基于分析墙面法模型的墙面摩擦力精确估算方法

Lei Zhou, Duo Wang, Bochao Cao, Hongyi Xu
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摘要

本文提出了一种新方法,通过近壁测量 A 型湍流边界层(TBL)中的时间平均速度剖面,准确确定局部壁面摩擦力。该方法基于新建立的 A 型湍流边界层分析壁律。零压力梯度平板(ZPGFP)上湍流的直接数值模拟(DNS)数据用于证明该方法的准确性和稳健性。为了验证该方法的可靠性和适用性,在中低雷诺数(Re)的 ZPGFP TBL 中进行了二维粒子图像测速(PIV)测量。通过利用单像素集合相关(SPEC)算法,ZPGFP TBL 中的速度剖面的空间分辨率得到了显著提高,从而大大提高了测量精度,并使我们能够准确捕捉近壁速度信息。然后,我们利用 ZPGFP TBL 数据对高雷诺数湍流的精确性进行了定量验证。研究表明,目前的方法可以精确估算壁面摩擦力,平均误差小于 2%,不仅具有对测量点的绝对壁面法向距离不敏感的优点,还能根据相当稀疏的速度剖面实验数据准确预测壁面剪应力。目前的研究表明,即使是在近壁区域测量或计算的单点速度,也能准确估算壁面剪应力。
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Accurate Method for Estimating Wall-Friction Based on Analytical Wall-Law Model
A novel method is proposed for accurately determining the local wall friction through the near-wall measurement of time-average velocity profile in a Type-A turbulent boundary layer (TBL). The method is based on the newly established analytical wall-law in Type-A TBL. The direct numerical simulations (DNS) data of turbulence on a zero-pressure-gradient flat-plate (ZPGFP) is used to demonstrate the accuracy and the robustness of the approach. To verify the reliability and applicability of the method, a two-dimensional particle image velocimetry (PIV) measurement was performed in a ZPGFP TBL with a low-to-moderate Reynolds number (Re). Via utilizing the algorithm of single-pixel ensemble correlation (SPEC), the velocity profiles in the ZPGFP TBL were resolved at a significantly improved spatial resolution, which greatly enhanced the measurement accuracy and permitted us to accurately capture the near-wall velocity information. The accuracy of the approach is then quantitatively validated for the high Reynolds number turbulence using the ZPGFP TBL data. The research demonstrates that the current method can provide the precise estimation of wall friction with a mean error of less than 2%, which not only possesses the advantage of its insensitivity to the absolute wall-normal distance of the measuring point, but also its capability of providing an accurate prediction of wall shear stress based on fairly sparse experimental data on the velocity profile. The current study demonstrates that the wall shear stress can be accurately estimated by a velocity even at a single-point either measured or calculated in the near-wall region.
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