Real Foam Research Articles

Study on flexural resilience of composite foam sandwich structures under hygrothermal environment

Under hygrothermal environments, the structural stability and strength of all-fiber composite aircraft are significantly affected during long-term flight use. The wing skin, as a critical structural component, plays a vital role in bearing and transmitting aerodynamic loads. Therefore, it is crucial to investigate the structural compressive stability and strength of the wing skin throughout the aircraft's entire life cycle under these conditions. This study employs a real wing carbon fiber foam sandwich structure to investigate the compressive stability and strength of the wing skin structure of a new energy aircraft under actual flight conditions, specifically during the entire process of the room temperature dry state (RTD) and elevated temperature wet state (ETW). Initially, three-point bending tests were conducted on carbon fiber reinforced polymer (CFRP) laminates, foam cores, and CFRP reinforced foam sandwich structures. The CFRP laminates fully rebounded after bending damage in both the RTD and ETW environments. While CFRP reinforced foam sandwich structures also rebounded fully in the RTD environment, their rebound performance diminished in hygrothermal conditions due to the thermoplastic mobility of the foam cores, resulting in only weak rebound capabilities. In hygrothermal environments, the thermoplastic mobility of the foam core leads to diminished resilience after bending damage, resulting in only weak rebound capabilities. Subsequently, compressive instability tests were conducted on the wing skin foam sandwich structure. The results indicated that the basic test study effectively predicted the structural test outcomes. Structural components in the RTD environment exhibited overall flexural instability under compressive load, with damage morphology resembling a circular curve; the damaged specimens fully rebounded after unloading. Conversely, specimens in the ETW environment displayed localized instability, characterized by a wrinkled damage profile, resulting in only weak rebound capabilities after unloading.

Direct Reconstruction of Wet Foam from Sparse‐View, Dynamic X‐Ray CT Scans

X‐ray imaging of wet foam dynamics with a high temporal resolution (e.g., 3D videos with a 10 Hz frame rate) requires fast rotation of either the foam sample or the X‐ray gantry. This, however, strongly limits the number of X‐ray projections per rotation that can be acquired. As a result, conventional computed tomography reconstruction methods generate 3D images with severe undersampling artefacts, complicating subsequent foam analysis. Herein, BubSub, a novel tomographic reconstruction approach that reconstructs a 4D (3D plus time) dynamic image of wet foam bubbles from sparse‐view X‐ray projections by leveraging prior knowledge about the evolving foam structure, is introduced. BubSub adapts a collection of subdivision surfaces with spherical topology to represent liquid–gas interfaces of foam bubbles. Estimation of bubble positions and shapes at each time point is achieved by minimizing the projection distance in relation to the measured projections. BubSub operates efficiently with minimal memory usage, exhibits robustness against noise, and provides accurate reconstructions, even when the available projections are limited, as evidenced by various experiments using both simulated and real wet foam X‐ray data.

Forced convective heat transfer performance of foam-like structures – comparison of the Weaire-Phelan and the Kelvin structures with real metal foam

Real foam and foam-liked structures have been widely used in the field of flow and heat transfer but whether foam-like structures can be used as an alternative to metal foams for forced convective heat transfer needs to be further investigated. In this study, three foam structures (Weaire-Phelan, Kelvin and metal foam) were compared by simulation under turbulent conditions and the flow heat transfer characteristics have been evaluated. The 3D models of the two foam-liked structures were constructed using CAD software and the 3D model of the metal foam was scanned and reconstructed using CT. All three structures were constrained by the same pore size parameters. The results reveal that neither the Weaire-Phelan structure nor the Kelvin structure can serve as a substitute model for the real metal foam. The Weaire-Phelan structure demonstrates the best effective overall heat transfer performance (OHTP) while the Kelvin structure exhibits the worst. With an inlet velocity of 10 m/s, the area goodness factor (j/f) of the Weaire-Phelan structure is similar to the metal foam structure which is 12.3 % higher than that of the Kelvin structure. With an inlet velocity of 25 m/s, the j/f value of the metal foam structure becomes comparable to that of the Kelvin structure. However, the j/f value of the Weaire-Phelan structure exhibits 12.18% higher than the other two structures.

Effect of pore size polydispersity on the acoustic properties of high-porosity solid foams

This study investigates the influence of pore size polydispersity on the acoustic behavior of high-porosity solid foams using numerical simulations. The effect of the size of the periodic unit cell (PUC) on the transport parameters is first examined. It is found that the size of the PUC required for properly estimating the acoustic properties of random foams depends on both the analyzed transport parameter(s) and level of polydispersity. Assuming identical and constant aperture ratio of membranes, the results indicate that (i) the viscous permeability is a reliable indicator regarding the size of the PUC (a more constraining property than the other transport parameters), and (ii) high-polydispersity foams require a larger number of pores in the PUC to achieve convergence with respect to morphological characteristics and acoustic properties. The influence of polydispersity on dimensionless transport parameters is then analyzed. It is found that polydispersity has a negligible effect on the high-frequency tortuosity but induces substantial variations in the remaining macroscopic parameters. Simulations further show that the ratio of the dimensionless transport parameters does not depend on membrane aperture ratio. This important result allows us to propose a fast method to estimate the acoustic properties of a random foam from the transport parameters of monodisperse foams with different pore sizes, for each studied transport parameter. The proposed method is finally employed to characterize the pore size and polydispersity in two real foams (with and without membranes), solving an inverse problem.

A study of pore scale flow and conjugate heat transfer characteristics in real and Kelvin anisotropic foams

Porous foam is a promising material in the field of science and engineering owing to its potential to offer heat transfer enhancement. In this work, an ideal Kelvin structure with considering anisotropy is constructed based on the characteristic parameters extracted from a real foam, and the flow and heat transfer characteristics in real and Kelvin foams is numerically investigated and compared by an in-house MRT-TLBM solver accelerated by a GPU. Results demonstrate that when the flow is along the elongation direction of the structure, the permeability is larger and Nusselt number is lower than those in the other directions for both real and Kelvin foams. Compared to the real foam, the Kelvin foam is more prone to inducing turbulence. For the overall performance of flow and heat transfer, the real foam behaves better at small Reynolds number (Rec <750), while Kelvin foam does when Rec exceeds 750 due to the different dominant mechanisms of heat transfer. In particular, the comprehensive factor (θ) of Kelvin foam is 12.8 % larger than that of the real foam at Rec=2000.

Persistent homology based goodness-of-fit tests for spatial tessellations

Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of stochastic models for a spatial tessellation are in accordance with a given dataset. Recently, tools from topological data analysis such as the persistence diagram have allowed to reach profound insights in a variety of application contexts. In this work, we establish the asymptotic normality of a variety of test statistics derived from a tessellation-adapted refinement of the persistence diagram. Since in applications, it is common to work with tessellation data subject to interactions, we establish our main results for Voronoi and Laguerre tessellations whose generators form a Gibbs point process. We elucidate how these conceptual results can be used to derive goodness of fit tests, and then investigate their power in a simulation study. Finally, we apply our testing methodology to a tessellation describing real foam data.

On the Question of the Sign of Size Effects in the Elastic Behavior of Foams

Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam’s mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory.In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is “cut” from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are “measured” directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.

The generalized self-consistent scheme applied to syntactic foams

Here, syntactic foams are considered as a linearly elastic composite medium, which consists of a homogeneous matrix containing hollow glass and unwanted voids. The composite is modeled by the generalized self-consistent scheme and combining the three-phase model and the four-phase model. The overall properties are obtained using a micromechanical approach based on Green’s function techniques and the interfacial operators. The model assumes that all constituents are elastic and perfectly bonded. Comparison with experimental and numerical results shows that the methodology used is capable of predicting, with good accuracy, the elastic moduli of real syntactic foams.

Effects of the physical characteristics of foams on conditioned soil’s flow behavior: A case study

Earth pressure balance shield (EPBS) is the excavation technique responding to the technical construction complexity of the future line 16–1 of the Grand Paris Express project. Its principle is based on the capacity of the excavated ground to transmit the forces needed to counterbalance the earth and water pressures of the working face. Additives are injected into the soil; on the cutting wheel, in the excavation chamber and in the screw conveyor. Their role is to assure the soil conditioning by modifying the soil’s workability and its hydromechanical and rheological parameters. Therefore, the soil conditioning produces a plastic medium able to transmit the pressure to maintain the front face. In addition, as a second objective, the additives aim to overcome uncertainties in the soil. Depending on the case, the additives can reduce the clogging, internal friction, abrasiveness, and permeability of the soil. The additives can include water, surfactant, polymer and bentonite. The combination of water and surfactant with or without polymer produces the foam. In order to increase the excavation perfomance, laboratory prelimenary tests are performed to deduce the optimal foam parameters. Since no test measuring the foam characteristics is standardized yet, this article sums up the tests mostly used in foam characterisation; half-life measurements, rheological tests, microstructural observations. As for the conditioned soil, slump test is frequently used by the tunnelling industry to recommend the optimal soil conditioning parameters in terms of workability. This test has been adapted in this study and the results are verified by rheological tests, then compared to the real foam injection data used for the project and their effect on mechanical parameters. For a specific type of excavated soil, the quality (type) of foam recommended by the laboratory work falls into the same choice of additive based on in-situ tunnelling excavation data. These findings are explained by the foams characteristics. Therefore, a correlation between foam and the conditioned soil (sandy soil with silt and low percentage of clay) with foam is deduced at different levels: micro, meso and macro (real) scales.

Improved body-centered cubic unit for accurately predicting the melting characteristics of metal foam composite phase change material

Metal foams have been widely used to enhance the heat storage performance of phase change materials (PCMs). For numerically simulating the metal foam composite PCMs, a body-centered cubic (BCC) unit has been proposed to represent the real foam structure. However, the original popular BCC unit is closed when its porosity is lower than 0.9395, which is very different from the actual metal foam. Besides, the effective thermal conductivity (ETC) of its paraffin composite is a key parameter that directly affects the melting performance. It is not always accurately predicted compared with the existing investigations. In the present work, various modified BCC units were built by regulating the structure of the original one to approach the open-cell structure of the real foam, and their melting performances characterized by the ETC were compared with the existing literature results. Through analyzing the structural parameter (γ, diameter ratio of the inscribed and corner spheres) and ETC, we found that when the porosity of the BCC unit is lower than 0.9395, improving the γ is helpful in gaining the open-cell structure to represent the actual metal foam. When the porosity is 0.876, γ ≥ 1.11474 means an open-cell structure, and the BCC unit with γ ≥ 1.062 is open-cell for the porosity of 0.909. Besides, when the porosity is larger than 0.9395, one can gradually approach the experimental ETC by improving γ. In a word, this study extends the accurate application of the original BCC unit in acting as metal foam.

Novel design of irregular closed-cell foams structures based on spherical particle inflation and evaluation of its compressive performance

Due to the high degree of randomness in the microstructure of real closed-cell foams, many reported numerical models in the literature are not able to capture precisely the local morphological features found in solid foams geometry. This is still the main impediment that restricts the investigation of this novel material and motivates the development of a sophisticated 3D solid model, which describes properly the complex geometry of real closed-cell foams. In this regard, this paper presents an original approach to generate a realistic and accurate 3D computational model of irregular closed-cell foams with relative density control and detailed finite element analysis of their mechanical performance under quasi-static loading up to densification. The solid model is constructed based on spherical particles inflation simulation. It resembles the real foams in terms of local features such as cell walls irregularities and thickness variation. The modeling approach was successfully verified by comparing cell-morphological details of the generated models with those produced experimentally available in the literature and by the high-quality of obtained 3D printed models containing complex shapes and irregular cell wall thickness distribution. The evolution of spherical particles during the inflation process is analyzed based on finite element (FE) simulations. It was found that it can produce varying relative densities of foam due to the gradual decrease in the gap between the inflated particles, this makes the geometrical model of the foam suitable for studying the effect of local morphological characteristics on the mechanical performance of closed-cell foam material. To demonstrate that the compressive performance of the proposed closed-cell foam models can be controlled by relative density, 3D foam models were extracted from different inflation times and then subjected to quasi-static compression tests up to densification using the Abaqus software. The results confirm that the plateau stress can be expressed as a function of foam relative density, its accuracy is validated by comparing it to the closed-cell aluminum foam power law equation existing in the literature. The new design method offers suitable numerical models for AM technology, plenty of experimental works on closed-cell foam can be reduced for engineering applications.

A sophisticated periodic micro-model for closed-cell foam based on centroidal constraint and capacity constraint

A deeper understanding of the uniaxial compression damage behavior and its microscopic mechanisms in closed-cell Polyurethane foam (PUF) at higher strains would be the first step to comprehend its energy absorption behavior in application. A physical-based micro-structure of the PUF model, therefore, is a crucial precondition in the prediction of the material property. A highly efficient physical-based model with adapted periodic boundary conditions (PBCs) is developed to simulate the mechanical behavior of the rigid closed-cell foam using 100 cells, much less than that mentioned in the literature (800 cells). The microstructure characteristics of PUF have been obtained by scanning electron microscopy (SEM), including the cell size distribution, the wall thickness, the cell aspect ratio, etc. Using these parameters, a periodic representative volume elements (RVEs) model based on the Laguerre tessellation with centroidal constraint and capacity constraint (LTCCC) has been proposed. The centroidal constraint and capacity constraint on the LTCCC has a sound physical meaning that the volume distribution of the cells in the RVEs model obtained by the iterations of the weights of the seed points can be precisely matched to that measured using the SEM. Meanwhile, the features of the RVEs model, including the number of the faces per cell and the number of the edges per face, also match those of the real foam. The anisotropic compressive behavior of the PUF is predicted and well validated using the experimental results. The quasi-static crushing progress of the cells as well as the struts is detailed discussed using the proposed model to reproduce the layer-wise collapse phenomena and reveal the reasons that cause the different crushing behavior in axial direction and perpendicular to the axis direction.

A Predicting Model for the Effective Thermal Conductivity of Anisotropic Open-Cell Foam

The structural anisotropy of open-cell foam leads to the anisotropy of effective thermal conductivity (ETC). To quantitatively analyze the effect of structural anisotropy on the anisotropy of ETC, a new predicting model for the ETC of anisotropic open-cell foam was proposed based on an anisotropy tetrakaidecahedron cell (ATC). Feret diameters in three orthogonal directions obtained by morphological analysis of real foam structures were used to characterize the anisotropy of ATC. To validate our proposed anisotropic model, the ETCs of real foam structures in three orthogonal directions predicted by it were compared with the numerical results, for which the structures of numerical models are reconstructed by X-ray computed tomography (X-CT). Using the present anisotropic model, the influences of the thermal conductivity ratio (TCR) and porosity of the foams on the anisotropic ratios of ETCs are also investigated. Results show that there is good consistency between the ETCs obtained by the anisotropic model and the numerical method. The maximum relative errors between them are 2.84% and 13.57% when TCRs are 10 and 100, respectively. The present anisotropic model can not only predict the ETCs in different orthogonal directions but also quantitatively predict the anisotropy of ETC. The anisotropies of the ETCs decrease with porosity because the proportion of the foam skeleton decreases. However, the anisotropies of ETCs increase with TCR, and there exist asymptotic values in anisotropic ratios of ETCs as TCR approaches infinity and they are equal to the relative Feret diameters in different orthogonal directions.

New model of pressure drop for the foam trays with dynamic bubbling process analysis

Open-cell foams as the column tray are promising candidates for the purpose of process intensification in the distillation process. In this paper, the real foam porous structure is obtained based on Micro Computed Tomography (µ-CT), and the bubble formation process on pore-scale foam tray is discussed based on the VOF-CSF model (volume of fluid method-continuous surface force). The results show that the wettability (CA), superficial gas velocity (Ug), porous structure, and clear liquid layer height (HCL) all affect a crucial factor of the foam tray - the liquid holdup in the porous channels (LHPC). It determines the effective porosity, which in turn affects the bubbling frequency and pressure drop. Meanwhile, the evolutionary mechanism of instantaneous pressure drop is analyzed based on the flow patterns, force analysis and interfacial phenomena. Moreover, the new model to predict pressure drop is proposed based on LHPC, which shows good consistency with experiments.

The microstructure characterization and elastic properties of closed-cell foams

The present study investigated the microstructure and compressive response of ALPORAS closed-cell foam. The micro-CT technique was adopted to study the interior structure of the foam. Image processing algorithms were then incorporated to measure the geometrical characteristics of the foam cellular microstructure, including the size, surface area, geometrical shape, aspect ratio, and sphericity of cells. The cells were irregular polyhedra with approximately 14–15 faces and 5 edges per face; they had longer dimensions in the gravitational direction than in the other two mutually orthogonal directions. Three statistical measurements were employed in the development of random 3D numerical models based on the Laguerre tessellation of random close packed spheres along with three probability density functions for sphere size distributions. The effects of parameters such as probability density functions, sphere volume fraction, and coefficient of variation in sphere volume on the geometrical characteristics of the developed numerical models were examined. The difference in geometric characteristics of the numerical models generated using different probability functions was nonsignificant. Numerical simulations were subsequently conducted using the developed numerical models. The comparison between numerical and experimental results revealed that numerical models overestimated the experimental value by a factor of approximately 3. This discrepancy can be attributed to the difference in detailed microstructural features between the generated numerical models and real foam.

Effects of micropore characteristics in the metal skeleton on heat and mass transfer in an open foam structure for thermal management in the hydrogen UAV

Aiming at solving the heat dissipation problem in a hydrogen unmanned aerial vehicle (UAV), this work uses an open metal foam as the enhanced heat transfer device in the air-cooling channel. The method of improving comprehensive heat transfer capacity and weight reduction by controlling the micropore directions and sizes in the metal skeleton is proposed. The real open cell metal foam structures are scanned and restructured using the X-ray computed tomography imaging system and corresponding computer software. The effects of micropore directions and sizes in the skeleton on pressure drops, conjugate heat transfer, volumetric heat transfer coefficient, comprehensive heat transfer capacity as well as weight reduction are discussed with the inlet velocity ranging from 10 m/s to 80 m/s. Results find that the micropore direction parallel to flow owns a higher comprehensive heat transfer capacity compared with that vertical to flow. There are existing a competitive relationship between heat conduction and heat convection in the metal skeleton. When the micropore size is 0.01, a best enhanced heat dissipation performance can be achieved. The structure with micropore size of 0.03 has a 8.49% weight reduction and 4.72–5.91% improvement of comprehensive heat transfer performance compared with that of the structure without micropores. The above findings can be applied to design a light and high comprehensive heat transfer device in the hydrogen UAV.

Microstructural Parameters for Modelling of Superconducting Foams.

Superconducting YBaCuO (YBCO) foams were prepared using commercial open-cell, polyurethane foams as starting material to form ceramic YBaCuO foams which are then converted into superconducting YBCO by using the infiltration growth process. For modelling the superconducting and mechanical properties of the foam samples, a Kelvin-type cell may be employed as a first approach as reported in the literature for pure polyurethane foams. The results of a first modelling attempt in this direction are presented concerning an estimation of the possible trapped fields (TFs) and are compared to experimental results at 77 K. This simple modelling revealed already useful information concerning the best suited foam structure to realize large TF values, but it also became obvious that for various other parameters like magnetostriction, mechanical strength, percolative current flow and the details of the TF distribution, a refined model of a superconducting foam sample incorporating the real sample structure must be considered. Thus, a proper description of the specific microstructure of the superconducting YBCO foams is required. To obtain a set of reliable data, YBCO foam samples were investigated using optical microscopy, scanning electron microscopy and electron backscatter diffraction (EBSD). A variety of parameters including the size and shape of the cells and windows, the length and shape of the foam struts or ligaments and the respective intersection angles were determined to better describe the real foam structure. The investigation of the foam microstructures revealed not only the differences to the original polymer foams used as base material, but also provided further insights to the infiltration growth process via the large amount of internal surface in a foam sample.

Visual Simulation of Turbulent Foams by Incorporating the Angular Momentum of Foam Particles into the Projective Framework

In this paper, we propose an angular momentum-based advection technique that can express the turbulent foam effect. The motion of foam particles, which are strongly bound to the motion of the underlying fluid, is viscous, and sometimes clumping problems occur. This problem is a decisive factor that makes it difficult to express realistic foam effects. Since foam particles, which are secondary effects, depend on the motion of the underlying water, in order to exaggerate the foam effects or express more lively foam effects, it is inevitable to tune the motion of the underlying water and then readjust the foam particles. Because of such a cumbersome process, the readjustment of the foam effects requires a change in the motion of the underlying water, and it is not easy to produce such a scene because the water and foam effects must change at the same time. In this paper, we present a method to maintain angular momentum-based force from water particles without tuning the motion of the underlying water. We can restore the lost turbulent flow by additional advection of foam particles based on this force. In addition, our method can be integrated with screen-space projection frameworks, allowing us to fully embrace all the advantages of this approach. In this paper, the turbulence of the foam particles was improved by minimizing the viscous motion of the foam particles without tuning the motion of the underlying water, and as a result, lively foam effects can be expressed.

Modeling of the Effective Permittivity of Open-Cell Ceramic Foams Inspired by Platonic Solids.

Open-cell solid foams are rigid skeletons that are permeable to fluids, and they are used as direct heaters or thermal dissipaters in many industrial applications. Using susceptors, such as dielectric materials, for the skeleton and exposing them to microwaves is an efficient way of heating them. The heating performance depends on the permittivity of the skeleton. However, generating a rigorous description of the effective permittivity is challenging and requires an appropriate consideration of the complex skeletal foam morphology. In this study, we propose that Platonic solids act as building elements of the open-cell skeletal structures, which explains their effective permittivity. The new, simplistic geometrical relation thus derived is used along with electromagnetic wave propagation calculations of models that represent real foams to obtain a geometrical, parameter-free relation, which is based only on foam porosity and the material’s permittivity. The derived relation facilitates an efficient and reliable estimation of the effective permittivity of open-cell foams over a large range of porosity.

Numerical Assessment of the Immersion Process of a Ceramic Foam Filter in a Steel Melt

Herein, the immersion process of a ceramic foam filter in a steel melt is investigated by means of numerical simulations, which are mainly based on the volume of fluid approach. The geometry of the used filters is modeled using an artificially generated beam model, which is convolved with a Gaussian kernel. The modeling approach enables the generation of filter geometries with, e.g., pore density and strut thickness similar to real ceramic foam filters. The main scope of the article is to show the effect of the immersion velocity of the filter on the formation of gas bubbles inside the pore cavities of the ceramic filter. Moreover, the influence of the contact angle on the volume fraction of gas bubbles, which remain in the filter, is investigated. For better understanding, the numerical results are underlined using 3D visualization and virtual reality.