Numerical Analysis of Heat Transfer and Pressure Drop in a Channel Equipped with Triangular Bodies in Side-By-Side Arrangement

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1 mercal Analyss of Heat Transfer and Pressure Drop n a Channel Equpped wth Trangular Bodes n Sde-By-Sde Arrangement E. Manay Department of Mechancal Engneerng, Faculty of Engneerng, Bayburt Unversty, Bayburt, Turkey S. Gunes, E.Akcadrc and V.Ozceyhan Department of Mechancal Engneerng, Faculty of Engneerng, Ercyes Unversty, Kayser, Turkey Abstract-The focus of presented numercal study s to nvestgate the ect of Reynolds number wth respect to both heat transfer and flow characterstcs n a channel equpped wth two trangular bluff bodes n sde by sde arrangement. (SST) k - turbulence model s used for smulatons and the second order upwnd numercal scheme and SIMPLE (pressure mplct wth splttng of operatons) algorthm are utlzed to dscretze the governng equatons. The flow s assumed twodmensonal and the calculatons are performed for a Reynolds number range varyng from 10,000 to 40,000 under steady state condtons. The calculatons are carred out on a four-noded structured mesh near channel wall and a three-noded unstructured mesh near trangular bodes n order to have a better descrpton of the boundary layer. The varaton of sselt number, skn frcton cocent along the channel and sselt number versus Reynolds number were presented. The calculatons are also compared to the results obtaned by H. Chattopadhyay. The comparson shows that the numercal results are of good agreement wth the results obtaned from that of Chattopadhyay, H. It was concluded that at Re=40,000 the best achevement n sselt number was obtaned as 463. Keywords-Trangular bluff body, sde-by-sde arrangement, heat transfer enhancement. I. INTRODUCTION Bluff bodes are generally used to promote turbulence n channels by dsturbng the flow. The studes over bluff bodes manly consst of cylnders, flat plates, rectangular bars. The flow around bluff bodes has been the subject of many studes n the past. Flow nterference caused by bluff bodes placed nto the channel s responsble for several changes n the characterstcs of heat transfer and flow. As known, there are several coherent structures for dfferent applcatons accordng to many knds of szes, shapes, flow patterns, etc. respectvely. In ths study, to examne the ects of body geometry placed nto the channel, dual trangles are studed. The studes made n ths feld showed that lots of parameters lke geometry and geometrcal arrangements are also affected on heat transfer and flow structure. Ths paper presents a detaled numercal study of the flow about a par of trangles n sde-by-sde arrangement. There are many studes about bluff bodes and the detaled lterature revew s gven below. Y. Du et al.[1] nvestgated numercally the ect of the gap rato of trangular bodes over flow characterstcs for dfferent gap ratos varyng from 0.1 to 0.48 at Re=470,000. For confrmng the observatons from numercal study, expermental results usng pont-to-pont method and partclemage velocmetry (PIV) measurements n a close wnd tunnel were also carred out. In ths study, two types of coherent structure are dentfed: Low gap rato 0.1 and Hgh gap rato The coherent structure s dvded by the gap flow nto two zones called the prmary recrculaton zone and the secondary recrculaton zone. Results showed that the structure of small gap rato s dfferent from that of large gap rato because the nteracton between two zones relates to the gap rato. The flow characterstcs of wake and base-bleed flow downstream of two bodes, wth dfferent cross-sectonal geometres n sde by sde arrangement were studed by C.-Y. We and J.-R. Chang []. The two-body arrangements were comprsed of flat plate and square cylnder, flat plate and crcular cylnder, and square cylnder and crcular cylnder. The results demonstrated that the characterstcs of wake and base-bleed flow are sgnfcantly related to the cross-sectonal geometres of the bluff body. The gap flow tended to deflect toward the narrow-wake sde downstream of the two body arrangement. L. Jan-zhong and hs frends [3] analyzed the modfcaton of flow by the combned ects of the rotaton and the Reynolds number on the flow past two rotatng crcular cylnders n a sde-by-sdearrangement. The analyss were performed usng Partcle Image Velocmetry (PIV) at a range of 45 Re 1130, 0 α 4 at one gap spacng rato. The results showed that the vortex sheddng was suppressed as rotatonal speed ncreased. The flow reached a steady state when the vortex sheddng for both cylnders was completely suppressed at crtcal rotatonal speed. H. Chattopadhyay [4] studed n the turbulent flow regme up to the Reynolds number of 40,000 As a result, t was reported that the exstence of a trangular body n a channel provdes approxmately 15% heat transfer enhancement. The nteracton among two spheres n tandem formaton were studed for a Reynolds number of 300 usng both steady and pulsatng nflow condtons by L. Prahl et al. [5]. The results showed that the separaton dstance played a sgnfcant role n changng the flow patterns and sheddng frequences at moderate separaton dstances, whereas ect Reference mber: W

2 on drag was observed even at a separaton dstance of 1 dameters. The ect of aspect rato on heat transfer to a cylnder n cross flow of ar has been studed expermentally by B.H. Chang et al. [6]. They reported that the heat transfer rates ncreased wth decreasng aspect rato at the centerplane on the rear of the cylnder. Consequently, the average sselt number correlatons are presented that account for the ects of aspect rato, tunnel blockage and free stream turbulence. Based on the results summarzed above, one fnds that the relatonshp between Reynolds number and the basng characterstc of the gap flow depends strongly on the geometry of the bluff body. Because many practcal engneerng problems are related to the flow feld downstream of bluff bodes wth dfferent cross-sectonal geometres, the present study focused on flow nteracton near two trangular bluff bodes n sde by sde arrangement and was performed for a Reynolds number range varyng from 10,000 to 40,000 under steady state condtons. II. CFD ANALYSIS Problem Descrpton In Fgure 1, the man features of the test rg doman are shown schematcally. The computatonal doman manly conssts of two-dmensonal channel and dual trangular bodes placed n sde by sde arrangement. As seen n Fgure 1, channel heght (H) of 4B, the placement of the bluff bodes (S) was mantaned at x = 8B, whle the channel length was 36B. For preventng from the negatve pressure ects at the outlet sectons, the nlet secton was selected long enough to get a fully developed flow. Fgure (1): Computatonal doman and the trangular bodes n sde by sde arrangement. mercal Procedure For determnng the velocty and temperature dstrbutons, CFD calculatons made by the ad of the computatonal flud dynamcs (CFD) commercal code of FLUENT verson 6.1. [9] are performed dependng on the numercal model, boundary condtons, assumptons, and numercal values. In all the numercal calculatons, segregated manner was selected as solver type, due to ts advantage whch helps to prevent from convergence problems and oscllatons n pressure and velocty felds of strong couplng between the velocty and pressure by usng. (SST) k- turbulence model s used for smulatons and the second orderupwnd numercal scheme and SIMPLE algorthm beng more stable and economcal n comparson wth the other algorthms are utlzed to dscretze the governng equatons. The convergng crterons are thought as 10-6 for the energy and 10 4 for other parameters. In momentum and contnuty equatons, the thermophyscal propertes are thought as constant, and, the flow s assumed two-dmensonal, steady contnuty. Contnuty conservaton: t Momentum conservaton: v 0 v v v t g P Energy conservaton: Where and k E t k P E h v E p T v T 3 v v vi (1) () (3) (4) v s the ectve conductvty. F.R. Menter [7] developed the shear-stress transport (SST) k model by blendng k model and k- model formulaton ectvely. In lterature, there exst varous numercal studes concernng wth channel flow whch are performed by usng (SST) k- turbulence model (S. Eamsaard and P. Promvonge [8], Kamal and Bnesh [10]. Nasruddn and Sddqu [11] nvestgated the heat transfer enhancement n a heat exchanger tube by nstallng a baffle numercally and he reported the (SST) k - model predcts succesfully and accurately the flow modfcaton due to the baffle accordng to other turbulent models. The (SST) k - model s able to calculate speedly two-dmensonal flow and also predct the nteractons wth the wall. Ths model s also advantageous because the model equatons behave compatble n both the near-wall and far-feld regons. In the dervaton of the k model, the flow s assumed to be fully turbulent. The Shear-Stress Transport (SST) k - model, the turbulence knetc energy, k, and the specfc dsspaton rate,, are obtaned from the followng transport equatons: (5) Reference mber: W

3 and (ρk ) t x k x j (ρ) t x x j ku k Gk Yk x j u G x j Y D In these equatons, G k represents the generaton of turbulence knetc energy due to mean velocty gradents. G represents the generaton of. k and represent the ectve dffusvty of k and, respectvely. Y k and Y represent the dsspaton of k and due to turbulence and D represents the cross-dffuson term. The calculaton of all of the above terms s gven detaled n FLUENT 6.1. [9]. Two parameters of nterest for ths study are the skn frcton cocent and the sselt number. The skn frcton cocent Cf s defned by C f s 1 U m (6) (7) (8) The heat transfer performance s evalauted by sselt number whch can be obtaned by the local temperature gradent as: T Z (9) The average sselt number can be calculated as follows: x L av x (10) where L s the length of computatonal doman. The frcton factor s determned from; f = P 1. U m L H (11) n whch pressure ΔP s pressure dfference between the channel nlet and ext: Unform velocty s mposed to nlet plane and the Reynolds number vares from to The outlet boundary condton s natural condton whch mples zero-gradent condtons at the outlet. III. RESULTS In ths work, the used numercal method to obtan results s valdated wth the study of Chattopadhyay [9] n whch the augmentaton of heat transfer n a channel usng a sngle trangular prsm s nvestgated. The results of sselt number and skn frcton cocent obtaned from CFD analyses are compared wth the results obtaned from Chattopadhyay [9]. Fgures (a) and (b) show comparson between the results of the used CFD model and Chattopadhyay [9]. As observed from these fgures that, there s a good agreement between the results of the used numercal model and Chattopadhyay [9]. These results gve confdence that the numercal method used s accurate. (a) Boundary Condtons The soluton doman of the consdered D channel flow s geometrcally qute smple, whch s a rectangle on the x z plane, enclosed by the nlet, outlet and wall boundares. The workng flud n all cases s water. The nlet temperature of water s consdered to be unform at 300 K. On walls, no-slp condtons are used for the momentum equatons. A constant surface temperature of 400 K s appled to the bottom wall of the channel. The upper wall s assumed to be adabatc. (b) Fgure (): The comparson of CFD values wth Chattopadhyay [4] at Re=0000 (a) Local sselt mber, (b) Local skn frcton cocent. Reference mber: W

4 The dstrbuton of local sselt number along the channel length s shown for dfferent Re numbers s llustrated n Fg. 3. The local sselt number takes a local maxmum at the placed poston of the upstream body. After the peak towards to the ext the sselt number decreases strongly due the ect of the perodcally sheddng vortces do not occur from the bodes for all cases. Separated shear layer from downstream body and mpngng of vortex formed from upstream body strongly ncreases heat transfer on downstream. On the other hand, as expected, these bodes cause a sgnfcant flud frcton as well, n comparson wth the smooth channel. The ncrease n local sselt number results n an ncrease n pressure drop, the frcton factor ncreases wth ncreasng Reynolds number due to the fact that nteracton between the bodes placed as sde by sde dsturb the entre flow feld and cause more frcton than the smooth channel. The local skn frcton cocent dstrbutons on the bottom channel wall are shown n Fgure 4 for dfferent Reynolds numbers. Smlarly wth local sselt number, the local skn frcton cocent takes a maxmum at the placed poston of the trangular bodes n sde by sde arrangement. In Fg. 4, the local dstrbuton of the skn frcton cocent for smooth channel, Re=10000 s also shown for comparson. The magntude of skn frcton s the hghest at Re= It s evdent from Fgure 4 that the local skn frcton cocent ncreases wth ncreasng Reynolds number when the flow encounters the blockages created by equlateral trangular bodes. IV. CONCLUSIONS Fgure (3): The dstrbuton of local sselt number along the channel length for dfferent Reynols numbers. However, the peak becomes obvous wth ncreasng Reynolds number. As expected local sselt number ncreases wth ncreasng Reynolds number,and, the heat transfer enhances especally for upstream flow regon concernng wth the generaton of vortces due to the trangular bodes as well as the role of turbulence n better mxng brngs n the enhancement n heat transfer from the channel wall. The local sselt number and skn frcton cocent take a local maxmum at the placed poston of the upstream body, and at the placed poston of the downstream body. The heat transfer enhances especally for upstream flow regon concernng wth the generaton of vortces due to the frst body as well as the role of turbulence n better mxng brngs n the enhancement n heat transfer from the channel wall. The ncrease n local sselt number results n an ncrease n pressure drop, the frcton factor ncreases wth decreasng spacng between the bodes due to the fact that the close nteracton between the bodes dsturb the entre flow feld and cause more frcton. V. ACKNOWLEDGMENTS Authors would lke to thank for the fnancal support of the TUBITAK (The Scentfc and Technologcal Research Councl of Turkey) under the contract: 107M508. REFERENCES Fgure (4): The dstrbuton of local skn frcton cocent along the channel length for dfferent Reynols numbers. [1] Y. Du, R. Qan and S. Peng, Coherent structure n flow over a sltted bluff body, Communcatons n Nonlnear Scence and mercal Smulaton, : [] C.Y. We and J.R. Chang, Wake and base-bleed flow downstream of bluff bodes wth dfferent geometry, Expermental Thermal and Flud Scence, 00, 6:39-5. [3] G. Xao-hu, L. Jan-zhong, T. Cheng-xu and W. Hao-l, Flow past two rotatng crcular cylnders n a sde by sde arrangement, Journal of Hydrodynamcs, 009,1(): [4] H. Chattopadhyay, Augmentaton of Heat Transfer n a Channel usng Trangular Prsm. Int. J. Therm. Reference mber: W

5 Sc. 007, 46: [5] L. Prahl, A. Jadoon and J. Revstedt, Interacton between two spheres placed n tandem arrangement n steady and pulsatng flow, Internatonal Journal of Multphase Flow, 009 (In press). [6] B.H. Chang and A.F. Mlls, Effect of aspect rato on forced convecton heat transfer from cylnders, Internatonal Journal of Heat and Mass Transfer, 004, 47: [7] F.R. Menter, Two-equaton eddy-vscosty turbulence models for engneerng applcatons, AIAA J. 1994, 3(8): [8] S. Eamsa-ard and P. Promvonge, mercal study on heat transfer of turbulent channel flow over perodc groove, Internatonal Communcatons n Heat and Mass Transfer, 008, 35, [9] FLUENT User s Gude, Fluent Incorporated. Centerra Resource Park, 10 Cavendsh Court., Lebanon. NH 03766, USA. [10] R. Kamal, A.R. Bnesh, The mportance of rb shape ects on the local heat transfer and flow frcton characterstcs of square ducts wth rbbed nternal surfaces, Internatonal Communcatons n Heat and Mass Transfer, 008, 35(8), [11] M.H. Nasruddn and K. Sddqu, Heat transfer augmentaton n a heat exchanger tube usng a baffle, Internatonal Journal of Heat and Flud Flow, 007, 8, Nomenclature B base of the trangular body C f skn frcton cocent f frcton factor H heght of the computatonal doman k knetc energy L length of doman n x drecton sselt number P Pressure S locaton of the trangular bodes mean velocty component n x drecton U m Greek symbols ρ Flud densty τ shear stress specfc dsspaton rate Subscrpts m mean s Smooth channel tb trangular body Reference mber: W