Power-optimization of multistage non-isothermal chemical engine system via Onsager equations, Hamilton-Jacobi-Bellman theory and dynamic programming

The research on the output rate performance limit of the multi-stage energy conversion system based on modern optimal control theory is one of the hot spots of finite time thermodynamics. The existing research mainly focuses on the multi-stage heat engine system with pure heat transfer and the multi-stage isothermal chemical engine (ICE) system with pure mass transfer, while the multi-stage non ICE system with heat and mass transfer coupling is less involved. A multistage endoreversible non-isothermal chemical engine (ENICE) system with a finite high-chemical-potential (HCP) source (driving fluid) and an infinite low-chemical-potential sink (environment) is researched. The multistage continuous system is treated as infinitesimal ENICEs located continuously. Each infinitesimal ENICE is assumed to be a single-stage ENICE with stationary reservoirs. Extending single-stage results, the maximum power output (MPO) of the multistage system is obtained. Heat and mass transfer processes between the reservoir and working fluid are assumed to obey Onsager equations. For the fixed initial time, fixed initial fluid temperature, and fixed initial concentration of key component (CKC) in the HCP source, continuous and discrete models of the multistage system are optimized. With given initial reservoir temperature, initial CKC, and total process time, the MPO of the multistage ENICE system is optimized with fixed and free final temperature and final concentration. If the final concentration and final temperature are free, there are optimal final temperature and optimal final concentration for the multistage ENICE system to achieve MPO; meanwhile, there are low limit values for final fluid temperature and final concentration. Special cases for multistage endoreversible Carnot heat engines and ICE systems are further obtained. For the model in this paper, the minimum entropy generation objective is not equivalent to MPO objective.