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MECH3780: Computational Mechanics
Assignment II: Computational Fluid Dynamics (CFD) Analysis of
Generalised Cardiovascular Medical Devices
Introduction:
In this assignment, you will develop your CFD capability by analysing a benchmark case
from a validation study sponsored by the U.S. Food & Drug Administration (FDA) and funded
by the FDA’s Critical Path Initiative. The study sought to produce validation data for CFD
simulations of blood flow through generalised medical device geometries. The initial study
produced experimental data at three independent labs for flow through (i) a nozzle with a
conical change in diameter at one end of the throat, and a sudden change at the other, and
(ii) a simplified centrifugal blood pump. Through 2008-2009 more than 25 research teams
and industry specialists submitted their CFD results for the administering body to compare
with the experimental findings. This data set still serves as a robust validation case for CFD
simulations of complex internal flows, with its use in new research articles and conference
papers still evident today.
For this assessment, you are required to submit a concise response that details your
findings for each task (in pdf format). This should include any comments,
justifications and discussions requested as well as figures and/or tables of results
that provide a clear depiction of your findings.
Learning Outcomes:
The following learning outcomes (LO) from the Electronic Course Profile will be assessed:
LO Description
L02
Apply engineering principles to reduce complex mechanical systems and fluid
flows (including the loads and constraints to which they are subjected) to a form
that can be analysed using finite element analysis (FEA) or computational fluid
dynamics (CFD), respectively.
L07 Model turbulence and heat transfer in fluid flows using commercial CFD software
and closure parameters calculated from fluid mechanical theory.
L08
Apply systematic mesh/grid refinement techniques to appropriately discretise (in
the context of standard quality metrics) solid/fluid geometries for FEA/CFD using
commercial software.
L09
Demonstrate the computational analysis workflow (model definition, dimensional
analysis, mesh/grid generation, application of boundary and initial conditions,
selection of solution strategy, interrogation of results) in FEA and CFD of
mechanical and fluid systems, respectively.
L10 Verify and validate the predictions of FEA and CFD using analytical solutions and
experimental data.
L11 Communicate the outcomes of FEA and CFD using appropriate visual aids (e.g.
plots, graphs) in formal technical reporting.
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Problem Context:
This assignment consists of two primary tasks (which may have several sub-tasks). The first
task requires you to develop simulations from scratch as well as analyse various aspects of
the results. The second task requires you to model a non-Newtonian fluid rheology to
incorporate the properties of blood when analysing flow through a nozzle (Figure 1).
1) Medical nozzle benchmark: the first study investigates the flow through an idealised nozzle
which shares several characteristics of blood-carrying medical devices including blood
tubing, hemodialysis sets, catheters, cannulas, syringes, and hypodermic needles [Stewart,
2012]. The geometry is provided in Figure 1 with sufficient measurements for you to recreate
as needed in Task 1. The flow condition in the geometry is defined based on the Reynolds
number in the throat,
𝑅𝑒 =
𝜌𝑈!”#𝑑
𝜇
.
Here, the density of the fluid 𝜌 = 1035𝑘𝑔/𝑚$ and the viscosity is 𝜇 = 0.0035 𝑃𝑎. 𝑠. You will
be testing a laminar case where the Reynolds number is 500, and a turbulent case where
the Reynolds number is 3500. The relevant inflow velocity is provided in the relevant Task.
2) Non-Newtonian rheology:
Under certain conditions experienced in the human body and in biomedical devices, the shear
thinning properties of blood are best described with a non-Newtonian rheology. The Carreau-Yasuda
model is commonly employed for this purpose,
𝜇(𝛾̇) = (𝜇% + (𝜇& − 𝜇%)(1 + (𝜆 𝛾̇)!)(()*)/!
Where 𝜇% is the infinite shear viscosity, 𝜇& is the zero shear viscosity, 𝛾̇ is the shear rate, 𝑎 is a
parameter to control the shear-thinning (𝑎 = 2 for the original Carreau model), and 𝑛 is the power
constant. In this task, you will need to conduct and compare a Newtonian and non-Newtonian
simulation in a 3D realisation of the nozzle in Figure 1.
Figure 1: Schematic of the cross section of the nozzle geometry required for simulation in Task 1. Note that
this is an axisymmetric geometry about the x-axis. The origin is specified on the pipe axis at the point of
sudden expansion (keep this in mind for profile lines referred to in Task 1).
x
y
0.117 m 0.18 m
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Project Tasks and Requirements
Task 1 [Total 75 marks]
In this Task you will perform a detailed CFD analysis, including a grid dependence study, validation
with experimental data, and a sensitivity analysis on various RANS models. For this Task, you are
initially requested to conduct 2D axisymmetric simulations of the nozzle in Figure 1. In the final
subtask you will compare this with a 3D simulation. You are required to model a laminar case, where
the Reynolds number in the throat is 500, and a turbulent case where the Reynolds number in the
throat is 3500. For both these simulations, the fluid has a density of 1035 kg/m3 and viscosity of
3.5e-3 Pa.s.
Task 1.1 Geometry Creation and Mesh Design [5 marks]
- Construct an axisymmetric domain for the nozzle geometry provided in Figure 1. You should
include a short description of the procedure you used to generate the geometry and a figure
that shows your geometry has the appropriate dimensions. Note: STAR-CCM+ requires the
axis of symmetry to be aligned with the x-axis for the axisymmetric flow solver. - Provide a short discussion comparing the benefits of conducting a 2D-axisymmetric
simulation compared to a 3D simulation and highlight under what circumstances you would
expect it to be necessary to conduct a full 3D simulation. - Based on your engineering knowledge, define refinement regions for your axisymmetric
geometry. You should include a figure indicating any mesh refinement zones you are looking
to use and comment on why they are required. If you plan to use different refinement zones
for the laminar and turbulent case, also comment on this here. Do not worry about prism
layers cells (i.e. boundary layer mesh) for this discussion, you will address this later.
Task 1.2 Simulation Setup and Preliminary Steady Simulation [15 marks] - Based on your mesh design from Task 1.1, generate an initial 2D simulation mesh. Comment
on the target cell size, number/location of prism layer cells, and the thickness of the prism
layer mesh for both the laminar and turbulent cases. State the total number of cells used in
each case (remembering that this is only a preliminary simulation to understand the flow). - Select the relevant Models required for the simulations. Provide an image of the Models
selected for each case. You may need to deselect Two-Dimensional to choose Axisymmetric. - The specified Reynolds numbers of 500 and 3500 at the throat correspond to average inlet
velocities for the inlet pipe of approximately 0.046m/s and 0.329m/s, respectively. Set up a
developed flow inlet condition remembering for developed pipe flow,
𝑢(𝑟) = 𝑢-!. @1 − A
𝑟
𝑅
B
/
C, 𝑢-!. = 2 × 𝑢!”#, 𝑅 = 𝑝𝑖𝑝𝑒 𝑟𝑎𝑑𝑖𝑢𝑠
Provide a figure to show this has been correctly implemented (e.g., contour plot of the Field
Function). For the outlet boundary, you can use a constant pressure outlet. - After setting the relevant boundary conditions (for the turbulent case, use a 5% turbulent
intensity and the k-w-SST model for now – you can leave other parameters at their default
values), run both cases until they reach a steady-state. Comment on how you determined
the simulations had converged, you are welcome to add additional Monitors. Create
contours of the velocity and pressure. Plot the mesh on the velocity contour and comment
on your prism layer design. If needed, adjust the thickness and number of boundary layer
elements. Provide these contour plots for both cases. For your turbulent case, include a Plot
showing the y+ value on the wall and discuss the appropriateness of this in relation to the
RANS turbulence models k-e and k-w.
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Task 1.3 Mesh Dependence Study [20 marks]
Based on Task 1.2, you should have a reasonable understanding of whether your mesh design will
accurately capture the boundary layer. You should also have a ‘good’ starting mesh to use for a
mesh dependence study. You will need to do this for both the laminar and turbulent cases.
To compare the results of your different mesh resolutions, extract three velocity profile lines. The
velocity in each case should be the velocity along the pipe. The three profile lines are:
(i) the x-axis;
(ii) a radial line at 0.008m before the sudden expansion;
(iii) a radial line at 0.024m after the sudden expansion.
Additionally, extract the maximum Velocity and maximum Wall Shear Stress in the domain for each
mesh resolution. Use the profile lines and the maximum values to determine if/when you have
achieved mesh independent results. - Succinctly document your mesh independence study, justifying the decisions you have
made, and the mesh selected. This should include figures showing the different mesh
resolutions, six plots in total (one for each profile line for each case-laminar/turbulent), a table
listing the cell count, iterations till convergence, CPU time and maximum values for each
resolution, and a brief comment on the quality metrics for your selected mesh.
Task 1.4 Comparison with Experimental Data [5 marks]
On Blackboard, there are three .csv files for each of the simulation cases (laminar and turbulent) that
have experimental results aligning with the locations of the three profile lines in Task 1.3. - Provide a total of six plots that compare the results of your selected mesh with those obtained
from the physical experiments. - Provide a short discussion on where the results agree, and if there are any differences, what
may have caused this.
Task 1.5 Influence of Turbulence Model [15 marks]
Select three different RANS model variants (one can be the k-w-SST model previously applied) and
use them to simulate the turbulent flow case. - Provide three plots showing the velocity result of each RANS model, along with the
experimental data, for the profile lines specified in Task 1.3. Provide a contour plot of
Turbulent Kinetic Energy for each RANS model. - Comment on any differences, including a discussion about which model best aligns with the
experimental data and if this was what you expected.
Task 1.6 Comparison of Axisymmetric with 3D Simulation [15 marks]
Based on your knowledge of mesh resolution from the axisymmetric cases, create a 3D simulation
for the turbulent flow case (note that you may need to consider compute cost constraints and will
should apply the developed flow profile from Task 1.2). - Provide three plots comparing the result of the Axisymmetric simulation, 3D simulation, and
experimental results on each profile line specified in Task 1.3. - The destruction of red blood cells, known as hemolysis, is often cited to occur at high shear
stresses determined by a threshold of approximately 400 Pa. Determine the maximum wall
shear stress and its location for the axisymmetric and 3D simulations. Provide a contour plot
of the wall shear stress for the 3D simulation. Comment on whether the maximum Wall Shear
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Stress value and location agrees between these simulations and whether hemolysis could
be expected at this flow condition.
Task 2 [Total 20 marks]
This task seeks to extend the 3D simulation conducted at the end of Task 1 and include non-
Newtonian effects that can occur due to the composition of blood. It is noted here that blood tends
to exhibit non-Newtonian behaviour only in thin-vessels and with relatively low Reynolds numbers
(Sarkar, 2024). Before analysing this, you will need to modify your 3D geometry to include a spherical
idealisation of an aneurysm at the start of the nozzle throat. Aneurysms occur when a blood vessel
wall weakens, bulging outwards to form a balloon like structure. This weakened structure can rupture
causing internal bleeding (haemorrhage) and leads to potentially life-threatening complications. As
such, being able to model these types of phenomena, including potential stint treatments is an active
area of research (Ishida, 2021).
To modify your 3D geometry from Task 1.6, you are required to create a spherical aneurysm with a
radius of 0.0035m located at (x, y, z) = (-0.04, 0.002, 0) m (noting the location of the origin as per
Figure 1).
For the Carreau-Yasuda previously given, and re-state for convenience as,
𝜇(𝛾̇) = (𝜇% + (𝜇& − 𝜇%)(1 + (𝜆 𝛾̇)!)(()*)/!,
blood is modelled with 𝜇& = 0.056 Pa.s, 𝜇% = 0.0035 Pa.s, 𝑛 = 0.3568, 𝜆 = 3.313 s, and 𝑎 = 2.
Task 2.1 Modification of Geometry [10 marks]
Modify the geometry as specified above and complete a Newtonian simulation with a throat Reynolds
number of 500 (note: you should still be applying the developed pipe flow profile as per Task 1).
Provide: - Figures to show your mesh resolution in key parts of the geometry (the resolution should be
based on your experience from Task 1.6). - Visualisation of your choice to indicate if a recirculation region has formed in the idealised
aneurysm. - Plot of the velocity profile line along the x-axis (as described in Task 1.3) with the simulation
and experimental results from Task 1.6 to indicate the impact of the geometry modification.
Task 2.2 Application of non-Newtonian rheology [10 marks]
At a Re of 500, the impacts of the non-Newtonian rheology are expected to be minimal. For this task,
alter the fluid rheology to implement the Carreau-Yasuda model introduced above. In your
simulation, reduce the throat Reynolds number to 50 (this is equivalent to an average inlet velocity
of 0.0046 m/s). Complete the simulation and provide: - Screenshot of your updated fluid rheology set up from STAR-CCM+.
- Contour of the XY-plane showing the viscosity of the fluid at steady-state.
- Contour of the XY-plane showing the velocity of the fluid at steady-state.
- Contour of the Wall Shear Stress and identification of location where this is at a maximum.
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Submission Requirements:
Document your responses to each task with headings based on the task number. Your
submission needs to be completed with a single pdf document. This will be uploaded through
TurnItIn on Blackboard to assess for similarity.
[5 marks] Appropriate presentation of results, correct grammar in comments, and written
responses free from spelling errors.
References:
Ishida F, Tsuji M, Tanioka S, et al. Computational Fluid Dynamics for Cerebral Aneurysms
in Clinical Settings. Trends in Cerebrovascular Surgery and Interventions (2021)
Sarkar, N., Sharma, S.D., Chakraborty, S. and Roy, S. A comparative study of Newtonian
and non-Newtonian blood flow through Bi-Leaflet Mechanical Heart Valve. Computers &
Fluids 279, 106337 (2024)
Stewart, S.F.C., Paterson, E.G., Burgreen, G.W. et al. Assessment of CFD Performance in
Simulations of an Idealized Medical Device: Results of FDA’s First Computational
Interlaboratory Study. Cardiovasc Eng Tech 3, 139–160 (2012).
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