|
End use |
fhot |
fdur |
|
Shower |
|
WFk × DLMk |
|
Bath | ||
|
Faucet |
0.50 |
1 |
|
Clothes washer |
0.22 | |
|
Dish washer |
1 |
The schedule of hot water use that drives energy calculations is derived from measured data as described in Appendix F (Kruis, 2019). That analysis produced 365 day sets of fixture water draw events for dwelling units having a range of number of bedrooms. The draws are defined in the file DHWDU.TXT (for single-family) that installs with CBECC-Res. Each draw is characterized by a start time, duration, flow rate, and end use. The flow rates given are the total flow at the point of use (fixture or appliance). This detailed representation allows derivation of draw patterns at 1-minute intervals as is required for realistic simulation of heat pump water heaters.
The fixture flow events are converted to water heater (hot water) draws by (1) accounting for mixing at the point of use and (2) accounting for waste and distribution heat losses:
Equation 1
VSk – VDk x ∫dur x VQk x ∫hot
Where
VSk = Hot water draw at the kth water heating system’s delivery point (gal)
VDk = Mixed water draw duration at an appliance or fixture (min) served by the kth water heating system, as specified by input schedule
VQk = Mixed water flow at an appliance or fixture (gpm) served by the kth water heating system, as specified by input schedule
fhot, fdur, fq = End-use-specific factors from the following:
|
End use |
fhot |
fdur |
|
Shower |
|
WFk × DLMk |
|
Bath | ||
|
Faucet |
0.50 |
1 |
|
Clothes washer |
0.22 | |
|
Dish washer |
1 |
Ts = Hot water supply temperature (ºF); assumed to be 115 °F
Tinlet = Cold water inlet temperature (ºF) as defined in Section B1.2. Note that Tinlet may be tempered by drain water heat recovery (DWHR).
WFk = Hot water waste factor
•WFk = 0.9 for within-dwelling-unit pumped circulation systems (see Table B-1)
•WFk = 1.0 otherwise
DLMk = Distribution loss multiplier (unitless), see Equation 5.
The individual water heater draws are combined to derive the overall demand for hot water.
For each hour of the simulation, all water heater draws are allocated to 1 minute bins using each draw’s starting time and duration. This yields a set of 60 VSk,t values for each hour that is used as input to the detailed heat pump water heater (HPWH) and instantaneous water heater models in later sections. For hourly efficiency-based models used for some water heater types, the minute-by-minute values are summed to give an hourly hot water requirement:
Equation 2
In cases where multiple dwelling units are served by a common water heating system, the dwelling unit draws are summed.
In cases where there are multiple water heating systems within a dwelling unit, the draws are divided equally among the systems. For minute-by-minute draws, this allocation is accomplished by assigning draws to systems in rotation within each end use weighted by the number of fixtures of each type are served by each system. This ensures that some peak draw events within each end use get assigned to each system. Since heat pump water heater performance is non-linear with load (due to activation of resistance backup), allocation of entire events to systems is essential. Note that the assignment scheme allocates draws by end use as opposed to specific draws to specific systems. Explicit draw assignment would require plumbing layout information – capturing that is deemed to impose an unacceptable user input burden.
