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研究了有限热容高温流体热源和无限热容低温环境间工作的多级内可逆卡诺热机系统,考虑热源与工质间传热服从广义对流传热定律[q∝(ΔT)m],在初态时刻和驱动流体初态温度均一定的条件下,应用最优控制理论导出了最大输出功率与流体温度最优构型相关的连续Hamilton-Jacobi-Bellman(HJB)方程.基于普适的优化结果,进一步导出了牛顿传热定律(m=1)下的解析解;对于非牛顿传热定律(m≠1),优化问题不存在解析解,将连续HJB方程离散化,运用动态规划方法编程实现获得了其完整的数值解,并深入讨论了系统最大输出功率与过程时间、流体温度三者间的关联耦合关系.研究结果对实际能量转化系统的最优设计与运行具有一定理论指导作用.
The multi-stage reversible Carnot engine system operating between a finite heat capacity high temperature fluid heat source and an infinite heat capacity low temperature environment is studied. The heat transfer between the heat source and the working fluid is governed by the generalized convective heat transfer law [qα (ΔT) m] The initial Hamiltonian and the initial fluid temperature are both constant, the continuous Hamilton-Jacobi-Bellman (HJB) equation is derived by using the optimal control theory, which is related to the optimal configuration of the maximum output power and the fluid temperature. Based on the universal optimization As a result, the analytical solution of Newton’s heat transfer law (m = 1) is further derived. For the non-Newtonian heat transfer law (m ≠ 1), there is no analytical solution to the optimization problem. The continuous HJB equation is discretized and programmed by dynamic programming The complete numerical solution is obtained and the relationship between the maximum output power of the system and the process time and fluid temperature is discussed in depth.The results of the study have certain theoretical guidance for the optimal design and operation of the actual energy conversion system.