Bell-Delaware Method Research Articles

Experimental and simulation study of a U-shaped water-cooled sleeve heat pipe radiator for high heat flux density

Effective heat dissipation methods are desperately needed to ensure heat transfer of the large quantity of heat generated by radioactive isotopes in restricted places. This study employs the Bell-Delaware method to design a U-shaped water-cooled sleeve heat pipe radiator (UWC-HP) intended for heat dissipation on a 16 cm2 surface area with a heat flux density of 200 W/cm2. We have established a 3D model, which was experimentally validated, showing an error within 5 %. Subsequently, as the refrigerant and structural design of the condenser segment are crucial factors leading to the limitations of UWC-HP, this study aims to evaluate the impact of the condenser segment on the heat dissipation performance. Specifically, we investigated the effects of different cooling water temperatures, flow rates, and fin designs on the heat dissipation performance of the UWC-HP. Based on this, We found that the rib height, the number of ribs, and the rib material can strengthen the performance of the heat sink by a maximum of 12.3 %, 10.1 %, and 3.7 %, respectively. The heat sink optimized by orthogonal experiments has a maximum heat source surface temperature of 506.22 K and Nu of 101.85, which reduces the maximum surface temperature of the heat source by a maximum of 22 K and strengthens the heat sink capacity of heat pipes by 20 %. This article achieves efficient heat transfer for isotopic decay heat in a confined space by designing a heat pipe heat exchanger. It reduces the equipment's temperature and enhances the safety of the nuclear reactor.

Configuration Optimization of a Shell-and-Tube Heat Exchanger with Segmental Baffles Based on Combination of NSGAII and MOPSO Embedded Grouping Cooperative Coevolution Strategy

A design indicators prediction model using the Bell-Delaware method for a shell-and-tube heat exchanger with segmental baffles (STHX-SB) is constructed and validated by experiment. The average errors of heat transfer capacity and tube-side pressure drop are 8.52% and 7.92%, respectively, and the predicted weight is the same as the weight obtained by Solidworks commercial software, which indicates the model’s reliability. Parametric influences of the outside diameter of the heat dissipation tube, clearance between heat dissipation tubes, heat dissipation tube length, and tube bundle bypass flow clearance on heat transfer capacity per tube-side pressure drop and heat transfer capacity per weight are studied, and it indicates that whether the interaction between factors is considered or not, both heat transfer capacity per tube-side pressure drop and heat transfer capacity per weight are the most sensitive to outside diameter of heat dissipation tube and the least sensitive to heat dissipation tube length based on the Sobol’ method. To avoid falling into local optima due to algorithm convergence being too fast and to improve the reliability of solving complex optimization problems, Non-Dominated Sorted Genetic Algorithm II (NSGAII) and Multi-Objective Particle Swarm Optimization (MOPSO) embedded grouping cooperative coevolution (NSGAII-MOPSO-GCC) is proposed to optimize the studied four configuration parameters to maximize heat transfer capacity per tube-side pressure drop and heat transfer capacity per weight for STHX-SB, simultaneously. Compared with the original structure, heat transfer capacity per tube-side pressure drop and heat transfer capacity per weight of the chosen solutions separately increased by 57.66% and 4.63%, averagely, and in the optimization comparison of NSGAII, MOPSO, and NSGAII-MOPSO-GCC, NSGAII-MOPSO-GCC has the best performance, which shows that the proposed method is effective and feasible and can supply beneficial solutions and valuable guidance for heat exchanger design and improvement.

Design and development of polymer composite heat exchanger tubes using an integrated thermal-hydraulic and material design framework

In the current study, thermal-hydraulic design of the heat exchanger and composite material design are integrated to develop polymer composite tube materials for heat exchanger applications. For preliminary analysis, the scheme utilizes basic thermal resistance equations, Kern and Bell-Delaware methods for the design of baffled shell and tube heat exchangers, and differential effective medium theory for the design of composite materials. The preliminary analysis clarifies that the thermal conductivity of tubes is a performance-limiting parameter in the case of liquid-liquid applications. The heat exchanger's design imposes that the tubes' thermal conductivity must be enhanced to ≥8.5 W/m.K for achieving heat transfer comparable to those of metal counterparts. To attain the threshold thermal conductivity, the design of polymer composites employing differential effective medium theory requires that high volume fractions (> 0.3) of high effective aspect ratio (> 10 or 0.1) thermally conductive fillers be incorporated in a polymer matrix. Finally, the samples are fabricated of polypropylene matrix and expandable graphite filler with variable volume fractions (0.1–0.4). The highest thermal conductivity of 8.3 W/m.K was achieved in a 40 vol% sample. The comparison of measured and computed thermal conductivity values shows an acceptable agreement supported by electron microscopy and thermal images.

Thermo-hydraulic rating of a shell and tube heat exchanger for acetone cooling using bell-delaware method

Shell and tube heat exchangers are becoming the most popular devices for the transfer of heat in industrial process applications. In the present work, the thermo-hydraulic rating of a shell and tube heat exchanger proposed to cool an acetone stream was carried out using the Bell-Delaware methodology. An overall heat transfer coefficient value of 426.70 W/m2.K, a calculated heat transfer area of 121.46 m2, and a percent excess area of 20.83% were obtained. Both the pressure drop of acetone and water had values of 1,622.36 Pa and 3,020.46 Pa, respectively. The proposed shell and tube heat exchanger can be used satisfactorily for the required application, since the percent excess area does not exceed the 25%, and the pressure drops of both fluid streams are below the limit values established by the process.

Thermal Design Optimization of No Phase Change Shell-and-Tube Heat Exchanger using Particle Swarm Algorithm

Shell-and-tube heat exchanger is designed to satisfy certain requirements such as heat transfer capability, allowable pressure drop and limitation of size. Beside such requirements, it is important to consider economical point of view to get lowest total cost. In this study, computational program and optimization for thermal design shell-and-tube heat exchanger were built for liquid to liquid with no phase change process in four variables design parameters using Bell-Delaware method. The design variables were tube size, tube length, baffle cut to shell inside diameter ratio and central baffle spacing to shell inside diameter ratio. Particle swarm algorithm was used as optimization method to get lower solution for economical point of view shell-and-tube heat exchanger. The results from two study cases show that particle swarm algorithm got lower total cost from the original design. The total cost decreased 28.84 % in first study case and 52.57 % in second study case from the original design.

Heat exchanger networks synthesis considering the rigorous equipment design and distinct parameters for capital cost estimation

In the present paper, a novel bi-level approach for the optimal synthesis of HENs is presented. A new capital cost parameter is iteratively updated in the capital cost function based on the shell and tube heat exchangers detailed design considering the shell diameter, tube length, the area as well as the other parameters needed to calculate a total cost correction factor, in such a way that the heat exchangers in the HEN have different capital cost parameters. At the outer level, a mixed-integer nonlinear programming (MINLP) model is proposed for the HEN synthesis. In the inner level, another MINLP model is used to rigorously design the shell and tube heat exchangers using the Bell-Delaware method as the HEN is being synthesized. Two case studies are performed, and considerable differences in the final HEN were observed when compared to those obtained using the same parameters in the capital cost function for all heat exchangers in the HEN. The results show that this strategy can provide more realistic solutions for costing than those presented previously in the literature.

Multi-Objective Optimization Tool of Shell-and-Tube Heat Exchangers Using a Modified Teaching-Learning-Based Optimization Algorithm and a Compact Bell-Delaware Method

The multi-objective optimization of heat exchangers can provide a reliable solution for both improved efficiency and reduction in cost. A computer program for the thermal and hydraulic design optimization of shell-and-tube heat exchangers is developed. Its user-friendly graphic-user interface provides an excellent feature for the teaching, learning, and preliminary design of shell-and-tube heat exchangers. In the present work, teaching-learning-based optimization (TLBO) algorithm is updated and implemented for better feasibility of optimum design. To improve the accuracy of the thermal and fluid analysis, the compact Bell-Delaware method (BDM) is newly implemented. Also, the effect of fouling is considered. The developed program using the updated TLBO and the compact BDM is validated against practical heat exchanger cases. The impacts of input parameters on the performance prediction of BDM and number of designs on finding optimum design of TLBO are also tested.

Comparison of the performance of different metaheuristic methods for the optimization of shell-and-tube heat exchangers

Shell-and-tube heat exchangers are important equipment used in every transformation industry. The mathematical models that describe the thermo-hydraulic behavior of these equipment generates a complex search space. Due this complexity, traditional gradient-based algorithms fail to converge in the neighborhood of the global optima. Metaheuristic methods are global search strategies that implements different operators to avoid local optima solution. In this work four case studies for the optimization of shell-and-tube heat exchangers are considered. For each case study the use of Kern's and Bell-Delaware methods is contemplated with discrete and continuous diameters of tubes, resulting in a total of 16 optimization problems (four optimization problems per case study), where the objective function is the total annual cost of the equipment. Seven metaheuristic algorithms are employed to solve each optimization problem; their performance is compared using statistical parameters such as the mean, median and standard deviation of the objective function. The metaheuristic algorithms with the best global performance are differential evolution and grey wolf optimization.

Modified Kinetic Gas Molecule Optimization for four fluids of Organic Rankine Cycle in shell and tube heat exchanger

Organic Rankine Cycle (ORC) is applied in the shell and tube heat exchanger to enhance the efficiency of the exchanger. Existing methods involves in applying the optimization method in ORC in shell and tube heat exchanger to improve the performance. In this paper, the modified Kinetic Gas Molecule Optimization (KGMO) method is applied in four fluids to improve the performance of the exchanger. Four fluids such as R245fa, R134a, R290, and R600a were used to evaluate the performance of modified KGMO method. In KGMO, the worst learning particles affects the performance of the optimization in the convergence. The modified KGMO method involves in applying the feedback learning method to improve the learning performance of worst particles in KGMO. The proposed modified KGMO method is compared with existing methods of Bell-Delaware and KGMO. The proposed modified KGMO method has the enhancement factor of 2.8 and Bell-Delaware method has 1.51 enhancement factor.

Parametric & CFD Analysis of Shell and Tube Heat Exchanger by Varying Baffles Geometry

The Shell and Tube Heat Exchanger are most commonly used in current industrial production. In this study, the effect of baffle spacing on pressure drop and heat transfer coefficient are considered in a shell and tube heat exchanger with single segmental baffles and staggered tube layout. The effects of number of baffles are considered 4, 6, 8, 10, 12, and 14 and baffle spacing are considered 366.67, 220,157.14, 122.22, 100, and 84.61 respectively with 38% baffle cut are investigated to study the effect of pressure drop and heat transfer coefficient.Shell and tube heat exchanger with single segmental baffles is designed with same input parameters using Kern’s theoretical method and Bell-Delaware method. From the CFD simulation results, heat transfer coefficient and pressure drop values for varying tube layout are provided.Variation of number of baffles with shell side pressure drop heat transfer coefficient are shown. It is discussed that for both methods (analytical calculation and CFD result) pressure drops will be increases with increases number of baffles. K- Standard turbulence model with second order discretization and fine mesh is selected for CFD simulation considered.The result are shown highly sensitive to tube layout orientation selection, it is observed for this heat exchanger geometry 30 tube layout and 14 baffle arrangement gives slightly better results. Keywords : CFD Ansys simulation, Heat transfer coefficient, Pressure drop DOI: 10.7176/IEL/10-3-03 Publication date: November 30 th 2020

Exergoeconomic optimization of a shell-and-tube heat exchanger

The paper presents an economic optimization of a STHX with two commonly adopted (i.e., Kern and Bell-Delaware) and one rarely explored (i.e., Wills-Johnston) methods. A detailed numerical code concerning thermal, hydraulic, exergy, and economic analysis of STHX is developed for all three methods. Normalized sensitivity analysis, parametric study, and Genetic Algorithm are used to ascertain the most influential parameters and optimize the total cost. It is observed that the calculations made using the Wills-Johnston method were reasonably close to the Bell-Delaware method. While the Kern method showed a significant deviation in the shell side calculations because of the several assumptions in this method. The parametric analysis showed that increasing the mass flow rate and the number of baffles increased the operating cost because of an exponential increase in the pressure drops. Finally, the optimization reduced the heat transfer area by ~26.4%, capital cost by ~20%, operational cost by ~50%, total cost by ~22%, and the stream cost by ~21%.

State-of-the-Art of Research on Optimization of Shell and Tube Heat Exchangers by Methods of Evolutionary Computation

This paper presents a comprehensive state-of-the-art review of optimization by evolutionary computation methods of shell and tubes heat exchangers (STHE) of single segmental baffles. It is seen that the heat transfer coefficient to the shell side is calculated by the Kern method or by the Bell Delaware method, and that the pressure drop to the shell side is calculated by the Kern method or by the Bell Delaware method or by the Peters and Timmershaus method. It is verified the use of evolutionary computation algorithms in single-objective and multiobjective optimization of STHE, and that most related work used the total cost function of STHE. And among the contributions presented, there were implementations and applications of different evolutionary computation algorithms, or study of the STHE optimization problem by different objective functions, such as ecological, entransy dissipation, field synergy, and cost of the life cycle. Also, it was possible to verify some gaps in the work related to STHE optimization, among them, can be cited the need for greater application of decision-making methods that relate technical, economic and managerial aspects applied to the solution of the STHE. And it is suggested for future work the development of the STHE model subject to delimited uncertainties; and the formalization of a standard STHE optimization problem, so that it can serve as a reference for comparing the different optimization algorithms, and applying metrics to evaluate the advantages that are obtained when using a new algorithm for the same problem.

Thermal Design Optimization of Shell-and-Tube Heat Exchanger Liquid to Liquid to Minimize Cost using Combination Bell-Delaware Method and Genetic Algorithm

Shell-and-tube heat exchanger is designed to satisfy certain requirements such as heat transfer capability, allowable pressure drop and limitation of size. Beside such requirements, it is important to consider economical point of view to get the lowest total cost. In this study, computational program and optimization for thermal design shell-and-tube heat exchanger were built for liquid to liquid with no phase change process in four variables design parameters using Bell-Delaware method. The design variables were tube size, tube length, baffle cut to shell inside diameter ratio and central baffle spacing to shell inside diameter ratio. The genetic algorithm was used as optimization method to get lower solution for economical point of view. The results from two study cases show that the genetic algorithm got lower total cost from the original design. The total cost decreased 28.83% in first study case and 52.56% in second study case from the original design.

Optimum Design of Shell and Tube Heat Exchangers using Modified Kinetic Gas Molecule Optimizer for the use of Low Temperature in Organic Rankine Cycles

Shell and Tube Heat Exchangers (STHEs) plays a crucial role in an effective design of Organic Rankine Cycle (ORC) power plants.The main aim of this research work is to design a cost-effective ORC in order to exploit low to medium temperature geothermal fluid or low grade industrial waste heat. In this research work, modified Kinetic Gas Molecule Optimization (KGMO) algorithm was developed forfinding the optimized parameter settings of the power plant. In modified KGMO algorithm, feedback learning stage was included for improving the fitness of individual worst particles. In addition, the proposed optimization algorithm was tested on two dissimilar fluids such asR245fa and R134a in order to show the effectiveness of proposed scheme. The experimental investigation showed that the proposed scheme effectively improved the heat exchanger performance as related to the existing schemes.The enhancement factor of proposed scheme was 2.8063 for R245fa fluid and 1.9346 for R134a fluid, which was better compared to the existing schemes; KGMO and Bell-Delaware method.

Theoretical and experimental studies on two-phase thermosyphon shell and shell heat exchangers

This work presents theoretical and experimental analyses on a shell and shell heat exchanger assisted by two-phase thermosyphons. This heat exchanger consists of two adjacent cylindrical shells that enclose a bank of two-phase thermosyphons. A prototype was built and tested as a water cooler for oils with different ranges of viscosity. A theoretical model is developed to predict the heat transfer rate. It combines the Bell-Delaware method for the shell side, the equivalent thermal circuit model for the two-phase thermosyphon and a proposed thermal coupling algorithm. The prototype was tested for several mass flow rates and inlet temperature levels of commercial thermal oil and a very viscous petroleum sample. Comparisons between the proposed model and the experimental data showed that the proposed model can predict the experimental heat transfer rate with an overall root mean square error of 20%, despite the use of literature correlations for the Nusselt number of a cross-flow over a tube bank out of their Prandtl number range, as very viscous fluids were tested.

Exergy analysis of a shell and tube heat exchanger using DETHE software

In this paper, a sensibility study of irreversibility due to geometrical parameters variation of a shell-and-tube heat exchanger is proposed by using an exergy analysis. The irreversibility calculation model has been implemented on design tubular heat exchangers (DETHE) software, where thermohydraulic calculations are based on Bell-Delaware method. A prior evaluation of thermohydraulic results of DETHE is provided against a commercial software. Through an exergetic analysis in the study case, formulation to be implemented in the software for irreversibility calculation is developed. A real case study of a heat exchanger located in a pre-heat train of atmospheric crude distillation unit is analysed. Irreversibility results due to key design parameters variation for this heat exchanger are provided and discussed.

Thermal-hydraulic analysis of water based ZrO2 nanofluids in segmental baffled shell and tube heat exchangers

Thermal-hydraulic characteristics of water based ZrO2 nanofluids has been investigated in a segmental baffled shell and tube heat exchanger in turbulent flow regime. The effect of Reynolds number, nanoparticle loading, mass-flow rate, and tube lay-out has been analysed on overall heat transfer coefficient. The effect of Reynolds number on the tube side pressure drop and convective heat coefficient have also been discussed. The effect of shell side mass-flow rate was also investigated on shell side heat transfer coefficient determined using Bell-Delaware method. The nanoparticle volume concentration is taken very low i. e. 0.2%, 0.4%, and 0.8%, respectively. The improvement in both tube side convective heat transfer coefficient and overall heat transfer coefficient has been observed. The maximum improvement in the convective heat transfer coefficient is found to be 14.1% for 0.8% ZrO2 nanofluids. However, the percentage enhancement in tube side pressure drop was higher than the percentage increment in the tube side heat transfer coefficient.

Analyze The Effects of Helical Baffles Angles Variation On Shell Side Heat Transfer Coefficient And Pressure Drop of Shell And Tube Heat Exchange

E-201-11 is one of the components of heat exchanger which serves to increase the temperature of distillated crude oil before it going into the furnace. The use of segmental baffles on the heat exchanger causes dead zone. The fouling phenomenon that arises from the deposition of the compound content in the service fluid in dead zone can result in leakage of the shell and tube. It affects the performance of heat exchanger and production efficiency. The use of discontinuous helical baffle on the shell side minimizes fouling. Research on the variation of helical baffle angle by using Bell-Delaware method resulted in performance value of heat transfer coefficient and pressure drop on the shell side. Fluid flow behavior on the shell side with helical baffle was analyzed by Computational Fluid Dynamics (CFD). The fluid flow velocity is a factor that affects the value of heat transfer coefficient and pressure drop. Heat exchanger with an angle of 10º have fluid flow velocity of 0,893m/s resulting in the highest heat transfer coefficient and pressure drop value compared to angles of 15º and 20º with values of 585.725W/m²K and 13642.395Pa. The heat exchanger with helical baffle at 10° helix angle presents the best performance among the others variant helical baffles

Detailed comparison of the methods used in the heat transfer coefficient and pressure loss calculation of shell side of shell and tube heat exchangers with the experimental results

ABSTRACT In this study, results of HTRI Xchanger software used in the analysis of shell and tube heat exchangers (STHE), and Kern and Bell-Delaware methods, which are the conventional methods used for calculation of shell side heat transfer coefficient (SSHTC) and pressure loss (PL), were compared with experimental data. An experimental study was considered for Heat exchanger (HE) dimensions and fluid properties from literature. Then SSHTC and PL values were calculated using Kern and Bell-Delaware methods and HTRI Xchanger software for the measured shell side flowrates. SSHTC and PL values calculated for lower shell side mass flowrates by Kern method deviated from experimental results at low ratios. In addition, deviations in high flowrates values increasingly moved away from experimental results. In the Bell-Delaware method, although low deviations were observed in the high shell-side mass flowrates, the deviations increased at low flow rates and diverged from the experimental results. The deviation of SSHTC values calculated by the HTRI Xchanger program was found to be massively independent from the shell side flowrate. In addition, as in Bell-Delaware method, it has been observed that deviations in the shell side pressure loss (SSPL) calculations increased with increasing shell-side mass flowrate. As a result, SSHTC was calculated with average deviations of + 17, −11, and + 18%, by Kern and Bell-Delaware methods and HTRI Xchanger software respectively. Similarly, shell side PL was found with + 64, −25, and −32% average deviation, respectively.

Thermal-Hydraulic Characteristics of Helical Baffle Shell-and-Tube Heat Exchangers

Shell-and-tube heat exchangers are frequently used in several industrial applications. A model was developed using engineering equations solver software to predict the performance of various baffle configurations of shell-and-tube heat exchangers. The model is based on the Bell-Delaware method for the segmental baffle, while mathematical correlations for the helical baffle are provided for design and analysis purpose. The accuracy of the present model is validated against the experimental data available in the literature. The results showed that helical baffles offer much higher performance compared to the segmental baffled heat exchanger. It was found that the performance of the helical baffle increases with increasing baffle angle until it reaches an optimum value; it then starts to decrease at an angle of 42°.