Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session ED: Instabilities in Jets |
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Chair: John F. Gibson, Georgia Institute of Technology Room: 002B |
Sunday, November 23, 2008 4:10PM - 4:23PM |
ED.00001: The twisted global instability of lifted flames on round variable-density jets Joseph W. Nichols, Jean-Marc Chomaz, Peter J. Schmid The theory of resonant modes is revisited and extended to finite length systems containing pinch points $(k_0, \omega_0)$ with arbitrary $\omega^0_{kk} = \partial^2 \omega / \partial k^2$. When ${\mathrm{Im}\left(\omega^0_{kk}\right)} > 0$, the pinch point is twisted, and the system may be destabilized by resonant modes with growth rates greater than that of the unbounded absolute mode, \emph{i.e.} the system may be globally unstable while locally only convectively unstable. Lifted flames on round variable-density jets serve as motivation for this theory since the premixing zone between the nozzle and flame is an example of a streamwise-confined system containing a twisted pinch point. This flow is studied by means of direct numerical simulation (DNS) and linear stability analysis, the latter of which is used to calculate the locus of resonant modes in the complex $k$- and $\omega$-planes. In agreement with DNS observations, inspection of the solution curve in the $\omega$-plane suggests both a mechanism for stabilization with decreasing system length $l$ and a mechanism for low-frequency fluctuations owing to beating between modes of closely-spaced frequencies. [Preview Abstract] |
Sunday, November 23, 2008 4:23PM - 4:36PM |
ED.00002: The Forced Motion of a Flag Michael Howe, Avshalom Manela The prevailing view of the dynamics of flapping flags is that the onset of motion is caused by linear instability of the initial planar state. This view is reexamined by considering the forced motion of a flag immersed in a high-Reynolds number flow and subject to vortex shedding from its cylindrical pole. Vortex shedding is represented by a ``street'' of discrete line vortices released periodically from the pole and convected in the mean wind over the surfaces of the flag. It is found that forced motion is possible when the flag is still temporally stable, which suggests that the present mechanism should be taken into account in future high-Reynolds experimental investigations. [Preview Abstract] |
Sunday, November 23, 2008 4:36PM - 4:49PM |
ED.00003: Static shapes and instability of hanging flags conveying fluid Tony S. Yu, Sunghwan Jung, Christophe Clanet We investigate the interaction between a fluid jet and a long, thin sheet, \emph{i.e.} ``flag'', clamped to the jet-nozzle. The jet wets and flows along one side of the flag from base (clamped end) to tip, which hangs freely. Experiments reveal a lateral force at the ``free'' end of the hanging flag; this force arises from the minimization of surface-energy as the jet detaches from the flag surface. At low Weber numbers (\emph{i.e.} low flow rates), the tip force produces stable, static flag shapes with wavelengths inversely proportional to the flow rate. The static shapes are well described by a simple model coupling linear beam bending and inviscid flow. At higher Weber numbers, static shapes become unstable, leading to periodic oscillations analogous to previous work on hanging cantilever tubes conveying fluid (Paidoussis, 1970; Doar\'e and Langre, 2002). The observed critical flow rates for instability agree well with those predicted by linear stability analysis. [Preview Abstract] |
Sunday, November 23, 2008 4:49PM - 5:02PM |
ED.00004: ABSTRACT WITHDRAWN |
Sunday, November 23, 2008 5:02PM - 5:15PM |
ED.00005: Global linear stability analysis of the jet in crossflow Shervin Bagheri, Philipp Schlatter, Dan S. Henningson, Peter J. Schmid The global linear stability analysis of the jet in crossflow to three-dimensional perturbations is numerically investigated. At velocity ratio $R=3$, defined as the ratio of jet velocity to free-stream velocity, the flow is globally linearly unstable. The baseflow for the stability analysis is a steady solution of Navier-Stokes, obtained by damping the unstable temporal frequencies using the selective frequency damping method (SFD). The steady state consists of a dominant counter-rotating vortex pair in the far field emerging from the near field vorticity of the shear layer. The eigenvalue problem is solved using the ARPACK library and the linearized DNS as a time stepper. The most unstable mode takes the shape of a localized wavepacket, wrapped around the counter-rotating vortex pair. Further, higher velocity ratios are considered in order the examine the transition from convective to absolute stability of the studied flow case. [Preview Abstract] |
Sunday, November 23, 2008 5:15PM - 5:28PM |
ED.00006: Open Loop Control of Self-Excited Transverse Jets Juliett Davitian, Cory Hendrickson, Daniel Getsinger, Robert M'Closkey, Ann Karagozian Recent experiments have explored the response of a gaseous, isodensity jet in crossflow to controlled acoustic forcing. Focusing on jet-to-crossflow velocity ratios R below 3.5, for which prior experiments \footnote{Megerian, et al., {\bf JFM}, 593, pp. 93-129, 2007} suggest that the upstream shear layer is globally unstable, alternative jet forcing amplitudes and temporal waveforms are explored. Very strong sinusoidal jet forcing at a frequency different from that of the global instability is observed to replace the self-excited mode, consistent with similar open loop forcing results for the globally unstable, low density jet in quiescent surroundings \footnote{Hallberg \& Strykowski, {\bf Phys. Fluids}, 20, 041703, 2008}. Yet in many cases for the forced, globally unstable transverse jet, sinusoidal excitation is not observed to have as great an effect on jet penetration and spread as does square wave forcing with the same $\rm U'_{j,rms}$; such forcing can introduce a characteristic time scale associated with optimal vorticity generation. When the upstream jet shear layer is convectively unstable, on the other hand, for values of R above 3.5, strong and moderate sinusoidal excitation can produce the same level of jet spread and penetration as does square wave forcing. [Preview Abstract] |
Sunday, November 23, 2008 5:28PM - 5:41PM |
ED.00007: Measurements of instability waves in a high speed liquid jet Enrique Portillo, Steven Collicott, Gregory Blaisdell Measurements of instability surface waves present in the near exit region of a high-speed liquid jet are presented. The backlit images, exposed at 1 $\mu $-sec, provide a statistically significant number of measurements so that wavelength and wave velocity can be determined. It is found that the waves stretch as they travel in the downstream direction and that the axial wavelength changes significantly depending on its streamwise location. These results emphasize the importance of stating the axial position of any analytical wavelength resulting from spatial stability analyses. Images also show a strong three dimensional flow, in the form of wave packets, in regions closest to the jet's exit. It is observed that these wave packets merge downstream. Stability analyses suggest the waves are generated by a pocket of absolute instability located at the exit of the jet, and the most dominant mode is determined by the location where the flow transitions to a region of convective instability. [Preview Abstract] |
Sunday, November 23, 2008 5:41PM - 5:54PM |
ED.00008: Numerical simulation of Kelvin-Helmholtz instability and liquid breakup Angel Bethancourt, Kunio Kuwahara, Akiko Mano, Masahiro Egami A diffuse interface model is used to model a two-phase flow. It is incorporated into an incompressible Navier-Stokes solver based on a multi-directional finite difference method with third-order upwinding. In order to test the reliability of the code, 2D simulations are performed of a jet into a still fluid. The evolution of the jet is captured with the instability manifesting itself as waves along the surface of the fluids. A simple comparison between the wavelength obtained here and that given by the Kelvin-Helmholtz instability theory shows excellent agreement with the discrepancy been less than 5{\%}. These instabilities grow, and finally break-up into separate chunks, filaments and droplets. This behavior is in qualitative agreement with those reported in the literature. The present results show the accuracy of the present method with consideration of compressibility effects left for future investigation. [Preview Abstract] |
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