Question 19.13: Determination of Multizone Index for a Building Consider a b......
Determination of Multizone Index for a Building
Consider a building* that can be characterized by the following quantities and assumptions: Conductive heat loss coefficient K_{cond} = 15 kW/K. Total heat loss coefficient K_{tot} = K_{min} = 15 + 10 = 25 kW/K during cold weather (with economizer off). K_{tot} = K_{max} = 15 + 25 = 40 kW/K during mild weather (with economizer on).
To allow simple steady-state analysis, assume the building is occupied and conditioned around the clock, with internal heat gains \dot{Q}_{gain} = 300 kW and T_{db,space} = 20°C.
Assumptions: There is a single air handler, the economizer control is designed to maintain constant supply air temperature, and the return air temperature is equal to T_{db,space}.
Then, the economizer equations of Section 19.6.2 are applicable, and the graph of \dot{Q} versus T_{o} has a slope of K_{cond} when T_{min} < T_{o} < T_{max} (economizer regime). When T_{o} < T_{min}, the economizer is turned off and the slope is K_{min}. This is shown in Figure 19.25, where two consumption patterns are indicated, as labeled: economizer (between T_{min} and T_{max}, excess heat gains are vented by economizer) and “ideal” one zone (assuming perfect mixing within building).
Find: \eta_{multiz,heat} of Equation 19.26.
\eta_{multiz,heat} = \frac{Q_{ann,heat,1-z}}{Q_{ann,heat}} and \eta_{multiz,cool} = \frac{Q_{ann,cool,1-z}}{Q_{ann,cool}} (19.26)
Lookup values: Annual heating degree-hours^{†} for several bases (temperatures are determined from bin data of HCB software), HDD(12.5°C) = 36,000 K · h, HDD(8°C) = 20,440 K · h, and HDD(1.25°C) = 5,840 K · h.
* These numbers are representative of a 12,000 m² office building in New Jersey which one of the authors have monitored in detail.
^{†} See Sections 10.2 and 10.3 for a discussion of the degree-day calculation method.
The economizer is turned off when T_{o} is below T_{min}:
T_{min} = \frac{K_{min} T_{bal} – K_{cond} T_{max}}{K_{min} – k_{cond}} (19.27)
The annual heating consumption \dot{Q}_{ann,heat,1-z} is easy to find because it corresponds to the straight line for T_{o} < T_{bal}. Hence, it is given by
\dot{Q}_{ann,heat,1-z} = K_{min} \times HDD(T_{bal}) (19.28)
where HDD(T_{bal}) is the annual heating degreehours for base T_{bal} and
T_{bal} = T_{i} – \frac{\dot{Q}_{gain}}{K_{min}} (19.29)
The annual heating consumption \dot{Q}_{ann,heat} with the economizer mode is a little more complicated because it corresponds to the solid line for T_{o} < T_{min} and to the dashed line for T_{min} < T_{o} < T_{max}. It is given by
\dot{Q}_{ann heat} = K_{cond} \times HDD (T_{max}) + (K_{min} – K_{cond}) \times HDD (T_{min}) (19.30)
The first term in this equation would be the answer if the consumption could follow the dashed line even below T_{min}; the second term adds the correction below T_{min}.
Inserting numerical values, we find
T_{bal} = 20 – \frac{300}{25} = 8°C for which
and
T_{max} = 20 – \frac{300}{40} = 12.5°C for which
HDD(12.5°C) = 36,000 K . h
The economizer is turned off when T_{o} is below T_{min}:
T_{min} = \frac{25 \times 8 – 15 \times 12.5}{25 – 15} = \frac{200 – 187.5}{10} = 1.25°C
The corresponding degree-hours are HDD(1.25°C) = 5840 K·h.
The heating loads are
\dot{Q}_{ann,heat,1-z} = 25 kW/K \times 20,440 K \cdot h = 511 MWh
\dot{Q}_{ann,heat} = 15 kW/K \times 36,000 K \cdot h + (25 – 15) kW/K \times 5,840 K \cdot h = 598 MWh
The multizone index for the economizer mode is
\eta_{multiz,heat} = \frac{\dot{Q}_{ann,heat,1-z}}{\dot{Q}_{ann,heat}} = \frac{511}{598} = 0.85
The overconsumption during the heating season is 598 − 511 = 87 MWh, or 87/598 = 15%.
Comments
There is overconsumption due to multiple zones even though the chiller does not run at all. In effect, the economizer is a form of simultaneous heating and cooling because it increases the airflow for the entire building even though some zones require heating. This penalty could be avoided by means of heat recovery and thermal storage, and the overconsumption index quantifies the potential savings. A simple solution that avoids at least some of this overconsumption is to install two separate air handlers, one for the interior zone and one for the exterior zone.