Athermal wheel is considered to recover heat from the exhaust air of 20,000 air-handling unit operating supplying a hospital in Denver, Colorado. The indoor temperature within the hospital is kept at T_{in} = 68°F during the winter and TT_{in} = 75°F during the summer. The effectiveness of the thermal wheel is 75 percent and it is operated during both the heating and cooling seasons 24 hours/day (365 days/year).
Determine the annual cost savings of using the thermal wheel if the gas-fired boiler efficiency is 80 percent and the chiller COP is 3.5. Use a bin analysis to estimate the annual savings in heating, cooling, and fan energy use. Estimate the payback period for installing the thermal wheel if its initial cost is $30,000. The gas cost is $1/MMBtu and electricity cost is $0.05/kWh. The static pressure added by the thermal wheel on both supply and exhaust fans is 0.55 in. of water.
Chapter 14
Q. 14.3
Step-by-Step
Verified Solution
The annual energy savings can be estimated using a bin analysis based on the following 5°F-bin data for Denver, Colorado (ASHRAE, 1997):
| Hours of Occurence (# of Hrs) |
Average Temperature (°F) |
Temperature Range (°F) |
| 4 | -8 | –10 to –6 |
| 32 | -3 | -5 to 0 |
| 31 | 2 | 0 to 4 |
| 74 | 7 | 5 to 9 |
| 110 | 12 | 10 to 14 |
| 207 | 17 | 15 to 19 |
| 500 | 22 | 20 to 24 |
| 706 | 27 | 25 to 29 |
| 700 | 32 | 30 to 34 |
| 660 | 37 | 35 to 39 |
| 665 | 42 | 40 to 44 |
| 671 | 47 | 45 to 49 |
| 741 | 52 | 50 to 54 |
| 663 | 57 | 55 to 59 |
| 655 | 62 | 60 to 64 |
| 708 | 67 | 55 to 69 |
| 514 | 72 | 70 to 74 |
| 353 | 77 | 75 to 79 |
| 360 | 82 | 80 to 84 |
| 258 | 87 | 85 to 89 |
| 131 | 92 | 90 to 94 |
| 17 | 97 | 95 to 99 |
The energy analysis of the thermal wheel can be divided into three parts:
• Heating energy savings: The annual heating energy savings can be estimated using a bin analysis. Each bin is characterized by an average outdoor temperature \overline{T}_{oa,b} , and a number of hours of occurrence N_{b}:
ΔE_{H}=\dot{m}_{a}.c_{p}.\sum\limits_{b}{N_{b}.(T_{in}-\overline{T}_{oa,b}}
Thus:
ΔE_{H}=(5,000 cfm)*(0.91 Btu/hr .°F.cfm)*\sum\limits_{b}{N_{b}*(68 °F-\overline{T}_{oa,b}}
The heating will be needed as long as the outdoor temperature is below the building heating balance temperature, assumed to be 60oF in this case (due to internal gains; see Chapter 6 for more details); that is \overline{T}_{oa,b}≤ 57°F .
The fuel use savings can be obtained from the heating energy savings ΔEH , and the boiler efficiency η_{b} ,as indicated below:
ΔFU_{H}=\frac {ΔE_{H}}{η_{b}}=\frac {ΔE_{H}}{0.80}
• Cooling energy savings: The sensible cooling energy savings can be estimated by following the same bin analysis considered for the heating energy savings. Thus, cooling energy use savings for each bin can be estimated as indicated below:
ΔEC =\dot{m}_{a} .c_{p} .N_{b} .η_{th} .(\overline{T}_{oa,b} −T_{in,c} )
Therefore:
ΔEC=(20,000 cfm) * (0.91 Btu/hr.°F.cfm)*N_{b}*0.75*(\overline{\bar{T}}_{oa,b} −75°F)
The electricity savings can be obtained from the cooling energy savings ΔEC , and the chiller COP as indicated below:
ΔkWh_{c}=\frac {ΔEC}{COP}*\frac {1 k Wh}{3.412 Btu}
• Fan energy penalty: Because the thermal wheel adds static pressure on both the supply and exhaust fans, additional fan energy is needed to move the air through the duct system. This additional electrical power for one fan can be estimated in terms of horsepower (see Chapter 7):
ΔHp_{fan}=\frac {cfm.ΔP_{s}}{6.356.η_{s}}=\frac {20,000 cfm*(0.45in)}{6.356*0.65}=2.18Hp
Thus, the total fan energy penalty for each bin is determined as follows:
ΔkWh_{fan} = (1.0Hp+ 2* 2.18Hp)*(0.746kW/Hp)*N_{b}
The calculation of the energy savings for both heating and cooling as well as the fan energy penalty has to be performed for each bin as indicated above. The cost savings can then be easily obtained based on the fuel and electricity rates which are, respectively $3/MMBtu and $0.05/kWh.
The results of the bin analysis are summarized in the table below:
| Total Cost Savings ($) |
Fan Energy Penalty (kWh) |
Cooling Electricity Savings (kWh) |
Fuel Use Savings (MMBtu) |
Temperature Range (°F) |
| 76 | 88 | 0 | 27 | –5 to–1 |
| 254 | 320 | 0 | 90 | 0 to 4 |
| 190 | 260 | 0 | 68 | 5 to 9 |
| 283 | 424 | 0 | 101 | 10 to 14 |
| 395 | 656 | 0 | 143 | 15 to 19 |
| 860 | 1,595 | 0 | 313 | 20 to 24 |
| 1,073 | 2,259 | 0 | 395 | 25 to 29 |
| 1,171 | 2,851 | 0 | 438 | 30 to 34 |
| 1,051 | 3,031 | 0 | 401 | 35 to 39 |
| 752 | 2,659 | 0 | 295 | 40 to 44 |
| 628 | 2,871 | 0 | 257 | 45 to 49 |
| 485 | 3,131 | 0 | 214 | 50 to 54 |
| 277 | 3,047 | 0 | 143 | 55 to 59 |
| 0 | 0 | 0 | 0 | 60 to 64 |
| 0 | 0 | 0 | 0 | 65 to 69 |
| 0 | 0 | 0 | 0 | 70 to 74 |
| -33 | 1,559 | 892 | 0 | 75 to 79 |
| 70 | 1,391 | 2784 | 0 | 80 to 84 |
| 114 | 940 | 3223 | 0 | 85 to 89 |
| 91 | 472 | 2293 | 0 | 90 to 94 |
| 3 | 12 | 75 | 0 | 95 to 99 |
| 7,739 | Total Annual Cost Savings: |
It should be noted that the thermal wheel is not operated during the period when the outdoor temperature is in the range of 60 to 74oF (when free cooling can be obtained). The results of the bin analysis indicate clearly that the thermal wheel should also not be operated when the temperature is in the range of 75 to 79ºF.
From the annual cost savings of $7,739, the simple payback period can be estimated to be:
SP=\frac{Initial— Cost}{Annual— Savings}=\frac{\$ 30,000}{\$7,739}=3.9 years
Therefore, the installation of the thermal wheel is cost-effective.