Determining surface pressure from skin friction

• Published in: Experiments in fluids Vol. 63; no. 9
• Main Authors: Cai, Zemin, Salazar, David M., Chen, Tao, Liu, Tianshu
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2022; Springer Nature B.V
• Subjects: Algorithms; Delta wings; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Fluid- and Aerodynamics; Friction; Heat and Mass Transfer; Inverse problems; Lagrange multiplier; Noise levels; Numerical analysis; Pressure; Research Article; Skin friction
• ISSN: 0723-4864; 1432-1114
• DOI: 10.1007/s00348-022-03500-y

This paper presents a general method to extract a surface pressure field from a skin friction field in complex flows as an inverse problem, focusing on its application to global luminescent oil-film (GLOF) skin friction measurements. The main technical aspects of this method are described, including the basic equation relating surface pressure to skin friction, variational method, numerical algorithm, and approximate method with the constant boundary enstrophy flux (BEF). The proposed method is evaluated through simulations in the Falkner–Skan flow and the flow over a 70°-delta wing to investigate the effects of the Lagrange multiplier, downsampling rate, noise level, and the value of a constant source term in the approximate method. Further, the approximate method is applied to the skin friction fields obtained by GLOF measurements in the flow over a 65°-delta wing and the square junction flow to obtain the normalized surface pressure fields. The proposed method provides a useful tool to obtain the high-resolution fields of both surface pressure and skin friction by GLOF measurements in complex flows (particularly at low speeds). Graphical abstract The normalized surface pressure field extracted from the skin friction field in the square junction flow, where skin friction lines are superposed.