Influence of Reynolds number on theoretical models for trailing vortices

Domínguez-Vázquez, Adrián; García-Ortiz, José Hermenegildo; Serrano-Aguilera, Juan José; Parras-Anguita, Luis; Del-Pino-Peñas, Carlos Manuel

Influence of Reynolds number on theoretical models for trailing vortices

Domínguez-Vázquez, Adrián,García-Ortiz, José Hermenegildo,Serrano-Aguilera, Juan José,Parras-Anguita, Luis,Del-Pino-Peñas, Carlos Manuel

Published: 2015-07-09
Repository: riuma.uma.es
Language: en

Abstract

We conduct direct numerical simulations for a NACA0012 airfoil at Reynolds numbers (Re) ranging from 300 to 7000 to determine the wake behavior behind this wing profile. We characterize the structure of the wing-tip vortex, finding a reasonable agreement with experimental results at Re=7000. In addition, we model the trailing vortex theoretically, thus obtaining the parameters for Batchelor’s and Moore and Saffman’s models. We compare the results of the best fitting for the axial vorticity and the azimuthal velocity, finding only small discrepancies. The main contribution of this research work is to study the evolution of these theoretical parameters as function of the Reynolds number. We observe that the wake becomes unstable at Re ≈1200, in agreement with previous results. These instabilities in the wake behind the wing produce a change in the trend of theoretical parameters (keywords: vortex dynamics, trailing vortices, theoretical models).

Full text

BIFURCATIONS AND INSTABILITIES IN FLUID DYNAMICS 2015 15-17 JULY, ESPCI, PARIS FRANCE INFLUENCE OF REYNOLDS NUMBER ON THEORETICAL MODELS FOR TRAILING VORTICES Adrián Domínguez-Vázquez1, J. Hermenegildo García-Ortiz2, Juan José SerranoAguilera2,3, Luis Parras2 and Carlos del Pino2 1Universidad Carlos III, Departamento de Bioingeniería e Ingeniería Aeroespacial, Madrid, Spain 2Universidad de Málaga, Escuela Técnica Superior de Ingeniería Industrial, Málaga, Spain 3CIEMAT-Plataforma Solar de Almería, Crta. de Senés, km. 4.5, E04200 Tabernas, Almería, Spain. Abstract We conduct direct numerical simulations for a NACA0012 airfoil at Reynolds numbers (Re) ranging from 300 to 7000 to determine the wake behavior behind this wing profile. We characterize the structure of the wing-tip vortex, finding a reasonable agreement with experimental results at Re=7000. In addition, we model the trailing vortex theoretically [1], thus obtaining the parameters for Batchelor’s [2] (see figure 1) and Moore and Saffman’s models [3]. We compare the results of the best fitting for the axial vorticity and the azimuthal velocity, finding only small discrepancies. The main contribution of this research work is to study the evolution of these theoretical parameters as function of the Reynolds number. We observe that the wake becomes unstable at Re ≈1200, in agreement with previous results [4]. These instabilities in the wake behind the wing produce a change in the trend of theoretical parameters (keywords: vortex dynamics, trailing vortices, theoretical models). Figure 1. Theoretical parameter Sof Batchelor’s model as function of Reynolds number. Best fitting for axial vorticity (triangles), azimuthal velocimetry (circles) and experimental data (squares). References [1] C. del Pino, L. Parras, M. Felli, R. Fernández-Feria. Structure of trailing vortices: Comparison between particle image velocimetry measurements and theoretical models , Physics of Fluids, 23, 113602 (2011). [2] G. K. Batchelor. Axial flow in trailing line vortices , Journal of Fluid Mechanics, 20, 645–658 (1964). [3] D. W. Moore and P. G. Saffman. Axial flow in laminar trailing vortices , Proceedings of the Royal Society, 333, 491–508 (1973). [4] K. Taira and T. Colonius. Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers , Journal of Fluid Mechanics, 623, 187–207 (2009).