Numerical simulations of rotating Rayleigh-Bénard convection

The Rayleigh-Bénard (RB) system is relevant to astro- and geophysical phenomena, including convection in the ocean, the Earth’s outer core, and the outer layer of the Sun. The dimensionless heat transfer (the Nusselt number Nu) in the system depends on the Rayleigh number Ra=ßg¿L 3/(¿¿) and the Prandtl number Pr=¿/¿. Here, ß is the thermal expansion coefficient, g the gravitational acceleration, ¿ the temperature difference between the bottom and top, and ¿ and ¿ the kinematic viscosity and the thermal diffusivity, respectively. The rotation rate H is used in the form of the Rossby number Ro=(ßg¿/L)/(2H). The key question is: How does the heat transfer depend on rotation and the other two control parameters: Nu(Ra, Pr, Ro)? Here we will answer this question by giving a summary of our result

Efficient point-based simulation of four-way coupled particles in turbulence at high number density

In many natural and industrial applications, turbulent flows encompass some form of dispersed particles. Although this type of multiphase turbulent flow is omnipresent, its numerical modeling has proven to be a remarkably challenging problem. Models that fully resolve the particle phase are computationally very expensive, strongly limiting the number of particles that can be considered in practice. This warrants the need for efficient reduced order modeling of the complex system of particles in turbulence that can handle high number densities of particles. Here, we present an efficient method for point-based simulation of particles in turbulence that are four-way coupled. In contrast with traditional one-way coupled simulations, where only the effect of the fluid phase on the particle phase is modeled, this method additionally captures the back-reaction of the particle phase on the fluid phase, as well as the interactions between particles themselves. We focus on the most challenging case of very light particles or bubbles, which show strong clustering in the high-vorticity regions of the fluid. This strong clustering poses numerical difficulties which are systematically treated in our work. Our method is valid in the limit of small particles with respect to the Kolmogorov scales of the flow and is able to handle very large number densities of particles. This methods paves the way for comprehensive studies of the collective effect of small particles in fluid turbulence for a multitude of applications

Geometrical statistics of the vorticity vector and the strain rate tensor in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from experiments in electromagnetically forced rotating turbulence. A range of rotation rates $\Omega$ is considered, from non-rotating to rapidly rotating turbulence with a maximum background rotation rate of $\Omega=5$ rad/s (with Rossby number much smaller than unity). Typically, in our experiments ${\rm{Re}}_{\lambda}\approx 100$. The measurement volume is located in the centre of the fluid container above the bottom boundary layer, where the turbulent flow can be considered locally statistically isotropic and horizontally homogeneous for the non-rotating case, see van Bokhoven et al., Phys. Fluids 21, 096601 (2009). Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. The experimental results show how the turbulence evolves from almost isotropic 3D turbulence ($\Omega\lesssim 0.2$ rad/s) to quasi-2D turbulence ($\Omega\approx 5.0$ rad/s) and how this is reflected by several statistical quantities. In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term.Comment: 17 pages, 6 figures, 3 table

Quasi-2D turbulence in shallow fluid layers

Flows in thin fluid layers, like in the Earth’s atmosphere or oceans, tend to behave as quasi-two-dimensional flows. Their dynamics is strikingly different from three-dimensional flows, and main features of the flow dynamics can be understood by considering two-dimensional (2D) fluid flows. Inviscid 2D flows are governed by conservation of vorticity due to absence of vortex stretching and tilting. Together with conservation of kinetic energy this results in the famous inverse energy cascade and the emergence and persistence of large-scale vortices. This also occurs in shallow fluid-layer flows even if they are neither purely inviscid nor perfectly two-dimensional. Basic phenomena for understanding the dynamics of 2D flows will be discussed and 2D flows on bounded domains, mainly dealing with the large-scale phenomenology of the flow, will be addressed: the self-organization of 2D turbulence in confined domains and the interaction of coherent structures with domain walls. This will be complemented with some observations from recent experiments on quasi-2D turbulence in shallow-fluid layers including the role and impact of bottom friction and out-of-plane motion on the flow evolution

Transport phenomena in rotating turbulence

The role of rotation on turbulence and some of its transport properties will be reviewed with emphasis on two specific cases: statistically steady or decaying rotating turbulence and rotating thermally driven turbulence. For this purpose we briefly address a few basic concepts relevant for understanding processes in rotating (turbulent) flows such as the emergence of coherent structures, the Taylor-Proudman theorem, quasi-two-dimensional turbulence, inertial waves and Ekman boundary layers. The effect of rotation on turbulence will subsequently be illustrated with two sets of laboratory experiments: one with steadily forced rotating turbulence and another with rotating turbulent convection

Preface

The book presents a state-of-the-art overview of current developments in the field in a way accessible to attendees coming from a variety of fields. Relevant examples are turbulence research, (environmental) fluid mechanics, lake hydrodynamics and atmospheric physics. Topics discussed range from the fundamentals of rotating and stratified flows, mixing and transport in stratified or rotating turbulence, transport in the atmospheric boundary layer, the dynamics of gravity and turbidity currents eventually with effects of background rotation or stratification, mixing in (stratified) lakes, and the Lagrangian approach in the analysis of transport processes in geophysical and environmental flows. The topics are discussed from fundamental, experimental and numerical points of view. Some contributions cover fundamental aspects including a number of the basic dynamical properties of rotating and or stratified (turbulent) flows, the mathematical description of these flows, some applications in the natural environment, and the Lagrangian statistical analysis of turbulent transport processes and turbulent transport of material particles (including, for example, inertial and finite-size effects). Four papers are dedicated to specific topics such as transport in (stratified) lakes, transport and mixing in the atmospheric boundary layer, mixing in stratified fluids and dynamics of turbidity currents. The book is addressed to doctoral students and postdoctoral researchers, but also to academic and industrial researchers and practicing engineers, with a background in mechanical engineering, applied physics, civil engineering, applied mathematics, meteorology, physical oceanography or physical limnology

Lattice Boltzmann method investigation of a reactive electro-kinetic flow in porous media: towards a phenomenological model

A model based on the Lattice Boltzmann method is developed to study the flow of reactive electro-kinetic fluids in porous media. The momentum, concentration and electric/potential fields are simulated via the Navier–Stokes, advection–diffusion/Nernst–Planck and Poisson equations, respectively. With this model, the total density and velocity fields, the concentration of reactants and reaction products, including neutral and ionized species, the electric potential and the interaction forces between the fields can be studied, and thus we provide an insight into the interplay between chemistry, flow and the geometry of the porous medium. The results show that the conversion efficiency of the reaction can be strongly influenced by the fluid velocity, reactant concentration and by porosity of the porous medium. The fluid velocity determines how long the reactants stay in the reaction areas, the reactant concentration controls the amount of the reaction material and with different dielectric constant, the porous medium can distort the electric field differently. All these factors make the reaction conversion efficiency display a non-trivial and non-monotonic behaviour as a function of the flow and reaction parameters. To better illustrate the dependence of the reaction conversion efficiency on the control parameters, based on the input from a number of numerical investigations, we developed a phenomenological model of the reactor. This model is capable of capturing the main features of the causal relationship between the performance of the reactor and the main test parameters. Using this model, one could optimize the choice of reaction and flow parameters in order to improve the performance of the reactor and achieve higher production rates

A study with the lattice Boltzmann method on the conversion efficiency of a packed-bed reactor with different oriented packed beads configurations

We consider packed-bed reactors with dielectric beads in a two-dimensional channel geometry, apply an electric field perpendicular to the walls, and explore numerically the sensitivity of reaction conversion efficiencies of a dissociation reaction on system parameters like shape, orientation, and size of the beads and porosity of packed-bed systems. We have developed a lattice Boltzmann (LB) model that allows for simultaneous simulation of the flow field, the electric field within fluid and (solid) beads, and transport of (charged) species, such as ions and reagents. It solves Navier–Stokes for the fluid flow and the concentration field for neutral and charged species by the advection–diffusion and Nernst–Planck equation, respectively, formulated in the LB framework. The model allows to compute electric field strengths in the fluid and in the beads, by solving the Poisson equation. The method is suitable for arbitrary geometries of the flow domain and does not require body-fitted meshes. Two important conclusions can be drawn. First, the proposed LB model enables simulation of a reactive electro-kinetic fluid in a reactor with dielectric packed beads of arbitrary shape, size, and orientation. The LB method is based on Cartesian meshes irrespective of the shape of the beads and is highly parallelizable and can be extended to three-dimensional packed-bed reactors. Second, we show that reactor conversion efficiency is sensitive to shape, orientation, and size of the beads and the porosity of the packed-bed reactor. Present observations will guide the parameter settings for the beads and packed-bed reactor of more realistic three-dimensional configurations

LBM investigations on a chain reaction in a reactive electro-kinetic flow in porous material

A 2D model is developed for a simplified reactive electro-kinetic fluid in dielectric porous media based on the Lattice Boltzmann Method (LBM). The momentum, concentration and electric fields are simulated via the Navier-Stokes, advection-diffusion/Nernst-Planck and Poisson equations, respectively. With this model, the density, velocity, concentration of the chemical constituents and electric fields, and the interaction between these fields, can be studied. This allows us to get an insight into the interplay between chemistry and fluid physics in the porous medium. In this work, two types of simplified reactions are studied, namely, surface reactions and dissociation reactions. The results show that the conversion efficiency of both reactions can be strongly influenced by the flow and reactor packing parameters such as the fluid velocity, reactant concentration and the porosity of the porous medium. These different effects make the reaction conversion efficiency display a non-trivial and non-monotonic behavior as a function of the flow and reaction parameters. An analytical model of a simplified chain reaction consisting of both reactions is further studied in this electro-kinetic fluid system. Using this model, one could optimize the choice of the flow and reaction parameters to improve the performance of the reactions and achieve higher production rates