Question 19.5: Analysis of CAV Systems under Part-Load Operation Consider t......
Analysis of CAV Systems under Part-Load Operation
Consider the CAV system that was analyzed under peak-load condition in Example 19.1. This example will serve to illustrate how the CAV system needs to be operated under part-load condition so as to maintain satisfactory indoor space conditions. We conditions. We will determine the cooling coil loads as well as the reheat energy required in this case. We assume the same zone and cooling coil outlet temperatures and the amount of ventilation air as stipulated in Example 19.1. The outdoor air conditions are 80°F and 60% RH, while the space cooling load is 70,000 Btu/h with SHR_{space} = 0.7.
Figure: See Figures 19.1 and 19.4.*
Assumptions: The location is at sea level. The supply air mass flow rate = 17,140 lb_{a}/h. The duct heat transfer and the fan air temperature rise are ignored for simplicity. The preheat and steam humidifier are inactive.
Given: SHR_{space} = 0.70, \dot{Q}_{space,tot} = 7 0,000 Btu/h, \dot{Q}_{space,sen} = 70,000 \times 0.7 = 49,000 Btu/h
Outdoor conditions: T_{db,o} = 80°F, \phi_{o} = 0.6, \dot{V}{0} = \dot{V}_{0} = 1000 ft^{3}/min
Cooling coil conditions: T_{db,3} = 58°F and \phi_{3} = 0.8.
Space condition: T_{db,6} = 78°F and supply air mass flow rate = 17,140 lb_{a}/h
Find: \dot{Q}_{cc,tot}, \dot{Q}_{cc,sen}, and \dot{Q}_{hc,tot}
Lookup values: Specific volume v_{0} = 13.9 ft^{3}/lb_{m}, humidity ratio W_{0} = 0.01325 lb_{w}/lb_{a}, W_{3} = 0.0082 lb_{w}/lb_{a}, specific heat of air c_{a} = 0.24 Btu/(lb_{a} · °F), and latent heat of vaporization h_{v} = 1075 Btu/lb_{w}
* Numerical values shown in the figure do not correspond to this example.
1. Calculate outdoor air mass flow rate
\dot{m}_{a,0} = \frac{\dot{V}_{0}}{v_{0}} = \frac{1000 ft^{3}/min \times 60 min/h}{13.9 ft^{3}/lb_{a}} = 4320 lb_{a}/h2. Calculate supply air temperature point 5 using sensible heat balance since the room thermostatic control is based on dry-bulb temperature.
Using sensible heat balance equation:
T_{db,5} = T_{db,6} – \frac{\dot{Q}_{space,sen}}{\dot{m}_{a} \times c_{a}}
= 78°F – \frac{49,000 Btu/h}{17,140 lb_{a}/h \times 0.24 Btu/(lb_{a} \cdot °F)}
= 66.1°F
3. Verify indoor comfort.
Calculate humidity ratio of air leaving room using a latent heat balance
or
W_{6} = W_{5} + \frac{\dot{Q}_{space,lat}}{\dot{m}_{a} \times h_{vap}} = 0.0082 lb_{w}/lb_{a}+ \frac{70,000 Btu/h \times (1 – 0.7)}{17,140 lb_{a}/h \times 1,075 Btu/lb_{w}} = 0.00934 lb_{W}/lb_{a}
This corresponds to an indoor relative humidity of \phi_{o} = 45%, which along with a dry-bulb temperature of 78°F is satisfactory for indoor human comfort.
4. Calculate mixed-air condition point 1.
A common assumption that simplifies the analysis is to assume a constant-specific heat of moist air c_{a}. The energy balance equation can then be expressed as
or
17,140 lb_{a}/h \times T_{db,1} = (17,140 – 7,320) lb_{a}/h \times 78°F + 4,320 lb_{a}/h \times 80°Fresulting in T_{db,1} = 78.5°F.
Similarly, the humidity is determined as W_{1} = 0.0103 lb_{w}/lb_{a}.
5. Determine cooling coil loads(process 1–3).
Using the simplified expressions for sensible and latent loads, we have
a. Sensible load (Equation 13.45)
\dot{Q}_{cc,sen} = 17,140 lb_{a}/h \times 0.24 Btu/(lb_{a} \cdot °F) \times (78.5 – 58)°F
= 84,329 Btu/h = 7.03 tons
b. Latent load (Equation 13.46)
\dot{Q}_{lat} = \dot{m}_{a} h_{vap} (W_{1} – W_{2} ) (13.46)
\dot{Q}_{cc,lat} = 17,140 lb_{a}/h \times 1075 Btu/lb_{w} \times (0.0103 – 0.0082) lb_{w}/lb_{a}
= 38,931 Btu/h = 3.24 tons
c. Total load
\dot{Q}_{cc,tot} = 84,329 + 38,931 = 123,260 Btu/h =10.27 tons
6. Determine reheat coil load.
Using the sensible heat equation, reheat load
\dot{Q}_{rh,tot} = 17,140 lb/h \times 0.24 Btu/(lb_{a} \cdot °F) \times (66.1 – 58) °F
= 73,320 Btu/h
Comments
The reheat is an energy penalty in that the single airstream supply to the space has to be overcooled in order to provide the dehumidication necessary for occupant comfort and then reheated in order to negate this overcooling. This is a good illustration of the concept of coil bucking stated earlier.