Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session E38: Flow Instability: General I |
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Chair: M.J. Philipp Hack, Stanford University Room: Sheraton Back Bay B |
Sunday, November 22, 2015 4:50PM - 5:03PM |
E38.00001: ABSTRACT WITHDRAWN |
Sunday, November 22, 2015 5:03PM - 5:16PM |
E38.00002: Effect of Prandtl number on the linear stability of compressible Couette flow Krishnendu Sinha, Ashwin Ramachandran, Bijaylakshmi Saikia, Rama Govindarajan Accurate prediction of laminar to turbulent transition in high speed flows is a challenging task. Compressibility, and the resultant large variations in transport properties can affect this transition significantly. Prandtl number (ratio of momentum and thermal diffusivities) is an important parameter which affects the linear stability of high Mach number wall-bounded flows. A two-dimensional compressible plane Couette flow having uniform viscosity and thermal conductivity with varying Prandtl numbers is our model problem. A temporal stability analysis shows that the variation of phase speed with Prandtl number leads to synchronization between acoustic modes, with peaks in growth rate at the synchronization points. Two types of branching patterns are observed, depending on the Prandtl number. The stability diagrams for varying Mach and Reynolds numbers show a destabilizing role of decreasing Prandtl number, both in terms of increased disturbance growth rates, and of larger regions of instability in the parameter space. It also results in a significant reduction in the critical Reynolds number of the flow, especially at high Mach numbers. [Preview Abstract] |
Sunday, November 22, 2015 5:16PM - 5:29PM |
E38.00003: Criteria for instability of helical disturbances in inviscid, swirling flows Christopher Douglas, Benjamin Emerson, Timothy Lieuwen This work considers the linear inviscid instability of columnar vortices with axial flow in unbounded domains subjected to 3D perturbations. The base flow parameters have a general dependence on the radial distance from the swirl axis. Following Howard and Gupta's approach, we develop two stability conditions in terms of an infinite set of helical disturbances via a normal modes expansion. We develop a generalization of Fj\o rtoft's necessary criterion which states that a wave-like disturbance may be unstable if the base shear velocity has an inflection point in the binormal direction of the helix which is also a vorticity maximum. A necessary condition for instability is that\[(W'-W'_0)d(\kappa\dot{\gamma}')/dr<0\]must be satisfied somewhere for any real constant $W'_0$ where $\kappa$ is the curvature of the helix, $W'$ is the binormal base velocity, and $\dot{\gamma}'$ is the binormal base shear rate. The second condition leads to a generalization of Rayleigh's criterion for centrifugal instability for helical disturbances. We find that a necessary and sufficient condition for instability is that\[Vd\Gamma'/dr<0\]be satisfied somewhere, where $V$ is the base azimuthal velocity and $\Gamma'$ is the base circulation due to the flux of vorticity tangent to the helical vortex tube. [Preview Abstract] |
Sunday, November 22, 2015 5:29PM - 5:42PM |
E38.00004: Three-dimensional instabilities in a rapidly counter-rotating split cylinder Paloma Gutierrez-Castillo, Juan M. Lopez The three-dimensional flow in a counter-rotating cylinder that is split at its mid-plane is studied numerically via spectral methods. The cylinder of radius $a$ and length $h$ is completely filled with fluid of kinematic viscosity $\nu$. The top half rotates with angular speed $\omega$ and the bottom half with angular speed $-\omega$. There are two nondimensional parameters governing the flow, $Re=\omega a^2/\nu$ and $\Gamma=h/a$. For small values of $Re$ and $\Gamma$ the flow is steady, axisymmmetric and reflection symmetric about the mid-height (with appropriate changes of sign for some flow components). In this regime the interior flow in each half of the cylinder rotate as solid-body rotation of opposite senses. Apart from the boundary layers on the cylinder walls, there is also an internal shear layer separating the two counter-rotating halves. Above a critical $Re$ that depends on $\Gamma$, this internal shear layer becomes unstable to low frequency instabilities that break both the axisymmetry and the reflection symmetry. For these cases there exist rotating waves associated with the shear-layer instability. The variation of the critical $Re$ and the azimuthal wavenumbers of the instability as a function of $\Gamma$ is studied, along with the nonlinear dynamics. [Preview Abstract] |
Sunday, November 22, 2015 5:42PM - 5:55PM |
E38.00005: Inertial instability of miscible fluid stratifications in square microchannels Xiaoyi Hu, Thomas Cubaud The stability of stratifications made between miscible fluids having large differences in viscosity is experimentally investigated in square microchannels. Parallel fluid layers with a fast central stream and a slow sheath flow are produced by focusing low-viscosity fluid with high-viscosity fluid in a straight microchannel. We examine in particular the formation and evolution of periodic wave trains at each fluid interface over a range of fluid viscosities and flow rates. This study shows that miscible fluid arrangements can be destabilized for moderate Reynolds numbers. Several relationships are developed for the propagating velocity, size, and frequency of generated waves. In the unstable regime, minute amount of high-viscosity fluid is entrained and blended into the low-viscosity fluid recirculating plumes formed by the traveling waves. This phenomenon provides new insights into the development of microfluidic methods for continuously mixing high- and low-viscosity fluids. [Preview Abstract] |
Sunday, November 22, 2015 5:55PM - 6:08PM |
E38.00006: Optimal Free-Stream Vortical Disturbances M.J. Philipp Hack In boundary layers exposed to moderate levels of free-stream disturbances, natural transition via the exponential amplification of Tollmien-Schlichting waves is \textit{bypassed} by a more rapid breakdown process. The external disturbances interact with the mean shear and induce the growth of highly energetic streaks, which cause transition to turbulence by virtue of the growth of inviscid secondary instabilities. The relationship between external vortices and boundary-layer perturbations is, however, not entirely understood. The present study provides a rigorous link between the dynamics in the free-stream and inside the boundary layer by computing the optimal free-stream vortical disturbances, i.e. the external disturbances which maximize the energy content of the resulting boundary-layer perturbations. The mathematical framework is based on a semi-norm formulation of the adjoint linearized compressible Navier-Stokes equations in curvilinear coordinates and enables the global analysis of disturbance sensitivity as well as the computation of optimal disturbances in flows with variable density and miscellaneous geometries. [Preview Abstract] |
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