arXiv subjects

Marc Avila

Publications and source records attributed to Marc Avila.

At least 37 records · Page 2Linked to original sources

arXiv2021

Effects of Pore-scale on the Macroscopic Properties of Natural Convection in Porous Media

Natural convection in porous media is a fundamental process for the long-term storage of CO2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy-Oberbeck-Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number (Ra) for high values of Ra (Ra>>1,300). Here, we perform Direct Numerical Simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto- plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies.

physics.flu-dyn↗

arXiv2021

Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flow

Laminar flows through pipes driven at steady, pulsatile or oscillatory rates undergo a sub-critical transition to turbulence. We carry out an extensive linear non-modal stability analysis of these flows and show that for sufficiently high pulsation amplitudes the stream-wise vortices of the classic lift-up mechanism are outperformed by helical disturbances exhibiting an Orr-like mechanism. In oscillatory flow, the energy amplification depends solely on the Reynolds number based on the Stokes-layer thickness and for sufficiently high oscillation frequency and Reynolds number, axisymmetric disturbances dominate. In the high-frequency limit, these axisymmetric disturbances are exactly similar to those recently identified by Biau (2016) for oscillatory flow over a flat plate. In all regimes of pulsatile and oscillatory pipe flow, the optimal helical and axisymmetric disturbances are triggered in the deceleration phase and reach their peaks in typically less than a period. Their maximum energy gain scales exponentially with Reynolds number of the oscillatory flow component. Our numerical computations unveil a plausible mechanism for the turbulence observed experimentally in pulsatile and oscillatory pipe flow.

physics.flu-dyn↗

arXiv2021

Resonances in pulsatile channel flow with an elastic wall

Interactions between fluids and elastic solids are ubiquitous in application ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple model for unsteady flow in elastic vessels. We numerically solve the equations governing the flow and the large-displacement elasticity and show that the system responds as a forced harmonic oscillator with non-conventional damping. We derive an analytical prediction for the amplitude of the oscillatory wall deformation, and thus the conditions under which resonances occur or vanish.

physics.flu-dyn↗

arXiv2020

Nonlinear hydrodynamic instability and turbulence in pulsatile flow

Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress sensitive endothelial cell layer.

physics.flu-dyn↗

arXiv2020

nsCouette -- A high-performance code for direct numerical simulations of turbulent Taylor-Couette flow

We present nsCouette, a highly scalable software tool to solve the Navier-Stokes equations for incompressible fluid flow between differentially heated and independently rotating, concentric cylinders. It is based on a pseudospectral spatial discretization and dynamic time-stepping. It is implemented in modern Fortran with a hybrid MPI-OpenMP parallelization scheme and thus designed to compute turbulent flows at high Reynolds and Rayleigh numbers. An additional GPU implementation (C-CUDA) for intermediate problem sizes and a basic version for turbulent pipe flow (nsPipe) are also provided.

physics.flu-dyn↗

arXiv2019

Inflow boundary conditions determine T-mixer efficiency

We report on a comprehensive experimental-computational study of a simple T-shaped mixer for Reynolds numbers up to $4000$. In the experiments, we determine the mixing time by applying the Villermaux--Dushman characterization to a water-water mixture. In the numerical simulations, we resolve down to the smallest (Kolmogorov) flow scales in space and time. Excellent agreement is obtained between the experimentally measured mixing time and numerically computed intensity of segregation, especially in the turbulent regime, which validates both approaches. We confirm that the mixing time is mainly determined by the specific power input, as assumed in most mixing-models. However, we show that by suitably manipulating the inflow conditions, the power input necessary to achieve a given mixing time can be reduced by a factor of six. Our study enables detailed investigations of the influence of hydrodynamics on chemical reactions and precipitation processes, as well as the detailed testing of turbulence and micromixing models.

physics.flu-dyn↗

arXiv2019

Topology optimization of unsaturated flows in multi-material porous media: application to a simple diaper model

We present a mathematical approach to optimize the material distribution for fluid transport in unsaturated porous media. Our benchmark problem is a simplified diaper model as an exemplary liquid absorber. Our model has up to three materials with vastly different properties, which in the reference configuration are arranged in parallel layers. Here, swelling is neglected and the geometry of a swollen diaper is assumed and treated as a porous medium of high porosity. The imbibition process is then simulated by solving an unsaturated flow problem based on Richards' equation. Our aim is to maximize the amount of absorbed liquid by redistributing the materials. To this end, a density based multi-material topology optimization (based on the well known SIMP model) is performed. A sensitivity analysis for the nonlinear transient problem is provided, which enables the application of first order optimization solvers. We perform two- and three-material optimization and discuss several variants of the problem setting. We present designs with up to 45% more absorbed liquid compared to the reference configuration.

physics.comp-ph↗

arXiv2019

Phase-field simulation of core-annular pipe flow

Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.

physics.flu-dyn↗

arXiv2018

The effect of pulsation frequency on transition in pulsatile pipe flow

Pulsatile flows are common in nature and in applications, but their stability and transition to turbulence are still poorly understood. Even in the simple case of pipe flow subject to harmonic pulsation, there is no consensus among experimental studies on whether pulsation delays or enhances transition. We here report direct numerical simulations of pulsatile pipe flow at low pulsation amplitude A<0.4. We use a spatially localized impulsive disturbance to generate a single turbulent puff and track its dynamics as it travels downstream. The computed relaminarization statistics are in quantitative agreement with the experiments of Xu et al. (J. Fluid Mech., vol. 831, 2017, pp. 418-432) and support the conclusion that increasing the pulsation amplitude and lowering the frequency enhance the stability of the flow. In the high-frequency regime, the behaviour of steady pipe flow is recovered. In addition, we show that when the pipe length does not permit the observation of a full cycle, a reduction of the transition threshold is observed. We obtain an equation quantifying this effect and compare it favourably with the measurements of Stettler & Hussain (J. Fluid Mech., vol. 170, 1986, pp. 169-197). Our results resolve previous discrepancies, which are due to different pipe lengths, perturbation methods and criteria chosen to quantify transition in experiments.

physics.flu-dyn↗

arXiv2017

Dynamo Action in a Quasi-Keplerian Taylor-Couette Flow

We numerically compute the flow of an electrically conducting fluid in a Taylor-Couette geometry where the rotation rates of the inner and outer cylinders satisfy $Ω_o/Ω_i=(r_o/r_i)^{-3/2}$. In this quasi-Keplerian regime a non-magnetic system would be Rayleigh-stable for all Reynolds numbers $Re$, and the resulting purely azimuthal flow incapable of kinematic dynamo action for all magnetic Reynolds numbers $Rm$. For $Re=10^4$ and $Rm=10^5$ we demonstrate the existence of a finite-amplitude dynamo, whereby a suitable initial condition yields mutually sustaining turbulence and magnetic fields, even though neither could exist without the other. This dynamo solution results in significantly increased outward angular momentum transport, with the bulk of the transport being by Maxwell rather than Reynolds stresses.

physics.flu-dyn↗

arXiv2017

Transport properties of the Azimuthal Magnetorotational Instability

The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles $ω\propto r^{q}$. We perform direct numerical simulations of a steep profile close to the Rayleigh line $q \gtrsim -2 $ and a quasi-Keplerian profile $q \approx -3/2$ and cover wide ranges of Reynolds ($Re\le 4\cdot10^4$) and magnetic Prandtl numbers ($0\le Pm \le 1$). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with $Rm_c \approx 50$, and angular momentum transport scales as $\sqrt{Pm} Re^2$ in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by $Rm$. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as $Rm$ increases. For the profile close to the Rayleigh line, the instability shares these properties as long as $Pm\gtrsim0.1$, but exhibits a markedly different character if $Pm\rightarrow 0$, where the onset of instability is governed by the Reynolds number, with $Re_c \approx 1250$, transport is via Reynolds stresses and scales as $Re^2$. At intermediate $Pm=0.01$ we observe a continuous transition from one regime to the other, with a crossover at $Rm=\mathcal{O}(100)$. Our results give a comprehensive picture of angular momentum transport of the MRI with an imposed azimuthal field.

astro-ph.SR↗

arXiv2017

Conditional statistics of supersonic turbulent boundary layer in the intermittent region

The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the traditional Reynolds/Favre decomposition contaminates the Reynolds stresses and thermal statistics. Our conditional statistics provide direct evidence that turbulent flow possesses positive Reynolds shear stress everywhere, whereas non-turbulent flow carries zero Reynolds shear stress. The thermal statistics of turbulent and non-turbulent flows exhibit opposite trends in the intermittent region, and the difference can be traced back to the variation of total temperature resulting from the Prandtl number.

physics.flu-dyn↗

arXiv2017

Hydrodynamic turbulence in quasi-Keplerian rotating flows

We report a direct-numerical-simulation study of Taylor-Couette flow in the quasi-Keplerian regime at shear Reynolds numbers up to $\mathcal{O}(10^5)$. Quasi-Keplerian rotating flow has been investigated for decades as a simplified model system to study the origin of turbulence in accretion disks that is not fully understood. The flow in this study is axially periodic and thus the experimental end-wall effects on the stability of the flow are avoided. Using optimal linear perturbations as initial conditions, our simulations find no sustained turbulence: the strong initial perturbations distort the velocity profile and trigger turbulence that eventually decays.

physics.flu-dyn↗

arXiv2017

Analysis and modeling of localized invariant solutions in pipe flow

Turbulent spots surrounded by laminar flow are a landmark of transitional shear flows, but the dependence of their kinematic properties on spatial structure is poorly understood. We here investigate this dependence in pipe flow for Reynolds numbers between 1500 and 5000. We compute spatially localized relative periodic orbits in long pipes and show that their upstream and downstream fronts decay exponentially towards the laminar profile. This allows to model the fronts by employing the linearized Navier-Stokes equations, and the resulting model yields the spatial decay rate and the front velocity profiles of the periodic orbits as a function of Reynolds number, azimuthal wave number and propagation speed. In addition, when applied to a localized turbulent puff, the model is shown to accurately approximate the spatial decay rate of its upstream and downstream tails. Our study provides insight into the relationship between the kinematics and spatial structure of localized turbulence and more generally into the physics of localization.

physics.flu-dyn↗

arXiv2017

Boundary-layer turbulence in experiments of quasi-Keplerian flows

Most flows in nature and engineering are turbulent because of their large velocities and spatial scales. Laboratory experiments of rotating quasi-Keplerian flows, for which the angular velocity decreases radially but the angular momentum increases, are however laminar at Reynolds numbers exceeding one million. This is in apparent contradiction to direct numerical simulations showing that in these experiments turbulence transition is triggered by the axial boundaries. We here show numerically that as the Reynolds number increases turbulence becomes progressively confined to the boundary layers and the flow in the bulk fully relaminarizes. Our findings support that turbulence is unlikely to occur in isothermal constant density quasi-Keplerian flows.

physics.flu-dyn↗

arXiv2017

Speed and structure of turbulent fronts in pipe flow

Using extensive direct numerical simulations, the dynamics of laminar-turbulent fronts in pipe flow is investigated for Reynolds numbers between $Re=2000$ and $5500$. We here investigate the physical distinction between the fronts of weak and strong slugs both by analysing the turbulent kinetic energy budget and by comparing the downstream front motion to the advection speed of bulk turbulent structures. Our study shows that weak downstream fronts travel slower than turbulent structures in the bulk and correspond to decaying turbulence at the front. At $Re\simeq 2900$ the downstream front speed becomes faster than the advection speed, marking the onset of strong fronts. In contrast to weak fronts, turbulent eddies are generated at strong fronts by feeding on the downstream laminar flow. Our study also suggests that temporal fluctuations of production and dissipation at the downstream laminar-turbulent front drive the dynamical switches between the two types of front observed up to $Re\simeq 3200$.

physics.flu-dyn↗

arXiv2016

Direct numerical simulation of water-ethanol flows in a T-mixer

The efficient mixing of fluids is key in many applications, such as chemical reactions and nanoparticle precipitation. Detailed experimental measurements of the mixing dynamics are however difficult to obtain, and so predictive numerical tools are helpful in designing and optimizing many processes. If two different fluids are considered, the viscosity and density of the mixture depend often nonlinearly on the composition, which makes the modeling of the mixing process particularly challenging. Hence water-water mixtures in simple geometries such as T-mixers have been intensively investigated, but little is known about the dynamics of more complex mixtures, especially in the turbulent regime. We here present a numerical method allowing the accurate simulation of two-fluid mixtures. Using a high-performance implementation of this method we perform direct numerical simulations resolving the spatial and temporal dynamics of water-ethanol flows for Reynolds numbers from 100 to 2000. The flows states encountered during turbulence transition and their mixing properties are discussed in detail and compared to water-water mixtures.

physics.flu-dyn↗

arXiv2016

Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier--Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.

physics.flu-dyn↗