Title: A study of simultaneous pitching and plunging motions of an airfoil using the spectral element method

Authors: Jose Gilberto Montiel-Galindo; Ruben Avila; Syed Shoaib Raza

Addresses: Faculty of Engineering, National Autonomous University of Mexico (UNAM), Coyoacan, Mexico City, Mexico ' Department of Thermofluids, Faculty of Engineering, National Autonomous University of Mexico (UNAM), Coyoacan, Mexico City, Mexico ' Faculty of Engineering, National Autonomous University of Mexico (UNAM), Coyoacan, Mexico City, Mexico

Abstract: In this study, the thermal convection of the laminar flow over a symmetric NACA 0012 airfoil with simultaneous pitching and plunging motions is presented. The non-steady, two dimensional, Navier-Stokes equations coupled with the energy equation, considering the Boussinesq approximation, are numerically solved by using the spectral element method. The influence of the Rayleigh number (the magnitude of the buoyancy force) on the aerodynamic coefficients and the Nusselt number (the heat transfer rate), is analysed. It is found, for a given value of the Reynolds number (Re = 1,000), that an increase of the buoyancy force leads to a decrease of the performance, although increasing the mean geometric angle of attack α_m reduces this effect. Moreover, we note that if α_m = 0°, the heat transfer is reduced as the buoyancy force increases; however, if α_m ≥ 10°, as the buoyancy force gets higher values, the heat transfer also increases.

Keywords: low Reynolds numbers; Rayleigh number; Nusselt number; pitching motion; plunging motion; heat transfer; buoyancy force; aerodynamic performance; SEM; spectral element method.

DOI: 10.1504/PCFD.2025.149929

Progress in Computational Fluid Dynamics, An International Journal, 2025 Vol.25 No.6, pp.319 - 335

Received: 07 Feb 2025
Accepted: 29 Apr 2025
Published online: 18 Nov 2025 *

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