Question 7 of 8: VAV systems, CO 2 -limited occupancy and thermal comfort

Question 7: VAV systems, CO₂-limited occupancy and thermal comfort (20 points)

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.

(a) Variable air volume systems — advantages, disadvantages and where they suit

A variable-air-volume system holds the supply air temperature approximately constant and varies the quantity of air delivered to each zone in response to that zone’s thermostat, using a throttling terminal box. It replaces the constant-volume reheat system, which met the same part-load condition by cooling all the air to the coldest zone’s requirement and then reheating most of it.

Advantages. The dominant one is energy: fan power falls roughly with the cube of flow, so a system spending most of the year near 60% flow uses well under a third of the fan energy of the constant-volume equivalent, and the simultaneous heating and cooling inherent in reheat is eliminated entirely. Because zones rarely peak together, the central plant and the main ducts may be sized on the block load rather than the sum of the peaks, giving 20–30% diversity savings in first cost and plant size. Individual zone control is genuinely good, terminal units are simple and have no coils or condensate to maintain, and the system is easy to extend or re-zone in a speculative office fit-out.

Disadvantages. The first is ventilation: as the box throttles towards minimum, the outdoor-air quantity delivered to that zone falls with it, and the critical-zone ventilation-rate procedure of ASHRAE Standard 62.1 must be applied to guarantee the required outdoor air at minimum flow. The second is dehumidification — at low flow the coil face velocity and load both drop, latent capacity falls faster than sensible, and space humidity can drift upward in mild, humid weather. The third is air distribution: at low flow the supply jet loses throw and the room can stratify or feel draughty near the diffuser, so terminals must be selected for the minimum setting, not the design one. Control complexity is higher (static-pressure reset, terminal calibration, careful commissioning), the system cannot heat a perimeter zone without reheat or a separate perimeter system, and poorly commissioned VAV is a common source of comfort complaints.

Where it is recommended. VAV suits buildings with many zones whose loads vary independently and are predominantly cooling — interior zones of office towers, institutional and commercial buildings, laboratories and hospitals (in specialised pressure-controlled form), and any building with a large diversity between zone peaks and block load. It is a poor choice where the load is steady and uniform, where a space needs constant airflow for pressurisation or contaminant control, in spaces with very high latent fraction, and in small single-zone buildings where its control complexity cannot be justified. Perimeter zones with a winter heating load are normally handled by VAV with reheat, fan-powered boxes, or a separate perimeter heating system.

(b) Occupancy limited by carbon dioxide concentration

Given.

Find. The maximum number of occupants for which the steady-state room CO₂ concentration remains below 1000 ppm.

Approach. Write a steady-state mass balance on carbon dioxide for the room: what the occupants generate must equal what the ventilation air carries away, which is the supply flow times the rise in concentration from supply to room.

1. Write the steady-state carbon dioxide balance. With complete mixing and no CO₂ source other than the occupants, generation equals removal: $$N\,G = \dot V\,(C_r - C_s)$$ where the concentrations are expressed as volume fractions.
2. Evaluate the ventilation capacity for carbon dioxide. $$\dot V (C_r - C_s) = 5000\,(1000 - 200)\times 10^{-6} = 4.00\ \text{cfm of CO}_2$$ This is the volumetric rate of carbon dioxide the airstream can carry out of the room while holding the room at the 1000 ppm limit.
3. Divide by the per-person generation rate. A sedentary adult doing light office work (1.2 met) exhales carbon dioxide at about 0.0106 cfm (0.30 L/min): $$N = \frac{4.00}{0.0106} = 377.4 \;\Rightarrow\; \boxed{377\ \text{people}}$$
4. Sanity-check against the ventilation standard. That occupancy corresponds to $\dot V/N = 5000/377 = 13.3$ cfm of supply air per person. ASHRAE Standard 62.1 requires 5 cfm/person plus 0.06 cfm/ft² for an office, so 13.3 cfm/person of outdoor air is generous — consistent with the fact that the supply is at 200 ppm, essentially outdoor air. If the supply were a recirculating mixture at a higher CO₂ concentration the permitted occupancy would fall sharply: at 600 ppm supply, only 189 people.
5. State the assumptions, as the question requires. (i) Steady state — the room has been occupied long enough for the concentration to level off (the transient takes about three air changes, so 20–30 minutes here). (ii) Complete and instantaneous mixing, so the exhaust and the breathing-zone concentrations are equal. (iii) The 5000 cfm is all outdoor air, or at least all air at the stated 200 ppm. (iv) The only CO₂ source is the occupants; combustion appliances, unvented heaters and CO₂-emitting processes would each reduce the allowable number. (v) Sedentary activity at 1.2 met with an average adult body surface area; at 2.0 met (light industrial work) generation roughly doubles and the permissible occupancy halves. (vi) Carbon dioxide is being used here as a surrogate for occupant-generated bio-effluents; it is not itself hazardous at 1000 ppm, and meeting this limit does not by itself demonstrate acceptable air quality where non-occupant contaminant sources exist.

(c) The ASHRAE comfort chart and the perception of thermal comfort

The ASHRAE comfort chart (ANSI/ASHRAE Standard 55) is a psychrometric chart on which two overlapping polygons are drawn: the acceptable ranges of operative temperature and humidity within which at least 80% of sedentary or slightly active occupants would find the environment thermally acceptable. Two zones are shown because clothing changes seasonally — a winter zone for about 1.0 clo of insulation, centred near 22 °C, and a summer zone for about 0.5 clo, centred near 24.5 °C, with roughly a 3 K spread about each centre. The zones are bounded above in humidity (historically around 12 g/kg, to limit mould growth, and skin wettedness) and have no strict lower humidity bound for comfort itself, though very dry air causes eye, skin and mucous-membrane complaints.

The horizontal axis is operative temperature, not air temperature: the average of air temperature and mean radiant temperature weighted by the respective heat transfer coefficients. This is the chart’s most important feature, because it says explicitly that a cold window or a warm ceiling is thermally equivalent to a change in air temperature. The zone boundaries themselves are contours of the predicted mean vote (PMV) at ±0.5, derived from Fanger’s heat-balance model of the human body.

Thermal comfort is defined in the standard as “that condition of mind which expresses satisfaction with the thermal environment” — a subjective judgement, assessed subjectively. It is governed by six variables: four environmental (air temperature, mean radiant temperature, air speed and humidity) and two personal (metabolic rate and clothing insulation). The chart holds the last two constant at assumed values, which is exactly why it must be re-entered, or the full PMV model used, for a gymnasium, a kitchen or a warehouse where activity or dress differs from the sedentary office assumption. Even inside the comfort zone, satisfaction is not universal: the PMV model predicts a predicted percentage dissatisfied (PPD) of at least 5% at the optimum, because individuals differ. Local discomfort must be checked separately — draught, vertical air temperature difference between head and ankles, radiant asymmetry, and warm or cold floors can each make an occupant uncomfortable while the whole-body index reads neutral. Finally, ASHRAE 55 also permits an adaptive comfort model for naturally ventilated buildings, in which the acceptable indoor temperature is allowed to drift with the prevailing outdoor mean because occupants who can open a window and change their clothing adapt their expectations.