周期性双势垒锯齿势中温差驱动的布朗热机

研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明：当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率. 关键词： 布朗热机 双势垒锯齿势 热漏 热力学性能     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine

Brownian particles moving in a spatially asymmetric but periodic potential (ratchet), with an external load force and connected to an alternating hot and cold reservoir, are modeled as a microscopic heat engine, referred to as the Brownian heat engine. The heat flow via both the potential energy and the kinetic energy of the particles are considered simultaneously. The forward and backward particle currents are determined using an Arrhenius' factor. Expressions for the power output and efficiency are derived analytically. The maximum power output and efficiency are calculated. It is expounded that the Brownian heat engine is always irreversible and its efficiency cannot approach the efficiency η_C of the Carnot heat engine even in quasistatic limit. The influence of the main parameters such as the load, the barrier height of the potential, the asymmetry of the potential and the temperature ratio of the heat reservoirs on the performance of the Brownian heat engine is discussed in detail. It is found that the Brownian heat engines may be controlled to operate in different regions through variation of some parameters.     

Heat flow and efficiency in a microscopic engine

We study the energetics of a thermal motor driven by temperature differences, which consists of a Brownian particle moving in a sawtooth potential with an external load where the viscous medium is periodically in contact with hot and cold heat reservoir along space coordinate. The motor can work as a heat engine or a refrigerator under different conditions. The heat flow via both potential and kinetic energy is considered. The former is reversible when the engine works quasistatically and the latter is always irreversible. The efficiency of the heat engine can never approach Carnot efficiency.     

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

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

一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.     

Thermodynamic characteristics of a Brownian heat pump in a spatially periodic temperature field

This paper has studied the thermodynamic performance of a thermal Brownian heat pump,which consists of Brownian particles moving at a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate.The heat flows driven by both potential and kinetic energies are taken into account.The analytical expressions for the heating load,coefficient of performance(COP) and power input of the Brownian heat pump are derived and the performance char...     

Maximum obtainable specific power of high-temperature waste heat engines

An endoreversible Carnot cycle is presented in this paper for a heat engine using higt-temperature waste heat. The endoreversible Carnot cycle is a modified Carnot cycle, where the heat-transferred between the heat engine and its surroundings is the only irreversible process. Since the energy input (waste heat) to the heat engine is free, the cost of the output power of the heat engine depends mainly on the size of the heat exchangers. A specific power, power per unit area of heat exchanger surface area, is adopted as the objective function for the performance analysis of the heat engine. The relation between the maximum obtainable specific power and the temperature range in which the high-temperature waste heat engine operates is found.     

Negative specific heat, phase transition and particles spilling from a potential well

For a finite number of noninteracting particles in a box with a potential well in the center, the microcanonical kinetic energy in dependence on the total energy as it is negative can be classified into three categories. The first exhibits a monotonical rise and the specific heat is positive. The second shows a diminishing sawtooth wave with a global rise. The last corresponds to the extreme case and takes the regular sawtooth wave form. The sawtooth wave portion associates periodically a kinetic energy fall in spite of an increase of the total energy; and we attribute to such a fall the negative specific heat. The phase transition can be defined when the relatively dense particle state in the well and relatively dilute particle state in the rest volume of the box coexist, and the appearance of the negative specific heat is sufficient but not necessary for the onset of the phase transition.     

以广义Redlich-Kwong气体为工质的不可逆回热式斯特林热机循环输出功率和效率

研究了热阻、回热损失和热漏等多种不可逆因素对以广义Redlich-Kwong气体为工质的斯特林热机性能的影响,给出了斯特林热机输出功率和效率的具体表达式并分析非理想回热特性及循环主要性能参数(如循环体积比及工质高低温比等)对循环输出功率和效率的影响.同时指出,只有在理想回热及无热漏的情况下,气体斯特林热机的效率才能达到卡诺效率.     

Irreversible Brownian Heat Engine

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine \(\eta =1-\sqrt{{T_{c}/T_{h}}}\) [23]. On the other hand, the maximum power efficiency of the engine approaches \(\eta ^{MAX}=1-({T_{c}/T_{h}})^{1\over 4}\). It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.     

Performance analysis of a tunneling thermoelectric heat engine with nano-scaled quantum well

A numerical model of a nano-scaled thermoelectric heat engine with InP/InAs/InP trilayer quantum well (QW) is investigated. The expressions of those performance parameters, such as current, power output, and efficiency are expressed. By numerical calculation, the resonant tunneling behavior of electrons in the QW is described, which seems like a very good energy selective electron mechanism for the heat engine. After considering the radiation heat leakage, for fixed layer thicknesses of the QW, the optimum working regions of the heat engine with respect to the chemical potentials and the bias voltage are obtained numerically under the economic criterion. From these results, the power output can be increased by narrowing down the layer thicknesses. In addition, owing to the radiant heat leakage, the efficiency initially increases in the working regions and then decreases when the layer thicknesses increase gradually, from which one can obtain a maximum efficiency by optimizing layer thicknesses of QW. These results calculated here may provide a guide for the optimum designs of tunneling thermoelectric devices.     

Maximum power output of a class of irreversible non-regeneration heat engines with a non-uniform working fluid and linear phenomenological heat transfer law

Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid, in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [q ∝ Δ(T ⁻¹)], are studied in this paper. Optimal control theory is used to determine the upper bounds of power of the heat engine for the lumped-parameter model and the distributed-parameter model, respectively. The results show that the maximum power output of the heat engine in the distributed-parameter model is less than or equal to that in the lumped-parameter model, which could provide more realistic guidelines for real heat engines. Analytical solutions of the maximum power output are obtained for the irreversible heat engines working between constant temperature reservoirs. For the irreversible heat engine operating between variable temperature reservoirs, a numerical example for the lumped-parameter model is provided by numerical calculation. The effects of changes of reservoir’s temperature on the maximum power of the heat engine are analyzed. The obtained results are, in addition, compared with those obtained with Newtonian heat transfer law [q ∝ Δ(T)].     

谐振电机耦合型双效斯特林燃气热泵系统研究

针对当前国家大力推行清洁能源技术和煤改气政策的供暖现状,本文探索了一种双效斯特林燃气热泵系统.全文基于热声学观点对系统进行了理论研究,并采用SAGE程序对其进行数值模拟和优化设计.计算表明,当加热、供热和冷端温度分别为923 K、333 K和273 K时,系统可获得的泵热量为7000 W,COPh为 1.79,系统?效...     

负载对热声发动机性能的影响

热声发动机作为一种完全没有运动部件的能量转化和传输机械具有广阔的应用前景.为了提高热声发动机的驱动性能,本文采用变负载法对热声发动机性能的影响因素进行了实验研究.实验结果表明,负载的阻力和容抗对热声发动机的加热温度、压比和声功引出有重要影响.同时,实验中还发现了能够使热声发动机瞬时消振和起振的实验方法,将极大方便对热声发动机的开关控制.     

A Three-Terminal Quantum Well Heat Engine with Heat Leakage

We propose a model for a three-terminal quantum well heat engine with heat leakage. According to the Landauer formula, the expressions for the charge current, the heat current, the power output and the efficiency are derived in the linear-response regime. The curves of the power output and the efficiency versus the positions of energy levels and the bias voltage are plotted by numerical calculation. Moreover, we obtain the maximum power output and the corresponding efficiency, and analyze the influence of the heat leakage factor, the positions of energy levels and the bias voltage on these performance parameters.     

Efficiency of Brownian heat engines

We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.     

Current,maximum power and optimized efficiency of a Brownian heat engine

A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs with maximum power and with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines.Received: 28 December 2003, Published online: 28 May 2004PACS: 05.40.Jc Brownian motion - 05.60.-k Transport processes - 05.70.-a ThermodynamicsMesfin Asfaw: Present address: Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany     

Open cycle traveling wave thermoacoustics: mean temperature difference at the regenerator interface

In an open cycle traveling wave thermoacoustic engine, the hot heat exchanger is replaced by a steady flow of hot gas into the regenerator to provide the thermal energy input to the engine. The steady-state operation of such a device requires that a potentially large mean temperature difference exist between the incoming gas and the solid material at the regenerator's hot side, due in part to isentropic gas oscillations in the open space adjacent to the regenerator. The magnitude of this temperature difference will have a significant effect on the efficiencies of these open cycle devices. To help assess the feasibility of such thermoacoustic engines, a numerical model is developed that predicts the dependence of the mean temperature difference upon the important design and operating parameters of the open cycle thermoacoustic engine, including the acoustic pressure, mean mass flow rate, acoustic phase angles, and conductive heat loss. Using this model, it is also shown that the temperature difference at the regenerator interface is approximately proportional to the sum of the acoustic power output and the conductive heat loss at this location.     

有热漏时定常态不可逆卡诺热机功率效率特性

对变热漏情况下定常态不可逆卡诺热机进行了有限时间热力学分析。导出最佳效率时的功率与等熵温比指数、效率与等熵温比指数的关系式,以及最佳面积比,进而得到最佳效率与功率关系。对最佳功率与最佳效率时的热机性能进行分析和讨论,给出一些有益的结论。