Finite-time thermodynamic analysis of a solar driven heat engine

The collective role of radiation and convection modes of heat transfer in a solar driven heat engine is investigated through a finite time thermodynamics analysis. Heat transfer from hot reservoir is assumed to be radiation and/or convection dominated. The irreversibilities due to these finite rate heat transfers were considered in determining the limits of efficiency and power generation that were discussed through varying process parameters. Results were compared with Curzon–Ahlborn and Carnot analysis cases. It is found that the upper limit of efficiency is a function of both the functional temperature dependence of heat transfer and relevant system parameters.     

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.     

Optimum operating conditions of irreversible solar driven heat engines

An optimal performance analysis of an internally and externally irreversible solar driven heat engine has been carried out. A Carnot-type heat engine model for radiative and convective boundary conditions was used to consider the effects of the finite-rate heat transfer and internal irreversibilities. The power and power density functions have been derived and maximization of these functions has been carried out for various design parameters. The optimum design parameters have been derived and the obtained results for maximum power (MP) and maximum power density (MPD) conditions have been compared. The effects of the technical parameters on the performance have been investigated.     

Maximum power-conversion efficiency for the utilization of solar energy

The overall efficiency of solar thermal power plants is investigated for estimating the upper limit of their practical performances. This study consists of the theoretical optimization of the heat engine and the optimization of the overall system efficiency, which is the product of the efficiency of the solar collector and the efficiency of the heat engine. In order to obtain a more realistic performance of the solar thermal power plant, the solar collector concentration ratio, the diffused solar radiation and the convective and radiative heat losses of the solar collector are taken into account. Instead of the classical Carnot efficiency, the efficiency at maximum power is used as the optimal conversion efficiency of a heat engine. By means of simple calculations, the optimal overall system efficiency and the corresponding operating conditions of the solar collector are obtained. The results of the present work provide an accurate guide to the performance estimation and the design of solar thermal power plants.     

Power-optimization of non-ideal energy converters under generalized convective heat transfer law via Hamilton-Jacobi-Bellman theory

A multistage irreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝m(ΔT)] and the irreversibility of heat resistance and internal dissipation is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine optimal fluid temperature configurations for maximum power output under the conditions of fixed duration and fixed initial temperature of the driving fluid. Based on general optimization results, the analytical solution for the case with Newtonian heat transfer law (m=1) is further obtained. Since there are no analytical solutions for the other heat transfer laws (m≠1), the continuous HJB equations are discretized and dynamic programming (DP) algorithm is adopted to obtain complete numerical solutions of the optimization problem, and the relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail.     

On optimized solar-pond-driven irreversible heat engines

Optimum operating temperature and design parameters are defined for a salt gradient solar pond in combination with an irreversible Carnot heat engine. The influence of the design limits of the heat engine and the design parameter of the pond on the operating temperature are considered. It was found that when a solar-pond-driven heat engine is designed to operate close to a maximum power point, the operating temperature must be increased. Apart from this, the heat engine will operate close to the maximum efficiency limit.     

Cogeneration of power and heat by using endoreversible Carnot engine

The annual worth for production of heat and power of an endoreversible Carnot engine is analyzed by using the methods of finite time thermodynamics. It was found that, in order to obtain the maximum annual worth of production of heat and power, in the design of such systems, the heat exchangers on the hot and cold sides of the Carnot engine must have equal products of their size and heat transfer coefficient. Also, for the maximum annual worth, the ratio of the lower and higher temperatures of the Carnot engine should have its optimal value.     

一类有限热源多级连续卡诺热机系统的最大输出功

对高低温热源均为有限热源的多级连续卡诺热机系统最大输出功的最优温度曲线进行了研究,利用最优控制理论得出了其最优温度曲线为驱动流体温度随流速和过程时间成指数变化,求出了其最大输出功,并与低温热源为无限热源下的结果进行了比较。     

Investigation on the optimal performance and design parameters of an irreversible solar-driven Braysson heat engine

An irreversible solar-driven Braysson thermal engine has been investigated, in which finite rate heat transfer with the radiation–convection mode from the high-temperature reservoir to the heat engine and the convection mode from the heat engine to the heat sink, and irreversible adiabatic processes are taken into account. Based on the thermodynamic analysis method, the analytic expressions of the power output and efficiency of the Braysson heat engine are derived. By using numerical value calculation, the effects of the isobaric temperature ratio, internal irreversibility parameter, temperature ratio of the thermal reservoirs as well as the allocation parameters involving the heat-transfer coefficients, and areas on the performance characteristics of the Braysson heat engine are analysed and discussed in detail. The results obtained in this paper are more general than the related conclusions published in the literature and may provide some parameter design reference for solar-driven heat engines.     

Optimization of solar-powered Stirling heat engine with finite-time thermodynamics

A mathematical model for the overall thermal efficiency of the solar-powered high temperature differential dish-Stirling engine with finite-rate heat transfer, regenerative heat losses, conductive thermal bridging losses and finite regeneration processes time is developed. The model takes into consideration the effect of the absorber temperature and the concentrating ratio on the thermal efficiency; radiation and convection heat transfer between the absorber and the working fluid as well as convection heat transfer between the heat sink and the working fluid. The results show that the optimized absorber temperature and concentrating ratio are at about 1100 K and 1300, respectively. The thermal efficiency at optimized condition is about 34%, which is not far away from the corresponding Carnot efficiency at about 50%. Hence, the present analysis provides a new theoretical guidance for designing dish collectors and operating the Stirling heat engine system.     

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.     

Assessment of Bejan’s heat exchanger allocation model under the influence of generalized thermal resistance,relaxation effect,bypass heat leak and internal irreversibility

This article reports an analytical investigation of the optimal heat exchanger allocation and the corresponding efficiency for maximum power output of a Carnot-like heat engine. To mimic a real engine, the generalized power law for the resistance in heat transfer external to the engine, relaxation effect in heat transfer, bypass heat leak and finally internal irreversibility of the power producing compartment of the engine is taken into consideration. From the engineering perspective the temperature ratio of the heat source and sink as well as to that of hot end and cold side of the working fluid is considered not to be the controllable parameters. A parametric study is presented for the other possible controllable variables. Selection of a power law over a linear model has a significant effect on the optimal heat exchanger allocation for maximum power output and the corresponding efficiency. For a higher degree of relaxation effect the drop in the maximum power efficiency is prominent along with the shift of equipartitioned allocation of heat exchanger inventory. Bypass heat leak and internal irreversibility exhibits relatively less pronounced effects on the maximum power efficiency and on the optimal heat exchanger allocation. Thus the endoreversible formulation of thermodynamic model is physically realistic. Strikingly when the optimal allocation of the heat exchanger inventory obeys the principle of equipartition in macroscopic organization for the linear law of the external heat resistance, the thermal efficiency appears to assume the representative documented value. Hence the linear model due to Bejan is also capable of capturing the essential features of a real power plant.     

Model of optimized solar heat engine operating on Mars

An endoreversible Carnot cycle is used to describe heat engine operation. This provides upper limits for real performance. The output power is maximized. Meteorological and actinometric data provided by the Viking Lander 1 are used as inputs. Four strategies of collecting solar energy are considered. Results concerning the following three parameters are briefly reported: (1) optimum solar collector surface area, (2) optimum solar collector temperature and (3) maximum output power.     

Development of an analytical model useful for micro heat engine analysis

A general endo-reversible heat engine model is presented for a combustion driven system. It is composed of a Carnot heat engine and a combustor operating at a specified temperature. The model is inspired by past work on ideal engine/combustor systems and the need for an analysis technique incorporating heat losses suffered by all practical micro engines. This latter consideration results from the necessary structural connections existing between the hot and ambient temperature sections of the engine. In the model developed here, a counterflow heat exchanger provides this structural connection while recovering a portion of the sensible heat in the exhaust flow. A thermal shunt resistance to the surroundings is used to account for conductive heat loss. Finally, a high degree of idealization is employed to obtain a closed form analytical solution for the operating conditions of the engine/combustor system which, in this case, is assumed to be at the maximum power point of the device.     

Optimum outlet temperature of solar collector for maximum work output for an Otto air-standard cycle with ideal regeneration

The optimum solar collector outlet temperature for maximizing the work output for an Otto air-standard cycle with ideal regeneration is investigated. A mathematical model for the energy balance on the solar collector along with the useful work output and the thermal efficiency of the Otto air-standard cycle with ideal regeneration is developed. The optimum solar collector outlet temperature for maximum work output is determined. The effect of radiative and convective heat losses from the solar collector, on the optimum outlet temperature is presented. The results reveal that the highest solar collector outlet temperature and, therefore, greatest Otto cycle efficiency and work output can be attained with the lowest values of radiative and convective heat losses. Moreover, high cycle work output (as a fraction of absorbed solar energy) and high efficiency of an Otto heat engine with ideal regeneration, driven by a solar collector system, can be attained with low compression ratio.     

Maximum power density for an endoreversible carnot heat engine

An analysis using maximum power-density criteria has been carried out for an endoreversible Carnot heat engine. The results have been compared with known results on maximum power analysis. The design parameters at maximum power density lead to smaller and more efficient endoreversible Carnot heat engines than those working at maximum power output.     

Optimization of Output Power and Thermal Efficiency of Solar‐Dish Stirling Engine Using Finite Time Thermodynamic Analysis

This paper presents an investigation on finite time thermodynamic (FTT) evaluation of a solar‐dish Stirling heat engine. FTTs has been applied to determine the output power and the corresponding thermal efficiency, exergetic efficiency, and the rate of entropy generation of a solar Stirling system with a finite rate of heat transfer, regenerative heat loss, conductive thermal bridging loss, and finite regeneration process time. Further imperfect performance of the dish collector and convective/radiative heat transfer mechanisms in the hot end as well as the convective heat transfer in the heat sink of the engine are considered in the developed model. The output power of the engine is maximized while the highest temperature of the engine is considered as a design parameter. In addition, thermal efficiency, exergetic efficiency, and the rate of entropy generation corresponding to the optimum value of the output power is evaluated. Results imply that the optimized absorber temperature is some where between 850 K and 1000 K. Sensitivity of results against variations of the system parameters are studied in detail. The present analysis provides a good theoretical guidance for the designing of dish collectors and operating the Stirling heat engine system.     

Thermodynamic analysis of a transcritical CO2 power cycle driven by solar energy with liquified natural gas as its heat sink

This paper proposes a transcritical CO₂ power cycle driven by solar energy while utilizing the cold heat rejection to an liquified natural gas (LNG) evaporation system. In order to ensure a continuous and stable operation for the system, a thermal storage system is introduced to store the collected solar energy and to provide stable power output when solar radiation is insufficient. A mathematical model is developed to simulate the solar-driven transcritical CO₂ power cycle under steady-state conditions, and a modified system efficiency is defined to better evaluate the cycle performance over a period of time. The thermodynamic analysis focuses on the effects of some key parameters, including the turbine inlet pressure, the turbine inlet temperature and the condensation temperature, on the system performance. Results indicate that the net power output mainly depends on the solar radiation over a day, yet the system is still capable of generating electricity long after sunset by virtue of the thermal storage tank. An optimum turbine inlet pressure exists under given conditions where the net power output and the system efficiency both reach maximum values. The net power output and the system efficiency are less sensitive to the change in the turbine inlet temperature, but the condensation temperature exerts a significant influence on the system performance. The surface area of heat exchangers increases with the rise in the turbine inlet temperature, while changes in the turbine inlet pressure have no significant impact on the heat exchanging area under the given conditions.     

A variational optimization of a finite-time thermal cycle with a nonlinear heat transfer law

In this paper we use a variational approach to study an endoreversible Curzon–Ahlborn–Novikov (CAN) heat engine under both maximum power and maximum ecological function conditions. By means of this procedure we analyze the performance of a CANheat engine with a nonlinear heat transfer law (the Dulong–Petit law) to describe the heat exchanges between the working substance and its thermal reservoirs. Our results are consistent with previous ones obtained by means of other procedures. In addition, we obtain expressions for the temperatures of the isothermal branches of the working fluid under maximum power conditions. Finally, we present an expression for a kind of nonendoreversible Carnot efficiency.     

Power generation from a new air-based Marnoch heat engine

This paper examines the performance of a new Marnoch heat engine, which uses dry air and a pneumatic piston assembly to convert thermal energy to electricity. The system has unique capabilities of operating over temperature differentials less than 100 K. Unlike a common Stirling engine, the heat exchangers and piston assembly are not co-located, which is beneficial for positioning of heat exchangers in various configurations. This paper presents an operational laboratory-scale, proof-of-concept Marnoch heat engine (MHE), including its performance and power generation capabilities. It also presents a thermodynamic analysis of the system. Based on the MHE results, component modifications are made to improve its performance. The configuration has an efficiency of about thirty percent of a Carnot heat engine operating in the temperature range between 272 K and 372 K. Experimental data is acquired to provide verification of the predictive model, as well as demonstration of the MHE’s capabilities for efficient generation of electricity from waste heat sources.