Kyongmin Yeo

Lagrangian statistics in turbulent channel flow

The Lagrangian dispersion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Lagrangian velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes. Among the schemes tested, the four-point Hermite interpolation in the homogeneous directions combined with Chebyshev polynomials in the wall-normal direction seems to produce most reliable Lagrangian statistics. Inhomogeneity of Lagrangian statistics in turbulent boundary layer is investigated by releasing many particles at several different wall-normal locations and tracking those particles. The fluid particle dispersion and Lagrangian structure function of velocity are investigated for the Kolmogorov similarity. The behavior of the Lagrangian integral time scales, Kolmogorov constants a0 and C0 of the velocity structure function near the wall are discussed. The intermittent behavior of the fluid particle acceleration is also examined by ...

Simulation of concentrated suspensions using the force-coupling method

Abstract The force-coupling method (FCM) represents the dynamics of low Reynolds number suspension flows through a distributed, low-order, finite force-multipole expansion and provides an efficient, matrix-free method to solve the mobility problem for the particle motion. In concentrated suspensions, strong short-range lubrication forces are generated between particles in close proximity as fluid in the intervening gap is displaced by the relative motion of the particles. These forces, together with near-surface contact forces, play an important role in the suspension rheology and self-diffusion of particles. However these forces lead to ill-conditioned problems for determining the particle stresses and particle motion in large systems of particles at higher volume fractions. A robust and effective iteration scheme for determining the particle stresslets is described together with a new scheme for including lubrication forces as near-field corrections to the FCM resistance problem. Both the lubrication and far-field interactions are solved as fully coupled systems in O ( N p log ( N p ) ) operations, for N p particles, using preconditioned conjugate gradient solvers. Numerical results for particles settling under gravity, particle pairs in linearly varying flows and in concentrated suspensions are compared with previous theoretical results and simulations. Numerical simulations with more than 4000 non-Brownian, spherical particles in a homogeneous shear flow provide results on the pair-distribution function and Lagrangian velocity correlations. The extension of the methods to simulate bidisperse systems or wall-bounded suspensions are discussed.

Dynamics of concentrated suspensions of non-colloidal particles in Couette flow

Fully three-dimensional numerical simulations of concentrated suspensions of O(1000) particles in a Couette flow at zero Reynolds number are performed with the goal of determining the wall effects on concentrated suspensions of non-colloidal particles. The simulations, based on the force-coupling method, are performed for 0.2 ≤ φ ≤ 0.4 and 10 < L y /a < 30, where φ denotes the volume fraction and L y and a are, respectively, the channel height and the particle radius. It is shown that the suspensions can be divided into three regions depending on the microstructures; the wall region where a structured particle layering is dominant, the core region in which the suspension field is quasi-homogeneous, and the buffer region which shows the characteristics of both the particle layer and the shear structure. The width of the inhomogeneous region (wall and buffer) is a function of φ and not sensitive to L y /a, once L y /a is larger than a threshold. Rheological properties in the inhomogeneous and quasi-homogeneous regions are investigated. The particle stresses are compared with previous rheological models.

Dynamic self-assembly of spinning particles

This paper presents a numerical study of the dynamic self-assembly of neutrally buoyant particles rotating in a viscous fluid. The particles experience simultaneously a magnetic torque that drives their individual spinning motion, a magnetic attraction toward the center of the domain and flow-induced interactions. Under specific conditions, a hydrodynamic repulsion balances the centripetal attraction of the magnetized particles, which leads to the formation of an aggregate of several particles. After a short transient, an aggregate of particles is formed that then rotates with a precession velocity related to the inter-particle distance. This dynamic self-assembly is stable (but not stationary) and the morphology depends on the number of particles. The numerical simulation is based on the Navier-Stokes equations coupled with the Lagrangian tracking of each individual particle. Multi-body interactions (at low but finite Reynolds number) are achieved by a local forcing of the momentum equations of the fluid flow. The agreement with experiments of spinning disks at a liquid-air interface is not only qualitative but also quantitative. Comparisons on the evolution of the characteristic scales of the aggregate with the rotation rate of individual particles clearly show that the numerical results are consistent with the experiments.

Dynamics and rheology of concentrated, finite-Reynolds-number suspensions in a homogeneous shear flow

We present the lubrication-corrected force-coupling method for the simulation of concentrated suspensions under finite inertia. Suspension dynamics are investigated as a function of the particle-scale Reynolds number Reγ and the bulk volume fraction ϕ in a homogeneous linear shear flow, in which Reγ is defined from the density ρf and dynamic viscosity μ of the fluid, particle radius a, and the shear rate γ as Reγ=ρfγa2/μ. It is shown that the velocity fluctuations in the velocity-gradient and vorticity directions decrease at larger Reγ. However, the particle self-diffusivity is found to be an increasing function of Reγ as the motion of the suspended particles develops a longer auto-correlation under finite fluid inertia. It is shown that finite-inertia suspension flows are shear-thickening and the particle stresses become highly intermittent as Reγ increases. To study the detailed changes in the suspension microstructure and rheology, we introduce a particle-stress-weighted pair-distribution funct...

On the near-wall characteristics of acceleration in turbulence

The behaviour of fluid-particle acceleration in near-wall turbulent flows is investigated in numerically simulated turbulent channel flows at low to moderate Reynolds numbers, Re τ = 180 ~ 600. The acceleration is decomposed into pressure-gradient (irrotational) and viscous contributions (solenoidal acceleration) and the statistics of each component are analysed. In near-wall turbulent flows, the probability density function of acceleration is strongly dependent on the distance from the wall. Unexpectedly, the intermittency of acceleration is strongest in the viscous sublayer, where the acceleration flatness factor of O(100) is observed. It is shown that the centripetal acceleration around coherent vortical structures is an important source of the acceleration intermittency. We found sheet-like structures of strong solenoidal accelerations near the wall, which are associated with the background shear modified by the interaction between a streamwise vortex and the wall. We found that the acceleration Kolmogorov constant is a linear function of y + in the log layer. The Reynolds number dependence of the acceleration statistics is investigated.

Eulerian and Lagrangian statistics in stably stratified turbulent channel flows

Using direct numerical simulation, we investigate the Eulerian and Lagrangian characteristics of the near-wall turbulence under stable stratification. In the near-wall region, large-scale motions are suppressed by stable stratification, while small-scale motions are enhanced, which leads to the increase of intermittency. It is shown that the modification of the Reynolds shear stress is caused by the increased intermittency and anisotropy. Investigation of acceleration and vorticity reveals that the length scales and timescales of the near-wall coherent vortices are reduced by stratification. The role of baroclinic torque around the near-wall turbulent structures is also discussed. The Lagrangian statistics indicate that the scaled dispersion in the streamwise direction remains unchanged, while those in the spanwise as well as in the wall-normal direction are suppressed by stratification.

Anomalous diffusion of wall-bounded non-colloidal suspensions in a steady shear flow

We investigate the shear-induced diffusion of concentrated non-colloidal suspensions in a Couette flow. The channel is divided into four zones based on the suspension microstructure and variances of the wall-normal and spanwise displacements for the particles in each zone. Due to the strong spatial coherency induced by the density fluctuations, the suspended particles exhibit anomalous diffusion. The diffusion in the wall-normal direction changes from superdiffusion for the particles next to the wall to subdiffusion for the particles near the core of the channel. It seems that the intermittent jumps and particle entrapment in particle layers are responsible for the anomalous diffusion near the wall, while the subdiffusion in the core is related to the overall confinement by the channel walls.

Deep learning algorithm for data-driven simulation of noisy dynamical system

Abstract We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Short-Term Memory (LSTM) network. It is shown that, when the numerical discretization is used, the function estimation problem can be solved by a multi-label classification problem. A penalized maximum log likelihood method is proposed to impose a smoothness condition in the prediction of the probability distribution. We show that the time evolution of the probability distribution can be computed by a high-dimensional integration of the transition probability of the LSTM internal states. A Monte Carlo algorithm to approximate the high-dimensional integration is outlined. The behavior of DE-LSTM is thoroughly investigated by using the Ornstein–Uhlenbeck process and noisy observations of nonlinear dynamical systems; Mackey–Glass time series and forced Van der Pol oscillator. It is shown that DE-LSTM makes a good prediction of the probability distribution without assuming any distributional properties of the stochastic process. For a multiple-step forecast of the Mackey–Glass time series, the prediction uncertainty, denoted by the 95% confidence interval, first grows, then dynamically adjusts following the evolution of the system, while in the simulation of the forced Van der Pol oscillator, the prediction uncertainty does not grow in time even for a 3,000-step forecast.