基于eN理论的转捩预测方法研究

Research on Transition Prediction Method Based on eN Theory

层流向湍流的转捩是流体力学中具有基础研究意义的领域。转捩对流动的热交换、摩擦阻力及边界层发展等均具有很大影响,所以对转捩机理的研究具有重要的工程意义。常采用的转捩位置预估方法是经大量实验数据拟合出经验公式,该方法简便,但适用范围较窄,且对实验要求较高。近年来,高精度数值模拟方法取得了极大进展,流场内划分很密的计算网格后求解Navier-Stokes方程,对流场内的速度、压力脉动项等进行精确计算,可准确模拟流动转捩发展的过程;但该方法计算量大,对计算机硬件要求较高,仍处于探索阶段。目前,工程上主要采用的转捩预测方法是半经验方法,即理论分析耦合实验数据,其中最常用的是基于小扰动理论的eN方法。通过耦合求解雷诺平均NS方程和边界层方程得到边界层内动量损失厚度、速度型分布等参数,代入求解线性稳定性方程得到流动的转捩位置。选取4组算例对该方法进行验证,计算得到的转捩位置与实验数据比较接近,验证了该方法的准确性和可靠性。

Laminar-to-turbulent transition prediction has always been a fundamental research field in fluid mechanics.Fluid transition has great influence on heat exchange,friction resistance and boundary layer development,so the study on transition mechanism has some important significance to engineering application.The commonly method used for predicting the transition position is the empirical formula fitted by a large number of experimental data.This method is simple,but have the shortage of narrow scope in application and high requirement in experiments.In recent years,great progress has been made in high precision numerical simulation methods,such as Direct Numerical Simulation(DNS)and Large Eddy Simulation(LES),solving Navier-Stokes equations on very fine computational grids in the flow field,and the progress of fluid transition could be predicted accurately based on the exact simulation of velocity distribution,pressure fluctuation term,etc.However,because of a large amount of calculation and a high requirement for computer hardware,this method is still in the exploratory stage.At present,the main transition prediction method used in engineering is semi-empirical method,i.e.theoretical analysis coupled with experimental data.Among them,the most commonly used method is eN method based on small perturbation theory.In this paper,the parameters of momentum loss thickness and velocity distribution in the boundary layer are obtained by solving the Reynolds Average NS equations and the boundary layer equations.The transition position of the flow is obtained by solving the linear stability equations based on the parameters in the boundary layer.Then,four groups of examples are selected to verify the method.The transition positions calculated by eN method are close to the experimental data,which verifies the accuracy and reliability of the method.