A model for predicting the acceleration variance of arbitrary-density finite-size particles in isotropic turbulence

The paper concerns the effects of particle inertia, density, and size on acceleration statistics. A simple analytical model for estimating the acceleration variance of particles suspended in an isotropic homogeneous turbulent flow field is developed. This model is capable of qualitative describing the particle acceleration variance over the entire range of the particle-to-fluid density ratio. Comparisons of model predictions with numerical simulations and experimental data are presented.     

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.     

Nonlinear dynamical systems and bistability in linearly forced isotropic turbulence

In this paper, we present an extensive study of the linearly forced isotropic turbulence. By using analytical method, we identify two parametric choices, of which they seem to be new as far as our knowledge goes. We prove that the underlying nonlinear dynamical system for linearly forced isotropic turbulence is the general case of a cubic Lienard equation with linear damping. We also discuss a FokkerPlanck approach to this new dynamical system, which is bistable and exhibits two asymmetric and asymptotically stable stationary probability densities.     

Subgrid-scale contributions to Lagrangian time correlations in isotropic turbulence

The application of large-eddy simulation （LES） to particle-laden turbulence raises such a fundamental question as whether the LES with a subgrid scale （SGS） model can correctly predict Lagrangian time correlations （LTCs）. Most of the currently existing SGS models are constructed based on the energy budget equations. Therefore, they are able to correctly predict energy spectra, but they may not ensure the correct prediction on the LTCs. Previous researches investigated the effect of the SGS modeling on the Eulerian time correlations. This paper is devoted to study the LTCs in LES. A direct numerical simulation （DNS） and the LES with a spectral eddy viscosity model are performed for isotropic turbulence and the LTCs are calculated using the passive vector method. Both a priori and a posteriori tests are carried out. It is observed that the subgrid;scale contributions to the LTCs cannot be simply ignored and the LES overpredicts the LTCs than the DNS. It is concluded from the straining hypothesis that an accurate prediction of enstrophy spectra is most critical to the prediction of the LTCs.     

Stochastic simulations of particle-laden isotropic turbulent flow

Numerical simulations are performed of dispersion and polydispersity of particles in isotropic incompressible turbulence. The mass loading of the particles is assumed to be small; thus the effects of particles on turbulence is neglected (one-way coupling). A stochastic model is employed to simulate the carrier phase. The results of the simulations are compared with direct numerical simulation (DNS) data and theoretical results. The stochastic model predicts most of the trends as portrayed by DNS and theory. However, the continuity effect associated with the crossing trajectories effect is not captured. Also, the peaking in the variation of the particle asymptotic diffusivity coefficient with the particle time constant is not observed. For evaporating particles, the stochastic model predicts thinner probability density functions (pdfs) for the particle diameter as compared with DNS generated pdfs. The model is implemented to investigate the effects of gravity on evaporation. It is shown that the depletion rate increases with increase of the drift velocity at short and intermediate times, but an opposite trend is observed at long times. The standard deviation and skewness of the particle diameter indicate peak values in their variations with the drift velocity. Dispersion of evaporating particles decreases with respect to that of non-evaporating particles at small drift velocities; an opposite trend is observed at large drift velocities. The effects of the initial evaporation rate and the particle Schmidt number on the evaporation in the gravity environment are also studied.     

Kinematics and dynamics of small-scale vorticity and strain-rate structures in the transition from isotropic to shear turbulence

We applied a technique that defines and extracts “structures” from a DNS dataset of a turbulence variable in a way that allows concurrent quantitative and visual analysis. Local topological and statistical measures of enstrophy and strain-rate structures were compared with global statistics to determine the role of mean shear in the dynamical interactions between fluctuating vorticity and strain-rate during transition from isotropic to shear-dominated turbulence. We find that mean shear adjusts the alignment of fluctuating vorticity, fluctuating strain-rate in principal axes, and mean strain-rate in a way that (1) enhances both global and local alignments between vorticity and the second eigenvector of fluctuating strain-rate, (2) two-dimensionalizes fluctuating strain-rate, and (3) aligns the compressional components of fluctuating and mean strain-rate. Shear causes amalgamation of enstrophy and strain-rate structures, and suppresses the existence of strain-rate structures in low-vorticity regions between enstrophy structures. A primary effect of shear is to enhance “passive” strain-rate fluctuations, strain-rate kinematically induced by local vorticity concentrations with negligible enstrophy production, relative to “active,” or vorticity-generating strain-rate fluctuations. Enstrophy structures separate into “active” and “passive” based on the level of the second eigenvalue of fluctuating strain-rate. We embedded the structure-extraction algorithm into an interactive visualization-based analysis system from which the time evolution of a shear-induced hairpin enstrophy structure was visually and quantitatively analyzed. The structure originated in the initial isotropic state as a vortex sheet, evolved into a vortex tube during a transitional period, and developed into a well-defined horseshoe vortex in the shear-dominated asymptotic state.     

Dispersion and clustering of bidisperse particles in isotropic turbulence

A statistical kinetic model describing the dispersion and clustering of particles with different inertia in homogeneous turbulence is presented. The model developed is used for calculating the relative velocity, the radial distribution function, and the particle collision kernel in a stationary bidisperse suspension. The results obtained are compared with the data of a direct numerical simulation.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 94–107. Original Russian Text Copyright © 2005 by Alipchenkov and Zaichik.     

Acceleration covariance in isotropic hydromagnetic turbulence

The present paper deals with the turbulent flow of an incompressible, viscous and conducting fluid which is isotropic, spatially homogeneous. The expression for acceleration covariance is derived. The obtained result shows that the defining scalars α(r, t) and β(r, t) of the acceleration covariance in MHD turbulence depend on the defining scalars of Q _ij , H _ij , Π _ij and S _{ik, j} .     

Aspects of large eddy simulation of homogeneous isotropic turbulence

HOMTY, a code for Large Eddy Simulation of homogeneous isotropic turbulence is proven by successful simulation of two experiments. The role of each term in the equations of motion and the concept of filtering is examined. It is shown that ‘prefiltering’ is unnecessary, and the resulting additional term in the equations, instead of transferring energy to the subgrid scales, backscatters energy from the resolved large wavenumerbers to the small ones. The kinetic energy decay exponent is shown to depend on the low wavenumber part of the velocity spectrum. Pressure statistics are computed and found to be in agreement with previous computations.     

Kinetic modeling of particles in stratified flow – Evaluation of dispersion tensors in inhomogeneous turbulence

The continuum equations for a dilute particle distribution in inhomogeneous turbulence are tested against results from a Langevin particle tracking simulation. Reeks’ version of the kinetic theory is used to generate the mass, momentum and kinetic stress equations for the particle distribution. The particle tracking data are used to directly evaluate the dispersion tensors λ and μ which serve as closure relations for the continuum equations. These exact forms are compared to approximate, local forms. Even for low Stokes numbers (corresponding to low particle inertia defined by τ/τ_p ? 1), the tensor λ is strongly affected by the inhomogeneity and depends on turbulence parameters in the volume corresponding to the particle path dispersion over the particle Lagrangian integral timescale τ. In contrast, the locally homogeneous form of the velocity dispersion tensor μ is a sufficient approximation, since it depends on the dispersion volume over the much smaller particle relaxation time τ_p. It is demonstrated that the body force due to the dispersion vector γ cannot be neglected. In the limit of passive tracers (zero stopping distance), γ is equal to the gradient of λ, if the physical setting is such that we can invoke constant tracer density in this limit.     

Second-order relative exponent of isotropic turbulence

Theoretical results on the scaling properties of turbulent velocity fields are reported in this letter. Based on the Kolmogorov equation and typical models of the second-order statistical moments (energy spectrum and the second-order structure function), we have studied the relative scaling using the ESS method. It is found that the relative EES scaling exponent S₂ is greater than the real or theoretical inertial range scaling exponent ξ₂, which is attributed to an evident bump in the ESS range.     

Modulation of homogeneous turbulence seeded with finite size bubbles or particles

The dynamics of homogeneous, isotropic turbulence seeded with finite sized particles or bubbles is investigated in a series of numerical simulations, using the force-coupling method for the particle phase and low wavenumber forcing of the flow to sustain the turbulence. Results are given on the modulation of the turbulence due to massless bubbles, neutrally buoyant particles and inertial particles of specific density 1.4 at volumetric concentrations of 6%. Buoyancy forces due to gravity are excluded to emphasize finite size and inertial effects for the bubbles or particles and their interactions with the turbulence. Besides observing the classical entrapment of bubbles and the expulsion of inertial particles by vortex structures, we analyze the Lagrangian statistics for the velocity and acceleration of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the small-scale kinetic energy is significantly enhanced. Unexpectedly, the modulation of turbulence depends only slightly on the dispersion characteristics (bubble entrapment in vortices or inertial sweeping of the solid particles) but is closely related to the stresslet component (finite size effect) of the flow disturbances. The pivoting wavenumber characterizing the transition from damped to enhanced energy content is shown to vary with the size of the bubbles or particles. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.     

On the evolution of decaying isotropic turbulence

A direct numerical simulation is performed on 256³ grids for decaying isotropic turbulence. The total kinematic energy, Taylor micro-scale, Taylor micro-scale Reynolds number and the velocity derivative skewness are calculated. The snapshots of energy spectra and energy transfer spectra are plotted. These measurements verify the DIA predictions: decaying isotropic turbulence has the energy propagation and occupies the final decay periods. The skewness remains to some level with small variation even in the final decay period.     

Assessment of the modulated gradient model in decaying isotropic turbulence

A recently introduced nonlinear model undergoes evaluations based on two isotropic turbulent cases: a University of Wiscosion-Madison case at a moderate Reynolds number and a Johns Hopkins University case at a high Reynolds number. The model uses an estimation of the subgrid-scale (SGS) kinetic energy to model the magnitude of the SGS stress tensor, and uses the normalized velocity gradient tensor to model the structure of the SGS stress tensor. Testing is performed for the first case through a comparison between direct numerical simulation (DNS) results and large eddy simulation (LES) results regarding resolved kinetic energy and energy spectrum. In the second case, we examine the resolved kinetic energy, the energy spectrum, as well as other key statistics including the probability density functions of velocities and velocity gradients, the skewness factors, and the flatness factors. Simulations using the model are numerically stable, and results are satisfactorily compared with DNS results and consistent with statistical theories of turbulence.     

Interaction of isotropic turbulence with a normal shock wave

The evolution of incompressible and compressible isotropic 2-d turbulent fields interacting with a normal shock wave up to Mach numbers of 2.4 was investigated by means of direct numerical simulation using an ENO scheme. A comparison of statistics with linear analysis results is presented. Vorticity amplification in the DNS agrees well with the linear theory. Energy spectra are enhanced more in the small scales than in the large scales for incoming incompressible turbulence. The amplification rate for initially compressible turbulence is comparatively small.     

Diffusion of suspended particles in an isotropic turbulence field

A model for turbulent motion is proposed which makes it possible to evaluate the pulsation characteristics and the diffusion coefficients of the dispersed phase and also makes it possible to describe the effect of the suspended particles on the turbulence of the dispersing medium. Specific calculations are made for the situation when the undisturbed turbulent field is isotropic.The diffusion of an admisture having inertia in a turbulent stream has been studied previously on the assumption that the three-dimensional turbulence characteristics have practically no effect on the behavior of the suspended particles, so that the random motion of the latter is described by ordinary differential equations containing the natural independent variable the motion travel time [1–4]. In many cases this assumption is incorrect and the corresponding theory is obviously deficient. For example, a fundamental result of this theory, asserting that the turbulent diffusion coefficients of the particles and of the fluid moles are equal for a long diffusion time, is obviously incorrect if the relative motion of the particles is significant [5].     

Advances in studies on two-phase turbulence in dispersed multiphase flows

Particle/droplet/bubble fluctuation and dispersion are important to mixing, heat and mass transfer, combustion and pollutant formation in dispersed multiphase flows, but are insufficiently studied before the 90 years of the last century. In this paper, the present author reports his systematic studies within nearly 20 years on two-phase turbulence in dispersed multiphase flows, including particle fluctuation in dilute gas-particle and bubble-liquid flows, particle-wall collision effect, coexistence of particle turbulence and inter-particle collisions, fluid turbulence modulation due to the particle wake effect and validation of the two-fluid RANS modeling using large-eddy simulation.     

The motion of microbubbles in a forced isotropic and homogeneous turbulence

We have studied the concentration distribution of microbubbles in forced isotropic turbulence. An initially uniform concentration field is shown to evolve to a highlyintermittent orspotty concentration distribution at long time due to the interactions of microbubbles with small-scale, intense, and coherent flow vortical structures. The maximum bubble concentration can be as large as 3,000 times the mean concentration and the local accumulations occur preferentially in the regions of high flow vorticity and low flow pressure. A quantitative measure of global nonuniformity in the concentration field is used to confirm that the preferential accumulation does follow Kolmogorov scaling, as opposed to the large-scale scaling commonly used for dispersion quantification.     

Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape

The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean-field homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori–Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed, which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are studied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.     

Direct Numerical Simulation of a Mach 2 shock interacting with isotropic turbulence

Direct Numerical Simulation (DNS) and linear analysis of a shock interacting with incompressible and compressible isotropic turbulence is conducted. A dependence of amplification ratios on the degree of compressibility of the incoming flow is found. It can be shown that the enhancement of rms values of turbulent quantities across the shock varies according to the ratio of compressible to incompressible kinetic energy (exact definition see eq. 8). Inflow conditions with high values of display reduced amplification ratios of TKE and thermodynamic quantities while vorticity fluctuations are enhanced more strongly. The different behaviour of the turbulent kinetic energy (TKE) is due to the reduced pressure diffusion term in the TKE-equation. Experiments show qualitatively a similar behaviour as the simulation with incompressible inflow conditions, but they could so far not confirm our findings of reduced amplification rates in the compressible case, one of the reasons being the lack of knowledge of all flow parameters upstream of the shock front and the inability to generate isotropic turbulence in real life experiments. For the DNS we use a third order in space shock-capturing scheme based on the ENO algorithm of Harten [10] together with an approximate Riemann solver. This non-TVD scheme turned out to have many advantages over other common Godunov-type high resolution schemes for the specific problem of a shock interacting with turbulent fields.