Hydrodynamic Characterization of Nickel Metal Foam,Part 2: Effects of Pore Structure and Permeability

In this article, the structural characterization of chemical vapor deposition (CVD) nickel metal foam is presented. Scanning electron microscope and post image processing were used to carefully analyze the surface of the nickel metal foams. Data on foam unit cell, ligament thickness, projected pore diameter, and averaged porosity was obtained. Unit cell and projected pore diameters of CVD nickel metal foam possess Gaussian-like distribution. Characteristics of pore structure and its effect on permeability in Darcian flow regime were analyzed. The relations between the permeability, pore size, and porosity are presented. Present and previous data are compared with these relations. Measurement results indicate that the permeability or the viscous conductivity of the CVD processed metal foam is affected not only by the pore size, and porosity but also by the ligament structure.     

Pressure drop and friction factor of steady and oscillating flows in open-cell porous media

Open-cell metal foams are often used in heat exchangers and absorption equipment because they exhibit large specific surface area and present tortuous coolant flow paths. However, published research works on the characteristics of fluid flow in metal foams are relatively scarce, especially for the flow oscillation condition. The present experimental investigation attempts to uncover the behavior of steady and oscillating flows through metal foams with a tetrakaidecahedron structure. In the experiments, steady flow was supplied by an auto-balance compressor and flow oscillation was provided by an oscillating flow generator. The pressure drop and velocity were measured by the differential pressure transducer and hot-wire sensor, respectively. The friction factor of steady flow in metal foam channel was analyzed through the permeability and inertia coefficient of the porous medium. The results show that flow resistance in the metal foams increases with increasing form coefficient and decreasing permeability. The empirical equation obtained by the present study indicates that the maximum friction factor of oscillating flow through the tested aluminum foams with specific structure is governed by the hydraulic ligament diameter-based kinetic Reynolds number and the dimensionless flow amplitude.     

Permeability of open-cell foams under compressive strain

A model for the behavior of low-density, open-cell foam under compressive strain is proposed. Using this model, a tractable relationship between the normalized permeability and the applied strain is developed. An experimental study of the effect of strain on the permeability of open-cell polyurethane foams is presented. The experiments are performed using a Newtonian fluid in the fully laminar regime, where viscous forces are assumed to dominate. The model is found to describe the experimental data well and be independent of the foam cell size, the direction of flow with respect to the foam rise direction, and the properties of the saturating fluid. In a companion paper, the model for the permeability of open-cell foam is combined with Darcy’s law to give the contribution of viscous fluid flow to the stress–strain response of a reticulated foam under dynamic loading.     

Effect of Confining Wall on Properties of Gas Flow Through Metal Foam: An Experimental Study

While the Darcy and Forchheimer relations are widely applied to determine the permeability and the form drag coefficient of open-cell metal foam, they both assume that the porous medium is infinite in all directions, i.e., large enough so that the effect of any confining walls is negligible. Many researchers, however, pay little or no attention to the size of metal foam samples in pressure-drop studies. The size of a foam sample perpendicular to the flow direction may be small enough such that wall effects are significant. This article experimentally investigates the wall effect on the permeability and form drag coefficient for two types of open-cell aluminum foam subjected to airflow entering the foam in the Forchheimer regime. The Forchheimer equation was recast in two different manners, which resulted in new non-dimensional numbers that correlated very well with the diameter of the foam samples measured in cells. The correlations are valid for a confining-tube-diameter-based Reynolds number ranging from approximately 13,000 to 105,000, and for diameters ranging from 12 to 36 cells and 24 to 60 cells for 10- and 20-pore per inch foam, respectively. The obtained correlations allow for determining pressure drop given only the velocity and the diameter of an aluminum foam sample.     

The Blocking Ability and Flowing Characteristics of Steady Foams in Porous Media

Foam flow experiments were carried out to study the influence factors such as surfactant concentration, foam quality, injection rate of liquid and gas, permeability of porous media, temperature, and oil saturation on blocking ability and flowing characteristics of steady foams in porous media. Foam blocking mechanisms and flowing characteristics were summarized according to the experimental results and foam migration behavior. The results showed that the pressure distribution of flowing foams was linearly descending in porous media at steady state. The results further showed that the foam size and quality in pores along the sand pack were almost uniform, that is, foam generation and destruction gradually reached dynamic equilibrium at steady state. In porous media, the blocking ability of steady foams increased with the concentration of the foaming agent and the increase in the permeability of porous media, but the blocking ability decreased with the increase in the temperature, the shearing rate, and the oil saturation of the porous media. Foam resistance factor reached maximal value at the foam quality of 85% in porous media.     

Predicting pressure drop in open-cell foams by adopting Forchheimer number

Interconnected struts arranged in 3-D foam structures pose a challenge in understanding fluid flow, which is significantly different from that in traditional porous media. Different flow regimes (Darcy, transition and weak inertia regimes) and thus, different flow laws in open-cell foams are used. The impact of characteristic lengths’ choices based on both, morphological and hydraulic parameters on flow law formulation has been studied. Ambiguities in definitions and measurements of several key parameters have been shown and limitations in the use of some parameters have been pointed out.An equivalent Reynolds number in the form of Forchheimer number (F_o) has been proposed to establish the friction factor relationship in order to avoid any morphological ambiguities. This number takes into account hydraulic characteristics of viscous and inertia regimes simultaneously. It has been observed that when F_o < 0.1, the flow through open-cell foams remains in the Darcy regime while the occurrence of weak inertia regime dominates when F_o > 1. Transition regime occurs in a narrow range of flow velocity when 0.1 < F_o < 1. The limits of transition for regime identification are found to be independent of foam morphologies. The form drag coefficient varies in relation with foam morphological parameters and is not a “universal” constant.Empirical correlations have been derived to predict hydraulic characteristics and friction factor data for different strut shapes and porosities. An excellent agreement has been obtained between predicted and numerical/experimental flow data.     

Equivalent particle diameter and length scale for pressure drop in porous metals

The internal architecture of metal foam is significantly different from that of traditional porous media. This provides a set of challenges for understanding the fluid flow in this relatively new class of materials. This paper proposes that despite the geometrical differences between metal foam and traditional porous media, the Ergun correlation is a good fit for the linear pressure drop as a function of the Darcian velocity, provided that an appropriate equivalent particle diameter is used. The paper investigates an appropriate particle diameter considering the physics of energy dissipation, i.e. the viscous shear and the form drag. The above approach is supported by wind tunnel steady-state unidirectional pressure drop measurements for airflow through several isotropic open-cell aluminum foam samples having different porosities and pore densities. For each foam sample, the equivalent particle diameter correlated well with the surface area per unit volume of the foam. This was also very well valid for previous porous metal pressure drop data in the open literature.     

A Theoretical Model with Experimental Verification to Predict Hydrodynamics of Foams

An experimentally validated theoretical model, based on hydraulic resistance network and scale analysis at the pore level, is developed to predict the pressure drop for flow through foams. The complex microstructure of the foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. New correlations for permeability and form drag (inertia) coefficient are presented as functions of the mean pore and ligament diameter as well as the foam porosity. The present model makes it possible to conduct parametric studies. Results obtained from the proposed model are successfully compared with our experimental data as well those found in the literature to observe good agreement.     

Can Moderately Rarefied Gas Transport Through Round and Flat Tight Channels of Fractured Porous Media be Described Accurately?

We study the generation and flow of foam through rough-walled, fractured marble rocks that mimic natural fracture systems in carbonate reservoirs. Flow was isolated to the fracture network because of the very low rock permeability of the marble samples and foam generated in situ during co-injection of surfactant solution and gas. The foam apparent viscosities were calculated at steady pressure gradients for a range of gas fractions, and similar to foam flow in porous media, we identified two flow regimes for foam flow in fractures: a high-quality flow regime only dependent on liquid velocity and a low-quality flow regime determined by the gas and liquid velocities. Variations in local fluid saturation during co-injection were visualized and quantified using positron emission tomography combined with computed tomography.

     

Impact of material processing and deformation on cell morphology and mechanical behavior of polyurethane and nickel foams

The cell morphology and mechanical behavior of open-cell polyurethane and nickel foams are investigated by means of combined 3D X-ray micro-tomography and large scale finite element simulations. Our quantitative 3D image analysis and finite element simulations demonstrate that the strongly anisotropic tensile behavior of nickel foams is due to the cell anisotropy induced by the deformation of PU precursor during the electroplating and heat treatment stages of nickel foam processing. In situ tensile tests on PU foams reveal that the initial main elongation axis of the cells evolves from the foam sheet normal direction to the rolling direction of the coils. Finite element simulations of the hyperelastic behavior of PU foams based on real cell morphology confirm the observation that cell struts do not experience significant elongation after 0.15 tensile straining, thus pointing out alternative deformation mechanisms like complex strut junctions deformation. The plastic behavior and the anisotropy of nickel foams are then satisfactorily retrieved from finite element simulations on a volume element containing eight cells with a detailed mesh of all the hollow struts and junctions. The experimental and computational strategy is considered as a first step toward optimization of process parameters to tailor anisotropy of cell shape and mechanical behavior for applications in batteries or Diesel particulate filtering.     

Correlations for the pressure drop for flow through metal foam

Steady-state unidirectional pressure-drop measurements for incompressible airflow through nine open-cell aluminum foam samples, having different porosities and pore densities, were undertaken. The pressure drop increased with increasing Darcian velocity following the quadratic Forchheimer equation. The lower-porosity foam produced significantly higher pressure drop. Both the permeability and the form drag coefficient correlated well with the porosity. The correlations predicted the results of some previous studies reasonably well, especially for the low-pore-density foam.     

Micromorphic continuum modelling of the deformation and fracture behaviour of nickel foams

An anisotropic compressible plasticity model is incorporated into the framework of the micromorphic continuum theory in order to describe some size effects observed in ductile nickel foams. This continuum model reproduces the fact that the presence of a machined hole in a foam plate does not affect its mechanical response when the hole size becomes comparable to the cell size of the material. Finite element simulations are compared to strain field measurements in nickel foam plates with a machined hole for different hole sizes, in order to identify the characteristic length of the model. Based on a simple ductile damage law, the model is then shown to be able to account for the strong anisotropy of the initiation of crack propagation in central crack panels made of nickel foams under mode I loading conditions.     

Simulation of Entry-Region Flow in Open-Cell Metal Foam and Experimental Validation

Open-cell metal foam is distinguished from traditional porous media by its very high porosities (often greater than 90 %), and its web-like open structure and good permeability. As such, the foam is a very attractive core for many engineered systems, e.g., heat exchangers, filtration devices, catalysts, and reactors. The flow field inside the foam is rather complex due to flow reversal and vigorous mixing. This complexity is increased by the possible presence of an entry region. The entrance region in metal foam is usually underestimated and ignored, just like its counterpart in traditional porous media. In this paper, the actual entry length is determined by simulation and direct experiment on commercial open-cell aluminum foam. It is shown to be dependent on flow velocity and to reach a constant value for higher velocities. The complex and intrinsically random architecture of the foam is idealized using a unit geometrical model, in order to numerically investigate the flow field and pressure drop inside the foam. The Navier–Stokes equations are solved directly, and velocity and pressure fields are obtained for various approach velocities using a commercial numerical package. The entry length is ascertained from the behavior of the velocity field close to the entrance. Comparisons to experimental data were also carried out. The commercial foam that was used in the experiment had 10 ppi and porosity of 91.2 %. Air was forced to flow inside the foam using an open-loop wind tunnel. Good qualitative agreement between the modeling and experimental results are obtained. The agreement lends confidence to the modeling approach and the determined entry length.     

Ceramic foam substrates for automotive catalyst applications: fluid mechanic analysis

Several properties of ceramic foams render them promising substrates for various industrial processes. For automotive applications, the foam properties that need to be further studied include the substrate impact on the exhaust gas flow, in terms of pressure drop and flow uniformity. In this paper, pressure drop measurements are performed with different honeycomb and ceramic foam substrates, and pressure drop correlations are discussed. The flow uniformity upstream and downstream of the substrates is evaluated using particle image velocimetry. The results show that ceramic foam substrates induce higher pressure drop, while increasing the uniformity of the flow. In contrast to honeycomb monoliths, the flow uniformity downstream of ceramic foams does not decrease with increasing flow velocity. The higher flow uniformity of ceramic foams is not only caused by their higher pressure drop, but also by flow homogenization that occurs inside the ceramic foam structure, as a result of the momentum exchange perpendicular to the main flow direction.     

冲击载荷下径向密度排布对泡沫金属力学性能影响的研究

参照层状密度梯度泡沫模型实现方法,利用3D-Voronoi技术设计了新型径向密度梯度泡沫模型,并用有限元软件,对它在不同冲击载荷下的力学行为进行数值模拟。研究冲击速度、密度梯度和平均相对密度对金属泡沫冲击端、支撑端应力和能量吸收能力的影响,发现:径向正梯度泡沫与层状正、负梯度泡沫相比,其两端的应力值均较小,可同时保护冲击端、支撑端物体;径向负梯度泡沫两端应力变化幅度较小,能够保证物体受力稳定;几种泡沫金属的能量吸收能力在不同冲击速度下发生交替变化。对于径向梯度泡沫,能量吸收能力对密度梯度大小不敏感,对梯度方向敏感,径向负梯度泡沫的能量吸收能力始终大于径向正梯度泡沫;平均相对密度越大,径向正、负梯度泡沫两端应力越大、吸能效果越好。     

Drag difference between steady and shocked gas flows passing through a porous body

Experimental and numerical investigations of gas flows through porous materials have been carried out. We have investigated steady and unsteady processes occurring when the gas flow interacts with porous materials. Densities and porosities of the four open-cell-type polyurethane foams which were investigated are kg/m and , with the foams having different structures. Experiments were conducted to determine the steady drag coefficient of the porous material at low Reynolds numbers, evaluated from the pressure drop. The Forchheimer equation was applied to determine the drag. Values of permeability coefficients () in the Forchheimer equation were estimated by comparing computed and experimental results. Results show that the drag coefficient is largely affected by the internal structure of the foam, and has almost no effect on the stress history, while the value of dominates the stress history variation. Differences of 1000 times exist between the steady flow and unsteady shock tube flow values. Received 15 May 1998/ Accepted 15 March 1999     

Aqueous foams and foam films stabilised by surfactants. Gravity-free studies

There are still many open questions and problems in both fundamental research and practical applications of foams. Despite the fact that foams have been extensively studied, many aspects of foam physics and chemistry still remain unclear. Experiments on foams performed under microgravity allow studying wet foams, such as those obtained early during the foaming process. On Earth, wet foams evolve too quickly due to gravity drainage and only dry foams can be studied. This paper reviews the foam and foam film studies that we have performed in gravity-free conditions. It highlights the importance of surface rheology as well as of confinement effects in foams and foam films behaviour.     

Self-lubricated transport of aqueous foams in horizontal conduits

The flow characteristics of aqueous foams were studied in a thin flow channel and a round pipe instrumented for pressure gradient and flow rate measurements. The quality of the foam was varied by controlling the volumetric flow rate of liquid and gas, and different flow types were identified and charted. Uniform foams move as a rigid body lubricated by water generated by breaking foam at the wall. A lubrication model leading to a formula for the thickness of the lubricating layer is presented. The formula predicts a layer thickness of 6–8 μm in the channel and 10–12 μm in the pipe. The thickness depends weakly on foam quality. An overall correlation for the friction factor as a function of Reynolds number which applies to both channel and pipe is derived. This correlation is consistent with a model in which a rigid core of foam is lubricated by laminar flow of a water layer in the range of measured thickness.     

液态泡沫渗流的机理研究进展

液态泡沫是具有高度自组织结构的非平衡系统. 泡沫中的微量液体在重力与毛细管力作用下, 在由薄膜、柏拉图通道以及交汇点形成的通道网络内的流动称为泡沫渗流(foamdrainage), 它直接影响泡沫结构的稳定性. 本文从泡沫物理学角度对液态泡沫的结构首先做了简单介绍, 并对泡沫材料与多孔介质之间的区别和联系做了简单介绍. 文章分析了由泡沫渗流、气泡粗化和液膜破裂而引起的泡沫结构演化规律, 着重介绍了目前泡沫渗流研究中对柏拉图通道边界条件的处理方法、相应的渗流模型及其在一维泡沫渗流中的应用, 并对泡沫渗流实验检测手段及微重力条件下的泡沫渗流实验和理论研究做了综述.      

Darcy–Brinkman Flow Through a Corrugated Channel

A perturbation analysis is carried out to the second order to give effective equations for Darcy–Brinkman flow through a porous channel with slightly corrugated walls. The flow is either parallel or normal to the corrugations, and the corrugations of the two walls are either in phase or half-period out of phase. The present study is based on the assumptions that the corrugations are periodic sinusoidal waves of small amplitude, and the channel is filled with a sparse porous medium so that the flow can be described by the Darcy–Brinkman model, which approaches the Darcian or Stokes flow limits for small or large permeability of the medium. The Reynolds number is also assumed to be so low that the nonlinear inertia can be ignored. The effects of the corrugations on the flow are examined, quantitatively and qualitatively, as functions of the flow direction, the phase difference, and the wavelength of the corrugations, as well as the permeability of the channel. It is found that the corrugations will have greater effects when it is nearer the Stokes’ flow limit than the Darcian flow limit, and when the wavelength is shorter. For the same wavelength and phase difference, cross flow is more affected than longitudinal flow by the corrugations. Opposite effects can result from 180° out-of-phase corrugations, depending on the flow direction, the wavelength, as well as the permeability.