Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 61 (2014) 799 – 802
The 6th International Conference on Applied Energy – ICAE2014
Prediction of temperature distribution in shell-and-tube heat exchangers Guo-yan Zhou*, Ling-Yun Zhu, Hui Zhu, Shan-tung Tu, Jun-jie Lei Key Laboratory of Pressurized System and Safety(MOE), School of Mechanical and Power Engineering East China University of Science and Technology, Shanghai 200237 Abstract On the basis of the differential theory, an accurate and simplified model for predicting temperature distribution in the shell-and-tube heat exchanger is proposed. According to the baffle arrangement and tube passes, the heat exchanger is divided into a number of elements with tube side current in series and shell side current in parallel. Two examples of BEU and AES heat exchangers with single-phase fluid are analyzed to demonstrate the application and accuracy of the proposed model in temperature distribution prediction, compared with the Cell model and HTRI method. The results show that the proposed model reproduces the temperature distribution given by the HTRI solution on the tube side flow with 0.19% accuracy for the BEU heat exchanger and 0.35% for the AES heat exchanger. It indicates that the prediction of the temperature distribution by the new model agrees reasonably well with that by HTRI method. © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2014 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and/or peer-review under responsibility of ICAE Peer-review under responsibility of the Organizing Committee of ICAE2014
Keywords: temperature distribution ; differential theory ; shell-and-tube heat exchanger ; single phase
1. Introduction The traditional process design of heat exchangers is based on the physical property under qualitative temperature of whole heat exchanger, which is relatively simple. However, when the mean temperature difference (EMD) of hot and cold fluid gets bigger, the fluid property changes significantly. The heat transfer area designed by this method will be large or small. In fact, fluid temperature changes along with heat exchanger length. The heat transfer coefficient and pressure are hence different at different everywhere in heat exchangers. So, it is particularly important to divide the heat exchanger into several segments to calculate the temperature accurately.
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[email protected].
1876-6102 © 2014 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of ICAE2014 doi:10.1016/j.egypro.2014.11.968
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With the development of physical property database, like ASPEN and PRO II, it is more convenient to accurately calculate the local temperature distribution by HTRI and HTFS+. But the detailed calculation procedure is not open. So, many studies have been carried out to predict heat exchanger temperature distribution. Gaddis and Schlunder [3-4] proposed a Cell model to calculate the temperature distribution and optimize heat exchangers. Based on the Cell model, Mikhailov and Ozisik [5] proposed a finite element method(FEM) for the calculation and it was proved to be more accurate by comparison with the theoretical results. It was improved laterly by Ravikumakur [6-7] and applied to the design of the condenser taking the temperature-dependent thermal properties into account [8]. Egwanwo [9] further verified it by a program source code in Qbasic with the backward substitution method. Heicunhuzhi [10] proposed a differential method to analyze the temperature distribution of heat exchangers. However, all the above methods can not design the heat exchanger precisely and satisfy the engineering requirement. In the present paper, based on the differentiation, a new simplified model is proposed to calculate the temperature distribution of heat exchanger. Taking the 1-2 BEU and AES type heat exchanger as examples, the feasibility and accuracy of this method is verified by the comparison with Cell model and HTRI program. 2. Model description
Fig.1 (a) 1-2 type shell-and-tube heat exchanger, (b) schematic diagram of modules
Taking one 1-2 type heat exchanger with baffle plate as an example (Fig.1). The heat exchanger is divided into ( Nb + 1) N s units and every unit is then divided into n ( N b + 1) subunits. If the baffles are fewer, equidistant units can be divided along the tube length. The tube-side fluid flows through each subunit, while the shell-side fluid flows through each unit. Where Nb is the baffle number, Ns the number of shell pass, n the number of tube pass. To simplify the calculation, the following assumptions have been made: 1) Overall heat transfer coefficient U, mass flow rate and the specific heat are constant. 2) The shell-side fluid is uniform on every cross sections, on which the temperature is also uniform. 3) When the baffle is enough [11], the MTD Δtm of the subunit is definded by the arithmetic mean. For a subunit in the x unit, the heat transfer equation of the shell-side and tube-side fluids are written as S Q = U x ( Tx − t I′ ) (1) n Q = Ct ( tI′ − tI ) (2) Then the input temperature is obtained for two adjacent subunits as follows: S S tI = tI′ − U x ( Tx − tI′ ) , tII = tII′ − U x (Tx − tII′ ) nCt nCt According to the the heat balance, the inlet temperature of the shell-side unit is obtained C T = T1 − t ( tI − tII ) Cs
(3)
(4)
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where Q is thermal duty, W; Sx heat transfer area of x unit, m2; T and Tx inlet and outlet temperature of the shell-side unit, K; t I ( t II )and t I′ ( t II′ ) the inlet and outlet temperature of the tube-side subunit (neighbour subunit), K; Ct and Cs are heat capacity flow rate on tubeside and shellside respectively, W⋅k-1. Boundary conditions of equations (3) and (4) are t I = t2 S =0 , t II = t1 S = 0 , Tx = T2 S = 0 ; t I′ = t I S = S , 1 t II′ = tII S = S , Tx = T S = S 1 1 The initial overall heat transfer coefficient can be assumed as: Q U req = S ⋅ Δt m where Ureq is required heat transfer coefficient, W⋅m-2⋅k-1; S total heat transfer area, m2. n The calculation will converge when tI ≥ tII , T ≈ T1 , S = ¦ Sn . After the first iteration, U req should be n =1 reduced properly if tI < tII . Otherwise, U req should be increased. 3. Model verification and discussion 3.1. Case of single-phase flow in tube side
Taking the 1-2 BEU type heat exchanger in software HTRI 5.x as case. The inlet/outlet temperature of shell-side process fluid are 298/478K, the flow rate is 0.536 kg·s-1. For the tube-side oil, they are 583/553K and 1.922kg·s-1, respectively. The temperature distribution of heat exchanger is calculated by present model, Cell model and HTRI program respectively. The tube-side and shell-side temperature distributions are calculated and shown in Figs. 2 and 3 respectively. The results show that the temperature calculated by the present model is much closer to that from the HTRI program. The Maximum and minimum deviations are 1.74% and 0.19% respectively. It implies that the temperature distribution of 1-2 BEU type heat exchanger calculated by present paper can meet the accuracy requirement.
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3.2. Case of single-phase flow in shell side
Another AES heat exchanger case is cited from the reference[13]. The inlet/outlet temperature of shellside Kerosene fluid are 472/394K, the flow rate is 5.67s-1. For the tube-side oil, they are 311K and 18.9 kg·s-1, respectively. The temperature distribution calculated by present model, Cell model and HTRI program are shown in Figs. 4 and 5. It can be seen that the temperature on tube side calculated by present model are much closer to that by HTRI. The maximum deviation is 0.35%. The maximum deviation between the calculated tubeside temperature from Cell model and from HTRI program is 6.44%. From Fig. 5, the calculated temperature by present model and Cell model agree well with that by HTRI. The maximum deviation between the results from present model and HTRI is -0.44%. The maximum deviation between the results from Cell model and HTRI is 1.69%.
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From the above analysis, it is indicated that the present method predicts the temperature distribution more accurately. In addition, it should be pointed out that Cell model needs to consider many factors[4], and the calculation procedure is much more complex. 4. Conclusions In the present paper, a simple and accurate temperature predicting model is developed for shell-andtube heat exchangers based on the differential method. Two engineering cases have been introduced and the results show that the calculated temperature is more accurate than that by Cell model and agrees well with that by HTRI program. It should be noted that the proposed model can be successfully used for all shell-and-tube heat exchangers with straight tube or U-tube types. While the Cell model is limited to predict the shell side temperature distribution of shell-and-tube heat exchangers with straight tubes. References [1] Liu W, Deng FY. Heat transfer design manual. 2nd ed. Beijing: China Petrochemical Press, 2008: 287. [2] Yuan JP. Theoretical and experimental study on shell-and-tube heat exchangers by cell method based on Bell algorithm. Shanghai: East China University of Science and Technology, 2009. [3] Gaddis ES, Schlünder, EU, Temperature distribution and heat exchange in multipass shell-and-tube exchangers with baffles. Heat Transfer Engineering, 1979, 1(1):43-52. [4] VDI Gesellschaft. VDI Heat Atlas. 2nd ed. Springer, 2010: 1586. [5] Mikhailov MD, Ozisik MN. Finite element analysis of heat exchangers. Heat exchangers, thermal and hydraulic fundamentals and design (Kakac s, Bergles A E and Mayinger, Eds.). Washington: Hemisphere, 1981. [6] Ravikumaur SG, Seetharamu KN, and Aswathanarayana PA. Application of finite elements in heat exchangers. Communications in Applied Numerical Method, 1986, 2: 229-234. [7] Ravikumaur SG, Seetharamu KN, Aswatha Narayana PA. Finite Element analysis of shell and tube heat exchanger. Comm. Heat Mass Transfer, 1988, 15: 151-163. [8] Moorthy CMD, Ravikumaur SG, Seetharamu KN, et al. FEM application in phase change exchangers. Warme and Stoffubertragung, 1991, 26: 137-140. [9] Egwanwo V, Lebele-Alawa BT. Prediction of the temperature distribution in a shell and tube heat exchanger using finite element model. Canadian Journal on Mechanical Science and Engineering, 2012, 3: 72-82. [10] Varma A, Morbidelli M. Mathematical Methods in Chemical Engineering. New York, Oxford Univeristy Press, 1997 [11] Shah RK. Influence of a einite number of baffles on shell-and-tube heat exchanger performance. Heat Transfer Engineering, 1997, 18: 82-94. [12] Lan Z, Ma XH, Zhou XD et al. Transition condensation heat transfer model with liquid-solid surface free energy difference effect. Journal of Chemical Industry and Engineering. 2006, 57: 2536-2542.(in Chinese) [13] Serth RW. Process Heat Transfer. Elsevier Ltd., 2007: 770. [14] Tubular Exchanger Manufacturers Association, Standards of the tubular exchanger manufacturers association, 9th ed., TEMA, New York: 2007.
Biography Dr. Guo-yan Zhou is an Associate Professor of Mechanical Engineering and now working at East China University of Science and Technology. She received her Ph. D. degree from the same university in 2007. Her interests of research include MCMS, development and optimization of compact heat exchanger and advanced manufacturing technology, etc.
