运用能耗率极值原理对几个半经验紊流模式的分析

Analysis of Turbulent Models with the Extremity Law of Energy Dissipation Rate

紊流运动极其复杂。为了将问题简化和封闭,人们已提出了许多半经验的紊流模式,然而这些模式中的有关待定参数(包括变数和常数)却无法从理论上加以确定。为此,本文运用能耗率极值原理对几个常用的模式作了分析,从理论上确定了这些模式中的未知参数的函数表达式,并进一步导得了考虑粘性剪力项及忽略粘性项时的流速分布公式。这一分析有助于对一些参数的物理意义的深入认识,也有助于帮助检验现行紊流模式具有多大的合理性及应该选取什么样的紊流模式更好些。紊流模式的不同直接影响着分析结果,因此,尽管能耗率极值原理在理论上提供了一个新的有效的独立方程,但它仅解决方程的封闭性问题,即它仅仅保证了能够从理论上给出方程中各未知量之解,要得到与实际情况相符的理论解,还取决于合理的紊流模式(亦即能耗率取极值时所需的限制条件)的建立。

By introducing the extremity law of energy dissipation rate to the investigation of turbulent flow, most of the unknown functions included in the present turbulent models can be solved theoretically. But whether the theoretical results agree with the observation results is largely related to the given constraits, i.e., the turbulent model. The author suggests a simple model as Eq, 8 shows. The ' n ' in Eq, 8 changes with Reynolds Number, When n is given, all the unknown functions and velocity distribution can be determined.