5 results
Experimental investigation of turbulent suspensions of spherical particles in a square duct
- Sagar Zade, Pedro Costa, Walter Fornari, Fredrik Lundell, Luca Brandt
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- Journal:
- Journal of Fluid Mechanics / Volume 857 / 25 December 2018
- Published online by Cambridge University Press:
- 26 October 2018, pp. 748-783
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We report experimental observations of turbulent flow with spherical particles in a square duct. Three particle sizes, namely $2H/d_{p}=40$, 16 and 9 ($2H$ being the duct full height and $d_{p}$ being the particle diameter), are investigated. The particles are nearly neutrally buoyant with a density ratio of 1.0035 and 1.01 with respect to the suspending fluid. Refractive index matched–particle image velocimetry (RIM–PIV) is used for fluid velocity measurement even at the highest particle volume fraction (20 %) and particle tracking velocimetry (PTV) for the particle velocity statistics for the flows seeded with particles of the two largest sizes, whereas only pressure measurements are reported for the smallest particles. Settling effects are seen at the lowest bulk Reynolds number $Re_{2H}\approx$ 10 000, whereas, at the highest $Re_{2H}\approx 27\,000$, particles are in almost full suspension. The friction factor of the suspensions is found to be significantly larger than that of single-phase duct flow at the lower $Re_{2H}$ investigated; however, the difference decreases when increasing the flow rate and the total drag approaches the values of the single-phase flow at the higher Reynolds number considered, $Re_{2H}=27\,000$. The pressure drop is found to decrease with the particle diameter for volume fractions lower than $\unicode[STIX]{x1D719}=10\,\%$ for nearly all $Re_{2H}$ investigated. However, at the highest volume fraction $\unicode[STIX]{x1D719}=20\,\%$, we report a peculiar non-monotonic behaviour: the pressure drop first decreases and then increases with increasing particle size. The decrease of the turbulent drag with particle size at the lowest volume fractions is related to an attenuation of the turbulence. The drag increase for the two largest particle sizes at $\unicode[STIX]{x1D719}=20\,\%$, however, occurs despite this large reduction of the turbulent stresses, and it is therefore due to significant particle-induced stresses. At the lowest Reynolds number, the particles reside mostly in the bottom half of the duct, where the mean velocity significantly decreases; the flow is similar to that in a moving porous bed near the bottom wall and to turbulent duct flow with low particle concentration near the top wall.
Suspensions of finite-size neutrally buoyant spheres in turbulent duct flow
- Walter Fornari, Hamid Tabaei Kazerooni, Jeanette Hussong, Luca Brandt
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- Journal:
- Journal of Fluid Mechanics / Volume 851 / 25 September 2018
- Published online by Cambridge University Press:
- 19 July 2018, pp. 148-186
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We study the turbulent square duct flow of dense suspensions of neutrally buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $\unicode[STIX]{x1D719}=0{-}0.2$, using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of 5600 is considered. We observe that for $\unicode[STIX]{x1D719}=0.05$ and 0.1, particles preferentially accumulate on the corner bisectors, close to the corners, as also observed for laminar square duct flows of the same duct-to-particle size ratio. At the highest volume fraction, particles preferentially accumulate in the core region. For plane channel flows, in the absence of lateral confinement, particles are found instead to be uniformly distributed across the channel. The intensity of the cross-stream secondary flows increases (with respect to the unladen case) with the volume fraction up to $\unicode[STIX]{x1D719}=0.1$, as a consequence of the high concentration of particles along the corner bisector. For $\unicode[STIX]{x1D719}=0.2$ the turbulence activity is reduced and the intensity of the secondary flows reduces to below that of the unladen case. The friction Reynolds number increases with $\unicode[STIX]{x1D719}$ in dilute conditions, as observed for channel flows. However, for $\unicode[STIX]{x1D719}=0.2$ the mean friction Reynolds number is similar to that for $\unicode[STIX]{x1D719}=0.1$. By performing the turbulent kinetic energy budget, we see that the turbulence production is enhanced up to $\unicode[STIX]{x1D719}=0.1$, while for $\unicode[STIX]{x1D719}=0.2$ the production decreases below the values for $\unicode[STIX]{x1D719}=0.05$. On the other hand, the dissipation and the transport monotonically increase with $\unicode[STIX]{x1D719}$. The interphase interaction term also contributes positively to the turbulent kinetic energy budget and increases monotonically with $\unicode[STIX]{x1D719}$, in a similar way as the mean transport. Finally, we show that particles move on average faster than the fluid. However, there are regions close to the walls and at the corners where they lag behind it. In particular, for $\unicode[STIX]{x1D719}=0.05,0.1$, the slip velocity distribution at the corner bisectors seems correlated to the locations of maximum concentration: the concentration is higher where the slip velocity vanishes. The wall-normal hydrodynamic and collision forces acting on the particles push them away from the corners. The combination of these forces vanishes around the locations of maximum concentration. The total mean forces are generally low along the corner bisectors and at the core, also explaining the concentration distribution for $\unicode[STIX]{x1D719}=0.2$.
Clustering and increased settling speed of oblate particles at finite Reynolds number
- Walter Fornari, Mehdi Niazi Ardekani, Luca Brandt
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- Journal:
- Journal of Fluid Mechanics / Volume 848 / 10 August 2018
- Published online by Cambridge University Press:
- 11 June 2018, pp. 696-721
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We study the settling of rigid oblates in a quiescent fluid using interface-resolved direct numerical simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle–particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio $AR=1/3$ and solid volume fractions $\unicode[STIX]{x1D719}=0.5{-}10\,\%$. The solid-to-fluid density ratio $R=1.02$ and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere with equivalent volume $Ga=60$. With this choice of parameters, an isolated oblate falls vertically with a steady wake with its broad side perpendicular to the gravity direction. At this $Ga$, the mean settling speed of spheres is a decreasing function of the volume $\unicode[STIX]{x1D719}$ and is always smaller than the terminal velocity of the isolated particle, $V_{t}$. On the contrary, in dilute suspensions of oblate particles (with $\unicode[STIX]{x1D719}\leqslant 1\,\%$), the mean settling speed is approximately 33 % larger than $V_{t}$. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity $V_{t}$ between $\unicode[STIX]{x1D719}=5\,\%$ and 10 %. The increase of the mean settling speed is due to the formation of particle clusters that for $\unicode[STIX]{x1D719}=0.5{-}1\,\%$ appear as columnar-like structures. From the pair distribution function we observe that it is most probable to find particle pairs almost vertically aligned. However, the pair distribution function is non-negligible all around the reference particle indicating that there is a substantial amount of clustering at radial distances between 2 and $6c$ (with $c$ the polar radius of the oblate). Above $\unicode[STIX]{x1D719}=5\,\%$, the hindrance becomes the dominant effect, and the mean settling speed decreases below $V_{t}$. As the particle concentration increases, the mean particle orientation changes and the mean pitch angle (the angle between the particle axis of symmetry and gravity) increases from $23^{\circ }$ to $47^{\circ }$. Finally, we increase $Ga$ from 60 to 140 for the case with $\unicode[STIX]{x1D719}=0.5\,\%$ and find that the mean settling speed (normalized by $V_{t}$) decreases by less than 1 % with respect to $Ga=60$. However, the fluctuations of the settling speed around the mean are reduced and the probability of finding vertically aligned particle pairs increases.
Reduced particle settling speed in turbulence
- Walter Fornari, Francesco Picano, Gaetano Sardina, Luca Brandt
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- Journal:
- Journal of Fluid Mechanics / Volume 808 / 10 December 2016
- Published online by Cambridge University Press:
- 27 October 2016, pp. 153-167
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We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, $Ga$. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6 %–60 % with respect to the terminal velocity of an isolated sphere in quiescent fluid as the ratio between the latter and the turbulent velocity fluctuations $u^{\prime }$ is decreased. Analysing the fluid–particle relative motion, we find that the mean settling speed is progressively reduced while reducing $\unicode[STIX]{x1D70C}_{p}/\unicode[STIX]{x1D70C}_{f}$ due to the increase of the vertical drag induced by the particle cross-flow velocity. Unsteady effects contribute to the mean overall drag by about 6 %–10 %. The probability density functions of particle velocities and accelerations reveal that these are closely related to the features of the turbulent flow. The particle mean-square displacement in the settling direction is found to be similar for all $Ga$ if time is scaled by $(2a)/u^{\prime }$ (where $2a$ is the particle diameter and $u^{\prime }$ is the turbulence velocity root mean square).
Sedimentation of finite-size spheres in quiescent and turbulent environments
- Walter Fornari, Francesco Picano, Luca Brandt
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- Journal:
- Journal of Fluid Mechanics / Volume 788 / 10 February 2016
- Published online by Cambridge University Press:
- 12 January 2016, pp. 640-669
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Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behaviour of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform direct numerical simulations of sedimentation in quiescent and turbulent environments using an immersed boundary method to account for the dispersed rigid spherical particles. The solid volume fractions considered are ${\it\phi}=0.5{-}1\,\%$, while the solid to fluid density ratio ${\it\rho}_{p}/{\it\rho}_{f}=1.02$. The particle radius is chosen to be approximately six Kolmogorov length scales. The results show that the mean settling velocity is lower in an already turbulent flow than in a quiescent fluid. The reductions with respect to a single particle in quiescent fluid are approximately 12 % and 14 % for the two volume fractions investigated. The probability density function of the particle velocity is almost Gaussian in a turbulent flow, whereas it displays large positive tails in quiescent fluid. These tails are associated with the intermittent fast sedimentation of particle pairs in drafting–kissing–tumbling motions. The particle lateral dispersion is higher in a turbulent flow, whereas the vertical one is, surprisingly, of comparable magnitude as a consequence of the highly intermittent behaviour observed in the quiescent fluid. Using the concept of mean relative velocity we estimate the mean drag coefficient from empirical formulae and show that non-stationary effects, related to vortex shedding, explain the increased reduction in mean settling velocity in a turbulent environment.