3 results for On the structure of vortex rings from inclined nozzles
On the structure of vortex rings from inclined nozzles
- Trung Bao Le, Iman Borazjani, Seokkoo Kang, Fotis Sotiropoulos
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- Journal:
- Journal of Fluid Mechanics / Volume 686 / 10 November 2011
- Published online by Cambridge University Press:
- 26 September 2011, pp. 451-483
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We carry out numerical simulations to investigate the vortex dynamics of laminar, impulsively driven flows through inclined nozzles in a piston–cylinder apparatus. Our simulations are motivated by the need to provide a complete description of the intricate vortical structures and governing mechanisms emerging in such flows as documented in the experiments of Webster & Longmire (Phys. Fluids, vol. 10, 1998, pp. 400–416) and Troolin & Longmire (Exp. Fluids, vol. 48, 2010, pp. 409–420). We show that the flow is dominated by the interaction of two main vortical structures: the primary inclined vortex ring at the nozzle exit and the secondary stopping ring that arises due to the entrainment of the flow into the cylinder when the piston stops moving. These two structures are connected together with pairs of vortex tubes, which evolve from the continuous vortex sheet initially connecting the primary vortex ring with the interior cylinder wall. In the exterior of the nozzle the key mechanism responsible for the breakup of the vortical structure is the interaction of the stronger inclined primary ring with the weaker stopping ring near the longest lip of the nozzle. In the interior of the nozzle the dynamics is governed by the axial stretching of the secondary ring and the ultimate impingement of this ring on the cylinder wall. Our simulations also clarify the kinematics of the azimuthal flow along the core of the primary vortex ring documented in the experiments by Lim (Phys. Fluids, vol. 10, 1998, pp. 1666–1671). We show that the azimuthal flow is characterized by a pair of two spiral saddle foci at the long and short lips of the nozzle through which ambient flow enters and exits the primary vortex core.
Vortex-induced vibrations of an elastically mounted sphere with three degrees of freedom at Re = 300: hysteresis and vortex shedding modes
- Suresh Behara, Iman Borazjani, Fotis Sotiropoulos
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- Journal of Fluid Mechanics / Volume 686 / 10 November 2011
- Published online by Cambridge University Press:
- 03 October 2011, pp. 426-450
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Fluid–structure interaction (FSI) simulations are carried out to investigate vortex-induced vibrations of a sphere, mounted on elastic supports in all three spatial directions. The reduced velocity () is systematically varied in the range , while the Reynolds number and reduced mass are held fixed at and , respectively. In the lock-in regime, two distinct branches are observed in the response curve, each corresponding to a distinct type of vortex shedding, namely, hairpin and spiral vortices. While shedding of hairpin vortices has been observed in several previous investigations of stationary and vibrating spheres, the shedding of intertwined, longitudinal spiral vortices in the wake of a vibrating sphere is reported herein for the first time. When the wake is in the hairpin shedding mode, the sphere moves along a linear path in the transverse plane, while when spiral vortices are shed, the sphere vibrates along a circular orbit. In the spiral mode branch, the simulations reveal hysteresis in the response amplitude at the beginning of the lock-in regime. Lower-amplitude vibrations are found as the sphere sheds hairpin vortices for increasing up until the beginning of the synchronization regime. On the other hand, higher-amplitude oscillations persist for the spiral mode as is decreased from the point of the start of the synchronization. The hairpin mode is found to be unstable for the value of reduced velocity where the spiral and hairpin solution branches merge together. When this point is approached along the hairpin solution branch, the sphere naturally transitions from shedding hairpin vortices and moving along a linear path to shedding spiral vortices and moving along a circular path in the transverse plane. The spiral mode was not observed in the work of Horowitz & Williamson (J. Fluid Mech., vol. 651, 2010, pp. 251–294), who studied experimentally the vibration modes of a freely rising or falling sphere and only reported zigzag vibrations. Our results suggest that this apparent discrepancy between experiments and simulations should be attributed to the fact that, for the range of governing parameters considered in the simulations, the elastic supports act to suppress streamwise vibrations, thus subjecting the sphere to a nearly axisymmetric elasticity constraint and enabling it to vibrate transversely along a circular path.
Lagrangian model of bed-load transport in turbulent junction flows
- CRISTIAN ESCAURIAZA, FOTIS SOTIROPOULOS
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- Journal of Fluid Mechanics / Volume 666 / 10 January 2011
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- 06 January 2011, pp. 36-76
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Motivated by the need to gain fundamental insights into the mechanisms of bed-load sediment transport in turbulent junction flows, we carry out a computational study of Lagrangian dynamics of inertial particles initially placed on the bed upstream of a surface-mounted circular cylinder in a rectangular open channel (Dargahi, J. Hydraul. Engng, vol. 116, 1990, pp. 1197–1214). The flow field at Re = 39000 is simulated using the detached eddy simulation (DES) approach (Spalart et al., In Advances in DNS/LES, ed. C. Liu & Z. Liu, 1997, Greyden), which has already been shown to accurately resolve most of the turbulent stresses produced by the low-frequency, bimodal fluctuations of the turbulent horseshoe vortex (Paik et al., J. Hydraul. Engng, vol. 131, 1990, pp. 441–456; Escauriaza & Sotiropoulos, Flow Turbul. Combust., 2010, in press). The trajectory and momentum equations for the sediment particles are integrated numerically simultaneously with the flow governing equations assuming one-way coupling and neglecting particle-to-particle interactions (dilute flow) but taking into account bed–particle interactions and the effects of the instantaneous hydrodynamic forces induced by the resolved fluctuations of the coherent vortical structures. The computed results show that, in accordance with the simulated clear-water scour condition (i.e. the magnitude of the particle stresses is near the threshold of motion), the transport of sediment grains is highly intermittent and exhibits essentially all the characteristics of bed-load sediment transport observed in laboratory and field experiments. Groups of sediment grains are dislodged from the bed simultaneously in seemingly random bursting events and begin to move, saltating or sliding along the bed. Furthermore, particles that are not entrained into the bed-load layer are found to form streaks aligned with near-wall vortices around the cylinder. The global transport of particles is studied by performing a statistical analysis of the bed-load flux to reveal scale-invariance of the process and multifractality of particle transport as the overall effect of the coherent structures of the flow. A major finding of this work is that a relatively simple Lagrangian model coupled with a coherent-structure resolving simulation of the turbulent flow is able to reproduce the sediment dynamics observed in multiple experiments performed under similar conditions, and provide fundamental information on the initiation of motion and the multifractal nature of bed-load transport processes. The results also motivate the development of new Eulerian bed-load transport models that consider unsteady conditions and incorporate the intermittency of the unresolved scales of sediment motion.