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Roberto Verzicco

Publications and source records attributed to Roberto Verzicco.

At least 73 records · Page 4Linked to original sources
arXiv2020

The effect of Prandtl number on turbulent sheared thermal convection

In turbulent wall sheared thermal convection, there are three different flow regimes, depending on the relative relevance of thermal forcing and wall shear. In this paper we report the results of direct numerical simulations of such sheared Rayleigh-Bénard convection, at fixed Rayleigh number $Ra=10^6$, varying the wall Reynolds number in the range $0 \leq Re_w \leq 4000$ and Prandtl number $0.22 \leq Pr \leq 4.6$, extending our prior work by Blass et al. (2020), where $Pr$ was kept constant at unity and the thermal forcing ($Ra$) varied. We cover a wide span of bulk Richardson numbers $0.014 \leq Ri \leq 100$ and show that the Prandtl number strongly influences the morphology and dynamics of the flow structures. In particular, at fixed $Ra$ and $Re_w$, a high Prandtl number causes stronger momentum transport from the walls and therefore yields a greater impact of the wall shear on the flow structures, resulting in an increased effect of $Re_w$ on the Nusselt number. Furthermore, we analyse the thermal and kinetic boundary layer thicknesses and relate their behaviour to the resulting flow regimes. For the largest shear rates and $Pr$ numbers, we observe the emergence of a Prandtl-von Karman log-layer, signalling the onset of turbulent dynamics in the boundary layer. Finally, our results allow to extend the Grossmann-Lohse theory for heat transport in Rayleigh-Bénard convection to the sheared case, universally describing $Nu(Ra,Pr,Re_w)$.

physics.flu-dyn↗
arXiv2020

A fully Eulerian solver for the simulation of multiphase flows with solid bodies: application to surface gravity waves

In this paper a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier-Stokes equations coupled with the volume of fluid technique for the modeling of the liquid phases with the interface, an immersed body method for the solid bodies and an iterative strong-coupling procedure for the fluid-structure interaction. The flow incompressibility is enforced via the solution of a Poisson equation which, owing to the density jump across the interfaces of the liquid phases, has to resort to the splitting procedure of Dodd & Ferrante [12]. The solver is validated through comparisons against classical test cases for fluid-structure interaction like migration of particles in pressure-driven channel, multiphase flows, water exit of a cylinder and a good agreement is found for all tests. Furthermore, we show the application of the solver to the case of a surface gravity wave propagating over a submerged reversed pendulum and verify that the solver can reproduce the energy exchange between the wave and the pendulum. Finally the three-dimensional spilling breaking of a wave induced by a submerged sphere is considered.

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arXiv2020

Double maxima of angular momentum transport in $η=0.91$ TC turbulence

We use experiments and direct numerical simulations to probe the phase-space of low-curvature Taylor--Couette (TC) flow in the vicinity of the ultimate regime. The cylinder radius ratio is fixed at $η=r_i/r_o=0.91$. Non-dimensional shear drivings (Taylor numbers $\text{Ta}$) in the range $10^7\leq\text{Ta}\leq10^{11}$ are explored for both co- and counter-rotating configurations. In the $\text{Ta}$ range $10^8\leq\text{Ta}\leq10^{10}$, we observe two local maxima of the angular momentum transport as a function of the cylinder rotation ratio, which can be described as either as "co-" and "counter-rotating" due to their location or as "broad" and "narrow" due to their shape. We confirm that the broad peak is accompanied by the strengthening of the large-scale structures, and that the narrow peak appears once the driving (Ta) is strong enough. As first evidenced in numerical simulations by Brauckmann \emph{et al.}~(2016), the broad peak is produced by centrifugal instabilities and that the narrow peak is a consequence of shear instabilities. We describe how the peaks change with $\text{Ta}$ as the flow becomes more turbulent. Close to the transition to the ultimate regime when the boundary layers (BLs) become turbulent, the usual structure of counter-rotating Taylor vortex pairs breaks down and stable unpaired rolls appear locally. We attribute this state to changes in the underlying roll characteristics during the transition to the ultimate regime. Further changes in the flow structure around $\text{Ta}\approx10^{10}$ cause the broad peak to disappear completely and the narrow peak to move. This second transition is caused when the regions inside the BLs which are locally smooth regions disappear and the whole boundary layer becomes active.

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arXiv2020

Flow organization in laterally unconfined Rayleigh-Bénard turbulence

We investigate the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection in a large box of aspect ratio $Γ=32$ for Rayleigh numbers up to $Ra=10^9$ and at a fixed Prandtl number $Pr=1$. A conditional averaging technique allows us to extract statistics of the LSC even though the number and the orientation of the structures vary throughout the domain. We find that various properties of the LSC obtained here, such as the wall-shear stress distribution, the boundary layer thicknesses and the wind Reynolds number, do not differ significantly from results in confined domains ($Γ\approx 1$). This is remarkable given that the size of the structures (as measured by the width of a single convection roll) more than doubles at the highest $Ra$ as the confinement is removed. An extrapolation towards the critical shear Reynolds number of $Re_s^{\textrm{crit}} \approx 420$, at which the boundary layer (BL) typically becomes turbulent, predicts that the transition to the ultimate regime is expected at $Ra_{\textrm{crit}} \approx \mathcal{O}(10^{15})$ in unconfined geometries. This result is in line with the Göttingen experimental observations. Furthermore, we confirm that the local heat transport close to the wall is highest in the plume impacting region, where the thermal BL is thinnest, and lowest in the plume emitting region, where the thermal BL is thickest. This trend, however, weakens with increasing $Ra$.

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arXiv2020

From Rayleigh-Bénard convection to porous-media convection: how porosity affects heat transfer and flow structure

We perform a numerical study of the heat transfer and flow structure of Rayleigh-Bénard (RB) convection in (in most cases regular) porous media, which are comprised of circular, solid obstacles located on a square lattice. This study is focused on the role of porosity $ϕ$ in the flow properties during the transition process from the traditional RB convection with $ϕ=1$ (so no obstacles included) to Darcy-type porous-media convection with $ϕ$ approaching 0. Simulations are carried out in a cell with unity aspect ratio, for the Rayleigh number $Ra$ from $10^5$ to $10^{10}$ and varying porosities $ϕ$, at a fixed Prandtl number $Pr=4.3$, and we restrict ourselves to the two dimensional case. For fixed $Ra$, the Nusselt number $Nu$ is found to vary non-monotonously as a function of $ϕ$; namely, with decreasing $ϕ$, it first increases, before it decreases for $ϕ$ approaching 0. The non-monotonous behaviour of $Nu(ϕ)$ originates from two competing effects of the porous structure on the heat transfer. On the one hand, the flow coherence is enhanced in the porous media, which is beneficial for the heat transfer. On the other hand, the convection is slowed down by the enhanced resistance due to the porous structure, leading to heat transfer reduction. For fixed $ϕ$, depending on $Ra$, two different heat transfer regimes are identified, with different effective power-law behaviours of $Nu$ vs $Ra$, namely, a steep one for low $Ra$ when viscosity dominates, and the standard classical one for large $Ra$. The scaling crossover occurs when the thermal boundary layer thickness and the pore scale are comparable. The influences of the porous structure on the temperature and velocity fluctuations, convective heat flux, and energy dissipation rates are analysed, further demonstrating the competing effects of the porous structure to enhance or reduce the heat transfer.

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arXiv2020

Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?

Recent findings suggest that wall-bounded turbulent flow can take different statistically stationary turbulent states, with different transport properties, even for the very same values of the control parameters. What state the system takes depends on the initial conditions. Here we analyze the multiple states in large-aspect ratio ($Γ$) two-dimensional turbulent Rayleigh--Bénard flow with no-slip plates and horizontally periodic boundary conditions as model system. We determine the number $n$ of convection rolls, their mean aspect ratios $Γ_r = Γ/n$, and the corresponding transport properties of the flow (i.e., the Nusselt number $Nu$), as function of the control parameters Rayleigh ($Ra$) and Prandtl number. The effective scaling exponent $β$ in $Nu \sim Ra^β$ is found to depend on the realized state and thus $Γ_r$, with a larger value for the smaller $Γ_r$. By making use of a generalized Friedrichs inequality, we show that the elliptical instability and viscous damping determine the $Γ_r$-window for the realizable turbulent states. The theoretical results are in excellent agreement with our numerical finding $2/3 \le Γ_r \le 4/3$, where the lower threshold is approached for the larger $Ra$. Finally, we show that the theoretical approach to frame $Γ_r$ also works for free-slip boundary conditions.

physics.flu-dyn↗
arXiv2020

From zonal flow to convection rolls in Rayleigh-Bénard convection with free-slip plates

Rayleigh-Bénard (RB) convection with free-slip plates and horizontally periodic boundary conditions is investigated using direct numerical simulations. Two configurations are considered, one is two-dimension (2D) RB convection and the other one three-dimension (3D) RB convection with a rotating axis parallel to the plate. We explore the parameter range of Rayleigh numbers Ra from $10^7 to $10^9$ and Prandtl numbers $Pr$ from $1$ to $100$. We show that zonal flow, which was observed, for example, by Goluskin \emph{et al}. \emph{J. Fluid. Mech.} 759, 360-385 (2014) for $Γ=2$, is only stable when $Γ$ is smaller than a critical value, which depends on $Ra$ and $Pr$. With increasing $Γ$, we find a second regime in which both zonal flow and different convection roll states can be statistically stable. For even larger $Γ$, in a third regime, only convection roll states are statistically stable and zonal flow is not sustained. For the 3D simulations, we fix $Ra=10^7$ and $Pr=0.71$, and compare the flow for $Γ=8$ and $Γ= 16$. We demonstrate that with increasing aspect ratio $Γ$, zonal flow, which was observed for small $Γ=2π$ by von Hardenberg \emph{et al}. \emph{Phys. Rev. Lett.} 15, 134501 (2015), completely disappears for $Γ=16$. For such large $Γ$ only convection roll states are statistically stable. In between, here for medium aspect ratio $Γ= 8$, the convection roll state and the zonal flow state are both statistically stable. What state is taken depends on the initial conditions, similarly as we found for the 2D case.

physics.flu-dyn↗
arXiv2020

Periodically modulated thermal convection

Many natural and industrial turbulent flows are subjected to time-dependent boundary conditions. Despite being ubiquitous, the influence of temporal modulations (with frequency $f$) on global transport properties has hardly been studied. Here, we perform numerical simulations of Rayleigh-Bénard (RB) convection with time periodic modulation in the temperature boundary condition and report how this modulation can lead to a significant heat flux (Nusselt number $\rm{Nu}$) enhancement. Using the concept of Stokes thermal boundary layer, we can explain the onset frequency of the Nu enhancement and the optimal frequency at which Nu is maximal, and how they depend on the Rayleigh number Ra and Prandtl number $\rm{Pr}$. From this, we construct a phase diagram in the 3D parameter space ($f$, $\rm{Ra}$, $\rm{Pr}$) and identify: (i) a regime where the modulation is too fast to affect $\rm{Nu}$; (ii) a moderate modulation regime, where $\rm{Nu}$ increases with decreasing $f$ and (iii) slow modulation regime, where $\rm{Nu}$ decreases with further decreasing $f$. Our findings provide a framework to study other types of turbulent flows with time-dependent forcing.

physics.flu-dyn↗
arXiv2020

What rotation rate maximizes heat transport in rotating Rayleigh-Bénard convection with Prandtl number larger than one?

The heat transfer and flow structure in rotating Rayleigh-Bénard convection are strongly influenced by the Rayleigh ($Ra$), Prandtl ($Pr$), and Rossby ($Ro$) number. For $Pr\gtrsim 1$ and intermediate rotation rates, the heat transfer is increased compared to the non-rotating case. We find that the regime of increased heat transfer is subdivided into a low and a high $Ra$ number regime. For $Ra\lesssim 5\times10^8$ the heat transfer at a given $Ra$ and $Pr$ is highest at an optimal rotation rate, at which the thickness of the viscous and thermal boundary layer is about equal. From the scaling relations of the thermal and viscous boundary layer thicknesses, we derive that the optimal rotation rate scales as $1/Ro_\mathrm{opt} \approx 0.12 Pr^{1/2}Ra^{1/6}$. In the low $Ra$ regime the heat transfer is similar in a periodic domain and cylindrical cells with different aspect ratios, i.e.\ the ratio of diameter to height. This is consistent with the view that the vertically aligned vortices are the dominant flow structure. For $Ra\gtrsim 5\times10^8$ the above scaling for the optimal rotation rate does not hold anymore. It turns out that in the high $Ra$ regime, the flow structures at the optimal rotation rate are very different than for lower $Ra$. Surprisingly, the heat transfer in the high $Ra$ regime differs significantly for a periodic domain and cylindrical cells with different aspect ratios, which originates from the sidewall boundary layer dynamics and the corresponding secondary circulation.

physics.flu-dyn↗
arXiv2020

Subcritical behaviour in double diffusive convection within the diffusive regime

We conduct two- and three-dimensional simulations for double diffusive convection in the diffusive regime, where the fluid flow is driven by a destabilizing temperature gradient and stabilized by a stably stratified salinity gradient. We study how the heat flux, Reynolds number, and flow structures change with the density ratio $Λ$, which is the ratio of the buoyancy force induced by the salinity gradient to that by the temperature gradient. When $Λ$ increases from zero, the flow first behaves similarly as in pure Rayleigh-Bénard (RB) convection, both with respect to flow structure and to heat transport. The linear stability analysis of Baines & Gill (J. Fluid Mech., vol. 37, 1969, pp. 289-306) had estimated the critical density ratio $Λ_c$, above which the flow becomes stable. However, here we show that by using a large-scale circulation as initial condition (rather than the linear profiles assumed in the linear stability analysis), DDC in the diffusive regime can exhibit subcritical behaviour when $Λ> Λ_c$, i.e., coexistence of states at the same control parameters. Even though the density ratio becomes thousands times that of the critical value $Λ_c$, there is still convection with strongly enhanced heat transfer properties compared to the pure conduction case. We reveal the corresponding flow structures and find an unstably-stratified region sandwiched between two stably-stratified layers. Our results demonstrate the importance of the initial condition for DDC in the diffusive regime, especially in the situation of a large density ratio, which occurs in high-latitude ocean regions.

physics.flu-dyn↗
arXiv2020

Calculation of the mean velocity profile for strongly turbulent Taylor--Couette flow and arbitrary radius ratios

Taylor--Couette (TC) flow is the shear-driven flow between two coaxial independently rotating cylinders. In recent years, high-fidelity simulations and experiments revealed the shape of the streamwise and angular velocity profiles up to very high Reynolds numbers. However, due to curvature effects, so far no theory has been able to correctly describe the turbulent streamwise velocity profile for given radius ratio, as the classical Prandtl--von Kármán logarithmic law for turbulent boundary layers over a flat surface at most fits in a limited spatial region. Here we address this deficiency by applying the idea of a Monin--Obukhov curvature length to turbulent TC flow. This length separates the flow regions where the production of turbulent kinetic energy is governed by pure shear from that where it acts in combination with the curvature of the streamlines. We demonstrate that for all Reynolds numbers and radius ratios, the mean streamwise and angular velocity profiles collapse according to this separation. We then derive the functional form of the velocity profile. Finally, we match the newly derived angular velocity profile with the constant angular momentum profile at the height of the boundary layer, to obtain the dependence of the torque on the Reynolds number, or, in other words, of the generalized Nusselt number (i.e., the dimensionless angular velocity transport) on the Taylor number.

physics.flu-dyn↗
arXiv2020

Diffusive interaction of multiple surface nanobubbles and nanodroplets: shrinkage, growth, and coarsening

Surface nanobubbles are nanoscopic spherical-cap shaped gaseous domains on immersed substrates which are stable, even for days. After the stability of a {\it single} surface nanobubble has been theoretically explained, i.e. contact line pinning and gas oversaturation are required to stabilize them against diffusive dissolution [Lohse and Zhang, Phys.\ Rev.\ E 91, 031003 (R) (2015)], here we focus on the {\it collective} diffusive interaction of {\it multiple} nanobubbles. For that purpose we develop a finite difference scheme for the diffusion equation with the appropriate boundary conditions and with the immersed boundary method used to represent the growing or shrinking bubbles. After validation of the scheme against the exact results of Epstein and Plesset for a bulk bubble [J. Chem. Phys. 18, 1505 (1950)] and of Lohse and Zhang for a surface bubble, the framework of these simulations is used to describe the coarsening process of competitively growing nanobubbles. The coarsening process for such diffusively interacting nanobubbles slows down with advancing time and thus increasing bubble distance. The present results for surface nanobubbles are also applicable for immersed surface nanodroplets, for which better controlled experimental results of the coarsening process exist.

physics.flu-dyn↗
arXiv2019

Convection-dominated dissolution for single and multiple immersed sessile droplets

We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Sh\sim Ra^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct regimes, namely the diffusively- and the convectively-dominated regime, exhibit different flow morphologies: when Ra>=10, a buoyant plume is clearly visible which contrasts sharply to the pure diffusion case at low Ra. For multiple droplet dissolution, the well-known shielding effect comes into play at low Ra so that the dissolution rate is slower as compared to the single droplet case. However, at high Ra, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal Ra at which the enhancement is maximized, because the single plume is narrower at larger Ra, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, that leads to non-trivial phenomena, contrasting the shielding effect.

physics.flu-dyn↗
arXiv2019

Non-universal transport mechanisms in vertical natural convection with dispersed light droplets

We present results on the effect of dispersed droplets in vertical natural convection (VC) using direct numerical simulations based on a two-way fully coupled Euler-Lagrange approach with a liquid phase and a dispersed droplets phase. For increasing thermal driving, characterised by the Rayleigh number, $Ra$, of the two analysed droplet volume fractions, $α= 5\times10^{-3}$ and $α= 2\times 10^{-2}$, we find non-monotonic responses to the overall heat fluxes, characterised by the Nusselt number, $Nu$. The $Nu$ number is larger when the droplets are thermally coupled to the liquid. However, $Nu$ retains the effective scaling exponents that are close to the ${1/4}$-laminar VC scaling, suggesting that the heat transport is still modulated by thermal boundary layers. Local analyses reveal the non-monotonic trends of local heat fluxes and wall-shear stresses: Whilst regions of high heat fluxes are correlated to increased wall-shear stresses, the spatio-temporal distribution and magnitude of the increase is non-universal, implying that the overall heat transport is obscured by competing mechanisms. Most crucially, we find that the transport mechanisms inherently depend on the dominance of droplet driving to thermal driving that can quantified by (i) the bubblance parameter $b$, which measures the ratio of energy produced by the dispersed phase and the energy of the background turbulence, and (ii) $Ra_d/Ra$, where $Ra_d$ is the droplet Rayleigh number, which we introduce in this paper. When $b \lesssim O(10^{-1})$ and $Ra_d/Ra \lesssim O(100)$, the $Nu$ scaling is expected to recover to the VC scaling without droplets, and comparison with $b$ and $Ra_d/Ra$ from our data supports this notion.

physics.flu-dyn↗
arXiv2019

Flow organization and heat transfer in turbulent wall sheared thermal convection

We perform direct numerical simulations of wall sheared Rayleigh-Bénard (RB) convection for Rayleigh numbers up to $Ra=10^8$, Prandtl number unity, and wall shear Reynolds numbers up to $Re_w=10000$. Using the Monin-Obukhov length $L_{MO}$ we identify three different flow states, a buoyancy dominated regime ($L_{MO} \lesssim λ_θ$; with $λ_θ$ the thermal boundary layer thickness), a transitional regime ($0.5H \gtrsim L_{MO} \gtrsim λ_θ$; with $H$ the height of the domain), and a shear dominated regime ($L_{MO} \gtrsim 0.5H$). In the buoyancy dominated regime the flow dynamics are similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed $Ra$ and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. For $L_{MO} \gtrsim 0.5H$ the Nusselt number $Nu$ effectively scales as $Nu \sim Ra^α$, with $α\ll 1/3$ while we find $α\simeq 0.31$ in the buoyancy dominated regime. In the transitional regime the effective scaling exponent is $α> 1/3$, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.

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arXiv2019

Controlling secondary flow in Taylor-Couette turbulence through spanwise-varying roughness

Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. Experimentally, we explore $\text{Ta}=\mathcal{O}(10^{12})$ and $0.61\leq \tilde s \leq 3.74$. For both approaches the radius ratio is fixed at $η=r_i/r_o = 0.716$, with $r_i$ and $r_o$ the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $\tilde{s}$. Both numerically and experimentally, we find a maximum in the angular momentum transport as function of $\tilde s$. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.

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