Fluent Course Work
MEC3028 Computational Heat and Fluid Flow
Semester 1 - Academic Year 2024-25
Instructions
The course work consists of two problems for a total of 100 marks.
Please read the instructions below and within the questions carefully and thoroughly before doing
the coursework. Failure to comply will result in a mark penalty.
1. The report should have a title page with your name, student number and module code.
2. The report should be typed and produced digitally. No hand written content is allowed.
3. Figures must have adequate resolution and their legend, labels and titles.
4. Use appropriate headings in boldface in the report when answering the questions. For instance, when
answering the item “A” of problem 1, one can write:
Answer to P1.A.
Your answer consists of text, figures and tables where applicable.
5. Please comply with the words/lines limits given for the comments and analysis.
6. Use of any AI tools in any capacity is prohibited.
MEC3028 - Semester 1 2024/25 Fluent Coursework
Problem 1: Flow over a rotating cylinder
[50 Marks]
Consider a circular cylinder of diameter D = 1 (m) positioned in a stream of fluid. The fluid flows
with the velocity of U∞ = 1 (m/s) towards positive x-direction (left to right in domain) as shown
in Fig.1(a). The flow Reynolds number based on the cylinder diameter D and the free stream
velocity U∞ is defined as Re = ρU∞D/µ = 200 where ρ (kg/m3) and µ (Pa.s) are density and
viscosity of fluid respectively. The cylinder rotates in counter-clockwise (CCW) direction with
the angular speed of ω (rad/s) as shown in Fig.1(a). Using the cylinder diameter D, free stream
velocity U∞ and angular speed of the cylinder ω, the dimensionless angular speed can be defined
as ω∗ = 0.5Dω/U∞.
Refinement Region
(b)
9D
8.5D
6D
U
∞ D
25D
ω Cylinder
(a)
10D 20D
Fluid domain
x
y
U
∞
x
y
Figure 1: Schematic of (a) The computational domain and related dimensions. (b) The location
of refined mesh. Note that the plot is not to the scale.
GEOMETRY: To simulate this problem, set up the domain as shown in Fig.1(a) where the
cylinder is positioned at the origin of coordinates at (xc, yc) = (0, 0) and has a diameter of D = 1
m. The fluid domain extends 10D upstream and 20D downstream of the cylinder in x-direction
respectively. Domain sides are positioned ±12.5D from the cylinder in the y-direction.
MESH: To tessellate the computational domain, divide the cylinder wall into 360 divisions and
create a boundary layer inflation with the first layer thickness of 2.5× 10−3 m and 45 layers with
expansion ratio of 1.2 over the cylinder wall. To balance the computational expense, set the mesh
“global size” to 1 m in the domain. Moreover, to accurately capture the wake region, refine the
mesh in the region shown in Fig.1(b) with the element size of 0.05.
SIMULATIONS: Consider the flow Reynolds number of Re = 200 for the simulations. Conduct
transient simulations for ω∗ = 0.25, 0.5, 1 using the Coupled Method with the time step size of
∆t = 0.1 s until Tfinal = 25 s. Set the relaxation factor for velocity and pressure to 1. Assume the
flow is laminar.
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MEC3028 - Semester 1 2024/25 Fluent Coursework
A. Provide a figure of (i) the mesh in the entire domain (ii) A close-up view of the region near
the cylinder. Provide these figures as a sub-figures of one single figure. [5 marks]
B. What Transient formulation is used? [5 marks]
C. Record the boundary conditions and their corresponding values in table 1. follow the example
below. [5 marks]
Example: For a stationary wall with no slip condition, the boundary condition should be
recorded as: Type: wall, Wall motion: Stationary, Shear condition: no slip
Table 1: Boundary conditions settings
Boundary Boundary conditions
Cylinder Wall
Left Boundary
Right Boundary
Top Boundary
Bottom Boundary
D. Calculate the Lift Coefficient CL = FLift/ (0.5ρU
2
∞D) over time for each case. Plot CL versus
time for all cases as overlay in a single plot. Set an appropriate limit for y-axis and 0-25 for
the x-axis. Label each clearly using their associated ω∗. [15 marks]
F. Plot the contours of velocity magnitude for each case at T = 25. Use the same minimum
and maximum for the velocity magnitude for all contour plots. Present the contour plots as
subplots of a single figure. [15 marks]
G. Analyse the flow dynamics based on the simulation results. Use CL plot you have already
provided in your analysis and explain how the lift force changes with ω∗ and why.(max 5
lines) [5 marks]
HINT: Set the fluid properties µ and ρ to produce the required Re number. I would recommend
using ρ = 1 (kg/m3) and compute the µ to have Re = 200.
HINT: Be advised not to confuse ω and ω∗.
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MEC3028 - Semester 1 2024/25 Fluent Coursework
Problem 2: Flow in a periodic channel [50 marks]
Laminar fluid flows through a two-dimensional channel of height H = 2 m, and length L = 0.2 m
in a periodic manner, which implies that the flow is between two infinitely long flat plates (see
Fig.2) and is fully developed. Periodic boundary conditions ensure that the fluid which leaves the
domain is reimposed at the inflow of the domain, thereby no inlet or outflow boundaries need to
be imposed in this case. The fluid has a viscosity of µ = 1/64 kg/(ms), a density of ρ = 1 kg/m3.
A constant pressure gradient ∂P/∂x = −1 Pa/m should be imposed in the axial flow direction.
Details on how to apply the periodic boundary conditions as well as imposing the pressure gradient
are provided in the Appendix at the end of this document.
wall
H
L
x
y
Figure 2: Schematic of the Taylor-Couette flow. (a) 3D view (b) top view (c) side view
A. Generate a series of computational meshes for this problem with the specifications for each
mesh given in the table 2. Please provide the plot of meshes in the report and clearly label
them. Assemble these plots of meshes as a sub-figures of a single figure [5 marks]
Note1: The domain geometry is fixed, but the mesh spacing is changed in different meshes.
Note2: Note that you should make the geometry for each mesh separately as Fluent might
causes problems with periodic conditions when duplicating the case setup.
Table 2: Mesh Specifications for Problem 2
No. X direction Y direction
1 2 equidistant divisions 4 equidistant divisions
2 2 equidistant divisions 6 equidistant divisions
3 2 equidistant divisions 20 equidistant divisions
4 2 equidistant divisions 100 equidistant divisions
5 2 equidistant divisions 40 divisions with a bias factor of 8 towards both walls
B. Conduct simulations using Fluent with different meshes given in table 2 using SIMPLE
algorithm. For each case (mesh) run the simulation for two different discretisation: 1st order
upwind and 2nd order upwind for the momentum equation. Record values of ∂u/∂y at the
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MEC3028 - Semester 1 2024/25 Fluent Coursework
bottom wall (H=0) for all the meshes and both discretisation schemes in table below (table
3). Use convergence criterion of 10−6 and at least 40,000 iterations for each simulation. The
values for ∂u/∂y can be obtained by the derivative function under Plots, x-y plot option.
[20 marks]
Table 3: Computed Velocity Gradient ∂u/∂y
Mesh 1st order 2nd order
4 equidistant divisions
6 equidistant divisions
20 equidistant divisions
100 equidistant divisions
40 divisions with a bias
Note 1: Export the data using write to file option and use exact numbers rather than reading
them from the plot Note 2: Report the numbers to the 4th decimal place for ∂u/∂y
C. Do the 1st order and 2nc order discretisation for ∂u/∂y give the same outcome? For either
yes or no, please comment and prove why. [10 marks]
D. Wall friction velocity uτ is one of the most important quantity to evaluate the shear stress in
wall bounded flows and it is defined as:
uτ = (
|τw|
ρ
)
1
2 (1)
where τw is the wall shear stress and ρ is the fluid density. Evaluate uτ for all the meshes
and all the numerical schemes used. Consequently compute the non-dimensional velocity
u+ = u/uτ where u is the velocity of the flow in the x-direction. The dimensionless distance
from the wall can be defined as y+ = (ρuτy/µ) where y is the dimensional distance from the
wall in the y-direction. Additionally, an analytical solution to this problem can be obtained
by using Eq.(2)
u+ = u/uτ = (−H2/2µ)[(y/H)2 − (y/H)] (2)
Plot u+ against y+ using the data obtained from Fluent simulations. Include the analytical
solution (Eq.(2)) in the plot as well. [15 marks]
Note 1: Please use different line colours for each line and label them appropriately.
Note 2: u+ should be on the ordinate (vertical axis) and y+ on the abscissa (horizontal axis)
Note 3: Use normal scale on for the ordinate and log scale for the abscissa Note 4: Plot the
data from the bottom wall to the middle of the channel
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MEC3028 - Semester 1 2024/25 Fluent Coursework
APPENDIX: Imposing periodic boundary conditions and pressure drop
Assume that the domain faces in question 2 at along the y-axis at x = 0 m and x = 0.2 m
are x-left and x-right respectively. In the case of question 2 both x-left and x-right should
be assigned interface boundary conditions under the boundary conditions tab as shown in
Fig.3(a) and Fig.3(b) below. This can be done by double clicking the Boundary Conditions
tab and then selecting the appropriate options.
(a) Interface BC for x-left (b) Interlace BC for x-right
Figure 3: Setting Interface boundary condition for the x-left and x-right
Once both x-left and x-right have been assigned as interface boundaries then expand the
Boundary Conditions tab on the left window in Fluent and then expand the Interface tab.
Select both x-left and x-right while pressing the Ctrl button on the keyboard. Then right
click and select Periodic as shown in Fig.4(a) below. A new window will appear as shown in
Fig.4(b) where the Auto Compute Offset box needs to be unchecked and the value for Offset
needs to be entered for X [m], which is 0.2m in this case. Once all the appropriate options
have been selected then click the Create button. This will create a new boundary condition
which will have the name as specified in the Zone name box as shown in Fig.5(a).
Once the new zone has been created, select the new zone, and then click on the Periodic
conditions button and a new window will appear as shown in Fig.5(b). Under the Pressure
Gradient option specify the pressure gradient as -1 Pa/m, and this will specify the constant
pressure drop condition Fig.5(b). Once all of these steps have been followed, you can continue
for the rest of required settings and conducting your simulations.
‘
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MEC3028 - Semester 1 2024/25 Fluent Coursework
(a) (b)
Figure 4: Setting Interface boundary condition for the x-left and x-right
(a) (b)
Figure 5: Setting Interface boundary condition for the x-left and x-right
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MEC3028 - Semester 1 2024/25 Fluent Coursework
End of the coursework
Good Luck
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