CD;totalA ¼ ðCD1A1ÞðCD2A2Þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðCD1A1Þ
2 þ ðCD2A2Þ
2
q (8)
With CD1 and CD2 the discharge coefficients of the inlet opening and
outlet opening, respectively, and A1 the inlet opening area and A2
the outlet opening area. Based on Eq. (8) it can be deduced that a
doubling of either the inlet or outlet opening area (A1 or A2) will
lead to an increase of CD,totalA from 1/√2 to 2/√5, i.e. with 26%, and
thus in a theoretical increase of the flow rate with 26% if the surface
pressures at the openings would remain the same. Only doubling of
both opening area A1 and A2 would potentially double the volume
flow rate for this hypothetical situation.
The contours of the CP and jVj/Uref are displayed in Fig. 9. The
figures show that the pressure distribution upstream of the windward
facade is almost identical for the three cases. However, from
Table 2 it can be seen that the local value of CP at the inlet opening
for A2x2_OR0.5 (CP ¼ 0.25) is lower than those obtained for A2
(CP ¼ 0.38) and A2x2_OR1 (CP ¼ 0.37). In addition, they also show
that double-span leeward sawtooth roofs (A2x2_OR1 and OR0.5)
strongly increase the absolute value of the underpressure zone
behind the first span compared to the reference case A2. Furthermore,
the absolute value of the underpressure behind the second
span is a bit lower than that behind the single span of the reference
case A2 (Table 2). Fig. 9 also clearly shows a lower internal positive
pressure in Fig. 9e for A2x2_OR0.5 (0.10 < CP < 0.03), compared to
A2x2_OR1 (0.12 < CP < 0.22), which can be attributed to the higher
pressure equalization resulting from the larger outlet openings for
case A2x2_OR0.5. This reduction in internal pressure increases the
velocity of the jet entering the building and the resulting volume
flow rate. This also explains why the volume flow rate for
A2x2_OR0.5 is higher than for A2x2_OR1 albeit the lower pressure
difference over the building openings. Fig. 9f also shows that the
inlet jet shifts to a slightly more horizontal direction. Note that the
average internal pressure for the double-span geometry A2x2_OR1
is about equal to the single-span geometry A2; i.e. CP z 0.17, and
therefore the volume flow rates of those geometries do not differ
that much.