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Lecture Objectives

Lecture Objectives. Unsteady State Simulation Example Modeling of PM. Computationally expensive Steps Identify the problem Many problems do not require unsteady-state simulation! Identify equations which should be unsteady-state Define the simulation period

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Lecture Objectives

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  1. Lecture Objectives • Unsteady State Simulation • Example • Modeling of PM

  2. Computationally expensive Steps Identify the problem Many problems do not require unsteady-state simulation! Identify equations which should be unsteady-state Define the simulation period Define the required time steps Adjust other simulation parameters turbulence model, mesh, convergence criteria, number of required iterations, etc. Require substantial investigation for each problem Unsteady-state (Transient)CFD simulations

  3. Computationally very expensive Change of  in volume dxdydz In Time Discretize equation System of equation for each time step ap and f are function of Dt f is function of previous value forF = x 1) Solve the system using the simple algorithm 2) Change the boundary conditions 3) Update the coefficient 4) Solve the new system of equations A F

  4. Steady-state, unsteady-stateor quasi-steady-state Examples • Airflow around the airplane • Airflow in the room • Airflow around the building • Injection of pollutant in the chamber experiment • Flow in the automobile engine cylinder • DNS simulation of flow in the boundary layer

  5. Simulation period Depends on the boundary condition of considered phenomenon Time step Depends on the time scale With too large time step quasi-steady-state simulation Simulation period and time step Set of steady state simulations (there is no link in-between previous and next time step)

  6. Time step Dt • Uniform • Variable • Linear • Piecewise • User defined

  7. Transient boundaries • For unsteady-state airflow created by transient boundaries

  8. Particulate matters (PM) • Properties • Size, density, liquid, solid, combination, … • Sources • Airborne, infiltration, resuspension, ventilation,… • Sinks • Deposition, filtration, ventilation (dilution),… • Distribution - Uniform and nonuniform • Human exposure

  9. Properties ASHRAE Transaction 2004

  10. Particle size distribution ASHRAE Transaction 2004 Ventilation system affect the PM concentration in indoor environment !

  11. Two basic approaches for modeling of particle dynamics • Lagrangian Model • particle tracking • For each particle ma=SF • Eulerian Model • Multiphase flow (fluid and particles) • Set of two systems of equations

  12. m∙a=SF Lagrangian Modelparticle tracking A trajectory of the particle in the vicinity of the spherical collector is governed by the Newton’s equation Forces that affect the particle • (rVvolume) particle∙dvx/dt=SFx • (rVvolume) particle∙dvy/dt=SFy • (rVvolume) particle∙dvz/dt=SFz System of equation for each particle Solution is velocity and direction of each particle

  13. Lagrangian Modelparticle tracking Basic equations - momentum equation based on Newton's second law Drag force due to the friction between particle and air - dp is the particle's diameter, - p is the particle density, - up and u are the particle and fluid instantaneous velocities in the i direction, - Fe represents the external forces (for example gravity force). This equation is solved at each time step for every particle. The particle position xi of each particle are obtained using the following equation: For finite time step

  14. Algorithm for CFD and particle tracking Unsteady state airflow Steady state airflow Airflow (u,v,w) for time step  Airflow (u,v,w) Steady state Injection of particles Injection of particles Particle distribution for time step  Particle distribution for time step  Airflow (u,v,w) for time step + Particle distribution for time step + Particle distribution for time step + Particle distribution for time step +2 ….. ….. One way coupling Case 1 when airflow is not affected by particle flow Case 2 particle dynamics affects the airflow Two way coupling

  15. Eulerian Model • Solve several sets of NS equations • Define the boundary conditions in-between phases Multiphase/Mixture Model • Mixture model • Secondary phase can be granular • Applicable for solid-fluid simulations • Granular physics • Solve total granular pressure to momentum equation • Use Solids viscosity for dispersed solid phase • Density difference should be small. • Useful mainly for liquid-solids multiphase systems There are models applicable for particles in the air

  16. Multiphase flow Multiphase flow can be classified in the following regimes: • gas-liquid or liquid-liquid flows • gas-solid flows • particle-laden flow: discrete solid particles in a continuous gas • pneumatic transport: flow pattern depends on factors such as solid loading, Reynolds numbers, and particle properties. Typical patterns are dune flow, slug flow, packed beds, and homogeneous flow. • fluidized beds: consist of a vertical cylinder containing particles where gas is introduced through a distributor. • liquid-solid flows • three-phase flows

  17. Multiphase Flow Regimes Fluent user manual 2006

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