扩散传质定律等温结晶过程积耗散最小化

Entransy Dissipation Minimization for Isothermal Crystallization Processes with Diffusive Mass Transfer Law

对一类给定结晶量下的等温结晶过程进行研究,考虑传质过程服从扩散传质定律[g∝Δ(c)],应用最优控制理论导出结晶过程积耗散最小时浓度最优构型,给出数值算例,并与熵产生最小、浓度一定和质流率一定的传质策略进行比较。结果表明,结晶过程积耗散最小时净结晶量的2/3次幂随时间呈线性规律变化,过程的积耗散率为常数,与等积耗散原则相一致,与以熵产生最小为目标的优化结果是显著不同的;浓度一定的传质策略下积耗散要小于质流率一定的传质策略下积耗散;积耗散最小和熵产生最小两种传质策略下的积耗散和熵产均小于其他两类传质策略下的积耗散和熵产。熵产生表征的是能量转化过程的不可逆性,质量积耗散表征的是质量传递过程的不可逆性,由于结晶过程不涉及能量转化,因此优化原则应为积耗散最小。

A class of isothermal crystallization process with the given total mass of crystals is investigated. The mass transfer process is assumed to obey the diffusive mass transfer law [ g oc A（c）], and the optimal concentration configuration for the minimum entransy dissipation of the crystallization process is obtained by applying optimal control theory. Numerical examples are provided, and the obtained results are also compared to those of the minimum entropy generation, constant concentration and constant mass flux operations. The results show that 2/3 power of the net mass of crystals for the minimum entransy dissipation of the process change with the time linearly, and the entransy dissipation rate of the process keeps constant, which coincides with the principle of equipartition of entransy dissipation and is significant different from that obtained for the minimum entropy generation of the process; the entransy dissipation for the mass transfer strategy of constant concentration is smaller than that for the mass transfer strategy of c^nstant mass flux; both the entransy dissipation and the entropy generation for the two mass transfer strategies of the minimum entransy dissipation and the minimum entropy generation are smaller than those for the other two mass transfer strategies. The entropy generation characterizes the irreversibility of energy conversion processes, and the mass entransy dissipation characterizes the irreversibility of mass transfer processes. Since the crystallization process is independent of the energy conversion, so the optimization principle should be entransy dissipation minimization.