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Energy Procedia 88 (2016) 566 - 573

CUE2015-Applied Energy Symposium and Summit 2015: Low carbon cities and urban

energy systems

Thermal analysis of cold storage: the role of porous metal

12 2 2 3 1*

Xiaohu Yang ' , Wenbin Wang , Shangsheng Feng ' , Linwen Jin ' , Tian Jian

Lu2'3'* , Yue Chai1, Qunli Zhang4

1Group of the Building Energy & Sustainability Technology, School of Human Settlements and Civil Engineering, Xi'an Jiaotong

University, Xi'an 710049, China 2Moe Key Laboratory for Multifunctional Materials and Structures, Xi'an Jiaotong University, Xi'an 710049, P.R. China 3State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi 'an 710049, China 4Beijing Municipal Key Lab of Heating, Gas Supply, Ventilating and Air Conditioning Engineering, Beijing University of Civil _Engineering and Architecture, Xicheng District, Beijing 100044, China_

Abstract

We conduct both analytical and numerical investigations on the solidification behavior of fluid saturated in highly porous open-cell metallic foams. Based on the pore-scaled thermal equilibrium assumption, an analytical extension is made to the classical Neumann's solution to solidifying fluid as an interstitial into metallic foams. To underlying the heat transfer mechanisms for phase change process and the role of inserted foam, an idealized tetrakaidecahedron unit cell geometric model was reconstructed and direct numerical simulations were conducted. Showing good agreement with experimental results and direct numerical simulations, the developed model is verified, favoring the assumption of local thermal equilibrium. The numerical simulation results at pore scale qualitatively demonstrate that: i) the solidification interface is globally flat within a pore; ii) the local natural convection does exist and it contributes to the evolution of solidification interface (9% promotion).

© 2016 The Authors.Publishedby ElsevierLtd. Thisis an open access article under the CC BY-NC-ND license

(http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of CUE 2015

Keywords: open-cell foam, cold storage, thermal equilibrium, pore-scale analysis, analytical model

1. Introduction

Cold storage and release for Heating, Ventilation and Air Conditioning (HVAC) systems has been showing more and more attractions for the resulted improved thermal efficiency for the HVAC systems

* Corresponding author. Tel.: +86-29-83395127; fax: +86-29-83395100 E-mail address: lwjin@xjtu.edu.cn; tjlu@xjtu.edu.cn.

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Peer-review under responsibility of the organizing committee of CUE 2015

doi:10.1016/j.egypro.2016.06.079

[1]. Typically, cold is stored and released through the phase change materials (PCMs) undergoing a change of phase, e.g. solidification and melting of water/water-ethylene glycol mixture. The cold storage and release process, however, suffers significantly from the relative low thermal conductivity of the engineering-utilized PCMs. To enhance the thermal conductivity of PCMs, various techniques have been developed such as adding micro-/nano-scaled particles, fin array and porous matrix [1]. Compared with the attainable enhancement by involving micro/nano particles, non-moving metallic matrix poses increasingly promising issues for their low cost, structural controllability and satisfactory thermal enhancement [2].

Efforts have been made to investigate the enhancement by porous matrix on phase change process [24]. Xiao et al. [3] gave a detailed description on how the PCM-foam composite was experimentally prepared. Siahpush et al. [5], Lafdi et al. [6], Zhao et al. [2], Li et al. [7] and Fleming et al. [8] experimentally examined how copper porous foam enhances the heat transfer performance in a solid/liquid phase change thermal energy storage system, and their results demonstrated that the involvement of metal foam can dramatically reduce the time for thermal storage. Feng et al. [4] experimentally examined the unidirectional solidification behavior of water saturating open-cell metallic foams under a constant temperature thermal boundary. They found that the thermal contact resistance can be readily neglected during the freezing process of water filled in open-cell foams.

Experimental observations are capable of both providing benchmark and giving direct demonstration of the history of transient solid-liquid phase interface. Volume-averaging-based numerical simulations are often utilized to simulate the solidification/melting processes in metallic foams, with particular focus on the effect of local thermal equilibrium and non-equilibrium. Tong et al. [9] numerically examined the enhancement of solidification by inserting Al foam into pure water. Li et al. [7], Mesalhy et al. [10], Yang and Garimella [11], Tian and Zhao [12], and Srivatsa et al. [13] numerically solved the volume-averaging equations (two temperature equations) for phase change in porous metal foams, with non-Darcy effect, local natural convection and thermal non-equilibrium considered.

To get an insight into the phase change phenomena, direct numerical simulations at pore scale are needed. Well-known Kelvin cell and its derived structures are applied to mimic the real foam topology. Fleming et al. [8] built a column of Kelvin cells saturated with water as the PCM and numerically modeled the solidification of the saturating water. Hu et al. [14, 15] numerically compared the phase interface propagation in body-centered-cubic lattice embedded with spherical micro-pores and volume-averaged simulations. They demonstrated that the DNS simulations can provide insight into the complicated heat transfer, a three-dimensional PCM melting front and temperature distribution. Moreover, the DNS results were also used to extract thermo-physical parameters such as effective thermal conductivity and interstitial heat transfer coefficients [15]. Feng et al. [16] compared the results obtained by direct simulations on pore-scaled sphere-centered Kelvin cells and volume-averaged numerical simulations. They suggested that the one-temperature model may be applicable with using the volume-averaged method.

To summarize the above-reviewed research investigations, the phase change behavior of paraffin saturated in porous foams have been intensively investigated by experimental and numerical approaches. The metal foams exploited for enhancing phase change heat transfer are mainly made by ERG Corporation, whose foam struts are solid due to the direct foaming fabrication routine. Little concern has been paid to the effect of hollow struts of metallic foams (fabricated by electroplating approach) on the phase change heat transfer. Further, the pore-scaled analysis for solidifying a fluid saturated in open-cell metal foam hasn't been examined sufficiently such as the effect of pore-scaled natural convection in a representative unit cell of open-cell foams.

The present study therefore aims to get a physical insight into the effect of foam hollow struts on the phase change heat transfer characteristics from a reconstructed representative unit cell mimicking the real

foam topology. Particular attentions have been also paid to quantify the contribution of pore-scaled natural convection to the overall phase change heat transfer. Besides, the local thermal equilibrium state is also examined from the direct numerical simulation and it is compared with extended Neumann's solution to solidification.

Nomenclature

Abbreviation

HVAC Heating, ventilation and air Conditioning

PCM Phase change material

Symbols

cP Specific heat

H Total height of the fluid-foam composite

k Thermal conductivity

L Latent heat

S(t) Solidified layer thickness

T Temperature

t Time

a Thermal diffusivity

s Porosity

y Inner-hollow ratio

À Positive root of a transcendental equation

Subscript

e Effective

f Saturating Fluid

i Initial State

m Solidification Point

s Metal Foam

w Wall

1 Solidified Phase

2 Liquid Phase

2. Numerical simulation

For the present cooling condition and foam configuration, heat is removed from the bottom, leading to significantly suppressed global natural convection in the liquid phase. Heat transfer mode in the fluid-

foam composite is therefore dominated by heat conduction, which is globally treated as one-dimensional (see the snapshot of the transient phase interface). To underlying the phase change heat transfer at pore scale, an idealized tetrakaidecahedron geometric model [5] with inner-hollow ligaments (see Fig. 2 (a)) was reconstructed using SOLIDWORKS 2013 as depicted in Fig. 2(a) according to the topology nature of open-cell metal foams due to their fabrication routine, as depicted in Fig. 2(b) for SEM image. Direct numerical simulations on the phase change of fluid saturated in foams are carried out, with exploiting the finite volume method (FVM) embedded within the commercially available software ANSYS-FLUENT 14.5. All tetrahedron elements are adopted to discretize solid and fluid domains; see Fig. 2(b). Constant temperature thermal boundary condition and thermal insulation boundary are separately imposed on the bottom and top faces, while the other four faces are kept at symmetry. To investigate the effect of local natural convection on overall phase change process, Boussinesq assumption was adopted to simulated the fluid convection.

Figure 1 (a) Idealized tetrakaidecahedron unit cell model; (b) SEM image of the hollow ligament

Figure 2 (a) Computational domain and (b) representative mesh.

3. Results and dicussion

3.1. Effect of hollow struts on solidification

From the image of open-cell copper foam (see Fig. 1(b)), it is qualitatively observed that the ligament is inner hollow but the overall topological features have not been changed due to the electrochemical plating fabrication approach for open-cell copper foams. Quantitatively speaking, hollow strut not only affect the relative density (1-porosity) but also the effective thermal conductivity of the bulk material. The

relative density can be readily determined by weighing the foam samples, while the influence of hollow ligaments upon effective thermal conductivity and its inherent contribution to the overall phase change process can be considered by the volume averaging theory for porous media.

Based on the local thermal equilibrium assumptions and the volume averaging theory for porous media, we extended Neumann's solution that originated for pure substance to the fluid-foam composite, expressed as:

S (t) = 2Ayjaet / H2 (1)

where S(t) is the solidification thickness, the effective thermal diffusivity ae can be determined by ae=ke/(pecpe); pe and cpe are as a function of weight fraction of each phase, ke can be predicted by Refs. [17-18]; X is the positive root of the following transcendental equation:

_ kf 2^(T - T)e^f '/ttf2 _ L (2)

erf (!) kf (T - Tw )erfc(^af J af 2) Cf i(T - T„ )

here, erf!) and erfc(X) are the Gaussian error function and the subscript "1" and "2" denote solidified and liquid phase of the saturating fluid.

____ model, 0.96

model, 0.98

■ expt, 0.96

▲ expt, 0.98

• expt, water

□ NS, 0.96

A NS, 0.98

O NS, water

2000 4000 6000 8000 10000 12000 14000 16000

10« s 1000 s 4000 s 8000 s

Figure 3 (a) Comparison of transient solidification locations obtained from analytical model, experiments [4] and pore-scaled numerical simulations; (b) Snapshot of transient solidification interface

Figure 3(a) compares the location of the transient solid-liquid phase interface of fluid saturated in open-cell metal foams with various pore morphological parameters, pure distilled water as the basis.

Achieving good agreement with experimental results [4] as well as the present direct numerical simulation (based on reconstructed geometric model), the extended Neumann's model is validated, favoring pore-scaled thermal equilibrium between foam ligaments and saturating fluid. The detailed solidification interface at pore scale is numerically shown in Fig. 3(b). As we can see, the solidification interface seems globally flat even the higher conductive metallic ligaments are inserted; there is only small portion of fluid next to the colder metallic ligament gets solidified.

3.2. Effect of local natural convection on solidification.

Conduction Natural dominated convection

Figure 4 Snapshot of transient solidification interface with and without natural convection

The effect of global natural convection upon phase change process, e.g. solidification for the present study is commonly neglected due to the thermal configuration (bottom cooling or top heating) in the experimental measurements. So does the volume-averaged numerical simulation. However, the pore-scaled observation of local natural convection and its contribution to the overall solidification interface evolution is not fully quantified. Figure 4 presents the numerically-simulated results of transient phase interface with and without considering local natural convection. It is observed in Fig. 4 that the solidliquid phase interface front with considering local natural convection is similar with that for conduction dominated case. Natural convection does exist in the liquid layer (red zone in Fig. 4) but the velocity is not noticeable (10-5 magnitude). Be that as it may, the local natural convection contributes a little to the evolution of solidification front; the solidified layer (S2) is a little bit thicker for natural convection case than that (Sj) without convection, i.e. S2/Sj=1.09. This can be also quantified in Fig. 3(a) that the numerical simulation results (conduction + convection) are 10% percent higher than model prediction (conduction only).

3.3. Role of metallic foam on solidification

Metal foam in the solidification process of fluid has two roles based on the location: i) for the solidified part, the existence of metal foam improves the overall effective thermal conductivity of foam-ice composite, favoring a higher efficiency of cold (sensible heat) removal from the cooling boundary to meet the further solidification; ii) for the liquid part, metallic ligaments help conduct the sensible heat for liquid phase, metallic ligaments and the latent heat for the newly-formed ice. Due to the local thermal

equilibrium at pore scale, the ligaments share the same temperature with the saturating fluid within a pore, indicating that the first role of metal foam is more important for enhancing phase change heat transfer.

4. Conclusion

The present study analytically and numerically deals with the solidification behavior of fluid saturated in open-cell metallic foams. The developed analytical model that is based on the pore-scaled thermal equilibrium and Neumann's solution shows good agreement with experimental results and numerical simulations. Direction numerical simulations on the reconstructed tetrakaidecahedron geometric model demonstrate that the temperature difference between metallic ligaments and interstitial fluid is negligible. Through analyzing the effect of open-cell foam on the phase change heat transfer, the dominating role of foams for enhancing solidification is to increase the thermal conductivity of the solidified layer, which is also favoring an efficient way in engineering to further enhance solidification through improve the conductivity of solidified layer.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51506160), China Post-doctoral Science Foundation Funded Project (2015M580845) the Beijing Key Lab of Heating, Gas Supply, Ventilating and Air Conditioning Engineering (NR2015K01 & NR2016K01).

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Biography

Dr. Jin Liwen obtained his Ph.D. from Nanyang Technological University of Singapore and then worked at National University of Singapore. He is currently a professor working at Xi'an Jiaotong University, China. His research interests include building energy analysis, solar/cold heat storage and heat transfer in microchannels.