A computer program for designing of shell-and-tube heat exchangers

Applied Thermal Engineering 24(2004) 1797 1805 www.elsevier.com/locate/apthermeng A computer program for designing of shell-and-tube heat exchangers Yusuf Ali Kara *, Ozbilen G uraras Department of Mechanical Engineering, Faculty of Engineering, University of Atat urk, 25240 Erzurum, Turkey Received 24August 2003; accepted 23 December 2003 Available online 4February 2004 Abstract In a computer-based design, many thousands of alternative exchanger configurations may be examined. Computer codes for design are organized to vary systematically the exchanger parameters such as, shell diameter, baffle spacing, number of tube-side pass to identify configurations that satisfy the specified heat transfer and pressure drops. A computer-based design model was made for preliminary design of shell-andtube heat exchangers with single-phase fluid flow both on shell and tube side. The program covers segmentally baffled U-tube, and fixed tube sheet heat exchangers one-pass and two-pass for tube-side flow. The program determines the overall dimensions of the shell, the tube bundle, and optimum heat transfer surface area required to meet the specified heat transfer duty by calculating minimum or allowable shell-side pressure drop. Ó 2004Elsevier Ltd. All rights reserved. Keywords: Heat exchanger; Shell-and-tube; Sizing; Single-phase flow 1. Introduction The design of a new heat exchanger (HE) is referred to as the sizing problem. In a broad sense, it means the determination of exchanger construction type, flow arrangement, tube and shell material, and physical size of an exchanger to meet the specified heat transfer and pressure drop. This sizing problem is also referred to as the design problem. Inputs to the sizing problem are: flow rates, inlet temperatures and one outlet temperature at least, and heat transfer rate. * Corresponding author. Tel.: +90-442-231-4845; fax: +90-442-236-0957. E-mail address: ykara@atauni.edu.tr (Y. Ali Kara). 1359-4311/$ - see front matter Ó 2004Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2003.12.014

1798 Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 Nomenclature A area (m 2 ) C heat capacity (W/K) c p specific heat (J/kg K) d tube diameter (m) F correction factor for multi-pass and crossflow heat exchanger h convective heat transfer coefficient (W/m 2 K) k thermal conductivity (W/m K) L length (m) _m mass flow rate (kg/s) N number Q heat rate (W) R thermal resistance T temperature ( C) P t tube pitch U overall heat transfer coefficient (W/m 2 K) DP pressure drop (Pa) DT temperature difference ( C) Subscripts b baffle c cold cb central baffle cf counter flow ex exchanger f fouling h hot i inlet, inner ib inlet baffle lm logarithmic mean m mean o outlet, outer s shell t tube w wall Kern [1] provided a simple method for calculating shell-side pressure drop and heat transfer coefficient. However, this method is restricted to a fixed baffle cut (25%) and cannot adequately account for baffle-to-shell and tube-to-baffle leakage. Kern method is not applicable in laminar flow region where shell-side Reynolds number is less than 2000. Although the Kern equation is not particularly accurate, it does allow a very simple and rapid calculation of shell-side heat transfer coefficient and pressure drop to be carried out.

Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 1799 The concept of considering the various streams through the exchanger was originally proposed by Tinker [2]. He suggested a schematic flow pattern, which divided the shell-side flow into a number of individual streams. TinkerÕs model has been the basis of stream analysis method, which utilizes a rigorous reiterative approach and is particularly suitable for computer calculations rather than hand calculation. TinkerÕs original analysis was quite complex and hard to understand. After an extensive series of experiments was carried out, a new method has emerged, commonly described as the Bell Delaware method [3]. The Delaware method uses the principles of TinkerÕs model but more suitable for hand calculation. In this method, correction factors for baffle leakage effects, etc., are introduced based on extensive experimental data. This method is widely used and most recommended. In manual design of an exchanger, the thermal design engineer cannot avoid the trial and error routine. Accordingly there is little interest in hand calculation method. For manual design, Saunders [4] proposed very practical method that simple design factors are provided which enable the method proposed by Bell to be used rapidly for a fixed set of geometrical parameters. In BellÕs work, the correction factors for heat transfer and pressure drop correlations are given in graphic form. For computer applications, Taborek [5] gives the correlations for all correction factors involving Bell methods. Wills and Johnston [6] have developed the stream analysis method that is viable for hand calculation. Hewitt provides a more readily accessible version of Wills and Johnston method [7]. Reppich and Zagermann [8] offers a computer-based design model to determine the optimum dimensions of segmentally baffled shell-and-tube heat exchangers by calculating optimum shellside and tube-side pressure drops from the equations provided in his work. The six optimized dimensional parameters are number of tubes, tube length, shell diameter, number of baffles, baffle cut, and baffle spacing. The proposed model carries out also cost analysis. Gaddis [9] presented a new procedure for calculating shell-side pressure drop, which is based principally on Delaware method. However, instead of using diagrams as in the Delaware method to calculate the pressure drop in tube bank, the present authors use equations previously presented in [10,11]. Li and Kottke have carried out series of experimental work on shell-and-tube heat exchangers to analysis shell-side heat transfer coefficient (HTC) and pressure loss. They employed a particular mass transfer measuring technique based on absorption, chemical and color giving reaction in their researches to obtain local shell-side HTC by applying the extended Lewis analogy between heat and mass transfer to mass transfer coefficient. They studied local shell-side HTC in shell-andtube heat exchangers with disc-and-doughnut baffles and segmental baffles [12 14]. They also investigated effect of leakage and baffle spacing on pressure drop and HTC in [15] and [16] respectively. Although design may be carried out by hand calculation, computer programs are widely employed anymore. These are often proprietary codes produced by design industry, large processing companies, and international research organizations such as Heat Transfer and Fluid Flow Service (HTFS) or Heat Transfer Research Inc. (HTRI) or Tubular Exchanger Manufacturers Association (TEMA). Unfortunately, it is hard to employ them as a heat exchanger subroutine of a computer simulation for any thermal system plant that one of its equipment is heat exchanger. Researchers usually tend to make a mathematical model and a computer

1800 Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 simulation of thermal systems for their theoretical analysis and when a heat exchanger exists in the system, a subroutine will be needed to solve thermo-hydraulic performance of heat exchanger. Our program can be easily employed as a subroutine to any simulation program for preliminary design purposes. 2. Model description The number of tubes that can be placed within a shell depends on tube layout, tube outer diameter, pitch size, number of passes, and shell diameter. These design parameters have been standardized and given as tabulated form that usually called tube counts. Many tube count tables are available in open literature [4,17,18]. In this work we use tube counts given by Saunders [4]. He presented a tube counts table for fixed tube sheet, U-tube and split backing ring floating type exchangers, having the 24-shell diameter from 203 to 3048 mm and 13 tube configurations. In these tube count tables both full count, which gives the maximum number of tubes that can be accommodated under the conditions specified, and reduced count, due to an internally fitted impingement baffles are given for every case. Because tube counts are used in this study, from the view point of quantitative analysis, we will consider that the selection of exchanger construction type, flow arrangement, tube layout and materials have already been completed, and the sizing problem is then reduced to determine the length of HE, heat transfer surface area, baffle sizing, and baffle number. Now, specification of a shell-and-tube HE that meets the process requirements can be achieved by successive iteration. This will constitute our design method. Although this can be carried out by hand calculation, a computer program is made for this purpose. Because there are many alternative designs that would satisfy a particular duty, it is necessary to optimize the design either in terms of capital cost or running cost. Capital cost involves minimization of heat transfer surface area to meet heat transfer service while running cost involves with minimum pressure drops. Our computer program considers minimum or allowable shell-side pressure drop as constraining criteria for optimum design. The program examines a series of exchangers from tube counts and chooses the optimal design on the basis of constraining criteria, namely running cost. Calculations for heat transfer and pressure loss for fluid flowing inside tubes is relatively simple. On the other hand, because of the complex flow conditions, the associated heat transfer rate and pressure loss within the shell of the exchanger are not straightforward. The calculation procedures have evolved over the years as discussed in the introduction. In order to calculate shell-side heat transfer coefficient and pressure drop, the model given by Taborek [5] based on the Bell Delaware method is employed. Taborek version of Delaware method is more suitable for computerbased applications than BellÕs original work since correlations for the correction factors are provided. Kakacß and Liu [18] gives a detailed review for tube-side heat transfer coefficient for both laminar and forced convection flow conditions. Considering his recommendations, to calculate tube-side heat transfer coefficient for laminar flow Schl under correlation is used and, Gnielinski equation is used for transition flow in the range of 2300 < Re < 10 4 and, Petukov Kirillov correlation is employed for turbulent flow in the range of 10 4 < Re < 5 10 6 [18].

The governing equations for design problem are usually given as follows: Heat rate Q ¼ C h ðt hi T ho Þ¼C c ðt co T ci Þ ð1þ where heat capacity rate for hot or cold fluid C ¼ _mc p ð2þ Log mean temperature difference for pure counter flow DT lm;cf ¼ ðt hi T ho Þ ðt ho T ci Þ ð3þ ln½ðt hi T co Þ=ðT ho T ci ÞŠ The effective mean temperature difference for crossflow DT m ¼ F DT lm;cf ð4þ where F is correction factor for multi-pass and crossflow heat exchanger and given for two-pass shell-and-tube heat exchangers as follows: pffiffiffiffiffiffiffiffiffiffiffiffiffi R F ¼ 2 þ 1 ln½ð1 PÞ=ð1 PRÞŠ p ðr 1Þ ln½ð2 PfðR þ 1 ffiffiffiffiffiffiffiffiffiffiffiffiffi p R 2 þ 1ÞgÞ=ð2 PfðR þ 1Þþ ffiffiffiffiffiffiffiffiffiffiffiffiffi ð5þ R 2 þ 1gÞŠ where R ¼ C c ¼ ðt hi T ho Þ ð6þ C h ðt co T ci Þ and P ¼ ðt co T ci Þ ð7þ ðt hi T ci Þ Overall heat transfer coefficient 1 U f ¼ d o d i h t þ d or fi d i Heat transfer surface area Q A ex ¼ U f DT m and length of the exchanger A ex Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 1801 þ d o lnðd o =d i Þ þ R fo þ 1 2k w h s L ex ¼ ð10þ pd o N t A FOTRAN 90 code is developed based on the model described above. Baffle spaces at inlet and outlet of the exchanger are assumed to be equal for simplicity. The program allows the user to choose the shell-side fluid and also to select optimization constraints, i.e., one is minimum shellside pressure drop and the other is allowable shell-side pressure drop. The flow diagram of the computer program is illustrated in the Fig. 1. ð8þ ð9þ

1802 Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 start INPUT Flowrates, temperatures, fouling factors, tube material Select shell-side fluid; cold or hot? Select optimum design criteria; minimum or allowable shell-side pressure drop? Calculate transport properties and heat rate READ Physical size of heat exchanger from tube count file Calculate shell-side and tube side HTC Calculate T m, U f, A ex, L ex, N b, L ib Calculate shell-side pressure drop Calculate tube-side pressure drop N All exchangers are examined? Y Select the exchanger that its shell-side pressure drop is minimum or less than an allowable value PRINTOUT Q, U f, P s, P t, A ex, L ex, N t, D s, d o, P t, N b, L cb, L ib, and type of exchanger stop Fig. 1. Flow diagram of the design program. 3. Results and discussion The sample operation conditions under which the program is run are given in Table 1. The program actually selects the optimum exchanger among the three different flow arrangement, namely one-pass, two-pass, and U-tube exchangers. The program is run for both cold and hot fluid as shell-side stream to show which one gives the best result. For instance, considering minimum shell-side pressure drop as constraining criteria for optimum design as shown in Table 2, circulating cold fluid in shell-side has some advantages on hot fluid as shell stream since the former causes lower shell-side pressure drop and requires smaller heat transfer area than the

Table 1 Sample operating conditions Hot fluid Cold fluid Fluid Water Water Fouling resistance [m 2 K/W] 0.000176 0.000176 Mass flow rate [kg/s] 13.88 8.33 Inlet temperature [ C] 67 17 Outlet temperature [ C] 40 Limitations Tube material Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 1803 Maximum allowable pressure drop ¼ 12 000 Pa Carbon steel, thermal conductivity ¼ 60 W/m K Table 2 Optimum design based on minimum shell-side pressure drop criteria Cold fluid is on shell-side Hot fluid is on shell-side Type of exchanger Two-pass U-pass Shell-pressure drop [Pa] 100 947 Tube-side pressure drop [Pa] 78 56 Heat rate [W] 801 368 801 368 Total HTC [W/m 2 C] 422 80 Heat transfer area [m 2 ] 64.15 340 Exchanger (tube) length [m] 0.516 4.82 Inside shell diameter [m] 1.219 1.219 Outer tube diameter [m] 0.01905 0.031 Number of tubes 2077 706 Central baffle spacing [m] 0.258 0.548 Inlet/outlet baffle spacing [m] 0.258 0.216 Number of baffles 1 9 latterõs. As a consequent, if there are no restrictions to allocation of streams, i.e., which fluid will flow through the shell, such as fouling fluid flow, high-pressure fluid flow or corrosive fluid, in general, it is better to put the stream with lower mass flow rate on the shell-side because of the baffled space. As it is shown from Table 2, minimum shell-side pressure drop as the constraining criteria for optimum design may always not give practically good results. For example, for cold fluid as shell stream in Table 2, shell diameter and tube length of the selected exchanger that has the lowest shell-side pressure drop are 1.219 and 0.516 m respectively. It is larger in diameter and shorter in length and such an exchanger is not practical. This can be explained with central baffle spacing that has a significant effect on shell-side pressure loss. Although there is no any correlation for central baffle spacing, some recommendations are available in HEDH. The recommended baffle spacing is somewhere between 0.4and 0.6 of the shell diameter [4,5,18] for 25% baffle cut. According to this assumption, the larger the shell diameter, the larger the central baffle spacing resulting in lower pressure drop. As a result, this is why the program selects the exchanger larger in shell diameter and shorter in exchanger length as an optimum design. In order to avoid this obstacle, allowable shell-side pressure drop can be considered as the optimum design constraints since, in general speaking, tube side pressure drop is expected to be lower than that of shell-side.

1804 Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 Table 3 Optimum design based on allowable shell-side pressure (<12000 Pa) drop criteria Cold fluid is on shell-side Hot fluid is on shell-side Type of exchanger Two-pass Two-pass Shell-pressure drop [Pa] 10 836 10 602 Tube-side pressure drop [Pa] 2960 875 Heat rate [W] 801 368 801 368 Total HTC [W/m 2 C] 1383 709 Heat transfer area [m 2 ] 19.6 38.2 Exchanger (tube) length [m] 1.11 2.1 Inside shell diameter [m] 0.489 0.540 Outer tube diameter [m] 0.01588 0.0254 Number of tubes 353 227 Central baffle spacing [m] 0.197 0.243 Inlet/outlet baffle spacing [m] 0.063 0.082 Number of baffles 6 9 The heat transfer surface area will then reduce on the contrary of pressure losses. The program is extended to select, first of all, exchangers that have maximum allowable shell-side pressure drop for each type of construction, and then to choose the one of them that has the smallest surface area. By this way, we try to optimize both pressure drop and surface area. Taking 12 kpa of the maximum allowable shell-side pressure drop, for instance, and choosing cold fluid as shell stream, diameter of shell and length of the exchanger selected are 0.489 and 1.11 m, respectively as shown in Table 3. This solution is more reasonable than the previous one just mentioned above. The heat transfer surface area of the exchanger reduces almost 3.3 times comparing to that of selected based on minimum shell-side pressure for the same allocation of stream. 4. Conclusions The program selects an optimum exchanger among total number of 240 exchangers. The program is restricted to single-segmental baffle having 25% baffle cut that is most frequently used, triangular-pitch layout that results in greatest tube density. The exchanger type covers only fixed tube sheet with one-pass and two-pass, and U-tube for E-type shell. This program can be extended to different exchanger configurations, such as square pitch, 4or 6 tube-pass, etc. by inserting data from tube counts. Working fluids other than water can also be introduced easily. References [1] D.Q. Kern, Process Heat Transfer, McGraw-Hill, New York, 1950. [2] T. Tinker, Shell-side characteristic of shell-and-tube heat exchangers, Parts II, III, and I, in: Proceedings of General Discussion on Heat Transfer, Institute of Mechanical Engineers and American Society of Mechanical Engineers, London, New York, 1951, p. 89.

Y. Ali Kara, Ö. G uraras / Applied Thermal Engineering 24 (2004) 1797 1805 1805 [3] K.J. Bell, Final report of the cooperative research program on shell-and-tube heat exchangers, University of Delaware Eng. Exp. Stat. Bull. 5 (1963). [4] E.A.D. Saunders, Heat Exchangers, John Wiley & Sons, New York, 1988 (Chapter 12). [5] J Taborek, Recommended method: principles and limitations, in: G.F. Hewitt (Ed.), HEDH, Begell House, New York, 2002 (Section 3.3.3). [6] M.J.N. Wills, D Johnston, A new and accurate hand calculation method for shell-side pressure drop and flow distribution, in: 22nd National Heat Transfer Conference, HTD, vol. 36, ASME, 1984. [7] G.F. Hewitt, Flow stream analysis method for segmentally baffled shell and tube heat exchangers, in: G.F. Hewitt (Ed.), HEDH, Begell House, New York, 2002 (Section 3.3.3). [8] M. Reppich, S. Zagermann, New design method for segmentally baffled heat exchangers, Comput. Chem. Eng. 19 (Suppl.) (1995) S137 S142. [9] S.E. Gaddis, V. Gnielinski, Pressure drop on shell side of shell-and-tube heat exchangers with segmental baffles, Chem. Eng. Process. 36 (1997) 149 159. [10] S.E. Gaddis, V. Gnielinski, Druckverlust in querdurchstr omten Rohurb undelin, Vt verfahrenstechnick 17 (1988) 410 418. [11] S.E. Gaddis, V. Gnielinski, Pressure drop in crossflow across tube bundles, Int. Chem. Eng. 25 (1985) 1 15. [12] H. Li, V. Kottket, Local heat transfer in the first baffle compartment of shell-and-tube heat exchangers for staggered tube arrangement, Exp. Thermal Fluid Sci. 16 (1998) 342 348. [13] H. Li, V. Kottket, Visualization and determination of local heat transfer coefficients in shell-and-tube heat exchangers for staggered tube arrangement by mass transfer measurements, Exp. Thermal Fluid Sci. 17 (1998) 210 216. [14] H. Li, V. Kottket, Analysis of local shell-side heat and mass transfer in the shell-and-tube heat exchanger with discand-doughnut baffles, Int. J. Heat Mass Transfer 42 (1999) 3509 3521. [15] H. Li, V. Kottket, Effect of the leakage on pressure drop and local heat transfer in shell-and-tube heat exchangers for staggered tube arrangement, Int. J. Heat Mass Transfer 41 (2) (1998) 425 433. [16] H. Li, V. Kottket, Effect of baffle spacing on pressure drop and local heat transfer in shell-and-tube heat exchangers for staggered tube arrangement, Int. J. Heat Mass Transfer 41 (10) (1998) 1303 1311. [17] K.J. Bell, Delaware method for shell-side design, in: R.K. Shah, E.C. Subbarao, R.A. Mashelke (Eds.), Heat Transfer Equipment Design, Hemisphere Publishing, New York, 1988, p. 145. [18] S. Kakacß, H. Liu, Heat Exchangers, Selection, Rating, and Thermal Design, CRC Press, New York, 1998 (Chapters 3 and 8).