A Numerical Study of Heat Transfer and Fluid Flow past Single Tube

Transcription

1 A Numercal Study of Heat ransfer and Flud Flow past Sngle ube ZEINAB SAYED ABDEL-REHIM Mechancal Engneerng Natonal Research Center El-Bohos Street, Dokk, Gza EGYP Abstract: - A numercal study of heat transfer and flud flow past sngle tube usng computatonal flud dynamc (CFD-Fluent 6.0) to predct the heat transfer and pressure drop characterstcs of turbulent flow past sngle tube s presented n ths work. he present study consders steady turbulent two-dmensonal ncompressble flow past sngle tube found n heat exchanger applcatons. For ncompressble flow, the contnuty, momentum and energy equatons are governed the present problem. he turbulence s modeled wth the k-ε model. he effect of aspect rato ((L/D) =0.0, 0.5, 1.0 and.0) at low Reynolds number (Re=39803) on heat transfer and pressure drop for the sngle tube s studed. he results comparson of the grd, resdual, statc pressure, statc temperature, velocty vector, turbulence knetc energy, effectve thermal conductvty, and wall fluxes: surface heat transfer coeffcent on the md-plane of the tube for the selected cases of sngle tube s presented at the same condtons, assumptons and the value of Reynolds numbers. A comparson s made between the present CFD predctons and reference measurements, [Iwak, et al. 004] for the velocty vector as flud flow past a crcle tube n cross flow for the selected values of Reynolds numbers Re D. he results show that the pressure drop decreases as the aspect rato ncreases. he flud s heated n the near wall and wake regons and the predcted temperatures serve as excellent benchmark data for assessng CFD predctve accuracy for the selected cases. he maxmum velocty ncreases as the aspect rato ncreases. he overall performance of sngle tube wth a lower aspect rato s preferable snce t provdes hgher heat transfer rate. Hgher turbulence knetc energy at the nlet and outlet computaton doman of the lowest aspect rato, and near the upper sde and the frst upper corner of the external surface of the tube wth the case. Key-Words: - Aspect rato (L/D), CFD predcton, flud flow, sngle tube, turbulent flow, two-dmenson. 1 Introducton he most mportant desgn varables of heat exchangers are the outsde heat transfer coeffcent of the tube and the pressure drop of the flud flowng externally. he effect of tube shape has a postve nfluence on heat transfer. Numercal experments on the flow past a cylnder at subcrtcal Reynolds number [1]. A challengng test case for large eddy smulaton: hgh Reynolds number crcular cylnder flow s reported n []. Large eddy smulaton of the flow past a crcular cylnder at Re= 3900 s nvestgated by [3]. Numercal studes of flow over a crcular cylnder at Re= 3900 s presented, [4]. Closure strateges for turbulent and transtonal flows are performed by [5], where the drect soluton of the Naver-Stokes equatons had been made possble by the development of fast dgtal computers, wth the frst smulaton of sotropc turbulence appearng. Dynamcs and low dmensonalty of a turbulent wake s presented by [6]. hey found that nadequate grd resoluton can cause early transton n the shear layers separatng from the cylnder whch leads to naccurate predctons of the nearwake flow statstcs. Flow around Crcular Cylnders s performed by [7]. he generalzed Lévêque Equaton and ts practcal use for the predcton of heat and mass transfer rates from pressure drop are performed by [8]. Numercal study of heat ppe applcatons n heat recovery s nvestgated by [9]. he man obectve of ths work s to use a computer code (Fluent 6.0) to predct the heat transfer and pressure drop characterstcs of turbulent flow past sngle tube. he present study consders steady turbulent two-dmensonal ncompressble flow past tube found n heat exchanger applcatons. he effect of rato ((L/D) =0.0, 0.5, 1.0 and.0) at low Reynolds number (Re=39803) on heat transfer and pressure drop for the sngle tubes s studed. ISBN:

2 he results comparson of the grd, resdual, statc pressure, statc temperature, velocty vector, turbulence knetc energy, effectve thermal conductvty, and wall fluxes: surface heat transfer coeffcent on the md-plane of the tube for the selected cases of the sngle tube s presented at the same condtons, assumptons and the value of Reynolds numbers. Mathematcal assumptons are as follows he flow s two-dmensonal, steady, turbulent and ncompressble he thckness of the tube s neglected he thermo-physcal propertes of the flud do not vary wth temperature he vscous heatng s neglected. 3 Soluton Method d segregated, k- solver s used to solve the governng dfferental equatons for the conservaton of the mass, momentum and energy equatons. he soluton s obtaned by usng a control-volumebased technque whch conssts of: 1. Dvson of the doman nto dscrete control volumes usng a computatonal grd,. Integraton of governng equatons on the ndvdual control volumes to construct algebrac equatons for the dscrete dependent varables (unknowns), such as velocty, pressure, temperature, and conserved scalars, 3. Lnearzaton of dscretzed equatons and soluton of the resultant lnear equaton system to yeld updated values of the dependent varables. 4 Governng Equatons and Numercal Method For ncompressble flow, the Naver-Stokes equatons, the contnuty, momentum and energy equatons can be wrtten as: V X 0.0 (1) V V 1 P V t X X t V X K V () (3) Where beng the knematc vscosty coeffcent and s denotng the Laplace operator. he turbulence modelng was performed usng the standard k- ε model, an nbult module n the commercal code (FLUEN 6.0). he standard k- ε model s an emprcal model based on model transport equatons for the turbulence knetc energy (k) and the specfc dsspaton rate (ε). he model transport equatons for k and ε are developed as explaned n [10]. hey are: k t ( U) k P k k (4) D P C 1 C Dt k k (5) Where C k (6) Where the standard values for all the model constants due to Launder and Sharma [11], are Cμ = 0.09, Cε1 = 1.44, Cε = 1.9, σ k = 1.0, σ ε = 1.3 and P τ = Boundary condtons and near wall treatments At nlet, unform profles for all dependent varables. At wall, a non-slp boundary condton s mposed on the wall of the tube. he velocty used n the smulaton s 1.0m/s. hs s typcal ar velocty value for 0.05m tube dameter heat recovery applcaton. In heat recovery applcatons the gas flow over the tube should be a hot stream. he approach ar flow temperature was set at 300 o K and the tube s nner wall set to 400 o K. Very close to the walls, vscous dampng reduces the tangental velocty fluctuatons, whle knematc blockng reduces normal fluctuatons. ISBN:

3 However, towards the outer part of the near-wall regon, the turbulence s rapdly augmented by the producton of turbulence knetc energy, due to the large gradents n the mean velocty. 4. Grd consderatons for turbulent flow smulatons Successful computatons of turbulent flows depend greatly on mesh generaton, due to the fact that strong nteracton of the mean flow and turbulence, the numercal results for the turbulent flows tend to be more susceptble to grd dependency than lamnar flows. Low-Reynolds-number varants were used, and n such a case the mesh gudelnes followed were smlar to those used for the enhanced wall treatment. 5 Correlaton he Nusselt number s based on average heat transfer coeffcent over partcular sothermal tube. he emprcal mean Nusselt correlaton due to a gas turbulent flow past a sngle crcular cylnder, Pr=0.71 (ar), for 4000 Re D 40000, [1]: _ Nu Re D D D Re pr V D 6 Results and Dscussons h 1 3 (7) (8) he obectve of ths work, s to study the effect rato (, 0.5, 1.0 and ) and ar flud turbulent flow past sngle tube on pressure drop and heat transfer for Re= Grd model at the md-plane of the tube for the selected cases sngle tube at Re=39803 s done. he contour of statc pressure for the selected rato (L/D) cases of the sngle tube at Re=39803 s presented n Fg. (1). As the rato of L/D ncreases the normalzed pressure drop decreases. he hgher values of pressure drop dstrbuton usually recorded near the ntal of the external tube surface n all cases. he contour of statc temperature for the selected L/D rato cases of sngle tube at Re=39803 s gven n Fg. (). he contours expose the temperature ncrease n the flud due to heat transfer from the tubes. he flud s heated n the near wall and wake regons. he results presented n ths fgure serve as excellent benchmark data for assessng CFD predctve accuracy for the selected L/D rato cases of sngle tube. hs behavor s a functon of the rato of the pressure drop to velocty squared terms n the calculaton of the temperature dstrbuton. It s found that the boundares temperature are all consdered as equal to man value of the flud temperature, for. he velocty vector, for the selected L/D rato cases of sngle tube at Re=39803 s llustrated n Fg. (3). As L/D rato ncreases the maxmum velocty n the passage between the upper and lower sde ncreases. Fgures show that the colder flud comes n contact wth the hot tube surface as the L/D rato ncreases. A small change n the heat transfer rate can be predcted snce the flud has almost the same behavor when the L/D rato s ncreased. It s necessary, for the selected cases, that the turbulence knetc energy s fne enough to be able to resolve the turbulent flow past sngle tube on the md-plane for Re D =39803, Fg. (4). It can be seen that the hgher values of turbulence knetc energy at nlet and outlet of the case, also, there s hgher turbulence knetc energy near the upper sde and the frst upper corner of the external surface of the tube, the case. Fgure (5) shows the effectve thermal conductvty on the md-plane of the tube for the selected cases of sngle tube for Re= he overall performance of the sngle tube wth a lower (, crcle) s preferable snce t provdes hgher heat transfer rate. he heat transfer enhancement s obtaned whch ndcates that crcular tube out performs flat tube. he present results confrm the ablty and potental of CFD analyss as a desgn tool, to provde detaled nsght nto complex heat transfer that would otherwse be dffcult to characterze expermentally. Wall fluxes: surface heat transfer coeffcent on the md-plane of the tube for the selected cases of the sngle tube for Re =39803 s llustrated n Fg. (6). Fgure (7) gves the normalzed pressure drop for the present cases of sngle tube for Re=39803 and Re=0895. It shows the mpact of L/Drato on the normalzed pressure drop. It can be clearly stated that the L/D rato has very lttle effect on pressure drop except for L/D =0. For valdaton of the CFD code, the mean Nusselt number was computed for Reynolds number=39803 and 0895 for each case, and the results was vald ISBN:

4 aganst gven Nusselt correlatons, Fg. (8), n ths fgure, the average Nusselt number as a functon of Reynolds number for the present L/d cases for Pr = In general, the average Nusselt number ncreases wth a lttle ncrease n Reynolds number. he Nusselt number s based on average heat transfer coeffcent over partcular sothermal tube. Comparson between present CFD predctons and reference measurements, Iwak, et al. (004) for the velocty vector as flud flow past crcle tube of the selected values of Reynolds numbers Re D s presented n Fg. (9). A reasonable agreement s observed. Re Reynolds number (= V D h / ) t tme, sec, temperature, K U, V Cartesan components of flud velocty, m.s -1 X Cartesan coordnate Greek symbols Dynamc vscosty, N.s.m -, Mass densty, kg.m -3 - Average value 4 Concluson hs work s an effort to predct and analyss the heat transfer and pressure drop characterstcs of turbulent flow past a sngle tube found n heat exchanger applcaton. he numercal results confrmed that: 1- he turbulent flows tend to be more susceptble to grd dependency than lamnar flows; also the grd model on the md-plane of flat tube depends on the aspect rato (L/D). - he pressure drop decreases as the aspect rato ncreases. 3- he flud s heated n the near wall and wake regons and the predcted temperatures serve as excellent benchmark data for assessng CFD predctve accuracy for the selected cases. 4- he maxmum velocty ncreases as the aspect rato ncreases. 5- he overall performance of sngle tube wth a lower aspect rato s preferable snce t provdes hgher heat transfer rate. 6- Hgher turbulence knetc energy at the nlet and outlet computaton doman of the lowest aspect rato, and near the upper sde and the frst upper corner of the external surface of the tube wth the case. Nomenclature D dameter, m K thermal conductvty, W. m -1. K -1 L P Pr length, m, Nu Nusselt number (=h D h /k) Pressure drop, pa Prandtl number (= C p /k) =0.7 (ar) References: [1] Beaudan, P. and Mon, P., Numercal experments on the flow past a cylnder at subcrtcal Reynolds number. Report No. F-6 Department of Mechancal Engneerng, Stanford Unversty, Stanford, Calforna, [] Breuer, M., A challengng tests case for large eddy smulaton: hgh Reynolds number crcular cylnder flow, Journal of Heat Flud Flow No. 1, 000, pp [3] Franke, J., and Frank, W., Large eddy smulaton of the flow past a crcular cylnder at Re = Journal of Wnd Engergy Ind. Aerodyn. No. 90, 00, pp [4] Kravchenko, A.G. and Mon, P., Numercal studes of flow over a crcular cylnder at Re 3900, Journal of Physcs Fluds No. 1(), 000, pp [5] Launder, B.E. and Sandham, N.D., Closure strateges for turbulent and transtonal flows, Cambrdge Unversty Press: Cambrdge, 00. [6] Ma, X., Karamanos, G.-S., and Karnadaks, G. E., Dynamcs and low dmensonalty of a turbulent wake, Flud Mechancs, No. 410, 000, pp [7] Zdravkovch, M.M., Flow around Crcular Cylnders, Oxford Unversty Press: Oxford, 1997 [8] Martn, H., he generalzed Lévêque Equaton and ts practcal use for the predcton of heat and mass transfer rates from pressure drop, Chemcal Engneerng SCI, No. 57, 00, pp [9] Ln S., Broadbent, J., McGlan R., Numercal Study of Heat Ppe Applcaton n Heat Recovery Systems, Journal of Appled hermal Engneerng, No. 5, 005, pp [10] Pope, S. B., urbulent flows, Cambrdge Unversty Press: Cambrdge, 000. ISBN:

5 [11] Launder B. E. and Sharma B. I., Applcaton of the energy-dsspaton model of turbulence to the calculaton of flow near a spnnng dsc, Journal of Heat and Mass ransfer No. 1, 1994, pp [1] Zhukauskas, A., Heat transfer from tubes n cross flow, Advances n Heat ransfer, No. 8, 197, pp Fg. (3): Vector velocty at the md-plane of the tube for the selected cases sngle tube at Re= Fg. (1): Pressure contour at the mdplane of the tube for the selected cases sngle tube at Re= Fg. (): emperature contour at the md-plane of the tube for the selected cases sngle tube at Re= Fg. (4): urbulence knetc energy, K, (m /s ) at the md-plane of the tube for the selected cases sngle tube at Re= ISBN:

6 Fg. (7): Normalzed pressure drop across the present cases of sngle tube wth L/D rato for Re=39803 and Re=0895. Fg. (5): Effectve thermal conductvty, W/m-K at the md-plane of the tube for the selected cases sngle tube at Re= Fg. (8): Effect of L/D rato at the average Nusselt number for the cases of sngle tube, Pr = 0.71, Re=39803 and Re=0895. Re=39803 Re=39800 Re=0895 Re=089 Fg. (6): Wall fluxes: surface heat transfer coeffcent, (W/m -K) at the md-plane of the tube for the selected cases sngle tube at Re= CFD Velocty vector predcton Of the present work Reference velocty vector measurements Fg. (9): Comparson between present CFD predctons and reference measurements, [Iwak, et al. 004] for the velocty vector as flud flow past crcle tube of the selected values of Reynolds numbers Re. ISBN: