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# Mathematical Modeling and Control of Pollutant Dynamics in Indoor Air

## Citation

Nazaroff, William W. (1989) Mathematical Modeling and Control of Pollutant Dynamics in Indoor Air. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/89WP-N863. https://resolver.caltech.edu/CaltechETD:etd-02092007-144249

## Abstract

To assess the total human-health and material-damage risks associated with air-pollutant exposure, the concentrations and fates of pollutants in indoor atmospheres must be understood. Three observations reinforce this point: (1) concentrations of many pollutants are commonly higher in indoor air than in outdoor air, (2) in many countries, people spend more time indoors than outside; and (3) many of the most precious material possessions of society are kept indoors. In this thesis, mathematical models are developed as tools to improve the understanding of pollutant dynamics in indoor air. These tools are applied to the problem of protecting works of art from damage due to air pollutant exposure, particularly for the purpose of understanding how to control soiling due to airborne particle deposition.

A deterministic mathematical model first is formulated to describe the time-dependent concentrations of chemically reactive gases and airborne particles in indoor air, then implemented as a computer program. Using a flexible, multichamber description of a building, the model accounts for the effects of ventilation, filtration, deposition onto surfaces, and direct emission for all pollutants. In addition, the influence of homogeneous photolytic and thermal chemical reactions is computed for gases that are present in the photochemical smog system. The model is capable of determining the chemical composition and size distribution of indoor aerosols, accounting for the effect of coagulation in addition to the processes itemized above. The model computes the fate of pollutants in indoor air, determining the absolute strengths of the sources and sinks for each species.

To permit the simulation of soiling problems, modeling calculations for the deposition of particles and other pollutants onto surfaces are particularly detailed. Equations that predict the rate of pollutant deposition onto indoor surfaces are developed, accounting for the effects of advection, diffusion, and, for particles, gravitational settling and thermophoresis. Three air flow regimes are analyzed: natural convection induced by a temperature difference between the surface and the nearby air, forced laminar flow parallel to a surface, and homogeneous turbulence in the core of the room. The analysis of a vertical isothermal flat plate in natural convection flow shows that, for this flow regime, thermophoresis is an important particle transport process within the boundary layer adjacent to the surface, effectively repelling particles larger than approximately 0.1 µm in diameter if the surface is even a few degrees K warmer than the nearby air.

To test model performance, and to investigate the dynamic behavior of indoor pollutants, the model is applied to several indoor air quality problems. In one case, modeling predictions are made of pollutant concentrations in a museum gallery in Southern California into which photochemical smog is introduced by the ventilation system. Good agreement is obtained between measured and modeled concentrations of NO, NO₂ and O₃. The model predicts substantial production of several species, including HNO₂, HNO₃, NO₃, and N₂O₅, due to chemical reaction within the museum atmosphere. The aerosol mechanics aspects are tested by applying the model to the problem of predicting the evolution of the aerosol size distribution following combustion of a cigarette in a single room having a low air-exchange rate, and good agreement is found between model predictions and measured values.

The completed indoor air quality model next is used to evaluate the soiling hazard to art objects in museums resulting from the deposition of particles containing elemental carbon (soot) or soil dust. Time-resolved measurements of the indoor and outdoor aerosol size distribution in three Southern California museums are reported. Model predictions of indoor aerosol characteristics based on measured outdoor aerosol characteristics and data on building dynamics agree well with measurements. The predictions also show that generally less than 1% of the fine particles (0.05-2 µm in diameter) entering the museums deposit onto the walls. Nevertheless, deposition calculations indicate that, at the rates determined for the study days, elemental carbon (soot) particles would accumulate on vertical surfaces in the museums at a rate sufficient to yield perceptible soiling in characteristic times of 1-40 years, depending on the museum studied. These are very short periods, considering that many art objects are to be preserved indefinitely.

To test the accuracy of the particle deposition calculations, model predictions are made of the annual mean deposition velocity of particles onto the walls of five Southern California museums, using the results of short-term monitoring of near-wall air velocities and long-term monitoring of surface-air temperature differences. The predictions are compared against the results of measurements in these museums of the deposition velocities of sulfates and of fine particles. The modeling and measurement results generally concur, revealing that the deposition velocities for a given particle size vary by a factor of as much as 30 among the sites studied, with the lowest values associated with laminar forced flow adjacent to the building walls, and highest values found in museums where deposition is driven by turbulence in the core of the room.

Methods for reducing the soiling rate of objects displayed in museums are identified and include the following: (1) reducing the rate of supply of outdoor air into the building; (2) increasing the effectiveness of particle filtration; (3) altering the air flow conditions within the building to reduce the particle deposition velocity onto surfaces of concern; (4) placing objects within display cases or framing objects behind glass; (5) managing the building site to achieve low outdoor concentrations; and (6) eliminating indoor particle sources. The mathematical model of indoor aerosol dynamics is combined with experimental data collected at an historic museum in Southern California to determine the potential effectiveness of these control measures. According to model results, with careful design of control measures the soiling rate can be reduced by at least two orders of magnitude, thereby extending to periods of a century or more the time before noticeable soiling will occur.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Environmental Engineering Science
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Environmental Science and Engineering
Thesis Availability:Public (worldwide access)
• Cass, Glen Rowan
Thesis Committee:
• Cass, Glen Rowan (chair)
• Shair, Fredrick H.
• Seinfeld, John H.
• Brooks, Norman H.
• Flagan, Richard C.
Defense Date:27 September 1988
Funders:
Funding AgencyGrant Number
Getty Conservation InstituteUNSPECIFIED
Earle C. Anthony FellowshipUNSPECIFIED
ARCS FoundationUNSPECIFIED
Air Pollution Control AssociationUNSPECIFIED
Switzer FoundationUNSPECIFIED
Record Number:CaltechETD:etd-02092007-144249
Persistent URL:https://resolver.caltech.edu/CaltechETD:etd-02092007-144249
DOI:10.7907/89WP-N863
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