Turbulent dispersed multiphase flows are common in many engineering and environmental applications. The stochastic nature of both the carrier-phase turbulence and the dispersed-phase distribution makes the problem of turbulent dispersed multiphase flow far more complex than its single-phase counterpart. In this article we first review the current state-of-the-art experimental and computational techniques for turbulent dispersed multiphase flows, their strengths and limitations, and opportunities for the future. The review then focuses on three important aspects of turbulent dispersed multiphase flows: the preferential concentration of particles, droplets, and bubbles; the effect of turbulence on the coupling between the dispersed and carrier phases; and modulation of carrier-phase turbulence due to the presence of particles and bubbles.

Turbulent Dispersed Multiphase Flow

▪ Abstract Relationships between small and large scales of motion in turbulent flows are of much interest in large-eddy simulation of turbulence, in which small scales are not explicitly resolved and must be modeled. This paper reviews models that are based on scale-invariance properties of high-Reynolds-number turbulence in the inertial range. The review starts with the Smagorinsky model, but the focus is on dynamic and similarity subgrid models and on evaluating how well these models reproduce the true impact of the small scales on large-scale physics and how they perform in numerical simulations. Various criteria to evaluate the model performance are discussed, including the so-called a posteriori and a priori studies based on direct numerical simulation and experimental data. Issues are addressed mainly in the context of canonical, incompressible flows, but extensions to scalar-transport, compressible, and reacting flows are also mentioned. Other recent modeling approaches are briefly introduced.

Scale-Invariance and Turbulence Models for Large-Eddy Simulation

The dynamic model for large-eddy simulation of turbulence samples information from the resolved velocity field in order to optimize subgrid-scale model coefficients. When the method is used in conjunction with the Smagorinsky eddy-viscosity model, and the sampling process is formulated in a spatially local fashion, the resulting coefficient field is highly variable and contains a significant fraction of negative values. Negative eddy viscosity leads to computational instability and as a result the model is always augmented with a stabilization mechanism. In most applications the model is stabilized by averaging the relevant equations over directions of statistical homogeneity. While this approach is effective, and is consistent with the statistical basis underlying the eddy-viscosity model, it is not applicable to complex-geometry inhomogeneous flows. Existing local formulations, intended for inhomogeneous flows, are most commonly stabilized by artificially constraining the coefficient to be positive. In this paper we introduce a new dynamic model formulation, that combines advantages of the statistical and local approaches. We propose to accumulate the required averages over flow pathlines rather than over directions of statistical homogeneity. This procedure allows the application of the dynamic model with averaging to in-homogeneous flows in complex geometries. We analyse direct numerical simulation data to document the effects of such averaging on the Smagorinsky coefficient. The characteristic Lagrangian time scale over which the averaging is performed is chosen based on measurements of the relevant Lagrangian autocorrelation functions, and on the requirement that the model be purely dissipative, guaranteeing numerical stability when coupled with the Smagorinsky model. The formulation is tested in forced and decaying isotropic turbulence and in fully developed and transitional channel flow. In homogeneous flows, the results are similar to those of the volume-averaged dynamic model, while in channel flow, the predictions are slightly superior to those of the spatially (planar) averaged dynamic model. The relationship between the model and vortical structures in isotropic turbulence, as well as ejection events in channel flow, is investigated. Computational overhead is kept small (about 10% above the CPU requirements of the spatially averaged dynamic model) by using an approximate scheme to advance the Lagrangian tracking through first-order Euler time integration and linear interpolation in space.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/783398B2D0BE53C120151E4E911CA833/S0022112096007379a.pdf/div-class-title-a-lagrangian-dynamic-subgrid-scale-model-of-turbulence-div.pdf

A Lagrangian dynamic subgrid-scale model of turbulence

This article reviews the physical processes responsible for the transport and deposition of particles and their theoretical modeling. Both laminar and turbulent processes are considered, emphasizing the physical understanding of the various transport mechanisms. State-of-the-art computational methods for determining particle motion and deposition are discussed, including stochastic Lagrangian particle tracking and a unified Eulerian advection-diffusion approach. The theory presented includes Brownian and turbulent diffusion, turbophoresis, thermophoresis, inertial impaction, gravitational settling, electrical forces, and the effects of surface roughness and particle interception. The article describes two example applications: the deposition of particles in the human respiratory tract and deposition in gas and steam turbines.

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Transport and Deposition of Particles in Turbulent and Laminar Flow

▪ Abstract A Lagrangian description of turbulence has unique physical advantages that are especially important in studies of mixing and dispersion. We focus on fundamental aspects, using mainly data from direct numerical simulations capable of great detail and precision when specific accuracy requirements are met. Differences between time evolution in Eulerian and Lagrangian frames illustrate the dominance of advective transport. We examine basic results in Kolmogorov similarity, giving an estimate of an inertial-range universal constant and the grid resolution and Reynolds number needed to attain the requisite scaling range of time lags. The Lagrangian statistics of passive scalars are discussed in view of current efforts in model development, with differential diffusion between multiple scalars being characterized by shorter timescales. We also note the need for new data in more complex flows and in other applications where a Lagrangian viewpoint is especially useful.

Lagrangian investigations of turbulence

Particle transport in fully‐developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Reτ, of 180 and 644 (based on friction velocity and channel half width); subgrid‐scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedings of the 7th Workshop on Two‐Phase Flow Predictions (1994)] and experimental measurements of Kulick et al. [J. Fluid Mech. 277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Reτ=180 are in good agreement with the DNS; reas...

Large eddy simulation of particle‐laden turbulent channel flow

Lagrangian statistics in turbulent channel flow

The extension of the fractional step method to three-dimensional, time-dependent incompressible flaws in non-orthogonal curvilinear coordinate systems is presented. A formulation based on block-LU decomposition is combined with a mixed implicit / explicit treatment of the discretized equations. Using local volume fluxes as dependent variables, the block-LU decomposition enables a unique definition of the sequential operations of the fractional step method for general coordinate systems. In this work a semi-direct scheme is developed for solution of the Poisson equation using series expansion along one coordinate direction that is discretized on a uniform, Cartesian grid. Also investigated in this study is solution of a simplified Poisson equation obtained by neglecting cross derivatives in the full Poisson equation. It is shown that for fractional step methods satisfaction of the zero-divergence constraint is still possible using the simplified Poisson equation, but the associated error is larger...

Qunzhen Wang

Papers

Large eddy simulation of particle‐laden turbulent channel flow

Lagrangian statistics in turbulent channel flow

Extension of the fractional step method to general curvilinear coordinate systems

Large eddy simulation of particle dispersion in a three-dimensional turbulent mixing layer