Wall shear-stress extraction by an optical flow algorithm with a sub-grid formulation
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RESEARCH PAPER
Wall shear-stress extraction by an optical flow algorithm with a sub-grid formulation The Hung Tran1 · Lin Chen2,3 Received: 16 March 2020 / Revised: 19 May 2020 / Accepted: 7 July 2020 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, we developed a novel optical-flow algorithm for determining the wall shear-stress on the surface of objects. The algorithm solves the thin-oil-film equation using a numerical scheme that recovers local features neglected by smoothing filters. A variational formulation with a smoothness constraint was applied to extract the global shear-stress fields. The algorithm was then applied to scalar images generated using direct numerical simulation (DNS) method, which revealed that the errors were smaller than those of conventional methods. The application of the proposed algorithm to recover the wall shear-stress on a low-aspect-ratio wing and on an axisymmetric boattail model taken as examples in this study showed a strong potential for analysing shear-stress fields. Compared to the methods used in previous studies, proposed method reveals more local features of separation line and singular points on object surface. Keywords Wall shear-stress · Optical flow · Thin-oil-film equation · Sub-grid model
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1 Introduction The wall shear-stress, along with pressure and temperature, are important parameters in fluid mechanics. In fact, the skin-friction drag due to the shear-stress for conventional aircraft during cruising can reach around 50% of the total drag [1]. In addition, the most complicated features of the wall shear-stress occur near the separation and reattachment regions, where flow behaviour suddenly changes. A good understanding of the shear-stress is important for analysing flow behaviour and for developing the most appropriate drag reduction strategy. The lines formed by wall shear-stress coincide with streamlines and determine the average flow fields near the interaction surfaces of the object and the fluid [2]. However, measuring the shear-stress is significantly complicated. Previously, point measurement techniques, such as the Pitot
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The Hung Tran [email protected] Faculty of Aerospace Engineering, Le Quy Don Technical University, Hanoi 10000, Vietnam Institute of Engineering Thermophysics, Chinese Academy of Sciences, Beijing 100190, China School of Aeronautics and Astronautics, University of Chinese Academy of Sciences, Beijing 100049, China
tube, hot-film sensors [3], sub-layer fence [4] and wall hotwire [5], have been applied for analysing the shear-stress at some positions on the surface. Clearly, the application of a sensor significantly disturbs the flow and reduces the accuracy of measurement [6]. An oil-flow visualization technique was developed and widely applied for visualizing surface shear-stress [7, 8]. However, that technique allows only qualitative measurement of skin-friction fields. Recently, de
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