Variable-temperature Heat Reservoirs Research Articles

Ecological, exergetic efficiency and heating load optimizations for endoreversible variable-temperature heat reservoir simple air heat pump cycles

This paper presents thermodynamic optimization of an endoreversible air heat pump with variable-temperature heat reservoirs and hot- and cold-side counter-flow heat exchangers. The expressions of the heating load, the exergetic efficiency and the ecological function of the heat pump cycle are derived. Performance comparisons among exergetic efficiency optimization objective, ecological optimization objective and traditional heating load optimization objective are performed. The influences of the pressure ratio of the compressor, the allocation of heat exchanger inventory and the heat capacity rate matching between the working fluid and the heat reservoirs on the optimal performance of the cycle are investigated by detailed numerical examples. When the performance optimization of the cycle is carried out by selecting the pressure ratio, three optimization objectives give different results; however, the results of three optimization objectives are consistent by optimizing the allocation of heat exchanger inventory and optimizing the heat capacity rate matching between the working fluid and the heat reservoirs. The results may provide guidelines for the design and optimization of practical air heat pump plants. Copyright The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org, Oxford University Press.

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.

Heating load, heating load density and COP optimisations for an endoreversible variable temperature heat reservoir air heat pump

AbstractThe performance optimisation has been studied for an endoreversible air heat pump with variable temperature heat reservoirs by taking heating load, coefficient of performance (COP) and heating load density, i.e. the ratio of heating load to the maximum specific volume in the cycle, as the optimisation objectives in this paper. The analytical relations of the heating load, the COP and heating load density are derived. The effects of pressure ratio, the effectiveness of the heat exchangers and the inlet temperature ratio of the heat reservoirs on the heating load, the COP and the heating load density are analysed. The cycle performance optimisations are performed by searching the optimum distribution of heat conductance of the hot and cold side heat exchangers for fixed total heat exchanger inventory and the optimum heat capacity rate matching between the working fluid and the heat reservoirs. The air heat pump plant design with heat loading density optimisation leads to a smaller size including the...

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.

Model of irreversible finite-heat capacity heat reservoir absorption heat transformer cycle and its application

An irreversible four-temperature-level absorption heat transformer cycle model with variable-temperature heat reservoirs is established, which considers the heat resistances between the heat reservoirs and the working fluid, the internal irreversibility due to internal dissipation of the working fluid, and the heat leakages between the heat reservoirs and the surrounding. The general relations between the heating load and the coefficient of performance are derived, and the general performance characteristic and the optimal performance characteristic are obtained using numerical examples. Moreover, the cycle model and the derived general relations are confirmed by comparing the prediction results of the model and engineering analysis results for real absorption heat transformer, and the cycle performance characteristic are discussed. The results obtained herein can provide some guidance for the optimal design of absorption heat transformer.

Power optimization of a regenerated closed variable-temperature heat reservoir Brayton cycle

In this paper, the power output of the cycle is taken as an objective for performance analysis and optimization of an irreversible regenerated closed Brayton cycle coupled to variable-temperature heat reservoirs in the viewpoint of finite time thermodynamics or entropy generation minimization. The analytical formulae about the relations between power output and pressure ratio are derived with the heat resistance losses in the hot- and cold-side heat exchangers and the regenerator, the irreversible compression and expansion losses in the compressor and turbine, the pressure drop losses at the heater, cooler and regenerator as well as in the piping and the effect of the finite thermal capacity rate of the heat reservoirs. The maximum power output optimization is performed in two aspects. The first is to search the optimum heat conductance distribution corresponding to the optimum power output among the hot- and cold-side of the heat exchangers and the regenerator for a fixed total heat exchanger inventory. The second is to search the optimum thermal capacitance rate matching corresponding to the optimum power output between the working fluid and the high-temperature heat source for a fixed ratio of the thermal capacitance rates of two heat reservoirs. The influences of some design parameters on the optimum heat conductance distribution, the optimum thermal capacitance rate matching and the maximum power output, which include the inlet temperature ratio of the heat reservoirs, the efficiencies of the compressor and the turbine, and the pressure recovery coefficient, are provided by numerical examples. The power plant design with optimization leads to a smaller size, including the compressor, turbine, and the hot- and cold-side heat exchangers and the regenerator. When the heat transfers between the working fluid and the heat reservoirs are carried out ideally, the pressure drop loss may be neglected, and the thermal capacity rates of the heat reservoirs become infinite. The results of this paper become those obtained in recent literature.

Optimum distribution of heat exchanger inventory and optimum thermal capacitance rate matching for power optimisation of a regenerated closed Brayton cycle

The power output of the cycle is taken as objective for performance analysis and optimisation of an irreversible regenerated closed Brayton cycle coupled to variable-temperature heat reservoirs. The analytical formulae about the relations between power output and pressure ratio are derived with the heat resistance losses in three heat exchangers, the irreversible losses in the compressor and turbine, the pressure drop losses in the piping and system, and the effect of the finite thermal capacity rate of the heat reservoirs. The power output optimisation is performed by searching the optimum heat conductance distribution among the three heat exchangers for the fixed total heat exchanger inventory, and by searching the optimum thermal capacitance rate matching between the working fluid and the heat reservoir.

Overall conductance and heat transfer area minimization of refrigerators and heat pumps with finite heat reservoirs

In the present study, the overall conductance and the overall heat transfer area per unit capacity of refrigeration and heat pump systems have been minimized analytically considering both internal and external irreversibilities with variable temperature (finite capacity) heat reservoirs. Hot and cold side refrigerant temperatures, conductance and heat transfer area ratios have been optimized to attain this goal. The results have been verified with the more elaborate numerical optimization results obtained for ammonia based vapour compression refrigeration and heat pump systems working with variable temperature reservoirs. It is observed that the analytical results for optimum refrigerant temperatures, minimum overall conductance and heat transfer area deviate marginally from the numerically optimized results (within 1%), if one assumes a constant heat rejection temperature. The deviation of minimum overall conductance and heat transfer area is more (about 20%), if one considers both the desuperheating and condensation regions separately. However, in the absence of complex and elaborate numerical models, the simple analytical results obtained here can be used as reasonably accurate preliminary guidelines for optimization of refrigeration and heat pump systems.

Power and entropy generation of an extended irreversible Brayton cycle: optimal parameters and performance

Finite time thermodynamics is used to solve a new model of an extended Brayton cycle with variable-temperature heat reservoirs and finite size heat exchangers. The model takes into account external and internal entropy generation and handles heat recovery and heat leaks to the environment in a novel way. The extended system considerations are very important for minimizing entropy generation and maximizing second law efficiency, profit and ecological criterion. An optimization analysis was developed on this new model to determine its maximum power and minimum entropy generation, and amid the most important findings were the global maximum net power, global minimum entropy generation, optimum global heat exchangers size distribution, best working fluid specific heat ratio and optimal fluid heat capacities, some of these never having been published previously.

Optimum performance comparison of an intercooled gas turbine cycle under power and power density conditions

SYNOPSIS In this paper, analytical formulae for the power and power density of an irreversible closed intercooled gas turbine cycle coupled to variable-temperature heat reservoirs are derived according to the theory of thermodynamic optimisation (or finite-time thermodynamics (FTT), or entropy generation minimisation (EGM), or endoreversible thermodynamics) with heat resistance losses in the hot- and cold-side heat exchangers and the intercooler, irreversible compression and expansion losses in the compressors and the turbine, and pressure drop loss in the piping. The intercooling pressure ratio and the heat conductance distributions among the hot- and cold-side heat exchangers and the intercooler are optimised for power and power density objectives, respectively. Optimisation performance comparison under maximum power and maximum power density conditions is carried out.

Cooling load and coefficient of performance optimizations for real air-refrigerators

Based on a simple irreversible variable-temperature heat reservoir air (Brayton) refrigeration cycle model, a performance analysis and optimization of a real air refrigerator is carried out using finite-time thermodynamics. To maximize the cooling load and the coefficient of performance (COP) of the cycle, the allocation of a fixed total heat-exchanger inventory and thermal-capacity rate matching between the working fluid and heat reservoirs are optimized, respectively. The influences of pressure ratio, the total heat-exchanger inventory, the efficiencies of the compressor and expander, the thermal capacity rate of the working fluid and the ratio of the thermal-capacity rates of the heat reservoirs on the performance of the cycle are shown by numerical examples. The results obtained provide guidances for the design of practical air-refrigeration plants.

Performance comparison of an irreversible closed variable temperature heat reservoir Carnot engine under maximum power density and maximum power conditions

SYNOPSIS In this paper, power density, defined as the ratio of power output to maximum specific volume in the cycle, is taken as the objective for performance analysis and optimisation of an irreversible Carnot heat engine from the viewpoint of finite time thermodynamics. The engine, coupled to variable temperature heat reservoirs, includes three types of irreversibilities: finite rate heat transfer, heat leakage and internal irreversibility. The results obtained here are compared with those obtained by using the maximum power criterion. The design parameters under optimal conditions have been derived analytically and the effects of the irreversibilities on the general and optimal performances are investigated. The results show that the design parameters at maximum power density lead to smaller and more efficient heat engines. It is also seen that the irreversibilities have a greater influence on the performance at maximum power density conditions than that at maximum power conditions. Also in this analysis, the optimum conductance allocation parameter is analysed at both maximum power density and maximum power conditions by assuming a constrained total thermal conductance. The analytical expressions between the conductance allocation parameter and the thermal efficiency are obtained. The obtained results generalise the results of previous studies and provide guidance for optimal design in terms of power, thermal efficiency and engine sizes for real heat engines. When the heat transfers between the working fluid and the heat reservoirs are carried out ideally and the thermal capacity rates of the heat reservoirs are infinite, the results of this paper then replicate those obtained in recent literature.

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.

06/00785 Power optimization of an endoreversible closed intercooled regenerated Brayton-cycle coupled to variable-temperature heat-reservoirs: Wang, W. et al. Applied Energy, 2005, 82, (2), 181–195.

06/00785 Power optimization of an endoreversible closed intercooled regenerated Brayton-cycle coupled to variable-temperature heat-reservoirs: Wang, W. et al. Applied Energy, 2005, 82, (2), 181–195.

Efficiency optimization of an irreversible closed intercooled regenerated gas-turbine cycle

Thermal efficiency is optimized for an irreversible closed intercooled regenerated gas-turbine cycle coupled to variable-temperature heat reservoirs in the viewpoint of the theory of thermodynamic optimization (or finite-time thermodynamics). It is first performed by searching the optimum intercooling pressure ratio and the optimum heat conductance distributions among the four heat exchangers (the hot- and cold-side heat exchangers, the intercooler, and the regenerator) for fixed total heat exchanger inventory. Secondly, the optimization is performed further with respect to the total pressure ratio of the cycle, the maximum efficiency is maximized twice and the double-maximum efficiency is obtained. Thirdly, the optimization is performed additionally with respect to the thermal capacitance rate matching between the working fluid and the heat reservoir, the double-maximum efficiency is maximized again and a thrice-maximum efficiency is obtained. In the optimization, the following effects are taken into account: the irreversibility of heat transfer 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 finite thermal capacity rates of the three heat reservoirs. The optimization method is applied to the conceptual design of a closed-cycle intercooled regenerated helium turbine power plant for high-speed warship propulsion. The numerical example shows that the method herein is valid and effective.

Performance comparison of an irreversible closed variable-temperature heat reservoir brayton cycle under maximum power density and maximum power conditions

The power density is taken as an objective for performance analysis of an irreversible closed Brayton cycle coupled to variable-temperature heat reservoirs. The analytical formulas about the relationship between power density and working fluid temperature ratio (pressure ratio) are derived with the heat resistance losses in the hot- and cold-side heat exchangers, the irreversible compression and expansion losses in the compressor and turbine, and the effect of the finite thermal capacity rate of the heat reservoirs. The obtained results are compared with those results obtained by using the maximum power criterion. The influences of some design parameters, including the temperature ratio of the heat reservoirs, the effectivenesses of the heat exchangers between the working fluid and the heat reservoirs, and the efficiencies of the compressor and the turbine, on the maximum power density are provided by numerical examples, and the advantages and disadvantages of maximum power density design are analysed. The power plant design with maximum power density leads to a higher efficiency and smaller size. When the heat transfers between the working fluid and the heat reservoirs are carried out ideally and the thermal capacity rates of the heat reservoirs are infinite, the results of this article become similar to those obtained in the recent literature.

05/02523 Performance analysis and comparison of an atkinson cycle coupled to variable temperature heat reservoirs under maximum power and maximum power density conditions

05/02523 Performance analysis and comparison of an atkinson cycle coupled to variable temperature heat reservoirs under maximum power and maximum power density conditions

Performance optimisation for an irreversible variable-temperature heat reservoir air refrigerator

SYNOPSIS The performance analysis and optimisation of an irreversible air refrigerator with variable-temperature heat reservoirs is carried out by taking the cooling load density, i.e., the ratio of cooling load to the maximum specific volume in the cycle, as the optimisation objective using finite-time thermodynamics (FTT) or entropy generation minimisation (EGM) in this paper. The analytical formulae for the relationships between cooling load density and pressure ratio, as well as between coefficient of performance (COP) and pressure ratio are derived with the heat resistance losses in the hot- and cold-side heat exchangers, and the irreversible compression and expansion losses in the compressor and expander. The influences of the effectiveness of the heat exchangers, the inlet temperature ratio of the reservoirs, and the efficiencies of the compressor and expander on the cooling load density versus and pressure ratio are provided by numerical examples. The cooling load density optimisation is performed by finding the optimum pressure ratio of the compressor, the optimum distribution of heat conductance of the hot- and cold-side heat exchangers for a fixed total heat exchanger inventory, and the optimum heat capacity rate matching between the working fluid and the heat reservoirs. The influences of some design parameters, including the effectiveness of the heat exchangers between the working fluid and heat reservoirs, the efficiencies of compressor and expander, the inlet temperature ratio of heat reservoirs, the heat conductance distribution and the heat capacity rate matching between the working fluid and the heat reservoirs on the maximum cooling load density are provided by numerical examples. Optimisation of refrigeration plant design leads to a reduction in size of the compressor, expander, and the hot- and cold-side heat exchangers.

A comparative performance analysis of an endoreversible heat engine with thermal reservoir of finite heat capacitance under maximum power density and maximum power conditions

SYNOPSIS This paper presents a finite time thermodynamic optimisation based on maximum power density criterion for an endoreversible Carnot heat engine model coupled to variable temperature heat reservoirs. Expressions for the power density and optimal efficiency at maximum power density conditions are derived with heat resistance losses in the hot and cold side heat exchangers. The results obtained are compared with those using the maximum power criterion. The influences of some design parameters on the maximum power density are provided by numerical examples, and the advantages and disadvantages of maximum power density are analysed. Power plant design for maximum power density leads to higher efficiency and smaller size.

Performance analysis and comparison of an Atkinson cycle coupled to variable temperature heat reservoirs under maximum power and maximum power density conditions

In this paper, performance analysis and comparison based on the maximum power and maximum power density conditions have been conducted for an Atkinson cycle coupled to variable temperature heat reservoirs. The Atkinson cycle is internally reversible but externally irreversible, since there is external irreversibility of heat transfer during the processes of constant volume heat addition and constant pressure heat rejection. This study is based purely on classical thermodynamic analysis methodology. It should be especially emphasized that all the results and conclusions are based on classical thermodynamics. The power density, defined as the ratio of power output to maximum specific volume in the cycle, is taken as the optimization objective because it considers the effects of engine size as related to investment cost. The results show that an engine design based on maximum power density with constant effectiveness of the hot and cold side heat exchangers or constant inlet temperature ratio of the heat reservoirs will have smaller size but higher efficiency, compression ratio, expansion ratio and maximum temperature than one based on maximum power. From the view points of engine size and thermal efficiency, an engine design based on maximum power density is better than one based on maximum power conditions. However, due to the higher compression ratio and maximum temperature in the cycle, an engine design based on maximum power density conditions requires tougher materials for engine construction than one based on maximum power conditions.