Experimental study in near-and far-field of trailing vortices and their active control

Supervised by:
  1. Carlos del Pino Peñas Director
  2. Luis Parras Anguita Co-director

Defence university: Universidad de Málaga

Fecha de defensa: 27 October 2017

  1. Miguel Angel Herrada Gutiérrez Chair
  2. José Francisco Velázquez Navarro Secretary
  3. Ivan Delbende Committee member

Type: Thesis

Teseo: 513442 DIALNET lock_openRIUMA editor


In order to predict the axial development of the wingtip vortices’ strength, an accurate theoretical model is required. Several experimental techniques have been used to that end, e.g. PIV or hotwire anemometry, but they imply a significant cost and effort. For this reason, we have carried out experiments using the smoke-wire technique to visualize smoke streaks in six planes perpendicular to the main stream flow direction. Using this visualization technique, we obtained quantitative information regarding the vortex velocity field by means of Batchelor’s model for two chord based Reynolds numbers, 𝑅𝑒𝑐 = 3.33 ⋅ 104 and 105. Therefore, this theoretical vortex model has been introduced in the integration of ordinary differential equations which describe the temporal evolution of streak lines as a function of two parameters: the swirl number, 𝑆, and the virtual axial origin, 𝑧0. We have applied two different procedures to minimize the distance between experimental and theoretical flow patterns: individual curve fitting at six different control planes in the streamwise direction as well as the global curve fitting which corresponds to all the control planes simultaneously. Both sets of results have been compared with those provided by del Pino et al. [2011a] and they are in good agreement. Finally, we have observed a weak influence of the Reynolds number on the values 𝑆 and 𝑧0 at low-to-moderate 𝑅𝑒𝑐. This experimental technique is proposed as a low cost alternative to characterising wingtip vortices based on flow visualizations. Secondly, we present a detailed analysis of experimental and numerical results for the flow of wingtip vortices behind a NACA0012 airfoil. 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=0.3×103 to 20×103. Spatialaveraged two-dimensional PIV velocity profiles are compared for 𝑅𝑒=7×103 by using direct numerical simulations (DNS) up to eleven chords from the wing. Once we validate our results, we fit the theoretical parameters as function of 𝑅𝑒. Five theoretical parameters are given from computational and experimental results: two corresponding to Batchelor’s model and three regarding Moore & Saffman’s model. Two critical Reynolds numbers were found. Our DNS computations verify that the onset of instability of the flow around the wing 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 10-20×103 as our results are compared with those given by other authors. Consequently, Reynolds number plays an important role in the stability analysis for trailing vortices not only taking into account viscous terms but also determining the input parameters for theoretical models. Finally, we have carried out a study of the blowing effect of continuous jets that are perpendicular to the moving direction, and blowing from the tip of a NACA0012 airfoil. We analyze three Reynolds numbers 𝑅𝑒 and four jet-to-crossflow blowing ratios 𝑅𝑗𝑒𝑡. We show how these jets are good candidates to reduce the strength of the wingtip vortices at the lowest Reynolds numbers considered, e.g. 𝑅𝑒 = 7×103. For higher Reynolds numbers up to 𝑅𝑒=20×103, the forcing has a weak influence on the vortex strength in the near-field once the rolling-up process has already finished, and especially at axial distances greater than 7 chords behind the wing. The reason for the presence of two different strength decays depending on the Reynolds number is explained by the ability of the continuous jet to break the vorticity sheet creating a counter-rotating vortex or co-rotating vortex at low or high values of 𝑅𝑒, respectively. This mechanism makes the wingtip vortex decrease or maintain its vortex strength as we apply different blowing ratios 𝑅𝑗𝑒𝑡. This effect is evident at the lowest Reynolds number at which we observe a strong vortex decay. Conversely, the continuous jet changes the characteristics of the vortex flow in the formation and the near-field evolution of the wingtip at high Reynolds numbers, but there is not an appreciable effect on the vortex strength and how it evolves downstream.