Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Indentation of sandwich beams with metal foam core

The quasi-static indentation behavior of sandwich beams with a metal foam core was investigated. An analytical model was developed to predict the large deflections of indention of the sandwich beams with a metal foam core subjected to a concentrated loading. The interaction of plastic bending and stretching in the local deformation regions of the face sheet was considered in the analytical model. Moreover, the effects of the shear strength of the foam core on the indentation behavior were discussed in detail. The finite element simulations were preformed to validate the theoretical model. Comparisons between the analytical predictions and finite element results were conducted and good agreement was achieved. The results show that the membrane force dominates indentation behavior of the sandwich beams when the maximum deflection exceeds the thickness of the face sheet.

The effects of relative density of metal foams on the stresses and deformation of beam under bending

The exact analytic solution of the pure bending beam of metallic foams is given. The effects of relative density of the material on stresses and deformation are revealed with the Triantafillou and Gibson constitutive law （TG model） taken as the analysis basis. Several examples for individual foams are discussed, showing the importance of compressibility of the cellular materials. One of the objects of this study is to generalize Hill＇s solution for incompressible plasticity to the case of compressible plasticity, and a kinematics parameter is brought into the analysis so that the velocity field can be determined.

Performance Evaluation of Electromagnetic Shield Constructed from Open-Cell Metal Foam Based on Sphere Functions

This study evaluates the performance of a model of open-cell metal foams generated by sphere functions.To this end,an electromagnetic shield constructed from the model was inserted between two horn antennas in an electromagnetic wave propagation simulation.The foam-hole diameter in the electromagnetic shield model was varied as d=2.5 and 5.0 mm,and the frequency of the electromagnetic waves was varied from 3 to 13 GHz.In the numerical experiments of shield effectiveness,the shields with foam holes of both diameters attenuated the electromagnetic waves across the studied frequency range.The shield effectiveness was enhanced at low frequencies and in the shield with smaller hole diameter.

Thermal Modeling and Analysis of Metal Foam Heat Sink with Thermal Equilibrium and Non-Equilibrium Models

In the present study,the thermal performance of metal foam heat sink was numerically investigated by adopting the local thermal non-equilibrium(LTNE)model and local thermal equilibrium(LTE)model.Temperature field distributions and temperature difference field distributions of solid and fluid phases were presented.Detailed thermal performance comparisons based on the LTE and LTNE models were evaluated by considering the effects of the relevant metal foam morphological and channel geometrical parameters.Results indicate that a distinct temperature difference exists between the solid and fluid phases when the LTNE effect is pronounced.The average Nusselt numbers predicted by both the LTE and LTNE models are approaching with the increase of porosity,pore density,Reynolds number,large thermal conductivity ratio,and large aspect ratio.This is attributed to the significant reduction of the interstitial convective thermal resistance between the solid and fluid phases,as a result,the LTE model can replace the LTNE model for thermal modeling in these conditions.In addition,the overall thermal performance assessment of metal foam heat sink is compared with the non-porous heat sink,and it shows that the thermal performance factor of metal foam heat sink is approximately two times of the non-porous heat sink.

Preparation of open-cell metal foams by investment cast

Metal foams are a new kind of materials with low densities and novel physical, mechanical, thermal, electrical and acoustic properties. They can be divided into closed and open cell structures. In this paper the open cell structures, called sponges, were treated. A new technique to manufacture sponges by plaster investment casting was described. Experimental results show that it is essential to make a sound plaster mould by casting plaster slurry into the polyurethane foams and infiltrate the open channels of the baked plaster mold by molten metal. The optimal processes include plaster slurry preparation, plaster mold baking, and molten metal infiltration. The sponge sample with porosity of 97% is presented.

A Modified Kelvin Model for Thermal Performance Simulation of High Mechanical Property Open-Cell Metal Foams

This paper proposes a modified Kelvin model for high mechanical property open-cell metal foams and investigates its application in thermal simulations. The thermal conductivity is simulated based on the steady state method and the results are consistent with experimental values. The melting process of phase change materials (PCMs) in Kelvin model and its modified model is numerically investigated under a temperature constant heat resource. By detecting the temperature variations, it shows that the metal foam greatly improves the heat transfer in energy storage systems. Besides, the comparison of the melting process in two foam models indicates that the systems based on high mechanical property metal foams have a shorter melting time. The melting process of paraffin in modified Kelvin metal foam models with three different porosities (65%, 70% and 75%) are numerically analyzed and compared.

Experimental Study on Heat Storage Properties Comparison of Paraffin/Metal Foams Phase Change Material Composites

Heat storage properties of phase change materials(PCMs) are essential characteristics that perform a key role in thermal heat energy storage systems.The thermal properties of PCMs can be improved by developing metal foam/PCM composites.The addition of metal foam in PCMs has a significant effect on the thermal characteristics of PCMs.In this paper,the heat storage properties of two different metal foam/PCM composites were experimentally examined.The behavior of paraffin in metal foam(copper and iron-nickel)/paraffin composites concerning pure paraffin at a constant heat flux of 1000 W/m^(2) in three directions simultaneously(x,y,and z) was studied.Paraffin was infiltrated into copper and iron-nickel foams to develop composite materials which resulted in enhancing the thermal conductivity of the paraffin.A comparative analysis is made on the heat storage properties of paraffin in copper and iron-nickel foams/paraffin composites.Inner temperature distribution during the phase transition process is experimentally evaluated.This comparison indicates that temperature uniformity in copper foam/paraffin composite is better than in iron-nickel foam/paraffin composite and pure paraffin at the same heat flux.Experimental results show that at heat flux of 1000 W/m^(2),the heat storage time for copper foam/paraffin composite is 20.63% of that of iron-nickel foam/paraffin composite.

Double-layered skeleton of Li alloy anchored on 3D metal foam enabling ultralong lifespan of Li anode under high rate

The high specific capacity and low negative electrochemical potential of lithium metal anodes(LMAs),may allow the energy density threshold of Li metal batteries(LMBs)to be pushed higher.However,the existing detrimental issues,such as dendritic growth and volume expansion,have hindered the practical implementation of LMBs.Introducing three-dimensional frameworks(e.g.,copper and nickel foam),have been regarded as one of the fundamental strategies to reduce the local current density,aiming to extend the Sand'time.Nevertheless,the local environment far from the skeleton is almost the same as the typical plane Li,due to macroporous space of metal foam.Herein,we built a double-layered 3D current collector of Li alloy anchored on the metal foam,with micropores interconnected macropores,via a viable thermal infiltration and cooling strategy.Due to the excellent electronic and ionic conductivity coupled with favorable lithiophilicity,the Li alloy can effectively reduce the nucleation barrier and enhance the Li^(+)transportation rate,while the metal foam can role as the primary promotor to enlarge the surface area and buffer the dimensional variation.Synergistically,the Li composite anode with hierarchical structure of primary and secondary scaffolds realized the even deposition behavior and minimum volume expansion,outputting preeminent prolonged cycling performances under high rate.

Study on the melting process of phase change materials in metal foams using lattice Boltzmann method

A thermal lattice Boltzmann model is developed for the melting process of phase change material (PCM) embedded in open-cell metal foams. Natural convection in the melt PCM is considered. Under the condition of local thermal non-equilibrium between the metal matrix and PCM, two evolution equations of temperature distribution function are pre-sented through selecting an equilibrium distribution function and a nonlinear source term properly. The enthalpy-based method is employed to copy with phase change problem. Melting process in a cavity of the metal foams is simulated using the present model. The melting front locations and the temperature distributions in the metal foams filled with PCM are obtained by the lattice Boltzmann method. The effects of the porosity and pore size on the melting are also investigated and discussed. The re-sults indicate that the effects of foam porosity play important roles in the overall heat transfer. For the lower porosity foams, the melting rate is comparatively greater than the higher porosity foams, due to greater heat conduction from metal foam with high heat conductivity. The foam pore size has a limited effect on the melting rate due to two counteracting effects between conduction and convection heat transfer.

Bestow metal foams with nanostructured surfaces via a convenient electrochemical method for improved device performance

Metal foams have been intensively studied as three-dimensional （3-D） bulk mass-support for various applications because of their high conductivities and attractive mechanical properties. However, the relatively low surface area of conventional metal foams largely limits their performance in applications such as charge storage. Here, we present a convenient electrochemical method for addressing this problem using Cu foams as an example. High surface area Cu foams are fabricated in a one-pot one-step manner by repetitive electrodeposition and dealloying treatments. The obtained Cu foams exhibit greatly improved performance for different applications like surface enhanced Raman spectroscopy （SERS） substrates and 3-D bulk supercapacitor electrodes.

A review on thermal application of metal foam

Heat exchangers embedded with metal foam are drawing increasing attention in the thermal application field,due to the performance of low density,large ratio of surface area to volume as well as high thermal conductivity. In these applications,compact heat exchanger,solar thermal facilities and thermal energy storage are the three core components. This paper focuses on the lasted advances in thermal applications,presenting a review of theoretical and experimental progress over metal foam in thermal application. The empirical and theoretical models for pressure drop,heat transfer coefficient and performance evaluation criteria of compact heat exchangers with metal foam are reviewed and discussed,especially different optimized configurations.There is a trade-off between heat transfer enhancement and increase of pressure drop. Some exploratory work performed by present authors are also introduced. The manufacturing,heat transfer and flow characteristics of tube bundle wrapped with metal foam are taken into account for optimization of heat exchanger. It is confirmed that the conversion mechanism of heat transfer is carried out that heat conduction is the dominative term at high dimension permeability. The correlations of heat transfer rate and pressure drop for staggered and single row tube bundle wrapped with metal foam are concluded,respectively. The effects of different bonding methods are revealed for point-contact in metal foam and base tube. The powder-sintering method can provide a stable and minimum-thickness bonding layer. Various types of solar thermal facilities utilized metal foam to improve the energy conversion efficiency from solar radiant energy to thermal energy are also reviewed and discussed,including solar collector for intermediate-low temperature utilization and solar receiver for high temperature utilization. The Last but not least,existing and future metal foam thermal application stations are overviewed.

Vibration and Buckling Analyses of Sandwich Plates Containing Functionally Graded Metal Foam Core

In the present work,free vibration and buckling analyses of sandwich plates with various functionally graded foam cores are carried out.Foam cores are assumed to be made of metal,and three different configurations of the porous distribution in the core layer are taken into consideration.To carry out a comparative study between the distributions of pores in the core foam,the mass of foam in all three cases is kept the same.The vibration and buckling behaviors of skew plates are also analyzed as a part of the current investigation.The principle of minimization of potential energy and Hamilton’s principle are used for the derivation of the governing equations,while a C-0 finite element-based higher-order zigzag formulation is developed to solve the free vibration and buckling problems.The influences of gradation laws,boundary conditions,skew angle and geometry of plates are studied in detail for the dynamic and stability characteristics.It is found that both the non-dimensional natural frequency and buckling load decrease with the increase in the thickness of the metal foam cores,while they show an increasing trend as the skew angle of the plate increases.

Theoretical and experimental advances on heat transfer and flow characteristics of metal foams

Open cell metal foam can be applied to greatly improve thermal performance of heat sink and heat exchanger,so that it has been widely used in the fields of thermal(or heat)control system of aerospace vehicle and energy utilization system and become a very important topic for research in the aerospace thermophysics field,and more and more attentions have been attracted.The optimal design of metal foam heat transfer devices is based on the understanding the flow and heat transfer characteristics in metal foam.This article reviews some recent progresses of theoretical and experimental researches on heat transfer enhancement and flow characteristics of metal foam.We found that the pore cell simplification models of metal foams generally fall into four categories,among which the most commonly used cell model is Kelivin model.Some exploratory works performed by the current authors are also introduced,such as the effect of boundary conditions on the heat transfer enhancement;the theoretical modelling of interfacial convective heat transfer taking into account heat conduction between foam ligaments;and the flow characteristics under relatively high velocity.The analytical results show that the flow characteristics of metal foam at relatively high speed are completely different from those at low speed,a further thorough study of the heat transfer and flow characteristics of metal foam is necessarily required.In this paper,two types of partial filling techniques are discussed.The heat transfer performance of partially filled tubes was evaluated by both the performance evaluation criteria and the performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving.The results show that the filling type of metal foam have a significant impact on its heat transfer enhancement performance.Therefore,the filling method of metal foam should be further studied,in order to optimize the thermophysical properties of heat transfer devices.

Compression behavior of metal foams with real pore structures through CT scan images

Based on the real pore structure obtained from computed tomography(CT)scan images,a three-dimensional(3D)model of the metal foam sample with specified porosity is established,and the model is compressed and simulated by finite element method with the simulation results compared with the experimental test results for validation.At the same time,based on the spatial distribution characteristics of cells extracted from 3D model construction,a widely used metal foam model with Voronoi pore structure or spherical pore structure was established and simulated under compression.The two compression simulation results with regular pore structure models were also compared with the experimental results and CT model results to study the influence of cell wall morphology on the compression performance of metal foams.The simulation results show that CT model agrees well with the experimental results and is more accurate than Voronoi pore or spherical pore model,which can provide a more reasonable option for investigation of metal foams.

Numerical Investigation on Pool Boiling Mechanism of Hybrid Structures with Metal Foam and Square Column by LBM

In the present study, pool boiling heat transfer performance and bubble behaviors of hybrid structures with metal foam and square column are investigated by lattice Boltzmann method. By using the vapor-liquid phase change model of Gong-Cheng and Peng-Robinson equation of state, the effects of structural parameters, including metal foam thickness, porosity, column height and ratio of column width(W) to gap spacing(D) are investigated in details. The results show that hybrid structure performs better than pure columnar structure in pool boiling heat transfer. The hybrid structure accelerates bubble growth by fluid disturbance while metal skeletons prevent the bubble escaping. The optimum ratio of column width to gap spacing decreases with the increase of heat flux and HTC(heat transfer coefficient) can achieve an increase up to 25% when W/D change from 5/3 to 1/3. The increase of column height enhances heat transfer by expanding surface area and providing space for bubble motion. The metal foam thickness and porosity have a little influence on pool boiling heat transfer performance, but they have an important effect on bubble motion in the regime.

Thermal Analysis of Metal Foam Matrix Composite Phase Change Material

In this paper,CPCM(Composite Phase Change Material)was manufactured with metal foam matrix used as filling material.The temperature curves were obtained by experiment.The performance of heat transfer was analyzed.The experimental results show that metal foam matrix can improve temperature uniformity in phase change thermal storage material and enhance heat conduction ability.The thermal performance of CPCM is significantly improved.The efficiency of temperature control can be obviously improved by adding metal foam in phase change material.CPCM is in solid-liquid two-phase region when temperature is close to phase change point of paraffin.An approximate plateau appears.The plateau can be considered as the temperature control zone of CPCM.Heat can be transferred fiom hot source and be uniformly spread in thermal storage material by using metal foam matrix since thermal storage material has the advantage of strong heat storage capacity and disadvantage of poor heat conduction ability.Natural convection promotes the melting of solid-liquid phase change material.Good thermal conductivity of foam metal accelerates heat conduction of solid-liquid phase change material.The interior temperature difference decreases and the whole temperature becomes more uniform.For the same porosity with a metal foam,melting time of solid-liquid phase change material decreases.Heat conduction is enhanced and natural convection is suppressed when pore size of metal foam is smaller.The thermal storage time decreases and heat absorption rate increases when the pore size of metal foam reduces.The research results can be used to guide fabricating the CPCM.

Comparative study on heat transfer enhancement of metal foam and fins in a shell-and-tube latent heat thermal energy storage unit

Metal foam and fins are two popular structures that are employed to enhance the heat transfer of phase change materials in shell-and-tube heat storage units.However,it remains unclear which structure is better in terms of energy storage performance.In this study,the heat transfer enhancement performances of metal foam and fins are compared to provide guidance on the optimal structure to be chosen for practical applications.Three fin structures(four fins,two vertical fins,and two horizontal fins)are considered.Under the full configuration(volume fraction of metal=3%),the unit with four fins was found to have a faster melting rate than those with vertical or horizontal fins.In other words,increasing the number of fins helps to accelerate the melting process.Nevertheless,the unit with metal foam enhancement has the highest melting rate.Under the half configuration(volume fraction of metal=1.5%),the melting rate of the unit enhanced by metal foam is significantly decreased,whereas there is no remarkable changes in the units enhanced by fins.However,metal foam is still shown to be the best thermal enhancer.The energy storage rate of the unit enhanced by metal foam can be up to 10 times higher than that of the unit enhanced by fins.

Solidification in a shell-and-tube thermal energy storage unit filled with longitude fins and metal foam:A numerical study

In this study,an innovative thermal energy storage design method was developed by adding the combination of metal foam and fin to phase change materials(PCMs).A numerical model was built and verified based on the comparison among the present model prediction,experimental measurements,and numerical results in open lit-erature.To highlight the novel design method,four cases including fin-PCM,foam-PCM,fin-foam-PCM,and PCM unit were compared by means of solidification features.The temperature distribution,solidification front propa-gation,and buoyancy-induced convection in the liquid PCM were accounted for.Numerical results demonstrated that metal foam outperformed fin regarding the improvement on solidification phase change.The combination of foam and fin achieved the best performance,leading to a 90.5%reduction in complete energy release time in comparison with the PCM unit.The proposed design method provided reference potentials for advancing energy storage engineering.However,buoyancy-induced convection in the liquid PCM before solidification was harmful to the formation of solidification front and its movement.A maximal 11.5%prolonging time for the complete solidification was found.

Experimental investigation of a latent heat thermal energy storage unit encapsulated with molten salt/metal foam composite seeded with nanoparticles

Molten salt has been widely used in latent heat thermal energy storage(LHTES)system,which can be incorporated into hybrid photovoltaic/thermal solar system to accommodate the built environment.Solar salt(60 wt.%NaNO 3 and 40 wt.%KNO 3)was employed as the phase change materials(PCMs)in this study,and both aluminum oxide(Al_(2)O_(3))nanopowder and metal foam were used to improve the properties of pure solar salt.The synthesis of the salt/metal foam composites seeded with Al_(2)O_(3)nanopowder were performed with the two-step and impregnation methods,and the composite PCMs were characterized morphologically and thermally.Then pure solar salt,the salt/2 wt.%Al_(2)O_(3)nanopowder and salt/copper foam composite seeded with 2 wt.%Al_(2)O_(3)nanopowder were encapsulated in a pilot test rig,respectively,where a heater of 380.0 W was located in the center of the LHTES unit.The charging and discharging processes of the LHTES unit were conducted extensively,whereas the heating temperatures were controlled at 240℃,260℃and 280℃respectively.Temperature evolutions at radial,angular and axial positions were recorded,and the time-durations and volumetric mean powers during the charging and discharging processes were obtained and calculated subsequently.The results show that physical bonding between Al_(2)O_(3)nanopowder and nitrate molecule has been formed from the morphological pictures together with XRD and FTIR curves.Slight changes are found between the melting/freezing phase change temperatures of the salt/metal foam composites seeded with Al_(2)O_(3)nanopowder and those of pure solar salt,and the specific heats of the salt/Al_(2)O_(3)nanopowder composite slightly increase with the addition of Al_(2)O_(3)nanopowder.The time-duration of the charging process for the salt/copper foam composite seeded with Al_(2)O_(3)nanopowder at the heating temperature of 240℃can be reduced by about 74.0%,compared to that of pure solar salt,indicating that the heat transfer characteristics of the LHTES unit encapsulated with the salt/copper foam composite seeded with Al_(2)O_(3)nanopowder can be enhanced significantly.Consequently,the mean volumetric powers of the charging process were distinctly enhanced,e.g.,the volumetric mean power of heat storage can reach 110.76 kW/m 3,compared to 31.94 kW/m 3 of pure solar salt.However,the additive has little effect on the volumetric mean power of heat retrieval because of the domination of natural air cooling.