矩方法及其在水凝结研究中的应用与发展

Method of moments and its application in phase transition of water

矩方法(Method of Moments,MOM),又可以称作内部坐标矩方法,通过求解液滴尺寸分布函数对内部坐标的各阶矩的输运方程,反映粒子数量及尺寸分布的演化。在各种有关伴随凝结流动的数值方法中,矩方法兼顾了计算效率和液滴分布信息,因此被广泛应用于水凝结的研究。本文首先介绍了经典矩方法,综述了矩方法的最新发展。然后应用经典凝结矩方法,研究了伴随同质凝结的Prandtl-Meyer膨胀流动问题,计算发现随着来流水蒸气饱和度的提高,凝结诱导的激波由定常状态向非定常状态转变,出现自激振荡现象;进一步,将经典凝结矩方法推广到异质凝结领域。通过引入"瞬间活化"假设,简化了异质成核模型,将此方法应用到伴随异质凝结的激波管问题中,进行了参数研究,加深了对异质凝结和流动相互作用的认识;最后针对经典矩方法无法处理相间相互作用的问题,将经典矩方法中的矩方程改写为基于液相平均速度的形式,发展了一套考虑相间质量、动量、能量交换的矩方法,应用此方法研究了伴随同质凝结的旋涡运动问题,分析了旋涡中凝结的产生过程,以及凝结与流动相互作用对液相分布的影响,计算结果显示了凝结生成的液滴在离心力作用下离开旋涡中心的现象。

By introducing the moments of the droplet size distribution over the internal coordinates,the method of moments(MOM)tracks the time dependence of the lower order moments to solve the evolution of droplet phase in flow.Among all the available numerical methods,MOM is widely applied to model the phase transition of water vapor because of its good balance of simulation efficiency and accuracy.The concept and development of the classical MOM for homogeneous condensation were introduced firstly.The method was used to investigate the Prandtl-Meyer corner expansion flow with homogeneous condensation of water vapor and it is found that the condensation wave changes from steady to unsteady when saturation ratio is increasing.Then,a simplified model of instantaneous-wetting for heterogeneous nucleation on solid particle surface was introduced and nucleation rate based on the particle size distribution was derived.So,the classic MOM was extended to unsteady flows with heterogeneous condensation.As a demonstration,the heterogeneous condensation in closed shock tube problem was simulated by the extended MOM.The waves induded by the heterogeneous condensation within expansion fan and evaporation behind trans-metted shock were observed clearly and the influence of phase transition on fluid flow could not be neglected.Finally,the classic MOM was extended to account the slips of velocity and temperature between the liquid phase and the gas phase in condensing flows.The interphase interaction is realized through source terms which include the mass,momentum and energy exchanges.As an example,the method was used to simulate the homogeneous homogeneous condensation in vortex flow.Due to the very strong velocity slip,a dry zone is found in the vortex core region,which confirms the experimental observation,but not discovered by the classic MOM.