Comparison of metal foam heat exchangers to a finned heat exchanger for low Reynolds number applications

International Journal of Heat and Mass Transfer 89 (2015) 1–9

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Comparison of metal foam heat exchangers to a finned heat exchanger for low Reynolds number applications Henk Huisseune ⇑, Sven De Schampheleire, Bernd Ameel, Michel De Paepe Ghent University, Department of Flow, Heat and Combustion Mechanics, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium

a r t i c l e

i n f o

Article history: Received 21 November 2014 Received in revised form 22 April 2015 Accepted 1 May 2015

Keywords: Open-cell metal foam Porous material Louvered fin Bare tubes Heat transfer Pressure drop

a b s t r a c t Due to its high porosity and large specific surface area, open-cell metal foam is an attractive material for heat transfer applications. In this article the performance of metal foam heat exchangers is compared to the performance of a bare tube bundle and the performance of an existing conventional louvered fin heat exchanger. A macroscopic model consisting of the Darcy–Forchheimer–Brinkman flow model and the thermal non-equilibrium energy model is used to perform two-dimensional simulations on metal foam heat exchangers. Because thermal design of heat exchangers is always a trade-off between heat transfer and pressure drop, both are considered together when evaluating the heat exchangers’ performance. The foamed heat exchangers show up to 6 times higher heat transfer rate than the bare tube bundle at the same fan power. If the fins are replaced by metal foam while keeping the overall dimensions the same, the finned heat exchanger shows in all cases the best performance. However, a metal foam heat exchanger can outperform the finned heat exchanger if the frontal area is changed. Optimization is required to select the best foam parameters, material and dimensions. This clearly shows the potential of open-cell metal foam for high performance heat exchanger designs. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction In many industrial and domestic processes energy is transferred as heat. Hence, heat exchangers are important elements as contributors to increased energy efficiency in industry, transport and buildings. In many applications air is one of the working fluids (e.g. heat pumps, air conditioning devices, refrigeration, compressed air cooling, etc.). When exchanging heat with air, the main thermal resistance is located at the air-side of the heat exchanger. Commonly, the heat transfer rate is increased by adding fins at the air-side. The current state-of-the-art fins are complex interrupted designs, such as louvered fins and slit fins [1], or surface protrusions, such as vortex generators [2]. Further improvements are possible by combining existing enhancement techniques [3]. An example of such compound heat exchangers is the combination of louvered fins and vortex generators [4]. Heat exchanger manufacturers are continuously searching for new and better designs. A promising option is the use of open-cell metal foam as alternative for the conventional fins. This porous structure consists of a network of solid ligaments (or struts) around the pores. Open-cell foam is characterized by a high

⇑ Corresponding author. Tel.: +32 92643289. E-mail address: [email protected] (H. Huisseune). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.013 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

volumetric porosity (>0.85; ratio of the air volume to the total volume) and thus low weight, high surface-to-volume ratio (up to 1500 m2/m3) and excellent fluid mixing due to the complex network of struts [5]. These properties, in combination with the high thermal conductivity of the metal (e.g. aluminum or copper), make these foams a promising structure for heat transfer applications [6–11]. Due to time constraints, microscopic analysis of metal foam is usually restricted to a limited number of cells [12]. Microscopic models are thus not appropriate to simulate actual metal foam applications which contain thousands of cells. As metal foams can be treated as porous media, a macroscopic analysis is possible using the volume averaging technique (VAT): the details of the original structure are replaced by their averaged counterparts [13–14]. The governing macroscopic equations for the phase averaged variables can be solved much faster than the traditional transport equations for local variables, which require direct numerical simulations (DNS). However, because the details of momentum and energy transfer between the fluid flow and solid structure are lost during the averaging, closure relations are required. These include relations for the interstitial heat transfer coefficients [15–17], the inertial loss factor and the permeability (which determines the viscous loss factor) [18–22]. Also relations for the macroscopic (or effective) properties as function of the microscopic

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Nomenclature Ac Ad Ao Cmin cp Dh Do f Fd Gc h H j k _ m NTU P Pd Pl Pr Pt Q R Re T tw

minimum cross sectional flow area [m2] relative heat exchanger frontal area (Eq. (18)) [m] overall heat transfer surface area [m2] minimum heat capacity [W/K] specific heat capacity [J/kgK] hydraulic diameter [m] outer tube diameter [m] Fanning friction factor [–] heat exchanger flow depth [m] mass flux through the minimum cross section [kg/m2s] convective heat transfer coefficient [W/m2K] heat exchanger height [m] Colburn j-factor [–] thermal conductivity [W/mK] mass flow rate [kg/s] number of transfer units [–] pressure [Pa] relative fluid pumping power (Eq. (20)) [m-2] longitudinal tube pitch [m] Prandtl number [–] transversal tube pitch [m] heat transfer rate [W] thermal resistance [K/W] Reynolds number (Eq. (5)) [–] temperature [K] tube wall thickness [m]

parameters are needed [23]. These include the effective thermal conductivities and thermal dispersion [15,18,24–25] as well as the effective viscosity [21]. These relations are obtained from experiments, analytical modeling or CFD simulations of a representative heat exchanger volume with a very fine mesh. They are only valid for the specific geometry and flow conditions under consideration. A detailed review on existing fluid and thermal transport models for open-cell metal foams can be found in [26–27]. When evaluating the performance of a metal foam heat exchanger it is important to compare the results to the performance of today’s used cooling solutions (e.g. finned heat exchangers, grooved tubes, etc.) to judge the metal foam’s potential. The closed macroscopic model can be used to examine metal foam heat exchangers. Under some assumptions (fully developed flow, constant thermophysical properties, neglecting the Forchheimer contribution, among others), analytical solutions for the velocity and temperature distributions can be deduced. Xu et al. [28] analytically examined a channel filled with metal foam. They used a Brinkman-Darcy model and two equation energy model (i.e. local thermal non-equilibrium). Based the performance criterion j/f1/3, they concluded that the foam channel has a higher performance than the empty channel in the porosity range 80–95%. They also studied a partially filled channel with foam on the upper and bottom plate of the channel [29]. Here the minimum foam thickness was determined which results in a higher j/f1/3 compared to the empty channel. In both studies no comparison to an internally finned/grooved channel is reported. Lu et al. [30] investigated a metal foam filled tube and concluded that the heat transfer performance can be improved up to 40 times compared to a plain tube, but at the expense of a higher pressure drop. Zhao et al. [31] extended this work and studied tube-in-tube heat exchangers with the inner tube as well as the annulus filled with open-cell metal foam. They showed that metal foam filled tube-in-tube heat exchanger outperforms the finned tube heat exchanger (inner grooved tube with external fins) from a heat transfer point of view.

U ~ v

vc

V d W

[W/m2K] overall heat transfer coefficient superficial velocity [m/s] maximum velocity in the heat exchanger (Eq. (8)) [m/s] relative heat exchanger volume (Eq. (19)) [m2] heat exchanger width [m]

Special characters b inertial loss factor [m1] e effectiveness [–] / porosity [–] go surface efficiency [–] j permeability [m2] l dynamic viscosity [Pas] q density [kg/m3] r contraction ratio [–] ro specific surface area [m2/m3] Subscripts and superscripts e effective f fluid in inlet m mean out outlet s solid sf interstitial

However, pressure drop results were not reported. In contrast to the analytical approach of the previous papers, numerical simulations using the closed macroscopic model are also possible. The computational time is acceptable as the macroscopic model is fast running. Chen et al. [32] used the Darcy-Brinkman-Forchheimer flow model and the two-equation energy model to study the heat transfer from multiple metal foam heat sinks in a horizontal channel under forced convection. They concluded that the cooling significantly improves if metal foam is mounted on the heat sources. The metal foam also causes a pressure drop penalty. However, these pressure drop results were not linked to the heat transfer results. Also a comparison with a conventional finned heat sink is missing. An air-cooled metal foam heat exchanger under a high speed laminar jet was numerically investigated by Ejlali et al. [33]. They showed that the metal foam outperforms a pin finned surface without increase of weight or pressure drop. A metal foam wrapped cylinder in cross-flow was examined by Odabaee et al. [34,35]. They assumed local thermal equilibrium, even though Lee and Vafai [36] showed that local thermal non-equilibrium yields more accurate predictions due to the large difference in thermal conductivity between the air and the solid foam material. The optimal foam layer thickness was determined. Comparison to a finned tube showed much higher heat transfer rate with reasonable pressure drop penalty. This numerical work was extended to a metal foam wrapped tube bank [37]. The effect of the tube pitches, foam thickness and foam parameters was studied. It is observed that the area goodness factor of the metal foam tube bundle is significantly better than that of the conventional finned tube heat exchanger. This higher performance was also confirmed by the experiments of Chumpia and Hooman [38]. They compared five foam wrapped tubes to a finned tube as benchmark. They found that a foam wrapped tube provides more heat transfer while keeping the pressure drop at the same level as that of the finned tube if the proper foam thickness is selected. T’Joen et al. [7] also compared metal foam wrapped tubes to finned tubes using

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an experimental approach. In contrast to Chumpia and Hooman [38] they did not consider a single tube, but a row of tubes in cross flow. Their wind tunnel measurements indicated the importance of a good metallic bonding between the foam and tubes. If brazed, metal foam covered tubes offer benefits at higher air velocities compared to helically finned tubes. Dai et al. [39] compared a flat-tube metal foam heat exchanger to a flat-tube serpentine louvered fin heat exchanger based on heat transfer and pressure drop correlations from literature. They concluded that for the same fan power and heat transfer, the metal foam heat exchanger can be made smaller and lighter, but is still much more expensive than the louvered fin heat exchanger. Sertkaya et al. [40] compared three metal foam heat exchangers (10, 20 and 30 PPI) to three finned heat exchangers with the same tube layout and overall dimensions. In contrast to most other studies, where the foamed heat exchangers outperform the finned heat exchangers, their measurements showed that the finned heat exchangers provide a higher heat transfer and a lower pressure drop than the foamed heat exchangers. This is also what Ribeiro et al. [8–9] concluded from their experiments. They compared three microchannel condensers with copper foam to a corrugated plain fin condenser and three louvered fin condensers. They found a lower thermal performance of the metal foam heat exchangers compared to finned heat exchangers for a given fan power. When comparing a foamed heat exchanger to a finned heat exchanger, it is important that the foam parameters as well as the fin parameters are optimal for the considered application to allow a fair judgement of the potential of metal foam. Huisseune et al. [41] showed that thermal hydraulic performance of metal foam heat exchangers strongly depends on the foam’s morphology and foam material. The current study focuses on round tube heat exchangers typically used in heat pumps and air conditioning devices. The objective is to compare the performance of metal foam heat exchangers to the performance of a bare tube bundle and an existing state-of-the-art finned heat exchanger. The latter was previously tested in a wind tunnel by De Schampheleire et al. [42] and is commercially used in a convector unit. For comparison a performance evaluation criterion is selected which takes heat transfer, pressure drop and volume constraints into account. For the considered application in HVAC&R, such a comparison between metal foam and an existing high performance finned heat exchanger with round tubes is unique. 2. Macroscopic thermal non-equilibrium model In previous work of our group, a macroscopic model for open-cell metal foams relevant for heat transfer applications (i.e. porosities > 88%) was suggested and experimentally validated [41,43]. This model will also be used here. The volume-averaged mass and momentum equations for an incompressible flow in a fluid-saturated and stationary porous medium are given by:

r:~ v¼0

qf /

~ v:r~ v ¼ /rP þ lef r2~ v

ð1Þ

lf ~ v  qf bk~ vk~ v j

ð2Þ

v is the superficial averaged fluid velocity, qf is the density of where ~ the fluid phase, P is the intrinsically averaged pressure, l is dynamic viscosity and / is the volumetric porosity. The remaining properties are hydraulic porous properties which bring microscopic information to the macroscopic scale: le is the effective viscosity in the Brinkman term, j is the permeability in the Darcy term and b is the inertial loss factor in the Forchheimer term [13]. Due to the large difference in thermal conductivity between the fluid and solid,

a thermal non-equilibrium between the air and the foam material is assumed, resulting in two energy equations. According to Lee and Vafai [36], this results in more accurate predictions compared to thermal equilibrium models. The volume averaged energy equations for the fluid and solid phase are: e

v:rT f ¼ r:kf rT f  Asf hsf ðT f  T s Þ ðqcp Þf ~

ð3Þ

e

0 ¼ r:ks rT s  Asf hsf ðT s  T f Þ

ð4Þ

where cp is the specific heat, Asf is the interstitial heat transfer surface and Tf and Ts are intrinsically averaged temperatures of the fluid and solid phase, respectively. Also here there are three macroe scopic thermal porous properties: kf is the fluid phase effective e

thermal conductivity, ks is the solid phase effective thermal conductivity and hsf is the interstitial heat transfer coefficient. The closure relations for the hydraulic and thermal properties listed above will not be repeated here, but can be found in De Jaeger et al. [43]. Notice that the thermal dispersion is not considered in this study. Simulations were performed for metal foam MF10.462 (see Table 1) including thermal dispersion using the empirical correlation suggested by Calmidi and Mahajan [15]. However, no noticeable differences in heat transfer were found compared to the results where thermal dispersion is not considered. It was calculated that the contribution of thermal dispersion relative to the effective stagnant thermal conductivity is less than 2% for the considered Reynolds number range in this study. That is why thermal dispersion is neglected here.

3. Computational domain and method The computational domain is the same as in Huisseune et al. [41]. The heat exchanger consists of two tube rows placed in a staggered tube layout. Each tube row counts 10 tubes. The metal foam block has a height equal to 256 mm and a flow depth of 24 mm. The geometrical details of the simulated metal foam heat exchangers are listed in Table 1. The corresponding two-dimensional computational domain is shown in Fig. 1. The metal foam is described using a volume averaged model. This means there will be no macroscopic flow variations in the direction of the tube length. A two-dimensional numerical model can thus be used to describe the macroscopic flow through the metal foam heat exchanger. Nine different metal foams are investigated. Their characteristics are listed in Table 2. For the 10 and 20 PPI foams the characteristics were determined via lCT scanning by De Jaeger et al. [44] on existing aluminum foam samples (PPI = pores per linear inch; also referred to as pore density). The macroscopic characteristics of the four other foams are calculated from the microscopic foam parameters provided by the manufacturer using the periodic unit cell reconstruction of open-cell foams developed by De Jaeger et al. [44]. / is the volumetric porosity (defined as the ratio of the air volume to the total volume) and ro is the specific surface area.

Table 1 Geometrical details of the metal foam heat exchanger. Parameter

Symbol

Unit

Value

Heat exchanger height Heat exchanger width Heat exchanger depth Tube outer diameter Tube wall thickness Transversal tube pitch Longitudinal tube pitch

H W F Do tw Pt Pl

mm mm mm mm mm mm mm

256 426 24 7.2 0.27 21 12

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Fig. 1. Two-dimensional computational domain of the metal foam heat exchanger.

Table 2 Foam parameters of the studied open-cell metal foam.

experiments (62.8 °C–65.5 °C), while the convective heat transfer coefficient is equal to the one determined during the experiments using the Gnielinski correlation [45] (4758–4865 W/m2K). No slip boundary conditions were applied on the tube outer walls. The contact resistance between the tubes and foam is modeled as an extra thermal resistance resulting in a temperature jump at the foam/tube interface. The values are reported in De Jaeger et al. [46]. The double precision pressure based solver was used. The coupled algorithm was applied for the pressure–velocity coupling. The discretization of the convective terms in the governing equations is done via a second order upwind scheme, while a second order central differencing scheme is applied for the diffusive terms. The gradients are evaluated via the least squares cell based method. The pressure gradient in the momentum equations is treated via a second order discretization scheme. Convergence criteria were set to 106 for continuity and velocity components and 1010 for energy. Setting smaller values for these criteria did not result in any notable differences in the flow field and heat transfer predictions. The air density was calculated as for an incompressible ideal gas and the air specific heat was calculated via a polynomial fit. The molecular viscosity was determined via the Sutherland approximation. The molecular thermal conductivity was determined based on the kinetic theory. The density, specific heat and thermal conductivity of the metal foam materials were considered constant (for aluminum AL1050: q = 2710 kg/m3, cp = 871 J/kgK and ks = 220 W/mK; for copper C10100: q = 8960 kg/m3, cp = 380 J/kgK and ks = 390 W/mK). Also the copper tubes have constant material properties. For each of the simulations the resulting heat balance closes within 0.2% and there were no noticeable differences in the mass balance. 4. Data reduction method

ID

PPI

/

ro (m2/m3)

MF10.380 MF10.462 MF20.580 MF20.720 MF20.860 MF30.1310 MF35.1515 MF40.1767 MF45.2080

10 10 20 20 20 30 35 40 45

0.951 0.932 0.967 0.937 0.913 0.914 0.913 0.907 0.903

380 462 580 720 860 1310 1515 1767 2080

The Reynolds number is based on the hydraulic diameter Dh and the velocity vc in the minimum cross sectional flow area:

ReDh ¼

ð5Þ

The hydraulic diameter Dh is calculated as in [47–48]:

Dh ¼ Each foam sample is assigned an ID number: MFxx.yyy with xx the PPI value and yyy the specific surface area. Besides the porous heat exchanger zone, three other zones can be distinguished in Fig. 1: the pre-extended region, the post-extended region and the tube walls. The pre-extended region equals 1.25 times the flow depth of the heat exchanger, while the post-extended region measures 4 times the flow depth of the heat exchanger. The tube walls were also meshed to take the heat conduction into account. At the inlet of the computational domain a uniform velocity in the x-direction and a constant air inlet temperature were imposed. The inlet velocity (1.2–3.2 m/s) and temperature (21.0 °C–24.1 °C) were the same as during the measurements by De Schampheleire et al. [42]. At the outlet the static pressure was set to 0 Pa (pressure outlet boundary condition). The walls of the flow channel are considered adiabatic (i.e. well insulated during the experiment). The tube wall with a thickness of 0.27 mm was meshed. During the experiments [42] there were two dummy tubes in the second tube row through which no water flowed. The inner surfaces of these tubes are modeled as adiabatic walls. On the inner walls of the other tubes a convective heat transfer coefficient and free stream temperature were applied. The free stream temperature is the same as the bulk water temperature measured during the

qair v c Dh lair

4Ac F d Ao

ð6Þ

with Ac the minimum cross sectional flow area, Fd the heat exchanger depth and Ao the total heat transfer surface area at the air-side. The contraction ratio r, defined as the ratio of the minimum cross sectional area Ac to the frontal heat exchanger area, is calculated as:

r¼/

P t  Do Pt

ð7Þ

Here / is the foam porosity, Pt is the transversal tube pitch and Do is the exterior tube diameter. The maximum velocity vc is then determined as:

vc ¼

v front r

ð8Þ

with vfront the air frontal velocity. For all simulated cases the Reynolds number ReDh is smaller than 2000. Such low Reynolds numbers are typically encountered in HVAC&R applications (e.g. air-conditioning devices, heat pumps, convectors, etc.).The pressure drop is expressed dimensionless as a Fanning friction factor f [49–51]:

f ¼

"  # Ac qm 2qin DP qin 2  ð1 þ r Þ  1 Ao qin qout G2c

ð9Þ

H. Huisseune et al. / International Journal of Heat and Mass Transfer 89 (2015) 1–9

qm is the mean density between inlet and outlet and Gc is the mass flux in the minimum cross sectional flow area Ac:

Gc ¼ qm v c

ð10Þ

The friction factor includes the entrance and exit pressure loss. The heat transfer results are reported dimensionlessly as Colburn j-factors. These are calculated from the VAT simulation results using the e-NTU method. The effectiveness e is determined as

e¼

Q C min  ðT tube  T air;in Þ

ð11Þ

with Q the total heat transfer rate, Cmin the air-side heat capac_  cp Þ and Ttube and Tair,in the free stream tube temperature and ity ðm the air inlet temperature applied in the 2D simulations, respectively. The NTU is then calculated as [52]:

e ¼ 1  expðNTUÞ

ð12Þ

The overall heat transfer resistance (UA)1 can then be determined as:

1 1 ¼ UA C min  NTU

ð13Þ

The overall heat transfer resistance consists of four parts: the convective resistance Ri at the tube side, the conductive resistance Rcond through the tube material, the contact resistance Rcontact at the tube-foam/air interface and the convective resistance Ro at the air-side. This results in:

1 ¼ Ri þ Rcond þ Rcontact þ Ro UA

ð14Þ

The contact resistance is calculated as:



1 1 þ Rcontact;foam Rcontact;air

Rcontact ¼

1 Ao  Ro

go ho 2=3 Pr qv c cp

ð15Þ

ð16Þ

ð17Þ

From a thermal hydraulic point of view, heat exchanger design is always a trade-off between heat transfer, which should be as large as possible, and fan power, which should be as small as possible. Cowell [55] introduced a general comparison method to compare compact heat transfer surfaces. He showed that for a given number of transfer units NTU, mass flow rate and inlet fluid temperature (and thus a given heat transfer rate) the relative values defined by:

Ad ¼

Dh

rReDh

½m

½m2 

ð19Þ

½m2 

ð20Þ

2

Pd ¼

fReDh 2

jDh

are directly proportional to the heat exchanger frontal area, the total heat exchanger volume and fluid pumping power, respectively. Here the relative performance plot Pd vs. V d for different values of Ad is used to compare the performance of the different heat exchangers. The same comparison method was applied by Ameel et al. [56] to compare louvered fin heat exchangers. 5. Grid independence and experimental validation A grid independency study and an experimental validation in a wind tunnel were performed. Details on both can be found in Huisseune et al. [41]. In summary, the selected grid has a mesh size of 0.2 mm and there is a very good match between experiments and simulations: the differences between the experimental and the simulated heat transfer rates are smaller than 3% (experimental uncertainty on heat transfer measurements is in average 1.4%) and the simulated pressure drops fall within the experimental uncertainty of the measured pressure drops (the experimental uncertainty is in average 6.5%). This validates the macroscopic model. 6. Comparison to a bare tube bundle and a finned heat exchanger 6.1. Reference heat exchangers

The surface efficiency go takes the effect of a finite foam thermal conductivity into account. Notice that the product of the surface efficiency and convective heat transfer coefficient are presented as one entity because the surface efficiency and the convective heat transfer coefficient clearly form one component of the total heat transfer resistance. Convective results have also been presented this way for interrupted fin designs [53–54]. The convective heat transfer coefficients are reported dimensionless as Colburn j-factors (including the surface efficiency) according to:

j¼

D2h rjReDh

1

with the values for the contact resistance previously determined experimentally by De Jaeger et al. [46]. With the air-side convective resistance Ro calculated from Eq. (14), the air-side convective heat transfer coefficient ho is then given by:

go  ho ¼

V d ¼

5

ð18Þ

To judge the potential of metal foam heat exchangers, their performance is compared to experimental data of two reference heat exchangers: a bare tube bundle and a finned heat exchanger. The bare tube bundle has an identical staggered tube layout as the metal foam heat exchangers. Its heat transfer rate and pressure drop are calculated using the Nusselt and Euler number correlations of Zukauskas for a staggered tube bundle [57]. The finned heat exchanger is an existing high-performance heat exchanger with an inclined louvered fin pattern (as studied by T’Joen et al. [58]). It is typically used in heating, ventilation and air conditioning applications (HVAC). The considered heat exchanger comes from a convector unit. It was previously tested in a wind tunnel for frontal velocities ranging between 1.2 m/s and 3.2 m/s [42]. This heat exchanger has the same overall heat exchanger dimensions and tube layout as the simulated metal foam heat exchangers (see Table 1). This allows a fair comparison. It has a fin pitch of 1.4 mm and a fin thickness of 0.115 mm. The measurements on the finned heat exchanger are compared here to the simulations of the metal foam heat exchangers. It should be noted that the finned heat exchanger is a so called ‘low capacity unit’, meaning that not all tubes are connected to the headers (in our case two tubes are not connected). As previously mentioned, in the simulations of the metal foam heat exchangers, these two tubes are considered adiabatic. This is clear from the temperature contour plots in Fig. 2. These plots are for the 20 PPI metal foam heat exchanger MF20.720 and an inlet velocity of 3.2 m/s. Fig. 2(a) shows the air temperature in the computational domain. Downstream the tubes, the wake zones are clearly visible (higher temperature). The walls of the two dummy tubes in the middle of the second tube row are not heated, which is clear from the contour plot. Fig. 2(b) presents the temperature of the foam material. The colder zones around the dummy tubes can also be observed. Due to the finite conductivity of the foam material the foam temperature decreases with growing

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H. Huisseune et al. / International Journal of Heat and Mass Transfer 89 (2015) 1–9

Fig. 2. Temperature contours of (a) the air and (b) the foam material for heat exchanger MF20.720 and inlet velocity of 3.2 m/s.

distance from the tube wall [59], as is also the case in finned heat exchangers [60]. During the wind tunnel measurements on the finned heat exchanger the tubes were heated with hot water. Hence, a temperature gradient existed at the waterside. The simulations of the metal foam heat exchangers on the other hand are two-dimensional assuming a fixed free stream water temperature. Calculating the total heat transfer of the simulated heat exchanger by multiplying the computed heat transfer (in W/m) with the heat exchanger width thus results in the overall heat transfer for a fixed fluid temperature in the tubes. To make a fair comparison between the measurements on fins and the simulations on foam, the experimental data on fins were recalculated to the situation with fixed water temperature. De Schampheleire et al. [42] determined the overall heat transfer resistance from the heat transfer measurements using the effectiveness-NTU relation for a mixed/unmixed configuration. The resulting overall heat transfer resistance was then recalculated to the heat transfer using the effectiveness-NTU relation for zero heat capacity ratio according to Eq. (12). This is the special case for constant fluid temperature at one side of the heat exchanger, corresponding to our simulations. In this case the heat transfer rate is independent of the flow arrangement [52].

6.2. Thermal-hydraulic analysis As the overall dimensions and tube layout are identical, a direct comparison as were the louvered fins replaced by metal foam is possible if the simulations are performed under the same boundary conditions as in the experiments (inlet air temperature and velocity and tube temperatures). This is what is done here. The pressure drop results are plotted in Fig. 3. The experimental uncertainties on the louvered fin data are also shown. The 45 PPI metal foam heat exchanger has the largest pressure drop. The pressure drop decreases with decreasing PPI value (or pore density). For a given pore density, the pressure drop decreases with increasing porosity. As explained in Huisseune et al. [41], the pressure drop is mainly determined by the porosity. The louvered fin heat exchanger has a pressure drop which is about 4.5 times smaller than the pressure drop of the 45 PPI heat exchanger. The pressure drop consists of viscous drag near the solid-fluid interface and form drag acting

Fig. 3. Pressure drop for the louvered fin and metal foam heat exchangers.

on the solid structure [61]. The latter is caused by the pressure difference across the interfacial surface area, especially the difference on the front pressure build up and the lower pressure in the wake behind an obstacle. Compared to fins, the number of frontal and wake zones in foams is considerably more due to the many struts. Consequently, a foam structure inherently has more form drag than a finned structure. This explains why the louvered fin heat exchanger has a specific fin surface area (thus without the tubes) which is much larger than the specific foam surface area of a metal foam heat exchanger having the same pressure drop (1427 m2/m3 for the louvered surface vs. a bit more than 720 m2/m3 for a foam structure), see Fig. 3. The pressure drop over a bare tube bundle is not shown in Fig. 3, as it is much lower than the pressure drop over foamed and finned heat exchangers: the pressure drop over the bare tube bundle is 8 to 15 times smaller than the pressure drop over the louvered fin heat exchanger. The heat transfer results are plotted in Fig. 4. All metal foam heat exchangers are made of Al1050 (ks = 220 W/mK), unless otherwise indicated (i.e. the 45 PPI foam represented by white square symbols is made of copper C10100 (ks = 390 W/mK)). The

H. Huisseune et al. / International Journal of Heat and Mass Transfer 89 (2015) 1–9

Fig. 4. Heat transfer for the louvered fin and metal foam heat exchangers.

metal foam heat exchangers have a 4 (for aluminum MF10.380) to 11 (for copper MF45.2080) times higher heat transfer rate than the bare tube bundle. The heat transfer rate decreases with decreasing pore density. For a given PPI, the heat transfer rate decreases with decreasing specific surface area. The latter is inversely proportional to the convective thermal resistance at the air-side, which is the main thermal resistance in gas-liquid applications. Comparing to the louvered fin heat exchanger shows that replacing the louvers by aluminum foam resulting in a heat exchanger with the same overall dimensions only makes sense for 40 PPI and 45 PPI foams. For a given mass flow rate, the 45 PPI Al1050 heat exchanger has a heat transfer rate which is about 8% higher than the louvered fin heat exchanger. The use of copper foam further increases the thermal performance: the MF45.2080 copper foam heat exchanger results in up to 18% higher heat transfer for a given mass flow rate. In Fig. 5 the heat transfer rate is plotted as function of the fan power. The fan power is calculated as the product of the pressure drop over the heat exchanger and the volumetric flow rate at the

Fig. 5. Performance plot: heat transfer vs. fan power.

7

heat exchanger inlet. The bare tube bundle, the louvered fin heat exchanger and the nine metal foam heat exchangers of Table 2 are shown. For the same fan power and overall dimensions, the heat transfer rate clearly increases with the specific surface area. The copper 45 PPI heat exchanger shows a 6 times higher heat transfer than the bare tube bundle at the same fan power. The louvered fin heat exchanger outperforms all metal foam heat exchangers. However, compared to the 45 PPI copper foam heat exchanger the difference is small: the louvered fin heat exchanger has a 4.6% higher heat transfer rate for given fan power and overall dimensions. The validation experiment also showed that the heat transfer simulations are slightly under predicted (up to 3%, see Huisseune et al. [41]). It is thus expected that the actual performance of the foamed heat exchangers is slightly better still. The 45 PPI foam has a strut diameter of about 0.1 mm. This dimension is comparable to the smallest fin thickness in current compact fin-and-tube heat exchangers (e.g. the louvered fin heat exchanger in this work has a fin thickness of 0.115 mm). Also notice that the specific surface area of the 45 PPI foam is much larger than the specific surface area of the louvered fins (respectively 2080 m2/m3 and 1427 m2/m3). This justifies the classification of metal foam as very compact heat transfer surface. To further improve the heat transfer rate, the pore density (and thus also the specific surface areas) could be further increased. Fig. 5 is for heat exchangers with the same overall dimensions and different mass flow rates. It is thus a one-to-one comparison if the fins would be substituted by metal foam. The question arises how the heat exchangers will perform if the mass flow rate is held constant and the frontal area or the total volume changes. A comparison method based on Eqs. (18)–(20) is used here. This method was previously applied by Cowell [55] and Ameel et al. [56]. The actual frontal area, heat exchanger volume and pumping power of any heat exchanger with the same heat transfer duty can be written as a constant times the relative value Ad , V d or Pd , respectively [55–56]. Comparing different heat exchangers can thus be done using the dimensionless performance plot P d  V d for a fixed heat transfer rate. The results are presented in Fig. 6. Notice that Fig. 6 shows the effects of varying volume and frontal area, even though the j and f factors were simulated for a fixed geometry (only foam parameters and Reynolds numbers were varied). The applied comparison method assumes that the simulated j- and ffactors are independent of the frontal area and the flow depth. Neglecting the impact of the frontal area on the j- and f-factors

Fig. 6. Dimensionless performance plot at constant heat transfer for louvered fin and 45 PPI heat exchangers.

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H. Huisseune et al. / International Journal of Heat and Mass Transfer 89 (2015) 1–9

corresponds to neglecting boundary effects. Neglecting the impact of the flow depth corresponds to the assumption of periodically fully developed flow. With these two assumptions, it is not necessary to perform simulations to predict the effect of the frontal area and the flow depth on the heat transfer rate or pumping power, because these effects are calculated analytically from the j- and f-factors. In Fig. 6 the louvered fin heat exchanger and two 45 PPI heat exchangers (i.e. aluminum Al1050 of 220 W/mK and copper C10100 of 390 W/mK) are shown. Next to each symbol the value of the relative frontal area Ad is indicated: the more to the right on each curve, the smaller the frontal area. For the same total volume (e.g. V d ¼ 1:1 106 m2), the aluminum foam has a pumping power which is about 30% larger than the louvered fins (Pd = 11.4 and 14.6  1011 m2), even though the flow depth is shorter as the frontal area is larger (about 8.9/5.3 = 1.7 times). In contrast, the copper foam has a 37% smaller pumping power than the louvered fins (Pd = 7.2 and 11.4  1011 m-2), while the frontal area is about 12.0/5.3 = 2.3 times larger. This means that the copper foamed heat exchanger can use a smaller fan, which is less expensive and uses less energy. Smaller fans also make less noise. This is clearly advantageous for HVAC applications. For the same pumping power (e.g. P d = 11.4  1011 m2), the louvered fins can perform the same heat duty as the aluminum foam but with a slightly smaller volume of 6% (V d = 1.08 and 1.14  106 m2). The frontal area of the aluminum foam is about double as large compared to the louvered fins (i.e. 10.1/5.3 = 1.9). The copper foam, however, requires a 13% smaller volume than the louvered fins (V d = 0.94 and 1.08  106 m2). The frontal area of the copper foam is 9.3/5.3 = 1.8 times larger and consequently the foamed heat exchanger is shorter in flow depth. Fig. 6 shows that it is possible to design a metal foam heat exchanger which performs better than the state-of-the-art louvered fin heat exchanger if the proper foam parameters and material are selected. Optimization is thus very important. Using a performance plot as in Fig. 6, cost-effective and energy efficient designs can be selected taking into account the volume constraints. Notice that the considered tube-and-fin heat exchanger is made of aluminum. If the heat exchanger was made of copper, it is expected that its thermal performance will be higher than the aluminum heat exchanger. Tube-and-fin heat exchangers with copper tubes and copper fins are used for mining applications. However, such heat exchangers are not common elsewhere and were not available to the authors for a comparison.

7. Conclusions Two-dimensional simulations using a Darcy-Forchheimer-Brinkman flow model and the thermal non-equilibrium energy model are performed on metal foam heat exchangers. The tube layout and dimensions of these heat exchangers are chosen the same as the geometry of an existing louvered fin heat exchanger which is used in a convector unit. Its heat transfer and pressure drop characteristics were previously measured in a wind tunnel. A velocity range typical for HVAC applications is considered. For the same mass flow rate, metal foam with a high pore density (i.e. PPI > 40) transfers more heat than the fins. However, the design of a heat exchanger is always a trade-off between heat transfer and pressure drop. Hence, both should be considered for a fair comparison. The foamed heat exchangers show up to 6 times higher heat transfer rate than the bare tube bundle at the same fan power. Replacing the louvered fins with foam while keeping the same overall dimensions is not advisable: the louvered fin heat exchanger outperforms all simulated foamed heat exchangers for the same fan power. However, if the overall dimensions are not fixed, a metal foam heat exchanger having a

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