Determination of Wall Friction Velocity of the Turbulent Boundary Layer by Two-Parameter Nonlinear Curve Fitting

利用双参数非线性拟合求解湍流边界层壁面摩擦速度

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received: 20 June 2019

Abstract

Hot-wire anemometer is a fundamental tool for flow field measurement, and has been widely adopted in research of turbulent flow. A turbulent boundary layer was generated by a trip wire and a piece of sandpaper in the low-speed wind tunnel, and the time-averaged velocity profiles at three different streamwise stations in the boundary layer were measured with IFA-300 constant temperature anemometer. Targeting the dimensionless velocity profile model White Law of the turbulent boundary layer, a nonlinear curve fitting MATLAB program for two parameters, which were theoretical original point of wall coordinate y₀ and wall friction velocity u_τ, was developed. Based on the measured time-averaged velocity profiles, the program was adopted to determine y₀ and u_τ of the three streamwise stations. It is found that the initial search domain and search step size of y₀ and u_τ have no effect on the fitting results if the physical solutions are included in the domain. It is also found that the selected fitting velocities data are closely related to the results. The value of the friction velocity with high precision will be obtained by this nonlinear curve fitting method if the highest fitting velocity data point dose not fall into the wake region. The method given in this paper is simple in programming and reliable in fitting results, and it is of practical to obtain the wall friction velocity of the turbulent boundary layer.

摘要

热线风速仪是流场测量的基本手段，广泛应用于湍流研究。在低速风洞中用绊线和粗糙带获得充分发展的湍流边界层流动，利用IFA-300恒温热线风速仪测量了湍流边界层不同流向站位的时均速度型。以湍流边界层的无量纲速度型模型White Law为目标曲线，分析了通过速度型拟合反推壁面摩擦速度方法的应用问题，编制了关于双参数壁面坐标理论零点位置y₀和壁面摩擦速度u_τ的非线性曲线拟合MATLAB程序。以实验测量的测点速度为原始拟合数据，讨论了初始搜索区间和搜索步长、拟合数据范围对拟合结果的影响，并最终求解得到y₀和u_τ。研究结果表明：所提方法编程思路简单，容易实现，合理选取用于曲线拟合的测点速度数据范围，利用该方法可以求得较高精度的壁面摩擦速度值。