Computation of temperature field by cell method and comparing with commercial software

IOP Conference Series: Materials Science and Engineering PAPER Computation of temperature field by cell method and comparing with commercial software To cite this article: M Pernica et al 2020 IOP Conf. Ser.: Mater. Sci. Eng. 776 012045 View the article online for updates and enhancements. This content was downloaded from IP address 147.229.117.44 on 29/07/2020 at 13:19 Content from this work may be used under the terms of theCreativeCommonsAttribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 1 Computation of temperature field by cell method and comparing with commercial software M Pernica, T Létal, P Lošák and M Naď Department of process engineering, Faculty of mechanical engineering BUT, Technická 2896/2, 616 69 Brno, Czech Republic E-mail: [email protected] Abstract. This paper deals with the temperature field of the shell and tube heat exchanger with segmental baffles. Two different types of shell and tube heat exchangers were analysed by a numerical model for thermal-hydraulic rating called the cell method. The cell method is a numerical computational model for calculating of temperature field of a shell and tube heat exchanger with segmental baffles. A huge benefit of the cell method is especially its simplicity. The computation of temperature field by the cell method is very fast and without the necessity of powerful hardware accessories. For analyses, two different types of shell and tube heat exchangers with segmental baffles were used. First, a co-current flow heat exchanger with a floating head and second a counter-current flow heat exchanger with a fixed tubesheet. Both analysed heat exchangers are horizontal, have one tube and one shell pass and segmental baffles. The results from cell method were compared with results from the commercial software for thermal-hydraulic rating HTRI, which is one of the most widely used commercial software for solving thermal-hydraulic rating of heat exchangers. The scope of this paper is to assess how exact the cell method is and if its results are useful for a mechanical design of shell and tube heat exchanger with segmental baffles. 1. Introduction Heat exchangers are used in wide range of industries to facilitate heat transfer between two fluids at different temperatures [1]. The heat transfer is usually forced through heat transfer area by convention, conduction, radiation or combination of these phenomena [2]. Many types of the heat exchangers are used in a great number of industry branches (shell and tube, compact, plate, etc.) [3]. For proper functionality a proper design of the heat exchanger is required. The heat exchanger design may be divided into the several steps. The first step is a design specification, when client and manufacturer discuss the client needs and manufacturer possibilities. The second step is a data collection, when the designer has to collect all process data. Generation of possible design solutions is the third step of heat exchanger design. Designer is finding a proper configuration, relying on his or her previous experience. Fourth step of design is an evaluation and selection [4]. Thermal-hydraulic rating and assessment of temperature field is very important step during heat exchanger design. The proper accomplishment is crucial for the correct function of heat exchanger, especially for executing correct heat duty and then for proper choice of design options of the heat exchanger. It is possible to use a great number of analytical models or commercial software for thermal hydraulic rating of heat exchangers. The selection of calculation model depends mainly on the type of analysed heat exchanger [4]. Nowadays, CFD (computational fluid dynamics) represents the state of the art. CFD simulations can yield very accurate results, but they can be very time consuming. CFD MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 2 approach allows us to include simulation of phenomena such as condensing, evaporation or fouling of the heat exchanger which are hard to solve by analytical methods [5–7]. The thermal stresses can cause grand failure of the shell and tube heat exchanger. These eventual failures can cause operating problems or problems with safety of plant. So, it is very important to have some utility for calculation of temperature field, which is crucial for thermal stresses calculation. Unfortunately, the thermal stress is often neglected during the shell and tube heat exchanger mechanical design due to high cost of software for calculation of temperature field. This paper deals with a simple method for calculation of temperature field for shell and tube heat exchangers. Results from this method are compared with commercial software for computation of the thermal hydraulic rating HTRI. This article also highlights the problems with initial data for cell method, especially with correct determination of the overall heat transfer coefficient. 2. Cell method description This method for the temperature field calculation is useful mainly for a single-phase single pass or multi pass shell-and-tube heat exchanger with segmental baffles [8]. The part of heat exchanger between baffles makes cells (figure 1). There is a cross flow in the space between baffles, or between tube sheets and baffles. In reality, the situation is slightly different. There are a leakage and bypass streams in the shell side, which are ignored in this model [3]. Figure 1. Heat exchanger conversion for cell method. Figure 2. Cell scheme [3]. The scheme of cell is shown in figure 2. The stream 1 flows through tube side of heat exchanger, stream 2 flows across tubes in the shell side of the heat exchanger. For this description the lower heat capacity of stream 1 then stream 2 is expected. If the heat capacity premise is executed, it is possible to write system of three equations [3]: 𝑄󰇗𝑐𝑒𝑙𝑙 =𝐶𝑃1∙(𝑇12 − 𝑇11) (1) 𝑄󰇗𝑐𝑒𝑙𝑙 = −𝐶𝑃2∙(𝑇22 − 𝑇21) (2) MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 3 𝑄󰇗𝑐𝑒𝑙𝑙 = 𝐸𝐶∙𝐶𝑃1∙(𝑇21 − 𝑇11) (3) where Ec is thermal effectiveness of the cell defined as [3]: 𝐸𝐶=𝑇12 − 𝑇11 𝑇21 − 𝑇11 (4) It is convenient to use the dimensionless temperatures defined as [3]: 𝜃 = 𝑇 − 𝑇1𝑖 𝑇2𝑖 − 𝑇1𝑖 (5) Where T1i is inlet temperature of stream 1, T2i is inlet temperature of stream 2. The inlet cell temperatures for each stream are identical with the exit temperatures of the preceding cells [1]. For all cells 0 ≤ Ɵ ≤ 1 and the dimensionless inlet temperatures are Ɵ1i = 0 and Ɵ2i = 1 for tube side and shell side respectively [3]. After assessment of dimensionless temperatures, equations (1) – (3) and (5) give the dimensionless equations which must be applied for all cells [3]: 𝜃12𝑖= 𝑎 ∙ 𝜃11𝑖+ 𝑏 ∙ 𝜃21𝑖 (6) 𝜃12𝑖= 𝑒 ∙ 𝜃21𝑖+ 𝑓 ∙ 𝜃11𝑖 (7) where: 𝑎 = 1 − 𝐸𝐶 (8) 𝑏 = 𝐸𝐶 (9) 𝑒 = 1 − 𝑅 ∙ 𝐸𝐶 (10) 𝑓 = 𝑅 ∙ 𝐸𝐶 (11) 𝑅 = 𝐶𝑃1 𝐶𝑃2 (12) The cell effectiveness Ec may be expressed by [3]: 𝐸𝐶= 𝑓(𝑁𝑇𝑈𝐶,𝑅, 𝑐𝑒𝑙𝑙 𝑓𝑙𝑜𝑤 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛) (13) where NTUC is number of transfer unit and it is defined as [3]: 𝑁𝑇𝑈𝐶=𝑈 ∙ 𝐴𝐶 𝐶𝑃1 (14) where U (W m–2 K–1) is overall heat transfer coefficient, AC (m2) is heat transfer area of cell and CP1 (J kg–1 K–1)) is the heat capacity of stream 1. It is possible to calculate only one thermal effectiveness for whole analysed heat exchanger but for this paper, it was calculated for each cell separately. Just as the thermal effectiveness, values of heat capacity are calculated for each cell. The solution was obtained by an iteration method. Just as thermal effectiveness, each number of transfer unit is calculated for each cell separately for more precise results. For calculating of number of transfer unit, the heat transfer coefficient is essential. Many methods can be used for evaluation of overall heat transfer coefficient. The easiest and fastest way is to use Kern method, but many more sophisticated methods can be used. For this paper Kern method was used [4]. Cell area is derived from MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 4 Kern method where it is defined as total heat transfer area, which is divided by number of heat exchanger cells for obtain a cell area. 3. Analysed heat exchangers As mentioned above, this article is focused on the shell and tube heat exchangers with segmental baffles. Two cases of heat exchanger are solved by cell methods as well as commercial software for thermal hydraulic ratings HTRI. Results from both methods will be compared. Case 1 The co-current shell and tube heat exchanger with floating head from TEMA database [9] was analysed first (figure 3). It has one shell and one tube pass and six segmental baffles. Number of tubes is 78 and their longitudinal is 1.77 m. Cold water flows through tubes, hot air flows in the shell side. The inlet temperature of cold water is 73 °C, the air inlet temperature is 276 °C and it is being cooled down to 121 °C. The water is heating up to 77 °C. Mass flow rate of hot stream (air) is 4680 kg h–1. Geometry data are shown in table 1. Input data for thermal hydraulic rating are showed in table 2. Figure 3. Analysed heat exchanger – Case 1. Table 1. Analysed heat exchanger data – Case 1. Quantity Value Flow configuration Co-current Tube side Tube side stream Cold Tube side fluid Water Tube arrangement Triangle 30° Tube pitch 19.844 mm Tube length 1829 mm Outer tube diameter 15.875 mm Wall thickness 1.651 mm Number of tubes 78 Shell side Shell side stream Hot Shell side fluid Air Shell diameter 257.287 mm Bundle diameter 206.872 mm MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 5 Table 2. Initial data for thermal-hydraulic rating – Case 1. Quantity Notation Value Number of tube passes nT 1 Number of shell passes nS 1 Number of baffles nB 6 Baffle cut Bafcut 40 % Hot stream inlet temperature THin 276 °C Hot stream outlet temperature THout 121 °C Cold stream inlet temperature TCin 73 °C Cold stream outlet temperature TCout 77 °C Hot stream mass flow rate mH 4680 kg h–1 Initial data from table 2 are required for cell method, and for estimate of overall heat transfer coefficient U (W m–2 K–1) by Kern method. Just as overall heat transfer coefficient, the heat transfer coefficient h (W m–2 K–1) on shell side and tube side was calculated by Kern method. Kern method results for the first case of calculated heat exchangers are listed in table 3. Table 3. Kern method results – Case 1. Quantity Notation Value Mean temperature hot stream THmean 198.5 °C Mean temperature cold stream TCmean 75.0 °C Logarithmic mean temperature dTlm 103.99 °C Heat rate Q 209.20 kW Heat transfer area Aht 8.03 m2 Overall heat transfer coefficient U 250.26 W m–2 ּK–1 Tube side Mass flow rate mC 12.47 kg s–1 Fluid velocity uC 1.32 mּ s–1 Reynolds number ReC 42841.28 Tube heat transfer coefficient hC 9232.77 W m–2 K–1 Shell side Mass flow rate mH 1.32 kg s–1 Fluid velocity uH 17.05 m s–1 Reynolds number ReH 43029.34 Shell heat transfer coefficient hH 303.29 W m–2 K–1 Analysed heat exchanger has rather small number of tubes and relatively small dimensions. The overall heat transfer coefficient for case 1 is only around 250 W m–2 K–1. The heat transfer area is 8 m2 which reflects tube parameters. Relatively high value of the Reynolds number, especially in tube side, may indicate susceptibility to vibrations. On the other hand, the high speed of water in tubes, which causes high value of Reynolds number, causes higher heat transfer coefficient on tube side. When parameters of heat transfer coefficients and geometry are known, it is possible to use the cell method to calculate the temperature field. Temperature field is very useful not only during the thermalhydraulic rating, but also for structural design. Thermal stress could have detrimental effect on structure, mainly on tubes, tube sheet or shell and could cause accident. Unequal heating of flange and bolts could cause flange leakage. These are reasons why the correct calculation of temperature field is very important during the heat exchanger design. There are listed all input data for cell method in table 4. In figure 3 is shown scheme of heat exchanger which is converted to cells for cell methods. MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 6 Table 4. Cell method input data – Case 1. Quantity Notation Value Number of baffles Nb 6 Tube side passes Nt 1 Number of tubes Ntube 78 Mass flow rate of cold stream mC 1.32 kg s–1 Mass flow rate of hot stream mH 12.47 kg s–1 Inlet temperature of cold stream TCin 276 °C Inlet temperature of hot stream THin 73 °C Tube length Lt 1.829 m For proper calculation, the heat capacities of both process fluids are needed. Process fluid in tube side is water. Its initial specific heat capacity is 52285 J kg–1 K–1. In the shell side, process fluid is air and its mass heat capacity is 1370.8 J kg–1 K–1. As written above, mass heat capacity changes in each iteration step according a temperature. Just as mass heat capacity, the effectiveness of cells is changing during the iteration steps. There is list of process fluid temperatures in cells along the analysed heat exchanger in the table 5. In figure 4, there is a plot of temperature profile along the heat exchanger. Red colour represents temperature profile in shell side, blue colour represents temperature profile in tube side. Table 5. Temperature field results (°C) – Case 1. Tubes Tin Tcell1 Tcell2 Tcell3 Tcell4 Tcell5 Tcell6 Tout 276.0 248.30 224.49 204.0 186.39 171.24 158.21 146.77 Shell Tin Tcell1 Tcell2 Tcell3 Tcell4 Tcell5 Tcell6 Tout 73.0 73.73 74.35 74.88 75.35 75.74 76.09 76.39 Figure 4. Heat exchanger temperature field – Case 1. Results shows that outlet temperature in tube side is rather similar to inlet temperature which was expected (table 3). However, the shell side outlet temperature indicates more than 20 °C difference in compare with initial data. It could be caused by using Kern method for estimation of the shell side condition. Kern method does not reflect bypass streams and leakage in shell side which can influence results negatively. The graph of temperature field is shown in figure 4. Red line represents hot stream, blue line represents cold stream. Hot stream shows the massive decrease trend which is opposite to cold stream. The cold stream trend is almost constant along the analysed heat exchanger. MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 7 Case 2 The second analysed case is a shell and tube heat exchanger with segmental baffles. It has 61 tubes welded in the fixed tubesheet. Flow configuration is counter-current. Process fluid is water in the tube side as well as in the shell side. The inlet temperature of water to shell side is 95 °C, the outlet temperature is 88 °C. In the tube side, the water is heated up from 32 to 37 °C. Other heat exchanger data are listed in table 6. Figure 5. Analysed heat exchanger – Case 2. Table 6. Analysed heat exchanger data – Case 2. Quantity Value Flow configuration Co-current Tube side Tube side stream Cold Tube side fluid Water Tube arrangement Triangle 30° Tube pitch 26.0 mm Tube length 954.0 mm Outer tube diameter 20.0 mm Wall thickness 2.0 mm Number of tubes 61 Shell side Shell side stream Hot Shell side fluid Air Shell diameter 284.24 mm Bundle diameter 232.37 mm Table 7. Initial data for thermal-hydraulic rating – Case 2. Quantity Notation Value Number of tube passes nT 1 Number of shell passes nS 1 Number of baffles nB 4 Baffle cut Bafcut 45 % Hot stream inlet temperature THin 95 °C Hot stream outlet temperature THout 88 °C Cold stream inlet temperature TCin 32 °C Cold stream outlet temperature TCout 37 °C Hot stream mass flow rate mH 7200 kg h–1 MMS2019 IOP Conf. Series: Materials Science and Engineering 776 (2020) 012045 IOP Publishing doi:10.1088/1757-899X/776/1/012045 8 Initial data for calculation of the overall heat transfer coefficient are listed in table 7. For cell method, it is crucial to estimate overall heat transfer coefficient. In this case by Kern method, its results are listed in next table 8. Table 8. Kern method results – Case 2. Quantity Notation Value Mean temperature hot stream THmean 91.5 °C Mean temperature cold stream TCmean 34.5 °C Logarithmic mean temperature dTlm 56.99 °C Heat rate Q 58.91 kW Heat transfer area Aht 2.08 m2 Overall heat transfer coefficient U 497.25 W m–2 ּK–1 Tube side Mass flow rate mC 2.82 kg s–1 Fluid velocity uC 0.23 mּ s–1 Reynolds number ReC 5054.67 Tube heat transfer coefficient hC 1231.78 W m–2 K–1 Shell side Mass flow rate mH 2.0 kg s–1 Fluid velocity uH 0.19 m s–1 Reynolds number ReH 8457.88 Shell heat transfer coefficient hH 2325.43 W m–2 K–1 From Kern method results, it is shown that case 2 has significantly smaller heat transfer area, which has great impact on overall heat transfer coefficient. However, these cases are not comparable, because of the different process fluids, flow rates and velocities. In table 8, it is shown that mass flow rate is relatively small just as the velocity of process fluids. Temperature field data obtained using cell method are given in table 9. Table 9. Cell method input data – Case 2. Quantity Notation Value Number of baffles Nb 5 Tube side passes Nt 1 Number of tubes Ntube 61 Mass flow rate of cold stream mC 2.0 kg ּs–1 Mass flow rate of hot stream mH 2.82 kg ּs–1 Inlet temperature of cold stream TCin 95 °C Inlet temperature of hot stream THin 32 °C Tube length Lt 0.954 m It was operated equally to case 1 with physical data of process fluids. The initial mass heat capacity of water in tube side was 4178 J kg–1 K–1, for shell side 4212 J kg–1 K–1. Cell methods results are listed in table 10. In figure 6 is shown temperature field of analysed heat exchanger. Table 10. Temperature field results (°C) – Case 2. Tubes Tin Tcell1 Tcell2 Tcell3 Tcell4 Tout 32.0 33.33 34.67 36.03 37.39 38.77 Shell Tin Tcell1 Tcell2 Tcell3 Tcell4 Tout 95.0 93.07 91.16 89.26 87.39 85.53