Homogeneous Isotropic Turbulent Flow Research Articles

Preferential concentration and rise velocity reduction of bubbles immersed in a homogeneous and isotropic turbulent flow

The behavior of small spherical bubbles immersed in a homogeneous isotropic turbulent carrier flow of a heavier fluid has been experimentally studied. Air bubbles with diameters between 10 and 900 μm were injected in the test section of a horizontal water channel and allowed to interact with the turbulence induced by a grid located at the entrance to the test section. Point measurements of the bubble diameter and convective and rise velocities were taken from light interferometry data, together with flow visualizations that showed the instantaneous concentration field of bubbles in the carrier flow. The effect of the turbulence on the bubbles was found to alter the concentration field of bubbles leading to preferential accumulation at small scales, a phenomenon referred to as clustering, and to a decrease in the rise velocity of bubbles in the flow below the value measured and predicted for bubbles in a stationary fluid. These results are interpreted in terms of the different forces acting on the bubble in an inhomogeneous flow and in particular as the effect of pressure fluctuations that drive the bubbles preferentially to the core of vortices.

Coherent Vorticity Simulation of Three-Dimensional Forced Homogeneous Isotropic Turbulence

Coherent vorticity simulation (CVS) is a multiscale method to compute incompressible turbulent flows based on the wavelet filtered Navier–Stokes equations. At each time step the vorticity field is decomposed into two orthogonal components using an orthogonal wavelet basis: the coherent vorticity, corresponding to the coefficients whose modulus is larger than a threshold, and the remaining incoherent vorticity. The threshold value only depends on the total enstrophy, which evolves in time, and on the maximal resolution, which remains constant. The induced coherent velocity is computed from the coherent vorticity using the Biot–Savart kernel. To compute the flow evolution one only retains the coherent wavelet coefficients and some of their neighbors in space, scale, and direction, which define the safety zone. Two different strategies are studied to minimize at each time step the number of degrees of freedom to be computed, either by increasing the threshold value or by reducing the width of the safety zone. Their efficiency is compared for a three-dimensional forced homogeneous isotropic turbulent flow at initial Taylor microscale Reynolds number . The quality of the results is assessed in comparison to a direct numerical simulation of the same flow. It is found that, as long as a safety zone is present, CVS well preserves the statistical predictability of the turbulent flow (even the vorticity and velocity probability distribution functions) with a reduced number of degrees of freedom.

Conditional Eulerian and Lagrangian velocity increment statistics of fully developed turbulent flow

Conditional statistics of homogeneous isotropic turbulent flow is investigated by means of high Reynolds number direct numerical simulations performed with 20483 collocation points. Eulerian as well as Lagrangian velocity increment statistics under several conditions are analyzed and compared. In agreement with experimental data, longitudinal probability density functions P(δl||u|εl) conditioned on a scale-averaged energy dissipation rate are close to Gaussian distributions over all scales within the inertial range of scales. Also transverse increments conditioned on either the dissipation rate or the square of the vorticity have quasi-Gaussian probability density functions (PDFs). Concerning Lagrangian statistics we found that conditioning on a trajectory averaged energy dissipation rate ετ significantly reduces the scale dependence of the increment PDFs P(δτui|ετ). By means of dimensional arguments we propose a novel condition for Lagrangian increments which is shown to reduce even more the flatness of the corresponding PDFs and thus intermittency in the inertial range of scales. The conditioned Lagrangian PDF corresponding to the smallest increment considered is reasonably well described by a prediction for the PDF of acceleration of a non-intermittent velocity field. Conditioned structure functions show approximately K41 scaling with a larger scaling range than the unconditioned ones.

Different methods to estimate the Einstein-Markov coherence length in turbulence

We study the Markov property of experimental velocity data of different homogeneous isotropic turbulent flows. In particular, we examine the stochastic "cascade" process of nested velocity increments ξ(r):=u(x+r)-u(x) as a function of scale r for different nesting structures. It was found in previous work that, for a certain nesting structure, the stochastic process of ξ(r) has the Markov property for step sizes larger than the so-called Einstein-Markov coherence length l(EM), which is of the order of magnitude of the Taylor microscale λ [Phys. Lett. A 359, 335 (2006)]. We now show that, if a reasonable definition of the effective step size of the process is applied, this result holds independently of the nesting structure. Furthermore, we analyze the stochastic process of the velocity u as a function of the spatial position x. Although this process does not have the exact Markov property, a characteristic length scale l(u(x))≈l(EM) can be identified on the basis of a statistical test for the Markov property. Using a method based on the matrix of transition probabilities, we examine the significance of the non-Markovian character of the velocity u(x) for the statistical properties of turbulence.

Statistical properties of the local structure of homogeneous isotropic turbulence and turbulent channel flows

Statistical properties of the local structure are investigated using the data of direct numerical simulation of homogeneous isotropic turbulence for Re λ=60.1∼287.6 and turbulent channel flows for Re τ = 180, 400, 800, and 1270. The dimensionless second invariant is used as the representative local structure, and is defined as the second invariant of a velocity gradient tensor normalized by the magnitude of the velocity gradient tensor. In homogeneous isotropic turbulence, the probability density function (pdf) profiles of the dimensionless second invariant show good agreement for different values of Reynolds number. The volume fraction, the average, and the variance of the dimensionless second invariant converge to certain values at high Reynolds number, respectively. For the turbulent channel flows, the pdf profiles of the dimensionless second invariant for different values of Reynolds number coincide very well for the distance from the wall in wall units. The probability density and the volume fraction of the dimensionless second invariant at the center of the channel are in good agreement with those of homogeneous isotropic turbulence.

Interaction of a deformable free surface with statistically steady homogeneous turbulence

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.

Measurement of inertial particle clustering and relative velocity statistics in isotropic turbulence using holographic imaging

We present the first measurements of relative velocity statistics of inertial particles in a homogeneous isotropic turbulent flow with three-dimensional holographic particle image velocimetry (holographic PIV). From the measurements we are able to obtain the radial relative velocity probability density function (PDF) conditioned on the interparticle separation distance, for distances on the order of the Kolmogorov length scale. Together with measurements of the three-dimensional radial distribution function (RDF) in our turbulence chamber, these statistics, in principle, can be used to determine interparticle collision rates via the formula derived by Sundaram and Collins (1997). In addition, we show temporal development of the RDF, which reveals the existence of an extended quasi-steady-state regime in our facility. Over this regime the measured two-particle statistics are compared to direct numerical simulations (DNS) with encouraging qualitative agreement. Statistics at the same Reynolds number but different Stokes numbers demonstrate the ability of the experiment to correctly capture the trends associated with particles of different inertia. Our results further indicate that even at moderate Stokes numbers turbulence may enhance collision rates significantly. Such experimental investigations may prove valuable in validating, guiding and refining numerical models of particle dynamics in turbulent flows.

Statistical models for predicting pair dispersion and particle clustering in isotropic turbulence and their applications

The purpose of this paper is twofold: (i) to advance and extend the statistical two-point models of pair dispersion and particle clustering in isotropic turbulence that were previously proposed by Zaichik and Alipchenkov (2003 Phys. Fluids15 1776–87; 2007 Phys. Fluids 19, 113308) and (ii) to present some applications of these models. The models developed are based on a kinetic equation for the two-point probability density function of the relative velocity distribution of two particles. These models predict the pair relative velocity statistics and the preferential accumulation of heavy particles in stationary and decaying homogeneous isotropic turbulent flows. Moreover, the models are applied to predict the effect of particle clustering on turbulent collisions, sedimentation and intensity of microwave radiation as well as to calculate the mean filtered subgrid stress of the particulate phase. Model predictions are compared with direct numerical simulations and experimental measurements.

Investigating an advective approach to subgrid modeling in large-eddy simulations

The purpose of this paper is to investigate and validate an alternative subgrid model to be used in large-eddy simulations, based on an advective formulation. Rather than modeling the subgrid tensor that appears in the LES formulation as is commonly done, the subgrid force vector, which is the divergence of the subgrid tensor, is modeled directly. It is designed to comply with two basic principles. First, it is required to act only on the smallest scales that the mesh can represent. Second, it must be of an advective nature, which means it must have a preferred direction aligned with the fluid velocity. The results for two benchmark test cases, including Homogeneous Isotropic Turbulence and Turbulent Channel Flow, show that this approach can successfully represent the effect of the small scales on the resolved ones, while guaranteeing numerical stability and greater robustness in adverse mesh environments, when compared to some traditional eddy-viscosity based models, such as the Smagorinsky and the dynamic model from Germano.

Coherent vorticity extraction in 3D homogeneous isotropic turbulence: influence of the Reynolds number and geometrical statistics

The coherent vorticity extraction method (CVE) is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. CVE decomposes each turbulent flow realization into two orthogonal components: a coherent and an incoherent random flow. They both contribute to all scales in the inertial range, but exhibit different statistical behavior. We apply CVE to 256 3 subcubes extracted from 3D homogeneous isotropic turbulent flows at different Taylor microscale Reynolds numbers (Rλ = 140, 240 and 680), computed by a direct numerical simulation (DNS) at different resolutions (N = 256 3 , 512 3 and 2048 3 ), respectively. We compare the total, coherent and incoherent vorticity fields obtained by using CVE and show that few wavelets coefficients are sufficient to represent the coherent vortices of the flows. Geometrical statistics in term of helicity are also analyzed and the λ2 criterion is applied to the filtered flow fields.

Cloud Droplet Growth by Condensation in Homogeneous Isotropic Turbulence

AbstractThe growth of cloud droplets by diffusion of water vapor in a three-dimensional homogeneous isotropic turbulent flow is considered. Within a simple model of advection and condensation, the dynamics and growth of millions of droplets are integrated. A droplet-size spectra broadening is obtained and it is shown to increase with the Reynolds number of turbulence by means of two series of direct numerical simulations at increasing resolution. This is a key point toward a proper evaluation of the effects of turbulence for condensation in warm clouds, where the Reynolds numbers typically achieve extreme values. The obtained droplet spectral broadening as a function of the Reynolds number is shown to be consistent with dimensional arguments. A generalization of this expectation to Reynolds numbers not accessible by direct numerical simulation (DNS) is proposed, yielding upper and lower bounds to the actual size spectra broadening. It is argued that the lower bound is the relevant limit at high Reynolds numbers. A further DNS matching the large scales of the system suggests consistency of the picture drawn. The assumptions underlying the model are expected to hold up to spatial scales on the order of 100 m; no direct comparison with in situ measures is possible. Additional effort is needed to evaluate the impact of this effect for condensation in more realistic cloud conditions.

Vortex Locking in Direct Numerical Simulations of Quantum Turbulence

Direct numerical simulations are used to examine the locking of quantized superfluid vortices and normal fluid vorticity in evolving turbulent flows. The superfluid is driven by the normal fluid, which undergoes either a decaying Taylor-Green flow or a linearly forced homogeneous isotropic turbulent flow, although the back reaction of the superfluid on the normal fluid flow is omitted. Using correlation functions and wavelet transforms, we present numerical and visual evidence for vortex locking on length scales above the intervortex spacing.

Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows

We present an LES-type variational multiscale theory of turbulence. Our approach derives completely from the incompressible Navier–Stokes equations and does not employ any ad hoc devices, such as eddy viscosities. We tested the formulation on forced homogeneous isotropic turbulence and turbulent channel flows. In the calculations, we employed linear, quadratic and cubic NURBS. A dispersion analysis of simple model problems revealed NURBS elements to be superior to classical finite elements in approximating advective and diffusive processes, which play a significant role in turbulence computations. The numerical results are very good and confirm the viability of the theoretical framework.

Scaling laws of turbulent dynamos

We consider magnetic fields generated by homogeneous isotropic and parity invariant turbulent flows. We show that simple scaling laws for the dynamo threshold, magnetic energy and Ohmic dissipation can be obtained depending on the value of the magnetic Prandtl number. To cite this article: S. Fauve, F. Pétrélis, C. R. Physique 8 (2007).

Coherent vortex extraction in 3D homogeneous isotropic turbulence using orthogonal wavelets

The coherent vortex extraction (CVE) decomposes each turbulent flow realization into two orthogonal components: a coherent and a random incoherent flow. They both contribute to all scales in the inertial range, but exhibit different statistical behaviour. The CVE decomposition is based on the nonlinear filtering of the vorticity field projected onto an orthonormal wavelet basis made of compactly supported functions. We decompose a 3D homogeneous isotropic turbulent flow at Taylor microscale Reynolds numbers Rλ = 140 computed by a direct numerical simulation (DNS) at resolution N = 256 3 . Only 3.7%N wavelet modes correspond to the coherent flow made of vortex tubes, which contributes to 92% of the enstrophy. Another observation is that the coherent flow exhibits in the inertial range the same k −5/3 slope in the energy spectrum and k 1/3 slope in the enstrophy spectrum as the total flow does. The remaining 96.3%N wavelet modes correspond to a random residual flow which is structureless, quasi equipartition of energy and a Gaussian velocity probability distribution function (PDF). We also analyse and visualize the Lamb vector, its divergence and curl and study the contributions coming from the coherent and incoherent components of vorticity and the induced velocity. Resume. L'extraction de tourbillons coherents (Coherent Vortex Extraction: CVE) decompose un ´ turbulent en deux composantes orthogonales: unecoulement coherent et un ´ aleatoire incoherent. Ces deux composantes contribuent aux grandesechelles dans la zone inertielle, mais ont des comportements statistiques differents. La decomposition CVE est basee sur le filtrage

Divergence-free Wavelets for Coherent Vortex Extraction in 3D homogeneous isotropic turbulence

In this paper we investigate the use of divergence-free wavelet bases for the Coherent Vortex Extraction (CVE) of turbulent flows. We begin with a short presentation of the construction of 3D divergence-free biorthogonal wavelets. We apply the CVE decomposition to a homogeneous isotropic turbulent flow, computed by a Direct Numerical Simulation (DNS) at resolution 2403 and upsampled to N=2563. First, the CVE is applied to the vorticity field. Using the divergence-free wavelets for the vorticity field makes sense since the vorticity also verifies an incompressibility condition when the velocity does. The coherent part of the vorticity field is reconstructed from the largest wavelet coefficients, corresponding to $ 3\% N$, while the complement constitutes the incoherent part. We show that the coherent part corresponds to the vortex tubes of the flow and retains most of the energy and enstrophy. These results are then compared to those obtained using non-divergent free wavelets, both orthogonal and biorthogonal ones. Then we also apply the CVE method, using divergence-free wavelets, to decompose the velocity field and subsequently compute the corresponding vorticity fields. The results show that the decomposition of velocity exhibit large smooth vortex structures in contrast to what is obtained with the decomposition of the vorticity.

Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles

The main purpose of this article is to investigate the effects of the subgrid fluid turbulence on the motion of nonsettling colliding particles suspended in steady homogeneous isotropic turbulent flow. An additional goal is to characterize the statistical properties of the subgrid fluid turbulence “viewed” by inertial particles to support the development of large eddy simulation (LES) approach for particle-laden turbulent flows. Two types of numerical experiments have been carried out: first, the discrete particle trajectories were computed using the fluid velocity field given by direct numerical simulation (DNS) in order to characterize the small-scale fluid velocity fluctuations “seen” by the particles. In a second stage, the particle trajectory simulations were performed using several filtered velocity fields computed from the DNS data to evaluate the effect of the subgrid fluid turbulence on the particle statistics (turbulent dispersion, kinetic energy, accumulation efficiency, particle-particle relative velocity and collision frequency). The first part of this study shows that particle inertia has a limited effect on the subgrid fluid turbulent statistics: subgrid kinetic energy and Lagrangian integral time scale measured along the particle trajectories. In addition, the subgrid fluid Lagrangian integral time scale is found to be nearly equal to the subgrid Eulerian integral time scale and proportional to the ratio of the filter width to the whole fluid turbulent velocity. The second part shows that the particle turbulent dispersion and kinetic energy are affected by the filtering only when a significant percentage of the turbulent kinetic energy was removed from the velocity field seen by the particles. In contrast, accumulation and collision phenomena are found to be significantly influenced by the subgrid fluid velocity fluctuations when the particle response time is of the same order or smaller than the subgrid Lagrangian integral time scale measured along particle paths. Finally, these results are used to characterize, in terms of particle response time to subgrid time scale ratio, the validity range of LES for the computation of gas-solid turbulent flow.

Effect of particle inertia on temperature statistics in particle-laden homogeneous isotropic turbulence

The fluid temperature statistics along particle trajectories is crucial to understand the mechanisms of turbulent non-isothermal or reactive fluid-particle flow, especially for the Lagrangian model of non-isothermal particle-laden turbulent flow. In the present study, direct numerical simulations were utilized to generate temperature field statistics in particle-laden incompressible stationary homogeneous isotropic turbulent flows, which is focused on the effect of particle response time on the Lagrangian statistics of the particle and the fluid temperature seen by particles. It shows that, for the particles with τ p / τ k τ p / τ k increased; while for larger particles ( τ p / τ k > 1), the trend is inversed. For small particles ( τ p / τ k R p T decreases as the particle inertia ( τ p / τ k ) increases. The trend is reversed for larger particles. The autocorrelation of fluid temperature along the particle path, R pf T , decreased as the particle inertia increased. And as the particle inertia increased, the autocorrelation coefficient of the fluid temperature seen by particle decreased more rapidly than that of the particle temperature. The mean temperature gradient contributes to the correlation between the particles velocity component and temperature fluctuations in the direction of the gradient. For the particles with τ p / τ k <1, the magnitude of the correlation coefficient increases as the particle inertia increases, while this value is independent of the particle time constant for larger particles.

Analysis of concentration patterns in volcanic rocks: Insights into dynamics of highly explosive volcanic eruptions

In this contribution we present new data resulting from the analysis of concentration patterns of mixed juvenile fragments ejected by a highly explosive volcanic eruption that occurred on Salina Island (Aeolian Islands, Italy) and our aim is to identify the fluid-dynamic regime characterizing the magma mixing process. Concentration patterns are studied by calculating the power spectrum of concentration variability along transects crossing the magma mixing structures. Results indicate that the slope of power spectrum has an average value of about −5/3, according to Kolmogorov law of turbulence, and suggest that the magma mixing process, in the studied conditions, can be approximated by considering the passive scalar mixing hypothesis in homogeneous isotropic turbulent flow. These results represent a first step towards a better understanding of magma mixing processes associated to highly explosive volcanic eruptions and this first step is taken by studying concentration patterns in volcanic rocks by coupling petrological and non-linear dynamics methods.

On the orientation of stiff fibres suspended in turbulent flow in a planar contraction

The influence of turbulence on the orientation state of a dilute density matched suspension of stiff fibres at high Reynolds number in a planar contraction is investigated. High-speed imaging and laser-Doppler velocimetry techniques are used to quantify fibre orientation distribution and turbulent characteristics. A nearly homogeneous isotropic grid-generated turbulent flow is introduced at the contraction inlet. Flow Reynolds number and inlet turbulent characteristics are varied in order to determine their effects on orientation distribution. The orientation anisotropy is shown to be accurately modelled by a Fokker-Planck type equation. Results show that rotational diffusion is highly influenced by inlet turbulent characteristics and decays exponentially with convergence ratio. Furthermore, the effect of turbulent energy production in the contraction is shown to be negligible. Also, the results show that the flow Reynolds number has negligible effect on the development of orientation anisotropy, and the influence of turbulence on fibre rotation is negligible for rotational Péclet number $\gt$10.