The improvement effect of quantum degeneracy on the work from a Carnot cycle

The efficiency of a Carnot (η_C) cycle is independent of the physical properties of the working gas. Therefore, η_C does not change due to quantum degeneracy of the gas. On the other hand, cycle work depends on the physical properties of the working gas since it is determined by the equation of state of the gas. Therefore, cycle work can be influenced by the quantum degeneracy of working gas. Here, Carnot power cycles working with ideal Bose and Fermi gases are examined under quantum degeneracy conditions. They are called Bose and Fermi Carnot cycles respectively. Cycle works of Bose and Fermi Carnot cycles (W_B and W_F) are derived. By dividing these works into the work of the classical Carnot power cycle (W_C), which works with classical ideal gas, work ratios are defined as R_W^B=W_B/W_C and R_W^F=W_F/W_C. Variations of R_W^B and R_W^F with high temperature of the cycle (T_H) are examined for a given temperature ratio τ=T_L/T_H and specific volume ratio r_v=v_H/v_L. It is shown that R_W^B>1 for some values of T_H while R_W^F<1 for all values of T_H. At high T_H values, R_W^B and R_W^F go to unity. For an optimum value of T_H, it is seen that R_W^B has a maximum, which is greater than unity and cannot be predicted by the classical ideal gas approximation. At the quantum degeneracy conditions, consequently, it is possible to produce more network output per cycle when a Bose gas is used as the working gas in a Carnot power cycle. For refrigeration and heat pump Carnot cycles, the use of a Bose gas persists to provide an advantage since it causes the heat pumped per cycle to increase. However, the use of a Fermi gas is always disadvantageous since it causes the network output in a power cycle and the heat pumped in the refrigeration and heat pump cycles to decrease.     

Exergoeconomic performance of an endoreversible Carnot heat pump with complex heat transfer law

The finite-time exergoeconomic performance of an endoreversible Carnot heat pump with a complex heat transfer law, including generalized convective heat transfer law and generalized radiative heat transfer law q∝ (Δ T ⁿ ) ^m , is investigated in this paper. The focus of this paper is to obtain the compromised optimization between economics (profit) and the energy utilization factor (coefficient of performance, COP) for the endoreversible Carnot heat pump, by searching the optimum COP at maximum profit, which is termed as the finite-time exergoeconomic performance bound. The obtained results include those obtained in much of the literature and can provide some theoretical guidance for the design of practical heat pumps.     

Maximum power of an endoreversible intercooled Brayton cycle

This paper describes an application of finite‐time thermodynamics to optimize the power output of endoreversible intercooled Brayton cycles coupled to two heat reservoirs with infinite thermal capacitance rates. The effects of intercooling on the maximum power and maximum‐power efficiency of an endoreversible Brayton cycle are examined. With appropriate temperature ratios of turbines and compressors being used, the maximum power output of an endoreversible intercooled Brayton cycle can be higher than that of an endoreversible simple Brayton cycle without lowering the thermal efficiency. New diagrams for maximum power, maximum‐power thermal efficiency, and optimum temperature ratios of turbines and compressors are reported. Copyright © 2000 John Wiley & Sons, Ltd.     

Effect of heat transfer law on the finite-time exergoeconomic performance of a Carnot refrigerator

The operation of a Carnot refrigerator is viewed as a production process with exergy as its output. The economic optimization of the endoreversible refrigerator is carried out in this paper. The Coefficient of Performance (COP) of the refrigerator is a secondary consideration of the practical engineering effort of maximizing cooling rate and exergy whose goodness is constrained by economical considerations. Therefore, the profit of the refrigerator is taken as the optimization objective. Using the method of finite-time exergoeconomic analysis, which emphasizes the compromise optimization between economics (profit) and the appropriate energy utilization factor (Coefficient of Performance, COP) for finite-time (endoreversible) thermodynamic cycles, this paper derives the relation between optimal profit and COP of an endoreversible Carnot refrigerator based on a relatively general heat transfer law q∝Δ(Tⁿ). The COP at the maximum profit is also obtained. The results obtained involve those for three common heat transfer laws: Newton's law (n=1), the linear phenomenological law in irreversible thermodynamics (n=−1), and the radiative heat transfer law (n=4).     

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.     

Comparative analysis of natural and conventional working fluids for use in transcritical Rankine cycle using low‐temperature geothermal source

Theoretical analyses of natural and conventional working fluids‐based transcritical Rankine power cycles driven by low‐temperature geothermal sources have been carried out with the methodology of pinch point analysis using computer models. The regenerator has been introduced and analyzed with a modified methodology considering the considerable variation of specific heat with temperature near the critical state. The evaluations of transcritical Rankine cycles have been performed based on equal thermodynamic mean heat rejection temperature and optimized gas heater pressures at various geothermal source temperature levels ranging from 80 to 120°C. The performances of CO₂, a natural working fluid most commonly used in a transcritical power cycle, have been indicated as baselines. The results obtained show: optimum thermodynamic mean heat injection temperatures of transcritical Rankine cycles are distributed in the range of 60 to 70% of given geothermal source temperature level; optimum gas heater pressures of working fluids considered are lower than baselines; thermal efficiencies and expansion ratios (Exp_r) are higher than baselines while net power output, volume flow rate at turbine inlet (V₁) and heat transfer capacity curves are distributed at both sides of baselines. From thermodynamic and techno‐economic point of view, R125 presents the best performances. It shows 10% higher net power output, 3% lower V₁, 1.0 time higher Exp_r, and 22% reduction of total heat transfer areas compared with baselines given geothermal source temperature of 90°C. With the geothermal source temperature above 100°C, R32 and R143a also show better performances. R170 shows nearly the same performances with baselines except for the higher V₁ value. It also shows that better temperature gliding match between fluids in the gas heater can lead to more net power output. Copyright © 2010 John Wiley & Sons, Ltd.     

Effects of unequal finite piston speeds on the optimal performances of endoreversible Carnot refrigeration and heat pump cycles

The performances of endoreversible Carnot refrigeration and heat pump cycles with loss of heat resistance and finite piston speeds are analysed and optimized by using the combination of finite time thermodynamics, finite speed thermodynamics and direct method. The unequal finite piston speed model on four branches is adopted. Expressions of cooling load of endoreversible Carnot refrigeration cycle and of heating load of endoreversible Carnot heat pump cycle are derived with a fixed cycle period and unequal finite piston speeds on the four branches. Numerical examples show that there exist optimal expansion ratios, which lead to maximum cooling load and maximum heating load for the fixed coefficient of performance (COP), respectively. The maximum cooling load, maximum heating load, optimal ratios of finite piston speeds and optimal hot- and cold-side working fluid temperatures versus COP characteristics for the endoreversible Carnot refrigeration and heat pump cycles are obtained. Moreover, the effects of design parameters on the performances of the two cycles are discussed.     

High Power Density Pyroelectric Energy Conversion in Nanometer-Thick BaTiO3 Films

Solid-state pyroelectric nanomaterials can be used for thermal-to-electrical energy conversion in the presence of temperature fluctuations. This article reports investigation of energy conversion in a 200 nm thick BaTiO₃ film using the pyroelectric Ericsson cycle at cycle frequencies up to 3 kHz. The high cycle frequencies were achieved due to the low thermal mass of the nanometer-scale film, unlike previous studies in which the electrical power output was limited by the rate of heat transfer through the pyroelectric material. A microfabricated platform that allowed precise thermal and electrical cycling enabled us to study the effect of electric field range, temperature oscillation amplitude, and cycle frequency on the electrical power output from pyroelectric Ericsson cycles. We measured a maximum power density of 30 W/cm³ for a temperature range 20–120°C and electric field range 100–125 kV/cm, which represents a significant improvement over past work on pyroelectric cycles. The approach presented in this article could lead to high-power waste heat harvesting in systems with high-frequency temperature oscillations.     

Thermodynamic analysis and parametric study of an intercooled–reheat closed-cycle gas turbine on the basis of a new isentropic exponent

The thermodynamic analysis and parametric study of an intercooled–reheat closed-cycle gas turbine is presented in this paper, on the basis of a new (harmonic mean) isentropic exponent. An analytical expression is derived for the optimum pressure ratio and maximum non-dimensional net work output. It is found that the optimum pressure ratio and the maximum non-dimensional net work are high when the ratio of extreme temperatures of cycle (i.e. T _max and T _min) and isentropic efficiencies of compressor and turbine (i.e. η_c and η_t) are high. The theoretical results are also compared with the practical conditions of power plant.     

Cost numerical optimization of the triple‐pressure steam‐reheat gas‐reheat gas‐recuperated combined power cycle that uses steam for cooling the first GT

Optimization is an important method for improving the efficiency and power of the combined cycle. In this paper, the triple‐pressure steam‐reheat gas‐reheat gas‐recuperated combined cycle that uses steam for cooling the first gas turbine (the regular steam‐cooled cycle) was optimized relative to its operating parameters. The optimized cycle generates more power and consumes more fuel than the regular steam‐cooled cycle. An objective function of the net additional revenue (the saving of the optimization process) was defined in terms of the revenue of the additional generated power and the costs of replacing the heat recovery steam generator (HRSG) and the costs of the additional operation and maintenance, installation, and fuel. Constraints were set on many operating parameters such as air compression ratio, the minimum temperature difference for pinch points (δT_ppm), the dryness fraction at steam turbine outlet, and stack temperature. The net additional revenue and cycle efficiency were optimized at 11 different maximum values of turbine inlet temperature (TIT) using two different methods: the direct search and the variable metric. The optima were found at the boundaries of many constraints such as the maximum values of air compression ratio, turbine outlet temperature (TOT), and the minimum value of stack temperature. The performance of the optimized cycles was compared with that for the regular steam‐cooled cycle. The results indicate that the optimized cycles are 1.7–1.8 percentage points higher in efficiency and 4.4–7.1% higher in total specific work than the regular steam‐cooled cycle when all cycles are compared at the same values of TIT and δT_ppm. Optimizing the net additional revenue could result in an annual saving of 21 million U.S. dollars for a 439 MW power plant. Increasing the maximum TOT to 1000°C and replacing the stainless steel recuperator heat exchanger of the optimized cycle with a super‐alloys‐recuperated heat exchanger could result in an additional efficiency increase of 1.1 percentage point and a specific work increase of 4.8–7.1%. The optimized cycles were about 3.3 percentage points higher in efficiency than the most efficient commercially available H‐system combined cycle when compared at the same value of TIT. Copyright © 2008 John Wiley & Sons, Ltd.     

Study on optimal performance and working temperatures of endoreversible forward and reverse carnot cycles

The connection between the expressions of optimization performances of Carnot heat engines, refrigerators and heat pumps, which operate subject to irreversible heat flow, is studied. We consider the endoreversible forward and reverse Carnot cycles and analyse the expressions which relate efficiency, refrigeration and heating coefficients to power, refrigeration and heating rates, respectively. It is found and proved that when one of the optimal relations is derived the others are also determined, and give the unified formulation of the related optimal working temperatures of the forward and reverse Carnot cycles by isentropic temperature ratio exponent. Finally, several new optimal performance relations are derived for forward and reverse Carnot cycles under nonlinear heat transfer, and some major results in the references are easily deduced and unified in this paper.     

Analysis and cost optimization of the triple‐pressure steam‐reheat gas‐reheat gas‐recuperated combined power cycle

Increasing the inlet temperature of gas turbine (TIT) and optimization are important methods for improving the efficiency and power of the combined cycle. In this paper, the triple‐pressure steam‐reheat gas‐reheat recuperated combined cycle (the Regular Gas‐Reheat cycle) was optimized relative to its operating parameters, including the temperature differences for pinch points (δT_PP). The optimized triple‐pressure steam‐reheat gas‐reheat recuperated combined cycle (the Optimized cycle) had much lower δT_PP than that for the Regular Gas‐Reheat cycle so that the area of heat transfer of the heat recovery steam generator (HRSG) of the Optimized cycle had to be increased to keep the same rate of heat transfer. For the same mass flow rate of air, the Optimized cycle generates more power and consumes more fuel than the Regular Gas‐Reheat cycle. An objective function of the net additional revenue (the saving of the optimization process) was defined in terms of the revenue of the additional generated power and the costs of replacing the HRSG and the additional fuel. Constraints were set on many operating parameters such as the minimum temperature difference for pinch points (δT_PPm), the steam turbines inlet temperatures and pressures, and the dryness fraction at steam turbine outlet. The net additional revenue was optimized at 11 different maximum values of TIT using two different methods: the direct search and variable metric. The performance of the Optimized cycle was compared with that for the Regular Gas‐Reheat cycle and the triple‐pressure steam‐reheat gas‐reheat recuperated reduced‐irreversibility combined cycle (the Reduced‐Irreversibility cycle). The results indicate that the Optimized cycle is 0.17–0.35 percentage point higher in efficiency and 5.3–6.8% higher in specific work than the Reduced‐Irreversibility cycle, which is 2.84–2.91 percentage points higher in efficiency and 4.7% higher in specific work than the Regular Gas‐Reheat cycle when all cycles are compared at the same values of TIT and δT_PPm. Optimizing the net additional revenue could result in an annual saving of 33.7 million US dollars for a 481 MW power plant. The Optimized cycle was 3.62 percentage points higher in efficiency than the most efficient commercially available H‐system combined cycle when compared at the same value of TIT. Copyright © 2007 John Wiley & Sons, Ltd.     

包含6种热机模型的普适内可逆热机循环(火用)经济性能优化

用有限时间热力学方法分析了工作在恒温热源TH、TL之间的普适定常流内可逆热机循环模型的炯经济性能，导出了循环利润率与工质温比、热效率与工质温比的关系式，以及利润率和效率的特性关系，并由数值计算分析了循环过程对循环性能的影响特点。所得结果包含了内可逆Carnot、Diesel、Otto、Atkinson、Brayton和Dual循环的有限时间炯经济性能。     

Maximum profit performance of a three‐heat‐reservoir heat pump

The operation of a three‐heat‐reservoir heat pump is viewed as a production process with exergy as its output. The relations between the optimal profit and COP (coefficient of performance), and the COP bound at the maximum profit of the heat pump are derived based on a general heat transfer law. The results provide a theoretical basis for developing and utilizing a variety of heat pumps. The focus of this paper is to search the compromised optimization between economics (profit) and the utilization factor (COP) for finite‐time endoreversible thermodynamic cycles. Copyright © 1999 John Wiley & Sons, Ltd.     

Analysis of an unconventional cycle as a new comparison standard for practical heat engines: the circular/elliptical cycle in T–S diagram

An unconventional cycle analysis in the T–S diagram has been carried out and the cycle characteristics such as thermal efficiency, work density (defined as the ratio of the network output to the maximum volume in the cycle), maximum volume and maximum pressure are determined. The obtained results for the unconventional cycle are compared with those of the Carnot cycle. It is proposed that the analysed unconventional cycle may be used as a better comparison standard than the Carnot cycle for practical heat engines when both size and thermal efficiency are considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal performance of an irreversible absorption refrigerator

On the basis of endoreversible absorption refrigeration cycle model with the sole irreversibility of heat transfer between the working fluid and the heat reservoirs, an irreversible model of absorption refrigeration cycle with heat transfer law of q∝Δ(T⁻¹), which includes the heat leak from the heat sink to the cooled space and irreversibilities due to the internal dissipation of the working fluid besides the finite-rate heat transfer between the working fluid and the external heat reservoirs, is established and used to derive the relation between the optimal coefficient of performance and the cooling load and the optimal distribution of the heat-transfer surface areas of the heat exchangers. The practical optimal regions of the cycle are determined and new bounds of the primary performance parameters are given. A numerical example is provided to illustrate the performance characteristic of endoreversible and irreversible cycles.     

Thermodynamic and thermoeconomic analyses of an irreversible combined Carnot heat engine system

A combined cycle model which includes the irreversibilities of finite‐rate heat transfer in heat‐exchange processes and heat leak loss of the heat source is used to analyse the performance of a multi‐stage Carnot heat engine system. The efficiency, power output, ecological function and profit of operating the combined system are optimized. The optimally operating region of the combined system is determined. The optimal combined conditions between two adjacent cycles in the combined system are obtained. Moreover, the cycle model is generalized to include the internal irreversibilities of the working fluids so that the results obtained here become more general. Copyright © 2001 John Wiley & Sons, Ltd.     

Parametric study on the thermoelectric conversion performance of a concentrated solar‐driven thermionic‐thermoelectric hybrid generator

A concentrated solar‐driven thermionic‐thermoelectric hybrid generator composed of solar heat collector, thermionic generator (TIG), thermoelectric generator (TEG), and radiator is introduced in this paper. A theoretical model of thermoelectric conversion performance for the hybrid generator is built up based on the heat source of the concentrated solar radiation rather than isothermal heat source. Based on the model, the impacts of related parameters on the internal temperature distributions, output power, and efficiency have been discussed. Moreover, the optimal operating conditions of the TIG‐TEG hybrid device at its maximum output power and efficiency have been determined. Results show that when cascading the TEG with the TIG, there is very little change of the TIG cathode temperature in most conditions, namely, T_C ≈ T_C′. Meanwhile, the anode temperature becomes higher, and the TEG cold end temperature T₂ is close to the anode temperature T_A′ for the single TIG system, ie, T_A > T_A′ ≈ T₂. In theory, the optimal concentrated solar radiation I₀ for the maximum output power P_max and the maximum efficiency η_max differs, which are I_0,P = 2.5 × 10⁶ W/m² and I_0,η = 2 × 10⁶ W/m², respectively, whereas the output power and efficiency of the TIG‐TEG hybrid system simultaneously reach their maximum values when the optimal TIG anode temperature T_A,opt = 1025 K, the optimal TIG output voltage V_opt = 2 V, and the optimal ratio of load resistance to internal resistance (R₂/R)_opt = 2. However, in practice, the parameter values of I₀, Φ_A, and T_A should be strictly controlled under 1.8 × 10⁶ W/m², 1.4 eV, and 660 K, respectively. Generally, the maximum output power and efficiency of the hybrid TIG‐TEG system are, respectively, 35% and 4% higher than that of the single TIG.     

Design and optimisation of a combination solar collector–thermal engine operating on Mars

A “dynamic” solar power plant (which consists of a solar collector–thermal engine combination) is proposed as an alternative for the more usual photovoltaic cells. A model for heat losses in a selective flat-plate solar collector operating on Mars is developed. An endoreversible Carnot cycle is used to describe heat engine operation. This provides upper limits for real performances. The output power is maximized. Meteorological and actinometric data provided by Viking Landers are used as inputs. Two strategies of collecting solar energy were considered: (i) horizontal collector; (ii) collector tilt and orientation are continuously adjusted to keep the receiving surface perpendicular on the Sun’s rays. The influences of climate and of various design parameters on solar collector heat losses, on engine output power and on the optimum sun-to-user efficiency are discussed.     

NUMERICAL MODEL AND PARAMETRIC ANALYSES OF AN INFLATABLE SOLAR HEATER

This paper presents a new solar heater model which is shaped as an inflatable hemisphere. It is called SOLARBALL©. This solar heater is above all distinguished by its small weight and volume. The final form is blown up by the user. The objective of this work was to develop a mathematical and a numerical model to analyse solar radiation and heat transfer in such a heater. The numerical model was verified by a series of experiments. After successful verification, the numerical model was used for the parametric analyses to establish the time required to heat water for different meteorological data, size of reflector and optical properties of the transparent cover, reflector and absorber surface. It was found out that typical optical efficiency and overall heat transfer coefficient of the hemispherical solar heater are between 0.45 to 0.5 and 0.6 to 1.6 W/m² K respectively. By standardised conditions (G_cov=700 W/m² and temperature difference T_w−T_a equal 50°C) the required heating time for heating 0.33 l of water varies between 15 and 25 min according to the construction parameters.