Numerical Study of Multi-Scale Sediment Dynamics in Estuaries and Coastal Oceans

Mixing sediment plumes in Gulf of Mexico (image credit: NASA Earth Observatory - http://earthobservatory.nasa.gov)Numerical Simulation of Turbulent Rayleigh-Taylor Instability Induced by the Suspension of Fine ParticlesYi-Ju Chou ()

Multi-Scale Flow Physics & Computation Lab.Institute of Applied MechanicsNational Taiwan University

Sediment River Plumeimage credit: NASA Earth Observatory - http://earthobservatory.nasa.gov)Ocean acidificationPhytoplankton bloomSubaqueous ecology

Parsons et al, 2001OutlineBackground and motivationMathematical formulationNumerical examples of RT instabilitySummary

Physics BackgroundPhysics Background

Balachandar & Eaton, Annual Rev. Fluid Mech., 2010Modeling strategy for dispersed two-phase turbulent flows :Review of Existing MethodSingle-phase method:

Has been employed to study a number of problems related to fine suspensions using DNS, LES, RANSEquilibrium state: A balance between drag and gravitational forceScalar limit:Zero-volume for particles

+ Basset history term+ Saffman lift force: Density ratio: Added-mass coefficient (1/2 for the sphere): Particle relaxation timeDragPressureAdded massGravityMotion of a Sediment GrainMotivationWhat are we trying to answer? How can the equilibrium state be a good approximation?What else are we missing, and how they effect bulk mixing? Can we improve the current model without too much extra computational effort? Mathematical FormulationA two-way coupled Euler-Euler solid-liquid system

Mathematical FormulationA two-phase fractional-step pressure projection method

Non-Boussinesq pressure Poison solver:Corrector: Pressure projectionDiffers from traditional models for solid-gas systems in Three-dimensional turbulence-resolving two-flow system (LES, DNS)Added mass effect (Auton, 1988)

Mixture incompressibility (a two-phase pressure projection method)

Mathematical FormulationMathematical FormulationWhat are we missing? (Chou et al., 2013b) Non-equilibrium particle inertia (NEPI)NEPI effect in the carrier flow (continuous phase)Mixture incompressibility

Particle Induced RT Instability-- A numerical study of two-phase effect in suspensions0.08 m (128)0.08 m (128)0.12 m (192)Simulation setup (Chou et al., 2013b) Growth of Initial Perturbations

Large-Scale Mixing

Growth of mixing zone

Energy SpectrumEnergetic

Slightly higher energy release induced by non-equilibrium particle inertia

Energetic

Feedbacks to the carrier flow are increasingly important

Energetic

* * 2-phase modeling without mixture incompressibilityDue to mixture incompressibility

SummaryWe aim to investigate effects of missing mechanisms induced by two-phase interactions in the common modeling approach for sediment suspension problems.

The two-phase effects include: -- non-equilibrium particle inertia (NEPI); -- NEPI in the carrier fluid; -- mixture incompressibility (MI)

A series of numerical experiments of RT reveals that -- In low volume fraction, NEPI slightly enhances the energy budget. -- As concentration increases, NEPI and MI become increasing important, which suppress energy. -- MI is significant to suppress energy budget at high concentration, which accounts for almost of the reduction of the PE release.

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