Lecture Objectives

- Finish with age of air modeling

- Introduce particle dynamics modeling

- Analyze some examples related to natural ventilation

Air-change efficiency (v)

• Depends only on airflow pattern in a room• We need to calculate age of air ()

Average time of exchange

• What is the age of air at the exhaust?

Type of flow– Perfect mixing– Piston (unidirectional) flow – Flow with stagnation and short-circuiting flow

2

2

2

2

2

2

z)(

y)(

x)()(

τtttzyx z

Vy

Vx

τV

[sec] ACH/1 τn

Contaminant removal effectiveness ()

• Depends on:- position of a contaminant source- Airflow in the room

• Questions

1) Is the concentration of pollutant in the room with stratified flow larger or smaller that the concentration with perfect mixing?

2) How to find the concentration at exhaust of the room?

Differences and similarities of Ev and Depending on the source position:

- similar or - completely different

air quality

v = 0.41

= 0.19 = 2.20

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

ASHRAE Transaction 2004

Properties

Particle size distribution

ASHRAE Transaction 2004

Ventilation system affect the PM concentration in indoor environment !

Human exposure

ASHRAE Transaction 2004

Two basic approaches for modeling of particle dynamics

• Lagrangian Model– particle tracking– For each particle ma=F

• Eulerian Model – Multiphase flow (fluid and particles)– Set of two systems of equations

Lagrangian Modelparticle tracking

A trajectory of the particle in the vicinity of the sphericalcollector is governed by the Newton’s equation

m∙a=F(Vvolume) particle ∙dvx/dt=Fx

(Vvolume) particle ∙dvy/dt=Fy

(Vvolume) particle ∙dvz/dt=Fz

System of equation for each particle

Solution is velocity and direction of each particle

Forces that affect the particle

Lagrangian Modelparticle tracking

Basic equations- momentum equation based on Newton's second law

eFF

tiV

PPd drag

3

6

- 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:

ii Vdt

dx

puufFdrag

Drag force due to the friction between particle and air

For finite time step

tdt

tdt

Algorithm for CFD and particle tracking

Airflow (u,v,w)

Steady state airflow Unsteady state airflow

Particle distribution for time step

Particle distribution for time step +

Particle distribution for time step +2

Steady state

Injection of particles

…..

Airflow (u,v,w) for time step

Particle distribution for time step

Particle distribution for time step +

Injection of particles

…..

Airflow (u,v,w) for time step +

Case 1 when airflow is not affected by particle flowCase 2 particle dynamics affects the airflow

One way coupling Two way coupling

Natural Ventilation:Science Park, Gelsenkirchen, Germany

Natural Ventilation and CFD simulation

• Wind driven outdoor flow• Buoyancy driven indoor flow

Solution approach– Model boundary condition in-between outdoor and indoor

domain– Couple CFD with

• 1) energy simulation program (buoyancy driven flow) • 2) multi-zone modeling program (inter-zonal flow)

External flow

Wind profile

Buoyancy driven indoor flow

Important parameters• Geometry• Heat sources

– Intensity (defined temperature or heat flux)– Distribution– Change (for unsteady-state problem)

• Openings Defined – Pressure– Velocity

Natural Ventilation:Stack-driven flow in an atrium

Natural Ventilation:Wind scoop

Natural Ventilation:Solar-assisted ventilation

Window Design

Natural Ventilation:

Natural Ventilation: