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Research on Flow and Heat Transfer in Metal Foams

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A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Porous Materials".

Deadline for manuscript submissions: closed (20 December 2022) | Viewed by 19040

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Prof. Dr. Vincenzo Naso

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Università degli studi di Napoli Federico II, Napoli, Italy
Interests: heat transfer and fluid flow; porous media; metal foams

Dr. Marcello Iasiello

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Department of Industrial Engineering, University of Naples Federico II, 80138 Napoli, Italy
Interests: porous media; thermal energy storage; phase change materials; bioheat; hyperthermia
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Dear Colleagues,

Metal foams are a relatively new class of porous materials. Their high heat transfer, specific surface area, effective thermal conductivity, and their tortuosity make them promising in applications where heat transfer needs to be enhanced, such as heat exchangers, heat sinks, thermal energy storage with phase change materials, volumetric solar receivers, and so on.

Experimental or predictive approaches are used to analyze heat transfer in metal-foams-equipped engineering devices. The latter approach is promising because of the complex foam morphology, which makes experiments challenging. Heat transfer and fluid flow in foams are modeled either in continuous macro-scale models by volumetrically averaging governing equations over a representative elementary volume (REV), or at the discrete pore level by reconstructing the foam geometry. The reconstruction is carried out with reference either to real foam samples, employing techniques such as computed tomography, or to idealized foam samples, employing models like those of Kelvin or Weaire–Phelan. Discrete approaches are useful to derive the so-called closing coefficients (permeability, inertial factor, volumetric heat transfer coefficient), the knowledge of which is mandatory to close equations for continuous models.

The aim of this Special Issue is to collect original research articles on the most recent analytical, numerical, and experimental research in this field, in order to provide guidelines for future research directions. Potential topics include, but are not limited to:

Open-cell foam microstructure;
Metal-foams-equipped heat transfer devices, with either continuous or discrete models;
Conductive, convective, and radiative heat transfer for pore-scale analyses.

Prof. Dr. Vincenzo Naso
Dr. Marcello Iasiello
Guest Editors

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Keywords

metal foams
heat transfer and fluid flow
heat exchangers
volumetric solar receivers
thermal energy storage
pore-scale analysis

Published Papers (9 papers)

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Research

21 pages, 4863 KiB

Open AccessArticle

Influence of Foam Morphology on Flow and Heat Transport in a Random Packed Bed with Metallic Foam Pellets—An Investigation Using CFD

by Ginu R. George, Marina Bockelmann, Leonhard Schmalhorst, Didier Beton, Alexandra Gerstle, Andreas Lindermeir and Gregor D. Wehinger

Materials 2022, 15(11), 3754; https://doi.org/10.3390/ma15113754 - 24 May 2022

Cited by 7 | Viewed by 1720

Abstract

Open-cell metallic foams used as catalyst supports exhibit excellent transport properties. In this work, a unique application of metallic foam, as pelletized catalyst in a packed bed reactor, is examined. By using a wall-segment Computational Fluid Dynamics (CFD) setup, parametric analyses are carried [...] Read more.

ϕ = 0.45 - 3 mm

and porosity

ε = 0.55 - 0.95

) and intrinsic conductivity on flow and heat transport characteristics in a slender packed bed

(N = D / d_{p} = 6.78)

made of cylindrical metallic foam pellets. The transport processes have been modeled using an extended version of conventional particle-resolved CFD, i.e., flow and energy in inter-particle spaces are fully resolved, whereas the porous-media model is used for the effective transport processes inside highly-porous foam pellets. Simulation inputs include the processing parameters relevant to Steam Methane Reforming (SMR), analyzed for low (

R e_{p} ~ 100)

and high (

R e_{p} ~ 5000)

flow regimes. The effect of foam morphologies on packed beds has shown that the desired requirements contradict each other, i.e., an increase in cell size and porosity favors the reduction in pressure drop, but, it reduces the heat transfer efficiency. A design study is also conducted to find the optimum foam morphology of a cylindrical foam pellet at a higher

R e_{p} ~ 5000

, which yields

ϕ

= 0.45,

ε

= 0.8. Suitable correlations to predict the friction factor and the overall heat transfer coefficient in a foam-packed bed have been presented, which consider the effect of different foam morphologies over a range of particle Reynolds number,

100 \leq R e_{p} \leq 5000

. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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21 pages, 6790 KiB

Open AccessArticle

Mono- and Multi-Objective CFD Optimization of Graded Foam-Filled Channels

by Gerardo Maria Mauro, Marcello Iasiello, Nicola Bianco, Wilson K. S. Chiu and Vincenzo Naso

Materials 2022, 15(3), 968; https://doi.org/10.3390/ma15030968 - 27 Jan 2022

Cited by 19 | Viewed by 2047

Abstract

Graded foam-filled channels are a very promising solution for improving the thermal performance of heat sinks because of their customized structures that leave large amounts of room for heat transfer enhancement. Accordingly, this paper proposes a comprehensive optimization framework to address the design of such components, which are subjected to a uniform heat flux boundary condition. The graded foam is achieved by parameterizing the spatial distributions of porosity and/or Pores Per Inch (PPI). Mono- and multi-objective optimizations are implemented to find the best combination of the foam’s fluid-dynamic, geometrical and morphological design variables. The mono-objective approach addresses the Performance Evaluation Criterion (PEC) as an objective function to maximize the thermal efficiency of graded foams. The multi-objective approach addresses different objective functions by means of Pareto optimization to identify the optimal tradeoff solutions between heat transfer enhancement and pressure drop reduction. Optimizations are performed by assuming a local thermal non-equilibrium in the foam. They allowed us to achieve a 1.51 PEC value with H* = 0.50, Re_H = 15000, i_ε = i_PPI = 0.50, ε(0) = 0.85, ε(1) = 0.97, PPI(0) = 5, PPI(1) = 40, and k_s_→f = 10⁴ as the design variables. For the three multi-objective functions investigated, one can extrapolate the optimum from the Pareto front via the utopia criterion, obtaining

\bar{h}

= 502 W/m² K and Δp = 80 Pa,

\bar{{Nu}_{H, unif}}

= 2790 and f = 42,

\bar{{⟨ T_{s}^{*} ⟩}^{s}}

= 0.011, and Δp* = 91. The optimal solutions provide original insights and guidelines for the thermal design of graded foam-filled channels. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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19 pages, 3682 KiB

Open AccessArticle

Preparation of Cast Metallic Foams with Irregular and Regular Inner Structure

by Ivana Kroupová, Martina Gawronová, Petr Lichý, Václav Merta, Filip Radkovský, Kamila Janovská, Isabel Nguyenová, Jaroslav Beňo, Tomáš Obzina, Iveta Vasková, Ivo Lána and Jiří Rygel

Materials 2021, 14(22), 6989; https://doi.org/10.3390/ma14226989 - 18 Nov 2021

Cited by 8 | Viewed by 1795

Abstract

The aim of this paper is to summarize the possibilities of foundry methods for the production of metallic foams. At present, there are a number of production technologies for this interesting material, to which increasing attention has been paid in recent years. What is unique about metallic foams is the combination of their physical and mechanical properties. As part of our research, we designed and verified four main methods of metallic foam production by the foundry technology, whose products are metallic foam castings with regular and irregular arrangements of internal cavities. All these methods use materials and processes commonly used in conventional foundry technologies. The main idea of the research is to highlight such technologies for the production of metallic foams that could be provided by manufacturing companies without the need to introduce changes in production. Moreover, foundry methods for the production of metallic foams have the unique advantage of being able to produce even complex shaped parts and can thus be competitive compared to today’s established technologies, the output of which is usually only a semi-finished product for further processing. This fact was the main motivation for the research. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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12 pages, 4696 KiB

Open AccessArticle

Analysing the Contact Conduction Influence on the Heat Transfer Intensity in the Rectangular Steel Bars Bundle

by Cezary Kolmasiak, Vazgen Bagdasaryan, Tomasz Wyleciał and Marek Gała

Materials 2021, 14(19), 5655; https://doi.org/10.3390/ma14195655 - 28 Sep 2021

Cited by 3 | Viewed by 1417

Abstract

Bundles of steel bars, besides metal foams, are an example of cellular solids. Such bundles constitute a charge during the heat treatment of bars. The paper presents a mathematical model of transient heat transfer in a bundle of rectangular steel bars based on the energy balance method. The key element of this model is the procedure of determining the effective thermal conductivity using the electrical analogy. Different mechanisms of heat transfer occurring within the analysed medium (conduction in steel and contact conduction) are assigned corresponding thermal resistances. The discussed procedure involves expressing these resistances with the use of arithmetic relationships describing their changes in the temperature function. Thermal contact resistance has been described with the use of the relationships determined experimentally. As a result of the performed calculations, the influence of contact conduction between the adjacent bars and bundle arrangement on its heating time was established. The results of the calculations show that the heating time of bundles can be lowered by 5–40% as a result of a decrease in the thermal contact resistance. This effect depends on the bar size and bundle arrangement. From the practical point of view, the analysed problem is connected with the optimization of the heat treatment processes of steel bars. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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20 pages, 14876 KiB

Open AccessArticle

Effect of Metal Foam Insert Configurations on Flow Boiling Heat Transfer and Pressure Drop in a Rectangular Channel

by Sanghyun Nam, Dae Yeon Kim, Youngwoo Kim and Kyung Chun Kim

Materials 2021, 14(16), 4617; https://doi.org/10.3390/ma14164617 - 17 Aug 2021

Cited by 2 | Viewed by 1624

Abstract

Heat transfer under flow boiling is better in a rectangular channel filled with open-cell metal foam than in an empty channel, but the high pressure drop is a drawback of the empty channel method. In this study, various types of metal foam insert configurations were tested to reduce the pressure drop while maintaining high heat transfer. Specifically, we measured the boiling heat transfer and pressure drop of a two-phase vertical upward flow of R245fa inside a channel. To measure the pressure and temperature differences of the metal foam, differential pressure transducers and T-type thermocouples were used at both ends of the test section. While the saturation pressure was kept constant at 5.9 bar, the steam quality at the inlet of the test section was changed from 0.05 to 0.99. The channel height, moreover, was 3 mm, and the mass flux ranged from 133 to 300 kg/m²s. The two-phase flow characteristics were observed through a high-speed visualization experiment. Heat transfer tended to increase with the mean vapor quality, and, as expected, the fully filled metal foam channel offered the highest thermal performance. The streamwise insert pattern model had the lowest heat transfer at a low mass flux. However, at a higher mass flux, the three different insert models presented almost the same heat transfer coefficients. We found that the streamwise pattern model had a very low pressure drop compared to that of the spanwise pattern models. The goodness factors of the flow area and the core volume of the streamwise patterned model were higher than those of the full-filled metal foam channel. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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12 pages, 3052 KiB

Open AccessArticle

On Determination of the Effective Thermal Conductivity of a Bundle of Steel Bars Using the Krischer Model and Considering Thermal Radiation

by Rafał Wyczółkowski, Vazgen Bagdasaryan and Stanisław Szwaja

Materials 2021, 14(16), 4378; https://doi.org/10.3390/ma14164378 - 5 Aug 2021

Cited by 5 | Viewed by 1664

Abstract

Cellular solid materials are commonly found in industrial applications. By definition, cellular solids are porous materials that are built of distinct cells. One of the groups of such materials contains metal foams. Another group of cellular metals contains bundles of steel bars, which create charges during the heat treatment of the bars. A granular structure connected by the lack of continuity of the solid phase is the main feature that distinguishes bundles from metal foams. The boundaries of the bundle cells are made of adjacent bars, with the internal region taking the form of an air cavity. In this paper, we discuss the possibility of using the Krischer model to determine the effective thermal conductivity of heat-treated bundles of steel bars based on the results of experimental tests and calculations. The model allows the k_ef coefficient to be precisely determined, although it requires the weighting parameter f to be carefully matched. It is shown that the value of f depends on the bar diameter, while its changes within the examined temperature range (25–800 °C) can be described using a third-degree polynomial. Determining the coefficients of such a polynomial is possible only when the effective thermal conductivity of the considered charge is known. Moreover, we analyze a simplified solution, whereby a constant value of the f coefficient is used for a given bar diameter; however, the k_ef values obtained thanks to this approach are encumbered with inaccuracy amounting to several dozen percentage points. The obtained results lead to the conclusion that the Krischer model cannot be used for the discussed case. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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17 pages, 10128 KiB

Open AccessArticle

Time-Resolved PIV Measurements and Turbulence Characteristics of Flow Inside an Open-Cell Metal Foam

by Youngwoo Kim, Chanhee Moon, Omid Nematollahi, Hyun Dong Kim and Kyung Chun Kim

Materials 2021, 14(13), 3566; https://doi.org/10.3390/ma14133566 - 25 Jun 2021

Cited by 2 | Viewed by 2188

Abstract

Open-cell metal foams are porous medium for thermo-fluidic systems. However, their complex geometry makes it difficult to perform time-resolved (TR) measurements inside them. In this study, a TR particle image velocimetry (PIV) method is introduced for use inside open-cell metal foam structures. Stereolithography 3D printing methods and conventional post-processing methods cannot be applied to metal foam structures; therefore, PolyJet 3D printing and post-processing methods were employed to fabricate a transparent metal foam replica. The key to obtaining acceptable transparency in this method is the complete removal of the support material from the printing surfaces. The flow characteristics inside a 10-pore-per-inch (PPI) metal foam were analyzed in which porosity is 0.92 while laminar flow condition is applied to inlet. The flow inside the foam replica is randomly divided and combined by the interconnected pore network. Robust crosswise motion occurs inside foam with approximately 23% bulk speed. Strong influence on transverse motion by metal foam is evident. In addition, span-wise vorticity evolution is similar to the integral time length scale of the stream-wise center plane. The span-wise vorticity fluctuation through the foam arrangement is presented. It is believed that this turbulent characteristic is caused by the interaction of jets that have different flow directions inside the metal foam structure. The finite-time Lyapunov exponent method is employed to visualize the vortex ridges. Fluctuating attracting and repelling material lines are expected to enhance the heat and mass transfer. The results presented in this study could be useful for understanding the flow characteristics inside metal foams. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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18 pages, 4340 KiB

Open AccessArticle

Review and a Theoretical Approach on Pressure Drop Correlations of Flow through Open-Cell Metal Foam

by Huizhu Yang, Yongyao Li, Binjian Ma and Yonggang Zhu

Materials 2021, 14(12), 3153; https://doi.org/10.3390/ma14123153 - 8 Jun 2021

Cited by 20 | Viewed by 2745

Abstract

Due to their high porosity, high stiffness, light weight, large surface area-to-volume ratio, and excellent thermal properties, open-cell metal foams have been applied in a wide range of sectors and industries, including the energy, transportation, aviation, biomedical, and defense industries. Understanding the flow characteristics and pressure drop of the fluid flow in open-cell metal foams is critical for applying such materials in these scenarios. However, the state-of-the-art pressure drop correlations for open-cell foams show large deviations from experimental data. In this paper, the fundamental governing equations of fluid flow through open-cell metal foams and the determination of different foam geometry structures are first presented. A variety of published models for predicting the pressure drop through open-cell metal foams are then summarized and validated against experimental data. Finally, two empirical correlations of permeability are developed and recommended based on the model of Calmidi. Moreover, Calmidi’s model is proposed to calculate the Forchheimer coefficient. These three equations together allow calculating the pressure drop through open-cell metal foam as a function of porosity and pore diameter (or strut diameter) in a wide range of porosities ε = 85.7–97.8% and pore densities of 10–100 PPI. The findings of this study greatly advance our understanding of the flow characteristics through open-cell metal foam and provide important guidance for the design of open-cell metal foam materials for different engineering applications. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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13 pages, 4279 KiB

Open AccessArticle

Melting of PCMs Embedded in Copper Foams: An Experimental Study

by Andrea Diani and Luisa Rossetto

Materials 2021, 14(5), 1195; https://doi.org/10.3390/ma14051195 - 4 Mar 2021

Cited by 19 | Viewed by 2087

Abstract

A smart possible way to cool electronics equipment is represented by passive methods, which do not require an additional power input, such as Phase Change Materials (PCMs). PCMs have the benefit of their latent heat being exploited during the phase change from solid to liquid state. This paper experimentally investigates the melting of different PCMs having different melting temperatures (42, 55 and 64 °C). Two copper foams, having 10 PPI and relative densities of 6.7% and 9.5%, i.e., porosities of 93.3% and 90.5%, respectively, are used to enhance the thermal conductivity of PCMs. The block composed by the PCM and the copper foam is heated from one side, applying three different heat fluxes (10, 15 and 20 kW m⁻²): the higher the heat flux, the higher the temperature reached by the heated side and the shorter the time for a complete melting of the PCM. The copper foam with a relative density of 9.5% shows slightly better performance, whereas the choice of the melting temperature of the PCM depends on the time during which the passive cooling system must work. The effect of the foam material is also presented: a copper foam presents better thermal performances than an aluminum foam with the same morphological characteristics. Finally, experimental dimensionless results are compared against values predicted by a correlation previously developed. Full article

(This article belongs to the Special Issue Research on Flow and Heat Transfer in Metal Foams)

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