換熱器外文文獻.pdf.pdf

International Journal of Thermal Sciences 46 2007 1311 1317 Performance analysis of finned tube and unbaffled shell and tube heat exchangers Joydeep Barman A K Ghoshal Department of Chemical Engineering Indian Institute of Technology Guwahati North Guwahati 781039 Assam India Received 15 May 2006 received in revised form 26 August 2006 accepted 6 December 2006 Available online 5 February 2007 Abstract This work considers an optimum design problem for the different constraints involved in the designing of a shell and tube heat exchanger consisting of longitudinally finned tubes A Matlab simulation has been employed using the Kern s method of design of extended surface heat exchanger to determine the behavior on varying the values of the constraints and studying the overall behavior of the heat exchanger with their variation for both cases of triangular and square pitch arrangements along with the values of pressure drop It was found out that an optimum fin height existed for particular values of shell and tube diameters when the heat transfer rate was the maximum Moreover it was found out that the optimum fin height increased linearly with the increase in tube outer diameter Further studies were also performed with the variation of other important heat exchanger design features and their effects were studied on the behavior of overall performance of the shell and tube heat exchanger The results were thereby summarized which would proclaim to the best performance of the heat exchanger and therefore capable of giving a good idea to the designer about the dimensional characteristics to be used for designing of a particular shell and tube heat exchanger 2007 Elsevier Masson SAS All rights reserved Keywords Fin height Heat exchanger Heat transfer rate Longitudinal fins Number of tube side passes Pressure drop Tube pitch layout 1 Introduction Fins have long been recognized as effective means to aug ment heat transfer The literature on this subject is sizeable Shell and tube heat exchanger with its tube either finned or bare is extensively taught in the undergraduate level Several text and reference books deal with the problems of longitudinal finned tube in a shell and tube heat exchanger 1 4 It is well under stood that with increase in fin height of a longitudinal fin heat transfer area increases to increase the heat transfer and at the same time the driving force decreases to decrease the heat trans fer However one important design aspect which probably is not discussed is presented here For a particular shell diameter capacity of tube numbers is decided depending on tube size and pitch arrangement In case of finned tube height of the fin also plays an important role Therefore with increase in fin height though surface area increases but number of tubes as well as Corresponding author E mail addresses joydeepb iitg ernet in J Barman aloke iitg ernet in A K Ghoshal 1290 0729 see front matter 2007 Elsevier Masson SAS All rights reserved doi 10 1016 j ijthermalsci 2006 12 005 efficiency of the fin decreases So there might be an optimum condition of tube number and fin height for a particular tube arrangement and a particular shell diameter for which the heat transfer rate is the maximum 5 A Matlab coding has been de signed to study the behavior of the overall performance of a heat exchanger on varying the important design features involved in it The important constraints involved in the designing of a heat exchanger are studied here using the Matlab program Several results and optimum conditions related to them are briefed out and tabulated in this literature to give a basic idea to the de signer about the requirements and limitations to be included while designing a finned tube and unbaffled shell and tube heat exchanger In the present article Kern s method of design 2 of ex tended surface heat exchanger is applied for a shell and tube heat exchanger problem Optimum conditions of fin height and number of tubes in cases of triangular pitch and square pitch arrangements are found out along with the values of pressure drop Other results concerning the various constraints of a heat exchanger like number of passes tube outer diameter and tube pitch layout were also studied and compared in this literature 1312J Barman A K Ghoshal International Journal of Thermal Sciences 46 2007 1311 1317 Nomenclature as at fluid flow area m2 Nf number of fins per tube Ao Aitube surface area m2 NT total number of tubes cs ctspecific heat capacity J kg 1K 1 Pt tube pitch m dthickness of each fin mPwwetted perimeter m deequivalent diameter for heat transferPrs PrtPrandtl number calculations mQoverall heat transfer rate per unit LMTD W K 1 D D1inner and outer diameter of tube mRes RetReynolds number D2inner diameter of shell mss stspecific gravity of fluid W m 2K 1 Dbtube bundle diameter mUoverall heat transfer coefficient Desequivalent diameter for pressure dropwtube side fluid s mass flow rate kg s 1 calculations mWshell side fluid s mass flow rate kg s 1 fs ftfriction factor of fluid W m 2K 1 Ps Ptpressure drop Pa hf heat transfer coefficient of fins Greek symbols hf i heat transfer coefficient of outside tube surface and s t wviscosity Pa s fins with respect to the inner tube W m 2K 1 ffin efficiency surface Subscriptshiheat transfer coefficient of inside tube W m 2K 1surface ffin Hfheight of each fin miinside of tube Gs Gtmass velocity of fluid kg m 2s 1ooutside of tube Ks Ktthermal conductivity W m 1K 1sshell side Llength of each tube mttube side nnumber of tube side passeswwall 2 The mathematical program model of Kern s method and solution procedure determination of tube bundle diameter and maximum number of tubes A shell and tube heat exchanger with an internal shell diam eter D2 consisting of finned tubes of outer diameter D1 inner diameter D length L with fins of height Hf and thickness d is considered here Total number of fins per tube isNf andtotal number of tubes isNT Tube bundle diameter isDb Db D1 2Hf NT K 1 M 1 The constants KandM are determined from Table 1 for dif ferent tube passes and tube pitch layouts for a tube pitch 3 Shell side calculations The flow area as wetted perimeter Pw equivalent diame ter de mass velocity Gs Reynold s number Resand Prandtl number Prsare calculated using Eqs 3 8 as follows as D2 4 NT D2 4 Nf d Hf 3 21 Pw NT D1 Nf d 2Nf Hf 4 de 4as Pw 5 Gs W as 6 Res de Gs s 7 Prs cs s Ks 8 The heat transfer coefficient for the outside tube and fin surfaces Pt 1 25 D1 2Hf 1 2 can be calculated using Sieder Tate correlation 4 Eqs 9 and 10 as shown below Tube bundle diameter is first calculated by iterative process for bare tubes henceforth maximum number of finned tubes NT is calculated from the derived tube bundle diameter from Eq 1 Table 1 Values of constants K and M 1 hf 1 86 Ks de Res Prs de L 1 3 9 for laminar flow Triangular pitchSquare pitch No of passes1246812468 K0 3190 2490 1750 07430 03650 2150 1560 1580 04020 0331 M2 1422 2072 2852 4992 6752 2072 2912 2632 6172 643 J Barman A K Ghoshal International Journal of Thermal Sciences 46 2007 1311 13171313 hf 0 027 Ks de Res0 8 Prs1 3 s w 0 14 10 for turbulent flow for turbulent flow Thus the overall heat transfer coefficient U with respect to the inside tube surface is given by Eq 23 4 Tube side calculations U hf i hi hf i hi 23 The tube side flow area at mass velocity Gt Reynolds Finally the heat transfer rate with respect to the inside tube sur face area Qper degree LMTD is calculated using Eq 24 as number Retand Prandtl number Prt for tube side fluid are follows calculated from Eqs 11 14 With the values of viscosity t specific heat capacity ctand thermal conductivity Kt forQ U Ai 24 tube side fluid and using the Sieder Tate correlation the heat transfer coefficient of inside tube surface hi can be calculated 7 Pressure drop calculations at NT D2 4n 11 Equivalent diameter for pressure drop calculations in case of Gt w atRet DGt t Prt ct t Kt 12 shell side fluid will be different from the diameter used for heat 13 transfer calculations This diameter is given by Eq 25 14 Des 4as Pw D2 25 5 Fin efficiency calculations The pressure drops for shell side and tube side fluid Psand Ptrespectively are calculated using Eqs 26 29 as follows The process is assumed as a steady state one and there isPs fs G2 L 5 22 1010 Des ss 26 a continuous flow of fluid in the axial direction both in thes shell and tube side Therefore for a particular value of radialfs 16 Res 27 location the temperature for any location in the axial directionfor laminar flow and would be almost same Further the angular directional variation fs 0 0035 0 24 Res0 42 28 of temperature is also neglected Thus the problem is reduced to a one dimensional heat conduction problem Hence the finfor turbulent flow efficiency is represented as fand calculated using Eqs 15 Here Res Des Gs s and 16 Pt ft Gt2 L n 5 22 1010 D st 29 f tanh mHf mHf 15 whereftis the tube side friction factor and can be calculated where as shown above Eqs 27 and 28 using tube side Reynolds m 2hf Kfd 1 2 16 number Ret ssandstare the specific gravities of shell side and tube side 6 Heat transfer calculationsfluids respectively 2 Heat transfer coefficient of outside surface and fins with8 Solution basis respect to the inner surface of tubes hf iand heat transfer coef An exemplary problem discussed below is used to study theficient of inside surface hi are given as below using Eqs 17 21 and 22 objectives as discussed Hot fluid 3 8 kg s 1 in shell side is hf i Hf P Nf f NT Ao hf Ai 17 to be cooled by a cold fluid 6 4 kg s 1 in tube side Inner di ameter of the shell and length of the shell are kept constant as AoandAiare the outside bare tube surface area and inside0 5 and 4 88 m respectively Inner and outer diameters of the surface area of tubes respectively wherePis the perimeter oftube are varied Number of fins with thickness 9 10 4m per a fin as given by Eqs 18 20 tube is 20 and is kept constant for all the calculations Ther Ao D1 Nfd NTL 18 mal conductivity of the fin material is 45 W m 1K 1 Hot and cold fluids are oxygen gas and water respectively The values Ai DNTL 19 for thermal conductivity viscosity and heat capacity of oxygen P 2 L d 20 gas and water are calculated at an average temperature of 353 and 305 K respectively The heat transfer coefficient for the inside tube surface can be calculated using Sieder Tate correlation 4 Eqs 21 and 22 9 Results and discussions as shown below hi 1 86 Kt D Ret Prt D L 1 3 for laminar flow hi 0 027 Kt D Re0t 8 Pr1t 3 t w 0 14 21 The Kern s method of designing of shell and tube heat ex changers with extended surfaces was used for the designing of the heat exchanger concerned in this paper The equations in 22 volved in this method are all simple and well established and 1314J Barman A K Ghoshal International Journal of Thermal Sciences 46 2007 1311 1317 were incorporated in a Matlab program specially coded for the purpose of this paper This program is simply a step wise cal culation and does not involve any iteration or any optimization technique that may lead to some numerical errors However the program was thoroughly checked and thereafter run to arrive at the reasonable conclusions as reported in the manuscript The results tabulated in Tables 2 5 and results shown graph ically in Figs 1 and 2 were found out for a tube outer diameter of 0 0254 m Tables 2 and 3 present the maximum number of finned tubes of different fin heights for triangular pitch and square pitch arrangements respectively which can be accom modated in the shell of inner diameter 0 5 m They also reflect the obvious nature of variations of the shell side and tube side pressure drops with variation of fin height keeping one tube pass only It is well understood that as the number of tubes decreases with the increase in fin height the tube side fluid flow area is decreased thereby increasing the pressure drop On the other hand the shell side flow area increases leading to decrease in pressure drop which is also shown through Figs 1 and 2 for tri angular pitch and square pitch arrangements respectively The variations of the heat transfer rates for both the pitches with variations of fin height are reported in Tables 2 and 3 respec tively The nature of the variations is shown through Figs 1 and 2 for triangular pitch and square pitch arrangements respec tively It is observed from the figures that there exists an opti mum fin height 0 4572 10 2m for triangular pitch and 0 4826 10 2m for square pitch arrangement which gives the highest heat transfer rate Corresponding to these optimum fin heights optimum number of adjustable finned tubes is 78 and 60 respectively Under these optimum conditions heat transfer rates are 7798 4 and 5843 0 W K 1 tube side pressure drops are 0 2985 and 0 4723 kPa and shell side pressure drops are 1 3217 and 0 8343 kPa for triangular and square pitch arrange ments respectively Tables 4 and 5 show the corresponding values of optimum fin height total number of tubes heat transfer rate and pres sure drop for different values of tube side passes We notice from these tables Tables 4 and 5 that for a constant shell inner diameter with increase in the number of tube side pass the maximum heat transfer rate corresponding to the optimum value of fin height decreases It is also noticed that as the total number of tubes decreases the tube side pressure drop values in creases largely which is a major drawback from economic and Fig 1 Variation of heat transfer rate and shell side pressure drop with increase in fin height for triangular pitch arrangement one tube side pass and for tube outer diameter 0 0254 m Fig 2 Variation of heat transfer rate and shell side pressure drop with increase in fin height for square pitch arrangement one tube side pass and for tube outer diameter 0 0254 m Table 2 Capacity of finned tubes of 0 0254 m outer diameter in the shell pressure drops and heat transfer rate values for triangular pitch arrangement and for one tube side pass Height of fin Hf 102 m 0 2540 3810 43180 45720 5080 55880 6350 762 Total number of tubes NT10286817873 696355 Shell side pressure drop Ps kPa1 43411 36921 33831 32171 28931 25691 2093 1 1335 Tube side pressure drop Pt kPa0 18820 2530 28270 29850 3330 36950 4295 0 546 Heat transfer rate per unit LMTD Q W K 1 7469 37767 17797 37798 47777 47730 57622 47371 2 Table 3 Capacity of finned tubes of 0 0254 m outer diameter in the shell pressure drops and heat transfer rate values for square pitch arrangement and for one tube side pass Height of fin Hf 102 m 0 2540 3810 40640 43180 45720 48260 5080 5334 Total number of tubes NT8268666462 605850 Shell side pressure drop Ps kPa0 87630 86050 85430 8480 84110 83430 8274 0 8191 Tube side pressure drop Pt kPa0 27650 37570 39850 4220 44610 47230 4985 0 5268 Heat transfer rate per unit LMTD Q W K 1 5522 45797 55820 45835 15842 45843 05837 65826 8 J Barman A K Ghoshal International Journal of Thermal Sciences 46 2007 1311 13171315 optimization point of views As expected the shell side pressure drop decreases with decrease in tube number but the decrease is much less in comparison to the increase for the tube side pressure drop So in this case the tube side pressure drop val ues bear more importance while selecting the number of passes Hence from the tabulated data obtained it can be said that one tube side pass is the best choice for the finest results of heat ex changer performance unless a constraint related to the number of tubes is faced when higher values of tube side pass could be considered Moreover it was also noticed that for a particular fin height the total number of adjustable tubes varies for the pitch arrangements As the number of tubes that could be ad justed in a square pitch arrangement were less in number than in triangular pitch arrangement so even the most optimum value of fin height in case of square pitch arrangement could not pro duce the same heat transfer rate as compared to the other But the shell side pressure drop is higher in magnitude in triangu lar pitch than in square pitch arrangement whereas the relation is just the opposite in case of tube side pressure drop values So in the absence of any pressure drop constraints the triangu lar pitch arrangement with the optimum value of fin height will prove to be the best choice The other tables i e Tables 6 9 give the values of different important parameters such asas Ai Ao Res Prs hf f hf i hiandU used and determined during the calculations Fig 3 shows the variation of optimum fin height with the change of tube outer diameters for a fixed number of tube side passes and for triangular pitch arrangement The relation between them is found to b