Finite-Time Thermodynamic Modeling and Optimization of Short-Chain Hydrocarbon Polymerization-Catalyzed Synthetic Fuel Process.

The short-chain hydrocarbon polymerization-catalyzed synthetic fuel technology has great development potential in the fields of energy storage and renewable energy. Modeling and optimization of a short-chain hydrocarbon polymerization-catalyzed synthetic fuel process involving mixers, compressors, heat exchangers, reactors, and separators are performed through finite-time thermodynamics. Under the given conditions of the heat source temperature of the heat exchanger and the reactor, the optimal performance of the process is solved by taking the mole fraction of components, pressure, and molar flow as the optimization variables, and taking the minimum entropy generation rate (MEGR) of the process as the optimization objective. The results show that the entropy generation rate of the optimized reaction process is reduced by 48.81% compared to the reference process; among them, the component mole fraction is the most obvious optimization variable. The research results have certain theoretical guiding significance for the selection of the operation parameters of the short-chain hydrocarbon polymerization-catalyzed synthetic fuel process.

Optimization Criteria and Efficiency of a Thermoelectric Generator.

The efficiency of a thermoelectric generator model under maximum conditions is presented for two optimization criteria proposed under the context of finite-time thermodynamics, namely, the efficient power criterion and the Omega function, where this last function represents a trade-off between useful and lost energy. The results are compared with the performance of the device at maximum power output. A macroscopic thermoelectric generator (TEG) model with three possible sources of irreversibilities is considered: (i) the electric resistance R for the Joule heating, (ii) the thermal conductances Kh and Kc of the heat exchangers between the thermal baths and the TEG, and (iii) the internal thermal conductance K for heat leakage. In particular, two configurations of the macroscopic TEG are studied: the so-called exoreversible case and the endoreversible limit. It shows that for both TEG configurations, the efficiency at maximum Omega function is always greater than that obtained in conditions of maximum efficient power, and this in turn is greater than that of the maximum power regime.

Finite-Time Thermodynamic Modeling and Analysis of Seawater Acidification Process in Electrochemical Acidification Cell.

The unsteady process of the acidification of seawater by using an electrochemical acidification cell (EAC) is studied in this paper. The model of the concentration of hydrogen ions (H+) in the effluent seawater and the cell voltage of EAC varying with time and working current are built by applying the theory of finite-time thermodynamics, respectively. The semi-empirical formulas of the concentration of H+ in the effluent seawater and the cell voltage under the constant current of the Ionpure EAC are obtained, respectively, by fitting the experimental data of the Ionpure EAC. Then, the simulated data are compared with the experimental data. The total work consumption and average power consumption of the Ionpure EAC are obtained from the semi-empirical formulas. The results show that the semi-empirical formulas can simulate the operation process of the Ionpure EAC well. The validity of the models is verified. The increase of the working current will increase the total work consumption and average power consumption of the Ionpure EAC. The proper current can be selected in engineering practice to achieve different goals, such as high efficiency or low energy consumption. The obtained results can provide some guidelines for the optimal design and optimization of EAC.

Thermodynamic Optimization of the Ethylene Oligomerization Chemical Process.

The use of olefin oligomerization in the synthesis of liquid fuel has broad application prospects in military and civil fields. Here, based on finite time thermodynamics (FTT), an ethylene oligomerization chemical process (EOCP) model with a constant temperature heat source outside the heat exchanger and reactor pipes was established. The process was first optimized with the minimum specific entropy generation rate (SEGR) as the optimization objective, then multi-objective optimization was further performed by utilizing the NSGA-II algorithm with the minimization of the entropy generation rate (EGR) and the maximization of the C10H20 yield as the optimization objectives. The results showed that the point of the minimum EGR was the same as that of SEGR in the Pareto optimal frontier. The solution obtained using the Shannon entropy decision method had the lowest deviation index, the C10H20 yield was reduced by 49.46% compared with the point of reference and the EGR and SEGR were reduced by 59.01% and 18.88%, respectively.

Four-Objective Optimizations of a Single Resonance Energy Selective Electron Refrigerator.

According to the established model of a single resonance energy selective electron refrigerator with heat leakage in the previous literature, this paper performs multi-objective optimization with finite-time thermodynamic theory and NSGA-II algorithm. Cooling load (R¯), coefficient of performance (ε), ecological function (ECO¯), and figure of merit (χ¯) of the ESER are taken as objective functions. Energy boundary (E'/kB) and resonance width (ΔE/kB) are regarded as optimization variables and their optimal intervals are obtained. The optimal solutions of quadru-, tri-, bi-, and single-objective optimizations are obtained by selecting the minimum deviation indices with three approaches of TOPSIS, LINMAP, and Shannon Entropy; the smaller the value of deviation index, the better the result. The results show that values of E'/kB and ΔE/kB are closely related to the values of the four optimization objectives; selecting the appropriate values of the system can design the system for optimal performance. The deviation indices are 0.0812 with LINMAP and TOPSIS approaches for four-objective optimization (ECO¯-R¯-ε-χ¯), while the deviation indices are 0.1085, 0.8455, 0.1865, and 0.1780 for four single-objective optimizations of maximum ECO¯, R¯, ε, and χ¯, respectively. Compared with single-objective optimization, four-objective optimization can better take different optimization objectives into account by choosing appropriate decision-making approaches. The optimal values of E'/kB and ΔE/kB range mainly from 12 to 13, and 1.5 to 2.5, respectively, for the four-objective optimization.

Maximum Profit Output Configuration of Multi-Reservoir Resource Exchange Intermediary.

A model of a multi-reservoir resource exchange intermediary also defined as a commercial engine is proposed according to analogies and similarities between thermodynamics and economics. The optimal configuration of a multi-reservoir commercial engine with a maximum profit output objective is determined by applying optimal control theory. The optimal configuration consists of two instantaneous constant commodity flux processes and two constant price processes, and the configuration is independent of a number of economic subsystems and commodity transfer law qualitatively. The maximum profit output needs some economic subsystems to never contact with the commercial engine during commodity transfer processes. Numerical examples are provided for a three-economic-subsystem commercial engine with linear commodity transfer law. The effects of price changes of an intermediate economic subsystem on the optimal configuration of a three-economic-subsystem and the performance of optimal configuration are discussed. The research object is general, and the results can provide some theoretical guidelines for operations of actual economic processes and systems.

Four-Objective Optimization of an Irreversible Magnetohydrodynamic Cycle.

Based on the existing model of an irreversible magnetohydrodynamic cycle, this paper uses finite time thermodynamic theory and multi-objective genetic algorithm (NSGA-II), introduces heat exchanger thermal conductance distribution and isentropic temperature ratio of working fluid as optimization variables, and takes power output, efficiency, ecological function, and power density as objective functions to carry out multi-objective optimization with different objective function combinations, and contrast optimization results with three decision-making approaches of LINMAP, TOPSIS, and Shannon Entropy. The results indicate that in the condition of constant gas velocity, deviation indexes are 0.1764 acquired by LINMAP and TOPSIS approaches when four-objective optimization is performed, which is less than that (0.1940) of the Shannon Entropy approach and those (0.3560, 0.7693, 0.2599, 0.1940) for four single-objective optimizations of maximum power output, efficiency, ecological function, and power density, respectively. In the condition of constant Mach number, deviation indexes are 0.1767 acquired by LINMAP and TOPSIS when four-objective optimization is performed, which is less than that (0.1950) of the Shannon Entropy approach and those (0.3600, 0.7630, 0.2637, 0.1949) for four single-objective optimizations, respectively. This indicates that the multi-objective optimization result is preferable to any single-objective optimization result.

Four-Objective Optimization for an Irreversible Porous Medium Cycle with Linear Variation in Working Fluid's Specific Heat.

Considering that the specific heat of the working fluid varies linearly with its temperature, this paper applies finite time thermodynamic theory and NSGA-II to conduct thermodynamic analysis and multi-objective optimization for irreversible porous medium cycle. The effects of working fluid's variable-specific heat characteristics, heat transfer, friction and internal irreversibility losses on cycle power density and ecological function characteristics are analyzed. The relationship between power density and ecological function versus compression ratio or thermal efficiency are obtained. When operating in the circumstances of maximum power density, the thermal efficiency of the porous medium cycle engine is higher and its size is less than when operating in the circumstances of maximum power output, and it is also more efficient when operating in the circumstances of maximum ecological function. The four objectives of dimensionless power density, dimensionless power output, thermal efficiency and dimensionless ecological function are optimized simultaneously, and the Pareto front with a set of solutions is obtained. The best results are obtained in two-objective optimization, targeting power output and thermal efficiency, which indicates that the optimal results of the multi-objective are better than that of one-objective.

Ecological Function Analysis and Optimization of a Recompression S-CO2 Cycle for Gas Turbine Waste Heat Recovery.

In this paper, a recompression S-CO2 Brayton cycle model that considers the finite-temperature difference heat transfer between the heat source and the working fluid, irreversible compression, expansion, and other irreversibility is established. First, the ecological function is analyzed. Then the mass flow rate, pressure ratio, diversion coefficient, and the heat conductance distribution ratios (HCDRs) of four heat exchangers (HEXs) are chosen as variables to optimize cycle performance, and the problem of long optimization time is solved by building a neural network prediction model. The results show that when the mass flow rate is small, the pressure ratio, the HCDRs of heater, and high temperature regenerator are the main influencing factors of the ecological function; when the mass flow rate is large, the influences of the re-compressor, the HCDRs of low temperature regenerator, and cooler on the ecological function increase; reasonable adjustment of the HCDRs of four HEXs can make the cycle performance better, but mass flow rate plays a more important role; the ecological function can be increased by 12.13%, 31.52%, 52.2%, 93.26%, and 96.99% compared with the initial design point after one-, two-, three-, four- and five-time optimizations, respectively.

Maximum Efficient Power Performance Analysis and Multi-Objective Optimization of Two-Stage Thermoelectric Generators.

Two-stage thermoelectric generators have been widely used in the aerospace, military, industrial and daily life fields. Based on the established two-stage thermoelectric generator model, this paper further studies its performance. Applying the theory of finite-time thermodynamics, the efficient power expression of the two-stage thermoelectric generator is deduced firstly. The maximum efficient power is obtained secondly by optimizing the distribution of the heat exchanger area, distribution of thermoelectric elements and working current. Using the NSGA-II algorithm, multi-objective optimizations of the two-stage thermoelectric generator are performed thirdly by taking the dimensionless output power, thermal efficiency and dimensionless efficient power as objective functions, and taking the distribution of the heat exchanger area, distribution of thermoelectric elements and output current as optimization variables. The Pareto frontiers with the optimal solution set are obtained. The results show that when the total number of thermoelectric elements is increased from 40 to 100, the maximum efficient power is decreased from 0.308W to 0.2381W. When the total heat exchanger area is increased from 0.03m2 to 0.09m2, the maximum efficient power is increased from 0.0603W to 0.3777W. The deviation indexes are 0.1866, 0.1866 and 0.1815 with LINMAP, TOPSIS and Shannon entropy decision-making approaches, respectively, when multi-objective optimization is performed on three-objective optimization. The deviation indexes are 0.2140, 0.9429 and 0.1815 for three single-objective optimizations of maximum dimensionless output power, thermal efficiency and dimensionless efficient power, respectively.

Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law.

This paper combines the mechanical efficiency theory and finite time thermodynamic theory to perform optimization on an irreversible Stirling heat-engine cycle, in which heat transfer between working fluid and heat reservoir obeys linear phenomenological heat-transfer law. There are mechanical losses, as well as heat leakage, thermal resistance, and regeneration loss. We treated temperature ratio x of working fluid and volume compression ratio λ as optimization variables, and used the NSGA-II algorithm to carry out multi-objective optimization on four optimization objectives, namely, dimensionless shaft power output P¯s, braking thermal efficiency ηs, dimensionless efficient power E¯p and dimensionless power density P¯d. The optimal solutions of four-, three-, two-, and single-objective optimizations are reached by selecting the minimum deviation indexes D with the three decision-making strategies, namely, TOPSIS, LINMAP, and Shannon Entropy. The optimization results show that the D reached by TOPSIS and LINMAP strategies are both 0.1683 and better than the Shannon Entropy strategy for four-objective optimization, while the Ds reached for single-objective optimizations at maximum P¯s, ηs, E¯p, and P¯d conditions are 0.1978, 0.8624, 0.3319, and 0.3032, which are all bigger than 0.1683. This indicates that multi-objective optimization results are better when choosing appropriate decision-making strategies.

Efficient Power Characteristic Analysis and Multi-Objective Optimization for an Irreversible Simple Closed Gas Turbine Cycle.

On the basis of the established irreversible simple closed gas turbine cycle model, this paper optimizes cycle performance further by applying the theory of finite-time thermodynamics. Dimensionless efficient power expression of the cycle is derived. Effects of internal irreversibility (turbine and compressor efficiencies) and heat reservoir temperature ratio on dimensionless efficient power are analyzed. When total heat conductance of two heat exchangers is constant, the double maximum dimensionless efficient power of a cycle can be obtained by optimizing heat-conductance distribution and cycle pressure-ratio. Through the NSGA-II algorithm, multi-objective optimizations are performed on the irreversible closed gas turbine cycle by taking five performance indicators, dimensionless power density, dimensionless ecological function, thermal efficiency, dimensionless efficient power and dimensionless power output, as objective functions, and taking pressure ratio and heat conductance distribution as optimization variables. The Pareto frontiers with the optimal solution set are obtained. The results reflect that heat reservoir temperature ratio and compressor efficiency have greatest influences on dimensionless efficient power, and the deviation indexes obtained by TOPSIS, LINMAP and Shannon Entropy decision-making methods are 0.2921, 0.2921, 0.2284, respectively, for five-objective optimization. The deviation index obtained by Shannon Entropy decision-making method is smaller than other decision-making methods and its result is more ideal.

Minimization of Entropy Generation Rate in Hydrogen Iodide Decomposition Reactor Heated by High-Temperature Helium.

The thermochemical sulfur-iodine cycle is a potential method for hydrogen production, and the hydrogen iodide (HI) decomposition is the key step to determine the efficiency of hydrogen production in the cycle. To further reduce the irreversibility of various transmission processes in the HI decomposition reaction, a one-dimensional plug flow model of HI decomposition tubular reactor is established, and performance optimization with entropy generate rate minimization (EGRM) in the decomposition reaction system as an optimization goal based on finite-time thermodynamics is carried out. The reference reactor is heated counter-currently by high-temperature helium gas, the optimal reactor and the modified reactor are designed based on the reference reactor design parameters. With the EGRM as the optimization goal, the optimal control method is used to solve the optimal configuration of the reactor under the condition that both the reactant inlet state and hydrogen production rate are fixed, and the optimal value of total EGR in the reactor is reduced by 13.3% compared with the reference value. The reference reactor is improved on the basis of the total EGR in the optimal reactor, two modified reactors with increased length are designed under the condition of changing the helium inlet state. The total EGR of the two modified reactors are the same as that of the optimal reactor, which are realized by decreasing the helium inlet temperature and helium inlet flow rate, respectively. The results show that the EGR of heat transfer accounts for a large proportion, and the decrease of total EGR is mainly caused by reducing heat transfer irreversibility. The local total EGR of the optimal reactor distribution is more uniform, which approximately confirms the principle of equipartition of entropy production. The EGR distributions of the modified reactors are similar to that of the reference reactor, but the reactor length increases significantly, bringing a relatively large pressure drop. The research results have certain guiding significance to the optimum design of HI decomposition reactors.

Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle.

Applying finite time thermodynamics theory and the non-dominated sorting genetic algorithm-II (NSGA-II), thermodynamic analysis and multi-objective optimization of an irreversible Diesel cycle are performed. Through numerical calculations, the impact of the cycle temperature ratio on the power density of the cycle is analyzed. The characteristic relationships among the cycle power density versus the compression ratio and thermal efficiency are obtained with three different loss issues. The thermal efficiency, the maximum specific volume (the size of the total volume of the cylinder), and the maximum pressure ratio are compared under the maximum power output and the maximum power density criteria. Using NSGA-II, single-, bi-, tri-, and quadru-objective optimizations are performed for an irreversible Diesel cycle by introducing dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density as objectives, respectively. The optimal design plan is obtained by using three solution methods, that is, the linear programming technique for multidimensional analysis of preference (LINMAP), the technique for order preferences by similarity to ideal solution (TOPSIS), and Shannon entropy, to compare the results under different objective function combinations. The comparison results indicate that the deviation index of multi-objective optimization is small. When taking the dimensionless power output, dimensionless ecological function, and dimensionless power density as the objective function to perform tri-objective optimization, the LINMAP solution is used to obtain the minimum deviation index. The deviation index at this time is 0.1333, and the design scheme is closer to the ideal scheme.

Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases.

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.

Performance Analysis and Four-Objective Optimization of an Irreversible Rectangular Cycle.

Based on the established model of the irreversible rectangular cycle in the previous literature, in this paper, finite time thermodynamics theory is applied to analyze the performance characteristics of an irreversible rectangular cycle by firstly taking power density and effective power as the objective functions. Then, four performance indicators of the cycle, that is, the thermal efficiency, dimensionless power output, dimensionless effective power, and dimensionless power density, are optimized with the cycle expansion ratio as the optimization variable by applying the nondominated sorting genetic algorithm II (NSGA-II) and considering four-objective, three-objective, and two-objective optimization combinations. Finally, optimal results are selected through three decision-making methods. The results show that although the efficiency of the irreversible rectangular cycle under the maximum power density point is less than that at the maximum power output point, the cycle under the maximum power density point can acquire a smaller size parameter. The efficiency at the maximum effective power point is always larger than that at the maximum power output point. When multi-objective optimization is performed on dimensionless power output, dimensionless effective power, and dimensionless power density, the deviation index obtained from the technique for order preference by similarity to an ideal solution (TOPSIS) decision-making method is the smallest value, which means the result is the best.

Multi-Objective Optimization of Braun-Type Exothermic Reactor for Ammonia Synthesis.

The exothermic reactor for ammonia synthesis is a primary device determining the performance of the energy storage system. The Braun-type ammonia synthesis reactor is used as the exothermic reactor to improve the heat release rate. Due to the entirely different usage scenarios and design objectives, its parameters need to be redesigned and optimized. Based on finite-time thermodynamics, a one-dimensional model is established to analyze the effects of inlet gas molar flow rate, hydrogen-nitrogen ratio, reactor length and inlet temperature on the total entropy generation rate and the total exothermic rate of the reactor. It's found that the total exothermic rate mainly depends on the inlet molar flow rate. Furthermore, considering the minimum total entropy generation rate and maximum total exothermic rate, the NSGA-II algorithm is applied to optimize seven reactor parameters including the inlet molar flow rate, lengths and temperatures of the three reactors. Lastly, the optimized reactor is obtained from the Pareto front using three fuzzy decision methods and deviation index. Compared with the reference reactor, the total exothermic rate of the optimized reactor is improved by 12.6% while the total entropy generation rate is reduced by 3.4%. The results in this paper can provide some guidance for the optimal design and application of exothermic reactors in practical engineering.

Entropic Balance Conditions and Optimization of Distillation Column System.

The paper considers the limitation problem of the distillation column systems separating multicomponent mixtures with serial and parallel structures. The solution takes into account the irreversibility of processes. Using entropic balance conditions, the dependence of load on heat consumption is obtained for a binary distillation column. This dependence is parameterized through two characteristic coefficients-reversible efficiency and irreversibility factor. This dependence was used to solve problems of distribution of heat and raw material fluxes in parallel column structure and selection of optimal separation order in serial structure. The obtained results make it possible to estimate the minimum heat consumption for the separation of a given flow of raw materials, the maximum productivity, and efficiency of the system.

Power and Thermal Efficiency Optimization of an Irreversible Steady-Flow Lenoir Cycle.

Using finite time thermodynamic theory, an irreversible steady-flow Lenoir cycle model is established, and expressions of power output and thermal efficiency for the model are derived. Through numerical calculations, with the different fixed total heat conductances (UT) of two heat exchangers, the maximum powers (Pmax), the maximum thermal efficiencies (ηmax), and the corresponding optimal heat conductance distribution ratios (uLP(opt)) and (uLη(opt)) are obtained. The effects of the internal irreversibility are analyzed. The results show that, when the heat conductances of the hot- and cold-side heat exchangers are constants, the corresponding power output and thermal efficiency are constant values. When the heat source temperature ratio (τ) and the effectivenesses of the heat exchangers increase, the corresponding power output and thermal efficiency increase. When the heat conductance distributions are the optimal values, the characteristic relationships of P-uL and η-uL are parabolic-like ones. When UT is given, with the increase in τ, the Pmax, ηmax, uLP(opt), and uLη(opt) increase. When τ is given, with the increase in UT, Pmax and ηmax increase, while uLP(opt) and uLη(opt) decrease.

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine.

Based on finite time thermodynamics, an irreversible combined thermal Brownian heat engine model is established in this paper. The model consists of two thermal Brownian heat engines which are operating in tandem with thermal contact with three heat reservoirs. The rates of heat transfer are finite between the heat engine and the reservoir. Considering the heat leakage and the losses caused by kinetic energy change of particles, the formulas of steady current, power output and efficiency are derived. The power output and efficiency of combined heat engine are smaller than that of single heat engine operating between reservoirs with same temperatures. When the potential filed is free from external load, the effects of asymmetry of the potential, barrier height and heat leakage on the performance of the combined heat engine are analyzed. When the potential field is free from external load, the effects of basic design parameters on the performance of the combined heat engine are analyzed. The optimal power and efficiency are obtained by optimizing the barrier heights of two heat engines. The optimal working regions are obtained. There is optimal temperature ratio which maximize the overall power output or efficiency. When the potential filed is subjected to external load, effect of external load is analyzed. The steady current decreases versus external load; the power output and efficiency are monotonically increasing versus external load.