211 research outputs found

### Two-Scalar Turbulent Rayleigh-Benard Convection: Numerical Simulations and Unifying Theory

We conduct direct numerical simulations for turbulent Rayleigh-B\'{e}nard
(RB) convection, driven simultaneously by two scalar components (say,
temperature and salt concentration) with different molecular diffusivities, and
measure the respective fluxes and the Reynolds number. To account for the
results, we generalize the Grossmann-Lohse theory for traditional RB
convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett.,
86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar
turbulent convection. Our numerical results suggest that the generalized theory
can successfully predict the overall trends for the fluxes of two scalars and
the Reynolds number. In fact, for most of the parameters explored here, the
theory can even predict the absolute values of the fluxes and the Reynolds
number with good accuracy. The current study extends the generality of the
Grossmann-Lohse theory in the area of the buoyancy-driven convection flows.Comment: 13 pages, 3 figures, and 1 tabl

### Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence

Small droplets in turbulent flows can undergo highly variable deformations
and orientational dynamics. For neutrally buoyant droplets smaller than the
Kolmogorov scale, the dominant effects from the surrounding turbulent flow
arise through Lagrangian time histories of the velocity gradient tensor. Here
we study the evolution of representative droplets using a model that includes
rotation and stretching effects from the surrounding fluid, and restoration
effects from surface tension including a constant droplet volume constraint,
while assuming that the droplets maintain an ellipsoidal shape. The model is
combined with Lagrangian time histories of the velocity gradient tensor
extracted from DNS of turbulence to obtain simulated droplet evolutions. These
are used to characterize the size, shape and orientation statistics of small
droplets in turbulence. A critical capillary number, $Ca_c$ is identified
associated with unbounded growth of one or two of the droplet's semi-axes.
Exploiting analogies with dynamics of polymers in turbulence, the $Ca_c$ number
can be predicted based on the large deviation theory for the largest Finite
Time Lyapunov exponent. Also, for sub-critical $Ca$ the theory enables
predictions of the slope of the power-law tails of droplet size distributions
in turbulence. For cases when the viscosities of droplet and outer fluid differ
in a way that enables vorticity to decorrelate the shape from the straining
directions, the large deviation formalism based on the stretching properties of
the velocity gradient tensor loses validity and its predictions fail. Even
considering the limitations of the assumed ellipsoidal droplet shape, the
results highlight the complex coupling between droplet deformation, orientation
and the local fluid velocity gradient tensor to be expected when small viscous
drops interact with turbulent flows

### Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

The phenomenon of drag reduction induced by injection of bubbles into a
turbulent carrier fluid has been known for a long time; the governing control
parameters and underlying physics is however not well understood. In this
paper, we use three dimensional numerical simulations to uncover the effect of
deformability of bubbles injected in a turbulent Taylor-Couette flow on the
overall drag experienced by the system. We consider two different Reynolds
numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$;
the deformability of the bubbles is controlled through the Weber number which
is varied in the range $We=0.01 - 2.0$. Our numerical simulations show that
increasing the deformability of bubbles i.e., $We$ leads to an increase in drag
reduction. We look at the different physical effects contributing to drag
reduction and analyse their individual contributions with increasing bubble
deformability. Profiles of local angular velocity flux show that in the
presence of bubbles, turbulence is enhanced near the inner cylinder while
attenuated in the bulk and near the outer cylinder. We connect the increase in
drag reduction to the decrease in dissipation in the wake of highly deformed
bubbles near the inner cylinder

### Deformable ellipsoidal bubbles in Taylor-Couette flow with enhanced Euler-Lagrange tracking

In this work we present numerical simulations of $10^5$ sub-Kolmogorov
deformable bubbles dispersed in Taylor-Couette flow (a wall-bounded shear
system) with rotating inner cylinder and outer cylinder at rest. We study the
effect of deformability of the bubbles on the overall drag induced by the
carrier fluid in the two-phase system. We find that an increase in
deformability of the bubbles results in enhanced drag reduction due to a more
pronounced accumulation of the deformed bubbles near the driving inner wall.
This preferential accumulation is induced by an increase in the resistance on
the motion of the bubbles in the wall-normal direction. The increased
resistance is linked to the strong deformation of the bubbles near the wall
which makes them prolate (stretched along one axes) and orient along the
stream-wise direction. A larger concentration of the bubbles near the driving
wall implies that they are more effective in weakening the plume ejections
which results in stronger drag reduction effects. These simulations which are
practically impossible with fully resolved techniques are made possible by
coupling a sub-grid deformation model with two-way coupled Euler-Lagrangian
tracking of sub-Kolmogorov bubbles dispersed in a turbulent flow field which is
solved through direct numerical simulations. The bubbles are considered to be
ellipsoidal in shape and their deformation is governed by an evolution equation
which depends on the local flow conditions and their surface tension

### The effect of roll number on the statistics of turbulent Taylor-Couette flow

A series of direct numerical simulations in large computational domains has
been performed in order to probe the spatial feature robustness of the Taylor
rolls in turbulent Taylor-Couette (TC) flow. The latter is the flow between two
coaxial independently rotating cylinders of radius $r_i$ and $r_o$,
respectively. Large axial aspect ratios $\Gamma = 7$-$8$ (with $\Gamma =
L/(r_o-r_i)$, and $L$ the axial length of the domain) and a simulation with
$\Gamma=14$ were used in order to allow the system to select the most unstable
wavenumber and to possibly develop multiple states. The radius ratio was taken
as $\eta=r_i/r_o=0.909$, the inner cylinder Reynolds number was fixed to
$Re_i=3.4\cdot10^4$, and the outer cylinder was kept stationary, resulting in a
frictional Reynolds number of $Re_\tau\approx500$, except for the $\Gamma=14$
simulation where $Re_i=1.5\cdot10^4$ and $Re_\tau\approx240$. The large-scale
rolls were found to remain axially pinned for all simulations. Depending on the
initial conditions, stable solutions with different number of rolls $n_r$ and
roll wavelength $\lambda_z$ were found for $\Gamma=7$. The effect of
$\lambda_z$ and $n_r$ on the statistics was quantified. The torque and mean
flow statistics were found to be independent of both $\lambda_z$ and $n_r$,
while the velocity fluctuations and energy spectra showed some box-size
dependence. Finally, the axial velocity spectra was found to have a very sharp
drop off for wavelengths larger than $\lambda_z$, while for the small
wavelengths they collapse

### Turbulence decay towards the linearly-stable regime of Taylor-Couette flow

Taylor-Couette (TC) flow is used to probe the hydrodynamical stability of
astrophysical accretion disks. Experimental data on the subcritical stability
of TC are in conflict about the existence of turbulence (cf. Ji et al. Nature,
444, 343-346 (2006) and Paoletti et al., A$\&$A, 547, A64 (2012)), with
discrepancies attributed to end-plate effects. In this paper we numerically
simulate TC flow with axially periodic boundary conditions to explore the
existence of sub-critical transitions to turbulence when no end-plates are
present. We start the simulations with a fully turbulent state in the unstable
regime and enter the linearly stable regime by suddenly starting a
(stabilizing) outer cylinder rotation. The shear Reynolds number of the
turbulent initial state is up to $Re_s \sim10^5$ and the radius ratio is
$\eta=0.714$. The stabilization causes the system to behave as a damped
oscillator and correspondingly the turbulence decays. The evolution of the
torque and turbulent kinetic energy is analysed and the periodicity and damping
of the oscillations are quantified and explained as a function of shear
Reynolds number. Though the initially turbulent flow state decays,
surprisingly, the system is found to absorb energy during this decay.Comment: Preprint submitted to PRL, 12 pages, 5 figure

### Radial boundary layer structure and Nusselt number in Rayleigh-Benard convection

Results from direct numerical simulations for three dimensional
Rayleigh-Benard convection in a cylindrical cell of aspect ratio 1/2 and Pr=0.7
are presented. They span five decades of Ra from $2\times 10^6$ to $2
\times10^{11}$. Good numerical resolution with grid spacing $\sim$ Kolmogorov
scale turns out to be crucial to accurately calculate the Nusselt number, which
is in good agreement with the experimental data by Niemela et al., Nature, 404,
837 (2000). In underresolved simulations the hot (cold) plumes travel further
from the bottom (top) plate than in the fully resolved case, because the
thermal dissipation close to the sidewall (where the grid cells are largest) is
insufficient. We compared the fully resolved thermal boundary layer profile
with the Prandtl-Blasius profile. We find that the boundary layer profile is
closer to the Prandtl Blasius profile at the cylinder axis than close to the
sidewall, due to rising plumes in that region.Comment: 10 pages, 6 figure

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