A Numerical Analysis on a Compact Heat Exchanger in Aluminum Foam

Transcription

1 Journal o Physics: Conerence Series PAPER OPEN ACCESS A Numerical Analysis on a Compact Heat Exchanger in Aluminum Foam To cite this article: B Buonomo et al 2016 J. Phys.: Con. Ser View the article online or upates an enhancements. Relate content - Development o Compact Heat Exchangers Accoring to the Results Stuy o the Regularities o Heat Exchange Enhancement Energy Saving V Ya Vasilev - A eormable heat exchanger separate by a helicoi F Rioran - Nuclear Power: Heat exchanger or ast reactors This content was ownloae rom IP aress on 18/08/2018 at 08:49

2 A Numerical Analysis on a Compact Heat Exchanger in Aluminum Foam B Buonomo 1, D Ercole 1, O Manca 1, S Narini 1 1 Dipartimenti i Ingegneria Inustrial e ell'inormazione, Secona Università egli Stui i Napoli, Via Roma 29, 81031, Aversa (CE), Italy oronzio.manca@unina2.it Abstract. A numerical investigation on a compact heat exchanger in aluminum oam is carrie out. The governing equations in two-imensional steay state regime are written in local thermal non-equilibrium (LTNE). The geometrical omain uner investigation is mae up o a plate in aluminum oam with insie a single array o ive circular tubes. The presence o the open-celle metal oam is moele as a porous meia by means o the Darcy-Forchheimer law. The oam has a porosity o 0.93 with 20 pores per inch an the LTNE assumption is use to simulate the heat transer between metal oam an air. The compact heat exchanger at ierent air low rates is stuie with an assigne surace tube temperature. The results in terms o local heat transer coeicient an Nusselt number on the external surace o the tubes are given. Moreover, local air temperature an velocity proiles in the smaller cross section, between two consecutive tubes, as a unction o Reynols number are showe. The perormance evaluation criteria (PEC) is assesse in orer to evaluate the eectiveness o the metal oam. 1. Introuction The metallic oams represent an eicient improvement or the heat transer in general, thanks to their huge value o surace area/volume ratio. They are similar to the heat sinks where the heat lows along the ins, while in this case the ligaments o the oam are responsible to the propagation o heat. Moreover they have low weight, goo rigiity an strength, amping o noise an high thermal conuctivity [1]. Owing to these avantages, the metal oams can be use in heat exchangers [2], uel cells[3], heat sinks[4] or solar thermal plants[5]. Various type o metallic oams have been investigate or their eectiveness in enhancement o the thermal behavior o the system, principally aluminum, copper, nickel. In act many parameters can be change in base o the possible application or the metal oam, such as the type o metal, the porosity (open cells or close cells), the ensity surace area an the overall costs. The metal oams were born aroun thirty years ago, in particular they are use or military applications, but now they are expaning in other sectors or commercial uses like heat exchanger, noise barrier, insulator or shock absorber. The eectiveness o the open-cell metal oam to buil an eicient compact the heat exchanger has been prove or a lot o cases [5-9] because it reuce the thermal inertia o the system, increase the surace heat exchange area an thus reuces the whole size o the heat exchanger. Zaari et al. [10] numerically investigate with a 3D simulation the heat transer insie a porous metal oam using a real geometry or the computational mesh obtaine through a micro-tomography images. The oam is not isotropic an the non-equilibrium thermal conition is assume. The results showe that the increment o the porosity brings about a Content rom this work may be use uner the terms o the Creative Commons Attribution 3.0 licence. Any urther istribution o this work must maintain attribution to the author(s) an the title o the work, journal citation an DOI. Publishe uner licence by Lt 1

3 ecrease o the pressure rop insie the oam ue to lower resistance along the oam. Moreover the thermal equilibrium between the air an metal happens only on a short length o the oam. Xu et al. [11] analyze the LTE an LTNE moels in metal oam or heat exchangers using the volumeaveraging metho. This metho uses a representative elementary volume (REV) as a reerence where the physical quantities are assume homogeneous. Obviously the REV size is larger than the pores o oam an smaller o a reerence size o the system. The results showe that the LTE moel overestimates the heat transer results respect to the LTNE moel. Lin et al [12] numerically investigate the thermal perormance o a porous graphite oam heat exchangers or vehicle cooling application. Four ierent geometric conigurations are analyze in orer to obtain the best perormance with lower low resistance. The CFD analysis showe that the wavy corrugate coniguration present the best thermal an ynamic perormance. Kim et al [13] experimentally investigate on the heat transer o an aluminum oam braze between two lat tubes o an in-waterair heat exchanger or ierent type o the porous oam at various porosity an PPI. The results showe that the thermal perormance are better respect to the conventional in although the oam brings about a higher pressure rop. Nevertheless with the oam the compactness o the heat exchanger is improve. A small compact heat exchanger with open-cell aluminum oam is experimentally investigate in Boomsma et al. [14]. The aluminum oam is braze onto a heat spreaer plate an it is crosse by the water as working lui. The ata showe that the compression rate in the oam increases the heat transer rate but even the pressure rop. Oabaee et al. [15] numerically investigate the metal oam perormance insie a cyliner with the local thermal equilibrium moel. The results were compare to those o a inne-tube heat exchanger an it was prove that the heat transer rate is higher even though the pressure rop is more evient. Moreover an optimal oam porosity is obtaine with a numerical stuy in [16] in orer to achieve the best compromise between the heat transer rate an the pressure rop insie a heat exchanger. A numerical comparison between the perormance o a metal oam heat exchanger an a conventional louvere in heat exchangers was mae in Huisseune et al. [17]. For the same an power, the metal oam heat exchanger has an heat transer rate higher than the conventional heat exchanger up to 6 times. For the same size the inne heat exchanger has better perormance respect to the metal oam heat exchanger. Ater this short review, it seems that the heat exchanger with metal oam is not been ully unerstoo, thereore in this paper the thermal perormances o a compact heat exchanger with oam is numerically analyze. The results in terms o air velocity an temperature proiles insie the oam, local heat transer coeicient along the tubes, average Nusselt number an PEC coeicient are presente. 2. Physical Moel A schematic 2D moel o the compact heat exchanger is shown in Figure 1. Five tubes are arrange in linear way along the height at miway o the aluminum oam space apart between them o 26 mm. An assigne constant temperature is assigne on the external surace o the tubes an assume equal to K (50.0 C). The compact heat exchanger is place in a parallel plates channel with a transversal section height o 200 mm. The thickness o the metal oam is 40 mm an the iameter o tubes is 12 mm. Figure 1: Schematic Moel 2

4 Thermal contact resistances between the metal oam an all the soli surace, the parallel plates an circular tubes, are consiere negligible. The bottom an top suraces o the channel are assume aiabatic. Air enters in the channel with an uniorm velocity an temperature an lows through the oam. The temperature an velocity istributions are very iicult to calculate locally insie the metal oam because it is a porous meia. The oam structure is not regular an thus a continuous approach is not suitable to simulate the thermal behavior insie the oam. Thereore, it is necessary to use the local volume averaging metho to moel this irregular porous meia as a continuous [18]. By using the local volume averaging metho the variables o the equations are written estimating the average o the local variables over an appropriate volume. In base o these aspects, the metal oam is moele with the Darcy-Forchheimer law: p V CF V V (1) L K Δp is the pressure rop, V is the vector velocity o lui phase (air), L is the thickness o the porous meia, μ an ρ are, respectively, the ynamic viscosity an the ensity o the air, K is the permeability o the porous meium an C is the rag actor coeicient. To evaluate K an C the relation o Calmii an Mahajan are use [19]: K p p (2) C F p (3) where ε is the porosity o the metal oam, an p are respectively the ligament an pore iameter o the metal oam. These iameters are in relation with the parameters o the metal oam by means o the ollowing relation [19]: p e 1(1 )/ (4) p (5) ω is the pore ensity o the metal oam, that is the number o pores across a linear inch. It is ixe at 20 pore per inch (PPI). Local Thermal Non-Equilibrium moel is employe. The lui phase an the soli phase are not in thermal equilibrium an thus two energy equations are necessary. Thereore, the hypothesis in this stuy are: 1) The physical omain is two-imensional 2) The aluminum oam is homogeneous an isotropic. 3) The air low is laminar an incompressible 4) Viscous issipation an work o pressure variation are negligible. 5) The thermophysical properties o the both phases are constant. 6) The thermal contact resistances are neglecte. The governing equations [20] are: 3

5 u v 0 x y (6) 2 2 u u p u C u u u v u 2 1/2 2 2 V ( ) (7) x y x K K x y 2 2 v v p v C v v u v v ( ) 2 V (8) 1/2 2 2 x y y K K x y u an v are the component velocity. It is important to see the Darcy term an the Forchheimer extension term in the momentum equations. Energy equation or the liqui phase: Cp u v k, e k, e hs s ( Ts T ) T T T T x y x x y y (9) Energy equation or the soli phase: Ts Ts 0 ks, e ks, e hs s ( T Ts ) x x y y (10) where c p is the speciic heat, T is the local temperature, k e is the eective thermal conuctivity, h s are the local heat transer coeicient an α s is the surace area ensity that inicates the whole contact area between the both phases. The subscript an s inicate respectively the lui phase an the soli phase. The calculation o k e is not reporte here or brevity but in Boomsma et al. [21] is escribe while or both α s an h s are aopte the ollowing correlation [19]: k Re Prpcm, 1Re 40 k hs 0.52 Re Prpcm, 40 Re 1000 k 0.26 Re Pr, 1000 Re pcm (11) s (1 e ) (12) p Where Re is the local Reynols number reerre to ligament iameter: Re V (13) The parameter o the metal oam are liste in table 1. 4

6 Table 1. Parameters o the aluminum metal oam. Parameters: PPI ε (m) p (m) K (m 2 ) c Values e e e Physical Moel The inite volume approach to solve the governing equations is use [22]. For the pressure-velocity coupling the SIMPLE algorithm is employe; the graient evaluation or the spatial iscretization is base on least square cell; the PRESTO algorithm is use or the pressure calculation is base on PRESTO an or energy an momentum equation the secon orer upwin scheme is utilize. A comparison between the moel with ive tubes an another moel with hal tube is accomplishe. The results are the same in term o heat transer coeicient an Nusselt number along the tube as it can be seen in igure 2. Thereore, in orer to reuce the computational cost, the computational omain is a hal tube with the symmetry surace conition as it showe in igure 3. Figure 2: Comparison between the array o ive tubes moel (moel A) an the hal tube moel (moel B) in term o heat transer coeicient along the tube. The gri consists in rectangular cells in the air channel an triangular meshes in the oam region. Figure 3: Computational omain. A stuy to obtain a solution inepenent rom the mesh is mae with three ierent meshes, cells, cells an cells. The irst mesh is chosen because it gives goo results an the computational cost is reuce. Moreover, the moel is then compare with the work o Oabaee et al. [15] or the valiation. The same bounary conitions, properties an mesh are use an the results present a goo agreement. 5

7 4. Results an Discussion The results are presente at ierent inlet velocity (0.12 ms -1 to 0.18 ms -1 ) an at assigne constant temperature to the tubes or simulating the HFT equal to K. The low is laminar an the LTNE moel is assume or the heat exchange between the air an the oam. For the imensionless number, the reerence length is the iameter o the tube (=0.012 m). (a) (b) Figure 4: Temperature (a) an velocity (b) proile at the centerline o the omain. The igure 4 showe the temperature an velocity proile or an inlet velocity o 0.12 m/s along the centerline o the oam. It can be seen that there are two temperature proiles, one or the air an another or the oam because the LTNE moel is assume an so there is not thermal equilibrium between the two phases. About the velocity, the presence o the metal oam uniorms the velocity proile at exit o the oam region an it becomes nearly equal to the inlet velocity proile. Figure 5: Nusselt number along the centreline at varying inlet velocity. A comparison between the ierent inlet velocity is mae in igure 5 in term o Nusselt Number. Obviously higher inlet velocity implies higher number o Nusselt number an thereore the heat transer is improve. To evaluate the eectiveness o the metal oam insie a heat exchanger a comparison is mae with the CLEAN case without the metal oam. The igure 6 showe the ratio 6

8 between the heat transer coeicient an pressure rop with an without the metal oam as unction o Reynols number. (a) (b) Figure 6: ratio h m /h clean (a) an Δp m /Δp clean (b) vs Reynols number. It is important to see that the heat transer is improve because the ratio between the heat transer coeicients is more than ten time but the pressure rop is not negligible with the metal oam. Finally the PEC is evaluate to unerstan the thermal perormance o the heat exchanger with the metal oam. The PEC utilize is the ollowing [23]: 1/3 Nu / m PEC (14) 1/3 Nu / Where Nu is the Nusselt number an is the riction actor. The subscripts m an clean are reerre respectively to the metal oam an clean case. The igure 7 showe the PEC at varying Reynols number. clean Figure 7: The PEC number vs Reynols number. 7

9 5. Conclusion In this paper a metal oam compact heat exchanger was numerically stuie. The heat transer rate rom a tube in cross-low can be increase by aing metal oam. Nevertheless there is an increase o the pressure rop. The thermal physical quantity presente the same paths o Oabaee et al [15] an Solmus [20]. Moreover, the PEC number is also evaluate in orer to compare this system with other system that using another enhancement application. Further investigations are neee to stuy the thermal contact resistance between the surace wall an metal oam an to overcome the large pressure rop insie the oam. Reerences [1] Dukhan N 2013 Metal oam: Funamentals an Applications (DESTech, PM, Lancaster) [2] Mahjoob S an Vaai A 2008 Int. J. Heat Mass Transer [3] Yuan W Tang Y Yang X Wan Z 2012 Appl. En [4] Fenga S S Kuanga J J Wena T Lua T J Ichimiyac K 2014 Int. J. Heat Mass Transer [5] Zhaoa W Franceb D M Yua W Kima T Singhc D 2014 Renew. En [6] C Y Zhao 2012 Int. J. Heat Mass Transer [7] Han X H Wang Q Park Y G Joen T Sommers C. Jacobi A 2012 Heat Transer Eng [8] Muley A Kiser C Sunén B Shah R K 2012 Heat Transer Eng [9] Aolabi L O Al-Kayiem H H Aklilu T B 2014 Appl. Mech. Mat [10] Zaari M Panjepour M Emami M D Meratian M 2015 App. Therm. Eng [11] Xu H J Gong L Zhao C Y Yang Y H Xu Z G 2015 Int. J. Therm. Sc [12] Lin W Sunen B Yuan J 2013 Appl. Therm. Eng [13] Kim S Y Paek J W Kang B H 2000 ASME J. Heat Transer [14] Boomsma K Poulikakos D Zwick F 2003 Mech. Mat [15] Oabaee M Hooman K Gurgenci H 2011 Trans. Porous Meia [16] Mao S Love N Leanos A Roriguez-Melo G 2014 Appl. Therm. Eng [17] Huisseune H De Schampheleire S Ameel B De Paepe M 2015 Int. J. Heat Mass Transer 89 1 [18] Niel D A Bejan A 1999 Convection in Porous Meia (secon E. Springer-Verlag, NY) [19] Calmii V V an Mahajan R L 2000 ASME J. Heat Transer [20] Solmus I 2015 Appl. Therm. En [21] Boomsma K Poulikakos D 2001 Int. J. Heat Mass Transer [22] Patankar S V 1980 Numerical Heat Transer an Flui Flow (McGraw Hill-Hemisphere NY) [23] Obaaee M Hooman K 2012 Appl. Therm. Eng