ALBERT

Description: Active circulation control of the two-dimensional unsteady separated flow past a semi-infinite plate with transverse motion is considered. The rolling-up of the separated shear layer is modelled by a point vortex whose time-dependent circulation is predicted by an unsteady Kutta condition. A suitable vortex shedding mechanism introduced. A control strategy able to maintain constant circulation when a vortex is present is derived. An exact solution for the nonlinear controller is then obtained. Dynamical systems analysis is used to explore the performance of the controlled system. The control strategy is applied to a class of flows and the results are discussed. A procedure to determine the position and the circulation of the vortex, knowing the velocity signature on the plate, is derived. Finally, a physical explanation of the control mechanism is presented. © 1994, Cambridge University Press. All rights reserved.

Description: We present a study of the rheological and optical behaviour of Kramers bead-rod chains in dilute solution using stochastic computer simulations. We consider two model linear flows, steady shear and uniaxial extensional flow, in which we calculate the non-Newtonian Brownian and viscous stress contribution of the polymers, their birefringence and a stress-optic coefficient. We have developed a computer algorithm to differentiate the Brownian from the viscous stress contributions which also avoids the order (δt)-1/2 noise associated with the Brownian forces. The strain or shear rate is made dimensionless with a molecular relaxation time determined by simulated relaxation of the birefringence and stress after a strong flow is applied. The characteristic long relaxation time obtained from the birefringence and stress are equivalent and shown to scale with N2 where N is the number of beads in the chain. For small shear or extension rates the viscous contribution to the effective viscosity is constant and scales as N. We obtain an analytic expression which explains the scaling and magnitude of this viscous contribution. In uniaxial extensional flow we find an increase in the extensional viscosity with the dimensionless flow strength up to a plateau value. Moreover, the Brownian stress also reaches a plateau and we develop an analytic expression which shows that the Brownian stress in an aligned bead-rod chain scales as N3. Using scaling arguments we show that the Brownian stress dominates in steady uniaxial extensional flow until large Wi, Wi ≈ 0.06N2, where Wi is the chain Weissenberg number. In shear flow the viscosity decays as Wi-1/2 and the first normal stress as Wi-4/3 at moderate Wi. We demonstrate that these scalings can be understood through a quasi-steady balance of shear forces with Brownian forces. For small Wi (in shear and uniaxial extensional flow) and for long times (in stress relaxation) the stress-optic law is found to be valid. We show that the rheology of the bead-rod chain can be qualitatively described by an equivalent FENE dumbbell for small Wi.

Description: Streamwise and quasi-streamwise elongated structures have been shown to play a significant role in turbulent shear flows. We model the mean behaviour of fully turbulent plane Couette flow using a streamwise constant projection of the Navier-Stokes equations. This results in a two-dimensional three-velocity-component (2D/3C) model. We first use a steady-state version of the model to demonstrate that its nonlinear coupling provides the mathematical mechanism that shapes the turbulent velocity profile. Simulations of the 2D/3C model under small-amplitude Gaussian forcing of the cross-stream components are compared to direct numerical simulation (DNS) data. The results indicate that a streamwise constant projection of the Navier-Stokes equations captures salient features of fully turbulent plane Couette flow at low Reynolds numbers. A systems-theoretic approach is used to demonstrate the presence of large input-output amplification through the forced 2D/3C model. It is this amplification coupled with the appropriate nonlinearity that enables the 2D/3C model to generate turbulent behaviour under the small-amplitude forcing employed in this study. © 2010 Cambridge University Press.

Description: In order to study the role of the passive deformation in the aerodynamics of insect wings, we computationally model the three-dimensional fluid-structure interaction of an elastic rectangular wing at a low aspect ratio during hovering flight. The code couples a viscous incompressible flow solver based on the immersed-boundary method and a nonlinear finite-element solver for thin-walled structures. During a flapping stroke, the wing surface is dominated by non-uniform chordwise deformations. The effects of the wing stiffness, mass ratio, phase angle of active pitching, and Reynolds number are investigated. The results show that both the phase and the rate of passive pitching due to the wing flexibility can significantly modify the aerodynamics of the wing. The dynamic pitching depends not only on the specified kinematics at the wing root and the stiffness of the wing, but also greatly on the mass ratio, which represents the relative importance of the wing inertia and aerodynamic forces in the wing deformation. We use the ratio between the flapping frequency, ω, and natural frequency of the wing, ω n, as the non-dimensional stiffness. In general, when ω/ ω n ≤ 0.3, the deformation significantly enhances the lift and also improves the lift efficiency despite a disadvantageous camber. In particular, when the inertial pitching torque is assisted by an aerodynamic torque of comparable magnitude, the lift efficiency can be markedly improved. © Copyright Cambridge University Press 2012.