A leakage model can be used to predict the leakage characteristics of a room or a building from measurements. The models used for leakage prediction are shown in Table 1. The relationship between air flow rate and pressure difference is an exponential equation, commonly referred to as the power law for narrow openings, and is given by equation (1). The exponent n is dependent on the Reynolds number as well as opening geometry (see Fig. 1). The square law for large openings (e.g., purpose-provided openings such as air vents) is given by equation (2). The square law is based on the power law, and becomes the same as the power law when
n = 2. Generally, there are various types of opening geometries, and they may be combined in parallel or in series (see Fig. 1). The parallel combination model is given by equation (3). The theoretical evidence for straight parallel openings with laminar flow favors the quadratic by equation (4) rather than the power law. The problem is to decide which flow equation is the most appropriate to adopt for combination. The parallel combination model can divide a specific effective leakage area (ELA, αA) into ELAs of narrow opening and large opening.
Table 2 presents the overall content of the dataset and contains the year of construction, size of the buildings and several variables related to this information. From daily life, the leakage is usually measured at pressure differences of approximately 10 to 50 Pa. And in the case of high airtight dwellings, the leakage is measured at pressure differences of approximately 30 to 100 Pa. Normally, the flow equation for series or parallel combination is not a power law. Figure 3 shows how the flow equations were fitted to the measured data on leakage (Table 3) of dwelling unit F1 (Fig. 2). Table 4 presents the measured data of the apartment houses given in Table 2. The quadratic equation can provide good fits for the measured data of plots of
Q and
ΔP (see Fig. 4). The parallel combination model's ability to provide a good fit was equivalent to that of the power law.
As shown in Table 5, the ELA at 9.8 Pa (ELA
10) of existing dwelling stocks (built in 1960-1970s) decreased by 30% or more by retrofitting. Retrofitted stocks and new constructions have leakage characteristics similar to narrow openings at low Reynolds number. In addition, differences in leakage characteristics are seen in the same building for different plans, as displayed in Fig. 5. A plan with many windows relative to floor area is reeky. The flow characteristics of cracks around doors and window frames are similar to those of purpose-provided openings (see Table 6). Although these cracks are often narrow, it is because length is short. On the other hand, background openings (e.g., cracks in walls and ceilings) are narrow, and their width (depth) is much less than their length.
Figure 6 shows a low correlation linear fit between ELA
10 per the floor area (ELA
F10) and “power law” exponent n. The relationship between “αA
N / (αA
N+αA
L)” and exponent
n is obtained by regression weighted by measurements (see Fig. 7), where “αA
N” means ELA
10 of the narrow opening at low Reynolds number, and “αA
L” means ELA
10 of the large opening. Therefore, “αA
N / (αA
N+αA
L)” refers to the crack opening ratio. The exponent
n becomes small in the order of stocks (+), retrofitted stocks (▲), and new constructions between 2003 and 2007 (●), and the crack opening ratio becomes high in the same order. This method is effective in the evaluation of retrofitting and leakage characteristics of apartments.
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