8 results
Turbulence statistics in a negatively buoyant multiphase plume
- Ankur D. Bordoloi, Chris C. K. Lai, Laura Clark, Gerardo V. Carrillo, Evan Variano
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- Journal:
- Journal of Fluid Mechanics / Volume 896 / 10 August 2020
- Published online by Cambridge University Press:
- 01 June 2020, A19
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We investigate the turbulence statistics in a multiphase plume made of heavy particles (particle Reynolds number at terminal velocity is 450). Using refractive-index-matched stereoscopic particle image velocimetry, we measure the locations of particles whose buoyancy drives the formation of a multiphase plume, together with the local velocity of the induced flow in the ambient salt–water. Measurements of the mean axial flow in the plume centreplane follow Gaussian profiles and that of the mean radial flow is consistent with integral plume theory. The turbulence characteristics resemble those measured in a bubble plume, including strong anisotropy in the normal Reynolds stresses. However, we observe structural differences between the two multiphase plumes. First, the skewness of the probability density function of the axial velocity fluctuations is not that which would be predicted by simply reversing the direction of a bubble plume. Second, in contrast to a bubble plume, the particle plume has a non-negligible fluid-shear production term in the turbulent kinetic energy (TKE) budget. Third, the radial decay of all measured terms in the TKE budget is slower than those in a bubble plume. Despite these dissimilarities, a bigger picture emerges that applies to both flows. The TKE production by particles (or bubbles) roughly balances the viscous dissipation, except near the plume centreline. The one-dimensional power spectra of the velocity fluctuations show a $-3$ power law that puts both the particle and bubble plume in a category different from single-phase shear-flow turbulence.
Mapping spheroid rotation modes in turbulent channel flow: effects of shear, turbulence and particle inertia
- Lihao Zhao, Niranjan R. Challabotla, Helge I. Andersson, Evan A. Variano
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- Journal:
- Journal of Fluid Mechanics / Volume 876 / 10 October 2019
- Published online by Cambridge University Press:
- 31 July 2019, pp. 19-54
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The rotational behaviour of non-spherical particles in turbulent channel flow is studied by Lagrangian tracking of spheroidal point particles in a directly simulated flow. The focus is on the complex rotation modes of the spheroidal particles, in which the back reaction on the flow field is ignored. This study is a sequel to the letter by Zhao et al. (Phys. Rev. Lett., vol. 115, 2015, 244501), in which only selected results in the near-wall buffer region and the almost-isotropic channel centre were presented. Now, particle dynamics all across the channel is explored to provide a complete picture of the orientational and rotational behaviour with consideration of the effects of particle aspect ratio ranging from 0.1 to 10 and particle Stokes number from 0 (inertialess) to 30. The rotational dynamics in the innermost part of the logarithmic wall layer is particularly complex and affected not only by modest mean shear, but also by particle inertia and turbulent vorticity. While inertial disks exhibit modest preferential orientation in either the wall-normal or cross-stream direction, inertial rods show neither preferential tumbling nor spinning. Examination of the co-variances between particle orientation, particle rotation and fluid rotation vectors explains the qualitatively different ‘wall mode’ rotation and ‘centre mode’ rotation. Inertialess spheroids transition between the two modes within a narrow zone ($15<z^{+}<35$) in the buffer region. If the spheroids have inertia, the transition zone between the two modes shifts to the inner part of the logarithmic layer, i.e. $z^{+}\geqslant 40$. We ascribe the transition of inertialess spheroids from the ‘wall mode’ to the ‘centre mode’ rotation to the changeover between the time scales associated with mean shear and small-scale turbulence. Inertial spheroids, however, transition between the two rotational modes when the Kolmogorov time scale becomes comparable to the time scale for particle rotation, i.e. the effective Stokes number is of order unity. The aforementioned findings reveal, in addition to the effects of particle shape and alignment, the importance of the characteristic local time scale of fluid flow for the rotation of both tracer and inertial spheroids in turbulent channel flows.
Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence
- Nimish Pujara, Greg A. Voth, Evan A. Variano
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- Journal:
- Journal of Fluid Mechanics / Volume 860 / 10 February 2019
- Published online by Cambridge University Press:
- 07 December 2018, pp. 465-486
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We examine the dynamics of slender, rigid rods in direct numerical simulation of isotropic turbulence. The focus is on the statistics of three quantities and how they vary as rod length increases from the dissipation range to the inertial range. These quantities are (i) the steady-state rod alignment with respect to the perceived velocity gradients in the surrounding flow, (ii) the rate of rod reorientation (tumbling) and (iii) the rate at which the rod end points move apart (stretching). Under the approximations of slender-body theory, the rod inertia is neglected and rods are modelled as passive particles in the flow that do not affect the fluid velocity field. We find that the average rod alignment changes qualitatively as rod length increases from the dissipation range to the inertial range. While rods in the dissipation range align most strongly with fluid vorticity, rods in the inertial range align most strongly with the most extensional eigenvector of the perceived strain-rate tensor. For rods in the inertial range, we find that the variance of rod stretching and the variance of rod tumbling both scale as $l^{-4/3}$, where $l$ is the rod length. However, when rod dynamics are compared to two-point fluid velocity statistics (structure functions), we see non-monotonic behaviour in the variance of rod tumbling due to the influence of small-scale fluid motions. Additionally, we find that the skewness of rod stretching does not show scale invariance in the inertial range, in contrast to the skewness of longitudinal fluid velocity increments as predicted by Kolmogorov’s $4/5$ law. Finally, we examine the power-law scaling exponents of higher-order moments of rod tumbling and rod stretching for rods with lengths in the inertial range and find that they show anomalous scaling. We compare these scaling exponents to predictions from Kolmogorov’s refined similarity hypotheses.
Rotations of small, inertialess triaxial ellipsoids in isotropic turbulence
- Nimish Pujara, Evan A. Variano
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- Journal:
- Journal of Fluid Mechanics / Volume 821 / 25 June 2017
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- 25 May 2017, pp. 517-538
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The statistics of rotational motion of small, inertialess triaxial ellipsoids are computed along Lagrangian trajectories extracted from direct numerical simulations of homogeneous isotropic turbulence. The total particle angular velocity and its components along the three principal axes of the particle are considered, expanding on the results of Chevillard & Meneveau (J. Fluid Mech., vol. 737, 2013, pp. 571–596) who showed results of the rotation rate of the particle’s principal axes. The variance of the particle angular velocity, referred to as the particle enstrophy, is found to increase as particles become elongated, regardless of whether they are axisymmetric. This trend is explained by considering the contributions of vorticity and strain rate to particle rotation. It is found that the majority of particle enstrophy is due to fluid vorticity. Strain-rate-induced rotations, which are sensitive to shape, are mostly cancelled by strain–vorticity interactions. The remainder of the strain-rate-induced rotations are responsible for weak variations in particle enstrophy. For particles of all shapes, the majority of the enstrophy is in rotations about the longest axis, which is due to alignment between the longest axis and fluid vorticity. The integral time scale for particle angular velocities about different axes reveals that rotations are most persistent about the longest axis, but that a full revolution is rare.
Rotational kinematics of large cylindrical particles in turbulence
- Ankur D. Bordoloi, Evan Variano
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- Journal:
- Journal of Fluid Mechanics / Volume 815 / 25 March 2017
- Published online by Cambridge University Press:
- 20 February 2017, pp. 199-222
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The rotational kinematics of inertial cylinders in homogeneous isotropic turbulence is investigated via laboratory experiments. The effects of particle size and shape on rotation statistics are measured for near-neutrally buoyant particles whose sizes are within the inertial subrange of turbulence. To examine the effects of particle size, three right-circular cylinders (aspect ratio $\unicode[STIX]{x1D706}=1$) are considered, with size $d_{eq}=16\unicode[STIX]{x1D702}$, $27\unicode[STIX]{x1D702}$ and $67\unicode[STIX]{x1D702}$. Here, $d_{eq}$ is the diameter of a sphere whose volume is equal to that of the particle and $\unicode[STIX]{x1D702}$ is the Kolmogorov length scale. Results show that the variance of the particle rotation rate follows a $-4/3$ power-law scaling with respect to $d_{eq}$. To examine the effect of particle shape, two cylinders with identical volumes and different aspect ratios ($\unicode[STIX]{x1D706}=1$ and $\unicode[STIX]{x1D706}=4$) are measured. Their motion also scales with $d_{eq}$ regardless of shape. Simultaneous measurements of orientation and rotation for $\unicode[STIX]{x1D706}=4$ particles allows a decomposition of rotation along the primary axes of each particle. This analysis shows that there is no preference for rotation about a particle’s symmetry axis, unlike the preference displayed by sub-Kolmogorov-scale particles in previous studies.
Turbulent transport of a high-Schmidt-number scalar near an air–water interface
- Evan A. Variano, Edwin A. Cowen
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- Journal:
- Journal of Fluid Mechanics / Volume 731 / 25 September 2013
- Published online by Cambridge University Press:
- 14 August 2013, pp. 259-287
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We measure solute transport near a turbulent air–water interface at which there is zero mean shear. The interface is stirred by high-Reynolds-number homogeneous isotropic turbulence generated far below the surface, and solute transport into the water is driven by an imposed concentration gradient. The air–water interface is held at a constant concentration much higher than that in the bulk of the water by maintaining pure ${\mathrm{CO} }_{2} $ gas above a water tank that has been initially purged of dissolved ${\mathrm{CO} }_{2} $. We measure velocity and concentration fluctuations below the air–water interface, from the viscous sublayer to the middle of the ‘source region’ where the effects of the surface are first felt. Our laboratory measurement technique uses quantitative imaging to collect simultaneous concentration and velocity fields, which are measured at a resolution that reveals the dynamics in the turbulent inertial subrange. Two-point statistics reveal the spatial structure of velocity and concentration fluctuations, and are examined as a function of depth beneath the air–water interface. There is a clear dominance of large scales at all depths for all quantities, but the relative importance of scales changes markedly with proximity to the interface. Quadrant analysis of the turbulent scalar flux shows a four-way balance of flux components far from the interface, which near the interface evolves into a two-way balance between motions that are raising and lowering parcels of low-concentration fluid.
Shape effects on turbulent modulation by large nearly neutrally buoyant particles
- Gabriele Bellani, Margaret L. Byron, Audric G. Collignon, Colin R. Meyer, Evan A. Variano
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- Journal:
- Journal of Fluid Mechanics / Volume 712 / 10 December 2012
- Published online by Cambridge University Press:
- 27 September 2012, pp. 41-60
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We investigate dilute suspensions of Taylor-microscale-sized particles in homogeneous isotropic turbulence. In particular, we focus on the effect of particle shape on particle–fluid interaction. We conduct laboratory experiments using a novel experimental technique to simultaneously measure the kinematics of fluid and particle phases. This uses transparent particles having the same refractive index as water, whose motion we track via embedded optical tracers. We compare the turbulent statistics of a single-phase flow to the turbulent statistics of the fluid phase in a particle–laden suspension. Two suspensions are compared, one in which the particles are spheres and the other in which they are prolate ellipsoids with aspect ratio 2. We find that spherical particles at volume fraction ${\phi }_{v} = 0. 14\hspace{0.167em} \% $ reduce the turbulent kinetic energy (TKE) by 15 % relative to the single-phase flow. At the same volume fraction (and slightly smaller total surface area), ellipsoidal particles have a much smaller effect: they reduce the TKE by 3 % relative to the single-phase flow. Spectral analysis shows the details of TKE reduction and redistribution across spatial scales: spherical particles remove energy from large scales and reinsert it at small scales, while ellipsoids remove relatively less TKE from large scales and reinsert relatively more at small scales. Shape effects are far less evident in the statistics of particle rotation, which are very similar for ellipsoids and spheres. Comparing these with fluid enstrophy statistics, we find that particle rotation is dominated by velocity gradients on scales much larger than the particle characteristic length scales.
A random-jet-stirred turbulence tank
- EVAN A. VARIANO, EDWIN A. COWEN
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- Journal:
- Journal of Fluid Mechanics / Volume 604 / 10 June 2008
- Published online by Cambridge University Press:
- 14 May 2008, pp. 1-32
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We report measurements of the flow above a planar array of synthetic jets, firing upwards in a spatiotemporally random pattern to create turbulence at an air–water interface. The flow generated by this randomly actuated synthetic jet array (RASJA) is turbulent, with a large Reynolds number and a weak secondary (mean) flow. The turbulence is homogeneous over a large region and has similar isotropy characteristics to those of grid turbulence. These properties make the RASJA an ideal facility for studying the behaviour of turbulence at boundaries, which we do by measuring one-point statistics approaching the air–water interface (via particle image velocimetry). We explore the effects of different spatiotemporally random driving patterns, highlighting design conditions relevant to all randomly forced facilities. We find that the number of jets firing at a given instant, and the distribution of the duration for which each jet fires, greatly affect the resulting flow. We identify and study the driving pattern that is optimal given our tank geometry. In this optimal configuration, the flow is statistically highly repeatable and rapidly reaches steady state. With increasing distance from the jets, there is a jet merging region followed by a planar homogeneous region with a power-law decay of turbulent kinetic energy. In this homogeneous region, we find a Reynolds number of 314 based on the Taylor microscale. We measure all components of mean flow velocity to be less than 10% of the turbulent velocity fluctuation magnitude. The tank width includes roughly 10 integral length scales, and because wall effects persist for one to two integral length scales, there is sizable core region in which turbulent flow is unaffected by the walls. We determine the dissipation rate of turbulent kinetic energy via three methods, the most robust using the velocity structure function. Having a precise value of dissipation and low mean flow allows us to measure the empirical constant in an existing model of the Eulerian velocity power spectrum. This model provides a method for determining the dissipation rate from velocity time series recorded at a single point, even when Taylor's frozen turbulence hypothesis does not hold. Because the jet array offers a high degree of flow control, we can quantify the effects of the mean flow in stirred tanks by intentionally forcing a mean flow and varying its strength. We demonstrate this technique with measurements of gas transfer across the free surface, and find a threshold below which mean flow no longer contributes significantly to the gas transfer velocity.