Alexander Yu. Gelfgat

Steady states and oscillatory instability of swirling flow in a cylinder with rotating top and bottom

In this study we present a numerical investigation of steady states, onset of oscillatory instability, and slightly supercritical oscillatory states of an axisymmetric swirling flow of a Newtonian incompressible fluid in a cylinder, with independently rotating top and bottom. The first part of the study is devoted to the influence of co‐ and counter‐rotation of the bottom on the steady vortex breakdown, which takes place in the well‐known problem of flow in a cylinder with a rotating top. It is shown that weak counter‐rotation of the bottom may suppress the vortex breakdown. Stronger counter‐rotation may induce a stable steady vortex breakdown at relatively large Reynolds numbers for which a vortex breakdown does not appear in the case of the stationary bottom. Weak corotation may promote the vortex breakdown at lower Reynolds numbers than in the cylinder with the stationary bottom. Stronger corotation leads to the detachment of the recirculation zone from the axis and the formation of an additional vorte...

Stability of stratified two-phase flows in horizontal channels

Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems, the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called “interfacial modes of instability”) or in the bulk of one of the phases (i.e., “shear modes”). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength.

Three-dimensional instability of a two-layer Dean flow

Stability of a two-layer Dean flow in a cylindrical annulus with respect to three-dimensional perturbations is studied by a global Galerkin method. It is shown that for large inner radius of the annulus (i) the instability becomes three-dimensional if one of the fluid layers is thin, (ii) its onset is not affected by possible small deformations of the interface, and (iii) multiple three-dimensional flow states are expected in a slightly supercritical flow regime. Stability diagrams and patterns of the three-dimensional perturbations are reported. It is concluded that even when the axisymmetric perturbation is the most dangerous, the resulting supercritical flow is expected to be three-dimensional. Possible multiplicity of supercritical three-dimensional states is predicted. The basis functions of the global Galerkin method are constructed so as to satisfy analytically the boundary conditions on no-slip walls and at the liquid–liquid interface. A modification of the numerical approach, accounting for small...

Experimental and numerical study of anomalous thermocapillary convection in liquid gallium

Thermocapillary Marangoni convection of liquid gallium was studied experimentally and numerically. A specially designed experimental setup ensured an oxide-free surface of the liquid gallium for a very long time. The convective flow at the free surface was found to be directed opposite to both buoyancy-driven and ordinary thermocapillary convection. The anomalous direction of the thermocapillary flow was explained by the presence of a small amount of a surface-active contaminant—lead adsorbed at the free surface. Two different approaches were used to describe the observed phenomenon. First, the flow was treated as a pure thermocapillary convection with a modified dependence of the surface tension on temperature so that to reproduce the measured velocity distribution. Second, a novel physical model was devised for the flow driven by the gradient of the surface tension induced by the temperature dependence of the concentration of the adsorbed layer of contaminant. In contrast to the ordinary thermocapillary...

Second International Symposium on Instability and Bifurcations in Fluid Dynamics

Hydrodynamic stability is of fundamental importance in fluid dynamics and is a well-established subject of scientific investigation that continues to attract great interest of the fluid mechanics community. Bifurcations and instabilities are observed in all areas of fundamental and applied fluid dynamics and remain a challenge for experimental, theoretical and computational studies. Hydrodynamic instabilities of prototypical character are, for example, the Rayleigh-Benard, the Taylor-Couette, the Benard-Marangoni, the Rayleigh-Taylor, and the Kelvin-Helmholtz instabilities. A fundamental understanding of various patterns of bifurcations such as identifying the most dominant mechanisms responsible for the instability threshold is also required if one is to design reliable and efficient industrial processes and applications, such as melting, mixing, crystal growth, coating, welding, flow re-attachment over wings, and others. Modeling of various instability mechanisms in biological and biomedical systems is currently a very active and rapidly developing area of research with important biotechnological and medical applications (biofilm engineering, wound healing, etc). The understanding of breaking symmetry in hemodynamics could have important consequences for vascular biology and diseases and its implication for vascular interventions (grafting, stenting, etc). The collection of papers in this volume is a selection of the presentations given at the Third International Symposium on Instability and Bifurcations in Fluid Dynamics, University of Nottingham, UK, 10–13 August 2009. With more than 100 invited and contributed papers the symposium gave an overview of the state-of-the art of the field including experimental, theoretical, and computational approaches to problems related to convection, effects of magnetic fields, wake flows, rotating flows, and many others. The complete program can be found at the conference website. The symposium was the follow-up of two previous symposia held in 2004 in Madeira, Portugal and in 2006 in Copenhagen, Denmark. The number of participants in these symposia has been steadily rising. The next symposium in the series will take place in Barcelona, Spain, 18–21 July 2011. See the conference website for further details. P Z Bar-Yoseph, M Brons, K A Cliffe, A Gelfgat and A Oron Editors