Transient indoor air pollutant concentration Consider a commercial kitchen with a volume of 80 m³ where natural gas is used as a cooking fuel. Assume that after cooking the indoor fume concentration is 1,000 μg/m³. The HVAC system works with a fresh air flow rate of 10 m³/s and an internal

Question

Transient indoor air pollutant concentration
Consider a commercial kitchen with a volume of 80 m³ where natural gas is used as a cooking fuel. Assume that after cooking the indoor fume concentration is 1,000 μg/m³. The HVAC system works with a fresh air flow rate of 10 m³/s and an internal recirculating air flow rate of 1/3 of the fresh air flow rate. Ignore the outdoor and indoor source other than cooking. The intake and recirculating filter efficiencies are both 90 % and the internal air cleaner has a flow rate of 1 m³/s and an efficiency of 95 %. Plot the indoor fume concentration over time.

Accepted Answer

The problem is simplified by ignoring the outdoor and indoor sources other than cooking. After cooking, [latex]\dot{s} = 0[/latex], and [latex]c_{0} = 0[/latex] in Eq. (14.23). This simplification leads to
[latex]c_{i\infty}=\frac{Q_{o}c_{o}(1 - \eta _{o}) + \dot{s}}{Q_{o} - Q_{r}(1 - \eta _{r}) + Q_{i}\eta _{i}}=0[/latex]

Then, Eq. (14.22) becomes
[latex]c_{i}(t)=(c_{i0}-c_{i\infty})\exp \left (-\frac{t}{ au } ight)+c_{i\infty}[/latex] (14.22)
[latex]c_{i}(t)=c_{i0}\exp \left(-\frac{t}{ au } ight)[/latex]

where the time constant is calculated using Eq. (14.24):
[latex] au =\frac{V}{Q_{o} - Q_{r}(1 - \eta _{r}) + Q_{i}\eta _{i}}=\frac{800}{10 - \frac{10}{3}(1 - 0.9) + 1 imes 0.95}=75.35 (s)[/latex]

Then we have
[latex]c_{i}(t)=1000\exp \left(-\frac{t}{75.35} ight)\left(\mu m/m^{3} ight)[/latex]

The plot over time is shown in Fig. 14.4.

In addition to the analytical models above, there are a variety of computation fluid dynamics (CFD) models that can be employed for the predication of indoor air quality and indoor air pollutant concentrations. Readers are recommended to learn these specialized models from other publications including those listed in the Reference section [10–20].

Question 14.4: Transient indoor air pollutant concentration Consider a comm...

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