MECH5770M Resit Coursework, 2021/22
Prepared by Dr Carl Gilkeson, © School of Mechanical of Engineering, University of Leeds, 2021 1




MECH5770M: Computational Fluid Dynamics Analysis

Resit Coursework: 2021/22

There is only one question. Please complete all parts of the question to be considered for all marks. The
deadline for submission is 12:00pm, Friday 29th April 2022 (submission details are on the last page of this
assignment).

Question 1
Introduction
Consider the external flow past a cylinder. This is of interest in fluid mechanics because it represents bluff-body flow
which is applicable to many fields of engineering e.g. flow past wheels on racing cars. In your solution to this
question, you will study the flow field around a 2D cylinder using Computational Fluid Dynamics.
Figure 1(a) shows a 2D cylinder of diameter, D (m), which has a fluid flowing past it at a free-stream velocity, U
∞

(m/s). Figure 1(b) shows the distribution of the pressure coefficient, C
p
, around the perimeter of one half of the
cylinder; C
p
is plotted starting at θ = 0° at the front stagnation point (point A) increasing to θ = 180° at the rear of the
cylinder (point B). The red line shows the theoretical inviscid solution, assuming no turbulence, whereas the purple
dashed line shows the typical pressure distribution measured from experimental data.









Figure 1: Comparison between inviscid and experimental data of the pressure coefficient, Cp, as a function of angle, θ

(a) (b)
D
U
∞
(m/s)
Point A Point B
MECH5770M Resit Coursework, 2021/22
Prepared by Dr Carl Gilkeson, © School of Mechanical of Engineering, University of Leeds, 2021 2

You should complete the following steps:
1) Create a 2D geometry which consists of a semi-cylinder within a rectangle of fluid as shown in Figure 2. The
cylinder can be of any diameter you choose but the height of the fluid should be no less than 10D. Please use
a symmetry plane so that you only need to model half of the fluid.






2) Discretise the solution domain using a mesh scheme of your choice. You are permitted to use a turbulence
model which uses either the wall function or the non-wall function approach; obviously this will have an
impact on your near-wall mesh design – you should justify the mesh settings.
3) Set up a simulation with a velocity inlet, assuming incompressible air use the working fluid. To calculate the
velocity, you should simulate airflow with a Reynolds number of 3900. The characteristic length should be
the diameter of the cylinder.
4) Choose a suitable turbulence model and investigate mesh independence by using three or more different
meshes. You should use 2nd order discretisation for all flow equations.
5) Based on the previous step, choose the solution which you think is most accurate. Create a custom field
function (see tutorial 6) and plot Cp on the surface of the cylinder as a function of the angle θ in the range 0-
180° (refer to Figure 1(b)).
6) Compare your data with (i) the experimental data provided in Table 1 on the next page and (ii) the
theoretical inviscid solution which is given by equation (1):
θCp
2sin41−= (1)
7) Investigate the flow field using qualitative plots and further quantitative analysis. You should focus on the
wake behind the cylinder and the effect this has on the stream-wise velocity profile.

Deliverable:
In no more than 15 pages, produce a clear and concise technical report which includes the following sections:
a) Introduction and Methodology: Briefly describe the problem set up including justification for any decisions
you make. Include all relevant information on your boundary conditions, specifying any parameters you use.
You must include images of the mesh you use in your simulations and describe the mesh parameters.
b) Results: This section must include both qualitative and quantitative results. You should show a comparison
between your results and the experimental and theoretical ones. Make sure you show results which
characterise the wake behind the cylinder. You can include any results which you seem necessary.
c) Discussion and Conclusions: Based on your results, discuss the accuracy of your simulations in the context of
the experimental and theoretical data. Comment on the steps you have taken to reduce the most common
sources of numerical error. You should also discuss the important features of your results.


Inlet Outlet
Symmetry plane Symmetry plane
Wall
MECH5770M Resit Coursework, 2021/22
Prepared by Dr Carl Gilkeson, © School of Mechanical of Engineering, University of Leeds, 2021 3

Table 1: Experimental data showing the pressure coefficient profile on the perimeter of a cylinder, as a function of
the angle, θ. Reference: (G. Kravchenko and P. Moin, Numerical studies of flow over a circular cylinder at Re = 3900,
Physics of Fluids, Vol 12 No 2, pp 403-417).

Cp θ
1.000 0.0
1.000 1.1
0.995 2.7
0.979 5.5
0.912 10.6
0.810 15.4
0.656 20.6
0.481 25.5
0.050 35.5
-0.181 40.5
-0.411 45.6
-0.647 50.6
-0.837 55.2
-1.007 60.4
-1.114 65.5
-1.156 68.5
-1.171 70.1
-1.166 72.0
-1.156 75.3
-1.084 80.4
-0.993 85.2
-0.926 90.3
-0.896 95.1
-0.881 100.2
-0.876 105.2
-0.871 110.3
-0.872 120.1
-0.882 130.2
-0.888 140.1
-0.889 150.2
-0.889 160.3
-0.890 170.2

Marking Criteria:
Marks will be allocated accordingly:
• Introduction and methodology (10%)
• Results (30%)
• Discussion and conclusions (40%)
• Presentation style (20%)
For each of these categories, you will be marked based on your ability to communicate concisely and effectively,
whether or not you have included the requested information and the insight provided based on your interpretation
of the results. Only include relevant information in the main body of your report. If you wish to include residual plots
for example, these can be put in an appendix. Please do not exceed the maximum page limit, any pages beyond the
15-page limit will not be considered for marking.

MECH5770M Resit Coursework, 2021/22
Prepared by Dr Carl Gilkeson, © School of Mechanical of Engineering, University of Leeds, 2021 4


Submission:
Please follow these instructions:
1) Save your final report as a pdf document called username.pdf where username is your own University
username. This should contain your answers to all parts of the question. This must be based on your own
work.
2) You do not need to include case and data files.
3) Submit this file on MINERVA via turnitin. The submission link is found under the Resit Coursework folder
which is in the Assessment folder for the module MECH5770M.
The deadline for submission is 12:00pm Friday 29th April 2022.
Important: You can only submit your file ONCE after the deadline has passed so bear this in mind for late
submissions. Furthermore, if you submit multiple attempts BEFORE the deadline you CANNOT submit again after
the deadline has passed.