Reference

r NBS

PUBLICATIONS

NAT L INST. OF STAND & TECH

AlllDb 3 1 7 T 0

NBSIR 85-3265

Indoor Air Quality Modeling

Phase I Report

Framework for Development of

General Models

Preston McNall

George Walton

Samuel Silberstein

James Axley

Kunimichi Ishiguro

Richard Grot

T. Kusuda

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Physics Division

Gaithersburg, MD 20899

October 1985

Prepared for U.S. Environmental Protection Agency (MD-56)

c nvironmental Monitoring Systems Laboratory

„.esearch Triangle Park, NC 2771

r. David Mage, Project Officer -QC100

TW3 research niFCEi^ACic:'! CENTER

NBSIR 85-3265

INDOOR AIR QUALITY MODELING

PHASE I REPORT

FRAMEWORK FOR DEVELOPMENT OF

GENERAL MODELS

Preston McNall

George Walton

Samuel Silberstein

James Axley

Kunimichi Ishiguro

Richard Grot

T. Kusuda

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Physics Division

Gaithersburg, MD 20899

October 1985

Prepared for U.S. Environmental Protection Agency (MD-56)

Environmental Monitoring Systems Laboratory

Research Triangle Park, NC 2771

1

Dr. David Mage, Project Officer

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director
ABSTRACT

This report presents a framework for the development of a model for

predicting the indoor air pollutant concentrations in a variety of building

types under practical conditions of weather, building occupancy, building

construction and pollutant source strengths. The general concepts needed

for developing an indoor air quality model are treated. Examples of the

current state of indoor air quality models are given. The pollutants

discussed are formaldehyde, radon, nitrogen oxides, tobacco smoke,

particulates, carbon dioxide, and carbon monoxide.

Key Words: Indoor air pollution; modeling; air pollutants; environmental

parameters; model concepts.
ACKNOWLEDGEMENT

This work was supported under an Interagency Agreement IAG DWI 3 93 1103-0 1-1

with the U. S. Environmental Protection Agency (MD-56) Environmental

Monitoring Systems Laboratory, Research Triangle Park, NC.
TABLE OF CONTENTS

Pa&e

1. Introduction 1

2. Concepts 2

3. Parameters Included 6

4. Review of Existing Models 9

4.1 Formaldehyde Emission Rate Models 9

4.2 Radon Emission Rate and Decay Models 13

4.2.1 NBS's Model 13

4.2.2 Geomet's Model 13

4.2.3 Radon Progeny Models 14

4.3 NO2 Emission Rate Models 15

4.4 Tobacco Smoke Models 16

4.5 CO

2 Emission Rate Models 16

4.6 CO Emission Rate Models 16

4.7 Water Vapor Models 16

4.8 Building Air Movement Models 17

4.9 Multi-Node Models 26

4.10 Transport Models 29

4.11 Empirical Models 32

5. Convection Simulation Models 34

6. Multi-Room Building System Models 49

7. Future Pollutant Algorithm Development 50

8. Future Model Development 51

References 52

IV
LIST OF TABLES

Table 1 Nonlinear Regression Analysis for ORNL HCHO Surface

Emission Rate Model 11

v
LIST OF FIGURES

Figure 1 Diagram of the general indoor pollution problem 3

Figure 2 Block diagram of the model concept 4

Figure 3 Measured underlayment surface emission rates of

formaldehyde compared to ORNL' s model 12

Figure 4 Predicted NO 2 concentrations from a convective kerosene

heater, a gas stove and a radiant kerosene heater with

I = 0.0 ACH 16

Figure 5 Predicted NO2 concentrations from a convective kerosene

heater, a gas stove and a radiant kerosene heater with

I = 1.0 ACH 16

Figure 6 Schematic representation of a single-compartment

indoor air quality model 18

Figure 7 Three zone one-node model 19

Figure 8 Typical air distribution system 26

Figure 9 Ventilation flow configurations 27

Figure 10 Basic concept for mixing-position (m-p) model 28

Figure 11 Plume types for various thermal stabilities 30

Figure 12 Plume concentration profiles and centerline location

in the vertical xz plane 31

Figure 13 Three-dimensional concentration profiles of a nonrising

point source and centerline of a rising plume for

diffusion calculations at distance x 31

Figure 14 The room configuration, cross-section ABC and grid

design used by Ishizu 40

Figure 15 Velocity vectors on cross-section ABC when air inlet

is at leftmost position on the ceiling (case 1) 41

Figure 16 Pollutant iso-concentration contours in cross section

ABC for case 1 41

Figure 17 Velocity vectors on cross section ABC when the air

inlet is at the center of the ceiling (case 2) 42

Figure 18 Pollutant iso-concentration contours in cross section ABC for case 2 42

Figure 19 Velocity vectors on cross section ABC when the air inlet

is at the rightmost position in the ceiling (case 3) ... 43

vi
Figure 20 Pollutant iso-concentration contours in cross section ABC for case 3 43

Figure 21 Pollutant iso-concentration contours in cross section ABC

for case 2 except that the source is moved to the lower

left corner of the room (case 4) 44

Figure 22 Pollutant iso-concentration contours in cross section ABC

for case 2 except that the source is moved to the lower

right corner near the air outlet (case 5) 44

Figure 23 Mixing factors and ventilation effectiveness for three

dimensional calculations (cases 1 through 5) and two

dimensional analysis (cases 6 through 10) 45

Figure 24 Logarithmic pollutant concentration decay at various

positions in the room under case 1 ventilation conditions 45

Figure 25 Logarithmic pollutant concentration decay at various

positions in the room under case 2 ventilation conditions 46

Figure 26 Logarithmic pollutant concentration decay at various

positions in the room under case 3 ventilation conditions 46

Figure 27 Isotherms in cross section ABC under case 2 ventilation

when the supply air temperature is colder than the floor . 47

Figure 28 Iso-concentration contours in cross section ABC under

case 2 ventilation when the supply air temperature is

colder than the floor 47

Figure 29 Isotherms in cross section ABC under case 2 ventilation

when the supply air is warmer than the floor 47

Figure 30 Pollutant iso-concentration contours under case 2

ventilation conditions when the supply air is warmer

than the floor 47

Figure 31 Logarithmic concentration decay at selected locations

in the room ventilated with cold air 48

Figure 32 Logarithmic concentration decay at selection locations

in the room ventilated with warm air 48

Figure 33 Comparison between the measured and calculated

velocities and concentrations in cross section ABC

under case 2 conditions 49

vii

Indoor Air Quality Modeling

Phase I Report

Framework for Development

of General Models

1

.

Introduction

Purpose : The purpose of this report is to present a framework for a model

which will allow the prediction of air pollutant concentrations in a variety of building types under practical conditions of weather, building

occupancy, building construction, and pollutant source strengths. The

model will provide concentrations of several important pollutants and

include both temporal and spatial variations of contaminants.

Need.: Since there are nearly 90 million dwelling units and approximately

four million other occupied buildings in the U.S., it appears impractical

to obtain enough field data to adequately assess the status of the

important pollutants and their distribution in this large number of

buildings. Almost all of them will have differences in their environments,

construction details and occupancies which will affect pollutant

concentrations. This will make predictions based upon a limited number of

studies and observations very difficult. A reliable prediction model is

needed to assess the extent and seriousness of the indoor air quality

problem for a variety of buildings under different occupancy and

environmental conditions.

A validated prediction model is needed so that a national program for

improved indoor air quality may be economically developed which makes use of results of field tests and health effects research. Health effects

research and field studies will be done outside the scope of this project.

There are several other uses for a model in the complex area of indoor air

quality research. In the short-term, a model will assist in:

1. The design of field and laboratory tests. What to measure, where

and how often, for example, so tests by several investigators can be better

coordinated

.

2. Evaluation of instrument requirements. What accuracy, what time

constant, integrating or continuous, etc.

3. Evaluation of existing experimental data for use in data bases.

4. Evaluation of data collected for suitability in data bases.

5. Providing methods whereby various investigators using different

models may produce consistent results.

In the longer term, a model will be useful for:

1. Evaluation of the effectiveness of various indoor air quality

options, such as increased ventilation, heat exchangers, particulate and

gaseous removal equipment, material substitution, and contaminant emanation

1
suppression techniques, as well as the evaluation of behavior modification

and providing sensitivity analyses on various control methods for practical

decision making.

2. Assisting in risk assessment studies for various pollutants by

predicting exposures as they vary with time (peak and average) and space.

3. Providing practical information for the establishment of

standards

.

2. Concents

Figure 1 shows a schematic diagram of the general problem to be solved.

There must be, for any pollutant of interest, a source or sources. A

source could be a concentration in the outdoor air, but more usually it

would be from the surrounding earth or water supply, as in the case of

radon, or from building materials and furniture, as in the case of

formaldehyde or from personal habits of occupants such as smoking. A

source may also be from equipment, combustion appliances and activities in

the space, as in cooking, cleaning, etc. Source emanation into the indoor

air is often complicated, being affected by indoor/outdoor weather

conditions, HVAC equipment, peoples activities, etc. Much work has been

done in source identification and the time variation of emanation [1-3].

Emanation from the source is introduced into the indoor air and is

transported by convection and diffusion throughout the space, until it is

removed from the air by outward air leakage, deposition on surfaces in the

space, removal by HVAC equipment or modified by chemical or other action.

There is some knowledge of these mechanisms for many pollutants [1].

Pollutants are then exposed to people in various activities as they move

into, through and out of that space, resulting in a personal exposure for

each person depending on his movement and activity.

This exposure then results in a personal dose of the pollutant. The dose,

in general, will be less than the cone entrat ion- time integration since the

person will have some natural defense mechanisms which reduce the dose [4].

The personal dose then produces an effect on the person, which may be only

an annoying odor, with no further effect. Odors are of interest to the

HVAC engineer, since human comfort is involved. It is supposed that odors

can affect human performance in some situations, and therefore they should

be a public health concern [5]. The pollutant may cause an acute health

effect, such as eye irritation or coughing, with no long-term effect after

the pollutant is removed. Many pollutants are suspected or proved to have

chronic effects, such as lung cancer in the case of radon. Such chronic

effects may take decades to appear in people [6].

The model contemplated in this study will be concerned with only the first

three blocks of Figure 1. It will be confined to the identification of the

sources, their transport and removal, and the resulting time and spatial

contaminant concentration predictions. It is expected that, if successful,

the concentration predictions can be extended to obtain personal exposures

by adding various scenarios of a persons time, position and, activities in

the space of interest.

2
1 1 (Emanation I (Pollutant 1 iPollutant

I

1 1 (into air. I (Concentration ( I Exposure 1 iPollution

1

\ (Pollution I V (in air, varies

|

\ Ito 1

I Source 1 / (Transport,

1

f (with time and ( / (Persons I

1 1 (Pollution ( Ispace 1 1

1 1 I removal I (

1 1 1

1 1 (from air 1 1 1 1 1

I

1 1 (Health |

1 1 1 and/or ( (Personal I \ (comfort | IPollutant

1

/ leffects

1 Dose | lo annoyance!

1 1 |o acute 1

1 1 1 o chronic 1

Diagram of the General Indoor Pollution Problem

Figure 1

The model contemplated will be modular, insofar as possible, so that many

pollutant algorithms can be introduced individually into a general

framework. Each pollutant will have an algorithm for its emanation rate,

varying with temperature, pressure, humidity, etc. as appropriate. Such

modularity will allow changes in algorithms to be accommodated simply, if

the future research data indicates that the algorithms should be modified

and updated.

It is also expected that the model will contain a number of algorithms for

other physical and environmental variables which have an influence on indoor air quality. Examples are: Algorithms for handling weather

conditions, construction details, interior geometry, HVAC systems and

pollutant removal systems, and activities and uses of the interior space.

Modularity will also be sought in the routines which handle the outputing

of pollutant concentration. Capability is planned to include onecompartment, mixed situations, two-node one-compartment cases, multi-room

cases, and ultimately field equation models suitable for multi-room cases. Practical considerations will dictate the necessary complexity for

solutions appropriate to the many situations.

Figure 2 shows a block diagram of the conceptual model, showing the variety

of inputs, internal calculations and outputs contemplated. Note that in

addition to the concentration predictions, the outputs of the model will

include comfort parameters and predictions of energy consumption. This

will permit the output of the model to be used for economic analysis as well as for the optimal environmental control.

General Model Structure: Figure 2 depicts an overall model in terms of

input, calculation requirements and output. The inputs include weather

parameters, building architectural data and occupancy data as well as the

contaminant source information. This extensive set of input data is

3
1- Temperature

1

1* Architectural

| I- OccupancyI | Type

1- Humidity

l Materials 1- Ventilation

i Location

1 1 I Requirements 1 1- Solar Radiation HVAC Systems 1 | - Source

1 1 |- Temperature 1 Strength

1- Wind |- Other Mechanical 1 Requirements 1

1 ( Systems 1 |- Temperature/

1“ Barometric 1 |- Humidity 1 Pressure

1 Pressure 1 1 Requirements 1 Humidity

1 1 1 1 Effects

|- Ground 1 |- Lighting 1

1 Temperature 1 1 Requirements |- Decay

1 1 1 1 Characteristics

1 1 (- Equipment 1 \J/ \k ^1/ Requirements \!/

I Local Weather I Building I Occupancy and I Use Data I

I Contaminant

I Data

I Solar heat gain

I Internal heat gain

I Internal moisture gain

|lnf iltration gain

I Conduct ion heat gain

I Ps vchrometrics

Heat and Moisture I I

I i Transfer Calculation ! I

I I

Contaminant

Emission Rate I

Mass/Energy

i Balance Calculations I

I Radiation Heat Balance

(Pressure Balance

I Heat Balance

iMoisture Balance

(Air Mass Balance

( Contaminant Mass Balance

Block Diagram of the Model Concept

Figure 2

4
required to accurately assess the strong interactions between the building

thermal environment and emanation and migration of the pollutants# Because

of the fact that emission and decay rates of many contaminants are

considered dependent upon their ambient temperature, humidity and air

motion, the prediction of the contaminant concentration level at a given

point in the building at a given time necessitates the simultaneous

determination of these environmental properties for the air as well as the

surface temperature and surface moisture content of the interior

furnishings. This applies not only to the detailed calculations for air,

moisture and heat transfer through the building envelope, but also to the

accurate energy and mass balance analysis between the heat and moisture

gain, considering the heating, cooling, humidifying and dehumidifying

capacities of the HVAC systems and its control equipment. The heat and

moisture storage capacity of the solid surfaces exposed to the room air

must also be taken into consideration. Detailed and accurate calculation

procedures are already available in the Thermal Analysis Research Program

(TARP) of the National Bureau of Standards [1], which has been developed

previously to simulate the hourly heating and cooling requirements of the

building

.

On the other hand, mass balance models for various contaminants have been

developed by several authors to predict the contaminant concentrations in

spaces as functions of source strengths, decay rates and dilution rates.

These will be discussed in more detail in section 4. All of these existing

models however, are applicable where the room air is well mixed so that its

temperature, humidity, contaminant concentration and air velocity are all

uniform throughout the space. While this single node assumption may be

adequate for assessing the effect of time average values for a day or for a longer period, these models fail to account for the localized peak

concentrations of certain contaminants, which are sometimes considered more

critical for health effects than the long time and overall average

exposures [7].

For the risk assessment of individuals, information is needed for the timefrequency data of the contaminant concentration for a period of time at a prescribed location in the building. Based upon these data, appropriate

control strategies, such as the installation of air filters, increased

ventilation, alteration of HVAC systems and/or interior furnishing, etc.

will have to be developed to modify the time-frequency profile. These

control strategies are, however, all costly and they must take into account

economic trade offs with respect to risk. The economic analysis, in turn

requires the accurate data for building materials, internal furnishings,

HVAC and air cleaning equipment and air handling systems and the energy

costs, maintenance, etc.

Although the model structure shown in figure 2 is designed to address all

of these complex and interwoven aspects of building thermal performance and

indoor air quality, it must be emphasized that it does not necessarily

depict actual flow of the calculation algorithms. In fact the three

sequential blocks, heat and moisture transfer calculation, mass/energy

balance calculation and temperature/humidity/concentrat ion determination

should ideally be handled in a single block, provided that the efficient

parallel processing algorithms are developed for modern high speed

computers

.

5
Expected Model Capabilities : Although comprehensive in scope, the model is

expected to be simple to use due to its modular structure. In this way,

predictions of concentrations can be made for a number of cases by

selecting the appropriate algorithms for a specific pollutant for specific

buildings under specific operating conditions, etc. from an extensive menu,

inserting them in the framework, and exercising the model. If this can be

accomplished, the model will be valuable in providing information to

fulfill the purposes outlined above.

Limitations : In order to provide a manageable scope to this very extensive

problem, certain limitations are necessary. The model results will be

pollutant concentration predictions in interior spaces, with appropriate

time and spatial variations. Personal exposures will not be included, but

will be left to others. Climate and building types and interior uses will

be limited to some extent. These limitations will be determined during

subsequent work. It is expected that enough variety to cover all important

situations will be included. Only certain pollutants will be included. A

list, and discussion and rationale for pollutant selection or rejection

will be given below.

3. Parameters Included

Pollutants, sources and sinks : The following pollutants to be considered

were agreed to in the workshop held at NBS in February 1985 [8], The order

of the pollutant in the listing is not necessarily in order of importance.

Radon - The first radioactive decay product of radium, radon is a gas which

can diffuse into buildings. Further decay products are adsorbed on particles which can lodge in the lung, where subsequent alpha particle

emissions can cause lung cancer. The most important source is the earth

around buildings, although well water in some locations is an important

source [9,10].

The source strength depends upon soil radium concentration, soil

permeability, pressure differences and perhaps temperature. No validated

algorithms exist. Both point and area sources may be involved.

The radon decays and forms solids which are attracted to and attach to

other dust particles, and are ultimately removed with the dust. The

process is well established, and though complex, some algorithms have been

developed, and others can be developed [11].

The spatial distribution algorithms are needed, but the process is

controlled by diffusion, convection and gravity. Therefore algorithms may

be developed employing other particle removal mechanisms.

Formaldehyde is widely used in many building products, furniture and

clothing. It is clearly an irritant, causing annoyance and acute eye and

respiratory affects. It is suspected of being a human carcinogen [12].

The source strength [13] depends upon area, temperature, humidity, source material, and time. Although complex, considerable laboratory and field

work has been done, and algorithms are well advanced [13].

6
The natural removal mechanisms of reactions with other substances in the

air, absorption in and desorption from materials occur, but models are not

yet developed. Water and water vapor as a potential sink, needs to be

considered.

Nitrogen Oxides . (NO 2 and NO) - NO 2 and NO are suspected of causing acute

health effects [7]. The sources are combustion processes causing nitrogenoxygen reactions in air at high temperatures.

Source strengths, from point sources, such as gas ranges and other unvented

combustion appliances are well developed [14]. Manufacturers are

developing appliances with lower NO2 production, which will affect source

strengths in the future [7].

There is some evidence of decay or chemical reaction of NO 2 and NO with

materials in spaces, but no models exist.

Tobacco Smoke - The health effects of tobacco smoke on smokers is well

known [15]. The effects of sidestream smoke on non-smokers has received

much attention, and recent research [16] suggests effects on the

respiratory tracts of children exposed. Increased probability of lung

cancer in spouses of smokers has also been indicated [16].

Tobacco smoke is a very complex mixture of particles and gases. Good

particulate models exist, but gaseous models need development to provide

optimal source strength algorithms.

Tobacco smoke does decay with time, due to natural particulate removal,

agglomeration and gaseous absorption, but better models are needed.

Particulates (other than tobacco smoke, including biomatter and allergens)

- other particulates, from household activities, office machines, etc.

should also be considered. Little is known about the source strengths.

Some allergens enter spaces with outdoor air. Some models can be developed

which may be useful in estimating source strengths.

Natural removal mechanisms, settling, agglomeration, deposition, chemical

reactions, and resuspension need considerable model development, although

some models exist. As seen below, this project will not include microorganisms and allergens per se.

Carbon Dioxide (CO 2

) - CO 2 is not suspected to be a comfort or health

hazard, per se, but is included here because it has been suggested as an indicator of other pollutants more difficult to measure [17]. Principal

sources are human metabolism, which is well modeled, and combustion

processes, which are also well modeled. Absorption and desorption may

occur, and are not well modeled.

Carbon Monoxide (CO) - The health effects of CO are well known, and good

models exist [18] provided the source strengths are known. The model

should be capable of handling CO.

Water Vapor (H2 O) - H2 O is not a pollutant, per se, but good models do

exist. The effects of water vapor levels on other pollutants is needed for

completeness. These effects need considerable study.

7
The following pollutants were considered by the workshop [8] and were set

aside from this study for various reasons. Some were felt impractical to

model with current knowledge, others (asbestos) were being handled

separately, or research was not advanced far enough for consideration in

the model.

Volatile Organic Compounds (VOC) (other than tobacco smoke and

formaldehyde) - A wide variety emanate from a muliplicity of sources.

Health effects of only a few have been studied.

Sulfur Dioxide (SO2) " The sources are mainly from combustion of wood, coal

and impure kerosene. The sources are highly variable and not predictable

enough to be modelled.

Pesticides - Source strength and removal mechanisms are not well known.

Micro-Organisms and Allergens - Although these are very important, the

necessary knowledge of source strength, removal and health effects need

much further study.

Ozone (O3) - O3 was not felt to be an important indoor pollutant for

buildings by the workshop participants [8].

Asbestos - Asbestos was not included, since it is being handled separately

as a specific public health problem.

In addition to the specific pollutants to be included in the model, the

following parameters should be included in the model where appropriate.

Generic sources of pollution -

- People, machines and peoples' activities

- Building materials and furnishings

- Consumer products

- HVAC equipment

- Outdoor air

- Water supply

- Combustion products

Source Strength Variations - The model should be able to handle the

following important parameters affecting some emanation rates -

Environmental factors - Time variations should be handled in

appropriate time steps so that necessary detail on peak and average

pollutant concentrations can be obtained. Effects of temperature,

humidity, pressure, air movement, etc. should also be considered.

Point sources, such as unvented kerosene heaters should be considered.

Area sources, such as emanation from wall coverings, carpets, etc.

should be handled.

The effects of permeation barriers, such as paints on plywood or particle board should be considered.

8
Volume sources, such as the production of radon daughters from radon

in the air should be considered.

Other parameters ; Parameters other than the pollutants which must be

considered in order to provide predictions of indoor pollutant

concentrations are listed below.

Weather - Local temperature, humidity, wind, solar radiation, pressure, and

ground temperature should be included. Correlation of nearest weather

station data with local conditions may sometimes be possible.

Architectural details - Building design, spatial relation of interior

spaces, doors and other openings between spaces, envelope details, and

building materials should be covered. Furnishings and other interior

treatments, and machines and processes in buildings must be known and

considered.

HVAC systems - The means of control of temperature, humidity, etc.

involving heating, cooling, humidification and dehumidification should be

known, as well as the equipment for removal of contaminants, both

particulate and gaseous. The model is expected to simulate typical HVAC

systems and equipment commonly found in residential as well as commercial

buildings

.

Vent i lat ion - The operation of the HVAC system in providing ventilation

must be known, as well as infiltration, natural ventilation and any local

intakes or exhausts. The outlets and returns in all spaces must be known

so local mixing and ventilation effectiveness can be predicted.

Within space conditions - The model should handle environmental parameters

(temperature, humidity, air motion) as well as concentration predictions

for:

1. Mixed air in a single zone

2. Mixed air in a 2 node single zone

3. Field equations in a single zone

4. Multizone (vertical and horizontal) adjacent spaces

Various time steps should also be possible with small enough time step

capability to predict peak concentrations for some pollutants.

The building occupancy and operating schedules are also necessary, covering

lighting, HVAC systems, other equipment, temperature, set points, etc.

4. Review of Existing Models

In this section, brief reviews of several models will be given. It is not

possible to cover all models here, but those mentioned are those chosen as being most appropriate for use in the general IAQ model.

4.1 Formaldehyde Emission Rate Models

On the basis of surface emission rates of under 1 aymen t , paneling and

medium-density fiberboard at different combinations of temperature,

relative humidity (RH), and ambient formaldehyde (HCHO) concentrations, Oak

9
Ridge National Laboratory (ORNL) [13] developed models that can predict

surface emission rates at nearby values of these parameters once the

surface emission rate at 23°C, 50% RH, and 100 ppb HCHO concentration is

determined. At any given temperature and RH, surface emission rate and

HCHO concentration obey the following equation relating the ambient and a bulk layer of air, each containing different HCHO concentrations:

S * a + b • C ( 1 )

where S *= HCHO surface emission rate, mg/m^'h

a= linear regression intercept giving HCHO surface emission rate at

0=0 ppb, mg/m^“h

b linear regression slope, mg/m^*h/ppb

C = HCHO concentration, ppb

The model developed by ORNL [13] predicts the ratio of S to S gtd> (its

value at standard conditions, 23°C, 50% RH and 100 ppb HCHO concentration).

S(T,RH,CV)

^std

_C (i 1

)

[ l+B(T-296) ]

* [l+E(RH-50) ]• [e T

“ 296

Cr

i

Bstd 0.1

(RH/50)A * CBstd - Cy]

( 2 )

where S

std

T

RH

A,B,C,E

C

B Cy

= HCHO emission rate (mg/m^h)

*= standard test conditions (i.e., 23°C, 50% RH, Cy

" temperature (K)

relative humidity (%)

= model coefficients for temperature and RH terms

* HCHO concentration in the bulk phase (ppm)

= HCHO vapor concentration (ppm)

0.1 ppm)

for T = 23°C and RH ** 50%, equation 2 reduces to:

$ (Cv) _

C

B.td - Cv

S8td '"ltd

" 0 '^

Equation 2 contains five coefficients: A, B, C, E, and c B gtd . The best

fit of these to measured data were determined by ORNL. Table 1 gives

values of the five coefficients for paneling, under layment, and mediumdensity fiberboard. (No physical meaning should be attributed to any of

the coefficients even though one of them, Cg g ^ d> is supposed to correspond

to the bulk phase HCHO concentration. The values of the coefficients are determined by numerical regression, not by any physical measurements, and

the model itself is an empirical one.)

The National Bureau of Standards (NBS) tested this model in a control ledenvironment chamber. The surface emission rates of paneling, under layment

,

and table tops made of medium-density fiberboard were measured at 23°C and

50% RH at various air exchange rates -- and hence various HCHO

concentrations — in specially constructed medium-sized measuring chambers.

10
The coefficients of equation 1 were determined by linear regression

analysis and S 8td was calculated for each specimen. The specimens, except

for several used as controls, were then placed into a prototype house

located in the controlled environment chamber to see how well HCHO

concentrations under more "real" conditions could be predicted from

measurements of individual specimens. Two underlayment specimens had to be

cut in order to cover the floor of the house. (The results of the house

study are not discussed here.) The specimens were then removed from the

prototype house and remeasured in the medium^sire chambers to see if the

functions relating surface emission rates to HCBO concentrations were

stable. The experiments in the controlled environment were repeated at 26°

and 60% RH. Resulting values of S/S 8t(j under both sets of conditions were

compared with predictions of the ORNL models [13]. As an illustration, we will present the results currently available for underlayment. For

underlayment, the ORNL models, using equation 2 and the coefficients in

table 1, are:

s/s.td

S/S Btd

The NBS results

equations

“ 1.38 - 0.0038’C at 23°C, 50% RH

“ 2.54 - 0.0048’C at 26°C, 60% RH

(3)

for uncut underlayment are best fit by the following

S/S6td *= 1.69 - 0.0069*C at 23°C, 50% RH before placing in the house

S/S g td

“ 1*61 “ 0.0061 *C at 23°C, 50% RH after placing in the house (4)

S/S

gt d = 3.21 - 0.0087*C at 26°C, 60% RH before placing in the house

The NBS results for cut underlayment are best fit by the following

equations

S/S6td = 1.69 - 0.0068*C at 23°C, 50% RH before placing in the house

S/S st d = 1.60 - 0.0060’C at 23°C, 50% RH after placing in the house (5)

S/S gtd = 3.12 - 0.0069*C at 26°C, 60% RH before placing in the house

Table 1 Nonlinear Regression Analysis for

ORNL ECHO Surface Emission Rate Model

Pressed-vood

C Product C A B std B E

Particleboard

Underlayment

9400 0.37 0.36 0.025 0.016

Paneling 6500 0.66 0.41 0.053 0.029

Medium Density

Fiberboard

5000 1.90 0.90 0.090 0.000

11
MCHO

.er/.er

100.23.50

HCMO

«e'/»er

100.23.50

HCHO

.er/aert

00.23.50

The NBS results and the predictions of the ORNL model are shown in figure

3. The magnitude of the slopes predicted by ORNL is about 40% smaller than

those found by NBS.

Underloyment (uncut; before house)

23 C, 80* Rh Underloyment (cut; before house)23 C, 50K »H

HC»-»0 concentrotion (ppb)

•. 2 e. 5. *. 8. . «. #. 10. 12. •. 18 MCHO concent rot 'On (ppb)

O. b - 12

Underloyment (uncut; after house)

23 C. bOX Rh Underloyment (cut; after house)23 C. bOX RH

Underloyment (uncut; before house) Underloyment (cut; befo r e house)

26 C. bOX RH 26 C. 60% Rm

Figure 3. Measured underlayment surface emission rates of

formaldehyde compared to ORNL's model (predicted

by equation 2 using coefficients in table 1).

12
4.2 Radon Emission and Decay Models

General radon emission rate models are not yet available. The Lawrence

Berkeley Laboratory (LBL) [10] has done considerable work on this and

useful models may be developed soon. However, radon and radon progeny

models have been developed, to predict decay rate as it occurs in the

indoor air [11].

4.2.1 NBS's model

A physical model for the dependence of radon decay on ventilation can be

expressed by the equations [11]:

dA0 --- = Q

- U0

+ I)A0 + IAq° (6)

dA

i = A-A.-_i - ( A • + I) A* + IA.- 0 for 1 < i < 4 (7)

dt xij. l l i __

where A = activity concentration of the radionuclide (pCi/L)

Q

= entry rate of radon (pCi/L*h)

A = radioactive decay rate (h”*)

I = infiltration rate (h“*)

t = time (h)

Subscript "i" refers to the i

fc ^ radionuclide (i = 0 to 4)

Superscript "o" refers to outdoor air.

Kusuda et al. [11] solved this set of equations for several typical

combinations of I and Q and presented the results in terms jpf equilibrium

total alpha particle energy concentration of radionuclides, E;

E C

iAo

( 8 )

where C^'s are predetermined constants representing potential alpha energy

per pC^ of each radionuclide. Using the unit of working level, WL, details

of which are found elsewhere (see for example reference 11), equation (8) can also be expressed as

Ao E WL (9)

lOOpCjL 1

4.2.2 Geomet's model

In research on indoor air quality Nagda et al. [18], developed the;

13
following model for predicting the indoor level of radon in equation 10,

where C

E

S

V

q

c

m

out

dc in Es

e 1

~dt" T * V

+ 1 (a o

c out + a

s cs^ “ Ic in

~ A °c

in

= indoor concentration (atoms/mJ

)

radon flux density per unit surface (atoms/h m^)

= exhaling surface area (m^)

- volume (m^)

= radon release rate from indoor source (i.e., water, etc.)

= outdoor concentration (atoms/m^)

( 10 )

= air exchange rate (h

_ M

= fraction of external air coming from outdoors

- fraction of external air coming from soil; a

0

+

a

g = 1

X° = radon decay rate (h

-

*)

4.2.3 Radon Progeny Models

The activity concentration indoors of the new generation of free radon

progeny, Af, and attached radon progeny, Aa

, may be stated as follows [9]:

dA| ,in

dt

dAp , in

IA£,out + X

1 Iflin + R*-“* X* la lin - (I + X* + x

+ XP) A^,in

( 11 )

*a 'dt

A^,out + X* (1-R*“*) Afl ,in + X A^,in - (I + X* + X d

) A^

,

in

where I = air exchange rate (h~^)

radioactive decay constant for ith progeny (pCi/L*hr)

R recoil factor to define detachment

X “ attachment rate

Xp “ deposition constant for free progeny (plateout)

Xd *= deposition constant for attached progeny

and subscript "in" and "out" refer to inside and outside air.

The mass balance for a given generation of radon progeny is determined by:

14
( 12 )

where X

# ! the settling rate,

4.3 Fniifigp Rate IMfiii

N02 emission rate models have been developed. However, the N02 emission

from combustion under various conditions needs refining. For example, a range burner flame, heating a pan of food from a cold start, produces N0 2

at a rate which varies with time. Many measurements have been made [7]

[18] (see Figures 4 and 5), but general predictive models for N0 2

generation are not yet available. In addition, N02 does react with unknown

materials in the environment at rates which are equivalent to air exhange

rates from zero to 0.5. N0 2 models of Geomet and Harvard [18] [19] are

given for kerosene heaters and gas ranges.

(13)

where C - the concentration of N02 indoors (yg m“^),

I air exchange rate (h“^)

Cout

c concentration of N02 outdoors (yg m

-^),

S = indoor emission rate of N02 (yg m“^ h"*),

k = first-order decay constant (h~*)

t = time (h)

C(t) = (1 - e

-1 '*) ~ + COe-1 ' 1 (14)

where C(t) = the concentration of N02 indoors (yg/m^).

I' = I + k.

S s + Icout» and

C° = the concentration of N02 indoors at time t Q

The exposure in a time interval (tj, t 2

) is given by

C(t)dt = C (t 2 “ t

x

) + ------ ie'1

' 1

! - e_I

' t 2). (15)

where E(t^,t 2

) is the exposure between time tj and time t 2

, and

C = S'/I', the steady-state indoor N02 concentration.

15
Figure 4. Predicted NO2 concentrations

from a convective kerosene heater, a gas stove and a radiant kerosene

heater with I 0.0 ACH

Figure 5. Predicted NO2 concentrations from a convective kerosene

heater, a gas stove and a radiant

kerosene heater with I * 1,0 ACH

4.4 Tobacco Smoke Models

Tobacco smoke particle emission rates have been intensively measured.

Emission rates vary with the types of cigarettes, and how individuals smoke

them.

However, for purposes here, Repace [16] indicates that particulate

generation per cigarette may be taken as 24 mg per cigarette +, 20%. Repace

also has examined tobacco smoke agglomeration and aging. The data showed

that when smoking continues, the new smoke tends to predominate, so good

approximations may be made by neglecting aging.

4.5 COo Emission Rate Models

Generally CO2 emission models are well developed, depending particularly on

the amount of carbon burned, or average metabolic measurements on people.

CO2 is non-reactive after introduction into the environment.

4.6 CO Emission Rate Models

CO is also non-reactive in the environment. However, its emission models

are known only for specific cases (cigarettes, specific combustion burner

situations, etc). Harvard [14] and LBL [7] have done considerable work,

but no general model exists to predict CO generation [19] from a wide range

of sources.

4.7 Water Vapor Models

Water vapor (H2O) is important to consider here, since it reacts with many

pollutants in the air. Emission rate models are well developed for many

cases (metabolism and perspiration of people, evaporation from cooking,

showering and bath taking, humidifiers, etc.). However, H 2 O is adsorbed

and desorbed in and from bui 1 ding mater ia 1 s and furnishings. Tsuchiya

[20] and later Kusuda and Miki [21] used a mass balance equation similar to

equation 10 to predict indoor air moisture content and obtained good

agreement with measured results. The absorption and desorption of H2 0 by

16
interior surfaces of buildings and internal furnishings is extremely

important as it is also believed to affect the emission characteristics of

other pollutants.

4.8 Building Air Movement Models

The simplest and most widely used model to predict space concentration

assumes uniform mixing in the space or spaces under consideration. This is

referred to as a one-node model in this report. See Figure 6.

Assuming complete mixing of the incoming air with the room air, the mass

balance of a pollutant in a single room may be written as eq. (16).

dC £

V

dtT

= ^ q° + q2^ C o

” ^1 + ^^i + s " R

Since the mixing of the incoming air with the room air is not uniform, a mixing factor (k) is used to account for the effect. This can be accounted

for by considering the equations below.

Air mass balance: q0 + q£ ~ <13 + q4

dCi

Pollutant mass balance: V--- = kq0

C

0 (l-F 0

) + kqjC^Cl-Fj) (17)

+ k<l2C

o “ k(<lo + ^1 + <l2^ Ci + S - R

In equations (16) and (17)

C

L

*= concentration indoors,

C Q

= concentration outdoors,

t = time,

q0 = volumetric flow for make-up air,

q^ = volumetric flow for recirculation,

^2 = volumetric flow for infiltration,

q3 = volumetric flow for exfiltration,

q4 = volumetric flow for exhaust,

F 0 c filter efficiency for make-up,

= filter efficiency for recirculation,

V = room volume,

S = indoor source emission rate,

17
R B indoor sink removal rate

k “ mixing factor

Infiltrated

Air

Make-Up

Air

Recirculated

Air

1

1

1

1

1

1 T

1 .

1

1

1

1 1 (Filter F 1

i °i

1 1 (Filter Fi 1

1 ... 1

I

! *2c

o ^

1UoM1-1^

^

1UiCid-Fi) ^

Room Volume *= V

Room Surface Area B A

Source Emission Rate B S

Sink Removal Rate B R

Indoor Concentration B

Mixing Factor B k

Exf iltrated

Air

! <Uc i

Exhaust

Air

i

Figure 6. Schematic representation of a Single-Compartment

Indoor Air Quality Model

The solution of the equation for the change in C^ with t, holding all other

factors constant and with boundary values C^ C

g at t 0, is

[k[q0

(l - F

0

) + q2

]C 0 + S - R]

k(qD qiF + q2>

[i-e ”( k/ v>(q0+

qiF i +q2 )t:

] (18)

+ c e “(k/V) (q0 + q1 F 1 +q2

)t

This one-node model is easily extended to more than one connected space, as shown in figure 7.

18
f

31

J

f 21 l f 32

1 I

( 1

1 1

& t r r

1 1 1

1 Zone 1 — Zone 2 — Zone 3 — Zone n 1 f 02 % ^on 1 lT

p ; cn. T

2

, 2Cp2, I

3

v

3Cp3

, T®, “Cpn, 92» t'2»g2» q3

.c 3 .g3

, 9n» cn»Sn » 4 » Vi

»6

V2

- v3 Vn

f 10 f 20 f 30 1

I f 12 *

1 f 23 * f 13 * I * —— — 1 fin ^2n ^nm

fno

Three Zone Example

Figure 7. Three Zone One-Node Model

Typical Zone

in

m Zone System

In general, airflow from any one zone to another must be considered.

Define a flowrate variable, f — , the interzone volumetric airflow rate,

such that fji indicates the volumetric flow rate from zone i to zone j (it

is understood that f,-,- = 0.0). Outdoor air exhaust and intake must be

. 1 J. (\ (X considered, fnQ and fQn , and HVAC supply and return, f gn and f_

r , local to

each zone, where each zone may be served by several HVAC systems,

a =1 ,2 , . . . ,N.

^ln —

]-> -j—

fnl

Interzone Inflow ***

1 y

* * • • • 8 • • •

• •

* Interzone Outflow

1 Zone n 1 ^mn -!—> ^nm

Tn» n»

CPn .a

f

c

X

sn ->

fnr

HVAC Supply • • • %

1 Y

1 • • • • | • • © HVAC Return

^n»^n

• Local Air Intake f on -Q- -j—

fno

Local Air Exhaust

Filter n n

(For the equations derived below a thermal zone may be taken to have a very

general meaning. An air duct and even an air system heating or cooling

"plant" could, conceivably, be considered to be thermal zones.)

Thermal Equations

For a typical zone 'n' within this building system equil librium is

necessary

;

19
where

or

where

where

i Cpn

vndTn/ dt + + z *°nr + *no^p n

Cpn

Tn *\^inp i Cp iT i

i*l a *1 i*l

% + ^onp o^po^o + snPs^pa

s^

a

s a=l

(20a)

T ° air temperature

p - bulk air density

Cp = specific thermal capacity of air

V = volume

q = thermal gains due to direct gain, transfer through shell, etc.

i = zone index, i=l,2,3,...m

i=0 = outdoor index

r = HVAC return index

8 = HVAC supply index

a = HVAC system index (for multiple HVAC systems)

[M2 KdT2 /dt> + {Cp 2

} [

F

2

] {T2

} = {E2

} (20b)

n {Tz

} = vector of zone air temperatures

- «!, x2 , t

3 ,... 1^>

T

O [MZ

] = zonal air capacitance matrix

iiag ^Pl^PlVj »P 2 Cp2V2 »P3CP3V3 , ... P m

CpmVm

)

<E2

} = vector of zone direct thermal excitations

~ E

2 , E

3

, .. • V

T

En

" q_ + f»„p„Cp-T_ + Mn onK o ‘O 0 7 sn

n n a

s Cps Ts a=l

[f 2

] * mass airflow matrix

j~ F

11 "f 21 ”f 31 * * * “fml n

1 -f 12 F 22

"f 32 • * * " fm2

] "f 13

“f 23 f 33 * * * -fm3

I • • • ••• ••• ••• ••• lm * * * • • • • • • Fmm

20
where F

,m N „ = (rf • + 7f a + f ) nn “nr ^o'

i=0 a=l

[f 2

] is in general, asymmetric ( f ^ j

# f

j £ ) ; zones need not exchange

equal volumes of air

r\ {Cp z

} = vector of zone air specific thermal capacities

= {piCpj ,P2 cP2>P3 cP3» •••

Continuity Equations ; Positive Definiteness of {F}

Zonal Continuity

Within the assumption of incompressible flow, consideration of flow

continuity requires that flow out of a zone must equal flow into the zone;

m N n m

, E£ni * E£ nr £no “«in +

1=1 a=l i=l

N a zf

a=l

sn

- f on

or m

EF

i=l

N

nn ^in + ^ sn

+ ^on

a=l

( 21 )

( 22 )

It then follows, since all airflow values are defined to be greater than or equal to zero, that the diagonal terms of the airflow matrix will always be

greater than or equal to the sum of the off-diagonal terms in a row;

^nn — ^ni

if n

(23)

or if any infiltration or HVAC supply exists in the airflow system, then at

least one of the diagonal terms will be strictly greater than the row sum,

and the airflow matrix will be positive definite.

The zonal air capacitance matrix, [M 2

], is diagonal and positive, by

definition. Thus the system of equations defined by equation (20b) may be

solved when the airflow matrix, [ F^ ] , is positive definite, when

infiltration or HVAC flow exists.

HVAC System Continuity

Flow continuity is required in the HVAC system(s); ”

f °ir “ fa

ro

= fa

os

= "*°si for a“l>2,..,N

i=l i=l

(24)

Flow-Pressure Equations (Momentum and Constitutive Relations)

While airflow between zones is physically driven by pressure differences it

is useful to model airflow as either a prescribed function of time;

[F2

] = [F 2

( t) 3 (25)

or as a pressure-driven flow;

21
[F (26) 2

] - [F 2 ((Ap})]

where {Ap} = mean pressure differences between zones and from zones to the

outdoor environment

APij Pj - Pi for pj > pi

“ 0.0 for pj ± pi

In either case, the flow rates must satisfy the continuity requirement of

equation (21).

Using prescribed flow rates, equation (25), an analysis may be conducted of

indoor air quality for the common situation where forced convection driven

by HVAC equipment dominates the flow without the need to consider pressure

differences explicitly.

An accurate evaluation of pressure-driven flows, modeled by the second

option, equation (26), that satisfy continuity, may be expected to be the

most problematic aspect of the well-mixed zone model.

These flows may be due to bouyancy effects, wind induced pressures, and

mechanically induced pressures and may be related to pressure differences

using approximate, empirical expressions of the form;

f ij " ^ i j(Ap i j) x ij (27)

where the flow coefficients, k^j and x^j, depend upon the geometry of the

flow boundary, and the nature of the flow, (laminar or turbulent, etc.).

Pressure differences due to bouyancy effects are critically dependent upon

small differences in zone densities that are, strictly speaking, dependent

upon temperatures and contaminant concentrations;

Pi - Pi(Ti.Ci) (28)

Contaminant Dispersal Equations

Nonreactive Contaminants

For a typical zone 'n' within this building system, contaminant mass

equilibrium is necessary for each contaminant, k, of interest:

Vn

dCkn

/dt + (?fni - i-1

* Wck

n

- ?£ inC\ a-1 i-1

8

k

n

+ fond-V^o * “\nck

a-1

( 29 )

where V - zone volume

C - contaminant concentration

g - contaminant generation rate

22
n = filter efficiency

k contaminant type index

or [V2 ]{dCkz /dt} + [F 2 ]{Ckz

> = {Skz } (30)

where {Ckz

} = vector of zone contaminant concentrations

«*!, Ck

2 , Ck3 , ... Ck

n>T

[Vz

] = zonal volume matrix

= diag{Vlf V2 , V3 , ... Vj

{Skz } = vector of contaminant source rates

= {Sjfc, s 2

k

, s

3

k

, ... sm

k

>T

where Sn

k - gk

n + f oa (l-ntt )Ck

0 + ”f sn

Ck

g S=1

Reactive Contaminants

If two contaminants, a and b, react to product a third species c;

a + b -v c

and the rate of production of c is dependent linearly upon

concentratons of a and b as;

dCc /dt = R

ab (Ca

, Cb

)

where C = concentration and Rab is the rate of production of c function of a and b

From the stoichiometry of the reaction;

(m

a

)a + (mb)b -* (mc)c

ma

+ mb = mc where m = mass

it follows that;

dC a /dt = ~(m

a )/(ma

+ mb

) dCc /dt = -(m

a )/(ma

+ mb

)Rab (C a

, C

b

) and

dCb /dt = ~(mb )/(ma + mb

) dCc /dt = -(mb )/(ma

+ mb

)Rab (C a

, Cb

)

or, defining;

g

ab (ca

> cb) = -(a,a)/(ma + mb

)Rab (C a

, C

b

)

g

ba (ca

> cb) . -( mb )/(ma. „b

)Rab (Ca

. C

k

)

the

(31)

as a

(32)

(33)

23
then

dC a/dt - g

ab (C a

, Cb

)

dCb /dt - g

ba (C a

8 C

b

) (34)

Thus it is seen that a reaction of two species has the effect of

introducing a negative generation rate, or sink, that may simply be added

to the generation term (species source), g

k

n , in the above equations.

Generalization to reactions of more than two species is straightforward so that for the general case of reactive contaminants we may replace the

simple source term, g\» above by;

+

Z ka +

E ekaB +

£ e kaS6

a

s n a 73 n a°3,S n

+ (35)

where k,a,3,<$ are contaminant species type indicies.

It must be remembered that all of these reaction-related terms depend upon

the state of concentration in the zone n and thereby couple the contaminant

dispersal equations nonlinearly.

The coefficient matrices of the thermal equations, (20a)(20b), are, in

general, nonconstant (i.e., vary in time), nonlinear (i.e., depend upon

zone temperatures, through both density and specific heat capacity),

and implicitly coupled to the concentration equation through the dependency

of both density and specific heat capacity on contaminant concentration.

The variation of density and specific heat capacity due to temperature and

concentration changes is likely to be small, yet must be accounted for if

bouyancy forces are important. It is reasonable to treat density and

specific heat capacity constant in the thermal equations, (20a)(20b), yet

account for density variations in the flow equations, (25)(26). This

approximation is equivalent, in essence, to the Boussinesq approximation

employed in the continuum formulation of bouyancy-driven equations and

serves to reduce, but not eliminate, the nonlinearity of the system of

equations and to uncouple the contaminant dispersal equation from the

thermal and airflow equations.

Since equations (20a)(20b) and (26) are coupled nonlinear equations it may

prove difficult to insure uniqueness of solution for bouyancy-driven flows

analogus to Benard convection (the motion that results when a fluid is

heated from below for Reynolds number above a critical value) and possibly

other f 1 ows as well.

Equations (20a) and (20b) define the thermal behavior of an interzonal

airflow network. They are identical in form to the general form of thermal

element equations (that may be assembled to form systems of equations that

govern the thermal behavior of complete thermal systems), and as such may

be considered to be just another class of thermal element - an "airflow

network element". This airflow network element may, then, be directly

assembled, along with other building thermal elements (e.g. resistance

elements, capacitance elements, conduction finite elements, MRT network

elements, HVAC elements, etc.) to form a coupled system of equations that

defines the coupled thermal behavior of the building system.

24
[C]{dT/dt} + [K]{T} = {E> (36)

where {T}

[C]

[K]

{E>

vector of building system temperatures and includes zonal

temperatures as well as other nodal temperatures in the

complete building system model

building system thermal capacity matrix

[M z

] + [

c

e

] ; the "direct assembly sum" of the zonal air

capacitance matrix and all building thermal elements

capacity matrices

building system thermal conductance matrix

{Cp^HF^] + [k e

]; the "direct assembly sum" of zonal

airflow conductance and all building thermal elements

conductance matrices

{E^} + (q e

) + {q ext

}; the "direct assembly sum" of zonal

direct gains, internally generated fluxes, and external

fluxes due to convection and fluxes to the external

boundaries of the building system.

The following procedures may be used to solve the collection of equations

presented above.

Stepping through time;

Initialization

1. An initial building system temperature distribution is assumed;

{T} q = assumed

Time Stepping Loop

2. The time step is incremented.

fc n+l = tn + 6t

3. The first estimate of the temperature distribution at the next time

step is made equal to the temperature distribution at the previous

step;

ttJVl - <T>c

Airflow-Thermal Iteration Loop

4. The airflow matrix is evaluated, equation (25), (26), (27) and (28),

using the current estimate temperatures, {T} l

n+ j.

- airflow continuity may be checked, equation (29) and (30).

- the airflow conductance {Cp}[F z

] is assembled into equation (36).

25
5 . The thermal equations (36) are solved (using an appropriate finite

difference schqme) to obtain a better estimate of current

temperatures, {T) 1+

n+ , for the current boundary conditions, imposing

current excitations (boundary conditions) and accounting for any

changes in the system matrices [C] and [K]

.

6. If (T)^ + ^n+ ^ has converged to {T}^a+ £, within acceptable tolerance,

proceed to step 7, otherwise go back to step 4.

Contaminant Dispersal Solution

7 . Solve the contaminant equation (29) (using an appropriate finite

difference scheme).

8. Go back to step 2.

If airflow is a prescribed function of time (equation 25), then iteration

will not be necessary.

If the airflow is dominated by forced convection, then convergence of the

airflow-thermal iteration will be rapid, as forced convection has the

effect of reducing the nonlinearity of thermal equations. Similarly, if

heat transfer within the building system is dominated by other phenomena

than airflow transfer then, again, convergence will be rapid. But as airflow becomes dominated by bouyancy-dr i ven flow, and airflow heat

transfer becomes a dominant mode of heat transfer, then convergence should

be expected to be slower.

For multiple contaminants, including water vapor, step 7 above would simply

be repeated for each contaminant. If the variation of water vapor, or any

other contaminant, is great enough to cause significant changes in zone

densities and specific heat capacities, the Boussinesq approximation may

not provide adequate accuracy. These sources of nonlinearity could be

accounted for within the interative loop above in step 5.

4.9 Multi-Node Models

The next extension of the one-node model is the two-node model. In this

case, the space is divided into two zones, chosen to be representative of

the important zone volumes, such as the occupied (lower) part of a space,

or near known pollution sources, etc. The second zone (node) would be the

balance of the space. The assumption is made that pollutant concentrations

are uniform within each zone, but different from the other zone. Three

such models will be discussed: 1) Two-chamber HVAC system model, 2)

Sandberg's model [22], [23], [24] for ventilation efficiency, and 3) The

m-p model of Ishizu [25]. Figure 8 shows a typical air distribution

system.

26
Q20

A two-chamber model for the HVAC system results in equations which give

ventilation ef f iciency , n v

:

QlOs = S(1-R)Q01 [1 + RS + (RS) 2 + ...]

QlOS S - SR

Qoi 1 - SR

Qoi " Qios l - s

T ' v

= Qio i":'sR

(37)

Qoi = flow rate of outdoor air

QlOs

= the amount of outdoor air that by-passes the occupied space and is

exhausted

S =the fraction of the supply air which by-passes directly to the

return inlet without mixing in the occupied zone

R = the fraction of the return air which is recirculated. The remainder

(1-R) is exhausted.

Sandberg and Skaret [22-24] have developed equations for ventilation

efficiency and a mixing factor. Sandberg's mixing factor, n , appears to be

related to the stratification factor, 8, by,

3 = 1-S, nv

= S

when R = 0

(38)

Figure 9 depicts examples of flows for various cases of idealized mixing.

Figure 9. Ventilation Flow Configurations

27
Japanese researchers [23] have developed a model called the m-p model which

results in the following system of equations: (Figure 10)

c - C^/V + C2V2 /V - Cxp C 2 (l“p) (39)

C

e

'= CiQj^/Q + CbQb /Q - C im + Cb (l-m) (40)

C

1

'- C

L - -- (41) 1 mQ

where m - mixing factor

The mQ portion of the supply air mixes completely with the

room air and the (l-m)Q portion by-passes without mixing

[25].

P position factor

Zone 1 is the region of volume pV where the pollutant

diffuses completely. Zone 2 is the fresh air region of volume

(l-p)V.

Q volumetric flow rate of supply air

G pollutant generation

V volume of the room (Vj,V2 represents volume of zone 1, zone 2)

C average concentration for the whole room

C

e " concentration in the exhaust air

Ci,C 2 “ concentration in the zone 1, zone 2

°b

" concentration in the by-pass air

C

i " concentration in the supply air

From equation (39) and (41), the concentration for the whole room is

C = (c2 + ~)p + c i (1 - p) - “ + c i (42) 1 mQ 1 mQ 1

and the exhaust concentration is

C

e

' (0^ + --)m + Ci(l - m) - £

+ Ci (43)

1 mQ 1 Q

1

28
Cf

mQ, (1-m)Q

Figure 10. Basic Concept for Mixing-Position (m-p) Model

Since the average concentration is proportional to p/m, to make p small

and/or to make m large can be a criterion for effective cleaning of the

indoor air pollutants with a fixed number of air changes.

4. 10 Transport Models

The models which describe how pollutants are transported into the

environment from point sources have had attention in outdoor situations.

This class of models could be used for predicting the local concentration

of contaminants without having to solve the full equation (see section 5).

The following discusses the possible use of these models in indoor

conditions

.

Atmospheric transport models are used to model the transport of pollutant

emitted by stacks [26,27]. They predict downwind concentrations at any

height, including ground level, for different atmospheric conditions and

for various types of terrain. We will concentrate on those aspects of

these models that may be applicable to indoor air quality modeling. The

models, properly modified, will presumably be usable whenever indoor

pollutants are emitted by identifiable point sources, for example,

cigarettes, ovens, gas ranges, and open paint or solvent containers. Using

these models for indoor conditions should be much less complex than for

their original purpose because terrain need not be considered, air velocity

and temperature gradients are very small if not negligible, photochemical

reactions are unimportant and, unlike power plant plumes, indoor "plumes"

would generally only rise by buoyancy and not as jets.

It will be necessary to model ceilings and walls, which obviously do not

restrict outdoor plumes; however, ceilings play the same role as temperature inversion layers, which effectively limit the rise of plumes,

and may be capable of being treated in a similar way. This is shown in

figure 11, which depicts different plume types. Indoors one would expect

either a horizontal spread from a pollutant source, if it is not a flame,

or a nearly vertical rise until the plume reaches the ceiling, after which

it would spread out as in the trapping or fumigating plume types (see

figure 11) until it reaches the walls, where part would reflect back into

the spreading plume while the other part descends. Absorption by surfaces

would have to be taken into account.

The general plume diffusion model, illustrated in figures 12 and 13, assumes that after becoming horizontal, plumes obey Gaussian distributions

29
along the two perpendicular axes transverse to their flow, with the

horizontal standard deviation (measured by a ) greater than the vertical

(measured by a y

). The diffusion equation is as follows [26]:

X(x,y,z) ------— exp [- i (~-) 2

]

* 2ira a zu 2 ay

1 Z““ft « 1 Z+n8 A (exp [- i (~-i)2 + exp [- ;

C-5~) 21>

z

z

1

z (44)

The variables are illustrated in figures 12 and 13. The model is valid for

any consistent set of units. Wind speed must be replaced by an appropriate

velocity for indoor use, for example, the rate at which the plume spreads

horizontally at the ceiling.

TRAPPING

with uniformly varying temperature with elevation: unstable,

adiabatic (neutral), and stable. The bottom three are caused by discontinuities in stability of atmospheric layers.

Note: T temperature; z height. (An adiabatic

temperature gradient is one in which there is no net heat

exchange between the plume and its surroundings).

30
The following equation is for plumes that do not rise:

X(x,y,z,ht 0) - — exp [- - (--) 2

] exp [- - (--) 21 ( 45 ) TTOy »a zU

These equations can predict concentrations at various heights and distances

from the sources, maximum concentrations, and where they occur. For

example, the ground-level concentration calculated from equation 45) is:

X(x,y,0,hB " 0) exp [- i (--) 2

] 2 a., (46)

71 ax » a

zu - -y

The maximum concentration for a given x is found on the centerline.

X(x ,0,0,h =0) (47)

Tra„ a_u

Figure 12. Plume concentration profiles and centerline location

in the vertical xz plane.

Z AXIS

Figure 13. Three-dimensional concentration profiles of a nonrising

point source and centerline of a rising plume for diffusion

calculations at distance x.

31
As mentioned above* these equations would have to be modified for

reflection and absorption by walls and ceilings.

There are specialised models to account for pollutants rising from multiple

stacks [27]; these may be useful for multiple point sources of indoor

pollutants

.

Equations 44 and 45 may be modified for particulates by tilting the

horizontal plume downward by an angle Vg/u, where the numerator is the

terminal velocity of the particulate, ana u is the wind speed. Terminal

velocities are given in reference [26]. An effective plume height, hep»

replaces h

e in the diffusion equation; it is given by:

hep (x) - he (x) - x*V

g

/u (48)

A different such equation must be used for each different value of V

g*(

NBS has also done modeling of smoke movement in spaces, [28-31] which may

also be usable for other pollutants. Smoke plumes in rooms from point

source fires, and the plume's movement to other spaces have been

considered.

4.11 Empirical Models

Empirical indoor air quality models are based on statistical evaluations of

experimental data. They are often analyzed using partial correlation and

linear regression techniques. The following are some examples of this type

of model.

Pickrell et al. [32] developed, for the release of formaldehyde, the

relation:

C - RLF (49)

where C « HCHO concentration (ppm)

R = release rate,

m^day

L = loading factor

F = conversion factor

Anderson et al. [33] used the equation:

(d T + e) (a_H + b) “73a

(mg HCHO/m3 air) (50)

for predicting formaldehyde levels due to particle board emission.

where a,b,c,d,and e empirical constants that are functions of the

type and surface coating of the particle boards.

32
T room air temperature (°C)

H - humidity (g H2 0/kg dry air)

I air change rate (hr

-

^)

a ratio of free particle board area in the room and

total volume of the room (m~^)

In the range of 17-32°C (63-90°F), 5-13 g H2 0/kg air (.005-. 013 lb H2 0/lb

air) and 0.4-3 ACH, the model predicted the actual concentrations of

formaldehyde well, with an average correlation coefficient of about 0.9

[33].

Gammage and Hawthorne [34] used the equation:

AS

1.25 VI

(51)

for relating the indoor concentration of formaldehyde to source strength

and ventilation rate.

where: C = calculated HCHO concentration (ppm)

A * active wall area emitting formaldehyde (m^)

• . mg

S = emission rate ( ) m^ hr

I = rate of air exchange (h“^)

V = room volume (m^)

1.25 = conversion factor

Dockery and Spengler Model [35]

For respirable particles and sulfates, Dockery and Spengler developed

empirically the following expression for the exposure to particulates:

E ” t home C

i + fc out C

o

+ tother ^ C

i + Nsmoke x

For sulfates, the average exposure, e, is given by

t in c

i + fc out c0

e — (53)

fc tot

In equation (52) and (53),

tfacme = time spent in home

t out

s * ^me ou tdoors

33
tin time spent indoors

fc other e time spent indoors away from home

t tot

B total sample length

Nsmoke 9 number of smokers to which a participant was exposed

and and Cq are the average concentrations in the respective areas.

In later work [36] Dockery and Spengler developed the following series of

equations

C

i \

(54)

for the average indoor concentration, where the overbar indicates 24-hour

average values.

In equation (54)

= concentration

P = B

x + b2 (A)

A is an indicator variable for fully air conditioned

B's are empirically determined

^

‘ B

3 < Ncig> + B4 ("W + Bs

<A > + B

o

where N

c £g

= estimated number of cigarettes smoked indoor per day.

For sulfates, they used:

S

q

B

3 ^cig) + b4

(ANcig ) + b

5 (g) + b

6 (AG) + B7 (A) + B

o (55)

where G is an indicator variable for cooking fuel

(1 for gas, 0 otherwise) and

B coefficients are determined by regression on indoor-outdoor

concentration data on the measured parameters.

5. Convection Simulation Models

Indoor air contaminant migration from sources to various zones and/or from

zone to zone in the building by assuming that the contaminant concentration

is constant throughout each zone, or there is perfect mixing in the zone,

has been covered above. While this assumption may be considered valid for

each zone where air is well recirculated and strong localized sources

and/or sinks of the contamintants do not exist, observed data often reveal

34
significant stratification and localized concentration gradients, even in a veil ventilated rooms.

Since the major portion of the mixing is accomplished by the convection

process, the molecular diffusion part being extremely small (approximately

the order of 0.1 air changes per hour), the imperfect mixing problem

requires that one solve for the convective transfer of contaminants in the room as affected by the forced ventilation and natural circulation due to

thermal draft.

The equation of air motion that governs the conventional room convection

process is

p — + (u*V)u *® - Vp + T + F

3t

(56)

where p = density

u *= velocity vector

p = pressure

t = time

V •= mathematical symbol for gradient

The terms of this equation of motion expressed per unit volume of fluid

element are, from left to right:

Rate of momentum increase,

Rate of momentum gain by convection,

Pressure force on element.

Rate of momentum gain by viscous transfer, and

Body force

Introducing an operator to include the effect of convection D/Dt such that

D/Dt = -- + (u* V) (57)

the above equation of motion takes a form of the familiar Newton's equation

DU -* / r rs \ p - “Vp + x + F (58) H Dt

Moreover, the viscous transfer term may be expressed by using the dynamic

viscosity such that

t = yV^u (59)

Another important relationship between the hydrostatic pressure gradient

and air density and that between the air density and air temperature lead

to the form commonly used for the buoyance force

35
( 60 )

-* -f F * g 3 Ti

z where g

83 gravitational acceleration

T s temperature above an arbitrary datum point

3 = the coefficient of thermal expansion

and i % ® the unit vector in the direction of gravity.

Thus the momentum equation for the convection cannot be solved without the

space distribution of air temperature, which in turn requires a solution

for the energy balance equation (neglecting the nonlinear viscous heating

terms), such as

D T o pc--_ =w! tt qh

(61)

where c s specific heat of air

k = thermal conductivity of air

p = air density

q^ = volume heat source strength

After equations (58) and (60) are solved simultaneously, they provide the

space distribution of u, which is essential for the contaminant mass

balance equation

DC

j- = V(DvVO + ,c (62)

where D

v

= diffusion coefficient of the contaminant in the air and q c is

the volumetric contaminant source strength.

Note that the forms of equations (61) and (62) become identical if the

thermal diffusivity k/p c and the mass diffusion coefficient D v are

constant. In addition there exists an additional and important equation

expressing the continuity of air mass such that

V*u “ 0 (63)

In order to predict the contaminant concentration C in the space, it is

essential that the space air velocity vector u and space air temperature T

be solved simultaneously by equations (58), (61) and (63). The solution

must also satisfy prescribed initial and boundary conditions and overall

mass balance relationships.

While the initial conditions for u may be set equal to zero and T and C

may be set at the mean room values, the boundary conditions are specific to

room configuration, air supply and return systems, and heat transfer

characteristics of the room envelope surfaces. The velocities are usually

36
considered zero except where air intakes and outlets are located.

Temperature and concentration at the supply air inlet must also be

provided, whereas those at the outlet are to be calculated to satisfy the

overall energy and mass balance such that total energy and mass generated

in the room is equal to those ventilated out by the exhaust air.

The temperature boundary conditions are usually more complicated, requiring

detailed surface heat balance calculations involving

o heat conducted into the solid surfaces

o long wavelength radiative heat exchange with the surrounding

surfaces

o short wavelength radiative heat input from the sources such as solar

heat gain and/or lighting systems

oheat generated at surfaces, such as heat sources, human bodies,

appliances, lighting fixtures, etc.

o heat convected into the air

o heat stored in the air

o heat stored by solids

Boundary conditions on the contaminant concentration must also include the

emission, adsorption and desorption characteristics of the boundary

surface.

Although equations (57) through (62) provide the fundamental relationships

to determine convective mixing of the indoor air pollutants, actual

solution of these equations applicable to realistic building situations are not easy because the room air motion is highly turbulent and three

dimensional. Its boundary surfaces are complicated by the irregular

geometries of room architecture and internal furnishings. Very difficult

and time consuming numerical calculations using finite difference and/or

finite element methods are necessary to solve these equations together with

additional equations for such properties as turbulent kinetic energy and

turbulent energy dissipation rate, details of which are not warranted in

this report. Numerous publications relating to the solution of room

convection problems are available, a comprehensive summary of which has

been published by Kaizuka [37].

Only recently a comprehensive treatise of turbulent room convection and its

effects upon the contaminant mixing and ventilation effectiveness have been

given by Ishizu [38,39], but only for a simple rectangular room with a simple ventilation system. A similar solution for a completely sealed

chamber has also been given by Rehm and Baum for the simulation of aerosol

migration at the onset of a room fire [40,41]. Some of Ishizu's

calculation results, transcribed from his published work on two dimensional

solutions as well as his unpublished work on three dimensional analysis,

presented at a recent NBS meeting, are illustrated in the attached figures.

Ishizu analyzed a cubic room as shown in figure 14, when the ventilation

inlets, outlets and contaminant point source are moved around to see the

effect of air mixing and ventilation effectiveness.

Figures 15 and 16 depict the air flow velocity vectors and isoconcentration contours in the mid-section (cross section ABC of figure 15)

of the room for case 1 when the air is supplied at the upper left corner of

37
analysis, the contaminant source is located above the middle of the floor,

indicating a relatively stagnant condition in the middle and upper right

corner of the room. Figures 17 and 18 show the similar plots for case 2 when the air inlet was moved to the center of the ceiling, whereas figures

19 and 20 show case 3 when the air inlet was moved near to the exhaust side

of the room indicating that a large portion of the room is unvented.

Figures 21 and 22 represent iso-concentrat ion contours for cases 4 and 5 when the sources are moved to the left corner and to the front of the air

outlet. Using the results of these calculations Ishizu determined the

mixing factor and ventilation effectiveness by integrating the local

concentration data as follows:

m

<c2_:_Ci)

(c""c.r

E = v

G

(Coo - C^Q

(64)

(65)

where m

Ea

G

Q

V

t

c

mixing factor

ventilation effectiveness (the reciprocal of Ishizu's —) see eq.

(23) m

pollutant generation rate

ventilation rate

room volume

time

initial pollutant concentration at t 0

pollutant concentration of supply air

room average pollutant concentration at time t

steady state room average pollutant concentration

Figure 23 summarizes the results of Ishizu's analysis where cases 6 through

10 are also presented to compare the similar analysis previously reported

[25] for the two dimensional room calculations.

This figure reveals the following interesting observations:

1. Mixing factor is independent of the location of the pollutant sources

and only the function of the location of the ventilation system.

2. Three dimensional calculations result in considerably different

results from the two dimensional solution, although the general trend

of ventilation efficiency is the same, being highest when the source

is near the exit and lowest when the mixing factor is the smallest.

38
3.

Although generally the mixing factor is larger as the airflow path in

the room is longer, case 2 mixing is slightly higher than case 1 indicating the complex nature of three dimensional air flow.

One of the intriguing results of the Ishizu analysis is shown in figures

24, 25 and 26, which are the logarithmic plots of local pollutant

concentration decay with respect to time determined at selected points for

cases 1, 2 and 3 when the pollutant emission was suddenly stopped at the

source. Also indicated in those figures are the logarithmic slope of the

room concentration decay representing perfect mixing, (m = 1). Although

the logarithmic concentration decays show almost identical slopes for all

the points investigated for a given room, they differ from case to case,

case 2 being the closest to the perfect mixing. That the local

concentration decay trends are identical, independent of their location in

the room, is somewhat difficult to believe, since some of the points in the

ventilating air stream should experience higher rates of decay than those

in the stagnant area. Although all of these calculations were performed for isothermal room

conditions, without regard to thermal convection, figures 27 through 32

depict results of calculations where the energy equation was simultaneously

solved to include the thermal convection effect. Temperature and

concentration profiles at cross section ABC of the room (figure 14) are

shown in figures 27 and 28 respectively in the case when the cold air

supplied to the room with the floor having a warmer temperature than the

average. Figures 29 and 30 represent the similar plots when the hot air was supplied to the room having the normal ambient temperature. Significant

changes in the concentration contour lines are evident. Also interesting

are plots of local concentration decay at several selected points in the

room as shown in figures 31 and 32. The mixing factors are considerably

lower when the cold air is supplied from the ceiling rather than the warm

air, which is contrary to the conventional understanding of the problem.

Although very interesting and comprehensive, the Ishizu calculations have

several problem areas which need attention before the results can be fully

accepted and extrapolated for general use:

1. The overall grid size used for the calculations was 10x10x10, in which

each boundary takes up two grids, is far too coarse to obtain an accurate

assessment of realistic room air convection and pollutant distribution.

This may be the reason for the peculiar results, such as shown in figures

24, 25 and 26.

2. Inlets and outlets are two grid sizes and too large and unrealistic in

reference to actual room situations.

3. The inlet air velocity profile was assumed straight downward, which is

not common in actual air diffuser systems.

4. Boundary layer calculations were oversimplified, assuming zero

gradients for velocity as well as for the temperature.

5. Mixing factors and ventilation effectiveness are not yet available for

the non-isothermal situations.

39
6. The validation of calculated concentration contours with the measured

data was done only for a 40 cm cube model and the agreements between the

calculated and observed velocity data are only quantitative (figure 33).

7. The model is restricted to extremely simple and elementary geometry and

internal furnishings are not included.

8. Only a single point source is treated.

9. The current model can not handle natural ventilation when the supply

air inlet velocity is zero.

10. Presently the momentum equation is coupled only to the energy

equation, ignoring the fact that the mass is, in reality, also coupled

because the pollutant concentration gradient also causes the buoyant force,

such as in the case when a heavy pollutant gas settles to the lower portion

of the room.

In order for the convection model to be able to provide accurate prediction

of the local concentration of a pollutant, the following research must be

carried out:

1. Ishizu's calculations must be validated with much finer grid. This

entails the vectorization of the calculation algorithms to expedite the

computational speed on very efficient modern computers such as CRAY or CYBER (see for example [40,41]).

2. Improvement of algorithms is needed to handle more realistic boundary

conditions, especially those representing air inlets and outlets.

3. Employment of finite element type calculations is needed, rather than

the finite difference approach, so that complex room geometries, especially

those pertaining to the internal obstructions, can be handled.

4. Through rigorous experimental investigations, reliable data for

checking the accuracy of the calculated concentration distribution,

turbulent energy and turbulent energy dissipation rate must be obtained for

typical rooms with more representative air inlets and outlets.

5. The two-equation model used by Ishizu should be extensively compared to

other simpler models to see under what conditions the latter may be

adequate.

40
z

I \

z

k

10

8

8

7

6

5

4

3

2

1

wo

y v////\

^

\/////

B

:

'

|

/7777777777777777

1234 56789 10 i0

Figure 14. The room configuration, cross section

ABC and grid design used by Ishizu

O

Figure 15. Velocity vectors on cross section ABC when

the air inlet is at the leftmost position

in the ceiling (case 1)

41
o

0

Figure 16. Pollutant iso-concentration contours in cross section ABC for case 1

Figure 17. Velocity vectors on cross section ABC when the air

inlet is at the center of the ceiling (case 2)

42
o

Figure 18. Pollutant iso-concentration contours

in cross section ABC for case 2

Figures 19. Velocity vectors on cross section ABC when the

air inlet is at the rightmost position in the

ceiling (case 3)

43
o

Figure 20. Pollutant iso-concentration contours in cross section ABC for case 3

O

Figure 21. Pollutant iso-concentration contours in cross section ABC

for case 2 except that the source is moved to the lower

left corner of the room (case 4)

44
Figure 22. Pollutant iso-concentration contours in cross section

ABC for case 2 except that the source is moved to the

lower right corner near the air outlet (case 5)

Case 123456789 10

fJ f;J

^ f) gJ

m 0.72 0.75 0.42 0.75 0.75 0.42 0.22 0.11 0.22 0.22

E 1.47 1.12 0.53 0.78 2.70 3.45 0.32 0.10 0.20 7.14

Figure 23. Mixing factors and ventilation effectiveness for three

dimensional calculations (cases 1 through 5) and two

dimensional analysis (cases 6 through 10)

45
10

Key

ooi 1 » *

0 100 200 Time (-)

300

Figure 24. Logarithmic pollutant concentration decay at

various positions in the room under case 1 ventilation conditions

Figure 25. Logarithmic pollutant concentration decay at various

positions in the room under case 2 ventilation conditions

46
T

c

o

c

*>u

c

ou

Time (-)

Figure 26. Logarithmic pollutant concentration decay at various

positions in the room under case 3 ventilation conditions

Figure 27. Isotherms in cross section

ABC under case 2 ventilation when the

supply air temperature is colder than

the floor.

Figure 28. Iso-concentration

contours in cross section ABC

under case 2 ventilation when

the supply air temperature is

colder than floor.

47
Figure 29. Isotherms in cross section

ABC under case 2 ventilation when the

supply air is warmer than the floor.

Figure 30. Pollutant isoconcentration contours under

case 2 ventilation conditions

when the supply air is warmer

than the floor.

Figure 31. Logarithmic concentration decay at selected locations

in the room ventilated with cold air.

48
Figure 32. Logarithmic concentration decay at selected locations

in the room ventilated with warm air.

Figure 33. Comparison between the measured and calculated

velocities and concentrations in cross section

ABC under case 2 conditions.

49
6. Multi“XOOB Building System Models

The development of a multiroom pollutant model will be baaed on procedures

learned in the development of multiroom thermal models. In many cases the

values computed by thermal models i.e., temperature) humidity, and

airflows, are critical parameters in the individual pollutant models.

Therefore the thermal model is an important part of the multiroom

pollutant model. Thermal analysis programs have traditionally been

segmented. They have sequentially computed the room loads, the air

handling system performance, and then the plant performance. Various means have been used to approximate the simultaneous performance of room, system,

and plant within the sequential framework, but these approximations are

believed to be inadequate in many cases.

The DOE-2 program [42] computes the heating or cooling loads of rooms at a constant room air temperature and then uses room air temperature weighting

factors to adjust the load as the room air temperatures change according to

the simulation of system performance. All these calculations are made

using a one hour timestep. This technique has the advantage of

computational speed, especially when several different systems are

simulated for the same building. A primary disadvantage is the inability

to compute the mean radiant temperature, which is important for comfort

analysis

.

The BLAST program [43] uses the heat balance method where the room loads

are computed by solving the simultaneous heat balance equations for room

air and building surface temperatures by approximating the performance of

the air handling system with a simple piece-wise linear model. This allows

great detail in the room simulation, such as radiant temperatures and

variable convection coefficients, but when the subsequent system simulation

indicates that system capacities have been exceeded there is no

recomputation of the room temperatures and loads.

The TARP program [44] is an extension of the BLAST program with an emphasis

on the calculation of infiltration and interroom airflows. Only the room

loads are computed. TARP includes a simple multiroom pollutant model based

on the assumptions of pollutants fully mixed within each room and constant

airflow conditions within each one hour timestep. The TARP program has

been extended to include a detailed calculation of moisture absorption and

desorption in a program called MADTARP [45]. This program includes some residential systems simulation capabilities but retains the one hour

timestep and segmented simulation structure of the earlier programs.

A class of unsegmented building simulations has been developed with a primary emphasis on simulating the control of the air handling system, a prime example of which is the GEMS [46] program. GEMS employs a "state

space" model which solves all the equations representing the controls,

equipment and building structure simultaneously in a small timestep. The

state space model provides a good theoretical framework for solving the

building simulation but it is very time consuming to solve for long

simulation time periods.

The HVACSIM+ program [47] reduces computation time by using different

timesteps for different components being simulated. This program

emphasizes the modular nature of bui lding/HVAC components and employs a

50
complex system of modular equation solving. Computer execution times are still much longer than for the simpler segmented programs.

7 . Future Pollutant Algorithm Development

As seen above, not all pollutants are well enough characterized to

adequately model source strengths or interactions with other materials in

space. A general summary of needed research is given for those pollutants

which are considered in the scope of this project. Further refinement and

definition of these factors would facilitate greater utility of the

prediction models to be developed in this project.

Radon - The source strength models are needed. Currently there is no known

method of assessing a situation (a residence, for example) knowing its

location and construction details, etc. and being able to predict radon

source strengths. Much is known about the geography of "hot spots" and

methods of radon entry, but more work is necessary. Good models exist on daughter production from radon in spaces. Work has also been done on the

interaction of daughters with particles in air and measuring attached and

unattached fractions of daughters. However, more work is needed on this

interaction with particles, space charging, and the effects of high

performance air cleaners. These results are needed in particular for

predictions of health effects resulting from the application of various

control options.

Formaldehyde - HCHO has been the focus of considerable work on emanation

rate modeling. Further work would be helpful on the effects of various

barriers (paints and films) on the emanation rates. Also the effects of

room air humidity interactions are not well enough known, as well as the

effects of absorption and desorption in and from building materials and

furnishings

.

Nitrogen oxides - As seen above, N(>2 has been extensively studied in a number of specific cases (ranges, with various cooking loads, space

heaters, tuned in particular ways, etc.). However, it is not yet possible

to predict the NO2 generated from a variety of cases without measuring

each. Prediction models are needed. In addition, laboratory and field

tests have indicated that NO2 reacts with the environment in the

unpredictable way. This also needs better predictive models.

Tobacco smoke particles - If it is decided that +. 20 % is not accurate

enough for a cigarette emission rate of particulate matter, further

quantification of this rate is needed. Since the rate varies with

different brands and smoking habits, it is felt that averages will have to

be used in the models, so no further work is recommended now. On the other

hand, the particle size and composition of the particles probably have

significant effects on health. Therefore better quantification of those

factors is indicated. In addition, more information on particulate

behavior in electric fields is needed. The effects of aging of smoke with

time may also need refinement in the future.

Carbon Dioxide - CO2 sources and movement within spaces seems to be

complete enough for modeling.

51
ji I Carbon Monoxide - CO needs better methods of predicting its source

strengths from gas ranges and combustion heaters under the wide variety of

combustion situations.

Water Vapor - The source strength of water vapor seems well enough known

but its absorption and desorption into and from building furnishings and

construction materials needs better quantification, as well as its effects

on various pollutants.

8 . Future Model Development

Subsequent work will involve expanding the existing framework based on the

extensive NBS Thermal Analysis Research Project (TARP) which includes a general pollutant model. The expansion will be confined in phase 2 to

residential situations. Specific known pollutant algorithms will be

introduced, involving complex sources and emanation rates. Further

development of the environmental and operational algorithms will be

undertaken. It is planned to include several pollutants in the inputs for

residences with central forced air HVAC systems. The outputs will be

confined to well mixed situations and single node, multiroom cases.

Research will be initiated on a 2 node model and its integration into the

extensive existing thermal models, so these interactions can be added, when

work is complete, at a later stage.

Work will be initiated on the convection model for a single space,

predicting concentrations as a function of time in a three dimensional grid

of the space. Single point sources of contaminants will be covered, as well as multiple point sources. Single and multiple area sources will also

be studied. It is not envisioned at present that a general convection

model can be incorporated in a comprehensive indoor air quality model.

However, studying the predictions of general convection models can give

indications of the limitations of simpler indoor air quality models and

potentially lead to simpler multi-node models which can take into

consideration poor mixing and ventilation effectiveness. It may also be

possible to use room convection models in conjunction with multi-zone

simulation models. In this case, the multi-zone simulation models would

generate the boundary conditions to be used in the convection models.

References

[1] Proceedings of the Third International Conference of Indoor Air Quality

and Climate : Swedish Council for Building Research; Stockholm, Sweden;

August 20-24, 1984; Five Volumes.

[2] "Indoor Air Pollution;" Environment International ; Pergamon Press;

Volume 8, Nos. 1-6, 1982.

[3] Indoor Pollutants ; National Academy of Sciences; National Academy

Press; Washington, DC; 1981.

[4] Repace, J. L. and Lowrey, A. H., "A Quantitative Estimate of

Nonsmokers Lung Cancer Risk from Passive Smoking," Environment

International . Vol. 11, pp. 3-22, 1985.

52
[ 5 ] Ventilation for Acceptable Indoor Air Quality ; ASHRAE Standard 62-

1981, American Society of Heating, Refrigerating, and Air-Conditioning

Engineers; Atlanta, GA; 1981.

[6] NIOSH Recommendation for Occupational Health Standards. MMWR, Vol. 32,

U.S. Department of Health and Human Services, Centers for Disease

Control, 1983.

[7] Traynor, G. W., "Field Monitoring Design Considerations for Assessing

Indoor Exposure to Combustion Pollutants," Lawrence Berkeley

Laboratory, LBL-19844, June 1985.

[8] McNall, P. E., "Indoor Air Quality Modeling Workshop Report," National

Bureau of Standards NBSIR 85-3150, 1985.

[9] Radon in Buildings: National Bureau of Standards Special Publication

581; 1980.

[10] Nero, A. V. and Nazaroff, W. W., "Characterizing the Source of Radon

Indoors," Lawrence Berkeley Laboratory, LBL-16636, 1983.

[11] Kusuda, T., Silberstein, S., McNall, P. E., "Modeling of Radon and Its

Daughter Concentrations in Ventilated Spaces." Journal of the Air

Pollution Control Association . (JAPCA), Vol. 30, pp. 1201-1207, 1980.

[12] Indoor Air Quality Research Strategy ; U.S. Interagency Committee on Indoor Air Quality; U.S. Environmental Protection Agency, Office of

Research and Development; Washington, DC; December 1, 1984.

[13] Matthews, T. G., Reed, T. J., Daffron, C. R., and Hawthorne, A.R.,

"Environmental Dependence of Formaldehyde Emissions from Pressed-Wood

Products: Experimental Studies and Mode 1 ing ." Proceedings . 18th

International Washington State University Particleboard/Composite

Materials Symposium." pp. 10-23, 1984.

[14] Ryan, B., Spengler, J. D., and Letz, R., "The Effects of Kerosene

Heaters on Indoor Pollutant Concentrations: A Monitoring and Modeling

Study," Atmosphere Environment . Vol. 17, pp. 334-447, 1983.

[15] Smoking and Health: A Report of the Surgeon General, U.S. Department

of Health, Education, and Welfare; Publication No. PHS 79-60066, 1979.

[16] Repace, J. L., "Modeling and Measurement of Indoor Pollution from

Sidestream Smoke," U.S Environmental Protection Agency, Sept. 1984.

[17] Janssen, J. E., "Ventilation Stratification and Air Mixing,"

Honeywell, Inc., St. Paul, MN, 1984.

[18] Nagda, N. L., Koontz, M. S., and Rector, H. E., "Energy Use,

Infiltration, and Indoor Air Quality in Tight, Well-Insulated

Residences," Geomet Report ERF-1461, Geomet, Rockville, MD, 1984.

[19] Letz, R., Ryan, P. B., and Spengler, J. D., "Estimated Distributions

of Personal Exposure to Respirable Particles," Eny ironmenta

1

Monitoring and Assessment . 1984.

53
[20] Tsuchiya, T., "Infiltration and Indoor Air Temperature and Moisture

Variation in a Detached Residence," Journal 1

' of the Society of Heating.

Air-Conditioning and Sanitary Engineers of Japan (SHASE), Vol. 54, No.

11, pp. 13-19, 1980.

[21] Kusuda, T. and Miki, M., "Measurement of Moisture Content for Building

Surfaces," Moisture and Humidity. Measurement and Control in Science

and Industry . Instrument Society of America, pp. 297-311, April 1985.

[22] Sandberg, M., "Ventilation Efficiency as a Guide to Design," ASHRAE

Transactions . Vol. 89, pt. 2B, 1983.

[23] Sandberg, M., "What is Ventilation Efficiency?," Building and

Environment . Vol. 16, No. 2., 1981.

[24] Skaret, E. and Mathison, H. M, "Ventilation Efficiency - A Guide to

Efficient Ventilation," ASHRAE Transactions. Vol. 89, Pt. 2B, 1983.

[25] Ishizu, Y. and Kaneki, K., "Evaluation of Ventilation Systems through

Numerical Computation and a Presentation of a New Ventilation Model,"

Transactions SHASE . (Japanese), Vol. 24, 1984.

[26] Strom, G. H., "Transport and Diffusion of Stack Effluents," Air

Pollution. Third Edition. Vol. I, Air Pollutants, Their Transformation

and Transport, pp. 401-501, A. C. Stern Ed., Academic Press, New York,

1976.

[27] Briggs, G. A., "Plume Rise from Multiple Sources," ATDL contribution

no. 91. Atmospheric Turbulence and Diffusion Laboratory, National

Oceanograhic and Atmospheric Laboratory, U.S. Department of Commerce,

Oak Ridge, TN, 1974.

[28] Cooper, L. Y., "Smoke Movement in Rooms of Fire Involvement and

Adjacent Spaces," Fire Safety Journal , 7, pp . 33-46, 1983.

[29] Mulholland, G., Handa, T., Sugawa, 0., and Yamamoto, H., "Smoke

Filling in an Enclosure," ASME/AICHE National Heat Transfer

Conference . 1981.

[30] Mulholland, G. and Ohlemiller, T. J., "Aerosol Characterization of a Smoldering Source," Aerosol Science and Technology. Vol. 1, pp. 59-71,

1982.

[31] Baum, H. R. and Mulholland, G. W., "Coagulation of Smoke Aerosol in a Buoyant Plume," Journal of Colloid and Interface Science . Vol. 72,

1979.

[32] Pickrell, J. A. et al., "Release of Formaldehyde from Various

Consumer Products," Inhalation Toxicology Research Institute, 1982.

[33] Anderson, I., "Indoor Air Pollution Due to Chipboard Used as a Construction Material," Atmos. Environ. . 1975.

[34] Gammage and Hawthorn, "Urea Formaldehyde Foam Insulation Study,"

Franklin Institute Report F-05316-01, 1981.

54
[35] Dockery, D. W. and Spengler, J. D., "Personal Exposure to Respirable

Particulates and Su 1 fates Journa 1 of the Air Pollution Control

Association, 31, pp. 153-159, 1981.

[36] Dockery, D.W. and Spengler, J. D., "Indoor-Outdoor Relationships of

Respirable Sulfate and Particles," Atmos. Environ.. Vol. 15, pp. 335-

343, 1981.

[37] Kaizuka, M., "Numerical Calculation of Air Currents in a Room,"

translated by the National Bureau of Standards from the Journal of the

Society of Heating. Air-Conditioning and Sanitary Engineers of Japan . (SHASE), Vol. 53, No. 3, pp. 13-23, 1984.

[38] Ishizu, Y., "Ventilation Efficiency and the Supply Air Inlet

Locations," paper presented at the SHASE Annual Meeting of 1984

(Japanese)

.

[39] Ishizu, Y., "Evaluation of Ventilation Efficiency through Three

Dimensional Numerical Calculations," lecture delivered at the National

Bureau of Standards, Workshop on Indoor Air Quality Modeling, February

11, 1985.

[40] Baum, H. B., and Rehm, R. G., "Caluc laticn of Three Dimensional

Buoyant Plumes in Enclosures," Combustion Science and Technology. Vol.

40, pp. 55-77, 1984.

[41] Baum, H. R., Rehm, R. G., and Mulholland, G. W., "Prediction of Heat

and Smoke Movement in Enclosure Fires," Fire Safety Journal . Vol. 6,

pp. 193-201, 1983.

[42] "DOE-2 User Guide," Lawrence Berkeley Labortory Report LBL-8698, May

1980.

[43] Hittle, D. C., "The Building Loads Analysis and System Thermodynamics

(BLAST) Program, Version 2.0: Users Manual, Vol. I," Construction

Engineering Research Labortory Report TR-E-153, June 1979.

[44] Walton, G. N., "Thermal Analysis Research Program (TARP) Reference

Manual," National Bureau of Standards . NBSIR 83-2655, March 1983.

[45] Fairey, P. W. and Keresteciog lu, A.A., "Dynamic Modeling of Combined

Thermal and Moisture Transport in Buildings: Effects on Cooling Loads

and Space Conditions," ASHRAE Transactions. Vol. 91, Pt. 2, 1985.

[46] Benton, R., MacArthur, J.W. Mahesh, J. K., and Cockroft, J. P.,

"Generalized Modeling and Simulation Software Tools for Building

Systems," ASHRAE Transactions . Vol. 88, Pt . 2, 1982.

[47] Kelly, G. E., Park, C., Clark, D. P., and May, W. B., "HVACSIM + , A

Dynamic Bui lding/HVAC/Contro 1 Systems Simulation Program,"

Proceedings of the Workshop on HVAC Controls Modeling and Simulation , presented at the Georgia Institute of Technology, Atlanta, GA,

February 2-3, 1984.

55
FORM NBS-114A (REV,) 1-84)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See Instructions)

1. PUBLICATION OR

REPORT NO. NBSIR 85^3265

2. Performing Organ. Report No. 3. Publication Date October 1985

4. TITLE AND SUBTITLE

Indoor Air Quality Modeling - Phase I Report

Framework for Development of General Models

5. authoR(S) Preston McNall, George Walton, Samuel Silberstein, James Axley,

Kunimichi ishiguro, Richard Grot, and T. Kusuda

6. PERFORMING ORGANIZATION (If joint or other than NBS, see In structlons)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Environmental Protection Agency

Environmental Monitoring Systems Laboratory

Research Triangle Park, NC

10. SUPPLEMENTARY NOTES

_3 Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si gnifi cant bibliography or literature survey, mention it here)

This report presents a framework for the development of a model for

predicting the indoor air pollutant concentrations in a variety of building

types under practical conditions of weather, building occupancy, building

construction and pollutant source strength. The general concepts needed

for developing an indoor air quality model are treated. Examples of the

current state of indoor air quality models are given. The pollutants discussed are formaldehyde, radon, nitrogen oxides, tobacco smoke, particulates,

carbon dioxide, and carbon monoxide.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Indoor air pollution; modeling; air pollutants; environmental

parameters; model concepts

13. AVAILABILITY

[3^j Unl imited

[33] For Official Distribution. Do Not Release to NTIS

"1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, DC

" 20402.

I ^ Order From National Technical Information Service (NTIS), Springfield, VA 22161

14. NO. OF

PRINTED PAGES

57

15. Price

USCOMM DC 85-4004