1. Lecture Objectives
Unsteady State Ventilation
Modeling of PM

2. 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)

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

4. 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

5. 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

6. 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

7. 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)

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

9. Transient boundaries For unsteady-state airflow created by transient

10. Transient boundaries For unsteady-state airflow created by transient

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

12. 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

13. 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

14. Properties
ASHRAE
Transaction 2004

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

16. 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

17. 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

18. 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

19. 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

20. 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

21. 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

22. Multiphase Flow Regimes
Fluent user manual 2006