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## Q. 14.3

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 T$T_{in}$ = 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. ## Step-by-Step ## Report Solution ## 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.