Set Of Multiple Optimum Solutions Research Articles

Effect of flow maldistribution on the optimal design of plate heat exchanger using constrained multi objective genetic algorithm

In this study, thermal and hydraulic optimization of plate heat exchanger is presented. In the thermal modeling of the plate heat exchanger, the effects of flow maldistribution for each side are also considered. A multi objective optimization is implemented based on the NSGA-II (Non-dominated Sorting Genetic Algorithm-II) algorithm to obtain the optimal trade-off (Pareto front) between effectiveness and pressure drop of hot side. The optimization variables in this study are considered as chevron angle, the number of plates, corrugation depth, corrugation pitch, horizontal distance of ports, vertical distance of ports, and port diameter and the goal is to achieve maximum effectiveness and minimum pressure drop. In addition, operational and geometrical constraints are also considered in the optimization procedure in order to take the advantage of the standard design and achieve feasible solutions. Next, a case study is presented to identify conflicting thermal-hydraulic behavior of plate heat exchanger. The results are reported as a set of multiple optimum solutions called ʺPareto optimal solutionsʺ. Moreover, the effect of changing these parameters on the optimal design is also presented and discussed in detail.

Design optimizations of the thermal performance and cost in an air-gap hollow fiber membrane contactor (AHFMC)

An air–gap hollow fiber membrane contactor (AHFMC) has been proposed and applied for fluid heating in the HVAC applications. The water and the liquid desiccant (solution) streams flow inside the neighboring hollow fiber membranes in a cross-flow arrangement. The solution is heated due to the absorption and mixing heats by absorbing the water vapor from the water stream. A mathematical model of the coupled heat and mass transports in the AHFMC is established by converting it into a parallel-plate one. The optimal design of the AHFMC is studied by using the multi-objective particle swarm optimization (MOPSO) algorithm to obtain the maximum thermal performance and minimum total annual cost together with the coupled heat and mass transfer model. A set of multiple optimum solutions, which are named as “Pareto optimal solutions”, are then obtained. Influences of geometric variables of the contactor length, width, height, fiber outer diameter and fiber distances in different directions on the heating performance and total annual cost are studied. The optimally geometrical parameters of the AHFMC are obtained using the MOPSO algorithm. These results are useful for the design of the AHFMC based on the desired temperature lift, the contactor constraint, and the available investment in the real applications.

Effect of discontinuous helical turbulators on heat transfer characteristics of double pipe water to air heat exchanger

Effect of typical and perforated discontinuous helical turbulators on flow and heat transfer in an air to water double pipe heat exchanger is experimentally studied. Experimental analysis is conducted for different values of open area ratio (0–0.0625), Reynolds number (6000–12,000) and pitch ratio (1.83–5.83). According to experimental data, correlations for Nusselt number, friction factor and thermal performance are presented as functions of variable parameters. Non-dominated Sorting Genetic Algorithm II (NSGA II) is applied to find the optimal designs of high efficiency heat exchanger. Pareto front is presented as set of multiple optimum solutions. Results show that friction factor and Nusselt number reduce with rise of open area ratio and pitch ratio. Thermal performance is an increasing function of open area ratio while it is a decreasing function of pitch ratio.

Multi-objective optimization of a rotary regenerator using tutorial training and self-learning inspired teaching-learning based optimization algorithm (TS-TLBO)

In the present work, tutorial training and self-learning inspired teaching-learning-based optimization (TS-TLBO) algorithm is proposed and investigated for the multi-objective optimization of a rotary regenerator. Two conflicting objectives, namely regenerator effectiveness and total pressure drop, are considered simultaneously for the multi-objective optimization. Six design variables such as frontal area, matrix rod diameter, matrix thickness, matrix rotation speed, split and porosity are considered for optimization. Application examples are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimal designs are presented in a set of multiple optimum solutions, called Pareto-optimal solutions. Moreover, to reveal the level of conflict between these two objectives, the distribution of each design variables in their allowable range is also shown in two-dimensional objective spaces. Furthermore, the effect of change in the value of design variables on the objective function value is also performed in detail. Looking at the different design points of Pareto front, 99.4% reduction in total pressure drop is observed at the cost of 97.9% reduction in regenerator effectiveness. Also, the matrix rod thickness, split and porosity were found to be important design variables that caused a strong conflict between the objective functions.

Optimum power performance of a new integrated SOFC-trigeneration system by multi-objective exergoeconomic optimization

Abstract In the present study a comprehensive thermodynamic modeling and multi-objective exergoeconomic optimization of a new integrated SOFC-trigeneration system is carried out to determine the optimum decision parameters, accounting for exergetic, economic and environmental factors. Results of optimal designs are obtained as a set of multiple optimum solutions, called the Pareto optimal solutions. An example of decision-making is presented and a final optimal solution is introduced. Moreover, the optimized results are compared with the working data from a base case design of an actual system. This new approach shows that by selecting final optimum solution, the trigeneration unit cost of products reduced by 13.88% and exergy efficiency increased from 62.85% in the base case to 64.5% in the optimum case. Also, the optimization results demonstrate that fuel cost, exergy destruction cost and environmental impacts (CO 2 emissions cost) are reduced by 17.54%, 17.05% and 18.22% respectively; although these are achieved with 8.03% increase in the capital investment cost. Finally, sensitivity analysis is carried out to examine the effect of changes in the Pareto optimal solutions to the system economic parameters.

Multi-objective shape optimization of double pipe heat exchanger with inner corrugated tube using RSM method

Integrated a fully developing three-dimensional heat transfer and flow model, a multi-objective optimization aims to fulfill the geometric design for double-tube heat exchangers with inner corrugated tube is investigated in this work with RSM. Dimensionless corrugation pitch (p/D), dimensionless corrugation height (H/D), dimensionless corrugation radius (r/D) and Reynolds number (Re) are considered as four design parameters. Considering the process parameters, the characteristic numbers involving heat transfer characteristic, resistance characteristic and overall heat transfer performance calculated by CFD, and are served as objective functions to the RSM (Nuc, fc, Nuc/Nus, fc/fs and η in this paper). The results of optimal designs are a set of multiple optimum solutions, called ‘Pareto optimal solutions’. It reveals the identical tendency of Nuc/Nus and fc/fs reflecting the conflict between them that means augmenting the heat transfer performance with various design parameters in the optimal situation inevitably sacrificed the increase of flow resistance. According to the Pareto optimal curves, the optimum designing parameters of double pipe heat exchanger with inner corrugated tube under the constrains of Nuc/Nus ≥ 1.2 are found to be P/D = 0.82, H/D = 0.22, r/D = 0.23, Re = 26,263, corresponding to the maximum value of η = 1.12.

Optimum dimension of geometric parameters of solar chimney power plants – A multi-objective optimization approach

In this communication, a multi-objective optimization method is implemented using evolutionary algorithm techniques in order to determine optimum configuration of solar chimney power plant. The two objective functions which are simultaneously considered in the analysis are power output and capital cost of the plant. Power output of the system is maximized while capital cost of the component is minimized. Design parameters of the considered plant include collector diameter (Dcoll), chimney height (Hch) and chimney diameter (Dch). The results of optimal designs are obtained as a set of multiple optimum solutions, called ‘the Pareto frontier’. For some sample points of Pareto, optimal geometric is presented. In addition, effect of changing design variables on both objective functions is performed. This multi-objective optimization approach is very helpful and effective for selecting optimal geometric parameters of solar chimney power plants. The results show that, power output of the plant increases linearly when solar irradiation increases and increase in ambient temperature causes slight decrease in power output of the plant.

Multi-objective optimization of outward convex corrugated tubes using response surface methodology

Multi-objective optimal designs of high efficiency corrugated tube heat exchangers applied in nuclear plants are presented in this paper. Dimensionless corrugation pitch (p/D), dimensionless corrugation height (H/D), dimensionless corrugation radius (r/D) and Reynolds number (Re) were considered as four design parameters. The analyses of heat transfer characteristic, resistance characteristic and overall heat transfer performance for the corrugated tube were conducted based on CFD to acquire the objective functions (Nuc, fc, Nuc/Nus, fc/fs and η in this paper) for combination of process parameters. The Response surface methodology (RSM) with Central composite design (CCD) was used to identify the relationships between the objective functions and the design variables. Variance of the linear term, quadratic term and interactive term for design parameters in the response variables were analyzed. Response surface analyses were applied to visualize the effects of the interactive term. The results of optimal designs are a set of multiple optimum solutions, called ‘Pareto optimal solutions’. It reveals that augmenting the heat transfer performance caused by various design parameters in the optimum situation would lead to the increase of the resistance. The optimum values of fc/fs = 1.22 and η = 1.42 are obtained in the condition of specific (fixed) Nuc/Nus ≥ 1.2.

Thermal-economic multi-objective optimization of shell and tube heat exchanger using particle swarm optimization (PSO)

Many studies are performed by researchers about shell and tube heat exchanger (STHE) but the multi-objective particle swarm optimization (PSO) technique has never been used in such studies. This paper presents application of thermal-economic multi-objective optimization of STHE using PSO. For optimal design of a STHE, it was first thermally modeled using e-number of transfer units method while Bell–Delaware procedure was applied to estimate its shell side heat transfer coefficient and pressure drop. Multi objective PSO (MOPSO) method was applied to obtain the maximum effectiveness (heat recovery) and the minimum total cost as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. In order to show the accuracy of the algorithm, a comparison is made with the non-dominated sorting genetic algorithm (NSGA-II) and MOPSO which are developed for the same problem.

Techno-economical and environmental optimization of natural gas network operation

In the present study, a multi-objective approach is proposed to find optimum operating condition of natural gas network. For this purpose, a thermodynamic modeling of natural gas through the main elements of the network i.e. pipelines and compressor stations (CSs) is performed. This study aims to find optimum values of three conflicting objective functions namely maximum gas delivery flow and line pack, and minimum operating cost (sum of fuel consumption and carbon dioxide emission costs), simultaneously. Here, fast and elitist non-dominated sorting genetic-algorithm (NSGA-II) is applied by considering fourteen decision variables: number of running turbo-compressors (TCs) and rotational speed of them in compressor stations as well as gas flow rate and pressure at injection points. The results of multi-objective optimization are obtained as a set of multiple optimum solutions, called ‘the Pareto optimal solutions’. Furthermore, a set of typical constraints, governing the pipeline operation, is subjected to obtain more practical solutions. To control the constraints satisfaction and to find better solutions in optimization process, the penalty functions are defined and applied. Sensitivity analysis of change in the objective functions, when the optimum decision variables vary, is also conducted and the degree of each parameter on conflicting objective functions is investigated.

Thermal-economic multiobjective optimization of heat pipe heat exchanger for energy recovery in HVAC applications using genetic algorithm

Cost and effectiveness are two important factors of heat pipe heat exchanger (HPHE) design. The total cost includes the investment cost for buying equipment (heat exchanger surface area) and operating cost for energy expenditures (related to fan power). The HPHE was thermally modeled using e-NTU method to estimate the overall heat transfer coefficient for the bank of finned tubes as well as estimating pressure drop. Fast and elitist non-dominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables was applied to obtain the maximum effectiveness and the minimum total cost as two objective functions. Pipe diameter, pipe length, numbers of pipes per row, number of rows, fin pitch and fin length ratio were considered as six design parameters. The results of optimal designs were a set of multiple optimum solutions, called ?Pareto optimal solutions?. The comparison of the optimum values of total cost and effectiveness, variation of optimum values of design parameters as well as estimating the payback period were also reported for various inlet fresh air volume flow rates.

Thermo-economic environmental optimization of Organic Rankine Cycle for diesel waste heat recovery

An Organic Rankine Cycle for diesel engine waste heat recovery is modeled and optimized. The design parameters are nominal capacity of diesel engine, diesel operating partial load, evaporator pressure, condenser pressure and refrigerant mass flow rate. In addition four refrigerants including R123, R134a, R245fa and R22 are selected and studied as working fluids. Then, the fast and elitist NSGA-II (Non-dominated Sorting Genetic Algorithm) is applied to maximize the thermal efficiency and minimize the total annual cost (sum of investment cost, fuel cost and environmental cost) simultaneously. The results of the optimal design are a set of multiple optimum solutions, called Pareto optimal solutions. The optimization results show that the best working fluid is R123 in both of economical and thermo dynamical view point for a specified value of output power. R245fa, R134a and R22 are placed in the next ranking, respectively. The optimum result of R123 shows the 0.01%, 4.39%, and 4.49% improvement for the total annual cost in comparison with R245fa, R22, and R134a, respectively. The above values for efficiency are obtained 1.01%, 12.79% and 10.57%, respectively. Furthermore R123 needs the highest investment cost while the environmental and fuel costs are the lowest.

Multi-objective optimization of a stirling-type pulse tube refrigerator

A genetic algorithm (GA) optimization method which is coupled to a one-dimensional finite volume method is proposed and implemented as a computer program for the modeling and optimization of a stirling-type pulse tube refrigerator (PTR). The multi-objective optimization procedure is applied to provide the optimization design parameters which are charge pressure, operating frequency, and temperature of after-cooler as well as swept volume of compressor. The procedure is selected to obtain the maximum coefficient of performance (COP) and the minimum cooling temperature (Tcold) as two objective functions. In order to validate the simulation code, the results were compared with the results of other models and experiments. The results showed a reasonably well agreement between simulation output and experimental data. The results of optimal designs are a set of multiple optimum solutions, called Pareto optimal solutions. Moreover, the closed form relations between two objectives are derived for Pareto optimal solutions of pulse tube refrigerator. Finally, a sensitivity analysis of the variation of each design parameter on both objective functions was carried out as well and the results are presented. As a result, the COP is more sensitive than Tcold in the optimum design points. The frequency of refrigerator is the most sensitive factor which affects the COP even with little changes.

Modeling and Second Law Based Optimization of Plate Fin and Tube Heat Exchanger Using MOPSO

In the present study, a comprehensive thermal modeling and optimal design of plain Fin-and-Tube Heat Exchanger (FTHE) is performed. Hence, method is applied to estimate the heat exchanger pressure drop and effectiveness. The design parameters of this scientific study are selected as: longitudinal pitch, transversal pitch, fin pitch, number of tube pass, tube diameter, cold stream flow length, no-flow length and hot stream flow length. In addition, Multi Objective Particle Swarm Optimization (MOPSO) is applied to obtain the minimum number of entropy generation units and total annual cost (sum of investment and operation costs) as two objective functions, simultaneously. The results of optimal designs are a set of multiple optimum solutions, called ‘Pareto optimal solutions’. It reveals that any geometrical changes which decrease the number of entropy generation units lead to an increase in the total annual cost and vice versa. Moreover, for prediction of the optimal design of the FTHE, an equation for number of entropy generation units versus the total annual cost is derived for the Pareto front. Furthermore, the sensitivity analysis of change in optimum number of entropy generation units and total annual cost with changes in design parameters of the fin tube heat exchanger is also performed in detail.

Multi-Objective Optimization of a Fin with two-Dimensional Heat Transfer Using NSGA-II and ANN

Two-dimensional heat transfer in a fin was modeled with acceptable accuracy and optimized. Bezier curve was used to estimate the fin geometry. The finite volume method coupled with the artificial neural network was developed to predict the temperature distribution through the fin with -1.5% to +1% and ± 0.5% accuracy for fin efficiency and rate of heat transfer, respectively. Locations of four control points in the Bezier curve were considered as design variables. Then, fast and elitist non-dominated sorting genetic algorithm (NSGA-II) was applied to find the maximum fin efficiency and the rate of heat transfer as two objective functions. The results of optimal designs were a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The maximum 72 percent for fin efficiency was found with 739W as its rate of heat transfer while the maximum rate of heat transfer was 962.3 W with 57 percent efficiency. In addition, the optimum results of two-dimensional heat transfer were compared with one-dimensional and the average 14.7 percent decreases in fin efficiency and the rate of heat transfer was found that show the deficiency of the one-dimension modeling. In the second case study, the Pareto front was derived for the rate of heat transfer and fin surface area as two objective functions. It was observed that the results of optimum fin configuration in the case of fin efficiency as objective function are the same with the results of fin surface area as objective function.

The optimum design of power distribution for pressurized water reactor

The aim of this work is to develop a two-level optimization method for designing the optimum initial fuel loading pattern and burnable poison placement in pressurized water reactors. At the lower level, based on the fuel loading pattern (LP) optimized by backward diffusion calculation theory, Pontryagin’s maximum principle is employed to investigate the optimum arrangement of burnable poison (BP) that can generate the lowest radial power peaking factor (PPF). At the upper level a multi-objective problem (MOP), with LP and BP as two objective functions, is proposed by coordinate the interrelationship of LP and BP, and optimized by non-dominated sorting genetic algorithm (NSGA-II). The results of optimum designs called ‘Pareto optimum solutions’ are a set of multiple optimum solutions. After sensitivity analysis is performed, the final optimum solution which is chosen based on a typical VVER-1000 reactor reveals that the method could not only save the fuel consumption but also reduce the PPF in comparison to published data.

Soft computing based multi-objective optimization of steam cycle power plant using NSGA-II and ANN

In this paper a steam turbine power plant is thermo-economically modeled and optimized. For this purpose, the data for actual running power plant are used for modeling, verifying the results and optimization. Turbine inlet temperature, boiler pressure, turbines extraction pressures, turbines and pumps isentropic efficiency, reheat pressure as well as condenser pressure are selected as fifteen design variables. Then, the fast and elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) is applied to maximize the thermal efficiency and minimize the total cost rate (sum of investment cost, fuel cost, and maintenance cost) simultaneously. The results of the optimal design are a set of multiple optimum solutions, called ‘Pareto optimal solutions’. The optimization results in some points show 3.76% increase in efficiency and 3.84% decrease in total cost rate simultaneously, when it compared with the actual data of the running power plant. Finally as a short cut to choose the system optimal design parameters a correlation between two objectives and fifteen decision variables with acceptable precision are presented using Artificial Neural Network (ANN).

Multi-Objective Optimization of Double-Tube Once-Through Steam Generator

This paper presents a double-tube once-through steam generator (DOTSG) consisting of the outer straight tube and the inner helical tube. The tube length and pressure drop of are important parameters in optimal design of DOTSG. For optimal design of such a system, it was modeled to estimate its tube length and pressure drop. Pitch of inner helical tube, flow distribution ratio of the primary fluid, and tube assemblage are considered as design parameters. Then fast and elitist nondominated sorting genetic algorithm-II (NSGA-II) method was applied to find the optimum values of design parameters. In the presented optimal design approach, the tube length and the total pressure drop are two objective functions. The results of optimal designs were a set of multiple optimum solutions, called “Pareto optimal solutions.” The sensitivity analysis of change in optimum tube length and pressure drop with change in design parameters of the DOTSG is also performed and the results are reported.

The optimum design of tight lattice reactor core with thin rod bundles

The fuel height, rod diameter, pitch, and the loading pattern are all important parameters in the reactor core design process. Based on the analysis of the core performance, optimization calculation is performed on the three objective functions of ABV-6M reactor, i.e., power density, coolant temperature difference between the inlet and outlet, and flow-induced vibration are proposed for optimization calculation. Then a multi-objective problem (MOP) model is applied and computed optimally by non-dominated sorting genetic algorithm (NSGA-II) with the aim of maximizing power density and temperature difference as well as minimizing the flow-induced vibration. The results of optimal designs called ‘Pareto-optimal solutions’ are a set of multiple optimum solutions, from which the final optimization can be chosen after sensitivity analysis is performed. On the basis of lattice parameters optimization, the radial one-dimensional fuel loading pattern was optimized for achieving the optimum fuel utilization. The typical optimum design considered to be safe in a verification check showed that tight lattice effectively improved the reactor performances and saved the fuel consumption.

Exergetic Optimization of Shell-and-Tube Heat Exchangers Using NSGA-II

In this article, a multi-objective exergy-based optimization through a genetic algorithm method is conducted to study and improve the performance of shell-and-tube type heat recovery heat exchangers, by considering two key parameters, such as exergy efficiency and cost. The total cost includes the capital investment for equipment (heat exchanger surface area) and operating cost (energy expenditures related to pumping). The design parameters of this study are chosen as tube arrangement, tube diameters, tube pitch ratio, tube length, tube number, baffle spacing ratio, and baffle cut ratio. In addition, for optimal design of a shell-and-tube heat exchanger, the method and Bell–Delaware procedure are followed to estimate its pressure drop and heat transfer coefficient. A fast and elitist nondominated sorting genetic algorithm (NSGA-II) with continuous and discrete variables is applied to obtain maximum exergy efficiency with minimum exergy destruction and minimum total cost as two objective functions. The results of optimal designs are a set of multiple optimum solutions, called “Pareto optimal solutions.” The results clearly reveal the conflict between two objective functions and also any geometrical changes that increase the exergy efficiency (decrease the exergy destruction) lead to an increase in the total cost and vice versa. In addition, optimization of the heat exchanger based on exergy analysis revealed that irreversibility like pressure drop and high temperature differences between the hot and cold stream play a key role in exergy destruction. Therefore, increasing the component efficiency of a shell-and-tube heat exchanger increases the cost of heat exchanger. Finally, the sensitivity analysis of change in optimum exergy efficiency, exergy destruction, and total cost with change in decision variables of the shell-and-tube heat exchanger is also performed.