Two-phase mixture numerical and soft computing-based simulation of forced convection of biologically prepared water-silver nanofluid inside a double-pipe heat exchanger with converging sinusoidal wall: Hydrothermal performance and entropy generation analysis
Introduction
The curved tubes have been proven to have a high heat transfer coefficient and thereby be efficient in heat recovery processes, refrigeration, air conditioning, etc. [1]. Li et al. [2] investigated the hydrothermal behavior and irreversibility of forced convection of Ag-Mg/water hybrid NF in a double-pipe heat exchanger. They showed that the heat transfer enhances as Re or ϕ escalates, while the pressure drop, irreversibility, and effectiveness are diminished. In addition, the increase in the amplitude of the sinusoidal tube caused the performance index of the heat exchanger to be decreased. The influence of magnetic field on the hydrothermal performance of a sinusoidal double-pipe heat exchanger with Fe2O3/water NF was studied by Mousavi et al. [3]. Their results showed that the sinusoidal shape of the inner tube has an important effect on the heat transfer of the heat exchanger. The findings also revealed that the cold boundary layer diffusion is increased as the magnetic field intensity escalates. Abhilash et al. [4] studied the turbulent flow of two NFs (Al2O3 and TiC) flowing inside a double-pipe heat exchanger. Based on the results, TiC NF had a better performance as compared to Al2O3 NF. Liu et al. [5] performed a 3D numerical analysis on forced convection laminar flow of a non-Newtonian NF (CNT/Fe2O3-water) inside a double-pipe heat exchanger. In that study, the water and NF flowed through the annulus and inner tube, respectively. The results of that study showed that the increase in the inlet temperatures of water and NF enhances the heat transfer rate and reduces the pumping power. Saleh and Sundar [6] investigated the hydrothermal behavior of a double-pipe U-bend heat exchanger with Multi-Walled Carbon Nanotube (MWCNT)/water considering Re of 3500-12000. Their results showed that for ϕ of 0.3%, the pressure drop and pumping power are escalated by 17.05% and 15.96%, respectively, as compared to the pure water flow. In addition, the number of the transfer unit and the effectiveness of the heat exchanger were increased by 2.75% and 2.49%, for ϕ of 0.3% as compared to the pure water. Bashtani et al. [7] applied six tabulators in a double-pipe heat exchanger considering Al2O3/water NF. Based on the results, Nu increased by 70% as the result of the fluid collision with the tabulator surface and breaking the boundary layer. In addition, it was concluded that the NF causes the number of the transfer unit, Nu, and effectiveness to be enhanced to 1.2, 1.21, and 1.19 times, respectively, as compared to the heat exchanger with the pure water. Maddah et al. [8] performed an experimental examination of the turbulent flow (Re = 3000-12000) and heat transfer of Al2O3-TiO2 hybrid NF in a double-pipe heat exchanger with twisted inserts. They showed that the increase in Re and ϕ, also the decrease in twist pitch leads to enhancing the exergy efficiency of the heat exchanger. Sundar et al. [9] performed a series of experiments to evaluate the hydrothermal performance of a double-pipe heat exchanger with Fe3O4 NF flow in an inner tube. Different pitch ratios and wire coil inserts were examined in that study considering Re of 16000-29000. The results demonstrated that Nu escalates by 9.76-14.26% within the studied range of Re for the ϕ of 6%. This range of Re augmentation was also shown to be increased by 25.39% and 37.90% when wire coil inserts are used in the studied heat exchanger. Shirvan et al. [10] conducted the numerical analysis of the hydrothermal characteristics of Al2O3 NF in a double-pipe heat exchanger for the Re = 50-250 and ϕ = 1-5%. The influences of Re and ϕ on the performance of the heat exchanger were investigated. Based on the findings, the Re and ϕ had positive effects on the heat exchanger effectiveness, while Nu decreased with the intensification of ϕ. Nakhchi et al. [11] investigated the influence of using the perforated cylindrical turbulators in a double-pipe heat exchanger considering the CuO nanoparticles. The hydrothermal performance of the system was examined and the entropy generation was determined. The authors found that 1.5% of nanoparticle concentration leads to obtaining a thermal performance of 1.93. In addition, it was found that the entropy generation rate escalates by 157% when Re increases from 6000 to 17000. Tiwari et al. [12] performed a numerical and experimental analysis to study the hydrothermal performance of a triple-tube heat exchanger considering the turbulent flow of WO3/water NF. Different inserts including twisted tape, rib, and porous plate were used in that analysis. Based on the results, the ribbed twisted type and ϕ = 1% provides the highest effectiveness of 1.87 as compared to the other studied inserts. Besides, the effectiveness and overall heat transfer performance were escalated by 11.84% and 12.38%, respectively, over the heat exchanger without inserts. Elsaid et al. [13] performed a 3D numerical analysis to investigate the turbulent flow of different NFs and mixed NFs in a triple-pipe heat exchanger considering six ribbed geometries (semi-circular, trapezoidal, semi-elliptical, rectangular, triangular, and square-shaped). Based on the outcomes, Al2O3/MWCNT-water mixed NF has the best hydrothermal performance among the studied nanoparticles (Al2O3, MgO, SiC, and MWCNT). Moreover, it was found that the semi-circular and staggered ribbed geometries enhance the Nu and the heat exchanger's effectiveness. Onyiriuka et al. [14] showed that Nu in a double-pipe heat exchanger is increased by 68% and the convective heat transfer coefficient is enhanced by twice at Re = 5000 if TiO2/water is used instead of water. In addition, it was found that Nu diminishes as ϕ increases. Kumar [15] investigated the application of Fe2O3/water NF in the inner tube of a double-pipe heat exchanger. Their results showed that Nu enhances by 14.7% with a pumping penalty of less than 10% for ϕ = 6% and Re = 30000 as compared to the case with pure fluid. The experimental analysis of TiO2/water NF flow inside a double-pipe heat exchanger was conducted by Qi et al. [16]. The volume flow rate, Re and ϕ were considered within the ranges of 1–5 L/min, 3000-12000, and 0-0.5%, respectively. In addition, the NF was considered to flow in the shell side or tube side of the heat exchanger. The results of that study showed that the heat transfer enhances by 10% and 14% for the ϕs of 0.1% and 0.5%, respectively, as compared to the pure water flow. In addition, the pressure drop of NF in the shell and tube sides escalated by 41% and 58%, respectively. Singh and Sarkar [17] investigated the application of using wire coiled inserts inside a double-pipe heat exchanger with Al2O3-MgO/water NF. Three different wire coil configurations (Converging, Diverging, and Conversing-Diverging (C-D) types) were examined in that work. Based on the results, the highest increase in the Nu and friction factor was observed for diverging configuration, which was respectively 84% and 64% higher than those obtained for the pure water flow inside the heat exchanger without inserts. The authors also found that the combination of hybrid NFs and wire coiled inserts significantly enhances the hydrothermal performance of double-pipe heat exchangers. In another research, Singh and Sarkar [18] performed an experimental analysis on a concentric tube heat exchanger with conical wire-coil inserts and considered two NFs (Al2O3/water and CNT/water) and a hybrid NF (Al2O3-CNT/water). Three-wire coil inserts (converging, diverging, converging-diverging) were examined. The findings demonstrated that the highest hydrothermal performance of the heat exchanger is obtained using the diverging wire coil configuration. The highest Nu number and friction factor were observed for the diverging configuration, which were 174% and 106% higher than those obtained for the heat exchanger without inserts and with pure water fluid flow. In addition, the entropy generation of the system with pure water flow was obtained higher than those with mono or hybrid NFs. The application of twisted tape inserts inside a double-pipe heat exchanger was numerically investigated by Karimi et al. [19]. They used Al2O3/water NF and applied the two-phase model for the numerical calculations. Based on the results, Nu was enhanced by 22% when the twisted tape was used. In addition, the heat transfer and pumping power were shown to be increased by 30% and 40%, respectively, by adding nanoparticles.
Based on the reviewed literature, the application of NFs in double-pipe heat exchangers has been vastly investigated. However, most of the existed studies include the flow of NF inside the double-pipe heat exchangers applying different inserts. To the best of the authors' knowledge, the first-law and second-law performance of a NF inside a double-pipe heat exchanger with a converging sinusoidal wall has not been investigated yet. In addition, the entropy generation analysis, which is firstly applied in such numerical 3D analysis, is a useful technique to detect the locations with high irreversibilities inside the computational geometry ([20] and [21]). The second law analysis helps designers eliminate or at least mitigate the irreversibilities, and thereby improve the hydrothermal performance of the studied heat exchangers. Moreover, an intelligent soft computing method [22] was applied to estimate an accurate model for the entropy generation and hydrothermal performance of the studied double pipe heat exchangers for the first in the present study. Therefore, this research is dedicated to this topic. The two-phase mixture model is applied to solve the velocity, pressure, and temperature fields of the NF considering the effect of Re, ϕ, amplitude, and wavelength of the sinusoidal wall. In the second part of this research, a soft computing-based investigation was addressed to accurately model three targets (i.e., total entropy generation of cold NF, total entropy generation of hot water, and performance ratio using the GPR approach, along with the numerical simulation.
Section snippets
Geometry, boundary conditions, and nanofluid properties
Fig. 1 depicts the schematics of three different studied geometries of the double-pipe heat exchangers namely; a) parallel double-pipe heat exchanger (PDHX), b) converging double-pipe heat exchanger (CDHX), c) sinusoidal converging double-pipe heat exchanger (SCDHX). The length and outer diameter of all three heat exchangers are 1 m and 2 mm, respectively. For PDHX, the inner diameter is 1 mm, while for CDHX, the diameter of the inner tube in the NF flow path decreases linearly from 1.5 mm to
Governing equations
The numerical calculations were performed under the steady-state conditions, for the incompressible fluid flow applying the mass, momentum, and energy balances. The SIMPLE algorithm was applied for coupling the velocity and pressure fields at the absence of radiation heat transfer and neglecting the heat loss to the environment. The numerical calculations of the pure water flowing inside the annulus was conducted based on the single-phase method, while for the NF coolant, the two-phase mixture
Numerical method and validation
In this research, the finite volume technique was used to perform the required simulations. Momentum and energy conservation equations are solved using the second-order upwind technique, and coupling of velocity and pressure is done using the SIMPLE technique. The convergence of the numerical solution is also subject to the convergence criterion of 10−6 for all variables.
Five different grids were prepared for each geometry, using which the NF output temperature and NF inlet pressure were
Numerical simulation results
The variations of heat transfer coefficient (h) versus Re and ϕ for three studied geometries are presented in Fig. 3. Here can be seen that the increase of Re from 500 to 2000 and ϕ from 0% to 1% leads to respectively 21.50% and 17.48% increase in h for three studied geometries. SCDHX has the highest h for all Re and ϕ values among the three geometries. While h is low for CDHX at low Re of less than 1500 and it will exceed the value of h for PDHX with the increase in Re to higher values. In
Conclusions
The present study numerically examines the hydrothermal behavior of three different configurations of a double-pipe counterflow heat exchangers (parallel double-pipe (PDHX), converging double-pipe (CDHX), and sinusoidal double-pipe (SCDHX)) in which the hot water stream is cooled down using the biological water-silver Nanofluid (NF) coolant. The 3D numerical analysis was performed in ANSYS Fluent software considering a two-phase model and Re numbers (1000, 2000, 3000, and 4000) as well as four
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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