Research Paper ANALYSIS AND OPTIMIZATION OF PLATE-FIN HEAT EXCHANGER USING COMPUTATIONAL FLUID DYNAMICS AND RESPONSE SURFACE METHODOLOGY R. Pachaiyappan, S. Gopalakannan Address for Correspondence 1 Department of Mechanical Engineering, Adhiparasakthi Engineering College, Melmaruvathur, India ABSTRACT The scope of this paper is to find the optimal values of design constrains in a Plate-fin heat exchanger. The design constraints chosen for optimization were Reynolds number, core length, fin height and core area. Computational Fluid Dynamics (CFD) (fluent) was used for analysis and Response Surface Method (RSM) has been fixed for Optimization. The results from CFD analysis have feed into RSM. A research on augmenting heat transfer rate in heat exchanger has been increasing. By fixing Nusselt number (maximum heat transfer) and friction factor (minimum pressure drop) as performance factors in RSM, optimization has done. Chosen design constraints were fixed as factors. Design expert 7.0 software used for proceeding RSM. The optimal values from optimization have found as Reynolds number 1600, Core length 1.24 m, Fin height and Core area 0.04 m 2. KEYWORDS: Plate-fin heat exchanger, RSM, CFD, Simulation of heat exchanger. INTRODUCTION A heat exchanger is heat transfer equipment that is used to transfer thermal energy between two or more fluids which are at different available temperature and at thermally contact with each other. There is no external heat and work interaction to that device. The classic example of a heat exchanger is found in an internal combustion engine in which a circulating fluid known as engine coolant flows through radiator coils and air flows past the coils, which cools the coolant and heats the incoming air. The fluids are separated by a surface, named as heat transfer surface. Heat exchanger is extensively used in refrigeration, power, air conditioning, process, petroleum, environmental engineering, manufacturing, food processing, transportation and other industries [1, 2]. RSM is more accuracy optimization method than other methods. Factors and responses have fixed before proceeding RSM. Level and number of each factor have an impact on number of runs [3-5]. CFD stands for Computational Fluid Dynamics. CFD is computational tool used in design and development of automobile, Gas turbine and various industries [6, 7]. CFD can be helpful to know about fluid flow, heat distribution, structural analysis of component at low cost. No needs of experimental equipment, saving material and labour cost, less time consuming for analysis are major advantage. Numerical Calculation is pre-programmed in software. With aid of CFD analysis, Fluid misdistribution, fouling, pressure drop, thermal analysis in design and optimization phase of heat exchanger can be predicted [8, 9]. It is speedy solution method and not expensive. The creativity of design will accommodate on heat exchanger and produces result as per construction and input. Some of CFD codes are ANSYS, CFX, FLUENT, ICEM. Here fluent has been chosen. Gopalakannan and Senthilvelan [10] conducted an experiment on Application of response surface method on machining of Al-SiC nano-composites. Optimization was accomplished by RSM of machining parameters such as voltage, pulse current; pulse on time and off time. RSM has completed for four factors at three levels by conducting 30 experiments. Optimized parameters are produced. Kocioglu et al. [11] carried out experimental investigation for optimization of design parameters in a rectangular duct with plate-fin heat exchanger by Taguchi method. Experiments were conducted for various design constraints. Optimization was done by Taguchi. The process of Taguchi method has been studied. Optimal values by Taguchi method of design parameters were found to achieve minimum pressure drop (friction factor) and maximum heat transfer (Nusselt number). Muhammad Mahmood Aslam Bhutta et al. [12] reviewed on the application of CFD in various heat exchangers design. CFD codes are FLUENT, CFX, STAR CD, FIDAP, ADINA, PHOENICS, CFD2000, etc. Using CFD analysis, fluid flow and thermal characteristics of heat exchanger will be analyzed. Non-uniformity in fluid flow is the foremost cause to create poor performance in Heat exchanger. Pressure drop suffers the heat transfer rate. Thermal analysis includes effect of physical characteristic and thermal coefficients. Heat exchanger performance is through the study of parameters like Nusselt number, Dean s number, Prandtl number (Pr), Friction factor (f), etc. With aid of CFD analysis, Fluid misdistribution, fouling, pressure drop, thermal analysis in design and optimization phase of heat exchanger can be predicted. It is speedy solution method and not expensive. The creativity of design will accommodate on heat exchanger and produces result as per construction and input. There are many models are used for analysis such as k-epsilon, SST k-omega turbulence model. Finally this review paper concluded that CFD is the efficient tool for predicting the performance and behavior of heat exchanger. EXPERIMENTAL DESIGN From observation and investigation of various journals and papers, Literature survey has done on the area of Plate-fin heat exchanger, optimization process (especially Response Surface method) and numerical analysis. While fixing plate-fin heat exchanger, dimensions of heat exchanger and fin are considered as important thing. Operating parameters like operating pressure, temperature, mass flow rate of hot and cold flow were fixed from literature survey. Physical setup has been set to perform under fixed operating conditions. The optimization had done by obtained values from CFD analysis. Before proceeding analysis, Parameters have been fixed.
Friction factor and Nusselt number were chosen as response and Reynolds number, core length of heat exchanger, fin height and core area were chosen as factor. On the basis of parameters need for optimization process, CFD analysis was done. Design expert 7.0 has been used for optimization process. The heat exchanger was designed as per Jainender Dewatwal [13]. The heat exchanger material was chosen as Aluminium and Nitrogen was chosen as flowing fluid. CCD (Central composite design) technique was chosen for experiment. Factors range at two levels (+1, -1) is illustrated in Table 1. Face centred CCD contains 30 runs which are shown in Table 2. Table 1. Factors with their level Parameter s Reynolds Labels Levels -1 0 1 A 1100 1350 1600 Core length B 1.237 1.931 2.625 Fin (m) length C 0.07 0.0815 0.093 Core area D 0.018489 0.031187 0.043884 CFD (m(fluent) 2 ) simulation starts with designing (modelling) the setup. Modelling of setup was drawn on ANSYS workbench. From table 1, the core length, fin height and core area are design parameters which were drawn for optimization. After completion of modelling, meshing was executed. Fine mesh was preferred for analysis to produce more accuracy. All elements in meshing had quad dominant elements. The parts on geometry should be named for further process and identification. Boundary conditions were entered for analysis and results were executed. Figure 1 shows the Geometry drawn on fluent design modular. The image itself reveals the design parameter on which dimension it drawn. Figure 2 shows the meshing and figure 3 is the result from fluent as plot. Figure 1 Heat exchanger on ANSYS Figure 2 Meshing of heat exchanger Figure 3 Result from fluent RESULTS AND DISCUSSION Friction factor and Nusselt number have been fixed as performance parameters for this study. These parameters were calculated from following formulae by applying results from analysis. Friction factor, (1) Nusselt number, (2) Where, Δp is the pressure difference between upstream and downstream (bar ); ρ is the density of fluid (kg/m 3 ); h is the heat convective coefficient (W/m 2 K); k is the thermal conductivity of material (W/mK); L is the length of core (m); U is the velocity of flow (m/s); H is the height of core (m). Table 3 and Table 4 shows the ANOVA table of friction factor and Nusselt number respectively. The model is significant when Prob>F values are less 0.05. In this project, Table 3 and Table 4 clearly show that model is significant. Adequate Precision (AP) value should be more 4 for navigating the model to design space. Here, AP= 6.011 for friction factor, AP=1331.565 for Nusselt number The response equations of friction factor and Nusselt number are shown below. Friction factor = +0.28-0.048*A - 9.457E -3 *B - 8.064E -3 *C + 0.11*D + 7.911E -3 *A*B - 2.686E -3 *A*C - 0.040*A*D-9.004E -3 *B*C + 1.226E -3 * B*D - 2.369E -3 *C*D - 6.894E -3 *A 2-0.084*B 2-0.062*C 2 + 0.16*D 2 Nusselt = +6.11 + 0.10*A - 0.21*B + 0.0*C + 0.12*D - 5.581E -3 *A*B + 0.000*A*C +3.208E -3 *A*D + 0.000*B*C-6.437E -3 *B*D + 0.000*C*D - 8.178E -3 *A 2 + 0.043*B 2-1.017E -4 *C 2-0.023*D 2 Figure 4 shows the response graphs of friction factor over a design constrains (Reynolds number, Core length, Fin height, Core area). Figure 4.(a) & 4.(b) show clearly that friction factor value decreases with increasing Reynolds number. Friction factor value increases with Core length upto 1.93 m and then it decreases. From Figure 4.(b), friction factor value increases with Fin height upto 0.08 m and then it decreases. Figure 4.(c) shows that friction factor value decreases with Core area upto 0.03 m2 and then it increases. Figures 4.(d), 4.(e), 4.(f) confirm the variations of factors with friction factor.
Table 2 Design layout and analytical result Run Factor 1 A:Reynolds Factor 2 B:Core length (m) Factor 3 C:Fin height (m) Factor 4 D:Core area (m 2 ) Response 1 friction factor Response 2 Nusselt 1 1600 1.237 0.07 0.043884 0.278571 6.559669 2 1350 1.931 0.0815 0.031187 0.227575 6.106456 3 1100 2.625 0.07 0.018489 0.21952 5.708313 4 1600 2.625 0.093 0.018489 0.182791 5.896227 5 1600 1.237 0.093 0.018489 0.20508 6.303551 6 1350 1.237 0.0815 0.031187 0.253723 6.356295 7 1350 1.931 0.0815 0.031187 0.227575 6.106456 8 1600 1.237 0.093 0.043884 0.278571 6.559669 9 1350 1.931 0.0815 0.043884 0.778226 6.200267 10 1350 1.931 0.0815 0.031187 0.227575 6.106456 11 1350 1.931 0.0815 0.018489 0.213586 5.967273 12 1100 2.625 0.07 0.043884 0.419938 5.925853 13 1600 1.237 0.07 0.018489 0.205088 6.303551 14 1100 1.237 0.07 0.018489 0.234037 6.095164 15 1100 2.625 0.093 0.043884 0.431919 5.925853 16 1600 1.931 0.0815 0.031187 0.242333 6.199775 17 1100 1.237 0.07 0.043884 0.479687 6.336601 18 1350 1.931 0.093 0.031187 0.326358 6.106456 19 1600 2.625 0.07 0.018489 0.173339 5.896227 20 1100 1.237 0.093 0.043884 0.479687 6.336601 21 1600 2.625 0.07 0.043884 0.37378 6.124747 22 1100 2.625 0.093 0.018489 0.156986 5.708313 23 1350 1.931 0.0815 0.031187 0.227575 6.106456 24 1350 2.625 0.0815 0.031187 0.24917 5.943486 25 1100 1.931 0.0815 0.031187 0.41513 5.996985 26 1100 1.237 0.093 0.018489 0.181082 6.095164 27 1350 1.931 0.0815 0.031187 0.227575 6.106456 28 1350 1.931 0.0815 0.031187 0.227575 6.106456 29 1600 2.625 0.093 0.043884 0.217851 6.124747 30 1350 1.931 0.07 0.031187 0.221522 6.106456 Table 3 ANOVA table for friction factor Source Sum of Squares DF Mean Square F p Model 0.360264 14 0.025733 2.914384 0.0242 A-Reynolds 0.041144 1 0.041144 4.659773 0.0475 B-Core Length (m) 0.00161 1 0.00161 0.182336 0.6754 C-Fin Height (m) 0.001171 1 0.001171 0.132573 0.7209 D-Core Area (m^2) 0.214888 1 0.214888 24.33699 0.0002 AB 0.001001 1 0.001001 0.113419 0.7410 AC 0.000115 1 0.000115 0.013073 0.9105 AD 0.025371 1 0.025371 2.873388 0.1107 BC 0.001297 1 0.001297 0.146913 0.7069 BD 2.41E-05 1 2.41E-05 0.002725 0.9591 CD 8.98E-05 1 8.98E-05 0.010169 0.9210 A^2 0.000123 1 0.000123 0.013945 0.9076 B^2 0.018359 1 0.018359 2.079259 0.1699 C^2 0.009859 1 0.009859 1.116527 0.3074 D^2 0.06656 1 0.06656 7.538252 0.0150 Residual 0.132445 15 0.00883 Lack of Fit 0.132445 10 0.013245 Pure Error 0 5 0 Cor Total 0.492709 29
Table 4 ANOVA table for Nusselt number Source Sum of Squares DF Mean Square F p Model 1.202201 14 0.085872 105311.2 < 0.0001 A-Reynolds 0.187949 1 0.187949 230497.1 < 0.0001 B-Core Length (m) 0.757474 1 0.757474 928952 < 0.0001 C-Fin Height (m) 0 1 0 0 1.0000 D-Core Area (m^2) 0.249742 1 0.249742 306278.5 < 0.0001 AB 0.000498 1 0.000498 611.1707 < 0.0001 AC 0 1 0 0 1.0000 AD 0.000165 1 0.000165 201.8899 < 0.0001 BC 0 1 0 0 1.0000 BD 0.000663 1 0.000663 813.0005 < 0.0001 CD 0 1 0 0 1.0000 A^2 0.000173 1 0.000173 212.5005 < 0.0001 B^2 0.004865 1 0.004865 5966.299 < 0.0001 C^2 2.68E-08 1 2.68E-08 0.032892 0.8585 D^2 0.001345 1 0.001345 1650.024 < 0.0001 Residual 1.22E-05 15 8.15E-07 Lack of Fit 1.22E-05 10 1.22E-06 Pure Error 0 5 0 Cor Total 1.202213 29 Figure 4 Response graph for friction factor
Figure 5 shows the response graphs of Nusselt number over a design constrains (Reynolds number, Core length, Fin height, Core area). Figure 5.(a) & 5.(b) show clearly that Nusselt number value increases with increasing Reynolds number. From Figure 5.(b), Nusselt number value decreases with increasing Core length. Figure 5.(c) shows clearly Nusselt number value increases with increasing Core area. Figures 5.(d), 5.(e), 5.(f) confirm the variations of factors with Nusselt number. The target of Optimization is to find a appropriate set of conditions that will meet goals. Table 5 shows the ranges and responses for desirability. Here, Reynolds number, Core length, Fin length, Core area is in is in range. Friction factor should be minimum and nusslet number should be maximum for augmenting heat transfer rate. The appropriate set of conditions that have highest desirability value is elected as optimum value. The highest desirability value in Table 6 is 0.972377. Therefore this set of conditions has been concluded as optimum value. Figure 6 shows the desirability graph of Optimization. Figure 5 Response graph for Nusselt number Figure 6 Desirability graph
Name Table 5 Range and responses for desirability Lower Upper Lower Upper Goal Limit Limit Weight Weight Importance Reynolds is in range 1100 1600 1 1 3 Core Length (m) is in range 1.237 2.625 1 1 3 Fin Height (m) is in range 0.07 0.093 1 1 3 Core Area (m 2 ) is in range 0.018489 0.043884 1 1 3 Friction factor Minimize 0.156986 0.778226 1 1 3 Nusselt Maximize 5.708313 6.559669 1 1 3 Table 6 Optimum value selection Reynolds Core Length (m) Fin Height (m) Core Area (m^2) friction factor Nusselt Desirability 1 1600 1.24 0.09 0.04 0.156984 6.513284 0.972377 Selected 2 1600 1.24 0.09 0.04 0.156986 6.512481 0.971892 3 1599.5 1.24 0.09 0.04 0.156982 6.511702 0.971421 4 1599.74 1.24 0.07 0.04 0.156982 6.510881 0.970924 5 1600 1.24 0.07 0.04 0.156984 6.508945 0.969752 6 1600 1.24 0.07 0.04 0.156989 6.508692 0.969596 7 1600 1.24 0.07 0.04 0.150684 6.507147 0.968662 8 1586.57 1.24 0.09 0.04 0.156986 6.506266 0.968128 9 1599.31 1.24 0.09 0.04 0.156983 6.505212 0.967489 10 1585.72 1.24 0.07 0.04 0.156984 6.503615 0.966519 11 1596.77 1.24 0.07 0.04 0.156982 6.503038 0.966168 12 1579.98 1.24 0.09 0.04 0.15698 6.500011 0.964327 13 1599.78 1.26 0.09 0.04 0.157245 6.499561 0.963851 14 1600 1.24 0.09 0.04 0.138544 6.496563 0.962225 15 1560.86 1.24 0.07 0.04 0.162919 6.493069 0.955494 16 1599.73 1.24 0.08 0.03 0.158054 6.483155 0.953185 17 1600 1.24 0.08 0.03 0.156986 6.481288 0.952855 18 1599.95 1.24 0.08 0.03 0.160964 6.480034 0.949029 19 1600 1.24 0.08 0.03 0.156995 6.474114 0.948416 20 1600 1.24 0.08 0.03 0.156989 6.47301 0.947737 21 1599.86 1.24 0.08 0.03 0.157002 6.472072 0.947146 22 1523.13 1.24 0.07 0.04 0.156994 6.469353 0.945465 23 1597.78 1.24 0.09 0.04 0.20333 6.53067 0.945452 24 1599.99 1.24 0.07 0.03 0.079042 6.44206 0.928362 25 1457.62 1.24 0.09 0.04 0.183204 6.447541 0.911949 26 1430.38 1.24 0.07 0.03 0.156989 6.415569 0.911447 27 1598.3 1.48 0.09 0.03 0.156988 6.386984 0.892839 28 1320.07 1.24 0.07 0.03 0.156975 6.348261 0.866995 29 1600 2.33 0.07 0.04 0.22411 6.144486 0.675996 CONCLUSION Analysis and Optimization of plate-fin heat exchanger has done in this research. CFD (fluent) was an analyzing tool and Design expert 7.0 was an optimization tool. The experiment was carried out using face centered central composite design of response surface method (RSM) by conducting 30 experiments for two factors at three levels. The investigation on effects of Reynolds number, Core length, fin height and Core area on friction factor and Nusselt number have done. Response graphs were obtained and it clearly explains the significances of design constrain over a performance parameters.
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