Environmental Engineering Reference
In-Depth Information
Fig. 15.11 Impermeable object in a flow field entering with an angle of 45
: isopotentials (
black
),
streamlines (
white
), velocity field (
arrows
)
flow with a permeable fracture or an impermeable obstacle as well as in the
atmosphere with a solid obstacle.
For the following it is assumed that the thickness of the object can be neglected,
so that it becomes a line object in the 2D model region. For the impermeable case
a solution has been given in form of a complex potential by Churchill and Brown
(
1984
):
i
p
z
2
a
2
F ¼ v
1
ðz
cos
ðaÞ
sin
ðaÞÞ
(15.14)
where
v
1
denotes the absolute value of velocity at infinity.
a
is the half length of the
line object. In Fig.
15.11
we show the result for
a ¼
2 and
a ¼
45
. Closer
evaluation shows that the real part potential has a jump across the line object.
With a rotation of the angle the complementary solution, in which real and
imaginary part of the solution of formula (
15.14
) are exchanged, can be used
also for highly permeable objects. This is considered in the following program.
Variable
perm
is to be used to switch between the two situations. In that case
the streamfunction has a jump at the line object, representing the flux through the
permeable formation.
