arXiv subjects

Roberto Verzicco

Publications and source records attributed to Roberto Verzicco.

At least 109 records · Page 6Linked to original sources

arXiv2017

AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters

The AFiD code, an open source solver for the incompressible Navier-Stokes equations ({\color{blue}\burl{http://www.afid.eu}}), has been ported to GPU clusters to tackle large-scale wall-bounded turbulent flow simulations. The GPU porting has been carried out in CUDA Fortran with the extensive use of kernel loop directives (CUF kernels) in order to have a source code as close as possible to the original CPU version; just a few routines have been manually rewritten. A new transpose scheme, which is not limited to the GPU version only and can be generally applied to any CFD code that uses pencil distributed parallelization, has been devised to improve the scaling of the Poisson solver, the main bottleneck of incompressible solvers. The GPU version can reduce the wall clock time by an order of magnitude compared to the CPU version for large meshes. Due to the increased performance and efficient use of memory, the GPU version of AFiD can perform simulations in parameter ranges that are unprecedented in thermally-driven wall-bounded turbulence. To verify the accuracy of the code, turbulent Rayleigh-Bénard convection and plane Couette flow are simulated and the results are in good agreement with the experimental and computational data that published in previous literatures.

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arXiv2017

The near-wall region of highly turbulent Taylor-Couette flow

Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders, have been performed. The study focuses on TC flow with mild curvature (small gap) with a radius ratio of $η=r_i/r_o=0.909$, an aspect ratio of $Γ=L/d=2π/3$, and a stationary outer cylinder. Three inner cylinder Reynolds of $1\cdot10^5$, $2\cdot10^5$ and $3\cdot 10^5$ were simulated, corresponding to frictional Reynolds numbers between $Re_τ\approx 1400$ and $Re_τ\approx 4000$. An additional case with a large gap, $η=0.5$ and driving of $Re=2\cdot10^5$ was also performed. Small-gap TC was found to be dominated by spatially-fixed large-scale structures, known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e. they transport angular velocity through Reynolds stresses. An additional simulation with inner cylinder Reynolds number of $Re=1\cdot10^5$ and fixed outer cylinder with an externally imposed axial flow of comparable strength as the wind of the TRs was also conducted. The axial flow was found to convect the TRs without any weakening effect. For small-gap TC, evidence for the existence of logarithmic velocity fluctuations, and of an overlap layer, in which the velocity fluctuations collapse in outer units, was found. Profiles consistent with a logarithmic dependence were also found for the angular velocity in large-gap TC, albeit in a very reduced range of scales. Finally, the behaviour of both small- and large-gap TC was compared to other canonical flows. Small-gap TC has similar behaviour in the near-wall region to other canonical flows, while large-gap TC displays very different behaviour.

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arXiv2017

Effects of the computational domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder

In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the computational domain ("box") size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes, with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to $η=r_i/r_o=0.909$, and the outer was kept stationary, while the inner rotated at a Reynolds number $Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is also found to play a significant role, as larger boxes allow for azimuthal wave-like patterns in the Taylor rolls to develop, which affects the statistics in the bulk region. For all boxes studied, the spectra does not reach a box independent maximum.

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arXiv2017

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 $Γ= 7$-$8$ (with $Γ= L/(r_o-r_i)$, and $L$ the axial length of the domain) and a simulation with $Γ=14$ 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 $η=r_i/r_o=0.909$, 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 $Re_τ\approx500$, except for the $Γ=14$ simulation where $Re_i=1.5\cdot10^4$ and $Re_τ\approx240$. 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 $λ_z$ were found for $Γ=7$. The effect of $λ_z$ and $n_r$ on the statistics was quantified. The torque and mean flow statistics were found to be independent of both $λ_z$ 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 $λ_z$, while for the small wavelengths they collapse.

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arXiv2017

Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection

In thermal convection, roughness is often used as a means to enhance heat transport, expressed in Nusselt number. Yet there is no consensus on whether the Nusselt vs. Rayleigh number scaling exponent ($\mathrm{Nu} \sim \mathrm{Ra}^β$) increases or remains unchanged. Here we numerically investigate turbulent Rayleigh-Bénard convection over rough plates in two dimensions, up to $\mathrm{Ra}=10^{12}$. Varying the height and wavelength of the roughness elements with over 200 combinations, we reveal the existence of two universal regimes. In the first regime, the local effective scaling exponent can reach up to 1/2. However, this cannot be explained as the attainment of the so-called ultimate regime as suggested in previous studies, because a further increase in $\mathrm{Ra}$ leads to the second regime, in which the scaling saturates back to a value close to the smooth case. Counterintuitively, the transition from the first to the second regime corresponds to the competition between bulk and boundary layer flow: from the bulk-dominated regime back to the classical boundary-layer-controlled regime. Our study clearly demonstrates that the local $1/2$ scaling does not signal the onset of asymptotic ultimate thermal convection.

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arXiv2017

Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A unifying view on turbulent transport enhancement through coherent structure manipulation

Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-Bénard (RB) convection, i.e. buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different {\it stabilizing forces} are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an {\it enhancement} in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organised morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL.

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arXiv2016

Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence

Direct numerical simulations (DNSs) are performed to analyze the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number $Ta=10^{10}$. The dimensionless torque $Nu_ω$ shows an effective scaling of $Nu_ω\propto Ta^{0.42\pm0.01}$, which is steeper than the ultimate regime effective scaling $Nu_ω\propto Ta^{0.38}$ seen for smooth inner and outer walls. It is found that at the inner rough wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough surfaces contribute little to $Nu_ω$. Thus, the log layer close to the rough wall depends on the roughness length scale, rather than on the viscous length scale. We then separate the torque contributed from the smooth inner wall and the rough outer wall. It is found that the smooth wall torque scaling follows $Nu_s \propto Ta_s^{0.38\pm0.01}$, in excellent agreement with the case where both walls are smooth. In contrast, the rough wall torque scaling follows $Nu_r \propto Ta_r^{0.47\pm0.03}$, very close to the pure ultimate regime scaling $Nu_ω\propto Ta^{1/2}$. The energy dissipation rate at the wall of inner rough cylinder decreases significantly as a consequence of the wall shear stress reduction caused by the flow separation at the rough elements. On the other hand, the latter shed vortices in the bulk that are transported towards the outer cylinder and dissipated. Compared to the purely smooth case, the inner wall roughness renders the system more bulk dominated and thus increases the effective scaling exponent.

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arXiv2016

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors.

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arXiv2016

Mixed convection in turbulent channels with unstable stratification

We study turbulent flows in planar channels with unstable thermal stratification, using direct numerical simulations in a wide range of Reynolds and Rayleigh numbers and reaching flow conditions which are representative of asymptotic developed turbulence. The combined effect of forced and free convection produces a peculiar pattern of quasi--streamwise rollers occupying the full channel thickness with aspect--ratio considerably higher than unity; it has been observed that they have an important redistributing effect on temperature and momentum. The mean values and the variances of the flow variables do not appear to follow Prandtl's scaling in the flow regime near free convection, except for the temperature and vertical velocity fluctuations, which are more affected by turbulent plumes. Nevertheless, we find that the Monin--Obukhov theory still yields a useful representation of the main flow features. In particular, the widely used Businger--Dyer relationships provide a convenient way of accounting for the bulk effects of shear and buoyancy, although individual profiles may vary widely from the alleged trends. Significant deviations are found in DNS with respect to the commonly used parametrization of the mean velocity in the light-wind regime, which may have important practical impact in models of atmospheric dynamics. Finally, for modelling purposes, we devise a set of empirical predictive formulas for the heat flux and friction coefficients which can be used with about $10\%$ maximum error in a wide range of flow parameters.

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arXiv2016

Deformation and orientation statistics of neutrally buoyant sub-Kolmogorov ellipsoidal droplets in turbulent Taylor-Couette flow

The influence of the underlying flow topology on the shape and size of sub-Kolmogorov droplets dispersed in a turbulent flow is of considerable interest in many industrial and scientific applications. In this work we study the deformation and orientation statistics of sub-Kolmogorov droplets dispersed into a turbulent Taylor-Couette flow. Along with Direct Numerical Simulations (DNS) of the carrier phase and Lagrangian tracking of the dispersed droplets, we solve a phenomenological equation proposed by Maffettone and Minale (\emph{J. Fluid Mech.} 78, 227-241 (1998)) to track the shape evolution and orientation of approximately $10^5$ ellipsoidal droplets. By varying the capillary number $Ca$ and viscosity ratio $\hat μ$ of the droplets we find that the droplets deform more with increasing capillary number $Ca$ and this effect is more pronounced in the boundary layer regions. This indicates that along with a capillary number effect there is also a strong correlation between spatial position and degree of deformation of the droplet. Regardless of the capillary number $Ca$, the major-axis of the ellipsoids tends to align with the stream-wise direction and the extensional strain rate eigen direction in the boundary layer region while the distribution is highly isotropic in the bulk. When the viscosity ratio between the droplet and the carrier fluid is increased we find that there is no preferential stretched axis which is due to the increased influence of rotation over stretching and relaxation. Droplets in high viscosity ratio systems are thus less deformed and oblate (disk-like) as compared to highly deformed prolate (cigar-like) droplets in low viscosity ratio systems.

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arXiv2016

Turbulent Taylor-Couette flow with stationary inner cylinder

A series of direct numerical simulations of Taylor-Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed, were performed. Three cases, with outer cylinder Reynolds numbers $Re_o$ of $Re_o=5.5\cdot10^4$, $Re_o=1.1\cdot10^5$ and $Re_o=2.2\cdot10^5$ were considered. The radius ratio $η=r_i/r_o$ was fixed to $η=0.909$ to mitigate the effects of curvature. The vertical aspect ratio $Γ$ was fixed to $Γ=2.09$. Being linearly stable, outer cylinder rotation TC flow is known to have very different behavior than pure inner cylinder rotation TC flow. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.

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arXiv2016

Drag reduction in numerical two-phase Taylor-Couette turbulence using an Euler-Lagrange approach

Two-phase turbulent Taylor-Couette (TC) flow is simulated using an Euler-Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using Direct Numerical Simulations (DNS) in an Eulerian framework, while the bubbles are tracked in a Lagrangian manner by modelling the effective drag, lift, added mass and buoyancy force acting on them. Two-way coupling is implemented between the dispersed phase and the carrier phase which allows for momentum exchange among both phases and to study the effect of the dispersed phase on the carrier phase dynamics. The radius ratio of the TC setup is fixed to $η=0.833$, and a maximum inner cylinder Reynolds number of $Re_i=8000$ is reached. We vary the Froude number ($Fr$), which is the ratio of the centripetal to the gravitational acceleration of the dispersed phase and study its effect on the net torque required to drive the TC system. For the two-phase TC system, we observe drag reduction, i.e., the torque required to drive the inner cylinder is less compared to that of the single phase system. The net drag reduction decreases with increasing Reynolds number $Re_i$, which is consistent with previous experimental findings (Murai et al. 2005, 2008). The drag reduction is strongly related to the Froude number: for fixed Reynolds number we observe higher drag reduction when $Fr < 1$ than for with$ Fr > 1$. This buoyancy effect is more prominent in low $Re_i$ systems and decreases with increasing Reynolds number $Re_i$. We trace the drag reduction back to the weakening of the angular momentum carrying Taylor rolls by the rising bubbles.

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arXiv2016

Scaling laws and flow structures of double diffusive convection in the finger regime

Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates, with fluid properties similar to the values of seawater. The DDC flow is driven by an unstable salinity difference and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: The non-dimensional salinity flux $Nu_S$ mainly depends on the salinity Rayleigh number $Ra_S$, which measures the strength of the salinity difference, and exhibits a very weak dependence on the density ratio $Λ$, which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity $Re$ and the non-dimensional heat flux $Nu_T$ are dependent on both $Ra_S$ and $Λ$. However, the rescaled Reynolds number $ReΛ^{α^{\rm eff}_u}$ and the rescaled convective heat flux $(Nu_T-1)Λ^{α^{\rm eff}_T}$ depend only on $Ra_S$. The two exponents are dependent on the fluid properties and are determined from the numerical results. Moreover, the behaviors of $Nu_S$ and $ReΛ^{α^{\rm eff}_u}$ agree with the predictions of the Grossmann-Lohse theory which was originally developed for the Rayleigh-Bénard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by $Λ^{α^{\rm eff}_u/2}$, collapse and obey a similar power-law scaling relation with $Ra_S$. When $Ra_S$ is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat-copper-ion system~(Hage and Tilgner, Phys. Fluids, 22, 076603, 2010).

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arXiv2016

Direct numerical simulation of Taylor-Couette flow with grooved walls: torque scaling and flow structure

We present direct numerical simulations of Taylor-Couette flow with grooved walls at a fixed radius ratio $η=r_i/r_o=0.714$ with inner cylinder Reynolds number up to $Re_i=3.76\times10^4$, corresponding to Taylor number up to $Ta=2.15\times10^9$. The grooves are axisymmetric V-shaped obstacles attached to the wall with a tip angle of $90^\circ$. Results are compared to the smooth wall case in order to investigate the effects of grooves on Taylor-Couette flow. We focus on the effective scaling laws for the torque, flow structures, and boundary layers. It is found that, when the groove height is smaller than the boundary layer thickness, the torque is the same as that of the smooth wall cases. With increasing $Ta$, the boundary layer thickness becomes smaller than the groove height. Plumes are ejected from the tips of the grooves and secondary circulations between the latter are formed. This is associated to a sharp increase of the torque and thus the effective scaling law for the torque vs. $Ta$ becomes much steeper. Further increasing $Ta$ does not result in an additional slope increase. Instead, the effective scaling law saturates to the "ultimate" regime effective exponents seen for smooth walls. It is found that even though after saturation the slope is the same as for the smooth wall case, the absolute value of torque is increased, and the more the larger size of the grooves.

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arXiv2016

Vertically bounded double diffusive convection in the fingering regime: comparing no-slip vs free-slip boundary conditions

Vertically bounded fingering double diffusive convection (DDC) is numerically investigated, focusing on the influences of different velocity boundary conditions, i.e. the no-slip condition which is inevitable in the lab-scale experimental research, and the free-slip condition which is an approximation for the interfaces in many natural environments, such as the oceans. For both boundary conditions the flow is dominated by fingers and the global responses follow the same scaling laws, with enhanced prefactors for the free-slip cases. Therefore, the laboratory experiments with the no-slip boundaries serve as a good model for the finger layers in the ocean. Moreover, in the free-slip case although the tangential shear stress is eliminated at the boundaries, the local dissipation rate in the near-wall region may exceed the value found in the no-slip cases, which is caused by the stronger vertical motions of fingers and sheet structures near the free-slip boundaries. This counter intuitive result might be relevant for properly estimating and modelling the mixing and entrainment phenomena at free-surfaces and interfaces.

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arXiv2016

Geostrophic convective turbulence: The effect of boundary layers

Rayleigh--Bénard (RB) convection, the flow in a fluid layer heated from below and cooled from above, is used to analyze the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotated while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier--Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\cdot10^{10}$, a constant Prandtl number~$Pr=1$, and vary the Ekman number in the range $Ek=1.3\cdot10^{-7}$ to $Ek=2\cdot10^{-6}$ which satisfies both requirements of super-criticality and strong rotation. We focus on the differences between the application of no-slip vs. stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at~$Ek\approx 9\times 10^{-7}$ for~$Ra=1\times 10^{10}$ and at~$Ek\approx 3\times 10^{-7}$ for~$Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in~$Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.

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arXiv2015

From convection rolls to finger convection in double-diffusive turbulence

Double diffusive convection (DDC), which is the buoyancy driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering enviroments. Of great interests are scalers transfer rate and flow structures. Here we systematically investigate DDC flow between two horizontal plates, driven by an unstable salinity gradient and stabilized by a temperature gradient. Counterintuitively, when increasing the stabilizing temperature gradient, the salinity flux first increases, even though the velocity monotonically decreases, before it finally breaks down to the purely diffusive value. The enhanced salinity transport is traced back to a transition in the overall flow pattern, namely from large scale convection rolls to well-organised vertically-oriented salt fingers. We also show and explain that the unifying theory of thermal convection originally developed by Grossmann and Lohse for Rayleigh-Bénard convection can be directly applied to DDC flow for a wide range of control parameters (Lewis number and density ratio), including those which cover the common values relevant for ocean flows.

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arXiv2015

Salinity transfer in bounded double diffusive convection

The double diffusive convection between two parallel plates is numerically studied for a series of parameters. The flow is driven by the salinity difference and stabilized by the thermal field. Our simulations are directly compared to experiments by Hage and Tilgner (\emph{Phys. Fluids} 22, 076603 (2010)) for several sets of parameters and reasonable agreement is found. This in particular holds for the salinity flux and its dependence on the salinity Rayleigh number. Salt fingers are present in all simulations and extend through the entire height. The thermal Rayleigh number seems to have minor influence on salinity flux but affects the Reynolds number and the morphology of the flow. Next to the numerical calculation, we apply the Grossmann-Lohse theory for Rayleigh-Bénard flow to the current problem without introducing any new coefficients. The theory successfully predicts the salinity flux both with respect to the scaling and even with respect to the absolute value for the numerical and experimental results.

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