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 AG: Instability: Jets and Wakes I |
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Chair: Gary Chandler, University of Cambridge Room: Salt Palace Convention Center 250 A |
Sunday, November 18, 2007 8:30AM - 8:43AM |
AG.00001: The effect of confinement on the stability of the Rankine vortex with axial flow Matthew Juniper It has been shown recently that two-dimensional inviscid jets and wakes become significantly more unstable when they are confined between two flat plates, due to the interaction of Kelvin-Helmholtz modes in the inner and outer flows. It has also been shown that swirl significantly destabilizes unconfined inviscid jets and wakes, due to the interaction between Kelvin-Helmholtz modes and inertial modes. In this paper, the Rankine vortex with axial flow is confined within a duct in order to test the combined effect of confinement and swirl. The flow's stability is calculated as a function of shear, density ratio, swirl and confinement using a classic spatio-temporal instability analysis. It is found that confinement particularly destabilizes the helical $m=1$ and $m=2$ modes. These are at their most unstable when the radius of the outer flow is 1.4 times the radius of the inner flow. Experiments on coaxial fuel injectors with this geometry have shown that confined shear flows exhibit a strong helical $m=1$ mode, which can be exploited to increase mixing in a combustion chamber. This paper explains this effect and shows how the presence of strong helical modes can be predicted with a low order model. [Preview Abstract] |
Sunday, November 18, 2007 8:43AM - 8:56AM |
AG.00002: The effect of surface tension on the absolute/convective stability of confined cylindrical jets and wakes Simon Rees, Matthew Juniper It has been shown recently that both two-dimensional and cylindrical jets and wakes become more unstable when they are confined within a duct. This paper examines the effect of surface tension on these flows. In the two-dimensional geometry, surface tension acts in the flow direction and provides a restoring force in the cross-stream direction. In the cylindrical geometry, the azimuthal component of surface tension leads to a further force in the radial direction. For the axisymmetric ($m=0$) mode, axial variations in this azimuthal component are always destabilizing and, above a threshold of surface tension, causes regions of absolute instability to extend to lower shear. For the helical ($m=1$) mode, there are no axial variations in the azimuthal component and the instability is only governed by the surface tension contribution in the flow direction. For all higher order ($m \ge 2$) modes, axial variations in the azimuthal component of surface tension are always stabilizing. Compared with unconfined flows, confinement causes the transition from convective to absolute instability to occur at lower shear and can cause surface tension to become destabilizing. This effect is examined over an infinite range of density ratios and confinement. [Preview Abstract] |
Sunday, November 18, 2007 8:56AM - 9:09AM |
AG.00003: Non-modal stability analysis of viscous confined two-dimensional jets and wakes with finite shear Gary Chandler, Colm Caulfield, Matthew Juniper Non-modal techniques have become increasingly popular for the investigation of simple flows in order to gain useful insight into their transient behavior. Using a linearized perturbation version of the Navier-Stokes equation within a spectral DNS solver, this study investigates the transient growth rate for confined and unconfined 2D viscous jets and wakes. A range of finite times were selected and the time-averaged maximum optimized energy growth rates for a a range of wave numbers were calculated and compared to the growth rate of the least stable eigenmode. The optimized initial conditions were found and used in full non-linear calculations to gain insight into the effect of the optimized initial conditions on stimulating non-linear flow regimes. Variable finite shear is included by superimposing two tanh profiles and its effect on the stability of the flow is also studied. The techniques used in this investigation can be extended to 3D flows with complex geometries, thus enabling the study of more realistic flows and eventually optimization for high transient growth rates in fuel injection processes. [Preview Abstract] |
Sunday, November 18, 2007 9:09AM - 9:22AM |
AG.00004: Absolute instability of hot round jets discharging from tubes W. Coenen, A. Sevilla, A.L. Sanchez The spatiotemporal, inviscid linear instability of hot gas jets emerging from a round tube of radius $a$ is studied for jet Reynolds numbers $Re \gg 1$. The analysis focuses on the influence of the injector length $l_t$ on the stability characteristics of the resulting jet, whose base velocity profile at the exit is computed in terms of the dimensionless tube length $L_t=l_t/(Re \, a)$ by integrating the boundary-layer equations along the injector. Both axisymmetric modes ($m=0$) and first azimuthal modes ($m=1$) of instability are investigated for values of the jet-to-ambient density ratio $S=\rho_j/\rho_{\infty}<1$. For short tubes $L_t \ll 1$ the jet becomes absolutely unstable for critical density ratios $S_c \simeq (0.66,0.35)$ for $m=(0,1)$, in agreement with previous results of uniform velocity jets. For increasing $L_t$ both modes are seen to exhibit absolutely unstable regions for all values of $L_t$ and small enough values of the density ratio. For $m=1$ we find a critical density ratio which increases monotonically with $L_t$, reaching its maximum value $S_c \simeq 0.5$ as the exit velocity approaches the parabolic profile for $L_t \gg 1$. In the case $m=0$ the critical density ratio achieves a maximum value $S_c\simeq 0.9$ for $L_t \simeq 0.04$ and then decreases to approach $S_c=0.7$ for $L_t \gg 1$. The absolute growth rates in this limiting case are however extremely small, in agreement with the fact that the parabolic velocity profile is neutrally stable to axisymmetric disturbances. [Preview Abstract] |
Sunday, November 18, 2007 9:22AM - 9:35AM |
AG.00005: Low Flow Jet Sources for Serial Crystallography D.P. DePonte, U. Weierstall, R.B. Doak, J.C.H. Spence, D. Starodub, G. Hembree, J. Warner, M. Hunter Motivated by the need for a high particle density, water encapsulated protein source we have examined the low-flow regime of thin jets in a co-flowing gas [1] as well as Rayleigh jets. The former method is a reliable source of micron size drops whereas the latter method was found to be unreliable for drop production less than twenty micron due to clogging. For a source consisting of two concentric tubes, we examine the high density region of the jet and effects of triggering, alignment, aperture size flow rate and pressure external to the source. \newline [1] A.M. Ganan-Calvo Phys. Rev. Lett. 80, 1998 [Preview Abstract] |
Sunday, November 18, 2007 9:35AM - 9:48AM |
AG.00006: Viscous and inviscid centre modes in vortices: the vicinity of the neutral curves David Fabre, St{\'e}phane Le Diz{\`e}s Le Diz\`es \& Fabre (2007) have recently demonstrated that if the Reynolds number is sufficiently large, all trailing vortices with non-zero rotation rate and non-constant axial velocity become unstable with respect to a class of viscous centre modes. They have provided an asymptotic description of these modes which applies away from the neutral curves in the $(q,k)$-plane, where $q$ is the swirl number which compares the azimuthal and axial velocities, and $k$ is the axial wavenumber. Here, we complete the asymptotic description of these modes for general vortex flows by considering the vicinity of the neutral curves. Five different regions of the neutral curves are successively considered. In each region, the stability equations are reduced to a generic form which is solved numerically. The study permits to predict the location of all branches of the neutral curve (except for a portion of the upper neutral curve where it is shown that near-neutral modes are not centre modes). We also show that four other families of centre modes exist in the vicinity of the neutral curves. The asymptotic results are compared to numerical results for the case of the $q$-vortex model, and a good agreement is demonstrated for all the regions of the neutral curve. [Preview Abstract] |
Sunday, November 18, 2007 9:48AM - 10:01AM |
AG.00007: Global modes of a lifted flame on a light round fuel jet Joseph W. Nichols, Peter J. Schmid The stability and dynamics of a lifted flame are studied by means of direct numerical simulation (DNS) and linear stability analysis of the reacting, low-Mach number equations. For light fuels (such as nonpremixed methane/air flames), the non-reacting premixing zone upstream of the lifted flame base supports self sustaining oscillations. Local linear stability analysis of the flow downstream of the flame base, however, shows that reaction stabilizes the flow. We show that the global dynamics of the lifted flame can then be interpreted as a superposition of global modes which are ``quenched'' by the change of local properties encountered at the flame base. The quenched global modes are extracted using a Krylov-subspace method about a steady, but unstable, spatially developing base flow obtained by selective frequency damping. The essential dynamics at the flame base are then recovered by finding the optimal superposition of the extracted global modes. [Preview Abstract] |
Sunday, November 18, 2007 10:01AM - 10:14AM |
AG.00008: Absolute secondary instability in variable-density round jets Jean-Marc Chomaz, Joseph W. Nichols, Peter J. Schmid Side jet formation in variable-density round jets is investigated by means of direct numerical simulation (DNS) and linear stability analysis. From DNS, it is observed that a light jet with density ratio $S = \rho_0 / \rho_j = 4$ supports sustained side jets which eject fluid from the center of the jet in a star-shaped pattern. It is conjectured that this behavior can be explained by a change in the local properties of the secondary instability from convective to absolute in nature. This hypothesis is tested by examining the spatio-temporal development of the wavepacket resulting from a small impulse, about non-diffusing periodic base states corresponding to the primary instability. Invoking Taylor's hypothesis, the local time periodicity of the primary instability is used to construct base states at varying axial locations in order to investigate the existence of a pocket of absolute secondary instability. The physical mechanism leading to side jet formation then may be identified by extracting the absolute mode at the upstream boundary of the pocket. Furthermore, azimuthal mode selection is considered by repeating this process for different integral azimuthal wavenumbers. [Preview Abstract] |
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