HEAT TRANSFER AND PRESSURE DROP CHARACTERISTICS OF A HORIZONTAL ANNULAR PASSAGE IN THE TRANSITIONAL FLOW REGIME

Transcription

1 HEAT TRANSFER AND PRESSURE DROP CHARACTERISTICS OF A HORIZONTAL ANNULAR PASSAGE IN THE TRANSITIONAL FLOW REGIME Ndenguma D.D., Dirker J.* and Meyer J.P. *Authr fr crrespndence Department f Mechanical and Aernautical Engineering, University f Pretria, Pretria, 0002, Suth Africa, jac.dirker@up.ac.za ABSTRACT Due t tube enhancements being used t imprve prcess efficiencies, heat exchangers are starting t perate in the transitinal flw regime. Unfrtunately, heat transfer and pressure drp perfrmances in this flw regime is un-explred fr many heat transfer gemetries. In this preliminary study, experiments were cnducted n the annular passage f a hrizntal cncentric cunter-flw tube-in-tube heat exchanger perated with water fr nn-fully develped flw assciated with a standard inlet gemetry type. The annular diameter rati, defined as the inner wall diameter ver the uter wall diameter, was An apprximate unifrm wall temperature n the inner annular wall surface was cnsidered fr varying annular mass flw rates that cvered all flw regimes. Bth heated and cled cases f the annulus were examined. It was fund that the heat transfer and pressure drp characteristics, based n the hydraulic diameter are different frm thse in circular tubes. The transitin frm laminar t turbulent flw, based n the Nusselt number, appeared t ccur earlier than based n the frictin factr. Nusselt numbers fr heated annulus case, based n Reynlds number, were high than that fr the cled case. Cnversely, the frictin factrs were higher fr the cled annulus case than fr the heated case, while the adiabatic frictin factrs were the lwest. INTRODUCTION Heat exchanger design guidelines nrmally advise that designs shuld be dne either fr the laminar r fr the turbulent flw regimes. Hwever, design cnstraints and energy requirements have ften lead t heat exchangers perating utside their design parameters. These parameters ften invlve the heat exchanger perating in the transitinal flw regime [1]. Unfrtunately, heat transfer and pressure drp perfrmances in the transitinal flw regime is un-explred fr many heat transfer applicatins including that f annular passages f tube-in-tube heat exchangers, ne f the mst cmmn heat exchanger types. The rati f the inner tube s uter diameter t the uter tube s inner diameter, knwn as annular diameter rati, has been reprted t have an influence n bth heat transfer and frictin factr characteristics in such a heat exchanger type [2]. NOMENCLATURE A s [m 2 ] Surface area c p [J/kg.K] Specific heat at cnstant pressure D [m] Diameter f [-] Frictin factr h [W/m 2 K] Cnvectin heat transfer cefficient k [W/m.K] Thermal cnductivity L dp [m] Pressure drp length L hx [m] Heat exchange length m [kg/s] Mass flw rate n [-] Number f thermcuples Nu [-] Nusselt number Re [-] Reynlds number p [kpa] Pressure drp Q [W] Heat transfer rate T [ C] Temperature V [m/s] Average velcity Special characters [kg/m 3 ] Density [kg/ms] Dynamic viscsity Subscripts 0 Outer tube inner wall 1 Inner tube uter wall b Bulk prperty h Hydraulic i Inner tube ii Inner tube inlet i Inner tube utlet iw Inner wall j Index number LMTD Lgarithmic mean temperature difference Annular passage i Annular passage inlet Annular passage utlet x Place hlder Analytical and numerical slutins fr heat transfer and fluid behaviur fr fully develped flw with pure frced cnvectin heat transfer in the laminar flw regime have been available fr many years, whereas thse fr turbulent flw are nrmally calculated frm empirical equatins based n experimental data. Accrding t Gnielinski [3], crrelatins fr heat transfer and frictin factrs in the turbulent flw regime are fund t be incnsistent with each ther. Sme crrelatins fr turbulent flw in annular passages are listed in [2] and [4]. 539

2 Prinsl et al. [4] investigated the heat transfer and pressure drp characteristics in the turbulent flw regime f the annuli f hrizntal tube-in-tube heat exchangers. Amng ther findings, they bserved that fr the same inlet water temperature the heated annulus had larger Nusselt numbers, thus transferring mre heat than the cled annulus. Hwever, a heated annulus had a smaller frictin factr cmpared t a cled ne. This was partly ascribed t the influence f wall and bulk fluid temperatures and the assciated fluid prperties. A cnvenient way t bserve the transitin between the laminar t turbulent flw regimes, is by cnsidering a plt f either the Nusselt number r the frictin factr against the Reynlds number. Fr flws withut free cnvectin influence, the nset f turbulence ccurs at apprximately Re = 2300 fr circular smth tubes with fully develped flw. Zhipeng [5] cnsidered the transitin regin as metastable and cmplicated. By summarizing results f earlier research wrk and by using a fluid flw mdel which is valid fr all flw regimes, Abraham et al. [6] prpsed a frictin factr and Reynlds crrelatin fr the entire range f Reynlds numbers which smthly bridged between the flw regimes. Practically, mst heat exchangers d nt perate with a flw that is fully develped, and in sme cases an influence f free cnvectin heat transfer may exist, which in turn creates secndary flw. Lu and Wang [7] investigated experimentally the characteristics f a nn-fully develped flw with secndary flw in a narrw annulus f hydraulic diameter and pressure drp length f 6.16 mm and 1410 mm, respectively. The results shwed different characteristics frm thse f a fully develped flw and pure frced cnvectin heat transfer. They realised that the flw characteristics can be related t the liquid temperature difference at the inlet and utlet f the annulus. The influences f temperature difference are significant in the laminar flw regime while nne were bserved in turbulent flw regime. The flw transitin (based n the frictin factr) frm laminar t turbulent in their investigatin ccurred in a lw Reynlds number range frm 1100 t 1500, while fully turbulent cnvective heat transfer fr heated water was achieved at a Reynlds number range frm 800 t Lu and Wang [8] als carried ut experiments t investigate heat transfer characteristics f water flw in a narrw annulus f hydraulic diameter and pressure drp length f 4.12 mm and 1500 mm, respectively. The results fr cnvective heat transfer were similar t thse in [7]. Many researchers have als investigated the flw and heat transfer characteristics in the transitinal flw regime fr micr channels. Jiang et al. [9] bserved that frictin factrs in micr channels were smaller than that in cnventinal-sized channels. Peng et al. [10] fund that the critical Reynlds number fr transitin frm laminar t turbulent in micr channels t ccurred at and fr fully develped flw at Reynlds numbers f Dirker et al. [11] investigated the effects f different types f inlets in rectangular micrchannels. They fund that the critical Reynlds number and the transitinal behaviur in terms f heat transfer and frictin factrs were influenced significantly by the inlet types. Mala and Li [12] measured the transitin at Reynlds number f in micr-tubes. On the basis f the previus research, sme f which is mentined abve, preliminary experiments were cnducted t investigate the characteristics f frictin factr and heat transfer fr a heated and cled annulus. Specific attentin was given t a transitinal regime. The experiments were carried ut n nn-fully develped flw with secndary flw. EXPERIMENTAL SETUP Figure 1, shws the schematic layut f the experimental facility that includes test sectin. The facility cnsisted f tw clsed lp water systems. The lay-ut depicted is that f a heated annulus set-up. By switching the cnnectrs at the test sectin inlets and utlets between the ht and cld lps, either cled r heated annular cases culd be investigated depending n the test requirements. Adiabatic cases culd be cnsidered by passing water frm ne flw lp thrugh bth the inner tube and annular passage f the test heat exchanger. The ht water lp was supplied by a 1000 litre reservir (item R1) fitted with a 36 KW electrical resistance heater. The ht water was circulated by a psitive displacement pump, CB620 (item P1) with a delivery range f kg/s. Since flw rates, much less than what the pump culd handle were required, a bypass valve (item RV1) was utilized t assist cntrl the flw rate f water. An accumulatr (item A1) was installed next t the pump t arrest pulsatins that were created by the pump. Flw rates were measured using a Crilis flw meter with an effective range f kg/s (item M1). T avid lse particles settling in the test sectin, and thereby cmprmising results, a filter (item F1) was installed in the lp. Figure 1 Schematic diagram f experimental facility. 540

3 Figure 2 Tube-in-tube heat exchanger test sectin. The cld water lp was very similar t the ht water lp. The cld water, hwever, had a 45 KW chiller unit cnnected t a 5000 litre reservir (item R2). A SP4 pump (item P2) with a delivery range f kg/s was utilized t circulate the water. A Crilis flw meter (item M2) with a range f kg/s was used t btain the mass flw rate. Other cmpnents like an accumulatr (item A2) and a filter (item F2) were als fitted in this lp. In additin, bth lps were fitted with relevant pressure relief valves, pressure gauges, nn-return valves (items NV1 and NV2) and apprpriate pipes and pipe fittings. Temperature, pressure drp and water flw rate readings were captured using Natinal Instruments data acquisitin system using Lab-view sftware. The test sectin, represented in Figure 2, was a tube-intube heat exchanger with an annular diameter rati f and a length f 5.5 m. The tubes were made f hard drawn cpper. The inner tube had inner and uter diameters f mm and 12.7 mm, respectively while fr the uter tube these diameters were 32.9 mm and 35 mm, respectively. Special care was taken with the inlet f the annular passage. The annular inlet gemetry was that f a 90 T- sectin fitting, similar t that fund in mst practical applicatins. The T-sectin was preceded by an adiabatic inlet length which ran parallel t the main test sectin length and which was cnnected t the heat exchanger by an elbw with a mid-pipe radius f 25 mm. The inlet length was 4.2 m lng with an inner diameter f 32.9 mm and was clamped t the uter tube f the heat exchanger by three wden clamps. It was designed t ensure repeatable flw inlet cnditins at the inlet f the heat transfer sectin by prducing fully develped hydrdynamic flw befre the elbw. T ensure cncentricity f the annular passage, the inner tube was supprted by hypdermic needles (0.8 mm in diameter) at eight equally spaced axial psitins. Each supprt psitin had fur equally spaced needles, held in place n the uter annular wall in thick-walled Perspex cnnectrs. The uter tube was therefre made up f nine cpper sectins linked t each ther via carefully manufactured Perpex cnnectrs, such that the uter wall f the annulus was smth and straight. Inlet and utlet fluid temperatures fr the inner tube were measured at adiabatic measuring statins each cnsisting f a shrt cpper length equipped with fur thermcuples cnnected 90 apart. Thermally, these measuring statins were insulated frm the heat exchanger by means f rubber hses. The inlet and utlet temperatures f the annular passage fluid were measured in a similar manner as fr the inner tube, except that each measuring statin was equipped with eight thermcuples t reduce the effective measurement uncertainty t C. A mixing sectin was placed befre the utlet temperature measuring statin t avid thick bundary layers and t ensure that the crrect water temperature was captured. In rder t btain heat transfer cefficients, the test sectin was equipped with a large number f inner wall thermcuple measuring psitins. Tw T-type thermcuples, each with measurement uncertainty f C, were inserted at each f the nine equally spaced statins alng the length f the inner tube. In rder t keep the annular passage, which was the fcus f this study clear, thermcuple leads had t pass thrugh inside f the inner tube. Each thermcuple junctin was sldered in a grve, 10 mm lng with a depth f 0.46 mm that was machined in the wall f the tube, such that the uter surface f the tube remained smth. The inlet and utlet ends fr the inner tube prvided exit prts fr thermcuple leads ut f the inner tube. T measure the lcal temperatures alng the annular passage tw thermcuples were attached n the surface f uter tube wall at intervals exactly midway between the inner tube measuring statins. Pressure measuring prts (1 mm inner diameter) were installed near the inlet and utlet f annular passage such that the pressure drp length was 5 m. A with 0.86 kpa pressure transducer (item PT), shwn in Figure 1, was utilized. The entire set-up was thermally well insulated frm the labratry. EXPERIMENTAL PROCEDURE Firstly, calibratin f all thermcuples and a pressure transducer was dne. The pressure transducer was calibrated using a water clumn and a manmeter with accuracy f 0.25%. Thermcuples were calibrated in situ using PT100 RTDs (Resistance Temperature Detectr) with accuracy f 0.1 C. Calibratin curves were created with which measured data were cnditined during the data-prcessing stages. 541

4 During experimental test-runs, three different tests types were cnducted with reference t the fluid in the annulus, namely: adiabatic, heated and cled. In all cases, the water in the inner tube and in the annular passage flwed in ppsite directins. Since the annular passage was the fcus f this investigatin, its flw was independent while the inner tube flw was depended n the annular flw. The annular flw ranged frm kg/s t 0.3 kg/s (260 t Reynlds number), in rder t ensure that all flw regimes were cvered. The flw in the inner tube was such that the difference in temperature between the inlet and utlet was always apprximately 1 C r lwer. This was dne in rder t apprximate a unifrm wall temperature bundary cnditin n the inner tube surface. By increasing the inner tube flw rate this temperature difference culd be reduced, but practical limitatins prevented this. The inlet temperatures fr ht and cld water were apprximately 50 C and 20 C, respectively fr diabatic test, while adiabatic test were cnducted at a temperature f 25 C. Data was lgged upn reaching a steady state cnditin. Steady state cnditin were deemed t have been reached when the change in energy balance between the inner tube and annular passage fluids were less than 0.1% and inlet and utlet temperature fluctuatin f 0.1 C r less was achieved, ver a perid f 1 minute. Up t 120 data pints were cllected fr each data lg. The average energy balance errr was 1.9 % while the maximum energy balance errr was 4% VALIDATION OF TEST PROCEDURE Prinsl, et al. [4] did a prtin f their investigatin using a similar test sectin; therefre, the present experiment was validated against their results. Fr this purpse, six f their test cases where reprduced, the data analysed, and the results cmpared with their published results. The results fr Prinsl et al. and present investigatins are shwn in Figure 3. It can be bserved that the calculated Nusselt numbers in this study cmpared well with thse f Prinsl et al. The slight difference f a maximum f 0.068% between the results culd be due t measurement uncertainties. PROCESSING OF RESULTS Cnvectin heat transfer rate fr an existing system at a specified temperature difference is determined by Newtn s law f cling: Q ha s T (1) LMTD Where h is the cnvectin heat transfer cefficient, A s is the surface area frm which cnvectin heat transfer takes place, and TLMTD is the lgarithmic mean temperature difference. Our interest is t get the cnvectin heat transfer cefficient; therefre, the rest f the parameters including the heat transfer rate in equatin (1) shuld be knwn r analysed first. The cnvectin heat transfer rate between the water in annular passage and the inner wall can be fund by: Nu [ ] Figure 3 Cmparisn f heat transfer fr tw similar experiments. p i Q m c T T (2) Here the mass flw rate was btained frm the reading f the relevant flw meter. The surface area f the utside wall f the inner tube in (1) was calculated as: A L (3) s Re [ ] hx D 1 By using equatin (4), the average temperatures fr the inner wall (x = iw ), the water inlets (x = ii r i ) and the water utlets (x = i r ) fr bth inner tube and annulus were calculated frm the measurements frm the relevant thermcuples. T T, n (4) x x j Here n is the number f thermcuples per measuring statin r thermcuple set. The lgarithmic mean temperature difference fr the annular passage can be calculated as: T LMTD ( Tiw Ti ) ( Tiw T ) (5) ln[( T T ) /( T T )] iw i The mean dimensinless Nusselt number fr annular passage was based n the hydraulic diameter and calculated as: iw Nu hd k (6) h Where the hydraulic diameter D h f the annulus was calculated as: D 0 D 1 (7) D h Current Prinsl's et al Prinsl et al. 542

5 Here D 0 and D 1 represent the uter and inner annular wall diameters respectively. The Reynlds number fr flw in annular passage was calculated as: Re m D A h Based n the measured pressure drp the frictin factr fr annular flw was calculated by: (8) f [-] 10 1 Cled Cled annulus Heated annulus Adiabatic f 2D p L h 2 pdv (9) 0.1 where the average velcity f water in the annulus was calculated as: V m A (10) All water prperties were calculated with the methd f Ppiel and Wjtkwiak [13] at the average bulk fluid temperature preliminary taken as the average between the measured inlet and utlet fluid temperatures f the relevant flw passage. RESULTS AND DISCUSSIONS As mentined, an apprximate unifrm wall temperature n the inner annular surface was cnsidered fr varying annular mass flw rates that cvered all flw regimes frm laminar t turbulent. The average wall temperatures fr the heated and cled cases were 49 C ± 1 C and 20.2 C± 1 C, respectively. Frictin factr characteristics were examined fr adiabatic, heated and cled cases, while heat transfer characteristics were, by definitin, nly cnsidered fr diabatic cases. The frictin factrs fr adiabatic, heated and cled cases f the water in the annular passage are pltted with respect t the Reynlds number in Figure 4. Fr all three case types, similar behaviur was bserved, namely that: frictin factrs rapidly decreased linearly in laminar flw regime and had a lwer rate f decrease in transitinal and turbulent flw regimes. In the laminar and transitinal regimes the frictin factrs fr the cled case was higher than bth the heated and adiabatic cases. The heating case fllwed the cling case and the adiabatic case had the lwest frictin factrs. Hwever, as the Reynlds number increased, the differences f frictin factrs fr the three cases in turbulent flw regime gt smaller. This phenmenn culd be a result f secndary flw in the laminar and transitinal regimes. In the Reynlds number range f , the frictin factrs fr the cled case were apprximately 2.02 times higher, than thse f the adiabatic case and 1.37 times higher than fr the heated case. Als shwn in Figure 4 are the perceived ranges f the transitinal flw regime as identified by a change in the data pint gradients (indicated visually fr the cled case). It was bserved that transitinal flw regime fr the adiabatic case Adiabatic Heated Re [-] Figure 4 Frictin factr characteristics fr adiabatic, heated and cled cases. was relatively shrt and ccurred at a Reynlds number f apprximately Fr the heated case the transitinal regime appeared t stretch frm a Reynlds number f abut 1200 t abut Fr the cled case, the transitinal flw regime s Reynlds number range was fund t be even wider at apprximately 1000 t Similarly, the average cmputed Nusselt numbers fr heated and cled cases are pltted with respect t the Reynlds number in Figure 5. Fr the tw case types similar behaviur was bserved, namely that: the Nusselt number increased rapidly in the laminar flw regime, then increased at a significantly lwer rate in the transitinal flw regime and increased again mre rapidly in the turbulent flw regime. The Nusselt numbers fr the heated case were n average 1.35 times higher than thse f cling case. The transitin frm laminar t turbulent flw, based n the Nusselt number, started earlier than the transitin based n the frictin factr, similar t the bservatin f Lu and Wang [7], but lasted lnger. Fr the heated case the transitinal regime appeared t stretch frm a Reynlds number f abut 700 t abut Fr the cled case, the transitinal flw regime Reynlds number range was fund t be apprximately 500 t It is bserved that the fully turbulent cnvective heat transfer fr bth the heated and cled cases are achieved at higher Reynlds number than the range that Lu and Wang [7] fund fr their narrw annulus. The difference culd be due t size f hydraulic diameter, annular diameter rati, annulus inlet gemetry, temperature difference, and the relative length f the test sectin. Table 1 summarizes sme f the gemetrical differences. Further t this, it is unclear whether Lu and Wang cntrlled the hydrdynamic flw cnditin at the inlet f their test sectin, r precisely what their thermal cnditin was 543

6 100 Cled annulus Heated annulus Heated transitin ccurred earlier than frictin factr transitin. Further bservatins indicated that the Nusselt number transitin was much lnger when cmpared t that f a narrw annulus investigatin by Lu and Wang [7, 8]. Further investigatin is required. Nu [-] Re [-] Cled Figure 5 Heat transfer characteristics fr heated and cled cases. Table 1 Differences between the current heat exchangers used by Lu and Wang and that f the current study. Lu and Wang Current study Hydraulic diameter 6.16 mm 20.2 mm Annular diameter rati Pressure drp length 1.41 m 5 m at the heat transfer wall. Since the annular space under cnsideratin in this study was significantly larger than that f Lu and Wang, secndary flw pattern develpment may have been enhanced in ur test cases. The aspects mentined abve might indicate that results frm transitinal flw regime investigatins may be gemetry specific. Further investigatins and data analyses are needed t be able t cmment n this t a deeper extent. It wuld be interesting t cnsider the behaviur f the lcal heat transfer cefficients alng the length f the test sectin within the transitinal flw regime. CONCULUSIONS A preliminary experimental investigatin was cnducted n heat transfer and pressure drp characteristics in a hrizntal annular passage. The heat transfer cefficients were higher fr the heated case than fr the cled case, while the ppsite was true fr the frictin factr. The frictin factr fr the adiabatic case was the lwest. The experimental results agreed in brad terms with data available in literature in the sense that the trends f bth Nusselt number and frictin factr graphs were similar. Als, the transitin frm laminar t turbulent based n the frictin factr and Nusselt number ccurred at different Reynlds numbers. The Nusselt number REFERENCES [1] Olivier J.A., and Meyer J.P., Single-phase heat transfer and pressure drp f the cling f water inside smth tubes fr transitinal flw with different inlet gemetries, American Sciety f Heating, Refrigerating and Air-Cnditining Engineers, Vl. 16, Issue 4, 2010, pp [2] Zyl W.R., Dirker J., and Meyer J.P., Single-phase cnvective heat transfer and pressure drp cefficients in cncentric annuli, Heat Transfer Engineering, Vl. 34, Issue 13, 2013, pp [3] Gnielinski, V., VDI - Heat Atlas, Sectin GD, VDI Verlag, Dϋsseldrf, Germany, [4] Prinsl F.P.A., Dirker J., and Meyer J.P., Heat transfer and pressure drp characteristics in the annuli f tube-in tube heat exchangers (Hrizntal lay-ut), Preceedings f the 15 th Internatinal Heat Transfer Cnference, Kyt, Japan, Paper number 9225, August, [5] Zhipeng D., New crrelative mdel fr fully develped turbulent heat and mass transfer in circular and nncircular ducts, Trans. ASME J. Heat Transfer, Vl. 134, [6] Abraham J.P., Sparrw E.M., and Minkwycz W.J., Internalflw Nusselt numbers fr the lw-reynlds number end f the laminar-t-turbulent transitin regime, Int. J. Heat Mass Transfer, Vl. 54, 2011, pp [7] Lu G., and Wang J., Experimental investigatin n flw characteristics in a narrw annulus, Heat and Mass Transfer, Vl. 44, 2008, pp [8] Lu G., and Wang J., Experimental investigatin n heat transfer characteristics f water flw in a narrw annulus, Applied Thermal Engineering, Vl. 28, 2008, pp [9] Jiang M.J., Lu X.H., and Liu W.L., Investigatin f heat transfer and fluid-dynamic characteristics f water flw thrugh micrchannels withut phase change, Jurnal f Beijing Unin University, Vl. 12, 1998, pp [10] Peng X.F., Petersn G.P., and Wang B.X., Frictinal flw characteristics f water flwing thrugh rectangular micrchannels, Jurnal f Experimental Heat Transfer, Vl. 7, 1995, pp [11] Dirker J., Meyer J.P., and Garach D.V., Inlet flw effects in micr-channels in the laminar and transitinal regimes n sinlephase heat transfer cefficients and frictin factrs, Internatinal Jurnal f Heat and Mass Transfer, Vl. 77, 2014, pp [12] Mala G.M., and Li D., Flw characteristics f water in micrtubes, Internatinal Jurnal f Heat Fluid Flw, Vl. 20, 1999, pp [13] Ppiel C.O., and Wjtkwiak J., Simple Frmulas fr Thermphysical Prperties f Liquid Water fr Heat Transfer Calculatins (frm 0 C t 150 C), Heat Transfer Engineering, Vl. 19, 1998 pp