Thermal Distribution Efficiency
As documented in a companion report (Warner 2005), the Home Energy Saver uses the hourly DOE-2 thermal simulation model to estimate heating and cooling consumption. The treatment of air distribution duct losses in DOE-2 has been revised in 2013 such that duct losses are computed each hour throughout the year based on the circumstances around the duct system and TMY weather data for the location being modeled.
The method employed estimates the effect of duct materials and the type of space in which the majority of their duct system is located, since duct losses differ significantly depending on these factors. We used the ASHRAE 152 duct model to estimate duct losses for use as an input to DOE-2 (ASHRAE 1997a). Although this model is intended to calculate seasonal or design duct efficiencies based on detailed diagnostic testing, we assumed typical values for most of the inputs (such as duct surface area, air film resistances, unsealed leakage rates, , and number of return ducts) so that the number of inputs required of the user is reasonable. In the implementation of the model, the duct efficiencies are calculated hourly, depending on duct characteristics, location, buffering of unconditioned spaces and potential regain of heat exchange (for instance, duct losses can moderate the temperatures in buffered spaces such as crawlspaces, attics, and basements such that thermal losses are reduced through surfaces enclosing the primary conditioned space).
Users are able to specify whether or not the ducts are insulated and/or sealed, and the duct location. Insulated ducts are assumed to have R-6 insulation. Based on the work of Lauvray (1978) uninsulated ducts are assigned an insulation value of R-2 (to account for the thermal resistance of the external air film on the ducts which are approximately 1.5 hr/sqft/F/Btu). It is important to note that the model is quite sensitive to duct insulation level and only uninsulated metal ducts should be input as uninsulated.
Unsealed ducts are assumed to have a leakage of 15% of the total air handler flow. Because concerted duct sealing efforts can typically reduce leakage by a significant amount, we assume that sealed ducts have a leakage rate of 3%. As this is a critical input, users are required to specify the duct location. If duct location is not input, its location is inferred based on foundation types and typical building practices.
The ASHRAE 152 model generates duct efficiencies for both the heating and cooling seasons, which are computed hourly. An average computed duct efficiency is passed to the DOE-2 model as an input to the thermal simulation for each hour. This hourly duct efficiency is determined based on the type of heating and cooling equipment in the house, the temperatures and enthalpy of the air surrounding the duct system and the insulation and leakage characteristics of the duct system.
There are a number of calculation steps in the estimates in the ASHRAE 152 model. First, the duct location is defined. Within the calculations, this, in turn, sets how the hourly environmental temperature around the ducts will vary and how much of the losses from the ducts will be regained to the conditioned space. The location data is summarized from the original 152 source, although some of the location parameters are simplified in the HES calculation. The simplified regain fractions used in the HES duct efficiency calculation are based on Walker, 1998 (LBNL-40588), Tables 8-10. Tin is the inside of the home’s conditioned zone. Tdesign in the case of our calculations is actually the hourly air temperature on the TMY record. Regain fraction is the portion of the computed duct losses that actually moderate unconditioned spaces and reduce heat lost through adjacent building components such as floor of the ceiling to attic interface.
Similarly, according to the original ASHRAE standard, modified values of the absolute moisture content of air outside versus inside are estimated for cooling influence from leaking duct return air leakage. Below, we show the relevant portions of the ASHRAE Standard 152 calculation with the original equations in engineering units indexed to the original standard equations.
Surface areas of supply and return ducts outside the conditioned space shall be determined using Equations 6-3a and 6-3b, respectively:
As=0.27 Afloor [Eq. 6-3a]
Ar= 0.05 Stories Afloor [Eq. 6-3b]
Delivery Effectiveness (DE) for Heating Systems
DE is calculated using high capacity (and air-handler fan flow) for design calculations.
The supply and return conduction fractions, Bs and Br, are calculated with the following equations:
where rin is the density of indoor air [use 1.2 kg/m3 (0.075 lb/ft3) at sea level], and Cp is the specific heat of air (0.24 Btu/(lb×°F). The duct leakage factors for the supply and return sides shall be calculated using Equations 6-18:
The temperature rise across the furnace, Dte, is calculated based on the equipment capacity (either input or estimated by DOE-2), Ecap, and the system air flow, Qe.
The difference between the building and the ambient temperature surrounding the supply, Dts, and return, Dtr, shall be calculated with Equations 6-21 and 6-22:
Dtr = tin - tamb,r [Eq. 6-22]
The heating delivery effectiveness shall be calculated using Equation 6-23:
Delivery Effectiveness (DE) for Cooling Systems
The delivery effectiveness is calculated using the system flow rate during cooling,
Bs and Br are determined using Equations 6-13 to 6-16; as and ar shall be determined using Equation 6-18. Dtr shall be determined using Equation 6-22. tsp is the supply plenum dry-bulb temperature, which depends on latent load and shall be calculated using ACCA Manual S 2nd Edition (1997)5 or assumed to be 55°F. The equipment capacity (Ecap) for cooling systems must be negative in Equation 6-25.
18.104.22.168 Enthalpy Calculations for Cooling Systems
The indoor air enthalpy shall be taken from prevailing indoor
conditions during the simulation. Enthalpies shall be calculated for return
duct locations using Equation 6-2b from the original Standard 152 calculations.
The dry-bulb temperature for those locations shall be determined from Table??a
or Table ?? The humidity ratio is the
difference between the indoor or outdoor air humidity ratio from that inside
the building and on the TMY weather tape.
h= 0.240t + w(1061 + 0.444t) [Btu/lb] [Eq. 6-2b]
It should be noted that the calculated duct leakage moisture enthalpy effects in the HES model are modified to account for the fact that only a part of the latent loads from additional added return-side moisture will be removed, in ratio of the sensible heat fraction of the air conditioning equipment (assumed to have an sensible heat ratio or SHR of 0.75). The added moisture not removed, causes the space relative humidity to rise, rather than additional machine power to be expended.
Solar Heat Gain Reduction
If the building simulated has a radiant barrier, low-absorptance roof or tile roof, it is assumed to benefit for cooling duct efficiency calculations if the ducts are located in the attic. The governing equation to calculate t amb,s—the temperature of air surrounding the duct-- from ASHRAE 152 procedure is:
tamb,s = 0.7(tattic)+0.3(tin)
6.5.4 Seasonal Distribution System Efficiency
The delivery effectiveness corrected for regain, DEcorr, shall be calculated using Equation 6-38:
The losses for non-ducted systems and systems with multiple duct locations in HES are described by the following logic:
Boiler pipes are assumed to have a baseline efficiency of 95%, Users are able to indicate whether their pipes are insulated. For insulated pipes we stipulate efficiency of 97.5%.
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