Sarma L. Rani

Clustering of aerosol particles in isotropic turbulence

It has been recognized that particle inertia throws dense particles out of regions of high vorticity and leads to an accumulation of particles in the straining-flow regions of a turbulent flow field. However, recent direct numerical simulations (DNS) indicate that the tendency to cluster is evident even at particle separations smaller than the size of the smallest eddy. Indeed, the particle radial distribution function (RDF), an important measure of clustering, increases as an inverse power of the interparticle separation for separations much smaller than the Kolmogorov length scale. Motivated by this observation, we have developed an analytical theory to predict the RDF in a turbulent flow for particles with a small, but non-zero Stokes number. Here, the Stokes number (St) is the ratio of the particles viscous relaxation time to the Kolmogorov time. The theory approximates the turbulent flow in a reference frame following an aerosol particle as a local linear flow field with a velocity gradient tensor and acceleration that vary stochastically in time

A locally implicit improvement of the equilibrium Eulerian method

Abstract The equilibrium Eulerian method is a simple way to determine the velocity field of a disperse system of particles. It avoids solving a partial differential equation for particle velocity, which makes it more efficient than the standard Eulerian–Eulerian method. It captures such essential disperse-phase physics as preferential concentration and turbophoretic migration––effects which are ignored by methods that set the particle velocity equal to the fluid velocity. Although the equilibrium Eulerian method works well for small particles, it fails for particles that are too large. This paper presents a straightforward improvement to the method which minimizes the error for larger particles, thereby extending the method’s range of applicability. In particular, it is demonstrated that the modified method captures a physical mechanism neglected by unmodified method: the memory a particle retains when it migrates to an adjacent layer of fluid. The improvement is demonstrated in a direct numerical simulation (DNS) of turbulent channel flow, where particles migrate toward the wall through a strong shear. It is also demonstrated that the modified method performs well in a case where no mean shear is present: a DNS of isotropic turbulence.

Boundary-Layer Equation-Based Wall Model for Large-Eddy Simulation of Turbulent Flows with Wall Heat Transfer

A new thermal boundary-layer model is developed that alleviates the stringent near-wall grid resolution requirement in large-eddy simulations of turbulent flows with wall heat transfer. The model is based on solving the turbulent temperature boundary-layer equation to determine the temperature profile in the near-wall region. The near-wall temperature profile is used to compute the instantaneous wall heat flux, which replaces the temperature (Dirichlet) wall boundary condition specified a priori. This approach is analogous to the wall stress model developed by Balaras et al. [1], in which the instantaneous wall shear stresses replace the no-slip wall boundary conditions. Three benchmark turbulent flows are studied using coarse-grid large-eddy simulations coupled with the new thermal wall model: (1) a fully developed turbulent channel flow with a heated top wall, (2) a backward-facing step flow with a heated bottom wall, and (3) an impinging jet on a heated circular plate. Large-eddy simulations are performed using the commercial code CFD-ACE+, with the localized dynamic subgrid kinetic energy model of Kim and Menon [2] providing the subgrid stresses. Turbulence statistics are compared with benchmark data from direct numerical simulations and experiments and also with data from resolved large-eddy simulations (i.e., near-wall y + ≈ 1). Excellent agreement among the data is obtained.

Computational assessment of subcritical and delayed onset in spiral Poiseuille flow experiments

For spiral Poiseuille flow with radius ratios η ≡ R i /R o = 0.77 and 0.95, we have computed complete linear stability boundaries, where R i and R o are the inner and outer cylinder radii, respectively. The analysis accounts for arbitrary disturbances of infinitesimal amplitude over the entire range of Reynolds numbers Re for which the flow is stable for some range of Taylor number Ta, and extends previous work to several non-zero rotation rate ratios μ ≡ Ω o /Ω i , where Ω i and Ω o are the (signed) angular speeds. For each combination of μ and η, there is a wide range of Re for which the critical Ta is nearly independent of Re, followed by a precipitous drop to Ta = 0 at the Re at which non-rotating annular Poiseuille flow becomes unstable with respect to a Tollmien-Schlichting-like disturbance. Comparison is also made to a wealth of experimental data for the onset of instability

Evaluation of subgrid scale kinetic energy models in large eddy simulations of turbulent channel flow

Purpose – To evaluate the performance of different subgrid kinetic energy models across a range of Reynolds numbers while keeping the grid constant.Design/methodology/approach – A dynamic subgrid kinetic energy model, a static coefficient kinetic energy model, and a “no‐model” method are compared with direct numerical simulation (DNS) data at two friction Reynolds numbers of 180 and 590 for turbulent channel flow.Findings – Results indicate that, at lower Reynolds numbers, the dynamic model more closely matches DNS data. As the amount of energy in the unresolved scales increases, the performance of both kinetic energy models is seen to decrease.Originality/value – This paper provides guidance to engineers who routinely use a single grid to study a wide range of flow conditions (i.e. Reynolds numbers), and what level of accuracy can be expected by using kinetic energy models for large eddy simulations.

A NEW ALGORITHM FOR COMPUTING BINARY COLLISIONS IN DISPERSED TWO-PHASE FLOWS

We present a new algorithm for computing binary collisions in gas particle flows. The algorithm is more efficient but less accurate than a proactive method, but more accurate than a purely retroactive method. The method is used in conjunction with a large-eddy simulation of a gas particle flow in a square duct.

Simplified Two-Fluid Models for Dilute Turbulent Multiphase Flows Using Equilibrium Closure

In two-fluid models of multiphase flow the dispersed phase is treated as a continuum and here we explore the consequences of the dispersed phase being in equilibrium with the surrounding flow. Under equilibrium the particle velocity field can be expressed as an explicit expansion in the surrounding fluid velocity. To the leading order the particle velocity is the same as the local fluid velocity and the first order correction will be shown to capture important physics such as preferential accumulation of particles and turbuphoretic particle migration. To verify the equilibrium expansion, we have performed direct numerical simulations of particles and bubbles in the canonical problems of isotropic turbulence and a turbulent channel flow, where “true” particles moved according to their Lagrangian equations of motion are compared with “test” particles moved according to the equilibrium particle velocity. For small particles the equilibrium expansion is shown to converge rapidly. The equilibrium concept will be extended to the rotational motion and thermal field of the particle. The equilibrium approximation for the particle provides a clean mechanism for two-way coupling and a rigorous set of equations for the description of multi-phase flow turbulence, in the limit of a dilute dispersion of small particles.Copyright