Topic: Efficiency performance curves published by equipment manufacturers may not be in a format helpful for energy modeling. This example presents a manufacturers condensing boiler, and derives a set of data points to which a curve can be fit using DOE2 routines.
The following efficiency curve is published by Aerco, representing the thermal performance of KC-1000 Series condensing boilers; the color annotations have been added by the author:
(click on the image to see a larger version)
The three curves on the chart represent firing rates of 37.5%, 75% and 100% from top to bottom. Thermal efficiency can be read on the vertical axis by knowing the firing rate and return water temperature. eQuest/DOE2 however requires input data points for boiler performance curves to be in entering water temp / leaving water temp / heat input ratio (inverse of thermal efficiency) format.
According to the chart, thermal efficiency is independent of both flow and supply water temperature, so the firing rate data curves and entering water temperature points should indicate efficiency regardless of the infinite combinations of flow rates and supply temperatures possible. This produces however, essentially an infinite number of efficiency curve solutions. To solve this problem, we must temper the manufacturer's published data with a measure of sound engineering judgement.
(click on the image to see a larger version)
Realizing that a low firing rate should occur at low load conditions, a high firing rate at high load conditions, and a mid firing rate somewhere in between, let us make the careful assumption that a high firing rate will result in a 40° (100%) ΔT, a mid firing rate in a 30° (75%) ΔT , and a low firing rate in a 15° (37.5%) ΔT across the boiler.
Using these ΔT's, we can now compute a corresponding leaving water temperature for each of the data points on the chart, except for the five at the extreme right. Efficiency is poorest here as entering water temperature approaches that of leaving water temperature. So dispensing with these data points should not detract much from the resultant accuracy of the curve fit, since our control system and operational sequencing should not allow the equipment to operate in this regime anyway.
Following is the BDL code required for a binomial quadratic curve fit of the Aerco KC-1000 condensing boiler's heat input ratio in terms of entering and leaving water temperatures:
"Aerco-KC1000-HIR" = CURVE-FIT
TYPE = BI-QUADRATIC-T
INPUT-TYPE = DATA
INDEPENDENT-1 = ( 80, 80, 80, 100, 100, 100, 120,
120, 120, 140, 140, 140, 160 )
INDEPENDENT-2 = ( 95, 110, 120, 115, 130, 140, 135,
150, 160, 155, 170, 180, 175 )
DEPENDENT = ( 1.010, 1.070, 1.093, 1.058, 1.111, 1.117, 1.093,
1.136, 1.143, 1.130, 1.143, 1.149, 1.136 )In addition to efficiency, another significant item that needs to be changed when comparing firetube to condensing boilers parametrically is the standby time, which figures directly into standby losses as a percentage of full load capacity.
For example, the default STANDBY-TIME of 0.027 (corresponding to a standby loss of 2.7%) in eQuest may be a bit high for larger firetube boilers; check the manufacturer's data as relative standby losses tend to decrease as boiler size increases. However, condensing boilers do not need to stay warm to avoid thermal shock; hence standby loss factors are on the order of one-tenth that of firetube boilers.
Per Cleaver-Brooks, the standby loss on a 1,000,000 BTU per hour Clearfire condensing boiler is 1810 BTUH or 0.1810%, which translates to a STANDBY-TIME of 0.00181 factor.
