Dispersion In Turbulent Flow Research Articles

Spectral analysis of dispersed multiphase flows in the presence of fluid interfaces

Spectral analysis of dispersed two-phase flows is highly desirable to reveal the interplay of the various flow scales, much larger or much smaller than the size of the dispersed bodies. This is a challenging task as the matching conditions at the body interfaces generate singularities in the fields describing the two-phase mixture. The nature of these singularities and their consequences on the spectra are theoretically analyzed for bubble or droplet flows. Results of direct numerical simulations are reported and spatial spectra of the mixture velocity, the flow forces and their power are examined. The regular part of the spectral densities of energy production, dissipation and transfers between scales are separated from their singular part. The resulting spectral energy balance, free of the footprint of the singularities, is found in agreement with coarse-grained simulations where the interfaces are filtered out before solving the Navier–Stokes equations. These results pave the way for the spectral analysis of more complex turbulent dispersed flows.

Probabilistic model of dispersed turbulent flow in channels with rough walls

An equation for the probability density function (PDF) for particle velocity and coordinates in a gas turbulent flow is derived. The system of equations for the first and second moments of particle...

Dynamic load balancing for a mesh‐based scientific application

SummaryCMT‐nek is a new scientific application for performing high fidelity predictive simulations of particle‐laden, explosively dispersed turbulent flows. CMT‐nek is compute‐intensive and targeted for deployment on exascale platforms. The moving particles are the primary source of load imbalance when the application is executed on parallel processors. In a demonstration problem, all the particles are initially in a closed container until a detonation occurs and the particles move apart. If all processors get an equal share of the fluid domain, then only some of the processors get sections of the domain that are initially laden with particles, leading to disparate loads on the processors. To eliminate load imbalance in different processors and to speed up the makespan, we present different load‐balancing algorithms for CMT‐nek on large‐scale multicore platforms. The load on a processor is determined using different techniques. The performance of the different load‐balancing algorithms is compared, and the associated overheads are analyzed. Evaluations of the application with and without load‐balancing are conducted, and these show that with load‐balancing, simulation time becomes faster by a factor of up to 9.97. The performance was further improved by a factor of up to 1.42 using machine‐learning–based algorithms.

A Simple Physically-Based Model for Wind-Turbine Wake Growth in a Turbulent Boundary Layer

The growth rate of wind-turbine wakes in the atmospheric boundary layer is a key parameter in analytical models used to predict wind-turbine wakes and their effects in wind farms. To date, the turbine-wake growth rate is determined empirically, owing to our limited understanding of the physical mechanisms leading to the recovery of the wakes in turbulent flows. Here, a simple physically-based model for wind-turbine wake growth is proposed based on the analogy with scalar dispersion in turbulent flows. The model is developed based on Taylor’s diffusion theory and intrinsically accounts for the effect of ambient turbulence intensity. In validations against large-eddy simulations of the wake flow of a turbine under different inflow turbulence conditions, it is found that the model yields good predictions of the growth of the turbine wakes. A slight underestimation of the wake growth rate is found only in the lowest ambient turbulence case, due to the non-negligible contribution of the turbine-induced turbulence in that case.

Large-eddy simulation of turbulent dispersed flows: a review of modelling approaches

In large-eddy simulation (LES) of turbulent dispersed flows, modelling and numerical inaccuracies are incurred because LES provides only an approximation of the filtered velocity. Interpolation errors can also occur (on coarse-grained domains, for instance). These inaccuracies affect the estimation of the forces acting on particles, obtained when the filtered fluid velocity is supplied to the Lagrangian equation of particle motion, and accumulate in time. As a result, particle trajectories in LES fields progressively diverge from particle trajectories in DNS fields, which can be considered as the exact numerical reference: the flow fields seen by the particles become less and less correlated, and the forces acting on particles are evaluated at increasingly different locations. In this paper, we review models and strategies that have been proposed in the Eulerian–Lagrangian framework to correct the above-mentioned sources of inaccuracy on particle dynamics and to improve the prediction of particle dispersion in turbulent dispersed flows.

Turbulent spectrum model for drop-breakup mechanisms in an inhomogeneous turbulent flow

Drop-breakup models for liquid/liquid dispersion in turbulent flow mostly derive from Kolmogorov and Hinze analysis. They are of a semi-empirical type, since they are based on power laws involving at least Weber and Reynolds numbers. The pre-factors are determined by fitting the experimental data on droplet diameters in the various configurations. The main cause for the discrepancies in the fitting constant between different flow types is the intrinsic spatial heterogeneity of the turbulent field, especially the turbulent kinetic energy (TKE) dissipation rate ε. This feature explains why there is no universal physical model suitable for breakup prediction throughout the range of flow geometries.In the present work, we investigate the drop size distribution by reference to Hinze's actual theory in a local approach, attempting a direct interpretation thanks to the turbulence spectra measured (by LDA) in the most dissipative locations of a flow which is basically inhomogeneous. This method allows estimation of droplet size with no constant fitting and with acceptable accuracy; however the knowledge of the turbulence field is required. The present study is carried out with low dispersed-phase fraction, so that the coalescence is negligible. Experiments show that the “typical value” for the TKE dissipation rate to fit the raw model of Hinze and Kolmogorov lies between the maximum and the mean value in the flow field. The issue of “typical ε value” hence avoided is discussed by physical arguments for the flow structure.

Adaptive stochastic trajectory modelling in the chaotic advection regime

Motivated by the goal of improving and augmenting stochastic Lagrangian models of particle dispersion in turbulent flows, techniques from the theory of stochastic processes are applied to a model transport problem. The aim is to find an efficient and accurate method to calculate the total tracer transport between a source and a receptor when the flow between the two locations is weak, rendering direct stochastic Lagrangian simulation prohibitively expensive. Importance sampling methods that combine information from stochastic forward and back trajectory calculations are proposed. The unifying feature of the new methods is that they are developed using the observation that a perfect strategy should distribute trajectories in proportion to the product of the forward and adjoint solutions of the transport problem, a quantity here termed the ‘density of trajectories’ $D(\boldsymbol{x},t)$. Two such methods are applied to a ‘hard’ model problem, in which the prescribed kinematic flow is in the large-Péclet-number chaotic advection regime, and the transport problem requires simulation of a complex distribution of well-separated trajectories. The first, Milstein’s measure transformation method, involves adding an artificial velocity to the trajectory equation and simultaneously correcting for the weighting given to each particle under the new flow. It is found that, although a ‘perfect’ artificial velocity $\boldsymbol{v}^{\ast }$ exists, which is shown to distribute the trajectories according to $D$, small errors in numerical estimates of $\boldsymbol{v}^{\ast }$ cumulatively lead to difficulties with the method. A second method is Grassberger’s ‘go-with-the-winners’ branching process, where trajectories found unlikely to contribute to the net transport (losers) are periodically removed, while those expected to contribute significantly (winners) are split. The main challenge of implementation, which is finding an algorithm to select the winners and losers, is solved by a choice that explicitly forces the distribution towards a numerical estimate of $D$ generated from a previous back trajectory calculation. The result is a robust and easily implemented algorithm with typical variance up to three orders of magnitude lower than the direct approach.

Numerical Investigation on Mass Dispersion in Turbulent Flows through Porous Media with High Porosity

With porous combustor as engineering background, the mass dispersion process of methane and air in highly porous media is studied numerically based on a simplified model for the periodical structure of the porous media. The computational results obtained from the microscopic flow field within a unit cell, i.e., a representative elementary volume, into which a low Reynolds number turbulent model is incorporated, are employed to compute the longitudinal and transverse dispersion coefficients through a volume average approach. The results are compared with experimental data and empirical formulas available in the literature, and a reasonable agreement is achieved.

Numerical simulation of nanoparticles diffusion and coagulation in a twin-jet via a TEMOM method

Purpose– The purpose of this paper is to study nanoparticles diffusion and coagulation processes in a twin-jet.Design/methodology/approach– Large eddy simulation (LES) and Taylor-series expansion moment method (TEMOM) are employed to deal with a nanoparticle-laden twin-jet flow.Findings– The numerical results show that the interaction of the two jets and turbulence eddy structures rolling-up, paring and shedding in flow sharply affects particles number concentration. Particle diameter grows quickly at the interfaces of jets. Coagulation shows more obvious effect at initial stage than that in the subsequent period. Then diffusion makes the particle diameter distribution much more uniform.Originality/value– In recent years a great number of attentions have been focussed on the issue of particulate dynamics processes including diffusion, coagulation and deposition, etc. However, up to now few works have been focus on the nanoparticles coagulation and dispersion in turbulent flows. The investigation on the diffusion and coagulation process of nanoparticles using TEMOM in a twin-jet flow has not been found.

A dynamic model for the Lagrangian stochastic dispersion coefficient

A stochastic sub-grid model is often used to accurately represent particle dispersion in turbulent flows using large eddy simulations. Models of this type have a free parameter, the dispersion coefficient, which is not universal and is strongly grid-dependent. In the present paper, a dynamic model for the evaluation of the coefficient is proposed and validated in decaying homogeneous isotropic turbulence. The grid dependence of the static coefficient is investigated in a turbulent mixing layer and compared to the dynamic model. The dynamic model accurately predicts dispersion statistics and resolves the grid-dependence. Dispersion statistics of the dynamically calculated constant are more accurate than any static coefficient choice for a number of grid spacings. Furthermore, the dynamic model produces less numerical artefacts than a static model and exhibits smaller sensitivity in the results predicted for different particle relaxation times.

Application of POD-based dynamical systems to dispersion and deposition of particles in turbulent channel flow

This paper concerns the numerical modeling of heavy particle motion in a turbulent flow. Instantaneous fluid velocity is simulated by low-order dynamical systems based on Proper Orthogonal Decomposition (POD), or the eigenfunction expansion, which is a mathematical tool that can be used to identify the most energetic structures of the flow. The POD basis was built using two-point velocity correlations obtained from the Direct Numerical Simulation (DNS) of a channel flow. In addition to the two proposals already described from the literature, a new dynamical system with considerably less modes was constructed. The dynamical systems were assessed by comparing the resulting fluid velocity statistics with the DNS data. The Lagrangian approach was used to track inertial particles, which were one-way coupled to the velocity field generated by these dynamical systems. In the dispersion study, where the particles are allowed to collide elastically with the walls, the particle number density profiles and velocity statistics were compared to the available DNS benchmark. In the case of particle wall separation, the results for deposition velocity were evaluated with experimental data. The characteristic features of the POD-based simulations of dispersed turbulent flows are shown, potential areas of application are suggested, and the limitations of the approach are discussed.

Lagrangian scale of particle dispersion in turbulence

Transport of mass, heat and momentum in turbulent flows by far exceeds that in stable laminar fluid motions. As turbulence is a state of a flow dominated by a hierarchy of scales, it is not clear which of these scales mostly affects particle dispersion. Also, it is not uncommon that turbulence coexists with coherent vortices. Here we report on Lagrangian statistics in laboratory two-dimensional turbulence. Our results provide direct experimental evidence that fluid particle dispersion is determined by a single measurable Lagrangian scale related to the forcing scale. These experiments offer a new way of predicting dispersion in turbulent flows in which one of the low energy scales possesses temporal coherency. The results are applicable to oceanographic and atmospheric data, such as those obtained from trajectories of free-drifting instruments in the ocean.

Numerical simulation of two-phase flow with bubble break-up and coalescence coupled with population balance modeling

A computational fluid dynamic (CFD) model was developed with an improved source term based on previous work by Hagesaether et al. [1] for bubble break up and bubble coalescence to carry out numerical prediction of number density of different bubble class in turbulent dispersed flow. The numerical prediction was based on two fluid models, using the Eulerian–Eulerian approach where the liquid phase was treated as a continuum and the gas phase (bubbles) was considered as a dispersed phase. Bubble–bubble interactions, such as breakage due to turbulence and coalescence due to the combined effect of turbulence and laminar shear were considered. The result shows that the radial distributions of number densities of lower bubble classes are more than its higher counterpart. The result also shows that the Sauter mean diameter increases with the increase of height up to 1m and then become steady. Simulated results are found to be in good agreement with the experimental data.

Dispersion in fully developed flow through regular porous structures: Experiments with wire-mesh sensors

Within this study the wire-mesh sensor is proposed as a suitable device to investigate radial and axial dispersion in tubular reactors. Axial dispersion in turbulent flow through a regular highly porous structure is addressed and the effect of reactor length on the estimated axial dispersion coefficient is discussed. We state that the gradual increase of turbulence intensity in the entrance section of the porous structure is an effect which leads to a length dependence of the dispersion coefficient. Furthermore, we present measurements of radial mixing by the wire-mesh sensor and compare it to reference measurements using laser induced fluorescence. By that we discuss the possible bias from non-homogeneous tracer distribution between the electrodes. Despite the differences of the measurement principles we found a good qualitative agreement between the results.

Flow regimes and drop break-up in SMX and packed bed static mixers

We present experimental investigations with SMX and packed bed (PBM) static mixers for power consumption during steady flow of Newtonian fluids and liquid–liquid dispersion in turbulent flow. Newton (Ne) and Reynolds (Re) numbers for obtaining power characteristics were calculated based on interstitial flow in the static mixers. The proposed correlations agreed well with those in literature and showed that at very high Re, meaning in fully turbulent flow, Ne for PBM is almost half of that for SMX. Furthermore, PBM and SMX were compared by measuring drop size distributions and pressure drops during formation of oil-in-water emulsions with different flow rates and residence times, the latter being varied by passing emulsions several times through static mixers of different lengths. The prediction of median drop diameter in terms of Weber (We) and Newton numbers using Kolmogorov–Hinze theory for isotropic turbulent-inertial flow regime involving specific energy dissipation rate is found to be valid only for SMX static mixer. In contrast, the turbulent flow is anisotropic in PBM resulting in higher exponents of We and Ne than theoretically predicted. In addition, the use of short static mixers enabled to present models including an empirical term to account for kinetic effects. However, the median diameters of drops formed in SMX and PBM are about the same at a given specific energy dissipation rate, even though the corresponding volume flow rate is higher in SMX than that in PBM.

Multi-particle and tetrad statistics in numerical simulations of turbulent relative dispersion

The evolution in size and shape of three and four-particle clusters (triangles and tetrads, respectively) in isotropic turbulence is studied using direct numerical simulations at grid resolution up to 40963 and Taylor-scale Reynolds numbers from 140 to 1000. A key issue is the attainment of inertial range behavior at high Reynolds number, while the small- and large-time limits of ballistic and diffusive regimes, respectively, are also considered in some detail. Tetrad size expressed by the volume (V) and (more appropriately) the gyration radius (R) is shown to display inertial range scaling consistent with a Richardson constant close to 0.56 for two-particle relative dispersion. For tetrads of initial size in a suitable range moments of shape parameters, including the ratio V2/3/R2 and normalized eigenvalues of a moment-of-inertia-like dispersion tensor, show a regime of near-constancy which is identified with inertial-range scaling. Sheet-like structures are dominant in this period, while pancakes and needles are more prevalent at later times. For triangles taken from different faces of each tetrad effects of the initial shape (isosceles right-angled or equilateral) are retained only for about one Batchelor time scale. In the inertial range there is a prevalence of nearly isosceles triangles of two long sides and one short side, representing one particle moving away from the other two which are still close together. In general, measures of shape display asymptotic scaling ranges more readily than measures of size. With some caveats, the simulation results are also compared with the limited literature available for multiparticle cluster dispersion in turbulent flow.

Computational Fluid Dynamics Application of the Diffusion-Inertia Model to Bubble Flows and Boiling Water Problems

This paper is aimed at the application of a model for simulating the dispersed turbulent flows. The presented model proceeds from a kinetic equation for the probability density function of the particle velocity distribution in turbulent flow. This approach is called the diffusion-inertia model (DIM). Applications of the model to droplet and bubble flows are presented. In the case of vaporized liquid, the interphase heat and mass transfer is introduced by adding the corresponding governing equations. This extended version of the DIM was applied to simulating the boiling water flow in a heated pipe.

Lagrangian particle dispersion in turbulent flow over a wall mounted obstacle

Large-eddy simulations (LES) of particle-laden turbulent flows are presented in order to investigate the effects of particle response time on the dispersion patterns of a space developing flow with an obstruction, where solid particles are injected inside the wake of an obstacle [Vincont, J.Y., Simoens, S., Ayrault M., Wallace, J.M., 2000. Passive scalar dispersion in a turbulent boundary layer from a line source at the wall and downstream of an obstacle. J. Fluid Mech. 424, 127–167]. The numerical method is based on a fully explicit fractional step approach and finite-differences on Cartesian grids, using the immersed boundary method (IBM) to represent the existence of solid obstacles. Two different turbulence models have been tested, the classical Smagorinsky turbulence model and the filtered structure function model. The dispersed phase was modelled either by an Eulerian approach or a Lagrangian particle tracking scheme of solid particles with Stokes numbers in the range St = 0–25, assuming one-way coupling between the two phases. A very good agreement was observed between the Lagrangian and Eulerian approaches. The effect of particle size was found to significantly differentiate the dispersion pattern for the inhomogeneous flow over the obstacle. Although in homogeneous flows like particle-laden turbulent channels near-wall particle clustering increases monotonically with particle size, for the examined flow over an obstacle, preferential concentration effects were stronger only for an intermediate range of Stokes numbers.

Telegraph-Type versus Diffusion-Type Models of Turbulent Relative Dispersion

Properties of two equations describing the evolution of the probability density function of the relative dispersion in turbulent flow are compared by investigating their solutions: the self-similar telegraph equation derived by Ogasawara and Toh and the Richardson diffusion equation with the drift term. The solution of the self-similar telegraph equation vanishes at a finite point, while that of the Richardson equation extends infinitely just after the initial time. Each equation has a similarity solution, which is found to be an asymptotic solution of the initial value problem. The time lag has a dominant effect on the relaxation process into the similarity solution. The approaching time to the similarity solution can be reduced by advancing the time of the similarity solution appropriately. The Batchelor scaling is observed only for the telegraph case. The Richardson constant is estimated using the similarity solutions of both equations for our previous direct numerical simulation of two-dimensional free convection turbulence.

Appraisal of energy recovering sub-grid scale models for large-eddy simulation of turbulent dispersed flows

Current capabilities of Large-Eddy Simulation (LES) in Eulerian-Lagrangian studies of dispersed flows are limited by the modeling of the Sub-Grid Scale (SGS) turbulence effects on particle dynamics. These effects should be taken into account in order to reproduce accurately the physics of particle dispersion since the LES cut-off filter removes both energy and flow structures from the turbulent flow field. In this paper, we examine the possibility of including explicitly SGS effects by incorporating ad hoc closure models in the Lagrangian equations of particle motion. Specifically, we consider candidate models based on fractal interpolation and approximate deconvolution techniques. Results show that, even when closure models are able to recover the fraction of SGS turbulent kinetic energy for the fluid velocity field (not resolved in LES), prediction of local segregation and, in turn, of near-wall accumulation may still be inaccurate. This failure indicates that reconstructing the correct amount of fluid and particle velocity fluctuations is not enough to reproduce the effect of SGS turbulence on particle near-wall accumulation.