scholarly journals Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles

Soft Matter ◽  
2021 ◽  
Author(s):  
Ryoichi Yamamoto ◽  
John Jairo Molina ◽  
Yasuya Nakayama
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Standard Procedure ◽  
Direct Numerical Simulations ◽  
Interacting Particles ◽  
Profile Method ◽  
Smoothed Profile Method ◽  
General Method

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds number. The method follows the standard procedure for...

Direct numerical simulations of sedimenting spherical particles at non-zero Reynolds number

RSC Advances ◽  
2014 ◽  
Vol 4 (96) ◽  
pp. 53681-53693 ◽  
Author(s):  
Adnan Hamid ◽  
John J. Molina ◽  
Ryoichi Yamamoto
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Dynamic Properties ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Inertial Effects ◽  
Profile Method ◽  
Volume Fractions ◽  
Wide Range ◽  
Smoothed Profile Method

We performed direct numerical simulations, using a smoothed profile method to investigate the inertial effects on the static and dynamic properties of a sedimenting suspension over a wide range of volume fractions from 0.01 to 0.4.

scholarly journals Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

scholarly journals Turbulent Coagulation of Aerosol Particles: New Insights From Direct Numerical Simulations and Holographic Imaging Experiments

2003 ◽  
Author(s):  
Lance R. Collins ◽  
Hui Meng ◽  
Aruj Ahluwalia ◽  
Lujie Cao ◽  
Gang Pan
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Search Algorithm ◽  
Concentration Field ◽  
Direct Numerical Simulations ◽  
Three Dimensions ◽  
Collision Kernel ◽  
Coagulation Rate ◽  
Subsequent Work ◽  
Turbulent Fluctuations

Particle collisions driven by turbulent fluctuations play a key role in such diverse problems as cloud formation, aerosol powder manufacturing and inhalation drug therapy to name a few. In all of these examples (and many others) turbulent fluctuations increase the rate of collisions relative to the background collision rate driven by Brownian motion. Furthermore, turbulence can spontaneously generate very large fluctuations in the particle concentration field. This “clustering” is caused by the inertial mismatch between the heavy particles and the lighter surrounding gas; vortices in the flow “centrifuge” the heavier particles out of vortex cores and into the straining regions that lie in between the vortices. Because collision is a binary process, concentration fluctuations further enhance the turbulent coagulation rate by as much as two orders of magnitude. An effect of this size must be accounted for in a rational model of turbulent coagulation. Sundaram & Collins (J. Fluid Mech. 1997) showed that the radial distribution function (RDF) of the particle population, evaluated at contact, precisely corrects the collision kernel for clustering. Subsequent work has explored the dependence of the RDF on the system parameters (e.g., particle size, concentration, response time and Reynolds number) using direct numerical simulations. These results have improved our understanding and ability to predict the effect of the first three parameters; however, owing to the limited range of Reynolds number that can be reached in a numerical simulation, questions remain over the scaling of the RDF with Reynolds number. This is a critical issue for high-Reynolds-number applications such as cloud physics, where values of the Reynolds number can be 1–2 orders of magnitude greater than can be simulated. We will present our highest Reynolds number simulations to date and show our attempts to resolve this issue. Recently, the ability to measure three-dimensional particle positions using holography has been realized (e.g., Meng & Pu, J. Opt. Soc. Am. 2003). With holography, the optical image that is produced contains fringes that, upon inverting the laser, reproduce the original image in three dimensions. The hologram can then be scanned using a digital camera to obtain the particle positions. An important consideration with this study is the need to differentiate individual particles. We developed a search algorithm that locates particle centers, even in the presence of optical aberations and speckle noise. The algorithm has been used to obtain the first experimental RDF measurements to date. Thus far we see good agreement between the experimentally obtained RDF and the simulations. Besides validating the simulations, experiments can span a much broader range of Reynolds numbers, providing critical data that may help resolve the open questions associated with this parameter.

scholarly journals Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall

2008 ◽  
Vol 600 ◽  
pp. 403-426 ◽  
Author(s):  
P. BURATTINI ◽  
S. LEONARDI ◽  
P. ORLANDI ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Friction Velocity ◽  
Streamwise Velocity ◽  
Negative Energy ◽  
Direct Numerical Simulations ◽  
Rough Wall ◽  
Local Isotropy ◽  
Taylor’S Hypothesis ◽  
Yielding Support

The turbulent flow in a two-dimensional channel with roughness on one wall is investigated using experiments and direct numerical simulations (DNS). The elements have a square cross-section with height k=0.1H (H is the channel half-width) and a streamwise spacing of 4k. The Reynolds number Reτr, based on the friction velocity at the rough wall and H, is in the range 300–1100. Particular attention is given to the rough-wall side. Measured turbulence intensities, length scales, leading terms in the turbulent kinetic energy budget, and velocity spectra are compared with those obtained from the DNS. Close agreement is found, yielding support for the simplifying assumptions in the experiment (notably local isotropy and Taylor's hypothesis) and the adequacy of the spatial resolution in the simulation. Overall, the profiles of the Reynolds normal stresses on the roughness side are almost independent of Reτr, when normalized by outer variables. Energy spectra at different locations above the rough wall collapse well at high wavenumbers, when normalized by Kolmogorov scales. In contrast to previous studies, a region of negative energy production near the location of the maximum streamwise velocity is not observed. Comparison with a smooth-wall channel, at similar values of the friction-velocity Reynolds number, highlights differences only in the streamwise velocity component near the wall.

Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations

2001 ◽  
Vol 427 ◽  
pp. 241-274 ◽  
Author(s):  
P. K. YEUNG
Keyword(s):  
Reynolds Number ◽  
Correlation Function ◽  
Numerical Simulations ◽  
Time Scales ◽  
Time Scale ◽  
Cross Correlation ◽  
Scalar Fields ◽  
Direct Numerical Simulations ◽  
Cross Correlation Function ◽  
Differential Diffusion

A study of the Lagrangian statistical properties of velocity and passive scalar fields using direct numerical simulations is presented, for the case of stationary isotropic turbulence with uniform mean scalar gradients. Data at higher grid resolutions (up to 5123 and Taylor-scale Reynolds number 234) allow an update of previous velocity results at lower Reynolds number, including intermittency and dimensionality effects on vorticity time scales. The emphasis is on Lagrangian scalar time series which are new to the literature and important for stochastic mixing models. The variance of the ‘total’ Lagrangian scalar value (ϕ˜+, combining contributions from both mean and fluctuations) grows with time, with the velocity–scalar cross-correlation function and fluid particle displacements playing major roles. The Lagrangian increment of ϕ˜+ conditioned upon velocity and scalar fluctuations is well represented by a linear regression model whose parameters depend on both Reynolds number and Schmidt number. The Lagrangian scalar fluctuation is non-Markovian and has a longer time scale than the velocity, which is due to the strong role of advective transport, and is in contrast to results in an Eulerian frame where the scalars have shorter time scales. The scalar dissipation is highly intermittent and becomes de-correlated in time more rapidly than the energy dissipation. Differential diffusion for scalars with Schmidt numbers between 1/8 and 1 is characterized by asymmetry in the two-scalar cross-correlation function, a shorter time scale for the difference between two scalars, as well as a systematic decrease in the Lagrangian coherency spectrum up to at least the Kolmogorov frequency. These observations are consistent with recent work suggesting that differential diffusion remains important in the small scales at high Reynolds number.

Smoothed Profile Method for Particulate Two-Phase Flow

2008 ◽  
Author(s):  
Xian Luo ◽  
Martin R. Maxey ◽  
George E. Karniadakis
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Integration Scheme ◽  
Force Density ◽  
Step Size ◽  
Time Step ◽  
Element Discretization ◽  
Profile Method ◽  
Time Step Size ◽  
Smoothed Profile Method

We re-formulate and demonstrate a new method for particulate flows, the so-called “Smoothed Profile” method (SPM) first proposed in [1]. The method uses a fixed computational mesh, which does not conform to the geometry of the particles. The particles are represented by certain smoothed indicator profiles to construct a smooth body force density term added into the Navier-Stokes equations. The SPM imposes accurately and efficiently the rigid-body constraint inside the particles. In particular, while the original method employs a fully-explicit time-integration scheme, we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. We show that the modeling error of SPM has a non-monotonic dependence on the time step size Δt. The optimum time step size balances the thickness of the Stokes layer and that of the profile interface. Subsequently, we present several numerical simulations, including flow past three-dimensional complex-shaped particles and two interacting microspheres, which are compared against full direct numerical simulations and the force coupling method (FCM).

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