Test of Model Performance: Evolution of Cigarette Smoke

To develop confidence in the capabilities of the model, it is important to test its predictions against experimental data taken in rooms. Unfortunately, data on the evolution of indoor airborne particles are sparse, and no experiments had been reported prior to the start of the present research effort that include all of the important factors influencing the particle-size distribution. The most suitable experimental data available in the existing scientific literature for testing the model recount the decay of cigarette smoke in a room having a low air-exchange rate (Offer- mann et al. 1985). That experiment was carried out in a closed, unoccupied room of a research “house.” A single cigarette was smoked by machine within the room at a rate of two puffs of 35 ml per minute for a period of six minutes, then automatically extinguished. The particle-size distribution was sampled continuously for 24 hours using a laser-based optical particle counter (PMS, Model LAS-X), with results reported seven times per hour. Simulations of this experiment are described below, and it is shown that by assuming reasonable values for unmeasured vari- ables, reasonable agreement between the measured and predicted aerosol size distribution is obtained.

The fate of the cigarette smoke measured during the experiments of Offermann et al. (1985) was examined using the new indoor-air-quality model. The simulations were initial- ized at 30 minutes following cigarette ignition. The subsequent evolution of the particle-size distribution was simulated for 11 hours; at the end of 11 hours the measured airborne particle concentration had decayed to 23% of its initial value. Calculations were conducted for two different sets of assumptions about the fluid mechanics governing particle deposition: (1) that the deposition process is governed by natural convection flows that occur due to small wall-air tem- perature differences, or (2) that deposition is governed by air turbulence in the core of the room. Predicted particle-size distributions are compared against the experimental data in Figures 3.2 and 3.3 (pp. 60, 61). Both methods of predicting particle-deposition rates are seen to yield model results that agree reasonably with the experimental measurements. Thus, in these simulations

Mathematical Modeling of Indoor Airborne Particle Dynamics

The fate of the cigarette smoke as predicted by the simulation used to generate Figure 3.2 (p. 60) is shown in Figure 3.4 (p. 62). For these circumstances, coagulation is an important loss mechanism for particles of less than approximately 0.2 µ m in diameter, shifting their mass to particles having a diameter in the vicinity of 0.5 µ m. Small particles are affected by coagulation to a greater degree than are large particles because of the greater number concentration of small particles and because of their higher mobility. Deposition to surfaces is an important loss mechanism for particles larger than approximately 0.4 µ m in diameter in this simulation. The large depositional losses for the largest particles are due to gravitational settling. In other situations, loss of particles due to ventilation would be a more important sink, but in this case the air-exchange rate for the room is unusually low.

The predicted size distribution of particle mass deposited during the 11-hour period on different surfaces is shown in Figure 3.5 (p. 63) for the two alternative approaches used to calculate deposition fluxes. For the floor, most of the deposition is due to gravitational settling, and so the results are similar for the two airflow regimes. This is the dominant site of deposition for particles larger than about 0.2 µ m in diameter. For the walls and ceiling, the deposition predictions depend strongly on assumptions concerning airflow. Using the natural convection model with the walls 1 K cooler than the air, uniformly smaller deposition rates are predicted than with the homogeneous turbulence model. Because of the competing effect of gravity, there is essentially no deposition onto the ceiling using the natural convection description; however, the assumed turbulence intensity is strong enough to overcome gravitational settling and cause some particle deposition onto the ceiling.

Mathematical Modeling of Indoor Airborne Particle Dynamics

Figure 3.1. Schematic representation of the ventilation and filtration components of the indoor aerosol model.

f i0

Exfiltration / mechanical exhaust

Return air f ii

f ix ixj

[Chamber i]

Filter

Recirculation / filtration

Mechanical intake

Make-up air (outdoor)

[Chamber h]

Mathematical Modeling of Indoor Airborne Particle Dynamics

Figure 3.2. Evolution of aerosol size distribution following combustion of a single cigarette. Measurements were conducted in a 35 m 3 room with a ventilation rate of 0.05 h -1 (Offermann et al. 1985). In the simulation, the natural convection description of airflow was used to account for particle-deposition rates. All surfaces were assumed to be 1 K cooler than the air in the core of the room. Particle density was assumed to be 1.4 g cm -3 .

400 T=3h

d {log (dp)}

T=7h 200

T = 11 h 200

Particle diameter (µm)

Mathematical Modeling of Indoor Airborne Particle Dynamics

Figure 3.3. Evolution of aerosol size distribution following combustion of a single cigarette. Conditions are unchanged from those of Figure 3.2, except the homogeneous turbulence description of airflow, with K c = 0.3 s -1 and ∆ T = 0, was used to determine the particle-deposition rates.

d {log (dp)}

T=7h 200

T = 11 h 200

Particle diameter (µm)

Mathematical Modeling of Indoor Airborne Particle Dynamics

Figure 3.4. Predicted fate of cigarette smoke. The conditions of the simulation were the same as those used to generate Figure 3.2. Note that coagulation represents a net sink for particles in the four smallest sections and a net source of particles in the larger sections.

dV/d(log [d 200

Particle diameter, µm Initial concentration

Coagulation Ventilation/filtration Deposition Final concentration, 11 h elapsed

Mathematical Modeling of Indoor Airborne Particle Dynamics

Figure 3.5. Predicted size distribution of cigarette smoke aerosol mass deposited per unit area to different surfaces of the test chamber, dJ/d(log d p ). The average deposited mass per unit area is plotted for each size section for the 11-hour period beginning 30 minutes after combustion of the cigarette. The simulation conditions correspond to those used to generate Figures 3.2 and 3.3.

Natural convection

Homogeneous turbulence

(∆T = -1 K)

(Ke = 0.3/s)

dJ Walls d{log dp}

Ceiling Distribution of deposited aerosol mass,

Particle diameter (µm)

Mathematical Modeling of Indoor Airborne Particle Dynamics

Test of Model Performance: Evolution of Cigarette Smoke