EFFECT OF THE SIZE OF GRADED BAFFLES ON THE PERFORMANCE OF CHANNEL HEAT EXCHANGERS

Transcription

1 EFFECT OF THE SIZE OF GRADED BAFFLES ON THE PERFORMANCE OF CHANNEL HEAT EXCHANGERS Djamel SAHEL 1, Houar AMEUR 2,*, and Bak TOUHAMI 3 1 Techncal Scences Department, Unversty of Amar Teldj, Laghouat, Algera *2 Insttute of Scence and Technology, Unversty Center of Naama (Ctr Unv Naama), 45000, Algera 3 Mechancal Engneerng Department, Unversty of scence and the technology, Oran, Algera * Correspondng author; E-mal: houar_ameur@yahoo.fr; Tel: The bafflng technque s well-known for ts effcency n terms of enhancement of heat transfer rates throught channels. However, the baffles nsert s accompaned by an ncrease n the frcton factor. Ths ssue remans a great challenge for the desgners of heat exchangers. To overcome ths ssue, we suggest n the present paper a new desgn of baffles whch s here called graded baffle-desgn. The baffles have an up- or downgraded heght along the channel length. Ths geometry s characterzed by two ratos: up-graded baffle rato and down-graded baffle rato whch are vared from 0 to For a range of Reynolds number varyng from 10 4 to 2x10 4, the turbulent flow and heat transfer characterstcs of a heat exchanger channel are numercally studed by the computer code Fluent. The obtaned results revealed an enhancement n the thermo-hydraulc performance offered by the new suggested desgn. For the channel wth a down-graded baffle rato equal to 0.08, the frcton factors decreased by 4-8%. Key words: Heat exchanger channel; Graded baffles; Turbulent flow; Frcton factor; CFD. 1. Introducton Several technques are developed to reduce the energy cost and to enhance the thermal performance of varous devces used n many nductral applcatons. In ths framework, rbs,baffles or obstacles play an mportant role n for the mprovement of the thermal transfer rate n varous thermal systems lke the heat exchangers, the gas turbnes blades, the solar collectors, the car radators and other applcatons of fluds mechancs such as the water desalnaton. Some expermental and numercal works have been acheved on the effect of dfferent geometrcal parameters of baffles as the shape, sze and spacng between baffles, the attack angle, the blockage rato and the porous space. The shape of baffles s a necessary parameter for the generaton of vortces [1-3]. Therefore, varous shapes have been developed, for example, the V-baffle shape [4-1

2 9], the W-baffle shape [10], the Z-baffle shape [11], mult V-type perforated baffles [12-17] and damond shape proposed by Srpattanappat et al. [18]. All these shapes permt an enhancement n the heat transfer rates, but wth catastrophc pressure drops. Dutta et al. [19] studed by experments the effct of baffle attack angle on the characterstcs of heat transfer and pressure drop n a rectangular channel wth nclned plate and perforated baffles. They showed the man dependency of the thermal transfer rates on the geometry, the orentaton and the poston of the second baffle. For a square channel Promvonge et al. [20] explored the effect of baffle nclnaton wth varous values of blockage ratos (BR). Wth the 45 nclned baffles and BR = , they found an ncrease n the thermal transfer rate from 150 to 850% accompaned wth pressure losses varyng from 2 to 70 tmes compared wth the smooth channel. In other works [21, 22], these authors found that the combnaton between the attack angle and the V-baffle shape allow an enhancement n heat transfer rates assocated wth losses n pressure. In the same framwork, Promvonge et al. [23] studed by experments the effects of the delta baffles shapes on the thermal performance of solar ar heater. They reported that the combnaton between the delta wnglet and the rb ensures consderable heat transfer mprovements (Nu/Nu 0 = ) and also yelds a moderate pressure drop ncrease (f/f 0 = ). Tandroglu et al. [24] explored n ther expermental study three cases of nclned baffles (45, 90 and 180 ) wth three values of dameter rato H/D = 1, 2 and 3 and they obtaned the best performance wth the 90 case for the forced convecton. In another work, Tandroglu [25] developed emprcal formulas for the calculaton of Nusselt numbers and the frcton coeffcents. The same author, tested n another artcle the entropy generaton for dfferent types of baffles [26]. The V-shaped baffle or rb s another technque to enhance the thermal performance due to the presence of two hgh thermal regons. Some researcher [27, 28] reported that the staggered arrangement of rbs gves less hgher heat transfer coeffcent than the symmetrc arrangement rbs. Further studes on the enhancement of heat transfer by the bafflng technque can be found elsewhere [29-32]. The effcency of porous baffles s confrmed by many researchers because the perforated space enables the agtaton of the flow stagnated behnd of baffles [33, 34], t ncreases the thermal transfer ntensty and elmnates the lowers heat transfer areas (LHTA) [35-38]. All studes n lterature confrm that the bafflng technque ncreases sgnfcantly the heat transfer rates. However, these works dd not correct the major problems of ths technque: the formaton of LHTA and the pressure losses. Amng to reduce the frcton factor n baffled channels, we propose here new desgned baffles wth up-graded and down-graded heght along the channel length. The performance of the new desgn has been nvestgated for dfferent flow rates. 2. Geometry of the problem studed The purpose of the present work s to study the flow and heat transfer characterstcs n a horzontal channel wth a baffle seres of up- and down-graded heght along the channel length (L). The baffles are nserted n a staggered array on the upper and lower walls of the channel (Fgure 1). Varatons n the baffle heght are defned by DBR (Fgure 1a) and GBR (Fgure 1b) for the decreased (.e. down-graded) and ncreased (.e. up-graded) baffle ratos, respectvely. The obtaned results from the baffled cases are compared wth those for a smooth channel (wthout baffles) havng the followng geometrcal parameters: H s the channel heght fxed to 0.1 m, 2

3 b s the baffle heght, e s the baffle thckness (e = 0.02H) and b/h s known as the blockage rato (BR). The spacng rato between baffles s S = s/h = 1. Effects of DBR and GBR where nvestgated by changng ther values for 0 to Fgure 1. Geometry of the problem studed 3. Mathematcal formulaton The numercal model for heat transfer and flud flow n the two-dmensonal channel s based on the above assumptons.the flow through the duct s governed by the Reynolds averaged Naver Stokes (RANS) equatons [39] and the energy equaton: Contnuty Equaton u 0 (1) x Momentum equaton u ' ' P u u j u u j x x x j x Where u' s a fluctuatng component of velocty. (2) Energy equaton T ut Γ Γ x x x t j velocty gradents as seen n the equaton below: 3 (3) Where: Γ s the molecular thermal dffusvty gven by: Pr Γ t s the turbulent thermal dffusvty gven by: t t Prt. The Reynolds-averaged approach to turbulence model requres the modelng of Reynolds ' ' stresses uu n Eq. (2). The Boussnesq hypothess relates the Reynolds stresses to the mean j

4 ' ' u u 2 u u u j t k t j x j x 3 x j (4) 1 ' ' Where k s the turbulent knetc energy defned by, k u u and δ j s the Kronecker delta. 2 j The RNG-based k-ε turbulence model s derved from the nstantaneous Naver-Stokes equatons [39], usng a mathematcal technque called renormalzaton group (RNG) methods. The steady state transport equatons are expressed as: t k k u Gk x j x j k x j t u C1 C 2 x x j x j k k 2 (5) (6) Where G k s the rate of generaton of the k-ε model C 1ε and C 2ε are constants. μ t s the turbulent vscosty defned by 2 t C ( k / ),C μ s a constant set to and derved usng the RNG theory. The frcton factor fs calculated by the followng equaton: 2 P f L D U 2 / h where Ps the pressure drop across the length of the channel L. To determne the heat transfer characterstcs, we defne the local Nusselt number as: hx Dx Nu( x ) (8) k f and the average Nusselt number as: 1 Nu ( x ) Nu( x ) A A (9) The thermal enhancement factor η s defned by: Nu / Nu / f / f 1/3 (10) 0 0 Where Nu 0 and f 0 stand for Nusselt number and frcton factor for the smooth channel, respectvely. 4. Numercal smulaton 4.1. Boundary Condtons Ar was used as a workng flud n all cases wth a unform nlet temperature (300 K, Pr = 0.7). Impermeable boundary and no-slp wall condtons have been mplemented over the channel wall as well as the baffle. The temperature of the bottom and upper plates s mantaned constant at 330 K whle the baffle s assumed as adabatc wall condton. The Reynolds number s changed from to (7) 4

5 4.2. Grd Generaton Geometry and mesh of the computatonal doman were created wth the computer tool Gambt. The mesh generated s quadrlateral wth regular grd elements. Mesh tests were realzed by a seres of grd selected n the unbaffled channel as follows: 25608, 36100, 40200, and elements. From the mesh wth elements, the devaton of the Nusselt number s not mportant (do not exceed 2%) wth the rase of the grd densty. Thus and for the next calculatons, the fnal selected grd number had elements. Usng the same approach for the other cases wth baffles, the selected grds were vared between and elements. The necessary detals on mesh test are resumed on Table 1. Computatons were acheved wth the CFD FLUENT, whch s based on the method of fnte volume to solve the governng equatons. The flow regme s consdered as turbulent and steady state. The QUICK numercal scheme coupled wth the SIMPLE (Sem-Implct Pressure Lnked Equaton) algorthm were used n the fnte volume method to solve all equatons. The RNGk-ε model was employed for the closure of the equatons. Default under-relaxaton factors of the solver are used to control the update of computed varables at each teraton. These factors are: 0.3, 1, 0.7 and 1 for pressure, densty, momentum and energy, respectvely. Solutons were consdered converged when the normalzed resdual values were below 10-5 for all varables and below 10-7 only for the energy equaton. Table 1. Tests of grd sensvlty for all confgurtatons Test 1 Test 2 Test 3 Test 4 Test 5 Grd 1 Nu Grd 2 Nu Grd 3 Nu Grd 4 Nu Grd 5 Nu Smooth channel DBR= DBR= DBR= DBR= GBR= GBR= GBR= GBR= Results and dscusson 5.1. Verfcaton of results for a smooth channel Our predcted results for the Nusselt number and frcton factor through a smooth channel are respectvely compared wth Dttus-Boelter and Blasus correlatons. These correlatons, whch are used by for the characterzaton of flud flow and heat transfer n ducts [24], are avalable n the lterature [40] as follows: Nu ReD h Pr (13) 0.25 Re (14) f

6 1000. f Nu Fgure 2a and 2b show, respectvely, a comparson of Nusselt number and frcton factor obtaned from the present study wth those from equatons (11) and (12). In these fgures, the presented results agree reasonably well wthn ±2.9% and ±5.5% for both frcton factor correlaton of Blasus and Nusselt number correlaton of Dttus-Boelter, respectvely. 55 Dttus-Boelter Smooth channel Re (a) 8,0 7,8 Smooth channel of present work Blasus correlaton 7,6 7,4 7,2 7,0 6,8 6, Re (b) Fgure 2.Verfcaton of (a) Nusselt number and (b) frcton factor for a smooth channel 5.2. Flow Structure For Re = and S = 1, the axal velocty s presented on Fgure 3 for DBR = 0.08, DBR =0.04, DBR/GBR = 0, GBR = 0.04 and GBR = Ths fgure shows the aerodynamc nature of the flow n the presence of baffles wth down- and up-graded heght. At the baffle, the flow s separated n three zones: a zone of recrculated flow behnd the baffles where the vortex appears clearly. The second zone s located n front of the frst zone where the axal velocty s very ntense, and the thrd zone s located between the frst and the second zones where the flow passes wth a mean velocty. Ths aerodynamc phenomenon depends on the sze of baffles and the drecton of changes n ther heght (up- or down-graded heght). Consequently, ths fgure shows that the rase of DBR/GBR decreases the formaton of the vortex structures. The effect of down- and up-graded sze of baffles on the formaton of vortex s llustrated n Fgure 3. The formaton of the vortex s clearly appearng n the case of channel wth down-graded sze of baffle DBR = 0.08 and On the other hand, the vortex sze n the case of channel wth upgraded sze of baffle GBR = 0.08 and 0.04 s small compared wth DBR = 0.08 and 0.04, respectvely. 6

7 Ths phenomenon s due to the development of the flow along the channel n the presence of baffles. Consequently, the down-graded sze of baffle ensures further ntensfed vortces despte of the reducton of baffles sze (DBR = 0.08). Therefore, the weaker vortex s observed wth the case GBR = 0.08, because that the small baffles located at the entrance of channel do not allow an effcent developed flow. (a) (b) (c) (d) (e) Fgure 3. Velocty contours for dfferent baffled channels (a) DBR = 0.08; (b) DBR = 0.04; (c) DBR, GBR = 0; (d) GBR = 0.04; (e) GBR =

8 5.3. Pressure losses 3,1 3,0 2,9 2,8 2,7 f / f 0 2,6 2,5 2,4 2,3 2,2 2,1 DBR, GBR = 0 (Smple baffle) DBR = 0.02 DBR = 0.04 DBR = 0.06 DBR = 0.08 GBR = 0.02 GBR = 0.04 GBR = 0.06 GBR = Re Fgure 4.Varaton of f/f 0 wth Reynolds number for varous baffled channels Fgure 4 presents the varaton of the normalzed frcton factor, f/f 0 wth Reynolds number values for dfferent GBR and DBR. As shown on ths fgure, the use of down-/up-graded heght of baffle leads to a consderable decrease n the frcton factor compared wth the smple baffles (GBR, DBR = 0). The DBR values present further ncreases n the frcton factor compared wth GBR values. Dependng on Reynolds number, the lowest value of frcton factor s obtaned wth DBR = 0.08, whch s consdered to be smaller by about 4-8% thant that of a smple baffle channel Heat transfer DBR, GBR = 0 (Smple baffle) DBR = 0.02 DBR = 0.04 DBR = 0.06 DBR = 0.08 GBR = 0.02 GBR = 0.04 GBR = 0.06 GBR = Re = Nu x ,0 0,2 0,4 X/L 0,6 0,8 1,0 Fgure 5. Axal varaton of Nu X along lower channel wall for varous baffled channels, Re = At Re = 18000, the axal varaton of Nu x along the lower channel wall s presented on Fgure 5 for dfferent values of DBR/GBR. The followng phenomena can be observed: The weak thermal transfer rate remarked on the bass of baffle, and partcularly behnd t, s caused by the formaton of hot pockets n ths regon. The hghest thermal transfer rates are observed n the zones where the flow s reattached (.e. whch between two successve baffles). 8

9 The smple baffle allows the hghest thermal transfer rates. However, the case GBR = 0.08 gves the lowest heat transfer rates. 7,5 7,0 6,5 6,0 DBR = 0.02 DBR = 0.04 DBR = 0.06 DBR = 0.08 DBR, GBR = 0 (Smple baffle) GBR = 0.02 GBR = 0.04 GBR = 0.06 GBR = 0.08 Nu / Nu 0 5,5 5,0 4,5 4,0 3,5 3, Re Fgure 6. Varaton of Nu/Nu 0 wth Reynolds number for varous baffled channels 3,8 3,6 3,4 3,2 3,0 2,8 2,6 2,4 2,2 DBR, GBR = 0 (Smple baffle) DBR = 0.02 DBR = 0.04 DBR = 0.06 DBR = 0.08 GBR = 0.02 GBR = 0.04 GBR = 0.06 GBR = Re Fgure 7. Thermal enhancement factor for varous baffled channels For a smple baffle, S = 1 and BR = 0.5, varatons of the average Nu/Nu 0 rato wth Reynolds number for dfferent down-/up-graded heghts of baffles are presented on Fgure 6. Ths fgure shows that the Nu/Nu 0 value ncreases wth the rase of Reynolds number values for all GBR and DBR cases. The use of smple baffle ensures a good thermal transfer rate and the baffles wth GBR = 0.02 reduces the heat transfer rate by 5% compared wth the smple baffle. The lowest thermal transfer rate whch s gven by the DBR = 0.08 tends to 16% compared wth the smple baffle. Fgure 7 shows the varaton of the thermal enhancement factor (η) wth Reynolds number for dfferent down-/up-graded heghts of baffles. The enhancement factor tends to ncrease wth the rase of Re for all cases. The cases of GBR = 0.02 and smple baffle (GBR = 0) present the same best enhancement factors (η) up to 3.6 tmes at the hghest value of Reynolds number. 6. Conclusons The turbulent flow and heat transfer characterstcs n a two-dmensonal channel equpped wth down-/up-graded heght of baffles have been explored numercally. The predcted results confrm that 9

10 the new desgn of baffles provdes an adequate reducton n frcton factors. Dependng on Reynolds number, the case of DBR = 0.08 presents the mnmum value of frcton factor whch s about 4 8% less than that of the smple baffled channel (DBR, GBR = 0). However, the frcton factor reducton s assocated wth a reducton n heat transfer rates tends to 5% as a maxmum value compared wth the smple baffled channel. Nomenclature b Smple baffle heght, [m] D Hydraulc dameter, [m] f Frcton factor, [-] h Heat transfer coeffcent, [Wm -2 K -1 ] H Channel heght, [m] G k Turbulent knetc energy producton k Turbulent knetc energy, [m 2 s -2 ] k f Thermal conductvty, [Wm -1 K -1 ] L Channel length, [m] Nu Nusselt Number Re Reynolds number,(= ρud/μ) S Spacng rato (= s/d) T Temperature,[K] u Mean velocty at the channel,[ms -1 ] Greek Letter ε Turbulent energy dsspaton μ Dynamc vscosty, [kgm -1 s -1 ] η Thermal enhancement factor, [-] ρ Densty,[kgm -3 ] Subscrpts j x drecton y drecton Abbrevatons BR Blockage rato (=b/d) DBR Down graded baffle rato (= Dhb/H) Dhb Down graded heght of baffle [m] GBR Up-Graded Baffle Rato (= Ghb/H) Ghb Up-Graded heght of baffle, [m] 10

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