Question 8 of 8: Carbon dioxide dilution and thermal comfort (20 marks)

Question 8: Carbon dioxide dilution and thermal comfort (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A ventilation dilution problem and a comfort assessment at a stated room state.

Find. (a) the occupancy at which the space just reaches 1,000 ppm, and (b) a comfort assessment of the stated state for three different occupant groups.

Approach. Part (a) is a steady-state contaminant mass balance on a completely mixed space; part (b) plots the room state against the ASHRAE Standard 55 comfort envelopes and then adjusts for the mean radiant temperature, the metabolic rate and the occupant group.

1. Part (a) — write the steady-state balance. At steady state the carbon dioxide generated in the space equals the net amount carried out by the ventilating air: $$N\,\dot{V}_{\text{CO}_{2}} = \dot{V}_{\text{air}}\,(C_{\text{space}} - C_{\text{supply}})$$ This is the same “source equals removal” statement as a dilution ventilation calculation for any contaminant; the ppm are volume fractions, so no unit conversion is needed on the right-hand side beyond the factor $10^{-6}$.
2. Part (a) — substitute and solve. With $\dot{V}_{\text{CO}_{2}} = 0.005\ \text{L/s} = 5 \times 10^{-6}\ \text{m}^{3}/\text{s}$ per person, $$N = \frac{\dot{V}_{\text{air}}\,(C_{\text{space}} - C_{\text{supply}})} {\dot{V}_{\text{CO}_{2}}} = \frac{3.2 \times (1000 - 260) \times 10^{-6}}{5 \times 10^{-6}} = \frac{2.368 \times 10^{-3}}{5 \times 10^{-6}} = 473.6$$ Occupancy is an integer and the limit must not be exceeded, so $$\boxed{N = 473\ \text{persons}}$$
3. Part (a) — check it against the ventilation standard. At 473 people the outdoor air per person is $3.2 \times 1000/473 = 6.8\ \text{L/s}$, which sits neatly between the 5 L/s per person of the older ventilation standards and the 8 to 10 L/s that ASHRAE Standard 62.1 requires for an assembly space once the floor-area component is included. In other words the 1,000 ppm criterion and the prescriptive ventilation rate are two expressions of the same requirement — which is exactly why 1,000 ppm became the conventional indoor limit. Two caveats belong with the answer: the result assumes complete mixing (a real room with an air-distribution effectiveness of 0.8 would support only about 380 people at the same limit), and 1,000 ppm is an odour and ventilation-adequacy criterion, not a health limit — the occupational exposure limit is 5,000 ppm.
4. Part (b) — fix the room state. At 70 °F dry bulb and 64 °F wet bulb the adiabatic-saturation relation gives $$W = 0.01136\ \text{lb/lb}, \qquad \phi = 72.6\ \%, \qquad t_{dp} = 60.8\ ^\circ\text{F}, \qquad h = 29.2\ \text{Btu/lb}$$ So the space is cool and distinctly humid: the humidity ratio is right at the 0.012 lb/lb upper bound that ASHRAE Standard 55 places on the comfort zone, and the dew point is only 1.4 °F below the 62.2 °F limit.
5. Part (b)(a) — lightly clothed and sedentary. Light clothing is about 0.5 clo, which is the summer assumption, and the summer comfort zone runs roughly 73 to 79 °F operative temperature. With no information to the contrary the mean radiant temperature equals the air temperature, so the operative temperature is 70 °F — 3 °F below the bottom of the zone. The group will feel slightly cool, and the high humidity makes it worse rather than better, because a nearly saturated environment suppresses evaporative loss at the skin without providing any warmth. The verdict is that the space is outside the comfort zone on the cool side, with humidity at its permitted maximum; more than the 20 % of occupants that Standard 55 allows would be expected to complain. The remedy is to raise the dry bulb to about 75 °F and dehumidify to 50 % relative humidity, which moves the state to the middle of the summer zone. (If the group were in fact wearing winter clothing at 1.0 clo, 70 °F would be acceptable on temperature — the winter zone runs 68 to 75 °F — and only the humidity would be marginal; the question specifies light clothing, so the cool verdict stands.)
6. Part (b)(b) — radiant temperature 78 °F, light activity. Two changes act in the same direction. First, comfort responds to the operative temperature, which for still air is the mean of air and radiant temperature: $$t_{o} = \frac{t_{db} + \text{MRT}}{2} = \frac{70 + 78}{2} = 74\ ^\circ\text{F}$$ so the warm surfaces have moved the effective condition to the lower part of the summer comfort zone. Second, going from sedentary (1.1 met) to light activity (about 1.6 met) raises metabolic heat production by roughly a half, and the neutral temperature falls by about 5 °F for that increase. The conclusion is that the group is now at or slightly above neutral rather than cool — the thermal complaint is resolved — but the moisture problem is aggravated, because a more active body needs to reject a larger fraction of its heat by evaporation and the 72.6 % relative humidity is precisely what prevents it. They will report feeling warm and sticky rather than cold. The correct fix is to attack the humidity: dehumidify to 50 % and, if the surfaces cannot be cooled, add air movement, since Standard 55 permits an elevated-air-speed offset of up to about 5 °F at 0.8 m/s for occupants with local control.
7. Part (b)(c) — a retired group playing cards. The research finding here is often misquoted, so it is worth stating carefully: Fanger showed that at the same activity and clothing elderly people prefer the same thermal environment as young adults, because their lower metabolic rate is offset by a lower evaporative loss. The reason they usually need warmer rooms is that their activity is lower. Card playing while seated is about 1.0 met against the 1.1 to 1.2 of ordinary sedentary work, so the neutral temperature rises by roughly 2 to 3 °F, and the 70 °F room that was already 3 °F too cool for the first group is now 5 to 6 °F too cool. Older occupants are also more sensitive to draught and to cold floors, and less able to detect and respond to a slow drift in temperature.
8. Part (b)(c) — so, is a change necessary? Yes. Raise the dry bulb to 75 to 76 °F and reduce the relative humidity to 45 to 50 %, which puts the state in the centre of the comfort zone for 0.5 clo at 1.0 met and simultaneously pulls the dew point down from 60.8 to about 54 °F. Keep the air speed below 0.15 m/s (30 fpm) in the occupied zone and avoid overhead cold-air dumping, keep the vertical air temperature difference between ankle and head below 5 °F, and keep the floor surface above 66 °F. If the group cannot be assumed to be lightly clothed, the alternative of asking them to add a light sweater (0.3 clo) would recover about 4 °F of the shortfall, but changing the room condition is the appropriate design response.