两类布朗热机和制冷机的热力学性能分析

发布时间：2018-07-07 10:18

本文选题：布朗热机(或制冷机) + 福克—普朗克方程　；参考：《南昌大学》2016年博士论文

【摘要】：布朗热机(马达),是一种利用非平衡的热涨落来引起布朗粒子产生定向的粒子流,从而实现有用功输出的装置。由于它强烈地依赖着热涨落,使得其只能在微观纳米尺度下才可能实现。因此,在当今对小尺度能源的需求和装置微型化趋势的形势下,其引起了人们广泛的关注。本文基于随机动力学和热力学理论主要研究了两类连续型和分立型布朗热机(制冷机)的热力学性能特征及其优化理论,具体内容如下:第一章,简单介绍了布朗热机的发展及热驱动的布朗热机模型的理论基础,同时介绍了本文研究的主要内容。第二章,利用Fokker-Planck方程研究了布朗粒子在周期性连续棘齿势和线性变化温度场中运动所构建的一类布朗热机及制冷机模型,分析了此类布朗热机及制冷机的热力学性能。在最大功率和最大品质因子的条件下,分别对热机和制冷机性能参数进行优化。将所得结论与分段均匀温度场分布的模型进行比较,发现后者的制冷系数低于前者。进一步,讨论了温度场的边界与棘齿势不重合时,布朗热机的性能参数与偏移量的关系。第三章,利用主方程研究了与两个温源同时接触的分立型费曼棘齿-棘爪制冷机模型,分析了制冷机的热力学性能特征。发现制冷系数和制冷率曲线为一闭合曲线,说明此制冷机是不可逆的。通过采用三个优化目标函数对制冷机进行优化,得到可通过恰当地选择参数使得制冷机工作在最优状态。最后,简单讨论了此模型作为热机的热力学性能特征。第四章,利用主方程研究了一类由简单的三态模型构造的布朗热机和制冷机模型,在非稳态情况下,分析了此模型的热力学性能,得到了性能参数随时间和系统各参量的演化规律。发现当时间趋于无穷大时,系统各性能参数趋于稳态时的值。第五章,研究了由两个多方过程和两个绝热过程构成的非卡诺制冷机模型。假设传热过程服从牛顿热传递规律,推导出制冷机的制冷系数与制冷率的表达式,画出了制冷率与制冷系数之间的特征曲线。并且通过数值模拟研究了在最大品质因子下制冷机的制冷系数。分析了在长时间和短时间的热接触条件下制冷系数的优化值,并与经典的Curzon-Ahlborn(CA)制冷系数进行比较。
[Abstract]:Brownian heat engine (motor) is a device which uses unbalanced heat fluctuations to cause Brownian particles to produce directional particle flow and thus realize the output of hard work. Because of its strong dependence on thermal fluctuations, it can only be realized at micro-nano-scale. Therefore, with the demand for small scale energy and the trend of miniaturization of devices, people pay more attention to it. Based on the theory of stochastic dynamics and thermodynamics, the thermodynamic characteristics and optimization theory of two kinds of continuous and discrete Brownian heat engines (refrigerators) are studied in this paper. The main contents are as follows: chapter 1, This paper briefly introduces the development of Brownian heat engine and the theoretical basis of Brownian heat engine model driven by heat, and introduces the main contents of this paper. In chapter 2, we study a kind of Brownian heat engine and refrigerator model based on the Fokker-Planck equation, and analyze the thermodynamic properties of the Brownian heat engine and refrigerator. Under the condition of maximum power and maximum quality factor, the performance parameters of heat engine and refrigerating machine are optimized respectively. The results are compared with the model of uniform temperature field, and the refrigeration coefficient of the latter is lower than that of the former. Furthermore, when the boundary of the temperature field is not coincident with the ratchet potential, the relationship between the performance parameters and the deviation of the Brownian heat engine is discussed. In chapter 3, the main equation is used to study the model of a separate Feynman ratchet chiller in contact with two temperature sources at the same time, and the thermodynamic characteristics of the refrigerator are analyzed. It is found that the refrigeration coefficient and the refrigeration rate curve are a closed curve, which indicates that the refrigerator is irreversible. By using three optimization objective functions to optimize the refrigerator, it is obtained that the refrigerating machine can work in the optimal state by selecting the appropriate parameters. Finally, the thermodynamic properties of the model as a heat engine are briefly discussed. In chapter 4, we study a kind of Brownian heat engine and refrigerating machine model constructed from simple three-state model by using master equation. In the case of unsteady state, we analyze the thermodynamic performance of this model. The evolution laws of performance parameters with time and system parameters are obtained. It is found that when the time tends to infinity, the performance parameters of the system tend to steady state. In chapter 5, a non-Carnot refrigerator model is studied, which consists of two multiparty processes and two adiabatic processes. Assuming that the heat transfer process is based on Newtonian heat transfer law, the expressions of refrigeration coefficient and refrigeration rate of the refrigerator are derived, and the characteristic curves between the refrigeration rate and the refrigeration coefficient are drawn. The refrigeration coefficient of the refrigerator under the maximum quality factor is studied by numerical simulation. The optimal refrigeration coefficient under long and short time thermal contact is analyzed and compared with the classical Curzon-Ahlborn (CA) refrigeration coefficient.
【学位授予单位】：南昌大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O55

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