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Publication# Particle subgrid scale modeling in hybrid RANS/LES of turbulent channel flow at low to moderate Reynolds number

Abstract

Particle dispersion in a periodic channel is studied using the elliptic relaxation hybrid RANS/LES (ER-HRL) model. This approach employs a four-equation linear eddy viscosity (LEV) model while in Reynolds Averaged Navier-Stokes (RANS) mode near the wall, and switches to the LES Smagorinsky dynamic model in the outer flow region. We perform a systematic analysis of the dispersion of six sets of particles having Stokes numbers St = 0.2, 1, 5, 15, 25, 125 at shear Reynolds numbers of Reτ=150, 590. To account for the effect of the unresolved scales on particle dispersion, a novel subgrid-scale model (SGS) is proposed based on the wall-normal RMS of the velocity transport equation. The ER-HRL model is validated against DNS and LES databases, with a globally good agreement. For higher Reynolds number i.e. Reτ = 590, the model, with a much coarser grid, outperforms the LES subgrid stochastic acceleration (LES-SSAM) approach.

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Reynolds number

In fluid mechanics, the Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents).

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Computational fluid dynamics

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.

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