On the thermal properties of expanded perlite – Metallic syntactic foam

International Journal of Heat and Mass Transfer 90 (2015) 1009–1014

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On the thermal properties of expanded perlite – Metallic syntactic foam T. Fiedler ⇑, I.V. Belova, G.E. Murch The University of Newcastle, School of Engineering, Callaghan, NSW 2287, Australia

a r t i c l e

i n f o

Article history: Received 1 March 2015 Received in revised form 26 May 2015 Accepted 10 July 2015

Keywords: Syntactic foam Thermal properties Steady-state method Thermal contact resistance Lattice Monte Carlo

a b s t r a c t This paper addresses the thermal properties of syntactic metal foam made by embedding expanded perlite particles in A356 aluminium matrix. Lattice Monte Carlo (LMC) analyses are conducted to determine the thermal characterisation of the foam. For increased accuracy, the complex geometry of the metallic foam is captured by micro-computed tomography imaging. Using the resulting detailed geometric models, the effective thermal conductivity tensor is computed with possible thermal anisotropy taken into consideration. The numerical results are verified by comparison with experimental measurements. To this end, an improved steady-state method is used to correct for thermal contact resistance. Furthermore, the effective heat capacity, average density and thermal diffusivity of perlite – metal syntactic foam are determined. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Materials with metallic matrix and internal porosity are commonly referred to as cellular metals. They are multi-functional and they typically show high strength to weight ratio [1], damping [2], and controlled energy absorption [3] combined with versatile thermal properties. Due to the high thermal conductivity of the metallic phase, cellular metals can be used for conductivity enhancement of energy storage composites [4,5] and as heat exchangers [6–8]. The present paper addresses the thermal properties of novel metallic syntactic foam (MSF). This subclass of cellular metals is created by combining hollow particles with a continuous metallic matrix [9]. For the material considered the hollow particles are expanded perlite and the matrix is A356 aluminium alloy. Syntactic metal foams have been previously fabricated by embedding metallic [10,11] glass [12] or ceramic spheres [13,14] into a metallic matrix. Due to their closed cell porosity MSFs are not usually suitable for conductivity enhancement or for use in heat exchangers. However, the novel expanded perlite MSF overcomes this limitation. Due to its low strength, the perlite, which is volcanic glass, can be readily removed (e.g. using a high pressure water jet) resulting in a porous aluminium structure with an interconnecting pore network. Such a material is referred to as a metallic sponge and is attractive for thermal applications due to its large accessible surface area and relatively high thermal conductivity. There has been a strong focus on structural applications of MSFs but previous work on the thermal properties is surprisingly scarce. ⇑ Corresponding author. Tel.: +61 (0)2 4921 6188. E-mail address: [email protected] (T. Fiedler). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.07.049 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

In [15,16] the effective thermal conductivity of syntactic steel foams containing hollow spheres was predicted using numerical analysis. Conductivities were found to decrease from 35 W/m K to 20 W/m K with increasing filler particle fraction. This work was extended for advanced pore morphology (APM) filler particles [17] in an aluminium matrix. Due to the higher intrinsic conductivity of aluminium, relatively high conductivities of the syntactic foam, between 32 W/m K and 41 W/m K, were found. Furthermore, the thermal expansion coefficient of MSF was studied for hollow SiC filler particles [18] and cenospheres [19]. This somewhat limited literature on thermal properties is dwarfed by research focusing on the thermal characterisation of metallic sponges that consider thermal energy transfer by conduction [20,21], convection [22,23] and radiation [24,25]. A thorough review thereof is far beyond the scope of this paper. This difference in research intensity is easily explained by the large field of thermal applications for cellular metals with interconnected porosity. The present paper addresses for the first time the thermal properties of MSF containing expanded perlite particles. Analytical and numerical approaches are combined with experimental measurements to determine the material density, specific heat capacity, effective thermal conductivity, and effective thermal diffusivity. 2. Methodology 2.1. Sample manufacturing Perlite aluminium syntactic foams were manufactured using infiltration casting. The expanded perlite particles (particle density 0.18 g/cm3 [26]) were approximately spherical in shape and

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Nomenclature Symbol CA356 CMSF D⁄ Deff hS kA356 keff kEP kR lR mAl mPE mS NJA NP

Description (Dimension) specific heat capacity of A356 alloy (J/kg K) specific heat capacity of MSF (J/kg K) dimensionless diffusivity (–) effective thermal diffusivity (m2/s) sample height (m) thermal conductivity of A356 alloy (W/m K) effective thermal conductivity (W/m K) thermal conductivity of expanded perlite (W/m K) thermal conductivity of reference body (W/m K) distance between temperature measurement locations (m) mass of aluminium (kg) mass of perlite (kg) mass of sample (kg) number of jump attempts per particle (–) number of probing particles (–)

particles with diameters between 2 and 2.8 mm were separated by sieving. These particles were filled into a mould and the resulting packed bed was infiltrated with liquid A356 aluminium alloy. A subsequent thermal T6 treatment enhances the mechanical properties of the syntactic foam [27]. A detailed description of the manufacturing procedure can be found in [26]. The resulting samples were of cylindrical shape as depicted in Fig. 1a. The three-dimensional reconstruction of micro-computed tomography (lCT) data shown in Fig. 1b only considers the metallic phase of the foam material. It can be seen that pores (i.e. the volume occupied by the expanded perlite particles) percolate as neighbouring particles touch during the infiltration casting. 2.2. Lattice Monte Carlo analysis Lattice Monte Carlo (LMC) is a finite difference based method that simulates diffusion in virtual models by random walks of probing particles [28,29]. The method is frequently used for the analysis of thermal [29–31] and mass diffusion problems [32,33]. Its major advantage over finite element methods is memory efficiency allowing the computation of a 109 voxel model on a standard desktop system (8 GB RAM). Further benefits are the simple model generation from lCT data and its high numerical stability. In the first step of the LMC analyses, virtual models of the MSF are created. Due to the complex meso-structure of the foam material, geometric models are derived from lCT scans of samples. A high voxel resolution (voxel side length 35.32 lm) ensures an

p q_ R RC,HE RC,R RS Rtot t TIF THE TR1, TR2 VAl

v UAl

q qAl

porosity (i.e. volume fraction of perlite particles) (–) heat flux (W) particle displacement (voxel) thermal contact resistance (m2 K/W) thermal contact resistance (m2 K/W) thermal material resistance of the sample (K/W) total thermal resistance (K/W) LMC temp (i.e. total number of jump attempts) (–) extrapolated temperature (K) temperature of the heating element (K) temperatures of the reference body (K) volume of aluminium (m3) anisotropy ratio (–) aluminium volume fraction (–) density of MSF samples (kg/m3) density of aluminium (kg/m3)

accurate geometric representation. In the present study, a total of six lCT data scans were obtained and their physical properties are summarised in Table 1. The result of the lCT scans is primitive cubic voxel data where the greyscale level of each voxel indicates the average density within its volume. Thus, segmentation allows the distinction between the high density aluminium and low density expanded perlite particles or pores. For this segmentation, the aluminium volume fraction UAl of the scanned MSF samples is determined. To this end, the sample is weighed on a precision scale to measure the sample mass mS (see Table 1). This value is corrected by the perlite mass mPE that had been determined prior to casting in order to obtain the aluminium mass mAl = mS – mPE. Using the density of A356 aluminium alloy (qAl = 2520 kg/m3 [34]) the aluminium volume VAl is calculated using VAl = mAl/qAl. The aluminium volume fraction is then determined by the division of the aluminium volume with the cylindrical sample volume VS (see Table 1), i.e. UAl = VAl/VS. During the segmentation of the lCT data the greyscale threshold is iteratively adjusted until the segmented volume fraction UAl in the numerical model coincides with this calculated value. In the next step, the cylindrical lCT data is truncated to make the largest possible prism and the geometry is mirrored relative to three perpendicular surfaces. This step is required in order to prescribe periodic boundary conditions on all surfaces of the numerical model. The truncated voxel data is converted into a primitive cubic lattice model by substituting each voxel with a lattice node located at its centre. The segmented material information (i.e. A356 aluminium or expanded perlite)

Fig. 1. Perlite metal syntactic foam (PMF): (a) cylindrical sample, (b) lCT reconstruction, (c) detailed view of the foam structure.

T. Fiedler et al. / International Journal of Heat and Mass Transfer 90 (2015) 1009–1014 Table 1 Physical properties of perlite MSF samples: numerical (N) and experiment (E). ID

Mass [g]

Volume [cm3]

Density [g/cm3]

Porosity [vol.%]

N1 N2 N3 N4 N5

33.80 32.74 33.82 34.25 32.17

33.29 32.20 32.27 32.35 32.25

1.04 1.02 1.05 1.06 1.00

61.2 64.1 61.4 60.4 64.4

E1 E2 E3 E4 E5

24.15 24.58 24.38 24.67 24.19

22.77 23.05 23.62 23.29 23.37

1.06 1.07 1.03 1.06 1.03

64.4 63.8 65.0 64.1 65.0

1011

where p is the volume fraction of the filler particles (in this paper also referred to as porosity). For the case when the embedded particles are connected, a better analytical expression for the effective conductivity is given by the Bruggeman (or differential effective-medium) approximation [40]: B

keff ¼ kA356 ð1  pÞ3=2

ð3Þ

It should be added that the theoretical upper limit of the Maxwell expression is approximately 66 vol.% of porosity whereas there is no limit for the application of the Bruggeman approximation. 2.4. Steady-state measurements

is stored for each lattice node. Due to the very low conductivity of expanded perlite kEP < 0.3 W/m K [35] in comparison to A356 aluminium alloy kA356 = 151 W/m K [36] its conductivity was considered to be negligible in all simulations. This approach significantly reduces computation times without noticeably affecting the simulation results [28,30]. Following the model generation, a large number of probing particles (N P = 105) are randomly distributed within the conducting aluminium phase. These probing particles then perform random walks within the lattice model of the MSF geometry and each particle has N JA ¼ 106 jump attempts. The numbers of probing particles N P and jump attempts N JA have been tested in preliminary analysis and were chosen sufficiently large so that further increase did not significantly affect the computed diffusivity (i.e. less than 0.5% deviation). Jump attempts are only possible between the current particle node and one of its six closest neighbours (primitive cubic topology). Apart from this restriction, the jump directions are random and there is no probing particle interaction. This random particle motion is governed by jump probabilities which in optimised LMC [28] are the scaled local thermal conductivities. Since the conductivity of the perlite phase is considered to be negligible, i.e. kEP  0, successful jump attempts are limited to the aluminium phase. After completion of all random walks, the Einstein–Smoluchowski equation [37,38] is used to calculate the dimensionless diffusivity D⁄

D ¼

hR2 i 2dt

ð1Þ

where R2 is the mean square particle displacement, d = 3 is the dimensionality and the LMC time t = 1011 is the total number of jump attempts per simulation. Directional conductivities for anisotropy analysis are computed the same way by considering only components of the particle displacement vectors R and decreasing the dimensionality to 1. For the considered MSF models containing a single conductive phase, the effective thermal conductivity keff is obtained by multiplication of the aluminium conductivity kA356 with the dimensionless diffusivity, i.e. keff = D* kA356. The numerical uncertainty of the computed conductivity can be quantified using pffiffiffiffiffiffi 1/ N P  0:32% [28]. 2.3. Analytical approach In addition to numerical calculations, analytical relations can be used to estimate the effective MSF conductivity. In [39] it was shown that the Maxwell expression gives a reasonable estimation for the theoretical value of the effective thermal conductivity for cases where the embedded particles have a lower conductivity than the matrix phase and are well separated from each other (namely, when most of the particles do not touch each other): M

keff ¼

2ð1  pÞkA356 2þp

ð2Þ

Complementing the computational and analytical analyses, thermal steady-state measurements of MSF thermal conductivity were conducted. To this end, a sample was positioned on a heating element with a constant surface temperature THE (see Fig. 2). A cylindrical reference body of solid A356 aluminium alloy with the known thermal conductivity kA356 = 151.3 W/(m K) [36], a diameter of 26.77 mm, and a height of 60 mm was positioned on the top of the sample. The reference contains two temperature sensors TR1 and TR2 that were used to obtain the thermal flux q_ passing through the stack. The assembly is completed by a watercooled heat sink sustaining a constant temperature gradient. Measurements were conducted within a vacuum chamber to eliminate convective heat transfer from the components and ensure one-dimensional heat flow. Radiation heat loss was minimised by the use of thermal radiation shields. The thermal contact resistances between heating element and sample (RC,HE) as well as sample and reference (RC,R) are of crucial importance for accurate measurements. Therefore, contact resistances were minimised by using thermally conducting paste (OMEGATHERMÒ 201) and by applying a compressive force (50 N) on the measurement stack. The residual contact resistances have been determined in preliminary measurements using two reference bodies of known conductivity. These cylindrical reference bodies were made of 99% pure copper (conductivity 398 W/m K [41]) with a diameter of 31.0 mm and heights of 30 mm and 60 mm, respectively. Their corresponding measurement lengths lR are 23.7 mm and 52.75 mm). The surfaces of these reference bodies have been machined in the same manner as the MSF samples (i.e. using an identical milling machine and tool) to ensure a comparable surface structure and thus a similar thermal contact resistance. Each reference body contains two temperature sensors and assuming a linear steady-state temperature distribution, the extrapolation of temperatures allows the determination of the temperature drop DT at the interfaces. The heat flux q_ passing through the stack can be calculated using q_ ¼ kR  ðT R1  T R2 Þ=lR where kR is the reference material conductivity and lR is the distance between the temperature measurement locations. The contact resistances normalised by area can then be calculated _ The corresponding temperature drops in the copusing R ¼ DT=q. per cylinders T R1  T R2 are 7.1 K (30 mm reference) and 15.7 K (60 mm reference). The extrapolated temperature drops DT at the interfaces are 3.8 K (reference – heating element) and 7.2 K (reference – reference). Accordingly, the contact resistances are RC,HE = 3.21E5 m2 K/W and RC,R = 6.08E5 m2 K/W (both ±1.76%). These contact resistances must be considered in the determination of the unknown effective conductivity keff of the MSF samples. A small error is introduced since the contact resistance of solid reference bodies may slightly deviate from the corresponding contact resistance of MSF samples. However, it is not possible to measure this contact resistance directly and RC,HE and RC,R provide good approximations. As depicted in Fig. 2 the total thermal resistance of a sample is:

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Fig. 2. Schematic representation of the experimental setup.

Rtot ¼ RC;HE =A þ RS þ RC;R =A

ð4Þ

where A is its cross sectional area. The total thermal resistance can be calculated using the measurement data as Rtot ¼ ðT IF  T HE Þ=Q_ where T IF is the extrapolated temperature at the contact surface of the reference (see Fig. 2). Eq. (4) can now be solved for the thermal material resistance RS of the sample and the effective MSF conductivity can be determined according to:

keff ¼

hS RS  A

ð5Þ

with the sample height hS . The sample heights were 40.45 mm, 40.95 mm, 41.97 mm, 41.38 mm, and 41.53 mm for samples E1–E5, respectively. Analysis of experimental uncertainty (all temperature measurements ±0.1 K, length ±0.01 mm) yields a relative variation of ±4.51% for the effective thermal conductivity. 3. Results 3.1. Effective thermal properties For a comprehensive thermal characterisation of MSF, their average density, specific heat capacity and effective thermal conductivity are required. Density (q) information is easily obtained by measuring sample mass and volume with the results q ¼ 1:00 . . . 1:07 g/cm3 shown in Table 1. The specific heat capacity of A356 aluminium alloy is given in the literature as CA356 = 963 J/kg K [36]. Perlite has an average MSF mass fraction of 9.8% and its specific heat is 387 J/kg K [42]. Disregarding the contribution from gas entrapped in the perlite particles, the specific heat of MSF is the mass weighted average of the constituents, i.e. CMSF = 907 J/kg K. Fig. 3 shows the effective thermal conductivity of MSFs plotted versus their porosity. As expected, the conductivity continuously decreases as the volume fraction of the non-conductive porosity increases. The different marker types represent numerical (LMC) and experimental results, respectively. Two different groups of low (61 vol.%) and high porosity (64 vol.%) samples can be distinguished. For better comparison, a linear regression curve keff ¼ ð135:0  167:9  qÞ W/m K was added based on the LMC data points (dotted line, R2 = 0.958). Importantly, excellent agreement between experimental and numerical data is found showing the validity of the numerical results. The analytical solutions for the

Fig. 3. Effective thermal conductivity vs porosity.

Maxwell (Eq. (2)) and Bruggeman (Eq. (3)) equations are plotted using full lines. It can be seen that both relations overestimate the effective thermal conductivity. The poor agreement of the Maxwell equation can be explained by the fact that the perlite particles are not separated but form a percolating porous network that significantly reduces the conductivity. The Bruggeman model only requires the matrix to percolate (without any requirements for the pore space) and hence gives a better estimate of MSF conductivity. Fig. 4 is an Ashby plot [43] for the effective thermal conductivity and density of common engineering materials. The graph was created using the Granta Design database [44] and complemented by MSF data of the present study, syntactic APM aluminium foam data taken from [17] and a study of open-cell AlSi7 foam [45]. Most noticeably, the data cloud representing perlite MSF intersects with previous data on Aluminium foam (Granta Design database) and AlSi7 foam. However, at the same density, perlite MSF exhibits a slightly lower conductivity. This can be explained by the presence of expanded perlite that increases the mass (average mass fraction is 9.8%) without noticeably contributing to its conductivity. Removal of the perlite particles (e.g. using a high pressure water jet) will decrease the foam density by 9.8%. The resulting data labelled Porous MSF has a similar conductivity to density ratio as the aluminium foam.

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Fig. 4. Ashby plot for thermal conductivity and density.

Einstein equation. The result is a complete representation of the conductivity tensor with two-dimensional projections shown in Fig. 5 below. For clarity, results are shown for only two representative samples with minimum (q = 1.00 g/cm3) and maximum (q = 1.06 g/cm3) density. Within the yz-plane (i.e. perpendicular to the infiltration direction during casting) isotropic behaviour is found indicated by the circular shape of the graphs. In agreement with Fig. 2, the radius of the high density (i.e. low porosity) structure is larger indicating a higher effective thermal conductivity. For the perpendicular xy- and xz-planes, a slight increase of the thermal conductivity is found for the casting (x) direction. This weak thermal anisotropy can be quantified by the ratio v of minimum and maximum directional conductivity. The ratios along with the effective thermal properties are listed in Table 2 for all numerical samples. Maximum anisotropy is found for the low density samples whereas almost perfectly isotropic behaviour (v ? 1) is observed for high density perlite-MSF. However, in all cases the deviation between maximum and minimum directional conductivity remains below 5%. Table 2 also shows the results for the effective thermal diffusivity which is calculated according to Deff ¼ keff =ðq  C MSF Þ.

Fig. 5. Thermal anisotropy.

3.2. Anisotropy 4. Conclusions A particular strength of the Lattice Monte Carlo analysis is the ability to investigate thermal anisotropy. This is achieved by considering directional components of the particle diffusion in the

This paper addressed the thermal characterisation of novel perlite syntactic metallic foam. The density of the material was found

Table 2 Thermal properties of numerical perlite-MSF samples. ID

Density [g/cm3]

keff [W/m K]

kmax [W/m K]

kmin [W/m K]

v

Deff [m2/s]

N1 N2 N3 N4 N5

1.04 1.02 1.05 1.06 1.00

32.5 28.9 32.2 32.9 25.2

33.4 29.7 32.6 33.5 25.9

31.9 28.2 31.9 32.3 24.5

0.96 0.95 0.98 0.97 0.95

3.45E05 3.12E05 3.38E05 3.42E05 2.78E05

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to vary between 1.00 and 1.07 g/cm3. The effective heat capacity 907 J/kg K of the syntactic foam was calculated as the mass weighted average of its constituents. Combined numerical and experimental analyses were conducted to determine the effective thermal material conductivity. Excellent agreement between the two approaches was found indicating an average conductivity of 30.3 W/m K. The thermal conductivity was found to reduce linearly with decreasing density. The analytical Bruggeman approximation for the effective thermal conductivity showed the better agreement with the numerically obtained values compared with the Maxwell approximation. Lattice Monte Carlo analysis further enabled the investigation of thermal anisotropy. Only a small directional variation of the effective thermal conductivity was found with less than 5% deviation between minimum and maximum values. The orientation of slightly higher conductivities coincided with the casting direction and anisotropy was somewhat more pronounced in the case of low density samples. Conflict of interest None declared. References [1] A.G. Evans, J.W. Hutchinson, M.F. Ashby, Cellular metals, Curr. Opin. Solid State Mater. Sci. 3 (1998) 288–303. [2] J. Banhart, J. Baumeister, M. Weber, Damping properties of aluminium foams, Mater. Sci. Eng., A 205 (1996) 221–228. [3] M. Vesenjak, T. Fiedler, Z. Ren, A. Öchsner, Behaviour of syntactic and partial hollow sphere structures under dynamic loading, Adv. Eng. Mater. 10 (2008) 185–191. [4] T. Fiedler, A. Öchsner, I. V. Belova, G. E. Murch, Thermal conductivity enhancement of compact heat sinks using cellular metals, 273–276, ed, (2008) 222–226. [5] Y. Tian, C.Y. Zhao, A numerical investigation of heat transfer in phase change materials (PCMs) embedded in porous metals, Energy 36 (2011) 5539–5546. [6] O. Andersen, J. Meinert, Heat transfer and fluid flow in sintered metallic fiber structures, Mater. Sci. Forum 638–642 (2010) 1884–1889. [7] M. Odabaee, S. Mancin, K. Hooman, Metal foam heat exchangers for thermal management of fuel cell systems – an experimental study, Exp. Thermal Fluid Sci. 51 (2013) 214–219. [8] S. Mao, N. Love, A. Leanos, G. Rodriguez-Melo, Correlation studies of hydrodynamics and heat transfer in metal foam heat exchangers, Appl. Therm. Eng. 71 (2014) 104–118. [9] D. Gupta, D.R. Campbell, P.S. Ho, Grain Boundary Diffusion, in: T.a.M. Poete (Ed.), Analytical Models, Wiley, New York, 1978, pp. 161–239. [10] M. Vesenjak, M. Borovinšek, T. Fiedler, Y. Higa, Z. Ren, Structural characterisation of advanced pore morphology (APM) foam elements, Mater. Lett. 110 (2013) 201–203. [11] M. Vesenjak, F. Gacnik, L. Krstulovic-Opara, Z. Ren, Mechanical properties of advanced pore morphology foam elements, Mech. Adv. Mater. Struc. 22 (2015) 359–366. [12] L. Peroni, M. Scapin, C. Fichera, D. Lehmhus, J. Weise, J. Baumeister, et al., Investigation of the mechanical behaviour of AISI 316L stainless steel syntactic foams at different strain-rates, Compos. B Eng. 66 (2014) 430–442. [13] J.B. Ferguson, J.A. Santa Maria, B.F. Schultz, P.K. Rohatgi, Al-Al2O3 syntactic foams-part II: predicting mechanical properties of metal matrix syntactic foams reinforced with ceramic spheres, Mater. Sci. Eng.: A 582 (2013) 423– 432. [14] I.N. Orbulov, Compressive properties of aluminium matrix syntactic foams, Mater. Sci. Eng., A 555 (2012) 52–56. [15] A. Öchsner, J. Grácio, On the macroscopic thermal properties of syntactic metal foams, Multidiscip. Model. Mater. Struct. 1 (2005) 171–181. [16] T. Fiedler, A. Öchsner, I.V. Belova, G.E. Murch, Recent advances in the prediction of the thermal properties of syntactic metallic hollow sphere structures, Adv. Eng. Mater. 10 (2008) 361–365. [17] T. Fiedler, M.A. Sulong, M. Vesenjak, Y. Higa, I.V. Belova, A. Öchsner, et al., Determination of the thermal conductivity of periodic APM foam models, Int. J. Heat Mass Transfer 73 (2014) 826–833.

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