Planar inviscid flows in a channel of finite length : washout, trapping and self-oscillations of vorticity

The paper addresses the nonlinear dynamics of planar inviscid incompressible flows in the straight channel of a finite length. Our attention is focused on the effects of boundary conditions on vorticity dynamics. The renowned Yudovich's boundary conditions (YBC) are the normal component of velocity given at all boundaries, while vorticity is prescribed at an inlet only. The YBC are fully justified mathematically: the well posedness of the problem is proven. In this paper we study general nonlinear properties of channel flows with YBC. There are 10 main results in this paper: (i) the trapping phenomenon of a point vortex has been discovered, explained and generalized to continuously distributed vorticity such as vortex patches and harmonic perturbations; (ii) the conditions sufficient for decreasing Arnold's and enstrophy functionals have been found, these conditions lead us to the washout property of channel flows; (iii) we have shown that only YBC provide the decrease of Arnold's functional; (iv) three criteria of nonlinear stability of steady channel flows have been formulated and proven; (v) the counterbalance between the washout and trapping has been recognized as the main factor in the dynamics of vorticity; (vi) a physical analogy between the properties of inviscid channel flows with YBC, viscous flows and dissipative dynamical systems has been proposed; (vii) this analogy allows us to formulate two major conjectures (C1 and C2) which are related to the relaxation of arbitrary initial data to C1: steady flows, and C2: steady, self-oscillating or chaotic flows; (viii) a sufficient condition for the complete washout of fluid particles has been established; (ix) the nonlinear asymptotic stability of selected steady flows is proven and the related thresholds have been evaluated; (x) computational solutions that clarify C1 and C2 and discover three qualitatively different scenarios of flow relaxation have been obtained

CFD Investigation of Effect of Depth to Diameter Ratio on Dimple Flow // Computational fluid dynamics investigation of effect of depth to diameter ratio on dimple flow dynamics

This study aimed to further the understanding of laminar flow through a dimple with the goal of mitigating flow separation. Dimples of various depth to diameter ratios (0.05, 0.15) were examined for three different dimple diameters and chordwise locations, corresponding to diameter based (ReD) and chordwise location based (Rex) Reynolds number combinations of ReD 20500\Rex 5000, ReD 20500 Rex 77000, and ReD 9000 Rex 21000. For the last combination, a dimple of depth to diameter ratio of 0.25 was also examined. The dimples were placed in a flat plate located in a diverging channel causing an adverse pressure gradient encouraging flow separation near the dimple location. The flow was modeled in the commercial CFD solver Fluent. Results indicate that dimple depth to diameter ratio has a significant effect on the structure of dimple flow. The shallowest dimples showed little change to the overall flow in the channel. Deeper dimples contained dynamic vortical flow structures with behavior varying between each dimple studied. This dynamic vortex activity was observed to be linked with variances in downstream flow. The 0.15 depth to diameter ratio dimples showed behavior very similar to 0.10 ratio dimples investigated elsewhere. The 0.25 dimple show flow different in nature than 0.15 dimples for the same ReD and Rex; the differences were not as stark as those between 0.05 and 0.15 dimples. In light of this and other studies, dimple flow behavior is found to depend on a combination of parameters that eludes direct quantitative parameterization. However, the conclusion is drawn that the most effective dimple will be just deep enough to develop dynamic vortical activity and vortex shedding