A NUMERICAL STUDY OF HEAT TRANSFER AND FLUID FLOW IN A BANK OF TUBES WITH INTEGRAL WAKE SPLITTER

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) ISSN 0976 6340 (Prnt) ISSN 0976 6359 (Onlne) Volume 5, Issue 12, December (2014), pp. 36-46 IAEME: www.aeme.com/ijmet.asp Journal Impact Factor (2014): 7.5377 (Calculated by GISI) www.factor.com IJMET I A E M E A NUMERICAL STUDY OF HEAT TRANSFER AND FLUID FLOW IN A BANK OF TUBES WITH INTEGRAL WAKE SPLITTER Mohammed Saad Kamel Department of Mechancal Technques, Al- Nassryah Techncal Insttute Southern Techncal Unversty, Dh Qar/ Al-Nassryah, Iraq ABSTRACT The present work represents a two-dmensonal steady state numercal nvestgaton of heat transfer and hydrodynamc characterstcs of ar flow across a 3 rows of crcular tube banks n trangular arrangement wth trangular wake spltters placed on each tube wth downstream drecton (wake regon). The effects of Reynolds number (from 5000 to 15000), the length of spltter are 0.5D, 1.0D, and 1.5D tmes of tube dameter. The study focuses on the Influence of the dfferent parameters of spltters on heat transfer and flud flow characterstcs of three rows tube banks. The characterstcs of total heat transfer per area for each tube wth and wthout spltter and total pressure drop are studed numercally by the ad of the computatonal flud dynamcs (CFD) commercal code of FLUENT 6.3. Velocty vector and streamlnes on the three rows tube bank for baselne and modfed models are plotted. The results showed ncreasng n the heat transfer wth the ncreasng of Reynolds number and that Increase n total heat transfer when the trangular wake spltter attachment as a result of extra surface area generated by the spltter plate t observed that about (45.14%, 45.67% and 64.65%) ncreasng n total heat transfer from tube1, tube2 and tube3 respectvely wth 1.5D chord at Reynolds number 15000 compared wth tubes wthout spltter. Also, t observed that the reducton n total pressure drop of trangular wake spltter wth length 1.5D at Reynolds 15000 about (9.79%) compared wth tubes wthout spltter. Keyword: Fluent-CFD, Tube Bank, Reynolds Number, Trangular Wake Spltter, Pressure Drop. 36

1. INTRODUCTION In the Present study consders numercal work for flow over tubes bank wth and wthout wake spltter (trangular spltter plate), And the effect of chord length on hydrodynamcs and heat transfer characterstcs. Flow over tube bank s a fundamental heat transfer problem whch s of practcal mportance havng large number of applcaton. Applcatons whch nvolve flow past cylnder nclude cross flow around rod bundles n heat exchangers of nuclear reactors, coolng of electronc equpments, ar flow around coolng towers, flow past flame stablzers n hgh speed combuston chamber, ppelnes etc. However, as Reynolds number ncreases, flow begns to separate behnd the cylnder causng symmetrc wake. Wake s a regon of recrculaton flow behnd a body caused due to flow separaton. Attached and symmetrc flow takes place for very low Reynolds number. Wake formaton reduces convectve heat transfer downstream because of low velocty recrculaton. To overcome ths problem, spltter plates are used downstream. Spltter plates are wake stablzers and have been used as a means of controllng varous aspects of wake formaton and vortex sheddng. Wake spltter s a rgd attachment to the body whch alters sheddng frequency and ncreases base pressure resultng n overall reducton of drag. Even though t reduces average heat transfer coeffcent, t provdes addtonal surface for convectve heat transfer and ncreases overall heat transfer. Varous confguratons of spltter plates can be used for enhancement of heat transfer and controllng vortex sheddng [1]. Many researchers tred to study the complex flow over cylnder and tube bank. Work has been carred out by Vvek Shrvastava and et.al [1]. Studed Effect of Trangular Wake Spltter on Flow and Heat Transfer over a Crcular Cylnder for Varous Chord Lengths numercally the results were found to be n good agreement wth avalable expermental and numercal work. Heat transfer wth trangular wake spltter has been found to be 17%, 53.4%, 115.7% more and drag coeffcent 1.176, 7.92 and 9.01 tmes lower compared to bare cylnder for three dfferent chord lengths. Performance of trangular wake spltter has been found to be smlar to rectangular wake spltter. Results pont towards cylnder wth trangular wake spltter beng more effcent than other confguratons. Oosthuzen and et.al [2] on two dmensonal square cylnder wth spltter plates. Twar, and et.al [3] have worked on crcular cylnder wth spltter plate of dfferent length and ther effect on coeffcent of pressure, local Nusselt number and overall heat transfer. Anderson and et.al [4] have worked on crcular cylnder for near subcrtcal Reynolds number. Mahr and et.al [5] have worked on Convectve heat transfer n unsteady flow past two cylnder n tandem arrangement wth varaton of L/D rato(center to center dstance rato) Local Nusselt number, Strouhal number, flow parameters were studed for Re=100 and Re=200. Sudhakar and et.al [6] have carred out work on oscllatng rectangular wake spltters and ts effect on flow characterstcs. Panchal and et.al [7] have worked on flow over square array of crcular cylnders for L/D rato (center to center dstance) 1.25 for Re= 40, 50, 100, 150 & 200 for dfferent prandlt number. Study on wake generaton and change n local Nusselt number was studed Patnak and et.al [8] have worked on heat transfer for lamnar flow past crcular cylnder wth ntegral wake spltter. Chandra and et.al [9] has carred out study on. Natural convecton Heat transfer from a heated sem crcular cylnder for the varous boundary condton e constant temperature and constant heat flux for varous Grshaoff number and prandtl number. Sparrow and Kang [10] have studed heat transfer and pressure drop characterstcs on longtudnally fnned tube banks. Roshko [11] studed vortex sheddng suppresson by usng spltter plate n crcular tube. Badam and et.al [12] have studed effect of rectangular and trangular spltter plates on cylnder and ther effect on wake length, coeffcent of pressure and coeffcent of drag. 37

2. MODEL DESCRIPTION 2.1 Physcal model Top vew of schematc dagram of a crcular-tube heat exchanger n trangular arrangement wth IWS s shown n Fgure (1). A spltter of trangular shape s putted as a fn surface symmetrcally on each crcular tube. Due to the symmetrc arrangement, the regon occuped by dashed lnes s selected as the computatonal doman as shown n fgure (2), whch s, consdered as a channel of heght H = D = 32 mm and length L = 10D =320 mm. The tube rows are arranged n a trangular formaton wth the transverse ptch-to-dameter rato 2.0 and longtudnal ptch-dameter rato 2.25. The spltter plate length-to-tube dameter rato was vared 0 to 1.5 n the ncrement of 0.5. The spltter plate thckness was 1/5 the tube dameter Fgure (1) Schematc dagram of the physcal problem Fgure (2): Computatonal doman 2.2 Governng equatons The arrangement of crcular tube banks n staggered wth cross arflow. The wall of the crcular tube s heated under constant temperature, and ar nlet at varable velocty V. force convecton heat transfer between heated crcular tube surface wth and wthout spltters and nlet arflow n a horzontal x-y plane. The two-dmensonal nstantaneous governng equaton of mass, momentum and energy equatons for study ncompressble n fully developed flow can be wrtten n conservaton form expressed n Cartesan coordnates as follows [13]: u = 0 ρu u ( ) p = + u [ µ ( u + ) ρu u ] (1) (2) 38

ρu T = k cp T ( ). (3) The Reynolds stress tensor ρu u can be determned accordng to the Boussnesq assumpton as ρ u u = u u 2 k µ t ( + ) δ ρ 3.. (4) -Where µ t s the turbulent eddy vscosty and s estmated by the (k-ε) two equatons turbulent model. µ t = cµρk2/ε. (5) The dfferental equaton of k and ε are gven as ( ρu k) = µ t k [( µ + ) ] + G σ k k ρε. (6) 2 ( ρu ε) µ t ε ε ε = [( µ + ) ] + Cε1Gε Cε 2ρ σ k k ε.. (7) u -Where Gk = ρ u u ( ) s the turbulent producton term. The remanng coeffcents that appeared n the above equaton are as quoted by[13] : Cµ=0.09,Cε 1 =1.44, Cε 2 =1.92, σ k =1 and σ ε =1.3 2.3 Parameter defnton The Reynolds number Re s defned as: Re= ρ U D/ µ (1) Where U s the mean velocty nlet n the mnmum flow cross-secton of the flow channel, and D s the dameter whch equals to 0.5St. Q = ha( T ).. (2) Where (h) s the average heat transfer (A) surface area and 2.4 Boundary condtons The boundary condtons for ths analyss are: T s the temperature dfference. At the nlet Chanel the flud s assumed to enter wth a unform horzontal velocty U and temperature (T ) U=U, T=T =300K, V=0; At the outlet Chanel: P=0 39

Symmetry condton: For the top and bottom surfaces of the computatonal doman excludng the tube surfaces, symmetry boundary condton s used. The mathematcal form of ths U T condton: =0, V=0, =0, y y Symmetry condton crcular tube wall surface: U = V = 0, T w = constant = 400 K. Trangular IWS wall surface: U = V = 0; T w = constant = 400 K. 3. NUMERICAL METHOD In ths present work (Fluent-CFD) software used to solve equatons for conservaton of mass, momentum, and energy usng a fnte volume technque to show dynamc flow and heat transfer around crcular tubes, The model geometry and mesh generaton are buld by (Gambt), Verson 2.2.30 as a show n Fgure (3). The grd s made up of trangular elements to mprove the qualty of the numercal predcton near the curved surfaces. The couplng between pressure and velocty s mplemented by SIMPLEC algorthm. To reduce numercal errors, second order upwnd dscrtzaton schemes are used n the calculatons. Each computatonal teraton s solved mplctly. The convergence of the computatonal soluton s determned on scaled resduals for the contnuty, energy equatons and for many of the predcted varables. More than 400 teratons are generally needed for convergence. 4. RESULTS AND DISCUSSION Fgure (3): the computatonal grd n gambt 2.3.1 Two-dmensonal forced convecton s studed for turbulent flow n a bank of tubes wth and wthout wake spltter wth a Prandtl number of 0.71. The controllng parameter, for the cases confguratons of the geometry as defned n the table (1). The range of Reynolds number used for the smulatons s 5000 Re 15000. The results of ths present study are dsplayed n terms of streamlnes and velocty vector. Moreover, the effects of heat transfer per area of the tubes and the pressure drop also shown. Table 1: The confguratons of the geometry for Study Cases Case No. Case name Length of spltter Case 1 Baselne(wthout 0D spltter) Case 2 Trangular spltter 0.5D Case 3 Trangular spltter 1D Case 4 Trangular spltter 1.5D 4.1 The grd senstvty study The senstvty of the numercal results can be seen from table (2).The dfference n total pressure drop at the nlet and 9.25D from computatonal doman are lsted n t. From the table t can be clearly seen that the maxmum dfferent of the pressure drop s less than 2% for three dfferent 40

grd systems. For the present study, the fnal grd number s selected as about (25552) cells. Smlar valdatons are also conducted for other cases. Table 2: Grd ndependent test 4.2 Effect of total pressure drop The fgure (4) llustrates the dfference n total pressure at nlet and 9.25D from length of computatonal doman. The energy loss s evaluated by calculatng pressure drop along secton. It can be seen that the total pressure drop ncrease as the Reynolds number ncreases for all cases because the pressure loss due to frcton s a functon of the mean velocty of the flow that s mean when velocty ncrease frcton ncrease and loss due to frcton ncrease. The ncreasng n trangular spltter plat length led to reducng n pressure drop exceptonal of L/D = 0.5D at Reynolds 150000 and 1.5D at Reynolds 5000 compared wth baselne (wthout spltter) that Because the larger pressure drag n the larger separaton regon, when added trangular wake spltter that wll serve to reduce sheddng vortces, also the trangular Wake spltter arranged flud flow makes vortces regon separated. The area of vortex regon reduces whch made the pressure has reduced. 90 80 70 pressure drop (pa) 60 50 40 30 20 10 0 case1 (0D) case2 (0.5D) case3 (1D) case4 (1.5D) Re 5000 Re 10000 Re 15000 Fgure (4): total pressure drop for varous L/D and Reynolds number. 4.3 Heat transfer from tube banks wth spltter plate From fgure (5) t can be observed that Increase n total heat transfer when the trangular wake spltter attachment as a result of extra surface area generated by the spltter plate. For all tube banks, The flow starts to create the vortexes behnd the tube when gong to hgh Reynolds number (Re>5000).the movement of flud around the surfaces heat transfer wll be fast at hgh Reynolds number, whch makes average heat transfer Coeffcent ncrease wth ncreasng flud flow. Because the temperature dfference between the flud and heat transfer surface s becomng hgh. However, accordng to fgure(), the total heat transfer rate per area mproves snce the spltter plates also act as fns, whch ncreases the surface contact area for better overall heat transfer process. Heat transfer characterstcs were studed for tubes wth dfferent L/D ratos under constant temperature condtons. Tube banks wth L/D = 1.5 yelded the hghest heat transfer rates. 41

Total heat transfer per area (q) w/m*2 17000 15000 13000 11000 9000 Re 5000 Re 10000 Re 15000 TUBE 1 7000 CASE1 CASE2 CASE3 CASE4 Total heat transfer per area (q) w/m*2 18000 16000 14000 12000 10000 8000 Re 5000 Re 10000 Re 15000 TUBE 2 6000 CASE1 CASE2 CASE3 CASE4 Total heat transfer per area (q) w/m *2 18000 16000 14000 12000 10000 8000 Re 5000 Re 10000 Re 15000 TUBE 3 6000 CASE1 CASE2 CASE3 CASE4 Fgure (5): Total heat transfer per area (q) from tubes for all cases wth Reynolds number 4.4 Flow Characterstcs and Velocty Vector From fgure (6), (7) t can be clearly seen that the comparson of velocty streamlnes and velocty vector for tube wthout spltter (baselne model) and tube wth trangular wake spltter (modfed model) of length 0.5D, 1D and 1.5D.fluent 6.3.26 has been used to obtan streamlnes. For low Reynolds number, flow remans attached to surface. Flow behaves as a potental flow domnated by vscous force and doesn't separate. As Reynolds number ncreases, nertal forces become strong 42

enough to overcome vscous force and flow separates. Ths can be seen from recrculaton wakes formed for hgher Reynolds number. Wth ncrease n Reynolds number, length of wake ncreases tll attanment of crtcal Reynolds number whch s n good agreement wth lnear stablty theory. Beyond ths, Von-Karman vortex sheddng was observed. In ths study velocty vector plotted at Re 10000 and streamlne plotted at Reynolds number 10000 also, and that observed the wake regon n baselne model and t s clear and vortex sheddng occur also, at same Reynolds number wth dfferent chord length of trangular spltter also plot and that was clear there s reducng n wake regon. The man purpose of usng wake spltter s to delay flow separaton and the onset von Karman vortex sheddng and reduce flow nduced vbraton and ths can be clearly seen n the plotted cases. At the baselne model velocty gradent near the sold boundary (Tubes) due to vscosty s vsble, also, separaton pont on the tubes surface was vsble. The flow over tubes wth dfferent length of trangular wake spltter s more dfferent from the case of flow over the Tubes wthout usng wake spltter (free) especally near the rear of Tubes and the wake behnd the Tubes. Spltter plates are used as passve means of controllng vortex formaton and vortex sheddng n the wake. It has been observed that wth ncrease n Reynolds number, the length of wake ncreases for steady symmetrc flow for the entre above mentoned confguraton. It s found that wake length for tubes wthout spltter for all Reynolds number to be more when compared wth trangular wake spltter. It s observed that the wake length for trangular wake spltter was reduced compared wth baselne. Fgure (6): Streamlnes on the three rows of tube bank wth and wthout models for Re = 10000 43

Fgure (7): velocty vector colored by velocty magntude at Re 10000 for all cases 5. CONCLUSIONS Numercal analyss has been performed for flow over tube bank wth and wthout wake spltter usng (fluent) verson 6.3.26. Results of total heat transfer per area have been consoldated and t can be concluded that total heat transfer per area for tube1, tube2 and tube3 wth trangular spltter at length 1.5D are (45.14%, 45.67% and 64.65%) greater than tubes wthout spltter. Ths makes tubes wth trangular spltter best possble confguraton for optmum heat transfer also, t was observed that the reducton n total pressure drop of trangular wake spltter wth length 1.5D at Reynolds 15000 about (9.79%) compared wth tubes wthout spltter. Vortex sheddng and pressure drop mostly depends on Reynolds number and tube spacng. Addton spltter plate on a tube can be attrbuted to the attenuaton of vortex sheddng n the wake and also reduced pressure drag sgnfcantly. Increase n total heat transfer can be also observed as a result of extra surface area generated by the spltter plate. 44

THE NOMENCLATURE D : crcular tube dameter ( m ) S L : longtudnal ptch S T : Transverse ptch L : length of computatonal doman (m) P : pressure (Nm-2) Gk : Turbulent producton term Pr : Prandtl number : Reynolds number based on the dameter of tube T : ar temperature k T w : wall temperature k U : ar velocty at nlet (ms-1) u, v : velocty components (ms-1) U, V : non-dmensonal velocty components W : heght of the nflow and outflow openngs x, y : Cartesan coordnates (m) IWS : Integral wake spltter H : heght of channel (m) L/D : Length to dameter rato of spltter Greek symbols α: angle of attack (o) v : knematc vscosty of the flud (m2s-1) ρ: densty of the flud (kgm-3) τ : shear stress (Pa) Cµ, Cε1, Cε2: Constants n k-ε equaton σ k, σ ε : Effectve Prandtl µ : dynamc vscosty, kg/m.s µ T : Turbulent vscosty, kg/m.s REFERENCES [1] Vvek Shrvastava, Pavan Badam, Saravanan V, K N Seetharamu, "Effect of Trangular Wake Spltter on Flow and Heat Transfer over a Crcular Cylnder for Varous Chord Lengths", Internatonal Journal of Scentfc & Engneerng Research, Volume 5, Issue 4, Aprl-2014 554 ISSN 2229-5518. [2] Mansngh, Vvek and P.H Oosthuzen. "Effects of Spltter Plates on the Wake Flow behnd a BluffBody," AIAA Journal: 778-783 (May 1990). [3] S. Twar, D. Chakraborty, G. Bswas, P.K. Pangrah Numercal predcton of flow and heat transfer n a channel n the presence of a bult-n crcular tube wth and wthout an ntegral spltter, nternatonal ournal of heat and mass transfer, volume 48 ssue 2, January 2005. [4] Anderson, E. A. & szewczyk, A.A 1995 "vortex sheddng from a straght and tapered crcular cylnder n unform and shear flow" proc sxth Intl conf. on flow nduced vbraton. [5] Mahr A, and zekerya A. "Numercal nvestgaton of convectve heat transfer n unsteady flow past two cylnders n tandem arrangements, Int. J. of Heat and Flud Flow 29 (2008) 1309-1318. [6] Y. Sudhakar, S. Vengadesan, vortex sheddng characterstcs of crcular cylnder wth oscllatngwake spltter plate, computers and flud, volume 53, 15 January 2012. [7] Panchal, Lakdawala, Numercal nvestgaton of thermal performance n cross flow around square array of crcular cylnders, NUCONE 2011. [8] B.S.V.P.Patnak, K N Seetharamu, P.AaswathaNarayana, smulaton of lamnar confned flow past, a crcular cylnder wth ntegral wake spltter nvolvng heat transfer, Int.J.Numer.Method Heat flow Flud Flow 6 (1996). [9] Chandra A., Chhabra R.P., Flow over and forced convecton heat transfer n Newtonan fluds from asem-crcular cylnder, Int. J. of H. and M. T. 54 (2011) 225-241. [10] E.M. Sparrow, S.S. Kang, Longtudnally-fnned cross flow tube banks and ther heat transfer an pressure drop characterstcs, Int. J. Heat Mass Transfer 28 (1985) 339 350. 45

[11] A. Roshko, on the drag and sheddng frequency of two dmensonal bluff bodes, Techncal Report TN 3169, NACA, 1954. [12] Vvek Shrvastava, Pavan Badam, Nandeesh Hremath, Saravanan V, K N Seetharamu, 'Numercal analyss of flow past crcular cylnder wth trangular and rectangular wake spltter', ICMAE, WASET, 2012. [13] Ferzgen, J. H. and Perc, M. "Computatonal methods for flud dynamc". 2 th edton, Sprnger. Berln, (1999). 46