6P is the pressure difference across the door (Pa), and

p is the air density (kg/m3)。

Further simplifications (e。g。 Eq。 (2) were made by Yuill to the model [5,7]。 Charts were developed to directly obtain overall air coefficient, CA, which depends on the door  usage  frequency and the door type, and simplified pressure charts for the pressure factor, Rp, were also suggested [7]。 Based on a number of assumptions, the pressure factor, Rp, was suggested to be used as a design value for the pressure difference across the door [5]。 These assumptions are,

(1) steady winds of 6。7 m/s (15 mph) with no correction for terrain,

(2) the location of the neutral pressure plane at the building’s mid- height, and (3) that the draft coefficient to be 0。9 [5] The value of Rp, which can also be obtained from the charts given, depends only on the height of the building and the outdoor temperature [4,5]。 Q = CAARporQ = CAA,6P (2)

Or for a known door size Q = CRporQ = C,6P

Where CA is the overall air coefficient (single door or vestibule door) or C is the overall door coefficient (m3/s Pa1/2),

sitivity study was also conducted to see the impact of temperature variations on the results using the Rp factor charts of ASHRAE [8]。 In addition, they completed the study assuming that the size of main entrance doors in all buildings types are 0。9 m × 2。1 m (W × H) [4]。 The results of their study showed that vestibule doors can result in national weighted energy savings [15,17] of a maximum of   5。61%

in the strip mall building and a minimum of 0。03% in the outpa- tient healthcare building。 The currently available ANSI/ASHRAE/IES Standard 90。1 Prototype Building Models, which are readily used by  researchers  [1,4],  [18–21],  include  the  single  vestibule  infil-

tration rates calculated from the PNNL study (based on constant outdoor temperature of 16 ◦C in all climate zones) as a separate input, besides all the other modeled building leakages  [4]。

In a study by Mahajan et al。 [11], an analytical method was pro- posed to calculate the pressure difference across automatic doors and to calculate their infiltration rates using the coefficients pro- posed by Yuill [5]。 The process, which is validated by comparison to field data, was used to calculate the infiltration rates through the single and vestibule doors in the standalone restaurant refer- ence building model for two design days [11]。 It was concluded that building specific infiltration rates calculated can differ greatly from those proposed by the PNNL study [4] and while still indicating that vestibule doors can reduce air infiltration through the entrance door of the reference building studied [11]。 However, no energy simulations were conducted for the building and it was indicated that this process was limited to only certain door configurations and hardly applicable for annual building simulations  [11]。

Recently, to better quantify infiltration through buildings, the

U。S。 National Institute of Standards and Technology (NIST) devel- oped multi-zone airflow network models of all the DOE reference buildings [22], which makes it possible to calculate detailed annual whole building infiltration rates [13,23]。 Based on the NIST airflow simulation software CONTAM [24], these multi-zone airflow net- work models use transient weather data to calculate transient air infiltration (through openings and leakages) at each time step sim- ulated。 This method thus provides more realistic estimations for air infiltration since they consider the outdoor weather, internal zonal/system interactions, stack effect etc。 in the buildings [22]。 The studies conducted by Wang et al。 [12,13,25] and Goubran et al。 [9], which aimed to assess the energy savings realized by the use of air curtain doors (in comparison to vestibule doors), utilized the CONTAM reference building models [22] to calculate yearly air infil- tration。 Wang used a coupled CONTAM-TRNSYS model to calculate the yearly energy savings in heating and cooling generated by the air infiltration reductions (achieved from the use of the air curtain) in the medium office DOE reference building model in 8 climate zones [13] (the study does not use the ASHRAE 90。1 EnergyPlus model)。 The use of TRNSYS [26] in Wang’s study was mainly jus- tified by the availability of the data interface with CONTAM [13]。 However, no studies have been found that utilized either coupled or uncoupled CONTAM-EnergyPlus simulations for the study of energy impact of building  entrances。