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Foam height effects on heat transfer performance of 20 ppi aluminum foams
Applied Thermal Engineering 49 (2012) 55e60
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Foam height effects on heat transfer performance of 20 ppi aluminum foamsq Simone Mancin, Claudio Zilio, Luisa Rossetto*, Alberto Cavallini Dipartimento di Fisica Tecnica, Università degli Studi di Padova, Via Venezia 1, 35131 Padova, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 October 2010 Accepted 9 May 2011 Available online 17 May 2011
This paper investigates the heat transfer performance of two 20 PPI (pores per linear inch) aluminum foams with constant porosity (around 0.93) and different foam core height (20 mm and 40 mm). The aluminum foams are cellular structure materials that present a stochastic interconnected pores distribution mostly uniform in size and shape. Most commercially available metal foams are based on aluminum, copper, nickel and metal alloys. Metal foams have considerable applications in multifunctional heat exchangers, cryogenics, combustion chambers, cladding on buildings, strain isolation, petroleum reservoirs, compact heat exchangers for airborne equipment, air cooled condensers and compact heat sinks for power electronics. The experimental measurements of the heat transfer coefficient and pressure drop have been carried out in a test apparatus built at Dipartimento di Fisica Tecnica of the Università di Padova. The foam core height effects on the heat transfer performance have been studied imposing three constant specific heat fluxes at the bottom of the samples: 25.0, 32.5 and 40.0 kW m2 and varying the frontal air velocity between 2.0 and 5.0 m s1. The experimental heat transfer coefficients and pressure gradients have been compared against the predictions obtained from two models recently suggested by present authors. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Metal foams Heat transfer Pressure drops Air flow
1. Introduction Metal foams are a class of cellular structured materials that present a stochastic interconnected pores distribution mostly uniform in size and shape. In the last decades, these porous media have been largely studied because of their interesting properties that cover several different technical fields. In fact, metal foams are lightweight, offering high strength, rigidity and high heat transfer surface area [1]. As shown in Fig. 1, metal foam consists of tortuous, irregularly shaped flow passages. The most important geometrical characteristics of the metal foams are the number of pores per inch (PPI) and the porosity. The first one is easily obtainable by counting the number of pores in 25.4 mm. The second one, the porosity 3, is defined as the ratio of total void volume to the total volume occupied by the solid matrix and void volumes. Several authors have studied the heat transfer and fluid flow characteristics of metal foams by varying the number of pores per linear inch and the porosity, among them: Boomsma and Poulikakos [2], Kim et al. [3], q Paper presented at Thermal and Environmental Issues in Energy System Conference and selected by the scientific commission to be suggested for a possible publication in a special issue of the International Journal: Applied Thermal Engineering. * Corresponding author. Tel.: þ39 049 8276869; fax: þ39 049 8276896. E-mail addresses: [email protected] (S. Mancin), [email protected] (C. Zilio), [email protected] (L. Rossetto), [email protected] (A. Cavallini). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.05.015
Liu et al. [4], Bhattacharya et al. [5], Calmidi and Mahajan [6] and Hsieh et al. [7]. In particular, Boomsma and Poulikakos [2] carried out several heat transfer and pressure drop measurements during liquid flow through 40 PPI aluminum foams with different porosities. The authors observed a great increasing of the pressure drops as the porosity decreased. Moreover, they found that the Nusselt number, defined on the hydraulic diameter of the empty channel with the heat transfer coefficient referred to the base area of the sample, increases with the compression ratio. Kim et al. [3] studied the effects of porosity and of number of pores on the heat transfer, testing 6 different porous fins in a plate and fin heat exchanger. They found that at 20 PPI, the volumetric heat transfer coefficients referred to the total heat transfer area times the surface area efficiency, decrease with increasing porosity. Liu et al. [4] investigated the fluid flow through seven different aluminum foams varying the number of pores per inch and the porosity. The authors suggested that the pressure drops increase with PPI while at 20 PPI the effects of porosity on the pressure gradient are negligible. Bhattacharya et al. [5] proposed a model for the estimations of the permeability and inertia coefficient of aluminum metal foams regressed on a database which includes pressure drop measurements of 22 different porous media. Part of their database has been collected by Calmidi and Mahajan [6], that studied the air forced convection in high porosity metal foams, measuring the heat
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S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
Fig. 1. Photo of the tested 20 PPI aluminum foam. Fig. 2. Schematic of the experimental set up.
transfer coefficients and pressure drops of seven aluminum foams (PPI ¼ 5e40 and 3 ¼ 0.90e0.97). They observed that, at constant PPI, the Nusselt number, based on the length of the heated section and defined on the heat transfer coefficient referred to the base area and to wall to air inlet temperatures difference, increases with porosity. Hsieh et al. [7] studied the heat transfer behavior of six aluminum foams with different numbers of pores per inch and porosities. The effects of porosity on the heat transfer have been obtained testing four different samples with 20 PPI. In particular, they found that the Nusselt number (based on the length of the test section and defined using the heat transfer coefficient referred to the base area) increases with porosity. All the cited experimental works on forced convection heat transfer in open cells metal foams have studied the effects of the most important geometrical characteristics: the porosity and the number of pores per inch (PPI). On the other hand, the foam-finned surface efficiency appears to be a critical parameter which controls the effective heat transfer behavior of metal foams. Recently, Dukhan et al. [8] proposed an analytical and experimental work on the heat transfer in a 10 PPI metal foam. They measured and estimated the temperature profile inside the foam during air heat transfer. They demonstrated that the temperature of the foam reaches that of the ambient at a dimensionless distance from the heated base of approximately 0.3. This means that over than 60% of the heat transfer area does not transfer any heat flow rate being at the air temperature. Moreover, Ghosh [9] suggested a model to estimate both the heat transfer coefficient and the foam-finned surface area efficiency. From his calculations, at 3 ¼ 0.85, the foam-finned surface area efficiency decreases with PPI. The foam-finned surface area efficiency is linked to the height of the foam core; in particular, it is expected that it decreases with increasing foam height. To understand how the foam height affects the heat transfer behavior of metal foams is useful in order to develop accurate heat transfer models. This paper presents original experimental measurements that show the foam height effects on the heat transfer performance of two 20 PPI aluminum samples with constant porosity 3 and two different core heights: 20 and 40 mm. The experimental heat transfer coefficients and pressure drops are compared against the predictions of two models recently suggested by present authors [10,11]. 2. Experimental set up and data reduction The experimental test rig is an open-circuit type wind tunnel with rectangular cross section, as shown in Fig. 2. The experimental set up consists of: (1) screw compressor, (2) R134a vapor compression system drier, (3) filters, (4) 500 L air receiver, (5) pressure control valve, (6) flow meter, (7) 70 L calm chamber, (8) inlet tube, (9) test section, (10) power supply, (11) discharge tube and (12) flow rate control valve.
The ambient air flows through a single stage, oil injected screw compressor driven by an electric motor with inverter driver. It provides a variable volumetric air flow rate (measured at ambient conditions) ranging between 0 and 90 m3 h1 at a constant gauge pressure of 0.7 MPa. The humid and oiled compressed air is dehydrated by a drier down to a dew point temperature of 3 C and then filtered by a set of filters, in order to remove water, oil and particulate materials. An additional activated charcoal filter is located before the 500 L air receiver to eliminate the residual oil down to 3 ppm. As plotted in Fig. 2, dry air at 0.7 MPa (gauge pressure) is elaborated by a pressure control valve designed for pressure reduction down to atmospheric pressure, and after that, flows through a volumetric orifice flow meter equipped with a high precision differential pressure transducer. The air flows into a stainless steel 70 L calm chamber and then through the inlet tube to the test section and finally it reaches the flow rate control valve and is discharged to the atmosphere. Two connection tubes from the chamber to the test section have been designed, both are 1.1 m long but they present two different rectangular cross sections: 100 20 and 100 40 mm2, respectively. The test section is made of stainless steel AISI 316L of size 300 mm width, 300 mm length and 200 mm height fitted with a suitable Bakelite channel. It consists of 3 parts: the top and the bottom plates that are bolted to allow inspection and maintenance operations and the core where the test sample is inserted. A 15 mm thick Teflon plate is machined to obtain a location for the copper heater where the sample is tightened. Under the Teflon plate another 15 mm thick plate of bakelite is positioned to reduce the heat loss from the bottom face of the heater. This is obtained from a 7 mm thick copper plate with the same test sample base area; a guide is milled in the copper to hold the electrical wire resistance. The electrical power is given by a stabilized direct current (DC) power supply that permits to provide up to 900 W. An infrared analysis of a prototype heater fed with 150 W in still air has proved the suitability of the selected heating technique; in fact, no hot spots were visible all over the surface, which presented a uniform temperature distribution, at around 93 C. The power is supplied from the bottom surface of the test sample. The electrical power is indirectly measured by means of a calibrated reference resistance (shunt) and by the measurement of the effective EDP (Electrical Potential Difference) of the resistance wire inserted in the copper heater. The temperatures at inlet and outlet of the specimen are obtained by means of two sets of probes, equipped with calibrated Ttype thermocouples (five for the 20 mm high sample and eight for the 40 mm one). The entire measuring chain (including the digital voltmeter/data logger) has been calibrated against a Pt100 probe having an accuracy of 0.02 K. To reduce air temperature non-uniformities over the cross section, a rectangular mixer consisting of several sets of louvers
S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60 Table 1 Uncertainty of transducers inserted in the test rig and of the experimental measurements. Measure-Transducer
Uncertainty
Temperature, T-type thermocouple Absolute Pressure Transducer (Full scale FS ¼ 0.6 MPa) Differential Pressure Transducer (Orifice, full scale FS ¼ 2000 Pa) Differential Pressure Transducer (Test section, full scale FS ¼ 1000 Pa) Electric Power Air flow rate, Orifice Flowmeter
0.05 K 330 Pa
2.5 Pa 0.13% of the reading 0.80% of the reading Mean 1.0% Max 2.2% 1.0% 0.7%
Heat Transfer Coefficient HTC* Permeability K Inertia Coefficient f
that produce a combination of shearing action and relative displacement on adjacent areas of air flow has been designed, realized and inserted in the bakelite channel before the temperature measurements. As displayed in Fig. 2, the absolute pressure is measured in two places by means of two transducers: one is located in the inlet flange of the volumetric flow meter while the other one is placed before the test section. Moreover, two differential pressure transducers are used to measure the pressure drops across both the calibrated orifice flow meter (accuracy of 2 Pa) and the test sample (accuracy of 2.5 Pa). Four static pressure taps at the center of each of the four air duct walls are located both upstream and downstream of the test sample. The absolute pressure transducer is connected to the four upstream taps, while the differential transducer is connected to the upstream and downstream taps. The uncertainties of the transducers including the related complete measuring chain used in the test rig are summarized in Table 1. Two 20 PPI aluminum foam samples were selected with almost the same porosity (3 around 0.93) and with two different foam core heights: 20 and 40 mm, respectively. As reported in Table 2, the number of pores per inch, the relative density and the surface area per unit volume were provided by the manufacturer. The fiber thickness and the fiber length were measured using several different high resolution photos which were taken at each side of the foam samples. The fiber length l and the fiber thickness t are two important geometrical parameters that are linked to the morphological structure of the foams. In particular in Table 2, the fiber thickness is the mean value of the thickness of the pore’s edges while, as length of the fiber, it is considered the length of the edge which connects two adjacent vertices. The two foam samples are 100 mm long and 100 mm wide while one is 40 mm high and the other 20 mm high. Each sample is brazed between two 10 mm thick aluminum plates where 12 holes
PPIa [in1] Porosity, 3a [] Relative density [%], rRa Height, H [m] Area per unit volume, asv [m2 m3] Fiber thickness [mm], t Fiber length [mm], l a
Provided by the manufacturer.
(1)
_ air is the air mass flow where PEL is the supplied electric power, m rate, Cp,air is the air specific heat at constant pressure and the last term is the air temperature difference between outlet and inlet of the test section. For all the collected data points the difference between the two terms of Eq. (1) were verified to be within 5.0% with a mean value around 2.0%. The tests were run at around atmospheric pressure, with inlet air temperature between 18 and 26 C, by varying the air mass flow rate between 0.01 and 0.025 kg s1 (frontal velocity u between 2 and 5 m s1) for the specimen 0.04 m high and between 0.005 and 0.015 kg s1 for the specimen 0.02 m high. Three different heat fluxes were imposed at the base plate of each sample: 25.0, 32.5 and 40.0 kW m2. The product of the heat transfer coefficient, HTC and the foamfinned surface efficiency, U* is defined as:
PEL ¼ HTC * Abase $Dtml
HTC$U* ¼
(2)
where the reference surface area, Abase is the base area of the test sample and Dtml is the logarithmic mean temperature difference between the wall temperature and the air:
tw;in tair;in tw;out tair;out tw;in tair;in ln tw;out tair;out
Dtml ¼
(3)
tw,in and tw,out indicate the heated wall temperatures at the inlet and outlet of the base plate respectively. The heat transfer coefficient HTC is referred to the base area of the test sample and it is also equal to
HTC ¼ a$asv $H
(4)
where a is the interstitial coefficient, asv is the heat transfer area per unit volume of the foam and H is the specimen height. The measured pressure drops were elaborated as suggested in the open literature. Permeability K, and the inertia coefficient f are estimated from experimental data. The experimental pressure gradient can be expressed as a function of:
dp dz
¼ EXP
m K
f $r u þ pffiffiffiffiu2 K
(5)
and then rewritten as follows:
dp dz
$ EXP
m f $r 1 ¼ þ pffiffiffiffiu ¼ a þ b$u u K K
(6)
From a regression analysis, it is possible to obtain the values of the a and b coefficients and then:
Table 2 Geometrical characteristics of the tested Aluminum foams. Parameter
were drilled to locate six thermocouples in the top plate and six in the bottom one, to measure the temperature of the plates at the bottom and top of the foam. The heat balance between the electric power and the air side heat flow rate can be written as follows:
_ air $cp $ tair;out tair;in PEL ¼ m
2 Pa
57
Al-20e7.0
Al-20e6.8
20 0.930 7.0 0.02 1169 0.315 1.175
20 0.932 6.8 0.04 1156 0.367 1.218
K ¼ f ¼
m a pffiffiffiffi b$ K
(7)
r
The thermophysical properties of air have been calculated at the mean temperature and pressure using NIST RefProp 7.0 [12]. Finally, as reported in Table 1, the error analyses have pointed out that the
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S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
heat transfer coefficient presents an average uncertainty of 1.0% with a maximum value of 2.2% (defined referring to PEL as in Eq. (2)). Considering the pressure drops, the permeability and inertia coefficient present an uncertainty of 1.0% and 0.7%, respectively. 3. Experimental results The experimental measurements of heat transfer coefficient and pressure drop obtained during single phase air heat transfer through two 20 PPI foam samples are here reported and commented. Fig. 3 displays the heat transfer coefficients plotted against the air mass velocity defined with reference to the frontal area of the empty channel. The database for these two samples has been subdivided considering the imposed heat flux: 25.0, 32.5 and 40.0 kW m2 to highlight that the heat transfer coefficient does not depend on it. Generally speaking, the heat transfer coefficient increases as the mass velocity increases. The heat transfer coefficients measured for the 20 mm high sample are higher than those obtained for 40 mm high foam. The experimental data can be interpolated by the following simple dimensional equation:
_ air m HTC ¼ cost$ Afront *
!B ¼ cost$G
B
(8)
where Afront is the area of the empty channel and HTC* is the global heat transfer coefficient as defined in Eq. (2). The values of the exponent B are almost the same for both the samples, equal to 0.43. This means that the heat transfer coefficient for both the aluminum foams rises with the mass flow rate exhibiting the same power. Since the two samples present the same pore density (i.e. PPI) and porosity, they also present the same heat transfer area per unit of volume (Table 2). Therefore, the 20 mm high foam has almost half heat transfer area than the 40 mm high sample. This means that the foam-finned surface area efficiency of the 20 mm high sample is more than double with respect to that of the 40 mm high sample. Considering the fluid dynamic behavior of these two aluminum foams, Fig. 4 reports the experimental pressure gradients plotted against the air mass velocity. It appears that the two samples exploit almost the same values of the pressure drops. Table 3
Fig. 4. Experimental pressure gradient plotted against the air mass velocity.
summarizes the values of permeability and inertia coefficient obtained from the experimental measurements. The 20 mm high foam exhibits slightly lower values of both permeability and inertia coefficient than those of the 40 mm high sample. 4. Heat transfer and fluid flow modeling Recently, present authors have developed two semi-empirical models to calculate the heat transfer coefficient and the pressure drop during single phase air flow through porous foams [10,11]. The models were developed as best fitting of the measurements of seven Aluminum foam samples with 5, 10, 20 and 40 PPI, porosity between 0.896 and 0.956; six of those were 40 mm high while one was 20 mm high. The heat transfer model permits to evaluate both the interstitial heat transfer coefficient a and the foam-finned surface efficiency U*, as:
1 þ U$asv $H $asv $H HTC$U* ¼ a$U* $asv $H ¼ a$ 1 þ asv $H
(9)
where asv is defined in Table 2. As described in Eq. (9), the foamfinned surface efficiency U* is a function of the foam efficiency U:
U ¼
tanhðm$LÞ m$L
(10)
The interstitial heat transfer coefficient a and the m value can be calculated as:
l a ¼ 0:02$Re0:9 $Pr0:33 t
m ¼
4$a lf $t
!0:5
(11)
Table 3 Values of Permeability and Inertia coefficient. Parameter
Fig. 3. Global Heat Transfer Coefficient plotted against the air mass velocity. HF: Heat Flux [kW m2]
PPI [in1] Porosity, 3 [] Relative density, rR* [%] Height, H [m] Permeability, K 107 [m2] Inertia Coefficient, f [e]
Al-20e7.0
Al-20e6.8
20 0.930 7.0 0.02 0.535 0.050
20 0.932 6.8 0.04 0.824 0.065
S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
59
Present authors have also developed a new computational procedure for pressure drop estimations [11]; the pressure gradient can be described by the following simple equation:
dp 2$F$G2 ¼ r$Dh dz
(14)
where the mass velocity G is defined as the ratio between the air mass flow rate and Afront, cross sectional area of the empty channel as:
G ¼ r$u ¼
_ air m Afront
(15)
The factor F is expressed as a function of porosity 3, the number of pores per inch PPI and the Reynolds number Re:
F ¼
1:765$Re0:1014 $32 PPI0:6
(16)
The Reynolds number Re and the characteristic length Dh can be calculated as: Fig. 5. Comparison between the calculated and experimental global heat transfer coefficients plotted against the air mass velocity. Present model Eqs. 9e13.
Finally, the Reynolds number Re and the equivalent fin length L can be calculated as:
Re ¼
G$t m$3
L ¼ 6:6$H$PPI0:99 ð0:0254 t$PPIÞ
(12)
(13)
where L, H and t are expressed in meters. As shown in Fig. 5, the results obtained from the above model highlight that there is a good agreement between the calculations and the experimental heat transfer coefficients for the 40 mm high sample while the model underestimates data for the 20 mm high sample. This may be due to an underestimation of the foam-finned surface area efficiency.
Re ¼
G$Dh m$3
0:0254 4$ t $l PPI Dh ¼ 0:0254 t þ l $2 PPI
(17)
(18)
As shown in Fig. 6, the model is in good agreement with the experimental pressure gradients. Data seem to be slightly underestimated at low mass velocity but the prediction capability improves when increasing mass velocity.
5. Conclusions This paper presents the experimental measurements of heat transfer coefficient and pressure drop obtained during single phase air heat transfer through two 20 PPI aluminum foams presenting the same porosity and different foam core heights, 20 mm and 40 mm, respectively. The measurements have been carried out varying the air mass velocity between 2.5 and 7.5 kg m2 s1 and imposing three different heat flow rates: 250, 325 and 400 W. The heat transfer coefficient for both the foams does not depend on the imposed heat flux. The results have shown that the 20 mm high aluminum foam presents higher heat transfer coefficients than those exhibited by the 40 mm high sample. The experimental results have also been compared with the calculated heat transfer coefficients; the model is in good agreement with data for the 40 mm high foam while it underestimates data for the 20 mm high sample. The pressure gradients are almost the same for both the 40 mm high and the 20 mm high samples. The model suggested for the prediction of the pressure gradients is in good agreement with the experimental results.
Acknowledgements
Fig. 6. Calculated vs. experimental pressure gradients. Present model Eqs. 14e18.
The support of University of Padova through the project 60A107011 and of the MIUR through the PRIN Project 2007TALBHJ_003 is gratefully acknowledged. The authors acknowledge useful discussion with B.D. Leyda and E. Ward at ERG Aerospace Inc.
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S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
Nomenclature Abase asv cp
Base area, [m2] Area per unit of volume, [m1] Specific heat of air at constant pressure evaluated at the mean air temperature, [J kg1 K1] Hydraulic diameter, [m]
Dh dp Experimental pressure gradient, [Pa m1] dz EXP dp Pressure gradient, [Pa m1] dz F Friction Factor as defined in Eq. (16), [] f Inertia coefficient, [] G Mass velocity, [kg m2 s1] H Specimen height, [m] HTC Heat transfer coefficient, [W m2 K1] HTC* Global heat transfer coefficient defined by Eq. (2), [W m2 K1] K Permeability, [m2] L Equivalent fin length as in Eq. (13), [m] l Fiber length, [m] _ air Air mass flow rate, [kg s1] m Electric power, [W] PEL Pr Prandtl number, [] PPI Pore per linear inch, [m1] Re Reynolds number, [] t Fiber thickness, [m] t air Mean air temperature, [ C] Inlet air temperature, [ C] tair,in Outlet air temperature, [ C] tair,out tw Mean wall temperature, [ C] Inlet wall temperature, [ C] tw,in Outlet wall temperature, [ C] tw,out u Frontal velocity, [m s1]
Greek symbols Interstitial heat transfer coefficient defined by Eq. (4), [W m2 K1]
a
Dtml 3 l lf m U U* rR r
Logarithmic mean temperature difference, [ C] Porosity, [] Air thermal conductivity evaluated at the mean air temperature, [W m1 K1] Foam thermal conductivity, [¼ 175 W m1 K1] Air dynamic viscosity evaluated at the mean air temperature, [Pa s] Foam-Finned efficiency, [] Foam-Finned Surface area efficiency, [] Relative density rR ¼ (1 3)$100, [%] Air density evaluated at the mean air temperature, [kg m3]
References [1] L.J. Gibson, M.F. Ashby, Cellular Solids-Structures and Properties, second ed. Cambridge Solid State Science Series, Cambridge Univ. Press, 1997, 510. [2] K. Boomsma, D. Poulikakos, The effects of compression and pore size variations on the liquid flow characteristics of metal foams, ASME J. Fluids Eng. 124 (2002) 263e272. [3] S.Y. Kim, B.H. Kang, J.-H. Kim, Forced convection from aluminium foam materials in an asymmetrically heated channel, Int. J. Heat Mass Tran. 44 (2001) 1451e1454. [4] J.F. Liu, W.T. Wu, W.C. Chiu, W.H. Hsieh, Measurement and correlation of friction characteristic of flow through foam matrixes, Exp. Thermal Fluid Sci. 30 (2006) 329e336. [5] A. Bhattacharya, V.V. Calmidi, R.L. Mahajan, Thermophysical properties of high porosity metal foams, Int. J. Heat Mass Tran. 45 (2002) 1017e1031. [6] V.V. Calmidi, R.L. Mahajan, Forced convection in high porosity metal foams, J. Heat Tran. 122 (2000) 557e565. [7] W.H. Hsieh, J.Y. Wu, W.H. Shih, W.C. Chiu, Experimental investigation of heattransfer characteristics of aluminum-foam heat sink, Int. J. Heat Mass Tran. 47 (2004) 5149e5157. [8] N. Dukhan, P.D. Quiñones-Ramos, E. Cruz-Ruiz, M. Vélez-Reyes, E.P. Scott, One-dimensional heat transfer analysis in open-cell 10-PPI meta foam, Int. J. Heat Mass Tran. 48 (2005) 5112e5120. [9] I. Ghosh, Heat transfer correlation for high porosity open-cell foam, Int. J. Heat Mass Tran. 52 (2009) 1488e1494. [10] S. Mancin, C. Zilio, A. Cavallini, L. Rossetto, Heat transfer during air flow in aluminum foams, Int. J. Heat Mass Tran. 53 (2010) 4976e4984. [11] S. Mancin, C. Zilio, A. Cavallini, L. Rossetto, Pressure drop during air flow in aluminum foams, Int. J. Heat Mass Tran. 53 (2010) 3121e3130. [12] NIST National Institute of Standard and Technology, RefProp Version 7.0 (2002) Boulder, Colorado, USA.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Foam height effects on heat transfer performance of 20 ppi aluminum foamsq Simone Mancin, Claudio Zilio, Luisa Rossetto*, Alberto Cavallini Dipartimento di Fisica Tecnica, Università degli Studi di Padova, Via Venezia 1, 35131 Padova, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 29 October 2010 Accepted 9 May 2011 Available online 17 May 2011
This paper investigates the heat transfer performance of two 20 PPI (pores per linear inch) aluminum foams with constant porosity (around 0.93) and different foam core height (20 mm and 40 mm). The aluminum foams are cellular structure materials that present a stochastic interconnected pores distribution mostly uniform in size and shape. Most commercially available metal foams are based on aluminum, copper, nickel and metal alloys. Metal foams have considerable applications in multifunctional heat exchangers, cryogenics, combustion chambers, cladding on buildings, strain isolation, petroleum reservoirs, compact heat exchangers for airborne equipment, air cooled condensers and compact heat sinks for power electronics. The experimental measurements of the heat transfer coefficient and pressure drop have been carried out in a test apparatus built at Dipartimento di Fisica Tecnica of the Università di Padova. The foam core height effects on the heat transfer performance have been studied imposing three constant specific heat fluxes at the bottom of the samples: 25.0, 32.5 and 40.0 kW m2 and varying the frontal air velocity between 2.0 and 5.0 m s1. The experimental heat transfer coefficients and pressure gradients have been compared against the predictions obtained from two models recently suggested by present authors. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Metal foams Heat transfer Pressure drops Air flow
1. Introduction Metal foams are a class of cellular structured materials that present a stochastic interconnected pores distribution mostly uniform in size and shape. In the last decades, these porous media have been largely studied because of their interesting properties that cover several different technical fields. In fact, metal foams are lightweight, offering high strength, rigidity and high heat transfer surface area [1]. As shown in Fig. 1, metal foam consists of tortuous, irregularly shaped flow passages. The most important geometrical characteristics of the metal foams are the number of pores per inch (PPI) and the porosity. The first one is easily obtainable by counting the number of pores in 25.4 mm. The second one, the porosity 3, is defined as the ratio of total void volume to the total volume occupied by the solid matrix and void volumes. Several authors have studied the heat transfer and fluid flow characteristics of metal foams by varying the number of pores per linear inch and the porosity, among them: Boomsma and Poulikakos [2], Kim et al. [3], q Paper presented at Thermal and Environmental Issues in Energy System Conference and selected by the scientific commission to be suggested for a possible publication in a special issue of the International Journal: Applied Thermal Engineering. * Corresponding author. Tel.: þ39 049 8276869; fax: þ39 049 8276896. E-mail addresses: [email protected] (S. Mancin), [email protected] (C. Zilio), [email protected] (L. Rossetto), [email protected] (A. Cavallini). 1359-4311/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2011.05.015
Liu et al. [4], Bhattacharya et al. [5], Calmidi and Mahajan [6] and Hsieh et al. [7]. In particular, Boomsma and Poulikakos [2] carried out several heat transfer and pressure drop measurements during liquid flow through 40 PPI aluminum foams with different porosities. The authors observed a great increasing of the pressure drops as the porosity decreased. Moreover, they found that the Nusselt number, defined on the hydraulic diameter of the empty channel with the heat transfer coefficient referred to the base area of the sample, increases with the compression ratio. Kim et al. [3] studied the effects of porosity and of number of pores on the heat transfer, testing 6 different porous fins in a plate and fin heat exchanger. They found that at 20 PPI, the volumetric heat transfer coefficients referred to the total heat transfer area times the surface area efficiency, decrease with increasing porosity. Liu et al. [4] investigated the fluid flow through seven different aluminum foams varying the number of pores per inch and the porosity. The authors suggested that the pressure drops increase with PPI while at 20 PPI the effects of porosity on the pressure gradient are negligible. Bhattacharya et al. [5] proposed a model for the estimations of the permeability and inertia coefficient of aluminum metal foams regressed on a database which includes pressure drop measurements of 22 different porous media. Part of their database has been collected by Calmidi and Mahajan [6], that studied the air forced convection in high porosity metal foams, measuring the heat
56
S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
Fig. 1. Photo of the tested 20 PPI aluminum foam. Fig. 2. Schematic of the experimental set up.
transfer coefficients and pressure drops of seven aluminum foams (PPI ¼ 5e40 and 3 ¼ 0.90e0.97). They observed that, at constant PPI, the Nusselt number, based on the length of the heated section and defined on the heat transfer coefficient referred to the base area and to wall to air inlet temperatures difference, increases with porosity. Hsieh et al. [7] studied the heat transfer behavior of six aluminum foams with different numbers of pores per inch and porosities. The effects of porosity on the heat transfer have been obtained testing four different samples with 20 PPI. In particular, they found that the Nusselt number (based on the length of the test section and defined using the heat transfer coefficient referred to the base area) increases with porosity. All the cited experimental works on forced convection heat transfer in open cells metal foams have studied the effects of the most important geometrical characteristics: the porosity and the number of pores per inch (PPI). On the other hand, the foam-finned surface efficiency appears to be a critical parameter which controls the effective heat transfer behavior of metal foams. Recently, Dukhan et al. [8] proposed an analytical and experimental work on the heat transfer in a 10 PPI metal foam. They measured and estimated the temperature profile inside the foam during air heat transfer. They demonstrated that the temperature of the foam reaches that of the ambient at a dimensionless distance from the heated base of approximately 0.3. This means that over than 60% of the heat transfer area does not transfer any heat flow rate being at the air temperature. Moreover, Ghosh [9] suggested a model to estimate both the heat transfer coefficient and the foam-finned surface area efficiency. From his calculations, at 3 ¼ 0.85, the foam-finned surface area efficiency decreases with PPI. The foam-finned surface area efficiency is linked to the height of the foam core; in particular, it is expected that it decreases with increasing foam height. To understand how the foam height affects the heat transfer behavior of metal foams is useful in order to develop accurate heat transfer models. This paper presents original experimental measurements that show the foam height effects on the heat transfer performance of two 20 PPI aluminum samples with constant porosity 3 and two different core heights: 20 and 40 mm. The experimental heat transfer coefficients and pressure drops are compared against the predictions of two models recently suggested by present authors [10,11]. 2. Experimental set up and data reduction The experimental test rig is an open-circuit type wind tunnel with rectangular cross section, as shown in Fig. 2. The experimental set up consists of: (1) screw compressor, (2) R134a vapor compression system drier, (3) filters, (4) 500 L air receiver, (5) pressure control valve, (6) flow meter, (7) 70 L calm chamber, (8) inlet tube, (9) test section, (10) power supply, (11) discharge tube and (12) flow rate control valve.
The ambient air flows through a single stage, oil injected screw compressor driven by an electric motor with inverter driver. It provides a variable volumetric air flow rate (measured at ambient conditions) ranging between 0 and 90 m3 h1 at a constant gauge pressure of 0.7 MPa. The humid and oiled compressed air is dehydrated by a drier down to a dew point temperature of 3 C and then filtered by a set of filters, in order to remove water, oil and particulate materials. An additional activated charcoal filter is located before the 500 L air receiver to eliminate the residual oil down to 3 ppm. As plotted in Fig. 2, dry air at 0.7 MPa (gauge pressure) is elaborated by a pressure control valve designed for pressure reduction down to atmospheric pressure, and after that, flows through a volumetric orifice flow meter equipped with a high precision differential pressure transducer. The air flows into a stainless steel 70 L calm chamber and then through the inlet tube to the test section and finally it reaches the flow rate control valve and is discharged to the atmosphere. Two connection tubes from the chamber to the test section have been designed, both are 1.1 m long but they present two different rectangular cross sections: 100 20 and 100 40 mm2, respectively. The test section is made of stainless steel AISI 316L of size 300 mm width, 300 mm length and 200 mm height fitted with a suitable Bakelite channel. It consists of 3 parts: the top and the bottom plates that are bolted to allow inspection and maintenance operations and the core where the test sample is inserted. A 15 mm thick Teflon plate is machined to obtain a location for the copper heater where the sample is tightened. Under the Teflon plate another 15 mm thick plate of bakelite is positioned to reduce the heat loss from the bottom face of the heater. This is obtained from a 7 mm thick copper plate with the same test sample base area; a guide is milled in the copper to hold the electrical wire resistance. The electrical power is given by a stabilized direct current (DC) power supply that permits to provide up to 900 W. An infrared analysis of a prototype heater fed with 150 W in still air has proved the suitability of the selected heating technique; in fact, no hot spots were visible all over the surface, which presented a uniform temperature distribution, at around 93 C. The power is supplied from the bottom surface of the test sample. The electrical power is indirectly measured by means of a calibrated reference resistance (shunt) and by the measurement of the effective EDP (Electrical Potential Difference) of the resistance wire inserted in the copper heater. The temperatures at inlet and outlet of the specimen are obtained by means of two sets of probes, equipped with calibrated Ttype thermocouples (five for the 20 mm high sample and eight for the 40 mm one). The entire measuring chain (including the digital voltmeter/data logger) has been calibrated against a Pt100 probe having an accuracy of 0.02 K. To reduce air temperature non-uniformities over the cross section, a rectangular mixer consisting of several sets of louvers
S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60 Table 1 Uncertainty of transducers inserted in the test rig and of the experimental measurements. Measure-Transducer
Uncertainty
Temperature, T-type thermocouple Absolute Pressure Transducer (Full scale FS ¼ 0.6 MPa) Differential Pressure Transducer (Orifice, full scale FS ¼ 2000 Pa) Differential Pressure Transducer (Test section, full scale FS ¼ 1000 Pa) Electric Power Air flow rate, Orifice Flowmeter
0.05 K 330 Pa
2.5 Pa 0.13% of the reading 0.80% of the reading Mean 1.0% Max 2.2% 1.0% 0.7%
Heat Transfer Coefficient HTC* Permeability K Inertia Coefficient f
that produce a combination of shearing action and relative displacement on adjacent areas of air flow has been designed, realized and inserted in the bakelite channel before the temperature measurements. As displayed in Fig. 2, the absolute pressure is measured in two places by means of two transducers: one is located in the inlet flange of the volumetric flow meter while the other one is placed before the test section. Moreover, two differential pressure transducers are used to measure the pressure drops across both the calibrated orifice flow meter (accuracy of 2 Pa) and the test sample (accuracy of 2.5 Pa). Four static pressure taps at the center of each of the four air duct walls are located both upstream and downstream of the test sample. The absolute pressure transducer is connected to the four upstream taps, while the differential transducer is connected to the upstream and downstream taps. The uncertainties of the transducers including the related complete measuring chain used in the test rig are summarized in Table 1. Two 20 PPI aluminum foam samples were selected with almost the same porosity (3 around 0.93) and with two different foam core heights: 20 and 40 mm, respectively. As reported in Table 2, the number of pores per inch, the relative density and the surface area per unit volume were provided by the manufacturer. The fiber thickness and the fiber length were measured using several different high resolution photos which were taken at each side of the foam samples. The fiber length l and the fiber thickness t are two important geometrical parameters that are linked to the morphological structure of the foams. In particular in Table 2, the fiber thickness is the mean value of the thickness of the pore’s edges while, as length of the fiber, it is considered the length of the edge which connects two adjacent vertices. The two foam samples are 100 mm long and 100 mm wide while one is 40 mm high and the other 20 mm high. Each sample is brazed between two 10 mm thick aluminum plates where 12 holes
PPIa [in1] Porosity, 3a [] Relative density [%], rRa Height, H [m] Area per unit volume, asv [m2 m3] Fiber thickness [mm], t Fiber length [mm], l a
Provided by the manufacturer.
(1)
_ air is the air mass flow where PEL is the supplied electric power, m rate, Cp,air is the air specific heat at constant pressure and the last term is the air temperature difference between outlet and inlet of the test section. For all the collected data points the difference between the two terms of Eq. (1) were verified to be within 5.0% with a mean value around 2.0%. The tests were run at around atmospheric pressure, with inlet air temperature between 18 and 26 C, by varying the air mass flow rate between 0.01 and 0.025 kg s1 (frontal velocity u between 2 and 5 m s1) for the specimen 0.04 m high and between 0.005 and 0.015 kg s1 for the specimen 0.02 m high. Three different heat fluxes were imposed at the base plate of each sample: 25.0, 32.5 and 40.0 kW m2. The product of the heat transfer coefficient, HTC and the foamfinned surface efficiency, U* is defined as:
PEL ¼ HTC * Abase $Dtml
HTC$U* ¼
(2)
where the reference surface area, Abase is the base area of the test sample and Dtml is the logarithmic mean temperature difference between the wall temperature and the air:
tw;in tair;in tw;out tair;out tw;in tair;in ln tw;out tair;out
Dtml ¼
(3)
tw,in and tw,out indicate the heated wall temperatures at the inlet and outlet of the base plate respectively. The heat transfer coefficient HTC is referred to the base area of the test sample and it is also equal to
HTC ¼ a$asv $H
(4)
where a is the interstitial coefficient, asv is the heat transfer area per unit volume of the foam and H is the specimen height. The measured pressure drops were elaborated as suggested in the open literature. Permeability K, and the inertia coefficient f are estimated from experimental data. The experimental pressure gradient can be expressed as a function of:
dp dz
¼ EXP
m K
f $r u þ pffiffiffiffiu2 K
(5)
and then rewritten as follows:
dp dz
$ EXP
m f $r 1 ¼ þ pffiffiffiffiu ¼ a þ b$u u K K
(6)
From a regression analysis, it is possible to obtain the values of the a and b coefficients and then:
Table 2 Geometrical characteristics of the tested Aluminum foams. Parameter
were drilled to locate six thermocouples in the top plate and six in the bottom one, to measure the temperature of the plates at the bottom and top of the foam. The heat balance between the electric power and the air side heat flow rate can be written as follows:
_ air $cp $ tair;out tair;in PEL ¼ m
2 Pa
57
Al-20e7.0
Al-20e6.8
20 0.930 7.0 0.02 1169 0.315 1.175
20 0.932 6.8 0.04 1156 0.367 1.218
K ¼ f ¼
m a pffiffiffiffi b$ K
(7)
r
The thermophysical properties of air have been calculated at the mean temperature and pressure using NIST RefProp 7.0 [12]. Finally, as reported in Table 1, the error analyses have pointed out that the
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S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
heat transfer coefficient presents an average uncertainty of 1.0% with a maximum value of 2.2% (defined referring to PEL as in Eq. (2)). Considering the pressure drops, the permeability and inertia coefficient present an uncertainty of 1.0% and 0.7%, respectively. 3. Experimental results The experimental measurements of heat transfer coefficient and pressure drop obtained during single phase air heat transfer through two 20 PPI foam samples are here reported and commented. Fig. 3 displays the heat transfer coefficients plotted against the air mass velocity defined with reference to the frontal area of the empty channel. The database for these two samples has been subdivided considering the imposed heat flux: 25.0, 32.5 and 40.0 kW m2 to highlight that the heat transfer coefficient does not depend on it. Generally speaking, the heat transfer coefficient increases as the mass velocity increases. The heat transfer coefficients measured for the 20 mm high sample are higher than those obtained for 40 mm high foam. The experimental data can be interpolated by the following simple dimensional equation:
_ air m HTC ¼ cost$ Afront *
!B ¼ cost$G
B
(8)
where Afront is the area of the empty channel and HTC* is the global heat transfer coefficient as defined in Eq. (2). The values of the exponent B are almost the same for both the samples, equal to 0.43. This means that the heat transfer coefficient for both the aluminum foams rises with the mass flow rate exhibiting the same power. Since the two samples present the same pore density (i.e. PPI) and porosity, they also present the same heat transfer area per unit of volume (Table 2). Therefore, the 20 mm high foam has almost half heat transfer area than the 40 mm high sample. This means that the foam-finned surface area efficiency of the 20 mm high sample is more than double with respect to that of the 40 mm high sample. Considering the fluid dynamic behavior of these two aluminum foams, Fig. 4 reports the experimental pressure gradients plotted against the air mass velocity. It appears that the two samples exploit almost the same values of the pressure drops. Table 3
Fig. 4. Experimental pressure gradient plotted against the air mass velocity.
summarizes the values of permeability and inertia coefficient obtained from the experimental measurements. The 20 mm high foam exhibits slightly lower values of both permeability and inertia coefficient than those of the 40 mm high sample. 4. Heat transfer and fluid flow modeling Recently, present authors have developed two semi-empirical models to calculate the heat transfer coefficient and the pressure drop during single phase air flow through porous foams [10,11]. The models were developed as best fitting of the measurements of seven Aluminum foam samples with 5, 10, 20 and 40 PPI, porosity between 0.896 and 0.956; six of those were 40 mm high while one was 20 mm high. The heat transfer model permits to evaluate both the interstitial heat transfer coefficient a and the foam-finned surface efficiency U*, as:
1 þ U$asv $H $asv $H HTC$U* ¼ a$U* $asv $H ¼ a$ 1 þ asv $H
(9)
where asv is defined in Table 2. As described in Eq. (9), the foamfinned surface efficiency U* is a function of the foam efficiency U:
U ¼
tanhðm$LÞ m$L
(10)
The interstitial heat transfer coefficient a and the m value can be calculated as:
l a ¼ 0:02$Re0:9 $Pr0:33 t
m ¼
4$a lf $t
!0:5
(11)
Table 3 Values of Permeability and Inertia coefficient. Parameter
Fig. 3. Global Heat Transfer Coefficient plotted against the air mass velocity. HF: Heat Flux [kW m2]
PPI [in1] Porosity, 3 [] Relative density, rR* [%] Height, H [m] Permeability, K 107 [m2] Inertia Coefficient, f [e]
Al-20e7.0
Al-20e6.8
20 0.930 7.0 0.02 0.535 0.050
20 0.932 6.8 0.04 0.824 0.065
S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
59
Present authors have also developed a new computational procedure for pressure drop estimations [11]; the pressure gradient can be described by the following simple equation:
dp 2$F$G2 ¼ r$Dh dz
(14)
where the mass velocity G is defined as the ratio between the air mass flow rate and Afront, cross sectional area of the empty channel as:
G ¼ r$u ¼
_ air m Afront
(15)
The factor F is expressed as a function of porosity 3, the number of pores per inch PPI and the Reynolds number Re:
F ¼
1:765$Re0:1014 $32 PPI0:6
(16)
The Reynolds number Re and the characteristic length Dh can be calculated as: Fig. 5. Comparison between the calculated and experimental global heat transfer coefficients plotted against the air mass velocity. Present model Eqs. 9e13.
Finally, the Reynolds number Re and the equivalent fin length L can be calculated as:
Re ¼
G$t m$3
L ¼ 6:6$H$PPI0:99 ð0:0254 t$PPIÞ
(12)
(13)
where L, H and t are expressed in meters. As shown in Fig. 5, the results obtained from the above model highlight that there is a good agreement between the calculations and the experimental heat transfer coefficients for the 40 mm high sample while the model underestimates data for the 20 mm high sample. This may be due to an underestimation of the foam-finned surface area efficiency.
Re ¼
G$Dh m$3
0:0254 4$ t $l PPI Dh ¼ 0:0254 t þ l $2 PPI
(17)
(18)
As shown in Fig. 6, the model is in good agreement with the experimental pressure gradients. Data seem to be slightly underestimated at low mass velocity but the prediction capability improves when increasing mass velocity.
5. Conclusions This paper presents the experimental measurements of heat transfer coefficient and pressure drop obtained during single phase air heat transfer through two 20 PPI aluminum foams presenting the same porosity and different foam core heights, 20 mm and 40 mm, respectively. The measurements have been carried out varying the air mass velocity between 2.5 and 7.5 kg m2 s1 and imposing three different heat flow rates: 250, 325 and 400 W. The heat transfer coefficient for both the foams does not depend on the imposed heat flux. The results have shown that the 20 mm high aluminum foam presents higher heat transfer coefficients than those exhibited by the 40 mm high sample. The experimental results have also been compared with the calculated heat transfer coefficients; the model is in good agreement with data for the 40 mm high foam while it underestimates data for the 20 mm high sample. The pressure gradients are almost the same for both the 40 mm high and the 20 mm high samples. The model suggested for the prediction of the pressure gradients is in good agreement with the experimental results.
Acknowledgements
Fig. 6. Calculated vs. experimental pressure gradients. Present model Eqs. 14e18.
The support of University of Padova through the project 60A107011 and of the MIUR through the PRIN Project 2007TALBHJ_003 is gratefully acknowledged. The authors acknowledge useful discussion with B.D. Leyda and E. Ward at ERG Aerospace Inc.
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S. Mancin et al. / Applied Thermal Engineering 49 (2012) 55e60
Nomenclature Abase asv cp
Base area, [m2] Area per unit of volume, [m1] Specific heat of air at constant pressure evaluated at the mean air temperature, [J kg1 K1] Hydraulic diameter, [m]
Dh dp Experimental pressure gradient, [Pa m1] dz EXP dp Pressure gradient, [Pa m1] dz F Friction Factor as defined in Eq. (16), [] f Inertia coefficient, [] G Mass velocity, [kg m2 s1] H Specimen height, [m] HTC Heat transfer coefficient, [W m2 K1] HTC* Global heat transfer coefficient defined by Eq. (2), [W m2 K1] K Permeability, [m2] L Equivalent fin length as in Eq. (13), [m] l Fiber length, [m] _ air Air mass flow rate, [kg s1] m Electric power, [W] PEL Pr Prandtl number, [] PPI Pore per linear inch, [m1] Re Reynolds number, [] t Fiber thickness, [m] t air Mean air temperature, [ C] Inlet air temperature, [ C] tair,in Outlet air temperature, [ C] tair,out tw Mean wall temperature, [ C] Inlet wall temperature, [ C] tw,in Outlet wall temperature, [ C] tw,out u Frontal velocity, [m s1]
Greek symbols Interstitial heat transfer coefficient defined by Eq. (4), [W m2 K1]
a
Dtml 3 l lf m U U* rR r
Logarithmic mean temperature difference, [ C] Porosity, [] Air thermal conductivity evaluated at the mean air temperature, [W m1 K1] Foam thermal conductivity, [¼ 175 W m1 K1] Air dynamic viscosity evaluated at the mean air temperature, [Pa s] Foam-Finned efficiency, [] Foam-Finned Surface area efficiency, [] Relative density rR ¼ (1 3)$100, [%] Air density evaluated at the mean air temperature, [kg m3]
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