# Statistical Analysis on Wall Shear Stress of Turbulent Boundary Layer in a Channel Flow using Micro Shear Stress Imager

**Norimasa Miyagi**

Nihon University, Tokyo, Japan

**Motoaki Kimura**

Department of Mechanical Engineering, College of Science and Technology, Nihon University

**Hideo Shoji**

Nihon University, Tokyo, Japan

**Atsushi Saima**

Department of Mechanical Engineering, College of Science and Technology, Nihon University, 1-8, Kanda Surugadai, Chiyodaku, Tokyo 101-8308, Japan

**Chih-Ming Ho**

Mechanical and Aerospace Engineering Department, University of California, Los Angeles Los Angeles, California 90095, USA

**Steve Tung**

Mechanical and Aerospace Engineering Department, University of California, Los Angeles Los Angeles, California 90095, USA

**Yu-Chong Tai**

Division of Engineering and Applied Science, California Institute of Technology Pasadena, California 91125, USA

## Abstract

Measurements of wall shear stress of a turbulent boundary layers in the channel flow were carried out using MEMS-based micro shear stress imaging chip. The study was carried out in a turbulent channel flow facility. One array of 25 micro shear sensors in the chip that covers a length of 7.5 mm is used measure the instantaneous span-wise distribution of the surface shear stress. The characteristics of high shear-stress area (streaks) were described with statistics. Based on the measurement, the physical quantities associated with the high shear-stress streaks, such as their length, width with the high shear stress level, were obtained.

To further explore the relationship between the shear stress slope and the peak shear stress, the probability density function (PDF) of the ratio of peak shear stress to shear stress slope at different Reynolds number *Re* are examined. As for the distribution of PDF, it was found out that the distribution concentrated toward a certain value in each Re. This result is extremely important because it points to the possibility of predicting the peak shear stress level based on the share stress distribution at the leading edge of the streaks.

By multiplying the ratio of peak to slope of shear stress at the peak value of the PDF by the measured front-end slope of individual streaks, we can "predict" the peak value of the shear stress in real-time due to the correlation between the two values. We then can determine the necessary input driving level to the actuator for reducing the shear stress. This result will be implemented into the algorithm for the integrated turbulent boundary layer control system.