Environmental Engineering Reference
In-Depth Information
v
above
v
ambient
Airfoil
v
below
FIGURE 2.29
Different points along the same streamline for the application of Bernoulli's equation.
can be cancelled out on both sides. Referring to
Figure 2.28
, the point la-
belled as 1 is a point on the streamline far in front of the airfoil labelled in
Figure 2.29
as ambient wind. The static pressure at point 1 is thus equated as
a point above the surface of the airfoil as observed in
Figure 2.29
,
Equation
2.9
can be expressed as
1
2
1
2
v
ambient
=
v
above
=
P
ambient
+
P
above
+
a constant
(2.10)
In another condition below the surface of the airfoil, point 1 seen in
Figure 2.28
is again a point on the streamline in front of the airfoil in
Fig
-
the same as the above-airfoil condition. Point 2 labelled in
Figure 2.28
is rep-
resented by a point below the surface of the airfoil observed in
Figure 2.29
.
Hence,
Equation 2.10
is restructured into
1
2
1
2
v
below
=
v
above
=
P
below
+
P
above
+
a constant
(2.11)
For horizontal wind flow, an increase in the wind speed would result in a
decrease in the static pressure. As such, when the air flowing over the top of
the airfoil
v
above
travels faster than the air flowing under the airfoil
v
below
, there
is less pressure on the top
P
above
than on the bottom
P
below
,resulting in the net
pressure expressed as
2
v
below
−
v
above
1
P
=
P
above
−
P
below
=
(2.12)
This resultant net pressure
P
is the input variable of the next power conver-
sion stage of the piezoelectric wind energy harvester, which is the cantilever
bending beam stage, described in the next section.
2.2.1.2 Cantilever Beam Theory
The main objective is to determine how much the vibration-based piezoelec-
tric wind energy harvester would vibrate when wind flows past the harvester.
As the positive/negative net pressure
P
generated due to the aerodynamic
effect of the blade swing is loaded on the tip of the cantilever beam, the beam
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