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 24 August 2003; accepted 23 December 2003 Available online 4 February 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 2004 Elsevier 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: [email protected] (Y. Ali Kara).

1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2003.12.014

¨ . G€uraras / Applied Thermal Engineering 24 (2004) 1797–1805 Y. Ali Kara, O

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Nomenclature A C cp d F h k L m_ N Q R T Pt U DP DT

area (m2 ) heat capacity (W/K) specific heat (J/kg K) tube diameter (m) correction factor for multi-pass and crossflow heat exchanger convective heat transfer coefficient (W/m2 K) thermal conductivity (W/m K) length (m) mass flow rate (kg/s) number heat rate (W) thermal resistance temperature (°C) tube pitch overall heat transfer coefficient (W/m2 K) pressure drop (Pa) 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.

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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

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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 < 104 and, Petukov–Kirillov correlation is employed for turbulent flow in the range of 104 < Re < 5
106 [18].

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The governing equations for design problem are usually given as follows: Heat rate Q ¼ Ch ðThi  Tho Þ ¼ Cc ðTco  Tci Þ

ð1Þ

where heat capacity rate for hot or cold fluid ð2Þ

_ p C ¼ mc Log mean temperature difference for pure counter flow DTlm;cf ¼

ðThi  Tho Þ  ðTho  Tci Þ ln½ðThi  Tco Þ=ðTho  Tci Þ

ð3Þ

The effective mean temperature difference for crossflow DTm ¼ F DTlm;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 R2 þ 1 ln½ð1  P Þ=ð1  PRÞ pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ F ¼ ðR  1Þ ln½ð2  P fðR þ 1  R2 þ 1ÞgÞ=ð2  P fðR þ 1Þ þ R2 þ 1gÞ where R¼

Cc ðThi  Tho Þ ¼ Ch ðTco  Tci Þ

ð6Þ

P¼

ðTco  Tci Þ ðThi  Tci Þ

ð7Þ

and

Overall heat transfer coefficient Uf ¼

1 do do Rfi do lnðdo =di Þ 1 þ þ þ Rfo þ 2kw hs di ht di

ð8Þ

Heat transfer surface area Aex ¼

Q Uf DTm

ð9Þ

and length of the exchanger Lex ¼

Aex pdo Nt

ð10Þ

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.

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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 ∆Tm, Uf, Aex, Lex, Nb, Lib

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, Uf, ∆ Ps, ∆ Pt, Aex, Lex, Nt, Ds, do, Pt, Nb, Lcb, Lib, 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

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Table 1 Sample operating conditions Hot fluid

Cold fluid

Fluid Fouling resistance [m2 K/W] Mass flow rate [kg/s] Inlet temperature [°C] Outlet temperature [°C]

Water 0.000176 13.88 67 –

Water 0.000176 8.33 17 40

Limitations Tube material

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 Type of exchanger Shell-pressure drop [Pa] Tube-side pressure drop [Pa] Heat rate [W] Total HTC [W/m2 °C] Heat transfer area [m2 ] Exchanger (tube) length [m] Inside shell diameter [m] Outer tube diameter [m] Number of tubes Central baffle spacing [m] Inlet/outlet baffle spacing [m] Number of baffles

Cold fluid is on shell-side

Hot fluid is on shell-side

Two-pass 100 78 801 368 422 64.15 0.516 1.219 0.01905 2077 0.258 0.258 1

U-pass 947 56 801 368 80 340 4.82 1.219 0.031 706 0.548 0.216 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 0.4 and 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.

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Table 3 Optimum design based on allowable shell-side pressure (