## Finite-size Effects in LES of Two-phase Flows

LES of two-phase flows commonly employs Eulerian equations for the carrier (continuum) fluid and Lagrangian formulation for the dispersed phase. The dispersed phase is treated as “point-particles” with advanced models for inter-phase mass-momentum, and energy transport.

In practical applications such as spray combustion, liquid atomization, plasma spray coating, fluidized beds, aerosol transport, bubbly and granular flows, sedimentation and bed-load transport etc., the local particle size and concentrations vary substantially.The dispersed particle size may become larger than the smallest resolved length scale in LES. The “point-particle” assumption is invalid in these regions. Effect of displacement of the carrier fluid by dispersed phase is not correctly captured by point-particle model in these regions.

Here, we extended the point-particle approximation by accounting for the finite-size of the dispersed phase. We validate this model by simulating capture Poisuille flow with solid particles arranged at the bottom of the channel (DNS by Choi & Joseph, JFM 2000). The standard point-particle approach does not predict any lift force on the particles and the particle layer moves in laminar layers. The finite-size model leads to Kelvin-Helmholtz type instability in the gas-phase velocity and lift of particles similar to the DNS.

We apply this model to simulate liquid film formation, spray evolution and breakup in the near injector region. In addition, several other applications such as fluidization by air jet, particle sedimentation, and turbulence modulation by dispersed phase are being studied.

Apte, S.V., Mahesh, K., & Lundgren, T., *“A Eulerian-Lagrangian model to simulate two-phase/particulate flows,”* Annual Research Briefs, Center for Turbulence Research, Stanford, 2003.

Apte, S.V., Mahesh, K., & Lundgren, T, *“Accounting for finite-size effects in LES of two-phase flows,”* IUTAM Symposium, Argonne National Lab, October, 2004.