On the bimodal dynamics of the turbulent horseshoe vortex system in a wing-body junction

Abstract

The turbulent boundary layer approaching a wall-mounted obstacle experiences a strong adverse pressure gradient and undergoes three-dimensional separation leading to the formation of a dynamically rich horseshoe vortex (HSV) system. In a pioneering experimental study, Devenport and Simpson [J. Fluid Mech. 210, 23 (1990)] showed that the HSV system forming at the leading edge region of a wing mounted on a flat plate at Re=1.15×105 exhibits bimodal, low-frequency oscillations, which away from the wall produce turbulent energy and stresses one order of magnitude higher than those produced by the conventional shear mechanism in the approaching turbulent boundary layer. We carry out numerical simulations for the experimental configuration of Devenport and Simpson using the detached-eddy-simulation (DES) approach. The DES length scale is adjusted for this flow to alleviate the well known shortcoming of DES; namely that of premature, laminar-like flow separation. The numerical simulations reproduce with good accuracy most experimental observations, including both the distributions of the mean flow and turbulence quantities and the bimodal dynamics of the velocity field in the HSV region. The only remaining discrepancy between experiments and simulations is the predicted location of the HSV, which is somewhat further upstream from the wing than the measured one. Proper orthogonal decomposition (POD) of the resolved flow field is employed to gain insights into the coherent dynamics of the flow. The POD analysis shows that 85% of the energy in the vortex region is accounted for by the first two POD modes whose dynamics is quasiperiodic. To elucidate the physical mechanisms that lead to the onset of the bimodal dynamics, we employ probability-density-function-based conditional averaging and visualization of the instantaneous three-dimensional structure of the HSV using the q criterion. We show that the bimodal dynamics is due to the continuous and aperiodic interplay of two basic states: an organized state with a coherent necklace-like HSV, and a disorganized state with hairpin vortices wrapping around the HSV. We argue that the emergence of hairpin vortices is the result of centrifugal instability.

Effects of wall roughness on turbulent junction flow characteristics

“…These fluctuations establish the unsteady behavior of the near-well jet of reversed fluid. The combined impact of the unsteadiness of the jet and its interplay with the PV play a pivotal role on the HVS destabilization mechanism proposed based on the episodic extraction of near-wall fluid (Paik et al 2007). Furthermore, increased TKE close to the origin of the coordinate system further supports the hypothesis for the intermittent presence of a CV (white arrow).…”

“…They also identify two major unresolved issues in the study of turbulent junction flows over smooth walls: 1) the discovery of a scheme capable of predicting the onset of the eruptive events and 2) the extension of research to higher Reynolds numbers. More recent studies have expanded earlier findings by emphasizing the role of smaller flow structures (hairpin vortices) in the destabilization of the HVS and the switching between the dominant flow modes (Paik, Escauriaza and Sotiropoulos 2007). The number and intensity of hairpins appear to increase with Reynolds number (Escauriaza and Sotiropoulos 2011).…”

Boundary layer effect on the vortex shedding of wall-mounted rectangular cylinder

“…They attribute these large stresses to the bimodal histograms of velocity fluctuations produced by a velocity variation that is bistable. More recently, Paik et al (2007) studied the Devenport and Simpson's configuration numerically. Their results corroborate those of Devenport and Simpson except for the position of the predicted location of the HVS.…”

Reynolds Number Effects on the Coherent Dynamics of the Turbulent Horseshoe Vortex System

“…Detached eddy-simulations (DES), a hybrid model proposed by Spalart et al [29] based on the Spalart-Allmaras turbulence model [28], has been able to capture the unsteadiness of the HSV system as reported in the recent study by Paik et al [18]. Paik et al successfully resolved the mean flow, turbulence statistics and bimodal velocity dynamics for the flow past the wall-mounted wing studied experimentally by Devenport and Simpson at Re = 1.15 × 10 5 [8].…”