Theory Of Finite Time Thermodynamics Research Articles

Optimal Configuration of a Bimolecular, Light-Driven Engine for Maximum Ecological Performance

An irreversible light-driven engine with a working fluid composed of the bimolecular reacting system \({2{SO}_3{\rm F} \rightleftarrows {S}_2{O}_6{F}_2}\) is studied in this paper. It is assumed that the heat transfer between the working fluid and the environment obeys Newton’s heat transfer law \({[q\propto \Delta T].}\) Piston trajectory for maximum ecological performance is determined for such an engine with rate-dependent loss mechanisms of friction and heat leakage. Optimal control theory is applied to determine the optimal configurations of piston motion trajectory and the fluid temperature. Numerical examples of optimal configuration for maximum ecological performance are provided, and the obtained results are compared with those for maximum work output and minimum entropy generation. The results show that taking maximum ecological optimization criterion as the objective makes larger improvement of the reduction of the entropy generation with the cost of a little decrease in the work output. Along the optimal path for maximum ecological performance, the time-parametrized piston velocity, temperature of the working fluid, piston position and area enveloped by the curves of temperature against piston position all lie between those along the optimal path for maximum work output and those along the optimal path for minimum entropy generation. This work can provide some guidelines for the optimal design and operation of practical light-driven engines and enriches our knowledge of finite time thermodynamic theory.

Optimization Analysis of Ship Steam Power System with Finite-Time Thermodynamics Theory

A basic model with both property of thermodynamic and heat transfer is obtained by simplifying the prime process of ship Steam Power System (SPS), which is converted into endoreversible Carnot Cycle by the introduction of mean temperature in the cycle process. The design parameters is analyzed and optimized in the view point of finite time thermodynamics (FTT) and entropy generation minimization. Results show that, the temperature ratio (α) and the heat transfer parameter ratio (β) of heat source and heat sink are two important influence factors of cycle system performance, and the increase of α and decrease of β will redound to the reduction of irreversible loss and enhancement of power output.

Power output analyses and optimizations of the Stirling cycle

Based on the finite time thermodynamics theory, the entransy theory and the entropy theory, the Stirling cycles under different conditions are analyzed and optimized with the maximum output power as the target in this paper. The applicability of entransy loss (EL), entransy dissipation (ED), entropy generation (EG), entropy generation number (EGN) and modified entropy generation number (MEGN) to the system optimization is investigated. The results show that the maximum EL rate corresponds to the maximum power output of the cycle working under the infinite heat reservoirs whose temperatures are prescribed, while the minimum EG rate and the extremum ED rate do not. For the Stirling cycle working under the finite heat reservoirs provided by the hot and cold streams whose inlet temperatures and the heat capacity flow rates are prescribed, the maximum EL rate, the minimum EG rate, the minimum EGN and the minimum MEGN all correspond to the maximum power output, but the extremum ED rate does not. When the heat capacity flow rate of the hot stream increases, the power output, the EL rate, the EG rate and the ED rate increase monotonously, while the EGN and the MEGN decrease first and then increase. The EL has best consistency in the power output optimizations of the Stirling cycles discussed in this paper.

Performance of irreversible Meletis–Georgiou vane rotary engine cycle with variable specific heats of working fluid

An irreversible cycle model of Meletis–Georgiou (MG) engine consisting of an isochoric heating branch, isochoric and isobaric cooling branches, two non-isentropic compression and two non-isentropic expansion branches and with heat transfer loss, internal irreversibility and the linear relation between specific heat of the working fluid and its temperature is established by using the theory of finite time thermodynamics. The analytical relations of the work output versus compression ratio, the efficiency versus compression ratio, as well as the work output versus efficiency are obtained by using numerical examples. The results show that the work output versus the efficiency characteristic of the irreversible MG cycle is a loop-shaped curve which is consistent with the general heat engine performance, and the cycle model considering the internal irreversibility and linear relation between specific heats of the working fluid and its temperature is closer to practice than the endo-reversible model with constant specific heats of the working fluid.

Optimal ratios of the piston speeds for a finite speed irreversible Carnot heat engine cycle

The performance of an irreversible Carnot heat engine cycle is analysed and optimized by using the theory of finite time thermodynamics based on Agrawal's [2009. A finite speed Curzon-Ahlborn engine. European Journal of Physics, 30 (3), 587–592] model of finite piston speed on the four branches and Petrescu et al.’s [2002b. Optimization of the irreversible Carnot cycle engine for maximum efficiency and maximum power through use of finite speed thermodynamic analysis. In: Proceedings of ECOS’2002, 3–5 July, Berlin, Germany, Vol. II, 1361–1368] model of a Carnot cycle engine with the finite rate of heat transfer, heat leakage from heat source to heat sink and irreversibilities caused by finite speed, friction and throttling through the valves. The finite piston speeds on the four branches are further assumed to be different, which is different from the model of constant speed of the piston on the four branches. Expressions of power output and thermal efficiency of the cycle are derived for a fixed cycle period and internal entropy generation rate. Numerical examples show that the curve of power output versus thermal efficiency is loop shaped, and there exist optimal finite piston speeds on the four branches which lead to the maximum power output and maximum thermal efficiency, respectively. The effects of the heat leakage coefficient and internal entropy generation rate on the optimal finite piston speed ratios are discussed.

Effects of Cut-Off Ratio on Performance of an Endoreversible Dual Cycle

—This study is aimed at investigating the effects of cut-off ratio on the endoreversible Dual cycle performance with considerations of heat transfer loss and specific heat ratio. By using finite time thermodynamics theory, the relations between the net work output and the compression ratio, between the thermal efficiency and the compression ratio, as well as the optimal relation between net work output and the thermal efficiency of the cycle, are derived. The results shows that if compression ratio is less than certain value, the net work output first decreases and then starts to increase as the cut-off ratio increases. While if compression ratio exceeds certain value, the increase of cut-off ratio make the net work output bigger. The results also shows that the maximum net work output and the optimal thermal efficiency corresponding to maximum net work output first increase and then start to decline as the cut-off ratio increases. The thermal efficiency and the working range of the cycle decrease when the cut-off ratio increased. The results obtained in this work can help us to understand how the cycle performance is influenced by the variation of the cut-off ratio, and they should be considered in practical cycle analysis.

Modeling and performance analysis of energy selective electron (ESE) engine with heat leakage and transmission probability

A model of an energy selective electron (ESE) engine with linear heat leakage and Lorentzian transmission probability is established in this paper. The expressions for the main performance parameters of the ESE engine operating as a heat engine or a refrigerator are derived by using the theory of finite time thermodynamics. The optimum performances of the ESE engine are explored and the influences of the heat leakage, the central energy level of the resonance, and the width of the resonance on the performance of the ESE engine are analyzed by using detailed numerical examples. The optimal operation regions of power output and efficiency (or cooling load and coefficient of performance (COP)) are also discussed. Moreover, the performances of the ESE engine with Lorentzian transmission probability are compared with those with rectangular transmission probability. It is shown that the power output versus efficiency (or cooling load versus COP) characteristic curves with and without heat leakage are all closed loop-shaped ones. The efficiency (or COP) of the ESE engine decreases as the heat leakage increases. It is found that as the resonance width increases, the power output and efficiency (or cooling load and COP) increase to a maximum and then decrease due to the finite range of energies which contribute positively to the power generation or refrigeration in the electron system. Especially, when heat leakage is taken into account, the characteristic curves of maximum efficiency (or maximum COP) versus half resonance width are parabolic-like ones, which are quite different from the monotonic decreasing characteristic curves obtained in previous analyses without considering heat leakage. The results obtained in this paper can provide some theoretical guidelines for the design and operation of practical electron energy conversion devices such as solid-state thermionic refrigerators.

Heating load and COP optimisations for a universal steady flow endoreversible heat pump model

The heating load and coefficient of performance (COP) of a class of universal steady flow endoreversible heat pump cycle model, which consists of one heating branch, two cooling branches and two adiabatic branches, are optimised using the theory of finite time thermodynamics. The analytical formulae for heating load and COP versus temperature ratio as well as COP versus heating load of the cycle model are derived. Effects of the total heat exchanger inventory on performances of heat pump cycles are shown by detailed numerical examples. The results obtained herein include the optimal performances of endoreversible Otto, Brayton, Atkinson, Diesel, Dual and Carnot heat pump cycles.

Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics

A total momentum filtered energy selective electron (ESE) heat pump model with heat leakage is established in this paper. The analytical expressions of heating load and coefficient of performance (COP) for both the total momentum filtered ( k r -filtered) ESE heat pump and the conventionally filtered ( k x -filtered) ESE heat pump in which the electrons are transmitted according to the momentum in the direction of transport only are derived, respectively. The optimal performance of the k r -filtered ESE heat pump is analyzed by using the theory of finite time thermodynamics (FTT). The optimal regions of COP and heating load for the k r -filtered heat pump are obtained. By comparing the performance of the k r -filtered device with that of the k x -filtered device, it is found that the heating load performance and the COP versus heating load characteristic curves of the k r -filtered heat pump are totally different from those of the k x -filtered device; and the maximum COP and maximum heating load of the k r -filtered device are generally higher than those of the k x -filtered device. The influences of heat leakage, resonance width, hot reservoir temperature and chemical potential on the performance of the total momentum filtered ESE heat pump are further analyzed by numerical calculations. The obtained results can provide some theoretical guidelines for the design of practical electron systems such as solid-state thermionic heat pump devices. ► A total momentum filtered energy selective electron heat pump model with heat leakage is established. ► Analytical expressions of heating load and COP for the heat pump are derived. ► The optimal performance of the heat pump is analyzed by using finite time thermodynamics.

Performance optimization of a total momentum filtered energy selective electron (ESE) heat engine with double resonances

A model of an energy selective electron (ESE) heat engine with double resonances which filter electrons according to their total momentum is established in this paper. The optimal performance of the double resonance ESE heat engine is analyzed by using the theory of finite time thermodynamics (FTT). The performance of the double resonance ESE heat engine is compared with that of the single resonance device. It is shown that the double resonance device can generate more power but at the same time becomes less efficient. Performance comparisons are also performed between the total momentum filtered ESE heat engine in which the electrons are transmitted according to the total electron momentum in all the three dimensions and the conventional ESE heat engine where the electrons are filtered according to the momentum in the direction of transport only. It is found that the total momentum filtered ESE heat engine outperforms the conventionally filtered ESE heat engine on both power output and efficiency performance. Moreover, the effects of resonance width, energy spacing of two resonances and cold reservoir temperature on the performance of the total momentum filtered double resonance heat engine are analyzed in detail by numerical calculations. In practical operation of the double resonance ESE heat engine, the values of resonance width, energy spacing and cold reservoir temperature should be small in order for the device to obtain higher efficiency.

Finite-time exergoeconomic performance optimization for a universal steady flow irreversible heat pump model

The finite-time exergoeconomic performance of a universal steady flow irreversible heat pump cycle model, which consists of two heat-absorbing branches, two heat-releasing branches and two adiabatic branches with the losses of heat transfer, heat leakage and internal irreversibility, is analysed and optimized by using the theory of finite-time thermodynamics. The analytical formulae for the heating load, coefficient of performance (COP) and profit rate function of the irreversible heat pump cycle model are derived. The optimal heating load, COP and profit rate characteristics are obtained by searching the optimal heat conductance distributions of the hot- and cold-side heat exchangers for a fixed total heat exchanger inventory. Moreover, analysis and optimization of the cycle performance are carried out in order to investigate the effects of heat leakage, internal irreversibility and price ratio on the performance of the cycle by using numerical examples. It is shown that the heat leakage changes the profit rate characteristics qualitatively, and internal irreversibility decreases the profit rate of the cycle quantitatively. The performance characteristics of the steady flow irreversible Diesel, Atkinson, Otto, Brayton, Dual, Miller and Carnot heat pump cycles are included in the universal results obtained herein.

Ecological optimisation of an irreversible-closed ICR gas turbine cycle

The ecological function is optimised for an irreversible-closed Intercooled-Recuperated (ICR) gas turbine cycle using the theory of Finite-Time Thermodynamics by searching the optimum intercooling pressure ratio and heat conductance distributions among the four heat exchangers for fixed total heat exchanger inventory and the results are compared with those at the maximum power. Numerical examples indicate that the efficiency at the maximum ecological function is larger than that at the maximum power, and the power at the maximum ecological function is close to the maximum power. It reflects that the ecological function is a compromise between the power and the efficiency.

Finite time thermodynamic modelling and analysis for irreversible IFGT cycles

<title/>Indirectly or externally fired gas turbines (IFGTs or EFGTs) are interesting technologies under development for small and medium scale combined heat and power supplies in combination with micro gas turbine technologies. The emphasis is primarily on the utilisation of the waste heat from the turbine in a recuperative process. The possibility also exists for burning biomass even ‘dirty’ fuel by employing a high temperature heat exchanger (HTHE) to avoid the combustion gases passing through the turbine. In this paper, the theory of finite time thermodynamics is used in the performance analysis of a class of irreversible closed IFGT cycles coupled to variable temperature heat reservoirs. The analytical formulae for the dimensionless power output and efficiency, as functions of the total pressure ratio, component (HTHE, hot and cold side heat exchangers) effectiveness, compressor and turbine efficiencies and the thermal capacity rates of the working fluid and the heat reservoirs, the pressure recovery coefficient, the heat reservoir inlet temperature ratio, are derived. Analyses are carried out based on the formulation. Indirectly fired gas turbine cycles are most efficient under low compression ratio ranges (2·0-5·0) and fit for low power output circumstances for integration with micro gas turbine technology. Optimal total pressure ratio π c under maximum power output is always higher than that under maximum cycle thermal efficiency. When either of the heat transfer effectiveness of the hot or the cold side heat exchanger, the pressure recovery coefficient, isentropic efficiencies of the gas turbine and the compressor and the heat reservoir inlet temperature ratio increase, the dimensionless power output, cycle efficiency and their corresponding optimal total pressure ratios increase. It must be noted that the optimal total pressure ratio π c under the maximum cycle thermal efficiency decreases with increase in heat transfer effectiveness of the HTHE. The model derived can be further used to optimise the operational parameters and forecast performance of practical IFGT configurations and choices.

Generalized model and optimum performance of an irreversible thermal Brownian microscopic heat pump

A generalized model of an irreversible thermal Brownian microscopic heat pump is established in this paper. It is composed of Brownian particles which are moving in a periodic sawtooth potential with external forces and contacting with alternating hot and cold reservoirs along the space coordinate. The generalized irreversible Brownian heat pump model incorporates heat flows driven by both the potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs. This paper derives the expressions for heating load, power input and coefficient of performance (COP) of the Brownian heat pump. The optimum performance of the generalized heat pump model is analyzed by using the theory of finite time thermodynamics (FTT). Effects of the design parameters, i.e., the external force, the heat leakage coefficient, barrier height of the potential, asymmetry of the sawtooth potential and heat reservoir temperature ratio on the performance of the Brownian heat pump are discussed in detail. The performance of the Brownian heat pump depends strictly on the design parameters. Through the proper choice of these parameters, the Brownian heat pump can operate in the optimal regimes. The optimum COP performance and the fundamental optimal relations between COP and heating load are studied by detailed numerical examples. It is shown that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, both the heating load and COP performances of the Brownian heat pump will decrease. The effective ranges of the external force and barrier height of the potential in which the Brownian motor system can operate as a heat pump are further determined.

Heating load and COP optimizations for a class of generalized irreversible universal steady-flow variable-temperature heat reservoir heat pump cycle model

The heating load and coefficient of performance (COP) of a class of generalized irreversible universal steady-flow heat pump cycle model with variable-temperature heat reservoirs and the losses of heat transfer, heat leakage and internal irreversibility are investigated by using the theory of finite-time thermodynamics. The universal heat pump cycle model consists of two heat-absorbing branches, two heat-releasing branches and two adiabatic branches. Expressions of heating load and COP of the universal heat pump cycle model are deduced, respectively. By means of numerical calculations, the heat conductance distributions between hot- and cold-side heat exchangers are optimized by taking the maximum heating load as objective. There exist both optimal heat conductance distributions and optimal thermal capacity rate matching between the working fluid and heat reservoirs which lead to the double maximum heating load. The effects of heat leakage, internal irreversibility, total heat exchanger inventory and thermal capacity rate of the working fluid on the optimal performance of the cycle are discussed in detail. The results obtained herein include the optimal performance of endoreversible and irreversible, constant- and variable-temperature heat reservoir Brayton, Otto, Diesel, Atkinson, Dual, Miller and Carnot heat pump cycles. The results obtained can provide some theoretical guidelines for the designs and operations of practical heat pumps.

Thermodynamic modelling and performance analysis of a closed endoreversible indirectly-fired gas turbine cycle

SYNOPSIS Indirectly or externally-fired gas-turbines (IFGT or EFGT) are interesting technologies under development for small and medium scale combined heat and power (CHP) supplies in combination with micro-gas-turbine technologies. The emphasis is primarily on the utilisation of the waste heat from the turbine in a recuperative process and the possibility of burning biomass (even “dirty” fuel) by employing a high temperature heat exchanger (HTHE) to avoid the combustion gases passing through the turbine. In this paper, the theory of finite time thermodynamics is used in the performance analysis of a class of endoreversible closed IFGT cycles coupled to variable temperature heat reservoirs. The analytical formulae for the dimensionless power output and efficiency, as functions of the total pressure ratio, component (HTHE, hot- and cold-side heat exchangers) effectivenesses, compressor and turbine efficiencies and the thermal capacity rates of the working fluid and the heat reservoirs, the pressure recovery coefficient and the heat reservoir inlet temperature ratio, are derived and analysed based on illustrations. IFGT cycles are most efficient under low compression ratio ranges (2.0–5.0) and fit for low power output circumstances for integrating with micro-gas-turbine technology. Optimal total pressure ratio πc under maximum power output is always higher than that under maximum cycle thermal efficiency. When either of the heat transfer effectivenesses of the hot or the cold-side heat exchanger, the pressure recovery coefficient and the heat reservoir inlet temperature ratio increases, the dimensionless power output and efficiency and their corresponding optimal total pressure ratios increase. It must be noted that the optimal total pressure ratio πc under the maximum cycle thermal efficiency decreases with the increase of heat transfer effectiveness of the HTHE. The model derived can be further used to optimise the operational parameters and forecast performance of practical IFGT configurations and choices.

Power density optimisation of an irreversible variable-temperature heat reservoir closed intercooled regenerated Brayton cycle

SYNOPSIS In this paper, power density, defined as the ratio of power output to maximum specific volume in the cycle, is analysed and optimised for an irreversible closed intercooled regenerated Brayton cycle coupled to variable-temperature heat reservoirs, according to the theory of finite-time thermodynamics. The analytical formulae for dimensionless power density and efficiency, as functions of the total pressure ratio, the inter-cooling pressure ratio, the component (i.e. regenerator, intercooler, and hot- and cold-side heat exchangers) effectivenesses, the compressor and turbine efficiencies, the thermal capacity rates of the working fluid and the heat reservoirs, the pressure recovery coefficients, the heat reservoir inlet temperature ratio, and the inlet temperature ratio of cooling fluid in the intercooler and the cold-side heat reservoir, are derived. The optimum dimensionless power density is obtained by optimising the intercooling pressure ratio. The maximum dimensionless power density is obtained by identifying the optimum heat conductance distributions between the hot- and cold-side heat exchangers for a fixed total heat exchanger inventory and fixed heat conductance distributions of the regenerator and the intercooler, and by identifying the optimum intercooling pressure ratio. When the optimisation is performed with respect to the total pressure ratio of the cycle, the maximum dimensionless power density can be maximised again, and a double maximum power density and corresponding optimum total pressure ratio are obtained. Further, as the optimisation is performed with respect to the thermal capacitance rate matching between the working fluid and the heat reservoir, the double-maximum power density is maximised again and a thrice-maximum power density is obtained. The effects of the heat reservoir inlet temperature ratio, the inlet temperature ratio of cooling fluid in the intercooler and the cold-side heat reservoir, the efficiencies of the compressors and the turbine, and the total heat exchanger inventory on the maximum power density and the corresponding efficiency, optimum intercooling pressure ratio, and optimum heat conductance distributions between the hot- and cold-side heat exchangers, the twice-maximum power density and the corresponding efficiency and optimum total pressure ratio, as well as the thrice-maximum power density are analysed by numerical examples. In the analysis, the heat resistance losses in the four heat exchangers, the irreversible compression and expansion losses in the compressors and the turbine, the pressure drop loss in the piping, and the effects of finite thermal capacity rate of the three heat reservoirs are taken into account.

Exergetic Efficiency Optimization for an Irreversible Carnot Heat Engine

AbstractIn this paper, an exergetic efficiency optimization method that combines the concept of exergy and finite-time thermodynamic theory is developed to analyze an irreversible heat engine. With the total thermal conductance constraint, the analytical solutions of optimal allocation of thermal conductance and the corresponding maximum exergetic efficiency, thermal efficiency, as well as operating temperatures of hot and cold sides are obtained under a fixed overall heat supply rate. The results show that the exergetic efficiency optimization method can effectively analyze an irreversible heat engine.

Exergetic efficiency optimization of a refrigeration system with multi-irreversibilities

Exergetic efficiency optimization has been carried out for a refrigeration system with multi-irreversibilities, including finite-rate heat transfer, internal dissipation of the working fluid and heat leak between the heat reservoirs. The exergetic efficiency is defined as the ratio of the rate of exergy output to the rate of exergy input in the refrigeration system and is considered as an objective function to be maximized. By combining the exergy concept and finite-time thermodynamic theory, the maximum exergetic efficiency is determined analytically. The optimum values of the cycle cooling rate and the coefficient of performance of the system are obtained simultaneously. The influences of various parameters on the maximum exergetic efficiency are investigated by numerical calculation. The allocation problem of a fixed total thermal conductance between the hot-side and the cold-side heat exchangers is also studied. The results show that the method of exergetic efficiency optimization is practical and effective for the evaluation of an irreversible refrigeration system.

Power density optimisation of an endoreversible closed variable-temperature heat reservoir intercooled regenerated Brayton cycle

SYNOPSIS Taking power density, defined as the ratio of power output to the maximum specific volume in the cycle, as the objective function, this paper applies the theory of finite time thermodynamics to find the optimal distribution of heat conductance of the hot- and cold-side heat exchangers, the optimal intercooling pressure ratio, the optimal total pressure ratio and the optimal heat capacity ratio between working fluid and heat reservoir of an endoreversible closed intercooled regenerated Brayton cycle coupled to variable-temperature heat reservoirs with heat resistance losses in the hot- and cold-side heat exchangers, the intercooler and the regenerator, by using detailed numerical calculation. The maximum power density, the double-maximum power density and the triple-maximum power density are obtained by optimisation. The effects of some design parameters, including the cycle inlet heat reservoir temperature ratio, the inlet temperature ratio of cooling fluid in the intercooler and the cold-side heat reservoir, and the total heat exchanger inventory, on the maximum power density and the corresponding efficiency, optimum intercooling pressure ratio, and optimum heat conductance distributions between the hot- and cold-side heat exchangers, the double-maximum power density and the corresponding efficiency and optimum total pressure ratio, as well as the triple-maximum power density, are analysed.