1. Lecture Objectives
Ventilation Effectiveness, Thermal Comfort, and other CFD results representation
Surface Radiation Models
Particle modeling

2. Thermal comfort
Temperature and relative humidity

3. Thermal comfort Velocity Can create draft
Draft is related to air temperature,
air velocity, and turbulence intensity.

4. Thermal comfort Mean radiant temperature potential problems Asymmetry
Warm ceiling (----)
Cool wall (---)
Cool ceiling (--)
Warm wall (-)

5. Prediction of thermal comfort
Predicted Mean Vote (PMV)
+ 3 hot
+ 2 warm
+ 1 slightly warm
PMV = 0 neutral
-1 slightly cool
-2 cool
-3 cold
PMV = [0.303 exp ( M ) ] L
L - Thermal load on the body
L = Internal heat production – heat loss to the actual environment
L = M - W - [( Csk + Rsk + Esk ) + ( Cres + Eres )]
Predicted Percentage Dissatisfied (PPD)
PPD = exp [ - ( PMV PMV2)]
Empirical correlations
Ole Fanger
Further Details: ANSI/ASHRAE standard 55, ISO standard 7730

6. Surface Radiation Models Combined with CFD
Example:
Heat transfer through
a window
Cavity:
CFD
Domain

7. 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

8. Properties
ASHRAE
Transaction 2004

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

10. Modeling of PM: We need to say something about 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

11. Multiphase Flow Regimes
Fluent user manual 2006

12. Two basic approaches for modeling of particle dynamics
PM Modeling
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

13. 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

14. 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

15. 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

16. Forces that affect the particle
The drag force is the most significant force and it depends on
Particle and fluid velocities
Reynolds number defined
for particle fluid velocity difference
Drag coefficient:       
a1, a2,a3 are constants that apply to smooth spherical particles
or for non spherical particles:
b1, b2,b3, b4 are constants that take into account non-spherical shape of
particles

17. Forces that affect the particle
For sub-micron particles Stokes drag law:
Velocities of air and particle
Where m is fluid viscosity and dp is particle diamete>
Ce is the Cunningham correction factor:
l is the molecular mean free path.
Overall: Drag force depends on the flow parameters such as Reynolds number,
turbulence level,…

18. Forces that affect the particle
External forces
Electrostatic
Thermophoretic
Gravitation
Lift force
Brownian
Brownian force – creates random movement of particles - for sub-micron particles,
Lift force - lift due to shear
Electrostatic – for charged particles
Thermophoretic Force
Small particles suspended in a gas that has a temperature gradient are exposed to
a force in the direction opposite to that of the gradient. This phenomenon is known
as thermophoresis.

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