Instabilities in unsteady boundary layers with reverse flow

Instabilities arising in unsteady boundary layers with reverse flow have been investigated experimentally. Experiments are conducted in a piston driven unsteady water tunnel with a shallow angle diffuser placed in the test section. The ratio of temporal (Pi(t)) to spatial (Pi(x)) component of the pressure gradient can be varied by a controlled motion of the piston. In all the experiments, the piston velocity variation with time is trapezoidal consisting of three phases: constant acceleration from rest, constant velocity and constant deceleration to rest. The adverse pressure gradient (and reverse flow) are due to a combination of spatial deceleration of the free stream in the diffuser and temporal deceleration of the free stream caused by the piston deceleration. The instability is usually initiated with the formation of one or more vortices. The onset of reverse flow in the boundary layer, location and time of formation of the first vortex and the subsequent flow evolution are studied for various values of the ratio Pi(x) (Pi(x) + Pi(t)) for the bottom and the top walls. Instability is due to the inflectional velocity profiles of the unsteady boundary layer. The instability is localized and spreads to the other regions at later times. At higher Reynolds numbers growth rate of instability is higher and localized transition to turbulence is observed. Scalings have been proposed for initial vortex formation time and wavelength of the instability vortices. Initial vortex formation time scales with convective time, delta/Delta U, where S is the boundary layer thickness and Delta U is the difference of maximum and minimum velocities in the boundary layer. Non-dimensional vortex formation time based on convective time scale for the bottom and the top walls are found to be 23 and 30 respectively. Wavelength of instability vortices scales with the time averaged boundary layer thickness. (C) 2015 Elsevier Masson SAS. All rights reserved.

Numerical study of driven flows of shear thinning viscoelastic fluids in rectangular cavities

In this work, we present a numerical study of flow of shear thinning viscoelastic fluids in rectangular lid driven cavities for a wide range of aspect ratios (depth to width ratio) varying from 1/16 to 4. In particular, the effect of elasticity, inertia, model parameters and polymer concentration on flow features in rectangular driven cavity has been studied for two shear thinning viscoelastic fluids, namely, Giesekus and linear PTT. We perform numerical simulations using the symmetric square root representation of the conformation tensor to stabilize the numerical scheme against the high Weissenberg number problem. The variation in flow structures associated with merging and splitting of elongated vortices in shallow cavities and coalescence of corner eddies to yield a second primary vortex in deep cavities with respect to the variation in flow parameters is discussed. We discuss the effect of the dominant eigenvalues and the corresponding eigenvectors on the location of the primary eddy in the cavity. We also demonstrate, by performing numerical simulations for shallow and deep cavities, that where the Deborah number (based on convective time scale) characterizes the elastic behaviour of the fluid in deep cavities, Weissenberg number (based on shear rate) should be used for shallow cavities. (C) 2016 Elsevier B.V. All rights reserved.