Lecture Objectives Unsteady State Ventilation Modeling of PM

Steady vs. Unsteady – State Flow Example of velocity at specific point for different activities door walking block fan 20 s recuperation 60 s recuperation Time (s) Velocity (m/s)

Steady vs. Unsteady – State Flow Example of temperature profile at two specific points for different activities

Unsteady-state (Transient) CFD simulations Computationally very expensive Steps Identify the problem Many problems do not require unsteady-state sim. 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

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 for F 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

Steady-state, unsteady-state or 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

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

Time period T and time step Dt Uniform Variable Linear Piecewise User defined

Transient boundaries For unsteady-state airflow created by transient

Transient boundaries For unsteady-state airflow created by transient

Transient Calculation Iterations in different time steps Change of the variable in time

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

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

Properties ASHRAE Transaction 2004

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

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

Lagrangian Model particle tracking A trajectory of the particle in the vicinity of the spherical collector is governed by the Newton’s equation m∙a=SF 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

Lagrangian Model particle 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

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

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

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

Multiphase Flow Regimes Fluent user manual 2006