Measurement of wall shear stress on an airfoil surface by using the oil film interferometry with PIV analysis applied to Fizeau fringes

Abstract

In this study, oil film interferometry (OFI) was applied to the flow around the suction surface of a twodimensional airfoil under high lift conditions to measure the wall shear stress. However, existing OFI methods have difficulty measuring the wall shear stress in images affected by reverse and secondary flows. Therefore, the particle image velocimetry (PIV) method was applied to the Fizeau fringe images to determine the direction of progress from the calculated velocity vector. An airfoil with a wing section of NACA0012 was used, the Reynolds number was set to 8 × 10 4 , and angle of attack was set at 11°. A direct spatial domain correlation was used for the PIV analysis method. At x/c = 0.75 to 0.83, the measured local skin friction coefficient was good agreeing with the large eddy simulation calculated results reported by Miyazawa et al. (Transaction of the JSME, Series B, Vol.72, No.721 (2006)). However, a large difference between the measured and calculated local skin friction coefficients occurred at x/c = 0.17 near the re-attachment point. The wall shear stress is determined by calculating the dominant frequencies using fast Fourier transform (FFT) analysis from the matrix data obtained by mean of the pixel intensities in the analysis region in the span direction. If the Fizeau fringe image is uniform in the span direction, the program can calculate the periodic waves. When the Fizeau fringes are tilted to the analysis range, the FFT analysis of the obtained matrix data results in an error because the dominant frequency cannot be calculated. Therefore, velocity vectors were detected near the re-attachment point by adapting PIV to the Fizeau fringe images. The local skin friction coefficients were calculated by OFI measurements with the Fizeau fringe images that were rotated by the angle of the velocity vector determined by PIV.

Improvement of extraction method of the Fizeau fringes spacing in the oil film interferometry and measurement of wall shear stress on an airfoil surface

“…The rate of temperature increase after the warm-up was approximately 0.0281 °C/min, according to the approximate a of the main flow temperature. Calculated as in a previous study (Imai et al, 2023), the uncertainty of the local skin friction coefficient was a maximum of approximately 0.17%, which was almost negligible. Therefore, in the following sections, the mainstream temperature is used as the oil temperature and the local skin friction coefficient is Imai, Suzuki and Miki, Journal of Fluid Science and Technology, Vol.19, No.2 (2024) calculated using the mean temperature during the measurements.…”

“…Therefore, Tanner and Blows (1976) first applied the thin oil film equation to measure wall shear stress. For an expansion of the equation, refer to our previous study (Imai et al, 2023).…”

“…This study focused on oil film interferometry (OFI), which is currently considered the most accurate wall shear stress measurement technique (Örlü and Vinuesa, 2020). For wall shear stress measurement techniques other than the OFI, related literature reviews, basic theory, and previous studies of the OFI, refer to our previous study (Imai et al, 2023). The OFI is widely used to measure the wall shear stress since it requires no calibration and provides accurate results using simple equipment.…”

“…Therefore, our final goal is to perform a two-dimensional measurement of the wall shear stress while retaining the advantages of the OFI. As a first step toward this goal, we measured the direction of wall shear stress in a previous study by applying the particle image velocimetry (PIV) analysis method to Fizeau fringes images (Imai et al, 2023). We calculated the wall shear stress by rotating the image at an angle obtained using PIV to match the direction of the Fizeau fringes progression with the OFI analysis direction.…”