线性唯象传热条件下给定周期的内可逆热机最大功率输出时最优构型

Optimal Configuration of an Endoreversible Heat Engine for Maximum Power Output with Fixed Duration and Linear Phenomenological Heat Transfer Law

对线性唯象传热条件下给定循环周期的内可逆热机最优构型进行研究,利用最优控制理论得出最大功率输出时热机的最优构型为六分支结构,其中包括两个等温分支和四个最大功率分支,而没有绝热分支。给出各分支过程的时间和热源及工质温度,求出最大功率输出和相应效率。通过计算可知随着高温热源温度的减小,最大功率分支过程时间减小,最大功率输出、所需输入能量和循环效率都减小。随着汽缸容积变化率的减小,最大功率分支过程时间增加,最大功率输出减小,所需输入能量增加,循环效率减小。随着热导率的减少,最大功率分支过程时间减小,最大功率输出和所需输入能量减小,循环效率增加。将所得结果与牛顿传热规律下的结果比较可知两种传热规律下的循环最优构型均由两个等温分支和四个最大功率分支组成,且均不包括绝热分支。两种传热规律下的两个等温分支的温度不同,四个最大功率分支的过程路径也不同。两种最优构型对应的各分支过程时间不相同,最大功率输出、所需输入能量和循环效率均不相同。

Optimal configuration of an endoreversible heat engine with fixed duration and linear phenomenological heat transfer law is determined. The optimal cycle that maximizes the power output of the engine is obtained by using optimal control theory. It is shown that the optimal cycle has six branches including two isothermal branches, four maximum power branches, and no adiabatic branches. The interval of each branch and the temperature of heat reservoirs and working fluid are obtained. The maximum power and the corresponding efficiency of the engine are obtained. The calculation results show that the process time of the maximum power branch, the maximum power output, the input energy and the efficiency of the cycle decrease with the decrease of the heat source temperature. The process time of the maximum power branch and the input energy increase and the maximum power output and the efficiency of the cycle decrease with the decrease of the change rate of cylinder volume. The process time of the maximum power branch, the maximum power output and the input energy decrease and the efficiency of the cycle increase with the decrease of the heat conductivity. The obtained results are compared with those obtained with the Newton＇s heat transfer law. The compared resuits show that the optimal cycles with two heat transfer laws both contain two isothermal branches and four maximum power branches, and no adiabatic branches. For two different heat transfer laws, the temperature of their isothermal branches is different, and the process paths of four maximum power branches are different as well. The process times are different for different branches under two different optimal configurations, the maximum work outputs, the required input energies and the thermal efficiencies of the cycles are different.