data for two different porous foam tubes. The first tube has a porous diameter of 0.6mm and porosity of 0.402, and the other tube has a diameter of 1.6mm and porosity of 0.462. The results show that the relative deviation of the flow pressure drop between the prediction and the experimental data are in the range from 5% to10% while the relative deviation of the overall heat transfer coefficient is about 20%. These deviations are acceptable for applications in engineering. So the feasibility of the Gibson-Ashby constitutive model to be used to predict the performance of flow resistance and convective heat transfer in porous foam ducts is satisfactorily validated.     

Thermal transport analysis in parallel-plate channel filled with open-celled metallic foams

Forced convective heat transfer in highly porous, open-celled metallic foams sandwiched between two infinite parallel plates is analytically modeled using the Brinkman-Darcy and two-equation models. With uniform heat flux, closed-form solutions for fully developed flow and heat transfer are obtained. Nusselt number with explicit expression is derived and the analytical results are verified by existing experimental data. To examine the effect of axial heat conduction neglected in the analytical modeling, numerical simulations, which are verified by the analytical solution, are performed. A modified fin analysis method with improved predicting accuracy compared with the conventional fin analysis method by introducing equivalent foam temperature is also put forward. The predictions obtained with the analytical model, the numerical simulation and the modified fin analysis method are compared with each other, and their pros and cons are discussed. Finally, a systematic parametric study is conducted on heat transfer in parallel-plate channels filled with metallic foams, with useful suggestions for practical designs obtained.     

Numerical investigation of the air flow through a bundle of IP-SOFC modules

The integrated-planar solid oxide fuel cell (IP-SOFC) consists of ceramic modules which have electrochemical cells printed on the outer surfaces. The cathodes are the outermost layer of each cell and are supplied with oxygen from air flowing over the outside of each module. The anodes are in direct contact with the ceramic structure and are supplied with fuel from internal gas channels. An IP-SOFC power plant will contain many modules closely packed together in an array inside a pressure vessel. The air flow is also used to cool the modules. This paper describes a three-dimensional numerical method for simulating the air flow. It uses an explicit time-marching scheme that incorporates a preconditioning method to increase the rate of numerical convergence at low flow velocities. The numerical method is used to simulate the air flow through an array of IP-SOFC modules. The scheme is straightforward to implement and can predict the recirculating flows existing between the modules within an array. The calculation procedure is used to investigate the effect of different sized gaps between modules on the local heat and mass transfer coefficients. The results show the effect of the module arrangement on the flow field and how increasing the gap between modules improves the heat and mass transfer at the module surfaces.     

椭圆管内对流换热与流动阻力特性研究

通过CFD技术,分别对5种长短轴之比的椭圆管管内湍流和层流状态时的换热与流动进行数值研究,分析了流体流动状态和椭圆管长短轴之比对换热系数与流动阻力的影响,并根据数值计算结果拟合出湍流区椭圆管管内换热系数的准则关系式,最后绘制每种类型椭圆管的局部换热系数曲线。研究结果表明:数值计算结果与实验值吻合良好;采用当量直径的方法计算椭圆管内换热系数误差较大;随着雷诺数的增加,每种类型的椭圆管管内阻力系数逐渐减小;而在相同的雷诺数下,随着长短轴之比K的增大,管内阻力系数逐渐增加;每种类型的椭圆管具有类似的局部换热特性,即长半轴两端点处局部换热系数最低,而短半轴两端点处具有最大局部换热系数。     

Fully developed forced convective heat transfer in an annulus partially filled with metallic foams: An analytical solution

An analytical solution for fully developed forced convective heat transfer in an annulus partially filled with metallic foam was proposed. The inner surface attached with an annular metallic foam layer was exposed to constant heat flux while the outer surface was adiabatic. In the metallic foam region, the Brinkman–Darcy equation was used to describe the fluid flow and the thermal non-equilibrium model was employed to establish the heat transfer equations. At the porous-fluid interface, no-slip coupling conditions were utilized to couple flow and heat transfer of the porous and open regions. A closed-form analytical solution was obtained for velocity and temperature profiles. The explicit form of friction factor and the Nusselt (Nu) number were also provided. The solutions were validated by two extreme cases: the empty annulus and the annulus fully filled with metallic foam. The effects of key parameters on friction factor, Nu number, and j/f^1/3 were examined. The relationship between flow heterogeneity and heat transfer was also discussed by introducing the flow heterogeneity coefficient. The porosity, pore density, and foam thickness for engineering applications were recommended. In the present analytical solution, a benchmark was also established for improving discretizing schemes in numerical works.     

Experimental and numerical studies of the pressure drop in ceramic foams for volumetric solar receiver applications

This paper presents experimental and numerical studies of the pressure drop in ceramic foams for solar air receiver applications. There are three main aims in this study. The first is to measure the pressure drop in the studied ceramic foams, and to build an empirical model based on the experimental results and a parametric numerical simulation. The second aim is to study flow field characteristics in the ceramic foams, especially in the vicinity of the interface. The third is to study the pressure drop characteristics of two modified structures (by manufacturing holes on the ceramic foams) that are expected to decrease the pressure drop in ceramic foams, but maintain good heat transfer properties. The experimental results from the samples, including two modified structures, along with the simulation results, show that the pressure drop in the ceramic foams follows a modified Darcy relationship. The experimental results also show that the two modified structures dramatically decrease the pressure drop (with pressure drop decreases up to 70% at a superficial velocity of 5 m/s). Based on both the experimental and the simulation results, a generalized model for predicting the pressure drop in ceramic foams was proposed.     

Finite-volume modelling of heat and mass transfer during convective drying of porous bodies – Non-conjugate and conjugate formulations involving the aerodynamic effects

In this study, a numerical procedure is outlined and representative results for heat and mass transfer during convective drying of porous bodies are presented. The Luikov model was implemented and applied both on individual samples of construction materials and agricultural products, as well as on a drying-chamber scale, with parallel flow of a hot air stream over rectangular slabs which represent the product to be dried. In the latter case the configuration is an experimental dryer in which the heat source is a solar air collector with evacuated tubes. A general approach was developed that allows a selection between modelling of phenomena either in the drying solid only, or considering an extended simulation domain encompassing, apart from the solid body, the flow of air as well. In the second case, the solution of the flow field is pursued along with a conjugate heat/mass transfer problem coupling the solid and fluid phenomena and in both cases phase change (evaporation) was taken into account. For the numerical simulation, the finite-volume method was used. The validation of the model was based on experimental and numerical results from the literature and results from simulations that were conducted in the pursuit of the energetic optimization of an experimental solar dryer of NCSR “Demokritos” are presented. In the latter case, the effect of the particular flow field features developing for a single and a double-plate configuration on the heat/mass transport and drying rates is demonstrated. Such a methodology could be used to analyze the transport phenomena in any type of convective dryer, including those utilizing solar energy as the heat source.