A complementary numerical and experimental study of the influence of Reynolds number on theoretical models for wingtip vortices

Abstract

We present a detailed analysis of experimental and numerical results for the flow of trailing vortices behind a NACA0012 wing model. Particular attention is paid to a specific value of the angle of attack, α=9°, and ultra-low and low chord-based Reynolds numbers ranging from Re=3 × 102 to 2 × 104. Spatial-averaged two-dimensional Particle Image Velocimetry (PIV) velocity profiles are in agreement with implicit Large Eddy Simulations (iLES) up to eleven chords from the wing for Re=7 × 103. Once we validate our numerical results through experiments, we fit the theoretical parameters such as normalized circulation (S, b), vortex decay exponent (n) and virtual origin (z¯0B,z¯0MS) as a function of Re. Thus, five theoretical parameters are given from computational and experimental results: two corresponding to Batchelor’s model (S, z0B) and three belonging to Moore & Saffman’s model (b, n, z0MS). Two critical Reynolds numbers were found. Our computations verify that the onset of wake instability at the first threshold ReC1 ≈ 1.3 × 103 captures the change in the trend of theoretical parameters. In addition, the theoretical parameters appear to become constant experimentally for a second critical Reynolds number ReC2 greater than 1–2 × 104 when our results are compared with those given by other authors. Consequently, Reynolds number plays an essential role in the stability analysis for trailing vortices, not only taking into account viscous terms but also determining the input parameters for theoretical models.