基于积分形式的湍流边界层壁面摩擦速度预测方法  

AN INTEGRAL METHOD FOR ESTIMATING WALL FRICTION VELOCITY IN TURBULENT BOUNDARY LAYERS

作　　者：孟响 卢兆麟 李栋 张凯[1,2] Meng Xiang;Lu Zhaolin;Li Dong;Zhang Kai(Department of Mechanics,School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;Tangshan Research Institute,Beijing Institute of Technology,Tangshan 063000,Hebei,China;School of Design&Arts,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学宇航学院力学系,北京100081 [2]北京理工大学唐山研究院,河北唐山063000 [3]北京理工大学设计与艺术学院,北京100081

出　　处：《力学学报》2025年第1期43-54,共12页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(52176149,52275234);河北省自然科学基金(A2024105014)资助项目.

摘　　要：湍流边界层流动广泛存在于自然界、航空航天以及环境工程等领域.壁面摩擦速度是湍流边界层理论研究和工程应用中的一个重要参数,对其进行准确预测具有十分重要的科学意义和工程价值.文章基于雷诺平均动量方程提出了一种利用湍流边界层平均速度和雷诺应力剖面预测壁面摩擦速度的积分方法.该方法仅需要同一流向位置、边界层外层的平均流场分布,显著降低了对近壁面流场数据的依赖性.通过文献中大量的直接数值模拟和实验数据验证,该方法的相对误差在±3%以内,且受积分上下限以及边界层厚度等模型参数的影响较小.通过与文献中具有相似积分形式的壁面摩擦速度预测方法比较,发现湍流边界层壁面摩擦速度预测方法的精度与选取的总切应力模型密切相关.本文提出的壁面摩擦速度预测方法适用于不可压缩、零压力梯度光滑及粗糙壁面湍流边界层流动,具有精度高和鲁棒性强等特点,研究结果可为航空航天及能源动力等领域重大工程应用中湍流壁面摩擦阻力的准确预测和调控提供理论指导.Turbulent boundary layer(TBL)flows widely exist in nature,as well as in aerospace and environmental engineering applications.Wall friction velocity serves as an important parameter for both theoretical analysis and practical applications in TBL,and its accurate prediction holds significant value from scientific and engineering perspectives.Based on an integral analysis of the Reynolds-averaged momentum equation,an integral method is proposed to determine the wall friction velocity in TBL using the wall-normal profiles of the mean velocity and Reynolds shear stress.The method only requires the mean profiles in the outer layer of the TBL at a single streamwise location,which significantly reduces the dependence on the near-wall data.A number of direct numerical simulation and experimental data available in the literature are used to evaluate the performance of the proposed method.The wall friction velocities obtained using the present method agree with those published values,typically within±3%.In addition,it is found that the lower and upper integration limits,as well as the boundary layer thickness have insignificant effects on the accuracy of the method.We also compared the present approach with other integral methods in the literature,demonstrating that the predictive accuracy of wall friction velocity in TBL is highly dependent on the total shear stress model used.In summary,the proposed method shows high accuracy and good robustness in both the incompressible smooth-and rough-wall TBL under zero pressure gradient.The present study provides theoretical guidance for the accurate prediction and control of turbulent wall friction drag in the major engineering applications,such as aerospace,and energy and power systems.

关 键 词：壁面摩擦速度 湍流边界层 直接数值模拟 实验测量 

分 类 号：O357.5[理学—流体力学]