5 results
Heat transfer in drop-laden turbulence
- Francesca Mangani, Alessio Roccon, Francesco Zonta, Alfredo Soldati
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- Journal:
- Journal of Fluid Mechanics / Volume 978 / 10 January 2024
- Published online by Cambridge University Press:
- 03 January 2024, A12
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Heat transfer by large deformable drops in a turbulent flow is a complex and rich-in-physics system, in which drop deformation, breakage and coalescence influence the transport of heat. We study this problem by coupling direct numerical simulation (DNS) of turbulence with a phase-field method for the interface description. Simulations are run at fixed-shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio: $Pr=1$, $Pr=2$, $Pr=4$ and $Pr=8$. The drop volume fraction is $\varPhi \simeq 5.4\,\%$ for all cases. Drops are initially warmer than the turbulent carrier fluid and release heat at different rates depending on the value of $Pr$, but also on their size and on their own dynamics (topology, breakage, drop–drop interaction). Computing the time behaviour of the drops and carrier fluid average temperatures, we clearly show that an increase of $Pr$ slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behaviour of the drop average temperature is self-similar, and a universal behaviour can be found upon rescaling by $t/Pr^{2/3}$. Accordingly, the heat transfer coefficient $\mathcal {H}$ (respectively its dimensionless counterpart, the Nusselt number $Nu$) scales as $\mathcal {H}\sim Pr^{-2/3}$ (respectively $Nu\sim Pr^{1/3}$) at the beginning of the simulation, and tends to $\mathcal {H}\sim Pr^{-1/2}$ (respectively $Nu\sim Pr^{1/2}$) at later times. These different scalings can be explained via the boundary layer theory and are consistent with previous theoretical/numerical predictions.
Propagation of capillary waves in two-layer oil–water turbulent flow
- Georgios Giamagas, Francesco Zonta, Alessio Roccon, Alfredo Soldati
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- Journal:
- Journal of Fluid Mechanics / Volume 960 / 10 April 2023
- Published online by Cambridge University Press:
- 29 March 2023, A5
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We study the dynamics of capillary waves at the interface of a two-layer stratified turbulent channel flow. We use a combined pseudo-spectral/phase field method to solve for the turbulent flow in the two liquid layers and to track the dynamics of the liquid–liquid interface. The two liquid layers have same thickness and same density, but different viscosity. We vary the viscosity of the upper layer (two different values) to mimic a stratified oil–water flow. This allows us to study the interplay between inertial, viscous and surface tension forces in the absence of gravity. In the present set-up, waves are naturally forced by turbulence over a broad range of scales, from the larger scales, whose size is of order of the system scale, down to the smaller dissipative scales. After an initial transient, we observe the emergence of a stationary capillary wave regime, which we study by means of temporal and spatial spectra. The computed frequency and wavenumber power spectra of wave elevation are in line with previous experimental findings and can be explained in the frame of the weak wave turbulence theory. Finally, we show that the dispersion relation, which gives the frequency ($\omega$) as a function of the wavenumber ($k$), is in good agreement with the well-established theoretical prediction, $\omega (k) \sim k^{3/2}$.
Energy balance in lubricated drag-reduced turbulent channel flow
- Alessio Roccon, Francesco Zonta, Alfredo Soldati
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- Journal:
- Journal of Fluid Mechanics / Volume 911 / 25 March 2021
- Published online by Cambridge University Press:
- 29 January 2021, A37
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We use direct numerical simulation (DNS) to study drag reduction in a lubricated channel, a flow instance in which a thin layer of lubricating fluid is injected in the near-wall region so as to favour the transportation of a primary fluid. In the present configuration, the two fluids have equal density but different viscosity, so that a viscosity ratio $\lambda =\eta _1/\eta _2$ can be defined. To cover a meaningful range of possible situations, we consider five different $\lambda$ in the range $0.25 \le \lambda \le 4$. All DNS are run using the constant power input (CPI) approach, which prescribes that the flow rate is adjusted according to the actual pressure gradient so as to keep constant the power injected into the flow. The CPI approach has been purposely extended here for the first time to the case of multiphase flows. A phase-field method is used to describe the dynamics of the liquid–liquid interface. We unambiguously show that a significant drag reduction (DR) can be achieved for $\lambda \le 2.00$. Reportedly, the observed DR is a non-monotonic function of $\lambda$ and, in the present case, is maximum for $\lambda = 1.00$ (${\simeq }13\,\%$ flow-rate increase). Upon a detailed analysis of the energy budgets, we are able to show the existence of two different DR mechanisms. For $\lambda =1.00$ and $\lambda =2.00$, DR is purely due to the effect of the surface tension – a localized elasticity element that separates the two fluids – which, decoupling the wall-normal momentum transfer mechanisms between the primary and the lubricating layer, suppresses turbulence in the lubricating layer (laminarization) and reduces the overall drag. For $\lambda < 1.00$, turbulence can be sustained in the lubricating layer, because of the increased local Reynolds number. In this case, DR is simply due to the smaller viscosity of the lubricating layer that acts to decrease directly the corresponding wall friction. Finally, we show evidence that an upper bound for $\lambda$ exists, for which DR cannot be observed: for $\lambda =4.00$, we report a slight drag enhancement, thereby indicating that the turbulence suppression observed in the lubricating layer cannot completely balance the increased friction due to the larger viscosity.
Breakage, coalescence and size distribution of surfactant-laden droplets in turbulent flow
- Giovanni Soligo, Alessio Roccon, Alfredo Soldati
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- Journal:
- Journal of Fluid Mechanics / Volume 881 / 25 December 2019
- Published online by Cambridge University Press:
- 24 October 2019, pp. 244-282
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In this work, we compute numerically breakage/coalescence rates and size distribution of surfactant-laden droplets in turbulent flow. We use direct numerical simulation of turbulence coupled with a two-order-parameter phase-field method to describe droplets and surfactant dynamics. We consider two different values of the surface tension (i.e. two values for the Weber number, $We$, the ratio between inertial and surface tension forces) and four types of surfactant (i.e. four values of the elasticity number, $\unicode[STIX]{x1D6FD}_{s}$, which defines the strength of the surfactant). Stretching, breakage and merging of droplet interfaces are controlled by the complex interplay among shear stresses, surface tension and surfactant distribution, which are deeply intertwined. Shear stresses deform the interface, changing the local curvature and thus surface tension forces, but also advect surfactant over the interface. In turn, local increases of surfactant concentration reduce surface tension, changing the interface deformability and producing tangential (Marangoni) stresses. Finally, the interface feeds back to the local shear stresses via the capillary stresses, and changes the local surfactant distribution as it deforms, breaks and merges. We find that Marangoni stresses have a major role in restoring a uniform surfactant distribution over the interface, contrasting, in particular, the action of shear stresses: this restoring effect is proportional to the elasticity number and is stronger for smaller droplets. We also find that lower surface tension (higher $We$ or higher $\unicode[STIX]{x1D6FD}_{s}$) increases the number of breakage events, as expected, but also the number of coalescence events, more unexpected. The increase of the number of coalescence events can be traced back to two main factors: the higher probability of inter-droplet collisions, favoured by the larger number of available droplets, and the decreased deformability of smaller droplets. Finally, we show that, for all investigated cases, the steady-state droplet size distribution is in good agreement with the $-10/3$ power-law scaling (Garrett et al., J. Phys. Oceanogr., vol. 30 (9), 2000, pp. 2163–2171), conforming to previous experimental observations (Deane & Stokes, Nature, vol. 418 (6900), 2002, p. 839) and numerical simulations (Skartlien et al., J. Chem. Phys., vol. 139 (17), 2013).
Turbulent drag reduction by compliant lubricating layer
- Alessio Roccon, Francesco Zonta, Alfredo Soldati
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- Journal:
- Journal of Fluid Mechanics / Volume 863 / 25 March 2019
- Published online by Cambridge University Press:
- 24 January 2019, R1
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We propose a physically sound explanation for the drag reduction mechanism in a lubricated channel, a flow configuration in which an interface separates a thin layer of less-viscous fluid (viscosity $\unicode[STIX]{x1D702}_{1}$) from a main layer of a more-viscous fluid (viscosity $\unicode[STIX]{x1D702}_{2}$). To single out the effect of surface tension, we focus initially on two fluids having the same density and the same viscosity ($\unicode[STIX]{x1D706}=\unicode[STIX]{x1D702}_{1}/\unicode[STIX]{x1D702}_{2}=1$), and we lower the viscosity of the lubricating layer down to $\unicode[STIX]{x1D706}=\unicode[STIX]{x1D702}_{1}/\unicode[STIX]{x1D702}_{2}=0.25$, which corresponds to a physically realizable experimental set-up consisting of light oil and water. A database comprising original direct numerical simulations of two-phase flow channel turbulence is used to study the physical mechanisms driving drag reduction, which we report between 20 and 30 percent. The maximum drag reduction occurs when the two fluids have the same viscosity ($\unicode[STIX]{x1D706}=1$), and corresponds to the relaminarization of the lubricating layer. Decreasing the viscosity of the lubricating layer ($\unicode[STIX]{x1D706}<1$) induces a marginally decreased drag reduction, but also helps sustaining strong turbulence in the lubricating layer. This led us to infer two different mechanisms for the two drag-reduced systems, each of which is ultimately controlled by the outcome of the competition between viscous, inertial and surface tension forces.