PREDICTION OF PRESSURE DROP IN HELICAL COIL WITH SINGLE PHASE FLOW OF NON-NEWTONIAN FLUID

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1 PREDICTION OF PRESSURE DROP IN HELICAL COIL WITH SINGLE PHASE FLOW OF NON-NEWTONIAN FLUID B.S.V.S.R.KRISHNA Department o Chemial Engineering, MIT, Manipal Univerity, Manipal , India E Mail: krihna.bandaru@manipal.edu Abtrat:The preure drop o ingle phae wa tudied experimentally with non-newtonian luid o Carboxy Methyl Celluloe (CMC). Single helial oil with ive dierent helix angle were ued in thi tudy to identiy the eet o helix angle on preure drop. The eet o helix angle i igniiant in moderate and high generalized Dean number o laminar region. The eet i inigniiant in low generalized Dean number range and turbulent region. Correlation were developed or prediting the ritional preure drop in laminar and turbulent region. Key word: non-newtonian luid, rheologial propertie, generalized Reynold number, Dean number, rition ator INTRODUCTION: Helial oil are ued widely in proeing indutrie or ooling and heating appliation ine the entriugal ore experiened by the luid at to promote ontat with the hannel wall, thereby tending to inure good ontat with the wall, and an enhaned heat traner Some o their main advantage over traight tube are high heat and ma traner oeiient, and pae eonomy in term o area per unit volume. Mot o the luid enountered in proeing appliation do not adhere to the Newtonian law o vioity and hene thee luid known a Non-Newtonian luid. Typial example inlude plati, upenion, polymeri melt, ood, dyetu, and pharmaeutial and the other multiphae mixture uh a oam, emulion, et. Coil are ued in hemial reator, agitated veel, and torage tank to heat and ool proe tream ranging rom inorgani and organi hemial to dairy produt; Furthermore, uh oil are alo ued or reovering heat rom wate liquor, vapour and gae. Curved paage an be ued to improve ma and heat traner rate uh a membrane blood oxygenarator, in kidney dialyi devie, and in revere omoi unit.when a luid low in a urved truture, there exit a eondary low due to the ation o entriugal ore a hown in Fig 1, and thi ha attrated muh attention [1], [2],[3],[4],[5],[6],[7]. Suh a eondary low reult in high ritional lo in urved pipe than that in traight pipe under imilar ondition, uh a low rate, temperature, preure. Fig 1.Shemati diagram o eondary low in helially oiled tube (P1 and P2 are two end). Experimental Newtonian luid:a number o equation have been propoed to alulate the axial preure drop in oil o ontant urvature or both laminar and turbulent ondition o ingle phae low. Mot o thee equation endeavour to predit either the uual Fanning rition ator or oil,, or the ratio o rition ator or the traight,, and oil oniguration,. The ingle-phae rition ator an be obtained rom the equation or luid low through a traight tube ater replaing the Fanning rition ator by. P=2 LV 2 /d ----(1) Beginning o the 20 th entury itel the theoretial work [2], dimenional analyi [3] wa attempted to olve the low o luid through helial oil.many orrelation have been availableto alulate the value o the rition ator and a eletion o ommonly ued uh orrelation i given here. White (1932) [8] extended the Dean' analyi and obtained a relationhip or the preure head lo in oil i.e (2) 11.6 De where De = Re (d/d) 1/2, the validity o the equation (2) i in the range 11.6 De 2000 while [9],[10] obtained a relation or or De >1 repetively log De (3) De /(70 De)...(4) International Journal o Applied Reearh in Mehanial Engineering (IJARME) ISSN: , Volume-2, Iue-1,

2 Predition o preure drop in Helial oil with ingle phae low o Non-Newtonian Fluid The ritial Reynold number may be deined a the highet value o thereynold number or whih the low in helix i till in the viou regime. Many reearher [6],[11],[12]havepropoed the empirial equation or ritial Reynold number. The widely aepted equation or ritial Reynold number over the entire range o d/d value whih i given below[12]. Re ritial =2100(1+12(d/D) 1/2 ) ---(5) For turbulent low, everal empirial equation or rition ator are available, orrelating the value o preure drop over a large range o Reynold number. Mot o thee relation are baed on either / or and Dean number(de).the ollowing [6] orrelation wa ued widely. = +0.01(d/D) 1/ (6) Non-Newtonian Fluid: Many Reearher have attempted ([13],[14]) non- Newtonian luid low in urved pipe.the eet o urvature on the low o non-newtonian luid in helial oil i igniiant and an be repreented a hown below [15]. For laminar region: 0.758n o.854; =3.14 0, Some[17] havetudied the low o water and everal peudoplati polymeri olution in helial oil o variou urvature ratio with ontant heix angle. Many reearher propoed the orrelation or prediting the oil rition ator. The above orrelation are widely aepted and predited the experimental reult well within the range o Dean number. Mot o thee orrelation have not onidered the eet o helix angle. The angle may vary rom 0 0 or irular helix to 90 0 or L bend.some tudie [18] oued on eet o thi helix angle on ritional preure drop. Numerial imulation alo tried to predit the low behaviour [19],[20]. Preet author like to ill thi gap o eet o helial angle on preure drop. Method and Material The experimental et up ued in the preent tudy i hematially hown in igure 2. The experimental etup onit o our etion onit o torage tank, liquid low meauring devie, low index meauring devie, tet etion.the preure drop wa meaured by uing arbon tetrahloride and merury illed U tube manometer. The liquid low rate wa International Journal o Applied Reearh in Mehanial Engineering (IJARME) ISSN: , Volume-2, Iue-1, ' 0.3 De (7) 10 < De <2000 ;60< Re < 6000; n 1.05 (Re =generalized Reynold number) Critial Reynold number i a tated in equation (5) provided Re i replaed by Re. For turbulent region : n Re 2.63 n 10.5 For 6000 <Re < d D 1/ 2 (8) Thee equation are qualitatively onitent with the theoretial analye.[13],[14].few tudie [16] have onentrated on eet o urvature ratio on preure drop and propoed the ollowing orrelation in laminar region (10De 2300). ' De (9) meaured by a alibrated rotameter. In the preent tudy, ive dierent tet etion were ued with ive dierent helix angle. Thee ive dierent etion were made uing a hoe pipe, o 25.3 mm in ID and 31 mm in OD. All thee etion are wrapped on a wrought iron pipe, o 220 mm OD. Liquid were pumped through Centriugal pump o 1 HP. Two pipeline viometer (apillary viometer) were ued to meaure the rheologial propertie o the non- Newtonian luid. The inide diameter o the tube i ½, 1 and the length aro whih preure drop wa meaured i 2.4 m. The length to diameter ratio maintained to make the end eet negligible. The ½ tube wa ued or more viou luid while the 1 tube wa ued to meaure the low behaviour o le viou luid.in order to invetigate the untional relationhip between the rition ator and Reynold number or non-newtonian luid and the other ytem parameter, the rheologial propertie were evaluated irt. Then the low experiment in the tet oil were perormed. The ytemati proedure ollowed or obtaining the deired data i given below.non-newtonian (CMC) liquid were ued a tet luid. The viometer data in term o low rate and preure drop, rom therotameter and manometer repetively, were onverted to wall hear tre nominal wall hear rate orm and were plotted on a log-log ale. Thi method wa ued to determine the

3 Predition o preure drop in Helial oil with ingle phae low o Non-Newtonian Fluid value o the apparent oniteny index (K ' ) and low behaviour index (n ' ). While onduting the experiment, it wa oberved that the temperature o the luid inreae due to the pumping ation. Thi eet wa appreiable or high onentration olution owing to their high vioity. A tudy o low behaviour hange with temperature wa alo made to ae the extent o thi phenomenon. The helix angle o eah tet etion wa meaured by uing a vernieraliper. The pith or eah tet etion i ontant and ha value o 31.2 mm, mm, 76.5 mm, 90.1 mm, mm and uing thi priniple the oil angle wa meaured(2.6, 3.7, 6.3, 7.4, 9.4). The denitie o the olution were meaured by uing peii gravity bottle. There wa little eet o temperature on the low behaviour index; on the other hand, it had more pronouned eet on oniteny index a een in the aorementioned igure. The low behaviour index and oniteny ontant dereaed with inreaing temperature. The degree o non-newtonian behaviour inreae with inreaing polymer onentration. Fig 3b. Eet o temperature on low behavior index and low oniteny index Fig 2. Shemati experimental etup Reult and Diuion Rheologial Propertie o non-newtonian luid:the CMC olution wa pumped through apillary viometer and meaured the low rate and preure drop. Thee are tranormed into ueul parametera given in equation (10). ' n dp ' 8V K -----(10) 4L d Thee data plotted on a log-log graphto determine the oniteny index (K ) and low behaviour index (n ). The eet o temperature on rheologial propertie i hown in Fig 3a and 3b or CMC olution. Fig 3a. Variation o Rheologial propertie o CMC olution Typial rheologial propertie o dierent onentration o CMC olution are tabulated in Table 1 at K and Table2 how the eet o temperature on thee propertie. S. CMC (kg/m 3 ) No. on. (Pa. n ) 1 2% Table1: Rheologial propertie o CMC at K S. No. CMC on. (kg/m ) K ' (Pa. n ) n Te mp ( 0 K) 1 2% % Table2. Eet o temperature on rheologial propertie o CMC olution. K ' n International Journal o Applied Reearh in Mehanial Engineering (IJARME) ISSN: , Volume-2, Iue-1,

4 Predition o preure drop in Helial oil with ingle phae low o Non-Newtonian Fluid Dimenionle preure gradient are uually expreed a rition ator and veloitie are expreed a Reynold number. The relation betweenpreure gradient and ma lux i expreed in dimenionle orm a a relation between therition ator and Reynold number. Thee relation alo an expre a plot uh a Moody plot. Depend on luid nature thi may be partitioned into three region: laminar, tranition and turbulent Preent tudy ha been retrited to Laminar and turbulent low o Non-newtonian luid low in traight pipe and helial oil. Straight Pipe Frition ator: The Reynold number wa modiied a generalized Reynold number or non-newtonian luid inorporating the eet o low behaviour and low oniteny index. Variation o rition ator with generalized Reynold number i hown in Fig 4 or Laminar low region. A the generalized Reynold number inreae the rition ator dereaed and turbulent region the rition ator almot tabilized with inreae in generalized Reynold number and hown in Fig 5. Preent author teted the theoretial relation o rition ator and Reynold number in Laminar region a peiied in Equation (11) and plotted the predited and experimental reult in Fig 6. The predited rition ator i in well agreement with experimental data with an RMS error o 19% while the predited rition ator in turbulent region wa having an RMS error o 21% with tandard orrelation o mooth pipe given in equation (12). = 16 Re.. (11) = (.).. (12) Re Helial Coil rition ator: For Helix angle o 3.7, the experimental data o preure drop wa onverted to oil rition ator by uing the equation (1) and modiied Dean number. In laminar region thee experimental value are ompared with the exiting orrelation[6],[15],[16] by replaing the De with modiied De. A een the preent reult are at variation with the inding [15], but are relatively loed to that o [6],[16]. Furthermore there doe not appear to be any eet o n. Fig 7. Comparion o Experimental reult with Literature Correlation or ame Helix angle. International Journal o Applied Reearh in Mehanial Engineering (IJARME) ISSN: , Volume-2, Iue-1,

5 Predition o preure drop in Helial oil with ingle phae low o Non-Newtonian Fluid Eet o Helix angle: To identiy the eet o Helix angle on oil rition ator in laminar region, the author ha eleted variou angle o helix angle, the data wa repreented in the below Fig 8 to 10. The eet o helix angle i igniiant at moderate to high generalized Reynold number (Re ) in the laminar region while at low Re the eet i negligible or variou onentration o CMC olution ranging rom 0.25% to 2%. It i learly evident that the exiting orrelation need to modiy/inorporate the eet o helix in the orrelation. The turbulent reult are hown in the Fig 11, the helix angle eet i negligible. Probably the low i tabilizing in the turbulent region.preent author ha propoed a orrelation to aount the Helix angle in the laminar region and without helix angle in turbulent region and the equation (13) and (14) are given below De ' in (13) De ' (14) The predited value are in exellent agreement with the experimental value and hown in Fig 12. The RMS error or laminar region i 24% while turbulent it i 16%. International Journal o Applied Reearh in Mehanial Engineering (IJARME) ISSN: , Volume-2, Iue-1,

6 CONCLUSIONS: Predition o preure drop in Helial oil with ingle phae low o Non-Newtonian Fluid The ollowing onluion an be drawn rom the tudy a) The eet o Temperature on Flow oniteny index and low behaviour index wa identiied. b) The rition ator and generalized Reynold number relation in traight tube wa ueully ollowed the theoretial relation in laminar region while turbulent region the uual orrelation o Newtonian luid ollowed. ) The eet o helix angle on rition ator wa identiied and modiied the exiting orrelation to inorporate the eet o helix angle in moderate and high Re in laminar region. d) The helial oil eet i negligible in low Re o Laminar and Turbulent region. Nomenlature d- diameter o oil (m) D- diameter o Helix (oil upport) (m) De- Dean number (Re(d/D) 0.5 ) - oil rition ator - linear pipe or traight rition ator K -low oniteny index, (Pa. n ) n - low behaviour index P- preure drop (Pa) Re Reynold number (dv / ) Re -Generalized Reynold number (d n v (2-n ) /(8 (n -1) K ) V veloity(m/) Greek letter Helix angle denity (kg/m 3 ) vioity (pa.) REFERENCES [7] Ito, H., Frition ator or turbulent low in urved pipe. Tran. Amer. So. Meh. Eng.J. Bai Eng. D81, [8] White, C.M., Fluid rition and it relation to heat traner. Tran. Int. Chem. Eng. (London) 10, [9] Mihra, P., Gupta, S.N., Momentum traner in urved pipe 1.Newtonian luid; 2. Non-Newtonian Fluid.Ind. Eng. Chem. Proe De. Dev. 18, [10] Hart, J., Ellenberger, J. &Hamerma, P. J Single- and two-phae low through helially oiled tube.chem. Engng Si. 43, [11] Kubair, V., Varrier, C.B.S., 1961/1962. Preure drop or liquid low in helial oil. Tran. Indian Int. Chem. Eng. 14, [12] Srinivaan, P.S., Nandapurkar, S.S., Holland, F.A., Preure drop and heat traner in oil. The Chem. Eng. (London), 218, CE [13] Jone, J.R.: Flow o a Non-Newtonian Liquid in a Curved Pipe, Q. J. Meh. Appl. Math. (1960) 13, pp [14] Thoma, R.H. and Walter, K.: On the Flow o an Elatioviou Liquid in a Curved Pipe under a Preure Gradient, J. Fluid Meh. (1963) 16, pp [15] Rajeekaran, S., Kubair, V. G., Kuloor, N. R., (1970), Indian Jr. o Teh., 8, [16] Mahelkar, R. A. and Devarajan, G. V.: Seondary Flow o Non-Newtonian Fluid: Part I Laminar Boundary Layer Flow o a Generalized Non-Newtonian Fluid in a Coiled Tube, Tran. Intn. Chem. Eng. (1976) 54, pp [17] Mujawar, B.A. and Rao, M.R.: Flow o Non-Newtonian Fluid through Helial Coil, Ind. Eng. Chem. Proe De. Dev. (1978) 17, No. 1, pp [18] Krihna B. S. V. S. R., Chhabra, Rajendra P. (2002),Preure drop or ingle and two-phae low o non-newtonian liquid in helial oil, The Canadian Journal o Chemial Engineering, 80 (2). pp [19] T.J. Huttl and R. Friedrih, Diret numerial imulation o turbulent low in urved and helially oiled pipe, Computer and Fluid 30, 591 (2001). [20] J.S.Jayakumar,, S.M. Mahajani, J.C. Mandal, K.N. Iyer, P.K. Vijayan, CFD analyi o ingle-phae low inide helially oiled tube, Computer and Chemial Engineering 34 (4), pp (2010). [1] Grindley, J.H., Gibon, A.H., On the ritional reitane to the low o air through a pipe, Pro. R. So. London, Ser.A 80, [2] Eutie, J., Flow o water in urved pipe. Pro. R. So. London, Ser. A 84, [3] Dean, W.R., Note on the motion o luid in a urved pipe. Philo. Mag. 4, [4] Dean, W.R., The treamline motion o luid in a urved pipe. Philo. Mag. 5, [5] White, C.M., Streamline low through urved pipe. Pro. R. So. London Ser. A 123, [6] Prandtl, L., Fuhrer dmhdiestromunglehre, 3rd Edition p. 159, Braunhweigh; Englih Tranl., Eential o Fluid Dynami, Blakie and Son, London, 1954, p International Journal o Applied Reearh in Mehanial Engineering (IJARME) ISSN: , Volume-2, Iue-1,