Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session GN: Instability: Boundary Layers II |
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Chair: Sharon Stephen, University of Birmingham Room: Salt Palace Convention Center 251 B |
Monday, November 19, 2007 10:30AM - 10:43AM |
GN.00001: Centrifugal instability of the wake-dominated curved compressible mixing-layers. Li Lin, Sharon Stephen The mixing layer is an interfacial region between two moving homogeneous fluids of different density, compressibility, velocity and temperature. G\"{o}rtler instability is a type of centrifugal instability which could arise from the mixing layer system owing to the dynamical effect of centreline curvature. The linear development of G\"{o}rtler vortices at high Reynolds number within both stably and unstably curved compressible mixing layers is investigated. The purpose behind this investigation is to determine if the presence of a G\"{o}rtler mode could enhance the mixing of two fluids in certain physical situations such as the mixing between fuel and oxidizer within a scramjet engine for the propulsion of hypersonic aircraft. The investigation is made by examining the growth rate and the location of the G\"{o}rtler modes in the limit of larger G\"{o}rtler number. An analytical Gaussian wake model is first used to predict the development of the G\"{o}rtler modes. A more accurate basic wake model has also been obtained numerically to compare with the earlier prediction. [Preview Abstract] |
Monday, November 19, 2007 10:43AM - 10:56AM |
GN.00002: Stability of axisymmetric boundary layers: Effects of transverse curvature Vinod Narayanan, Rama Govindarajan We investigate the stability of laminar boundary layer on an axisymmetric cylinder steadily translating through a fluid in a direction parallel to its axis. The aim is to study the effects of transverse curvature on instability and transition. Squire's theorem does not apply and non-axisymmetric modes are found to be unstable at the lowest Reynolds number. In an extension of Rayleigh's and Fjortoft's theorem to axisymmetric boundary layers, the present case is shown to be inviscidly stable. The helical (n=1) mode is unstable over a significant axial extent of the cylinder, but is stable for curvatures above some critical value. Higher non-axisymmetric modes are linearly unstable only for very small range of curvatures. Here the curvature is defined as the ratio of momentum thickness to the body radius. Overall there is a stabilizing effect due to transverse curvature. A secondary instability analysis of the flow shows that secondary modes remain unstable at curvatures for which the linear modes are stable. However there is a maximum curvature, above which all disturbances decay. It is found that the most unstable secondary modes are always subharmonic and those whose azimuthal wavenumbers (m+ and m-) are related to that of the linear mode (n) by m+=2n and m-=-n. [Preview Abstract] |
Monday, November 19, 2007 10:56AM - 11:09AM |
GN.00003: Stability of the boundary layer on a compliant rotating disc Sharon Stephen, Jo-Anne John Transition to turbulence of the three-dimensional boundary layer on a rotating disc can be preceded by the emergence of crossflow vortices that are stationary with respect to the disc. These result from an inviscid instability mechanism associated with an inflexion point in the boundary layer velocity profile or a mechanism induced by the balance between viscous and Coriolis forces. Past studies for other flows have shown that compliance can substantially postpone the onset of transition. We use numerical and asymptotic methods to investigate the effect of compliance on this instability by considering the flow over a rotating finite depth viscoelastic layer. Growth rates are calculated and neutral solutions produced for both inviscid and viscous modes. The results obtained are compared to recent experiments. [Preview Abstract] |
Monday, November 19, 2007 11:09AM - 11:22AM |
GN.00004: ABSTRACT WITHDRAWN |
Monday, November 19, 2007 11:22AM - 11:35AM |
GN.00005: Instability of the 3D boundary layer flow over a rotating cone. Zahir Hussain, Sharon Stephen The flow over a rotating cone is susceptible to crossflow and centrifugal instability modes, depending on the sharpness of the cone nose. The boundary layer instability is visualized by the formation of spiral vortices, which wrap around the cone surface in a helical nature. For parameters ranging from propeller nose cones to rotating disks, the instability triggers co-rotating vortices, whereas for sharp spinning missiles, counter-rotating vortices are observed. In the presence of a forced free-stream, the flow is essentially a battle between the oncoming axial flow and the azimuthal shear flow due to the rotating surface. Experiments in the literature have shown that increasing the incident free-stream has a stabilizing effect on these spiral vortices. We derive the mean flow boundary layer equations and investigate the asymptotic stability of the flow to inviscid crossflow modes at large Reynolds number for a cone in still fluid as well as in axial flow. The influence of the cone half-angle and axial flow strength on the number and orientation of the spiral vortices is examined, with comparisons made with previous experimental and numerical results. [Preview Abstract] |
Monday, November 19, 2007 11:35AM - 11:48AM |
GN.00006: Global stability of the boundary layer over a rotating disk in an annulus Bertrand Viaud, Eric Serre, Jean-Marc Chomaz Spectral Direct Numerical simulation is applied to the investigation of the transition process in the boundary layer over a rotating disk. The configuration is made of two parallel co-rotating disks, with a forced inflow at the hub and a free outflow at th rim. The flow is controled by the rotation rate and the mass flow rate. The DNS code is used to conduct both local and global stability analysis. Local results show that the boundary layer undergoes transition to absolute instability for the same control and modal parameters as in the case of the single disk. As far as global behaviour is concerned, the flow proves to be linearly globally stable, wich is consistent with former numerical results of Davies \& Carpenter [J.FLUID MECH. 486 287 2003], and experiments by Othman \& Corke [J.FLUID MECH. 565 63 2006]. But on the other hand, its response to a sufficiently strong impulse perturbation shows that it is non-linearly globally unstable. Moreover, the characteristics of the non-linear global mode are in full agreement with Pier's [J.FLUID MECH. 487 315 2003] description of an elephant mode in the case of the single infinite disk. The role of this elephant mode in the transition process is further investigated. In this prospect, it's stability with regard to secondary perturbation is studied. [Preview Abstract] |
Monday, November 19, 2007 11:48AM - 12:01PM |
GN.00007: Travelling crossflow vortices in the B\"{o}dewadt boundary layer Natalie Culverhouse, Sharon Stephen Recent experiments studying the boundary layer over a stationary plane where fluid in the far-field is rotating (the B\"{o}dewadt layer) have used rotor-stator devices and spin-down methods to successfully show travelling instabilities with the presence of crossflow vortices. The boundary layer structure is investigated analytically for large Reynolds numbers using an asymptotic approach. Eigenrelations are derived for neutral stability modes and given a specific wave speed the radial and azimuthal wavenumbers are determined. Some limiting cases of these solutions are analysed to show the physical nature of the flow at these points. [Preview Abstract] |
Monday, November 19, 2007 12:01PM - 12:14PM |
GN.00008: ABSTRACT WITHDRAWN |
Monday, November 19, 2007 12:14PM - 12:27PM |
GN.00009: Low-Dimensional Dimensional Description of Klebanoff Modes Maria Higuera, Jose Vega The spanwise evolution of a generic Klebanoff mode in a three-dimensional boundary layer attached to a flat plate is examined. These modes are known to be induced by free stream turbulence and correspond to three-dimensional perturbations of the (two-dimesional) steady Blasius solution, and exhibit low-frequency and long-wavelength perturbations in the streamwise direction, but oscillate rapidly in the spanwise direction. We present a low-dimensional Galerkin description of the Klebanoff modes. The comparison with results obtained through an optimization procedure applied to the adjoint problem (Luchini, JFM 2000), seems to indicate that the development of the instability may be understood on the basis of amplitude equations associated with the relevant Galerkin modes. [Preview Abstract] |
Monday, November 19, 2007 12:27PM - 12:40PM |
GN.00010: Experimental demonstration of scaling law for transition in subcritical channel flows Jimmy Philip, Alexander Svizher, Jacob Cohen Scaling law for the threshold amplitude of perturbations to trigger nonlinearity in subcritical plane Poiseuille flow as function of the Reynolds number is demonstrated experimentally. The process is composed of a linear stage followed by a non linear one. The disturbances are introduced through an almost streamwise independent slot drilled at the bottom wall of a horizontal air channel flow. For low injection rates, long counter-rotating pair of vortices is observed undergoing transient growth, where as, above a critical injection rate of the disturbance, the pair of vortices undergo secondary instability leading to the nonlinear phenomenon of the initiation of hairpin vortices. The normalized critical injection rate ($v_0$) scales with the Reynolds number ($Re$) as $v_0 \sim Re^{-3/2}$, as predicted by Chapman [J. Fluid Mech. {\bf{451}}, 34 (2002)], using asymptotic theory. However, unlike in the theory which requires an impractical channel length of $O(R)$ for the growth of an infinitesimal small amplitude of vertical velocity ($v_0$) to $O (1)$ vertical vorticity, in the experiments a much shorter channel is used to obtain the same results by increasing the initial disturbance amplitude instead. [Preview Abstract] |
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