Access over 20 million homework documents through the notebank

Get on-demand Q&A homework help from verified tutors

Read 1000s of rich book guides covering popular titles

Anonymous

Simulate the steady laminar and turbulent pipe flow using Ansys Fluent as shown in the figure. Choose

proper fluid properties and inlet velocity to simulate flows of Reynolds number (based on the diameter

of the pipe) equaling 655 for laminar flow and 111,569 for turbulent pipe flow, respectively. (see the files attached)

The theoretical document for verification. (see the files attached)

EML 6930 Computational Fluid Dynamics, Spring, 2020
Homework 5
Please submit answers, all figures and tables in a single pdf or docx format. Submit the required Excel
file as well. For the simulation files, only submit .cas.gz and .dat.gz for each simulation (total 8
simulations).
Problem 1 (50 pts)
Simulate the steady laminar and turbulent pipe flow using Ansys Fluent as shown in the figure. Choose
proper fluid properties and inlet velocity to simulate flows of Reynolds number (based on the diameter
of the pipe) equaling 655 for laminar flow and 111,569 for turbulent pipe flow, respectively.
Table 1 - Main Dimensions
Parameter
Radius of Pipe, R
Diameter of Pipe, D
Length of the Pipe, L
Unit
m
m
m
Value
0.02619
0.05238
7.62
Uniform Grid
Non-uniform Grid
Axis
Inlet
Outlet
Velocity Profile
Pipe Wall
Uniform velocity profile is specified at inlet, and the flow will reach the fully developed regions after a
certain distance downstream. No-slip boundary condition will be used on the wall, and zero gauge
pressure for the outlet. You may consider creating a quarter of the pipe to take the advantage of
symmetry of the geometry. This could greatly decrease the number of cells in your mesh.
a) List the material properties and inlet velocities used for your simulations, both laminar and
turbulent flows.
b) Create three different 3D meshes: coarse, medium, and fine (Note the maximum allowed
number of cells is 512k for the student version). List parameters you changed when creating the
meshes, total number of cells, and minimum Orthogonal Quality. Also use the 2D mesh provided
to perform simulations (When launching Fluent, choose 2D mode and change to Axisymmetric in
Physics>Generalβ¦ tab). Conducting simulations for all meshes (total number of simulations is 8).
Plotting residuals and check the mass balance.
c) Create lines shown in the table below. Here, we assume the x axis is in the axial direction. You
may need to change the coordinates according to the orientation of your geometry.
Line Name
Inlet-line
x=10D
x=20D
x=40D
x=60D
x=100D
Outlet-line
x0
0
0.5238
1.0476
2.0952
3.1428
5.2380
7.62
y0
0
0
0
0
0
0
0
x1
0
0.5238
1.0476
2.0952
3.1428
5.2380
7.62
y1
0.02619
0.02619
0.02619
0.02619
0.02619
0.02619
0.02619
Use XY Plot to plot velocity profiles at these lines in a single figure for laminar and turbulent
simulations, respectively. Similarly, plot static pressure and velocity magnitude along the
centerline. For all these figures, only show results from the fine 3D mesh and 2D mesh.
d) Extract the Wall Shear Stress values (π ) along the axial direction on the pipe wall. You can save
it as a .xy file from Fluent and open it with a text editor, and copy the value at xβ7 to the Excel
file. Similarly, extract the pressure value along the centerline to calculate pressure drop from
the inlet to the outlet. Extract the velocity values along the βoutlet-lineβ and copy them to the
Excel. It will be used for plotting the fully-developed velocity profile with analytical or empirical
data (AFD used later is the abbreviation of it). List the y+ value at the end of pipe for all
turbulent simulations.
e) Fill the blanks in the Excel table below for verification and validation. Show proper procedures
for obtaining AFD data. Discuss which mesh solution is closest to the AFD data, and explain why
this is the case? Plot the fully-developed velocity profiles from all meshes with AFD data in a
single figure for laminar and turbulent flows, respectively (You can do it in Excel). Discuss the
developing length for laminar and turbulent pipe flows and compare them with that using the
formulas in the theoretical document.
To know more about analytical or empirical solutions of laminar and turbulent pipe flows, refer to the
theoretical document attached.
In the Excel file, create a table like this and fill the blanks accordingly. U m is the maximum/centerline
velocity at the outlet.
sims
Coarse grid:
laminar
Medium
grid:
laminar
CFD,
Pressure
drop
AFD,
pressure
drop
CFD, π at
xβ7
AFD, π
CFD, Um at
xβ7
AFD, Um
Fine grid:
laminar
2D grid:
laminar
Coarse grid:
turbulent
Medium
grid:
turbulent
Fine grid:
turbulent
2D grid:
turbulent
Theoretical Fluid Mechanics for Laminar and Turbulent Pipe Flow
For a uniform flow inlet, the flow can be divided into two regimes: developing profile region
and fully-developed flow region. The corresponding velocity profiles and pressure drops are
showing in the figure.
For a laminar flow, the entrance length can be estimated by πΏπ βπ· β
.06π
π, where D is the
diameter of the pipe and characteristic length used in the Re number. For a turbulent flow, the
entrance length is πΏπ βπ· ~4.4π
π 1/6.
The skin friction coefficient is a dimensionless skin shear stress which is nondimensionalized by
ππ€
the dynamic pressure of a free stream, πΆπ = 0.5ππ
2 , where ππ€ is the local wall shear stress and
V is mean velocity at the inlet. For a laminar flow, the skin friction coefficient is related to
16
Reynolds number as πΆπ = π
π. For a turbulent pipe flow, the empirical solution is πΆπ =
0.079π
π β0.25. The Darcy friction factor f is also widely used in the literature, which is related to
the skin friction coefficient as π = 4πΆπ .
It is well-known that the fully-developed velocity profile shows a parabolic shape in a laminar
π 2
π’
pipe flow from HagenβPoiseuille equation as, π = 1 β (π
) , where R is the radius of the pipe,
π
ππ = 2π is the maximum velocity and V is the mean velocity.
π’β
π’
π
For a turbulent flow in a circular pipe, π = 1 β 2.5 π ππ π
βπ, where the maximum velocity
π
π
β
ππ = (1 + 1.326βπ)π, and the friction velocity π’ = βππ€ βπ.
...

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

This question has not been answered.

Create a free account to get help with this and any other question!

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors