Scaling of Vorticity Flux and Entrance Length Effects in Zero-Net Mass-Flux Devices

Abstract

Two-dimensional numerical simulations are used to examine the vorticity flux and slot entrance effects in zero-net mass-flux devices. The simulations allow us to extract a simple scaling law for the vorticity flux which provides insight into the relative importance of the various operational parameters. In addition to this, a semi-analytical model is proposed in order to determine the pressure loss across an orifice or slot for oscillatory flows. A key parameter in this model is the normalized entrance length and numerical simulations are used to determine the variation of this parameter with the jet Strouhal number. Nomenclature d = slot width, m D = cavity depth, m * Graduate Student, Student Member AIAA.

Coherent structures produced by the interaction between synthetic jets and a laminar boundary layer and their surface shear stress patterns

“…This functional relationship is also supported by the numerical finding by Raju et al [15]. For a given laminar boundary layer and an actuator with fixed geometry such as the case in the present study, d and c f do not change.…”

The near wall effect of synthetic jets in a boundary layer

“…This is true for both hairpin vortices and stretched vortex rings and suggests that the conditions for enhancing the flow control effectiveness of synthetic jets by the generation of vortical structures of relatively high strength that persist in the near wall region depends on limiting VR (ideally <0.38 for the current set of cases) whilst increasing L and hence Re L . This assessment also correlates with the previously defined scaling law derived by Raju et al (2005), which shows that the vorticity flux of a synthetic jet embedded in a zero-pressure gradient laminar boundary layer varies as a linear function of L and VR -1 . In the present study for a fixed SJA geometry and given set of freestream conditions, L is a function of the peak-to-peak diaphragm displacement, ∆ (Eq.…”

“…The functional dependence of the effectiveness of a synthetic jet on the dimensionless parameters given in Eq. (7) also correlates with a scaling law derived by Raju et al (2005). Using a non-linear regression analysis on data obtained by numerical simulation, a scaling law for the vorticity flux of a synthetic jet was extracted for the case of a zero-pressure gradient laminar boundary layer, in which the vorticity is influenced by a Strouhal number based on the jet velocity (equivalent to L in the present study), a jet to freestream velocity ratio, a boundary layer thickness to slot width ratio and a jet Reynolds number.…”

Effects of a synthetic jet acting on a separated flow over a hump

“…Note that the injection through the actuator creates a pair of counter-rotating vortices (cf. Raju et al 2005), but this contributes no net vorticity flux regardless of the velocity profile. For simplicity, while the separation vortex is growing, we assume that α is fixed so that l is proportional to Γ , and l R so that the curvature of the hump surface is negligible.…”