1. Lecture Objectives Learn about particle dynamics modeling
Discuss project and result accuracy evaluation

2. 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

3. Properties
ASHRAE
Transaction 2004

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

5. Human exposure
ASHRAE Transaction 2004

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Multiphase Flow Regimes
Fluent user manual 2006

13. Challenging Problem: Application of CFD in a large space
EXAMPLE:
Five-Story Parking Garage Ventilation
Multi-space building
Course grid model properties
- The geometry should present correct geometry around large openings
- The ratio between the total flow area and the floor area should be the same as in full scale
- Air supply and return openings should be defined in a coarse grid sufficient for momentum and energy flow predictions
The result will define global air and energy flow between zones but accuracy is insufficient for an analysis of the detail air velocity distribution in the zones.

14. Detail air velocity distribution in room
Detail description
of geometry
Simple Description of Interior
Furnishings can be described as
A volume with additional pres-
sure drop in the momentum
Equations:

15. Engineering Application
Unlimited number of problems!
For example:

16. Human Exposure Airflow in the room vs. Airflow in vicinity of occupant
CO2 distribution
- Course mesh
- Simple geometry
CO2
sources
Occupied zone

17. Simulation of an occupant
Detailed geometry:
Good for local convection coefficient calculation at the skin
Effect of breathing an movement decrease accuracy

18. Different level of geometry details
Avaraged geometry can be used for global effects
Simple geometry can be used for semi-global effects
Detailed geometry should be used for local effects
Conclusions from geometry analysis (Peter Nielsen)
Semi-global effect
Differences in geometry have a small influence on
velocity, temperature distribution, contaminant distribution
far from the manikin
Local effect
Differences in geometry have an effect on velocity and
concentration distribution close to a person and exposure of
a person

19. We Often Need Experimental Validation
Room with nonuniform temporal
and spatial distribution of particles
(for example smoke)
Validation results for 0.74 m S1
CFD model
Monitoring
Position S1
Monitoring
Position S2 S2
Pollution Source
active 2 minutes
Experiment

20. Examples of CFD application in Indoor environment research
Some hot topics
Particle Transport in a boundary layer
Surface Chemistry
Air and particle flow in lung
Various analyses of fluid flow in building components and HVAC systems