非周期混合流中映射方法的应用研究

【作者】 张红平；

【导师】 欧阳洁；

【作者基本信息】 西北工业大学 ， 应用数学， 2005， 硕士

【摘要】 液-液混合问题在同常生活和生产实践中经常出现,对其进行研究具有重要的理论价值和实践意义。与周期液-液混合流相比,目前非周期混合流问题的物理流态以及混合质量分布等研究尚不完善,本文主要针对此问题,基于周期混合流分析中的映射方法,对非周期混合流进行研究。 本文首先简要叙述了映射方法的提出、定义、性质和发展趋势等。在周期混合流计算中,映射方法不需要重复计算映射矩阵,但是在非周期混合流中映射方法不存在这样的优势,因此针对非周期混合流的特点,本文对映射方法进行了改进并对理论方法进行了讨论和研究,其中包括在映射方法计算步骤中加入网格重构过程,并定义用于网格重构中映射量准确传递的变量——重构映射矩阵;为了减少计算量,对映射方法中的重要参数映射矩阵进行了算法优化:针对映射矩阵是大型稀疏矩阵的特点,建立了映射矩阵非零分量的搜索范围。最后,通过矩形腔驱动混合流的数值模拟得到了以下结论:混合质量呈先线性后指数的趋势增长;层流混合中两相间的界面面积呈指数趋势增长:解决了非周期混合流中相近混合质量无从比较的问题;使用改进后的映射方法可以成功地描述初始阶段的非周期混合流混合形态。更多还原

【Abstract】 Liquid-liquid mixing is a topic of significant interest, because of both widespread occurrence of such phenomena in nature and its importance for industrial applications. By now, research technique of no-periodic flow liquid-liquid mixing is still in its infancy. So, this dissertation concentrates on applying mapping method to discuss the motion characteristic and mixing quality distribution in no-periodic flow mixing.Firstly, a brief description of the definition, characters and the trend of development for mapping method is presented.Based on mapping method, the second part discusses the computation method of the no-periodic flow. The discrete Navier-Stokes equation and corresponding mapping technique are included. Fine algorithm of calculating mapping matrix for decreasing calculation load is programmed. And for reducing calculation error that is caused by the intensity of segregation formula, the restructured mapping matrix for transfer parameters is defined.In the last part, rectangle cavity driven mixing flow is simulated. The author has satisfactorily come to some significant conclusion: the mixing quality grow linearly at the initial stage and grow exponentially afterward with time; the interfacial area can grow exponentially with time; and different no-periodic mixing flows that are seemed mixed equally can be compared.As a result, validity of the mapping method in no-periodic mixing flow is approved, that is mapping method is suitable for simulation of the initial stages of no-periodic flow mixing.更多还原