Chen Lingen, Ma Kang, Ge Yanlin, Feng Huijun
Institute of Thermal Science and Power Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China.
Entropy (Basel). 2020 Jun 29;22(7):720. doi: 10.3390/e22070720.
Based on the theoretical model of a heated ideal working fluid in the cylinder, the optimal motion path of the piston in this system, for the maximum work output, is re-studied by establishing the changed Lagrangian function and applying the elimination method when the initial internal energy, initial volume, finial volume and the process time are given and generalized radiative heat transfer law between the working fluid and heat bath is considered. The analytical solutions of the intermediate Euler-Lagrange arc with square, cubic and radiative heat transfer laws are taken as examples and obtained. The optimal motion path of the piston with cubic heat transfer law, which is obtained by applying the elimination method, is compared with that obtained by applying the Taylor formula expansion method through numerical example. The comparing result shows that the accuracy of the result which is obtained by applying the elimination method is not affected by the length of time of the expansion process of the working fluid, so this result is more universal.
基于气缸内受热理想工作流体的理论模型，在给定初始内能、初始体积、终了体积和过程时间，并考虑工作流体与热库之间广义辐射传热规律的情况下，通过建立变化的拉格朗日函数并应用消元法，重新研究了该系统中活塞为实现最大功输出的最优运动路径。以具有平方、立方和辐射传热规律的中间欧拉 - 拉格朗日弧的解析解为例并得出结果。通过数值算例，将应用消元法得到的具有立方传热规律的活塞最优运动路径与应用泰勒公式展开法得到的结果进行比较。比较结果表明，应用消元法得到的结果精度不受工作流体膨胀过程时间长短的影响，因此该结果更具通用性。
