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 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 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.

The dynamics of a laminar flow in a symmetric channel with a sudden expansion

2001 ◽  
Vol 436 ◽  
pp. 283-320 ◽  
Author(s):  
T. HAWA ◽  
Z. RUSAK
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Sudden Expansion ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Stable Mode ◽  
Symmetric States ◽  
Asymmetric Equilibrium

Bifurcation analysis, linear stability study, and direct numerical simulations of the dynamics of a two-dimensional, incompressible, and laminar flow in a symmetric long channel with a sudden expansion with right angles and with an expansion ratio D/d (d is the width of the channel inlet section and D is the width of the outlet section) are presented. The bifurcation analysis of the steady flow equations concentrates on the flow states around a critical Reynolds number Rec(D/d) where asymmetric states appear in addition to the basic symmetric states when Re [ges ] Rec(D/d). The bifurcation of asymmetric states at Rec has a pitchfork nature and the asymmetric perturbation grows like √Re − Rec(D/d). The stability analysis is based on the linearized equations of motion for the evolution of infinitesimal two-dimensional disturbances imposed on the steady symmetric as well as asymmetric states. A neutrally stable asymmetric mode of disturbance exists at Rec(D/d) for both the symmetric and the asymmetric equilibrium states. Using asymptotic methods, it is demonstrated that when Re < Rec(D/d) the symmetric states have an asymptotically stable mode of disturbance. However, when Re > Rec(D/d), the symmetric states are unstable to this mode of asymmetric disturbance. It is also shown that when Re > Rec(D/d) the asymmetric states have an asymptotically stable mode of disturbance. The direct numerical simulations are guided by the theoretical approach. In order to improve the numerical simulations, a matching with the asymptotic solution of Moffatt (1964) in the regions around the expansion corners is also included. The dynamics of both small- and large-amplitude disturbances in the flow is described and the transition from symmetric to asymmetric states is demonstrated. The simulations clarify the relationship between the linear stability results and the time-asymptotic behaviour of the flow. The current analyses provide a theoretical foundation for previous experimental and numerical results and shed more light on the transition from symmetric to asymmetric states of a viscous flow in an expanding channel. It is an evolution from a symmetric state, which loses its stability when the Reynolds number of the incoming flow is above Rec(D/d), to a stable asymmetric equilibrium state. The loss of stability is a result of the interaction between the effects of viscous dissipation, the downstream convection of perturbations by the base symmetric flow, and the upstream convection induced by two-dimensional asymmetric disturbances.

Direct numerical simulations of bubbly flows Part 2. Moderate Reynolds number arrays

1999 ◽  
Vol 385 ◽  
pp. 325-358 ◽  
Author(s):  
ASGHAR ESMAEELI ◽  
GRÉTAR TRYGGVASON
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Dimensional System ◽  
Two Dimensional ◽  
Reynolds Stresses ◽  
Bubble Distribution ◽  
Moderate Reynolds Number

Direct numerical simulations of the motion of two- and three-dimensional finite Reynolds number buoyant bubbles in a periodic domain are presented. The full Navier–Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The rise Reynolds numbers are around 20–30 for the lowest volume fraction, but decrease as the volume fraction is increased. The rise of a regular array of bubbles, where the relative positions of the bubbles are fixed, is compared with the evolution of a freely evolving array. Generally, the freely evolving array rises slower than the regular one, in contrast to what has been found earlier for low Reynolds number arrays. The structure of the bubble distribution is examined and it is found that while the three-dimensional bubbles show a tendency to line up horizontally, the two-dimensional bubbles are nearly randomly distributed. The effect of the number of bubbles in each period is examined for the two-dimensional system and it is found that although the rise Reynolds number is nearly independent of the number of bubbles, the velocity fluctuations in the liquid (the Reynolds stresses) increase with the size of the system. While some aspects of the fully three-dimensional flows, such as the reduction in the rise velocity, are predicted by results for two-dimensional bubbles, the structure of the bubble distribution is not. The magnitude of the Reynolds stresses is also greatly over-predicted by the two-dimensional results.

scholarly journals Влияние числа Рейнольдса на распределение пульсационной составляющей вихря скорости по сечению плоского канала

2019 ◽  
Vol 89 (3) ◽  
pp. 347
Author(s):  
Ю.Г. Чесноков
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Cross Section ◽  
Liquid Flow ◽  
Direct Numerical Simulations ◽  
Mean Square ◽  
Flat Channel ◽  
Analysis Of Results ◽  
The Cross ◽  
Vortex Velocity

AbstractBased on the analysis of results from different authors using direct numerical simulations of the liquid flow in a flat channel, the effect of Reynolds number on the distribution of mean-square values of projections of a pulsed component of vortex velocity through the cross-section of a flat channel has been studied.

Sign in / Sign up

Export Citation Format

Share Document