The previous section treated the common space air-conditioning problem with the assumption that the system was operating steadily at the design condition. Most of the space requires only a part of the designed capacity of the conditioning equipment most of the time. A control system functions to match the required cooling or heating of the space to the conditioning equipment by varying one or more system parameters. The reheat, variable volume, dual-duct, and multizone systems were discussed in Sec. 2-4.
These systems accommodate off-design partial load conditions, as well as nonstan- dard conditions such as very high latent loads (low SHF). All of these systems gener- ally depend on control of the flow of air and the heating and cooling fluids through the coils common to all systems. Some general understanding of the behavior of heat- ing and cooling coils is required. The physical geometry of a coil is usually dictated by some design condition, probably the peak cooling or heating load. It is then nec- essary to match the coil to the load under varying load conditions. The geometry is fixed; therefore, only a limited number of variables remain for control purposes. These are the fluid flow rates and entering fluid temperatures. The entering air temperature is a function of the load condition and cannot be changed. The other fluid tempera- ture, say water, cannot be varied rapidly enough for control and remains relatively constant for finite periods of time. Thus, two practical methods remain to control the coil. Changing either or both of the fluid flow rates changes the mean temperature dif- ference between the fluids. For example, decreasing the flow rate of chilled water in a coil will tend to raise its leaving temperature. Likewise, reducing the flow rate of the air will tend to lower its leaving temperature. The overall effect is to reduce the coil capacity. The flow rate of the water may be varied by a two-way throttling valve con- trolled to maintain a fixed leaving temperature. The flow of air over the coil may be varied by terminal units in the space or by coil bypass based on air temperature in the space. The effects of these control methods are discussed below.
3-7 Space Air Conditioning—Off-Design Conditions 75
Figure 3-22 Psychrometric diagram for Fig. 3-21.
0.024 0.022 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.026 0.028
Humidity ratio (W),pounds of moisture per pound of dry air
60
55
50
45
40
35
120 30
115
110
105
10095
90
85
80
75
70
6560
55
50
45
4035
25 12.5 30 35
45 50
55 60
10 15 20
d
0 0'
13 2
x
25
40 Dry bulb,F
Dry bulb temperature, F 20%
75 80
85
70 F Wet bulb 14.5 volume, ft
per pound of dry air3 15.0
40%
14.0
13.5
13.0
60% Relative humidity 80%
80 85
35 40
45 50
55 60
65 70
75
15 20
25 30
35 40
45 50
Saturation temperature, F Enthalpy, Btu per pound of dry air
Se nsible heat =SHF
T otal heat–0 .1
–0.3 –0.5
–1.0 –2.0
–48.0.02.0 1.0 1.0
0.8 5000
3000 2000
1500 1000
0.6 0.5 0.4
0.3 0.2 0.1 Space, 0.8
t0' i1i3
i2 iw
t0 t1t3 tx
W1 W2
0.030
Control of the coolant flow rate should be provided for all coils using fluids such as water. This is also important to the operation of the chillers, hot water boilers, and the associated piping systems. Consider what might occur when the load on a variable- air-volume system decreases and the amount of air circulated to the space and across the coil has decreased but the flow rate of chilled water remains constant. Due to the lower air-flow rate through the coil, the air is cooled to a lower temperature and humidity than normal. The space thermostat acts to maintain the space temperature, but the humidity in the space will probably decrease. Further, the space SHF may increase or decrease, complicating the situation even more. This explains why control of the coolant flow rate is desirable. Decreasing the coolant flow rate will tend to increase the leaving air temperature and humidity to a point where the space condi- tion is nearer the design point.
The behavior of the coil in a constant-air-volume face and bypass system is sim- ilar to the VAV system because the coil leaving air temperature and humidity decrease with decreased air flow. However, bypassed air and air leaving the coil are mixed before going to the space. As the space load decreases and more bypass air is used, the space humidity will become quite high even though the design temperature in the space will be maintained. Again, the SHF for the space may increase or decrease, causing further complications. This is a disadvantage of a multizone face and bypass system. Control of the coolant flow rate helps to correct this problem.
In the case of a constant-air-volume system with only coolant flow rate control, the temperature and humidity of the air leaving the coil will both increase with decreased load. The room humidity ratio cannot be maintained since the leaving coolant temperature will increase, reducing the removal of moisture from the air. For this reason, water control alone is not usually used in commercial applications, but is used in conjunction with VAV and face and bypass as discussed earlier. The follow- ing example illustrates the analysis of a VAV system with variable water temperature.
EXAMPLE 3-11
A VAV system operates as shown in Fig. 3-23. The solid lines show the full-load design condition of 100 tons with a room SHF of 0.75. At the estimated minimum load
Figure 3-23 Schematic psychrometric processes for Example 3-11.
0.024 0.022 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.026 0.028
Humidity ratio (W),pounds of moisture per pound of dry air
60
55
50
45
40
35
120 30
115
110
105
100
95
90
85
80
75
70
65
60
55
50
45
4035
25 12.5 30 35
45
50 55
60
10 15 20
d d' 2' 2
3 1
0
25
40 Dry bulb,F
Dry bulb temperature, F 20%
75 80
85
70 F Wet bulb 14.5 volume, ft
per pound of dry air3 15.0
40%
14.0
13.5
13.0
60% Relative humidity 80%
80 85
35 40
45 50
55 60
65 70
75
15 20
25 30
35 40
45 50
Saturation temperature, F Enthalpy, Btu per pound of dry air
Se nsib
le heat =SHF T otal heat–0
.1 –0.3
–0.5 –1 .0 –2.0
–48.0.02.0 1.0 1.0
0.8 5000
3000 2000
1500 1000
0.6 0.5 0.4
0.3 0.2 0.1 0.9
0.75
i2i2' i3
tdtd',t2't2' t3 t1 t0
0.030
of 15 tons with SHF of 0.9, the air-flow rate is decreased to 20 percent of the design value and all outdoor air is shut off. Estimate the supply air temperature and appara- tus dew point of the cooling coil for minimum load, assuming that state 3 does not change.
SOLUTION
The solution is carried out using Chart 1a, as shown in Fig. 3-23. Because the outdoor air is off during the minimum-load condition, the space condition and coil process lines will coincide as shown by line 3–2′–d. This line is constructed by using the pro- tractor of Chart 1awith a SHF of 0.9. The apparatus dew point is seen to be 55 F, as compared with 50 F for the design condition. The air-flow rate for the design condi- tion is given by
or
Then the minimum volume flow rate is
and the minimum mass flow rate may be estimated by assuming a value for v2′:
State point 2′may then be determined by computing i2′:
Then, from Chart 1a, the air condition leaving the coil is 60.5 F db and 57.5 F wb.
Calculation of the coil water temperature is beyond the scope of this analysis; how- ever, the mean water temperature would be increased by about 7 degrees from the design to the minimum load condition due to decreased flow rate. The use of outdoor air during part load is discussed below.
Reheat was mentioned as a variation on the simple constant-flow and VAV systems to obtain control under part-load or low SHF conditions. Figure 3-24 shows how this affects the psychrometric analysis for a typical zone. After the air leaves the cooling coil at state 2, it is heated to state 2′and enters the zone at a higher temperature to accom- modate the required condition. Reheat may be utilized at the central terminal or at the zone terminal boxes where air flow may be regulated as with a VAV reheat system.
A dual-duct system is similar to multizone operation except that mixing occurs at the zone where VAV may also occur. Additional examples for reheat (Example WS3-2), coil bypass (Example WS3-3), and dual-duct VAV (Example WS3-4) are given on the website in both IP and SI units.
The economizer cycle is a system used during part-load conditions when outdoor temperature and humidity are favorable to saving operating energy by using more outdoor air than usual. One must be cautious in the application of such a system,
i i q
m
m m
′ = − = − =
2 3 ˙ 29 4 15 12 000 38 400 24 7
˙ . ( , )/ , . Btu/ lbma
˙ ( )/ . ,
mm =8500 60 13 28 =38 400 lbma/ hr
˙ . ( , )
Qm =0 2 42 700 =8500 cfm
˙ ˙ / , ( . )/ ,
Q2 = m v2 2 60=193 550 13 25 60 =42 700cfm
˙ ˙( )
˙ ( , )
. . ,
m q i i m
2 3 2
2
100 12 000
29 4 23 2 193 550
= −
= − = lbma / hr
3-7 Space Air Conditioning—Off-Design Conditions 77
however, if the desired space conditions are to be maintained. Once the cooling equip- ment and especially the coil have been selected, there are limitations on the quantity and state of the outdoor air. The coil apparatus dew point can be used as a guide to avoid impossible situations. For example, a system is designed to operate as shown by the solid process lines in Fig. 3-25. Assume that the condition line 2–3 does not change, but state 0 changes to state 0′. Theoretically a mixed state 1′located anywhere on the line 0′–3 could occur, but the air must be cooled and dehumidified to state 2.
To do this the coil apparatus dew point must be reasonable. Values below about 48 F are not economical to attain. Therefore, state 1′must be controlled to accommodate the coil. It can be seen in Fig. 3-25 that moving state 1′closer to state 0′lowers the coil apparatus dew point rapidly and soon reaches the condition where the coil process line will not intersect the saturation curve, indicating an impossible condition. It is obvious in Fig. 3-25 that less energy is required to cool the air from state 1′to 2 than from state 1 to 2. There are situations where the outdoor air may be very cool and dry, such as state 0′′in Fig. 3-25. There is no reasonable way to reach state 3 from state Figure 3-24 A simple constant-flow system with reheat.
0.024 0.022 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.026 0.028
Humidity ratio (W),pounds of moisture per pound of dry air
60
55
50
45
40
35
120 30
115
110
105
10095
90
85
80
75
70
65
60
55
50
45
4035
25 12.5 30 35
45 50
55 60
10 15 20 25
40 Dry bulb,F
Dry bulb temperature, F 20%
75 80
85
70 F Wet bulb
15.0
40%
13.5
13.0
60% Relative humidity 80%
80 85
35 40
45 50
55 60
65 70
75
15 20
25 30
35 40
45 50
Saturation temperature, F Enthalpy, Btu per pound of dry air
Se nsible heat =SHF
T otal heat–0 .1
–0.3 –0.5
–1.0 –2.0
–48.0.02.0 1.0 1.0
0.8 5000
3000 2000
1500 1000
0.6 0.5 0.4
0.3 0.2 0.1
Reheat
3
2 2′
1
0
14.5 volume, ft
per pound of dry air3 14.0
0.030
Figure 3-25 Psychrometric processes for an economizer cycle.
0.024 0.022 0.020 0.018 0.016 0.014 0.012 0.010 0.008 0.006 0.004 0.002 0.026 0.028
Humidity ratio (W),pounds of moisture per pound of dry air
60
55
50
45
40
35
120 30
115
110
105
10095
90
85
80
7570
6560
55
50
45
4035
25 12.5 30 35
45
50 55
60
10 15 20
0' 1'
0"
1
0
2 3
25
40 Dry bulb,F
Dry bulb temperature, F 20%
75 80
85
70 F Wet bulb 14.5 volume, ft
per pound of dry air3 15.0
40%
14.0
13.5
13.0
60% Relative humidity 80%
80 85
35 40
45 50
55 60
65 70
75
15 20
25 30
35 40
45 50
Saturation temperature, F Enthalpy, Btu per pound of dry air
Sen sible heat =SHF
T otal heat–0 .1
–0.3 –0.5
–1.0 –2.0
–4.8.002.0 1.0 1.0
0.8 5000
3000
2000
1500 1000
0.6 0.5 0.4
0.3 0.2 0.1
i2
i1 i1'
0.030
0′′and save energy. However, it may be acceptable to use all outdoor air, control the space temperature, and let the space humidity float as it may. There are many other possibilities, which must be analyzed on their own merits. Some may require more or less outdoor air, humidification, or reheat to be satisfactory.
REFERENCES
1. R. W. Hyland and A. Wexler, “Formulations for the Thermodynamic Properties of the Saturated Phases of H2O from 173.15 K to 473.15 K,”ASHRAE Transactions,Vol. 89, Part 2A, 1983.
2. R. W. Hyland and A. Wexler, “Formulations for the Thermodynamic Properties of Dry Air from 173.15 K to 473.15 K, and of Saturated Moist Air from 173.15 K to 372.15 K, at Pressures to 5 MPa,”
ASHRAE Transactions, Vol. 89, Part 2, 1983.
3.ASHRAE Handbook, Fundamentals Volume, American Society of Heating, Refrigerating and Air- Conditioning Engineers, Inc., Atlanta, GA, 2001.
4. James L. Threlkeld,Thermal Environmental Engineering, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1970.
5. R. B. Stewart, R. J. Jacobsen, and J. H. Becker, “Formulations for Thermodynamic Properties of Moist Air at Low Pressures as Used for Construction of New ASHRAE SI Unit Psychrometric Charts,”
ASHRAE Transactions, Vol. 89, Part 2, 1983.
6. ASHRAE Psychrometric Analysis CD, American Society of Heating, Refrigerating and Air- Conditioning Engineers, Inc., Atlanta, GA, 2002.
PROBLEMS
3-1. A space is at a temperature of 75 F (24 C), and the relative humidity is 45 percent. Find (a)the partial pressures of the air and water vapor,(b) the vapor density, and(c) the humidity ratio of the mixture. Assume standard sea-level pressure.
3-2. Determine the humidity ratio, enthalpy, and specific volume for saturated air at one standard atmosphere using perfect gas relations for temperatures of (a)80 F (27 C) and(b)32 F (0 C).
3-3. Suppose the air of Problem 3-2 is at a pressure corresponding to an elevation of (a)5000 ft and (b)1500 m.
3-4. What is the enthalpy of moist air at 70 F (20 C) and 75 percent relative humidity for an eleva- tion of (a)sea level and(b)5000 ft (1525 m).
3-5. The inside surface temperature of a window in a room is 40 F (4 C) where the air has a tem- perature of 72 F (22 C) db, 50 percent relative humidity, and a pressure of 14.696 psia (100 kPa) pressure. Will moisture condense on the window glass?
3-6. What is the mass flow rate of dry air flowing at a rate of 5000 ft3/min (2.36 m3/s) where the dry bulb temperature is 55 F (13 C), the relative humidity is 80 percent, and the pressure inside the duct corresponds to (a)sea level and (b)6000 ft (1500 m)?
3-7. Determine the dew point of moist air at 80 F (27 C) and 60 percent relative humidity for pres- sures corresponding to (a)sea level and (b)5000 ft (1225 m).
3-8. A room is to be maintained at 72 F (22 C) db. It is estimated that the inside wall surface tem- perature could be as low as 48 F (9 C). What maximum relative and specific humidities can be maintained without condensation on the walls?
3-9. Air with a dry bulb temperature of 75 F and a wet bulb temperature of 65 F is at a barometric pressure of 14.2 psia. Using the program PSYCH, find (a)the relative humidity of the air, (b)enthalpy,(c)dew point,(d)humidity ratio, and (e)the mass density of the dry air.
3-10. One thousand cfm of air with a temperature of 100 F db and 10 percent relative humidity (RH) at a barometric pressure of 14.7 psia is humidified under adiabatic steady-flow conditions to 40 percent relative humidity with saturated vapor at 14.7 psia. Use the program PSYCH to find:
(a)the final temperature of the air, (b)the mass of water vapor added to the air, and (c)the leaving volume flow rate.
Problems 79
3-11. Air is cooled from 80 F db and 67 F wb until it is saturated at 55 F. Using Chart 1a, find (a)the moisture removed per pound of dry air,(b)the heat removed to condense the moisture,(c)the sensible heat removed, and (d)the total amount of heat removed.
3-12. Conditions in a room are measured to be 80 F db and 65 F wb, respectively. Compute the humidity ratio and relative humidity for the air at (a)sea level and (b)5000 ft.
3-13. Complete Table 3-3 using the program PSYCH for (a)sea level,(b)5000 ft elevation; (c)com- pare parts (a)and (b).
3-14. The environmental conditions in a room are to be regulated so that the dry bulb temperature will be greater than or equal to 72 F (22 C) and the dew point will be less than or equal to 52 F (11 C). What maximum relative humidity can occur for standard barometric pressure?
3-15. Air enters a cooling coil at the rate of 5000 cfm (2.4 m3/s) at 80 F (27 C) db, 68 F (20 C) wb and sea-level pressure. The air leaves the coil at 55 F (13 C) db, 54 F (12 C) wb. (a)Determine the SHF and the apparatus dew point. (b) Compute the total and sensible heat transfer rates from the air.
3-16. Air flowing in a duct has dry and wet bulb temperatures of 78 F (24 C) and 65 F (18 C), respec- tively. Use psychrometric Charts 1aand 1bto find the enthalpy, specific volume, humidity ratio, and relative humidity in (a)English units and (b)SI units.
3-17. The air in Problem 3-16 is cooled to a temperature of 54 F db and 52 F wb. Use the program PSYCH to compute the heat transfer rate if 4000 ft3/min is flowing at state 1.
3-18. The air in Problem 3-16 is heated to 120 F. Use the program PSYCH to compute the heat trans- fer rate if 4000 ft3/min is flowing at state 1.
3-19. Using the program PSYCH, investigate the effect of elevation on the relative humidity, enthalpy, specific humidity, and density, assuming constant values of 85 F db and 68 F wb tem- peratures at sea level and 6000 ft elevation. If 5000 cfm of air is flowing in a duct, how does the mass flow rate vary between the two elevations?
3-20. Determine the heat transfer rate for a process where 5000 cfm of air is cooled from 85 F db and 70 F wb to 60 F db and 57 F wb using the program PSYCH. (a)For 1000 ft elevation and (b)for 6000 ft elevation. (c)Compute the percent difference relative to the heat transfer rate at 1000 ft elevation.
3-21. Air at 100 F (38 C) db, 65 F (18 C) wb, and sea-level pressure is humidified adiabatically with steam. The steam supplied contains 20 percent moisture (quality of 0.80) at 14.7 psia (101.3 kPa). The air is humidified to 60 percent relative humidity. Find the dry bulb tempera- ture of the humidified air using (a)Chart 1aor 1band (b)the program PSYCH.
3-22. Air is humidified with the dry bulb temperature remaining constant. Wet steam is supplied for humidification at 20 psia (138 kPa). If the air is at 80 F (32 C) db, 60 F (16 C) wb, and sea- level pressure, what quality must the steam have (a)to provide saturated air and (b)to provide air at 70 percent relative humidity?
3-23. Air at 38 C db and 20 C wb is humidified adiabatically with liquid water supplied at 60 C in such proportions that a relative humidity of 80 percent results. Find the final dry bulb temperature.
Table 3-3 Psychrometric Properties for Problem 3-13
Dry Wet Dew Humidity Ratio Enthalpy Relative Mass Density Bulb, F Bulb, F Point, F W, lbv/bma i, Btu/bma Humidity, % ρ, bma/ft3
85 60
75 40
30 60
70 0.01143
100 50
3-24. Two thousand cfm (1.0 m3/s) of air at an initial state of 60 F (16 C) db and relative humidity of 30 percent is to be heated and humidified to a final state of 110 F (43 C) db and 30 percent relative humidity. Assume sea-level pressure throughout. The air will first be heated followed by adiabatic humidification using saturated vapor at 5 psia (34.5 kPa). Using the psychromet- ric chart, find the heat transfer rate for the heating coil and the mass flow rate of the water vapor and sketch the processes on a skeleton chart showing pertinent data. Use (a)English units and (b)SI units.
3-25. Air at 40 F (5 C) db and 35 F (2 C) wb is mixed with warm air at 100 F (38 C) db and 77 F (25 C) wb in the ratio of 2000 cfm cool air to 1000 cfm warm air. Find the resulting humidity ratio and enthalpy using psychrometric Chart 1aon the basis of volume flow rates.
3-26. Rework Problem 3-25, using Chart 1a, with the mixture condition computed on the basis of the mass flow rates rather than volume flow rates. What is the percent error in the mixture enthalpy and humidity ratios?
3-27. The design cooling load for a zone in a building is 250,000 Btu/hr (73 kW), of which 200,000 Btu/hr (59 kW) is sensible cooling load. The space is to be maintained at 75 F (24 C) dry bulb temperature and 50 percent relative humidity. Locate the space condition line on Charts 1aand 1band draw the condition line.
3-28. Assume that the air in Problem 3-27 is supplied to the space at 53 F (12 C). Compute the vol- ume flow rate of the air required in (a)English units and (b)SI units.
3-29. Reconsider Problems 3-27 and 3-28 using the program PSYCH for (a)sea level and (b)2000 ft elevation, respectively. Assume a supply air temperature of 56 F.
3-30. Rework Problem 3-29 using the program PSYCH for 5000 ft elevation.
3-31. The sensible heat loss from a space is 500,000 Btu/hr (146 kW) and the latent heat loss due to infiltration is 50,000 Btu/hr (14.6 kW). The space is to be maintained at 72 F (22 C) and 30 percent relative humidity. Construct the condition line on (a)Charts 1aand 1b. (b)If air is sup- plied at 115 F (46 C), what is the volume flow rate?
3-32. Air enters a refrigeration coil at 90 F db and 75 F wb at a rate of 1400 cfm. The apparatus dew point temperature of the coil is 55 F. If 5 tons of refrigeration are produced, what is the dry bulb temperature of the air leaving the coil. Assume sea-level pressure.
3-33. Air at 80 F db and 50 percent relative humidity is recirculated from a room and mixed with outdoor air at 97 F db and 83 F wb at a pressure corresponding to 2000 ft elevation. Use the program PSYCH to determine the mixture dry bulb and wet bulb temperatures if the volume of recirculated air is three times the volume of outdoor air.
3-34. A building has a calculated cooling load of 20 tons, of which 5 tons is latent load. The space is to be maintained at 72 F db and 50 percent relative humidity. Ten percent by volume of the air supplied to the space is outdoor air at 100 F db and 50 percent relative humidity. The air supplied to the space cannot be less that 55 F db. Assume barometric pressure at sea level, and using the program PSYCH, find (a)the minimum amount of air supplied to the space in cfm, (b)the amounts of return air and outdoor air in cfm,(c)the conditions and volume flow rate of the air entering the cooling coil, and (d)the capacity and SHF for the cooling coil. (HINT: Estimate the amount of outdoor air and supply relative humidity and iterate.)
3-35. Rework Problem 3-34 for an elevation of 5000 feet.
3-36. A building has a total heating load of 200,000 Btu/hr. The sensible heat factor for the space is 0.8 and the space is to be maintained at 72 F db and 30 percent relative humidity. Outdoor air at 40 F db and 20 percent relative humidity in the amount of 1000 cfm is required. Air is sup- plied to the space at 120 F db. Water vapor with enthalpy of 1150 Btu/lbma is used to humid- ify the air. Find (a)the conditions and amount of air supplied to the space,(b)the temperature rise of the air through the furnace,(c)the amount of water vapor required, and (d)the capac- ity of the furnace. Assume sea-level pressure.
3-37. Reconsider Problem 3-36 for an elevation of 5000 feet.
Problems 81