Sign-up for free online course on ANSYS simulations!| Panel |
|---|
| Wiki Markup |
| {panel}
Author: Rajesh Bhaskaran, Cornell University Problem Specification |
Problem Specification
Consider fluid flowing through a circular pipe of constant cross-section. The pipe diameter D = 0.2 m and length L = 8 m. The inlet velocity Ūz = 1 m/s. Consider the velocity to be constant over the inlet cross-section. The fluid exhausts into the ambient atmosphere which is at a pressure of 1 atm. Take density ρ = 1 kg/ m3 and coefficient of viscosity µ = 2 x 10-3 kg/(ms). The Reynolds number Re based on the pipe diameter is
| Wiki Markup |
|---|
University {color:#ff0000}{*}Problem Specification{*}{color} [1. Create Geometry in GAMBIT|Laminar Pipe Flow - Pre-Analysis & Start-Up] [2. Mesh Geometry in GAMBIT|Laminar Pipe Flow - Geometry] [3. Specify Boundary Types in GAMBIT|Laminar Pipe Flow - Mesh] [4. Set Up Problem in FLUENT|FLUENT - Laminar Pipe Flow Step 4] [5. Solve\!|FLUENT - Laminar Pipe Flow Step 5] [6. Analyze Results|FLUENT - Laminar Pipe Flow Step 6] [7. Refine Mesh|Laminar Pipe Flow - Verification & Validation] [Problem 1|Laminar Pipe Flow - Exercises] [Problem 2|FLUENT - Laminar Pipe Flow - Problem 2] {panel} h2. Problem Specification !Fluent_pipeflow.jpg|width=32,height=32! Consider fluid flowing through a circular pipe of constant cross-section. The pipe diameter _D_ = 0.2 m and length _L_ = 8 m. The inlet velocity _Ū{_}{_}{~}z{~}_ = 1 m/s. Consider the velocity to be constant over the inlet cross-section. The fluid exhausts into the ambient atmosphere which is at a pressure of 1 atm. Take density _ρ = 1 kg/ m{_}{_}{^}3{^}_ and coefficient of viscosity _µ = 2 x 10{_}{_}^\-3{^}_ _kg/(ms)._ The Reynolds number _Re_ based on the pipe diameter is {latex} \large $$ {Re} = {\rho {\bar{U}}_zD \over \mu} = 100 $$ {latex} |
where
...
Ū
...
z
...
is
...
the
...
average
...
velocity
...
at
...
the
...
inlet,
...
which
...
is
...
1
...
m/s
...
in
...
this
...
case.
...
Solve
...
this
...
problem
...
using
...
FLUENT.
...
Plot
...
the
...
centerline
...
velocity,
...
wall
...
skin-friction
...
coefficient,
...
and
...
velocity
...
profile
...
at
...
the
...
outlet.
...
Validate
...
your
...
results.
...
Note:
...
The
...
values
...
used
...
for
...
the
...
inlet
...
velocity
...
and
...
flow
...
properties
...
are
...
chosen
...
for
...
convenience
...
rather
...
than
...
to
...
reflect
...
reality.
...
The
...
key
...
parameter
...
value
...
to
...
focus
...
on
...
is
...
the
...
Reynolds
...
no.
...
Preliminary
...
Analysis
...
We
...
expect
...
the
...
viscous
...
boundary
...
layer
...
to
...
grow
...
along
...
the
...
pipe
...
starting
...
at
...
the
...
inlet.
...
It
...
will
...
eventually
...
grow
...
to
...
fill
...
the
...
pipe
...
completely
...
(provided
...
that
...
the
...
pipe
...
is
...
long
...
enough).
...
When
...
this
...
happens,
...
the
...
flow
...
becomes
...
fully-developed
...
and
...
there
...
is
...
no
...
variation
...
of
...
the
...
velocity
...
profile
...
in
...
the
...
axial
...
direction,
...
x
...
(see
...
figure
...
below).
...
One
...
can
...
obtain
...
a
...
closed-form
...
solution
...
to
...
the
...
governing
...
equations
...
in
...
the
...
fully-developed
...
region.
...
You
...
should
...
have
...
seen
...
this
...
in
...
the
...
Introduction
...
to
...
Fluid
...
Mechanics
...
course.
...
We
...
will
...
compare
...
the
...
numerical
...
results
...
in
...
the
...
fully-developed
...
region
...
with
...
the
...
corresponding
...
analytical
...
results.
...
So
...
it's
...
a
...
good
...
idea
...
for
...
you
...
to
...
go
...
back
...
to
...
your
...
textbook
...
in
...
the
...
Intro
...
course
...
and
...
review
...
the
...
fully-developed
...
flow
...
analysis.
...
What
...
are
...
the
...
values
...
of
...
centerline
...
velocity
...
and
...
friction
...
factor
...
you
...
expect
...
in
...
the
...
fully-developed
...
region
...
based
...
on
...
the
...
analytical
...
solution?
...
What
...
is
...
the
...
solution
...
for
...
the
...
velocity
...
profile?
...
We'll
...
create
...
the
...
geometry
...
and
...
mesh
...
in
...
GAMBIT
...
which
...
is
...
the
...
preprocessor
...
for
...
FLUENT,
...
and
...
then
...
read
...
the
...
mesh
...
into
...
FLUENT
...
and
...
solve
...
for
...
the
...
flow
...
solution.
...
Go
...
to
...
...
...
...
...
...