Hamilton-Jacobi-Bellman equations and dynamic programming for power-optimization of a multistage heat engine system with generalized convective heat transfer law
Hamilton-Jacobi-Bellman equations and dynamic programming for power-optimization of a multistage heat engine system with generalized convective heat transfer law
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DOI：
10.1007/s11434-010-4095-2
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发表时间：
2011-04
影响因子：
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通讯作者：
Shaojun Xia;Lingen Chen;F. Sun
中科院分区：
文献类型：
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作者：
Shaojun Xia;Lingen Chen;F. Sun
本文研究了一个在有限热容量高温贮液器和无限热容量低温环境之间运行的多级内可逆卡诺热机系统，系统具有广义对流换热规律[q <$（ΔT）m]。应用最优控制理论推导出连续的Hamilton-Jacobi-Bellman（HJB）方程，在固定初始时间和固定驱动流体初始温度的条件下，确定了最大功率输出的最优流体温度配置。基于普适优化结果，还得到了牛顿传热定律（m=1）的解析解。由于没有其他传热规律的解析解，连续的HJB方程离散和动态规划算法执行，以获得完整的数值解的优化问题。详细讨论了系统的最大输出功率、过程周期和流体温度之间的关系。所得结果为实际能量转换系统的优化设计和运行提供了理论指导。
A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with generalized convective heat transfer law [q∝(ΔT)m] is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman (HJB) equations, which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid. Based on the universal optimization results, the analytical solution for the Newtonian heat transfer law (m=1) is also obtained. Since there are no analytical solutions for the other heat transfer laws (m≠1), the continuous HJB equations are discretized and dynamic programming algorithm is performed to obtain the complete numerical solutions of the optimization problem. The relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail. The results obtained provide some theoretical guidelines for the optimal design and operation of practical energy conversion systems.