广义流传递过程的广义耗散最小化
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摘要
广义热力学优化理论研究的重要内容之一是追求优化结果的普适性.本文首先在回顾现有文献关于传热、传质、电容器充电、经济贸易过程等不可逆过程动态优化研究工作的基础上,基于广义热力学优化理论的研究思路,通过定义广义势、广义力、广义流、广义势容、广义耗散、广义耗散力等物理量,建立了一类广义流传递过程的广义热力学物理模型,形成了相应的动态优化问题,即在广义流守恒方程约束下求解广义流传递过程广义耗散最小化.然后,分别应用欧拉-拉格朗日方程和平均最优控制理论导出了普适的优化结果即最优性条件,并基于普适的优化结果得到了一些新结论.接着,进一步讨论了上述研究结果和结论在换热过程、等温节流、单向等温传质、双向等温传质、等温结晶过程、电容器充电过程、经济贸易过程等特例中的应用.最后,提出了不可逆过程"广义热力学动态优化"的研究思想.本文的研究结果丰富和完善了广义热力学优化理论.
One of the important research contents of generalized thermodynamic optimization theory is to pursue universality of optimization results. Firstly, on the basis of summarizing and inducing the reasearch contents of dynamic optimizationsfor various irreversible transport processes, including heat transfer, mass transfer, capacitor charging, and resource exchange, this paper defines some physical quantities including generalized potential, generalized force, generalized flow, generalized potenetial capacity, genralized dissipation, generalized dissipation force, and further establishes a generalized therodynamic physical model of a class of generalized flow transfer processes based on generalized thermodynamic optimization theory. The corresponding dynamic optimization problem is formulated. Secondly, the universal optimization result, i.e. the optimality condition as shown in this paper, is obtained by using Euler-Lagrangian method and averaged optimal control theory, respectively. Some new conclusions are obtained based on these universal results. Thirdly, those new results and conclusions are further applied to some special examples, including heat transfer,isothermal throttling, one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, isothermal crystallization,capacitor charging, economic trade processes and so on. Finally, the research idea of "generalized thermodynamic dynamicoptimization" is put forward. The results in this paper enriches and consummates the generalized thermodynamic optimization theory.
One of the important research contents of generalized thermodynamic optimization theory is to pursue universality of optimization results. Firstly, on the basis of summarizing and inducing the reasearch contents of dynamic optimizationsfor various irreversible transport processes, including heat transfer, mass transfer, capacitor charging, and resource exchange, this paper defines some physical quantities including generalized potential, generalized force, generalized flow, generalized potenetial capacity, genralized dissipation, generalized dissipation force, and further establishes a generalized therodynamic physical model of a class of generalized flow transfer processes based on generalized thermodynamic optimization theory. The corresponding dynamic optimization problem is formulated. Secondly, the universal optimization result, i.e. the optimality condition as shown in this paper, is obtained by using Euler-Lagrangian method and averaged optimal control theory, respectively. Some new conclusions are obtained based on these universal results. Thirdly, those new results and conclusions are further applied to some special examples, including heat transfer,isothermal throttling, one-way isothermal mass transfer, two-way isothermal equimolar mass transfer, isothermal crystallization,capacitor charging, economic trade processes and so on. Finally, the research idea of "generalized thermodynamic dynamicoptimization" is put forward. The results in this paper enriches and consummates the generalized thermodynamic optimization theory.
引文
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