Performance analysis of a two-stage irreversible heat pump under maximum heating load per unit total cost conditions

A performance optimization of a two-stage irreversible combined heat-pump system has been carried out. The irreversibility of heat transfer across finite temperature differences, the heat-leak loss between the external heat reservoirs and the internal dissipation of the working fluids are considered. The heating load per unit total cost is taken as an objective function for the optimization. The maximum of the objective function and the corresponding optimal performance and design parameters have been derived analytically. The global and the optimal performance characteristics curves are presented in terms of technical and economical parameters. The irreversibility effects and economical aspects on the general and optimal performances have been investigated.     

Performance analysis and optimization of heat exchangers: a new thermoeconomic approach

A thermoeconomic performance optimization has been carried out for a single pass counter-flow heat exchanger model. In the considered model, the irreversibilities due to heat transfer between the hot and cold stream are taken into account and other irreversibilities such as pressure drops and flow imbalance are ignored. The objective function is defined as the actual heat transfer rate per unit total cost considering lost exergy and investment costs. The optimal performance and design parameters which maximize the objective function have been investigated. The effects of the technical and economical parameters on the general and optimal thermoeconomical performances have been also discussed.     

Performance analysis of two stage combined heat pump system based on thermoeconomic optimization criterion

A thermoeconomic performance analysis based on a new kind of optimization criterion has been performed for a two stage endoreversible combined heat pump cycle model. The optimal performances and design parameters that maximize the objective function (heating load per unit total cost) are investigated. The optimal temperatures of the working fluids, the optimum performance coefficient, the optimum specific heating load and the optimal distribution of the heat exchanger areas are determined in terms of technical and economical parameters. The effects of the economical parameter on the global and optimal performances have been discussed.     

Parametric Study and Optimization of Staggered Inclined Impinging Jets on a Concave Surface for Heat Transfer Augmentation

The characteristics of the fluid flow and heat transfer of staggered inclined impinging jets on a concave surface have been investigated numerically using three-dimensional Reynolds-averaged Navier-Stokes analysis using the shear stress transport turbulence model. Shape optimization of the impinging jet has been performed with a weighted-average surrogate model. A constant temperature condition has been applied to the concave surface. The inclination angle of the staggered jet nozzles and the distance between the jet nozzles are chosen as the design variables, and their effects on the heat transfer performance have been evaluated. It is found that the overall heat transfer increases with the pitch of vertical jet nozzles, and the staggered inclination of jet nozzles improves the heat transfer on the concave surface. For the optimization of the impinging jet, the area-averaged Nusselt number on the concave surface is set as the objective function. Latin hypercube sampling is used to determine the training points as a design of experiment, and the surrogate model is constructed using the objective function values at the training points. Sequential quadratic programming is used to search for the optimal point from the constructed surrogate model. Through the optimization, the heat transfer performance has been improved by nearly 60% compared to the reference design.     

Thermoeconomic analysis of a solar driven heat engine

Thermoeconomic optimization has been carried out for an endoreversible solar driven heat engine using finite-time/finite-size thermodynamic theory. In the considered heat engine model, heat transfer from the hot reservoir is assumed to be radiation mode and the heat transfer to the cold reservoir is assumed to be convection mode. The power output per unit total cost is taken as objective function and the optimum performance and design parameters have been investigated. The effects of the technical and economical parameters on the thermoeconomic performances have been also discussed.     

Multi-Objective Optimization of an Inverse Trapezoidal-Shaped Microchannel

The microchannel with inverse trapezoidal cross section in a micro heat sink has been optimized using three-dimensional Navier–Stokes analysis and a multi-objective evolutionary algorithm. Thermal resistance and pressure drop were selected as objective functions to evaluate the performance of the microchannel heat sink. Three design variables related to the width, depth, and angle of the channel, respectively, were selected for optimization. Parametric study has been performed with the three design variables prior to the optimization to analyze the variation of objective functions with the design variables, and thus to determine the design space for the optimization. Using a finite-volume solver, Navier–Stokes and energy equations for laminar flow and conjugate heat transfer were solved for the constant mass flow rate of 0.000598 kg/s. Latin hypercube sampling was utilized to select the design points. A surrogate model for each objective function was constructed using the values of the objective function calculated at the design points. Pareto-optimal solutions were obtained to find the optimal designs of the microchannel. Pareto sensitivity analysis was performed for the design variables along the Pareto optimal front, and it was found that both the objective functions were most sensitive to the design variable that is related to the width of the microchannel.     

The application of field synergy number in shell-and-tube heat exchanger optimization design

In the present work the field synergy principle is applied to the optimization design of the shell-and-tube heat exchanger with segmental baffles. The field synergy number which is defined as the indicator of the synergy between the velocity field and the heat flow is taken as the objective function. The genetic algorithm is employed to solve the heat exchanger optimization problems with multiple design variables. The field synergy number maximization approach for heat exchanger optimization design is thus formulated. In comparison with the initial design, the optimal design leads to a significant cost cut on the one hand and an improvement of the heat exchanger performance on the other hand. The comparison with the traditional heat exchanger optimization design approach with the total cost as the objective function shows that the field synergy number maximization approach is more advantageous.     

Performance analysis and optimization of irreversible air refrigeration cycles based on ecological coefficient of performance criterion

In this paper, a performance optimization based on ecological coefficient of performance (ECOP) criterion has been carried out for an irreversible air refrigeration cycles. The considered model includes irreversibilities due to finite-rate heat transfer, heat leakage and internal dissipations. The ECOP objective function is defined as the ratio of cooling load to the loss rate of availability (or entropy generation rate). The maximum of the ecological performance criterion and the corresponding optimal conditions have been derived analytically. The effects of irreversibility parameters on the general and optimal performances discussed detailed. The obtained results may provide a general theoretical tool for the ecological design of air refrigerators.     

An approach for the optimum design of heat exchangers

In this paper, an approach for the optimum design of heat exchangers has been presented. Traditional design method of heat exchangers involves many trials in order to meet design specifications. This can be avoided through the present design method, which takes the minimization of annual total cost as a design objective. In alternative optimum design methods, such as Lagrange multiplier method, by changing one variable at a time and using a trial–error or a graphical method, optimum results are obtained in a long time. In the present design optimization problem, the total annual cost has been taken as the objective function and heat balance, and rate equation have been taken as equal constraint. The method using the penalty function transforms the constrained problem into a single unconstrained problem. To solve the optimal problem, the method of steepest descent has been used. Initial design variables include the tube‐inside coefficient of heat transfer, tube‐outside coefficient of heat transfer, temperature difference and outside tube area of heat transfer. The changes in variables are considered simultaneously to reach an optimum solution. The results show that the present approach is a powerful tool for optimum design of heat exchangers and is expected to be beneficial to energy industry. Copyright © 2004 John Wiley & Sons, Ltd.     

Shape optimization of three-dimensional channel roughened by angled ribs with RANS analysis of turbulent heat transfer

A numerical procedure for optimizing the shape of three-dimensional channel with angled ribs extruded on both walls is presented to enhance turbulent heat transfer. The response surface based optimization is used as an optimization technique with Reynolds-averaged Navier–Stokes analysis of fluid flow and heat transfer. Shear stress transport (SST) turbulence model is used as a turbulence closure. Computational results for heat transfer rate show good agreements with experimental data. Four dimensionless variables such as, rib pitch-to-rib height ratio, rib height-to-channel height ratio, streamwise rib distance on opposite wall to rib height ratio, and the attack angle of the rib are chosen as design variables. The objective function is defined as a linear combination of heat transfer and friction loss related terms with a weighting factor. D-optimal method is used to determine the training points as a mean of design of experiment. Sensitivity of the objective function to each design variable has been evaluated. And, optimal values of the design variables have been obtained in a range of the weighting factor.     

Multi-objective optimization of a multi water-to-water heat pump system using evolutionary algorithm

This paper deals with the energy recovery in the dairy industry. Thermodynamic, economic and environmental optimization of three water-to-water heat pumps has been studied in order to replace totally or partially a fuel boiler used to produce heat at different temperature levels in a cheese factory. These heat pumps have their evaporators connected to one effluents source and two of them are equipped by storage tanks at the condenser side. Multi-objective optimization permits optimal repartition of mass flow rates of effluents and optimal choice of electrical power of the compressors and volumes of storage tanks. The thermodynamic objective is based on the exergy destruction in the whole system. The economic objective is based on the investment cost and the operating cost obtained with the heat pump system. The environmental impact objective has been defined and expressed in cost terms by considering a CO₂ taxation (carbon tax) on the GHG emissions. This objective has been integrated with the economic objective. Multi-objective genetic algorithms are used for Pareto approach optimization.     

Thermo-ecological optimization of a solar collector

The depletion of non-renewable natural exergy resources (the thermo-ecological cost) has been accepted as the objective function for thermo-ecological optimization. Its general formulation has been cited. A detailed form of the objective function has been formulated for a solar collector producing hot water for household needs. The following design parameters have been accepted as the decision variables: the collector area per unit of the heat demand, the diameter of collector pipes, the distance of the pipe axes in the collector plate. The design parameters of the internal installation (the pipes, the hot water receiver) have not been taken into account, because they are very individual. The accumulation ability of hot water comprising one day has been assumed. The objective function contains the following components: the thermo-ecological cost of copper plate, copper pipes, glass plate, steel box, thermal insulation, heat transfer liquid, electricity for driving the pump of liquid, fuel for the peak boiler. The duration curves of the flux of solar radiation and absorbed heat have been elaborated according to meteorological data and used in the calculations. The objective function for economic optimization may have a similar form, only the cost values would be different.     

Multi-objective approach in thermoenvironomic optimization of a benchmark cogeneration system

Multi-objective optimization for designing of a benchmark cogeneration system known as CGAM cogeneration system has been performed. In optimization approach, the exergetic, economic and environmental aspects have been considered, simultaneously. The thermodynamic modeling has been implemented comprehensively while economic analysis conducted in accordance with the total revenue requirement (TRR) method. The results for the single objective thermoeconomic optimization have been compared with the previous studies in optimization of CGAM problem. In multi-objective optimization of the CGAM problem, the three objective functions including the exergetic efficiency, total levelized cost rate of the system product and the cost rate of environmental impact have been considered. The environmental impact objective function has been defined and expressed in cost terms. This objective has been integrated with the thermoeconomic objective to form a new unique objective function known as a thermoenvironomic objective function. The thermoenvironomic objective has been minimized while the exergetic objective has been maximized. One of the most suitable optimization techniques developed using a particular class of search algorithms known as multi-objective evolutionary algorithms (MOEAs) has been considered here. This approach which is developed based on the genetic algorithm has been applied to find the set of Pareto optimal solutions with respect to the aforementioned objective functions. An example of decision-making has been presented and a final optimal solution has been introduced. The sensitivity of the solutions to the interest rate and the fuel cost has been studied.     

Ecological performance analysis of an endoreversible regenerative Brayton heat-engine

A performance analysis based on an ecological performance criterion has been performed for an endoreversible regenerative Brayton heat-engine. In the model, the heat-transfer irreversibilities were considered and other irreversibilities were neglected. The ecologic objective-function, defined as the power output minus the loss rate of availability is taken as the optimization criterion. The optimum performance parameters that maximize the ecological objective function are investigated. The effect of the regenerator effectiveness on the global and optimal performance have been discussed. The results obtained are compared with those of the maximum-power criterion.     

Objective function proposed for optimization of convective heat transfer devices

In this work, a general method using exergy analysis has been proposed to achieve a compromise between heat transfer effectiveness and pressure loss in heat transfer optimization problems involving internal channels. The proposed method is applied to the design optimization of a channel roughened by staggered arrays of dimples for heat transfer augmentation. Optimization is performed using surrogate-based optimization techniques and three-dimensional Reynolds-averaged Navier–Stokes analysis. Three nondimensional design variables are defined using the dimpled channel height, dimple print diameter, dimple spacing, and dimple depth. The objective function is defined as the net exergy gain considering the exergy gain by heat transfer, and exergy losses generated by friction and heat transfer. Twenty design points are generated using Latin hypercube sampling, and the Kriging model is used as a surrogate model to approximate the objective function values in the design space. Through optimization, the objective function is successfully improved with respect to the reference geometry.     

变温热源内可逆中冷回热布雷顿循环功率密度优化

以功率密度为目标,用有限时间热力学的方法,通过数值计算,对变温热源条件下的内可逆中冷回热布雷顿循环的高、低温侧换热器的热导率分配和中间压比、循环总压比和工质与热源间的热容率匹配进行优化。分别得到了最大功率密度、双重最大功率密度和三重最大功率密度,并分析了热力学参数对高低温侧换热器的热导率最优分配、最佳中间压比、最大功率密度和双重最大功率密度的影响。     

Performance analysis and optimization of straight taper fins with variable heat transfer coefficient

In the present paper, the thermal analysis and optimization of straight taper fins has been addressed. With the help of the Frobenius expanding series the temperature profiles of longitudinal fin, spine and annular fin have been determined analytically through a unified approach. Simplifying assumptions like length of arc idealization and insulated fin tip condition have been relaxed and a linear variation of the convective heat transfer coefficient along the fin surface has been taken into account. The thermal performance of all the three types of fin has been studied over a wide range of thermo-geometric parameters. It has been observed that the variable heat transfer coefficient has a strong influence over the fin efficiency. Finally, a generalized methodology has been pointed out for the optimum design of straight taper fins. A graphical representation of optimal fin parameters as a function of heat duty has also been provided.     

Shape Optimization of a Dimpled Channel to Enhance Turbulent Heat Transfer

ABSTRACT

Numerical optimization of a dimpled channel has been carried out to enhance the turbulent heat transfer. The response surface-based optimization is used as an optimization technique with three-dimensional Reynolds-averaged Navier–Stokes analysis. Computational results for heat transfer rate show good agreement with the experimental data. The objective function is defined as a linear combination of heat transfer- and friction loss-related terms with a weighting factor. Twenty-seven training points obtained by full factorial designs for three design variables construct a reliable response surface. In the sensitivity analysis, it is found that the objective function is most sensitive to the ratio of dimple depth to dimple print diameter. Optimal values of the design variables have been obtained in a range of the weighting factor.     

Exergy-based ecological optimization for a generalized irreversible Carnot heat-pump

The optimal exergy-based ecological performance of a Newton’s law generalized irreversible Carnot heat-pump, with losses due to heat-resistance, heat leak and internal irreversibility, is derived by taking into account an ecological optimization criterion as the objective function. This consists of maximizing a function representing the best compromise between the exergy-output rate and exergy-loss rate (i.e. entropy-production rate) of the heat-pump. Numerical examples are given to show the effects of heat leakage and internal irreversibility on the optimal performance of the generalized irreversible heat-pump.     

广义不可逆卡诺热机的生态学最优性能

以反映热机功率与熵产率之间最佳折衷的“生态学”准则为目标，综合考虑热阻、热漏及其它不可逆性对卡诺热机性能的影响，导出牛顿传热规律下循环的生态学最优性能，由数值计算分析比较了热漏、内不可逆性的影响特点。生态学优化以牺牲小部分输出功率为代价，较大地降低了循环的熵产率，而且在一定程度上提高了热机效率。因此，生态学目标函数不仅反映了输出功率和熵产率之间的最佳折衷，而且反映了输出功率和热效率之间的最佳折衷。