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0.25
0.2
0.15
0.1
0.05
0
0
20
40
60
80
100
Iterations
Fig. 6.
Variation of the drag coefficient with number of iterations for the case shown in Fig. 5
3.4
Hull Drag Calculation
For a body in incompressible flow, the total drag is due to pressure and friction forces,
which are calculated by integrating the pressure (
C
p
) and skin friction (
C
f
) distribu-
tions over the hull surface. The pressure coefficient is defined as
C
p
(
p
-
p
∞
)/
q
∞
,
where
p
is the local static pressure,
p
∞
is free-stream static pressure, and
q
∞
=
(1/2
≡
2
) is the dynamic pressure, with
ρ
∞
as the free-stream density, and the
V
∞
free-stream velocity. The skin friction coefficient is defined as
C
f
ρ
∞
V
∞
≡
τ
/
q
∞
, where
τ
is
the shear stress. Typical
C
p
and
C
f
distributions are shown in Fig. 5.
The total drag coefficient is defined as
C
D
d
/(
q
∞
S
), where
d
is the total drag
force, and
S
is the reference area. Here, we use the frontal-area of the hull as the ref-
erence area. The drag coefficient is the sum of the pressure and friction drag, or
≡
,
C
=
C
+
C
(3)
D
Dp
Df
where
C
Dp
is the pressure drag coefficient and
C
Df
is the skin friction drag coefficient.
The CFD analysis yields static pressure and wall shear stress values (which are non-
dimensionalized to give
C
p
and
C
f
) at the element nodes (Fig. 7). The pressure acts
normal to the surface and the shear stress parallel to it. The pressure drag coefficient
is calculated by integrating from the leading-edge of the nose to the trailing-edge of
the tail
L
C
=
2
π
C
(
x
)
sin
θ
(
x
)
r
(
x
)
dx
(4)
,
Dp
p
0
where
C
p
(
x
) is assumed to vary linear between the element nodes,
(
x
) is angle of
each element relative to the
x
-axis, and
L
is the length of the hull. Similarly, the skin
friction drag coefficient is calculated as
θ
L
C
=
2
π
C
(
x
)
cos
θ
(
x
)
r
(
x
)
dx
(5)
.
Df
f
0
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