Helical structure of longitudinal vortices embedded in turbulent wall-bounded flow

Abstract

Embedded vortices in turbulent wall-bounded flow over a flat plate, generated by a passive rectangular vane-type vortex generator with variable angle β to the incoming flow in a low-Reynolds-number flow (Re = 2600 based on the inlet grid mesh size L = 0.039 m and free stream velocity U ∞ = 1.0 m s −1 ), have been studied with respect to helical symmetry. The studies were carried out in a low-speed closed-circuit wind tunnel utilizing stereoscopic particle image velocimetry (SPIV). The vortices have been shown to possess helical symmetry, allowing the flow to be described in a simple fashion. Iso-contour maps of axial vorticity revealed a dominant primary vortex and a weaker secondary one for 20 • 6 β 6 40 • . For angles outside this range, the helical symmetry was impaired due to the emergence of additional flow effects. A model describing the flow has been utilized, showing strong concurrence with the measurements, even though the model is decoupled from external flow processes that could perturb the helical symmetry. The pitch, the vortex core size, the circulation and the advection velocity of the vortex all vary linearly with the device angle β. This is important for flow control, since one thereby can determine the axial velocity induced by the helical vortex as well as the swirl redistributing the axial velocity component for a given device angle β. This also simplifies theoretical studies, e.g. to understand and predict the stability of the vortex and to model the flow numerically.

Alteration of helical vortex core without change in flow topology

“…2 The effects of the secondary vorticity are, however, substantially reduced by mounting the generators in a cascade in a fashion producing counter-rotating primary vortices that are spaced densely enough. Hence, the net effect of each actuator is basically a monopole.…”

“…From the velocity plots, it is clear to see that each generator in the cascade induces only one strong vortex, but not the accompanying secondary vortex, which was well pronounced in our former experiments with a single vortex generator. 2 The absence of these weaker secondary structures in the present case simplified our study, reducing the result of each vortex generator to merely one primary vortex. The wake behind vortex generators is usually divided into three parts: near wake portrayed by the first profile in Figure 1 (z=h < 1) where the vortex forms; far wake (1 < z=h < 10 and above) where the vortex is well pronounced; and lastly a zone behind the far wake where the vortex core cannot be separated from other flow disturbances.…”

“…2 This model is characterized by a zero radial vorticity component, a fixed linear correlation between the axial and circumferential vorticity components, and a Gaussian axial distribution 3…”

“…Note that the same vortex model (2), in the sense of the Batchelor's or q-vortex, 2,3 is commonly used in instability studies of swirling flows to describe vortex breakdown. [3][4][5][6] This well-known phenomenon is characterized by three specific features: 4 (1) a change in flow topology; (2) a change in axial velocity from a jet-like profile before breakdown to a wake-like profile after breakdown; and (3) a structural change resulting in vortex core expansion.…”

Self-Similarity and helical symmetry in vortex generator flow simulations

“…Theoretical models include, e.g., the one by Smith [12] and a model presented by Velte et al [13] that was developed and applied to show the helical symmetry of the vortices generated by a passive rectangular vane-type vortex generator. As for models incorporated into codes, most are variants of the practical BAY-model by Bender et al [14], which introduces body forces using source terms in the Navier-Stokes equations to simulate the presence of a vane.…”