Finish • Thermal Comfort and • Air Quality analyses in CFD

Start particle modeling

Lecture Objectives

Thermal comfort

Temperature and relative humidity

Thermal comfort

VelocityCan create draft

Draft is related to air temperature, air velocity, and turbulence intensity.

Thermal comfort

Mean radianttemperature

potential problems

AsymmetryWarm ceiling (----)Cool wall (---)Cool ceiling (--)Warm wall (-)

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 ( -0.036 M ) + 0.028 ] 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 = 100 - 95 exp [ - (0.03353 PMV4 + 0.2179 PMV2)]

Empirical correlations Ole Fanger

IAQ parametersNumber of ACH

quantitative indicator ACH - for total air - for fresh air

Ventilation effectiveness qualitative indicator takes into account air distribution in the space

Exposure qualitative indicator takes into account air distribution and source position and intensity

IAQ parameters

- Age-of-air

air-change effectiveness (EV)

- Specific Contaminant Concentration

contaminant removal effectiveness

Single value IAQ indicators Ev and ε

1.Contaminant removal effectiveness ()

concentration at exhaust average contaminant concentration

Contamination level

2. Air-change efficiency (v)

shortest time for replacing the air average of local values of age of air

Air freshness

C

Cε e

τ2

τEv n

[sec] ACS/1τn

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 τ,τ2τ nexe

Air exchange efficiency for characteristic room ventilation flow types

Flow patternAir-changeefficiency

Comparison with average time of exchange

Unidirectional flow 1 - 2 n < exc < 2n

Perfect mixing 1 exc = n

Short Circuiting 0 - 1 exc > n

τ2τexe

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

Particles Properties and sources

ASHRAE Transaction 2004

ASHRAE Transaction 2004

Properties

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

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