Foam Model Research Articles

High heat transfer performance of foam freezing in phase change cold energy storage process

Phase change material (PCM) has high energy storage density, but the cold energy charging rate of PCM decreases seriously with the increase of frozen thickness. The foam freezing produced by cold air flow can sharply increase the freezing rate. This research attempts to establish a theoretical model to quantify the heat transfer performance of foam freezing. The internal structure of the foam was obtained by experiment. The heat transfer process of single bubble was simulated by FLUENT, and analytical models for single bubble and foam were established. It was found that the tangent bubble array had the same heat transfer effect as the actual foam in freezing, and the bubble temperature variation obeyed the exponential distribution. The radius of more than 50% bubbles was about 2.5 mm, and the convective heat transfer coefficient in the bubble was 65 W/(m2. K). The maximum completed heat transfer rate of foam freezing was 688 kW/m3, when the air temperature was -20 °C. Foam freezing was compared with common ice storage structures, and was found had an order of magnitude higher than those structures in the heat transfer coefficient of unit volume.

Equivalent Parallel Strands Modeling of Highly-Porous Media for Two-Dimensional Heat Transfer: Application to Metal Foam

A new geometric modeling of isotropic highly-porous cellular media, e.g., open-cell metal, ceramic, and graphite foams, is developed. The modelling is valid strictly for macroscopically two-dimensional heat transfer due to the fluid flow in highly-porous media. Unlike the current geometrical modelling of such media, the current model employs simple geometry, and is derived from equivalency conditions that are imposed on the model’s geometry a priori, in order to ensure that the model produces the same pressure drop and heat transfer as the porous medium it represents. The model embodies the internal structure of the highly-porous media, e.g., metal foam, using equivalent parallel strands (EPS), which are rods arranged in a spatially periodic two-dimensional pattern. The dimensions of these strands and their arrangement are derived from equivalency conditions, ensuring that the porosity and the surface area density of the model and of the foam are indeed equal. In order to obtain the pressure drop and heat transfer results, the governing equations are solved on the geometrically-simple EPS model, instead of the complex structure of the foam. By virtue of the simple geometry of parallel strands, huge savings on computational time and cost are realized. The application of the modeling approach to metal foam is provided. It shows how an EPS model is obtained from an actual metal foam with known morphology. Predictions of the model are compared to experimental data on metal foam from the literature. The predicted local temperatures of the model are found to be in very good agreement with their experimental counterparts, with a maximum error of less than 11%. The pressure drop in the model follows the Forchheimer equation.

An Investigation on Mechanical and Microstructural Properties of Porous Nickel-Based Alloy Fabricated by Investment Casting as an Implant Materials

In this study, Nickel-Chrome-Molybdenum alloy is manufactured using investment casting method with centrifugal casting device from a polyurethane foam model in a regular and open-pore form, as a hard tissue implant. The samples produced have 10, 20, and 30 (±3) pores per inch and 0.0008, 0.0017, and 0.0027 g/mm3 densities, respectively. Young’s modulus, hardness and mechanical behaviors of the samples were investigated by SEM, EDS and compressive test. As a result, it is seen that the pore size and the pore wire diameter of the samples could be controlled thus compression strength and young modulus. In this way it was understood that an implant material could be produced with similar mechanical properties to the human bone.

Danlou Tablets Inhibit Atherosclerosis in Apolipoprotein E-Deficient Mice by Inducing Macrophage Autophagy: The Role of the PI3K-Akt-mTOR Pathway.

Atherosclerosis (AS) is a type of chronic vascular disease, and its etiology is not yet fully understood. AS is characterized by lipid deposition, atherosclerotic plaque formation, vascular stenosis or even complete blockage of the blood vessel wall. Clinical studies have shown that Danlou tablets (DLTs) can improve the heart function, quality of life, and prognosis of patients with coronary heart disease and myocardial infarction. However, its mechanism of action remains unknown. Our study revealed that DLTs ameliorated ApoE−/−AS mouse aortic atherosclerotic plaques [hematoxylin-eosin (HE) staining and small animal ultrasound] and reduced CD68+ macrophage infiltration, the expression of the inflammatory factor interferon-gamma (IFN-γ), vascular smooth muscle α-actin, and serum lipid levels. In vitro, in the macrophage foaming model, DLTs partially restored the activity of RAW264.7 cells, reduced the uptake of lipid droplets, and inhibited lipid droplet accumulation and apoptosis within BMDMs. We also found that Torin1, an autophagy agonist, reduced intracellular lipid deposition in BMDMs, as did DLTs. Moreover, DLTs upregulated the expression of the autophagy-related protein LC3II and decreased p62 accumulation in RAW264.7 cells. DLTs also inhibited the phosphorylation of p-PI3K, p-Akt, and p-mTOR, leading to upregulated autophagy in RAW264.7 cells. In summary, our results suggested that DLTs can promote autophagy in macrophages by inhibiting the PI3K/Akt/mTOR signaling pathway, thereby reducing foam cell formation and improving atherosclerosis.

Ultrahigh-energy photons from LHAASO as probes of Lorentz symmetry violations

The Large High Altitude Air Shower Observatory (LHAASO) is one of the most sensitive gamma-ray detector arrays currently operating at TeV and PeV energies. Recently the LHAASO experiment detected ultra-high-energy (UHE; ${E}_{\ensuremath{\gamma}}\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{TeV}$) photon emissions up to 1.4 PeV from twelve astrophysical gamma-ray sources. We point out that the detection of cosmic photons at such energies can constrain the photon self-decay motivated by superluminal Lorentz symmetry violation (LV) to a higher level, thus can put strong constraints to certain LV frameworks. Meanwhile, we suggest that the current observation of the PeV-scale photon with LHAASO may provide hints to permit a subluminal type of Lorentz violation in the proximity of the Planckian regime, and may be compatible with the light speed variation at the scale of $3.6\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$ recently suggested from gamma-ray burst (GRB) time delays. We further propose detecting PeV photons coming from extragalactic sources with future experiments, based on LV-induced threshold anomalies of ${e}^{+}{e}^{\ensuremath{-}}$ pair-production, as a crucial test of subluminal Lorentz violation. We comment that these observations are consistent with a D-brane/string-inspired quantum-gravity framework, the space-time foam model.

Effective spin foam models for Lorentzian quantum gravity

Making the Lorentzian path integral for quantum gravity well-defined and computable has been a long standing challenge. In this work we adopt the recently proposed effective spin foam models to the Lorentzian case. This defines a path integral over discrete Lorentzian quantum geometric configurations, which include metric and torsion degrees of freedom. The torsion degrees of freedom arise due to an anomaly, which is parameterized by the Barbero–Immirzi parameter. Requiring a semi-classical regime constrains this parameter, but the precise bound has to be determined by probing the dynamics. The effective models provide the computationally most efficient spin foam models yet, which allows us to perform first tests for determining the semi-classical regime. This includes explorations specific to the Lorentzian case, e.g. investigating quantum geometries with null lengths and null areas as well as geometries that describe a change of spatial topology.

Development of a crushable foam model for human trabecular bone

Finite element (FE) simulations can be used to evaluate the mechanical behavior of human bone and allow for quantitative prediction of press-fit implant fixation. An adequate material model that captures post-yield behavior is essential for a realistic simulation. The crushable foam (CF) model is a constitutive model that has recently been proposed in this regard. Compression tests under uniaxial and confined loading conditions were performed on 59 human trabecular bone specimens. Three essential material parameters were obtained as a function of bone mineral density (BMD) to develop the isotropic CF model. The related constitutive rule was implemented in FE models and the results were compared to the experimental data. The CF model provided an accurate simulation of uniaxial compression tests and the post-yield behavior of the stress-strain was well-matched with the experimental results. The model was able to reproduce the confined response of the bone up to 15% of strain. This model allows for simulation of the mechanical behavior of the cellular structure of human bone and adequately predicts the post-yield response of trabecular bone, particularly under uniaxial loading conditions. The model can be further improved to simulate bone collapse due to local overload around orthopaedic implants.

Fatigue analysis of closed-cell aluminium foam using different material models

The fatigue analyses of AlSi7 closed-cell aluminium foam were performed using a real porous model and three different homogenised material models: crushable foam model, isotropic hardening model and kinematic hardening model. The numerical analysis using all three homogenised material models is based on the available experimental results previously determined from fatigue tests under oscillating tensile loading with the stress ratio R=0.1. The obtained computational results have shown that both isotropic and kinematic hardening models are suitable to analyse the fatigue behaviour of closed-cell aluminium foam. Besides, the kinematic hardening material model has demonstrated significantly shorter simulation time if compared to the isotropic hardening material model. On the other hand, the crushable foam model is recognized as an inappropriate approach for the fatigue analyses under tension loading conditions.

Performance assessment of a range-extended electric vehicle under real driving conditions using novel PCM-based HVAC system

In this research paper, a novel Heating, Ventilation, and Air Conditioning (HVAC) system is proposed to mitigate the unfavorable effects of conventional HVAC systems on the Electric Vehicle (EV) range. The HVAC system is composed of a heat pump (HP) system with an additional phase change material (PCM) heat exchanger, which is a shell and tube heat exchanger and is parallel to the external heat exchanger of the heat pump cycle. This heat exchanger is designed to function as both condenser and evaporator in the cycle temporarily. The n-hexadecane is selected as the PCM in the shell, and R134a is the refrigerant in the tubes. The specific melting point of PCM in the comfort zone range leads to diminishing the compressor's power consumption and consequently the whole system. A copper foam is used to enhance the low thermal conductivity of the PCM. The enthalpy-porosity technique with the Volume Averaged Method (VAM) for modeling of the PCM-copper foam is applied for Computational Fluid Dynamics (CFD) analysis of the PCM's melting and solidification cycles in ANSYS Fluent software, and the results are obtained for modeling the heat exchanger in the heat pump cycle. A comprehensive thermal model is developed for the vehicle's cabin to improve the accuracy of the results. Nissan Leaf is modeled as the selected EV at different weather temperatures in the range of −5 °C to 50 °C with the Urban Dynamometer Driving Schedule (UDDS) driving cycle in Simcenter Amesim software. The results show that the proposed system increases the vehicle range by 19% and 11% compared with the conventional heat pump systems at the weather temperatures of 10 °C and 0 °C, respectively. Moreover, the energy consumption of various components in the cold start and hot start are compared and the results are interpreted.

Development and investigation of the applicability of microstructural models for polymeric low density foams directly obtained from computed tomography data

Nowadays, there are several methods to obtain simulation models for foams which consider important microstructural features. This research study presents a method to obtain low density foam models directly from computed tomography (CT) data. Finite element meshes are created from CT measurement results of a polypropylene extrusion foam with two different densities. Sensitivity studies with regard to the tension behaviour are performed with the microstructural models. The study shows that the tension behaviour highly depends on the examined area of the foam because the microstructure and density vary through the foam. Furthermore, the simulation results are validated with experimental results. The validation shows that the tension behaviour of the investigated foams characterised by the simulation approach is in good agreement with the experimentally observed behaviour and that specific microstructural characteristics (e.g. anisotropic cell shapes) are captured in the model.

Development of Ignition Time and Mass Loss Rate Prediction Models for Rigid Polyurethane Foam with Multi-Step Thermal Degradation Under Various External Heat Flux Conditions

Development of Ignition Time and Mass Loss Rate Prediction Models for Rigid Polyurethane Foam with Multi-Step Thermal Degradation Under Various External Heat Flux Conditions

Response of functionally graded polymeric foam under axial compression

Polymeric foams are widely used for many impact protection applications, and functionally graded foam materials with density-gradient strategies have been increasingly studied for their flexible and designable energy absorption applications. This study aims to develop an analytical model to predict the responses of functionally graded polymeric foam (FGPF) under uniaxial compression loads. The expanded polystyrene (EPS), which is the most common polymeric foam, was selected as a representative foam in this study. The constitutive model for uniform-density EPS foam under uniaxial compression was first developed and then validated by the uniaxial quasi-static and dynamic compression experiments. Based on the assumption that FGPF is a combination of numerous independent uniform-density EPS foam layers, the idealised rigid-perfectly plastic-locking (R-PP-L) model was adopted to develop an analytical model for predicting the stress-strain correlations of FGPF under uniaxial compressive loads. Based on the validated constitutive model of EPS foam, the FGPF finite element model was also established to validate the analytical model. It is demonstrated that the analytical model can be applied to predict the compressive stress-strain relations of FGPF under the loading conditions of low to moderate strain-rates (10−3 s−1 ∼ 102 s−1). This study also showed that FGPF can be designed using the optimization method to maximise its crashworthiness performance. The proposed analytical method and the optimization procedure could be used for other functionally graded foam materials.

Foam Flow in Different Pore Systems—Part 2: The Roles of Pore Attributes on the Limiting Capillary Pressure, Trapping Coefficient, and Relative Permeability of Foamed Gas

Summary The limiting capillary pressure of foam (Pc*) and foam trapping in porous media are pore-scale foam properties that affect foam transport in porous media. They are strongly influenced by the characteristics of rock pores and throats. Because of experimental limitations, these foam properties are difficult to measure at core scale. As a result, our understanding of their relationship with different pore characteristics is limited. In this paper, novel coreflood and graphical analysis techniques were used to measure Pc* and the foam-trapping coefficient (FTC) at core scale. FTC is a new parameter synonymous to Land’s (1968) trapping coefficient, which describes foam-trapping behavior across an entire range of saturation as opposed to a single endpoint trapped saturation. The scalability of these two foam properties with permeability and other pore characteristics [average pore size (PS), average throat size (TS), average aspect ratio (AR), coordination number (CN), surface area/volume ratio, and reservoir-quality index (RQI)] were also investigated. Pore characteristics of 12 different rock samples were measured from 3D pore-network models generated from high-resolution X-ray computed-microtomography images. The heterogeneity of the rock samples were quantified by the Dykstra-Parsons index (Dysktra and Parsons 1950), while the RQI and J-function methods were used to classify them according to their storage and flow properties. Each of the measured pore characteristics and their combination [combined pore character (CPC)] were then correlated with Pc* and FTC to understand their respective roles. Furthermore, the data points obtained from the graphical analysis of the coreflood data provided the required input data for a mechanistic foam model for relative permeability of foamed gas (Kovscek and Radke 1994). The estimated relative permeability of foamed gas was then used to study foam mobility in the different pore geometries. The overall results showed the following: P c * has strong negative correlations with all pore characteristics except AR, which has a weak positive correlation. P c * has the strongest correlation with RQI, CPC, and permeability; a moderate correlation with CN and TS; and a very weak correlation with PS. Foam trapping has positive correlations with all pore characteristics except AR, which has a negative correlation. Low AR appears to be responsible for significant trapping of foam in high-permeability rocks. Low AR favors more foam trapping, while high AR favors trapping of oil and gas during water imbibition in water-wet rocks. Foam trapping appears to have the dominant control on foam mobility.

Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior

Abstract In the present investigation, a two-dimensional (2D) finite element (FE) model of closed-cell AlSi12Mg1Cu1 alloy foam (AAFs) of 0.35 relative density of different cell shapes, i.e., square, hexagonal, octagonal, and circular shaped cell established with the help of ABAQUS simulation software. Experimentation is also done for 0.35 relative density metal foam to report its compressive behavior. The plateau stress σ p l $\left(\right.{\sigma }_{pl}$ ) and energy absorption capacity (E ab) of AAFs (ρ rd = 0.35) properties are calculated from the plotted stress–strain graph and a significant effect of cell shape on compressive performance observed. By SEM characterization, it was noted that the experimental specimen also had near circular cells. The strength and energy absorption values are calculated for square-shape, circular-shaped, octagonal-shaped, and hexagonal-shaped cells in descending order from maximum to minimum. A convergence study is also carried out concerning the number of elements to obtain the most accurate FE results.

The Lunar Mare Ring‐Moat Dome Structure (RMDS) Age Conundrum: Contemporaneous With Imbrian‐Aged Host Lava Flows or Emplaced in the Copernican?

AbstractRing‐moat dome structures (RMDSs) are small circular mounds of diameter typically about 200 m and ∼3–4 m in height, surrounded by narrow, shallow moats. They occur in clusters, are widespread in ancient Imbrian‐aged mare basalt host units and show mineralogies comparable to those of their host units. Based on these close associations and similarities, a model has been proposed for the formation of RMDS as the result of late‐stage flow inflation, with second boiling releasing quantities of magmatic volatiles that migrate to the top of the flow as magmatic foams and extrude through cracks in the cooled upper part of the flow to produce the small RMDS domes and surrounding moats. In contrast to this model advocating a contemporaneous emplacement of RMDSs and their host lava flows, a range of observations suggests that the RMDS formed significantly after the emplacement and cooling of their host lava flows, perhaps as recently as in the Copernican Period (∼1.1 Ga to the present). These observations include: (a) stratigraphic embayment of domes into post‐lava flow emplacement impact craters; (b) young crater degradation age estimates for the underlying embayed craters; (c) regolith development models that predict thicknesses in excess of the observed topography of domes and moats; (d) landform diffusional degradation models that predict very young ages for mounds and moats; (e) suggestions of fewer superposed craters on the mounds than on the adjacent host lava flows, and (f) observations of superposed craters that suggest that the mound substrate does not have the properties predicted by the magmatic foam model. Together, these observations are consistent with the RMDS formation occurring during the period after the extrusion and solidification of the host lava flows, up to and including the geologically recent Late Copernican, that is, the last few hundreds of millions of years of lunar history. We present and discuss each of these contradictory data and interpretations and summarize the requirements for magma ascent and eruption models that might account for young RMDS ages. We conclude with a discussion of the tests and future research and exploration that might help resolve the RMDS age and mode of emplacement conundrum.

A new crushable foam model for polymer-foam core sandwich structures

An elastic-plastic, viscoelastic damage model to accurately describe the crushing and energy absorption of polymer foams in sandwich panels was implemented in ABAQUS Explicit. Good agreement was found between ABAQUS predictions and experimental results with Divinycell H100 foams under triaxial compression, triaxial compression-tension and triaxial compression-shear. The elastic-plastic viscoelastic damage model was used to simulate the response of a doubly curved foam core composite sandwich shell subjected to direct pressure pulse and water pressure pulse loading. Results using the new crushable foam model were compared to those using the ABAQUS built-in isotropic crushable foam model. It was found that sandwich panels with the more commonly used, isotropic crushable foam model overestimated the stiffness, strength and energy dissipation of sandwich shells with Divinycell H100 foam cores. The proposed elastic-plastic-viscoelastic-damage model would provide more accurate results and offer better protection of composite sandwich structures than the isotropic crushable foam model.

Recurrent neural network modeling of the large deformation of lithium-ion battery cells

As the automotive industry transitions from combustion to electric motors, there is a growing demand for efficient computational models that can describe the homogenized large deformation response of Li-ion batteries. Here, a detailed three-dimensional unit cell model with periodic boundary conditions is developed to describe the large deformation response of a typical anode-separator-cathode lay-up of a pouch cell. The model makes use of a Deshpande-Fleck foam model for the porous polymer separator and Drucker-Prager cap models of the granular cathode and anode coatings. Using the unit cell model, the stress-strain response of a battery cell is computed for 20’000 random loading paths in the six-dimensional strain space. Based on this data, a recurrent neural network (RNN) model is trained, validated and tested. It is found that an RNN model composed of two gated recurrent units in series with a deep fully connected network is capable to describe the large deformation response with a high level of accuracy. As a byproduct, it is shown that advanced conventional constitutive models such as the anisotropic Deshpande-Fleck model cannot provide any predictions of satisfactory accuracy.

Dynamic responses of metal foam sandwich beams to repeated impacts

The phenomena of repeated impacts are very common, especial in the field of ship and ocean engineering. When the ship structures suffering from repeated impact loadings, the deformation and damages will accumulate, leading to failure even damage of the structures, which may cause serious accident. In order to study the dynamic behaviors of metal foam sandwich beams (MFSBs) under repeated impact loadings, the nonlinear finite element model was established based on the material model of crushable foam by using Abaqus-Explicit, and the approach to achieve repeated impacts in the software was proposed. The accuracy of the numerical simulation was verified by comparing the permanent deflections of front and back face sheets. Based on the results of the numerical simulations, the deformation modes, loading and unloading process as well as the energy absorption behavior of the MFSBs under repeated impacts were analyzed. Results show that during repeated impacts, the deformation of the MFSBs is accumulated gradually, the front face sheet mainly experiences global bending and local indentation, and the metal foam core suffers from local compression, while the back face sheet is subjected to global bending. During the repeated impacts, the loading and unloading stiffness increases with the impact number. The energy absorption of front face is larger than that of back face and metal foam core in all the impacts. As the impact number increases, the energy absorbed by front face sheet and foam core declines gradually, while that of the back face sheet increases, approaching a constant value. The plastic deformation energy of the MFSBs decreases with the impact number, on the opposite, the rebound energy of the MFSBs increases gradually with the impact number, while both of them trends to be stable. The proposed finite element method can be applied to accurately predict the dynamic responses of the MFSBs suffering from repeated impact loadings, and provide technical supports for the anti-impact design of metal foam sandwich structures.

Pore-scale convection-conduction heat transfer and fluid flow in open-cell metal foams: A three-dimensional multiple-relaxation time lattice Boltzmann (MRT-LBM) solution

Flow and heat transfer in porous foams are usually simulated based on averaged properties that are far from the actual values and can lead to substantial inaccuracies in the results. The pore-scale simulation could provide accurate and realistic models for such properties. Accordingly, a multiple-relaxation time lattice Boltzmann (MRT-LBM) code is extended for pore-scale direct numerical simulation (DNS) of fluid flow and conductive-convective heat transfer in open-cell metal foams (OCMFs) using the Palabos code, an open-source parallel LB solver. Three foam models with different numbers of pores per inch (PPI) are generated, and through simulations, the permeability, the non-Darcy coefficient β, the onset of non-Darcy flow, and Nusselt number (Nud) are determined. The results show that by increasing the PPI of the samples from 20 to 40, the flow becomes more complex, and velocity and permeability are reduced by up to 70%. On the other hand, the heat transfer coefficient increases significantly so that in the same Reynolds number (Re), the overall heat transfer coefficient of sample 3 (40 PPI) is on average 110% higher than that of sample 1 (20 PPI). Finally, the global Nusselt number (Nud) is determined as a function of Re, and the related correlations are presented.

Application of computed tomography data–based modelling technique for polymeric low density foams, Part A: Model development

In this research study, a methodology is introduced for generating finite element simulation models for low density closed cell foams based on computed tomography (CT) measurement results. Creating this kind of simulation models can be very expensive with regard to modelling and computational effort. Hence, a combined modelling technique based on CT data and Voronoi diagrams is developed that minimizes this effort, but nevertheless, generates simulation models with a realistic microstructure. In this article, the generation of simulation models using this modelling method and the necessary adaptation of the models concerning microstructural features to consider, for example, anisotropic properties of the foam, are described. Furthermore, simulations are performed to investigate the mechanical performance of the foam models and to compare the results with several analytical models and experimental data. Finally, conclusions regarding the applicability and possible further extensions of the model are provided.