Download - CFD Course Work 3rd Year Sam Mailer
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Samuel Mailer
200943702
Analysis of Airflow through a
Duct
Mechanical Engineering
3rd
Year
Semester 2
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Contents
1.0 Abstract................................................................................................................3
2.0 Methodology
2.1 Introduction to Gambit..........................................................................3
2.2 How the Model was created in Gambit.................................................3
2.3 Exporting the Mesh and Fluent Analysis...............................................4
2.4 Solving the Model in Fluent..................................................................5
2.5 Obtaining Vector and Contour Plots for the Solution...........................5
2.6 Changing the Flow Velocity.................................................................5
3.0 Results............................................................................................................6-12
4.0 Conclusions.....................................................................................................12
Abstract
Fluid analysis is a very important part of many engineering applications. Fortunately the
process has been made much easier by the continued development of Computational Fluid
Dynamics computer software packages. In this report discussing how air flows through a converging-
diverging duct with a cylinder in the middle, both the Gambit and Fluent packages were utilised to
first construct the duct and mesh it and then run the actual analysis of the fluid flowing.
After Gambit had been used to construct and mesh the duct, the mesh was imported to
Fluent where all of the settings and boundary conditions were set and the analysis was run. From
this, pressure and velocity plots could be drawn up to give an idea of how they varied within the
duct. Also graphs could be drawn up to go with the plots as mentioned, along with graphs of how
the coefficients of lift and drag varied on the cylinder in the duct.
After this original system had been analysed, the inlet velocity of the air was changed and
the same process was run again to draw a comparison with the original results. The comparisons
showed some very interesting results and showed a good representation of the phenomenon of
vortex shedding, as the cylinder in the middle of the duct caused a turbulent wake within the duct.
The results link together how the Reynolds and Strouhal number can be used to determine many
characteristics of the system.
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1.0 Introduction
In this analysis, air is forced through a convergent-divergent duct with a cylinder positioned
in the middle as shown infigure 1. The speed air flow is such that the flow stays laminar over the
cylinder, which means that no Von-Karmen vortex shedding will occur in the wake of it. Fluent can
now be used to solve the flow through the duct and over the cylinder as the flow regime is steady
state. Analysis of this duct was carried out in 2D and all the dimensions are in relation to the
diameter of the cylinder, which in this case was taken to be 0.1m (which is an important factor later
on in the investigation). As shown infigure 1, the duct has one plane wall at the bottom, and the top
wall being curved to make the duct convergent-divergent.
2.0 Methodology
2.1Introduction to Gambit
To start the analysis the duct had firstly to be modelled in the pre-processor package
Gambit, which defines the geometry of the model and the boundary conditions for the situation
such the fluid velocity and the drag generated on the walls. A model mesh is then created which can
be imported into fluent for analysis.
2.2 How the Model was created in Gambit
To start off the model, firstly the specified geometry had to be input from the dimensions
from the given specifications. The coordinates for the outer edges of the ducts were plotted and
then joined using the straight edge function. The curved upper wall was created using nurbs
option putting a curve through three coordinates on the top edge. The cylinder in the centre was
modelled using two points on the circumference of the cylinder and the centre point. The circle
function was then used to create the cylinder in the centre of the duct.
After the basic outline of the duct was complete, the programme needed to be told
that the cylinder was a separate part in the duct so that when a mesh is created it fixes itself around
Figure 1
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the cylinder and not over it. This was done by making the duct and cylinder two separate faces and
then splitting them from one another to create one single face that could be easily meshed.
Before meshing though, boundary layers need to be created on the upper and lower walls of
the duct and also the outer edge of the cylinder. Once all of the specified boundary layer had been
set to the corresponding edges, the edge meshes could now be put in place. The edge mesh is
essential as this will give a very detailed analysis of how the air will flow around the cylinder and
against the walls. The edge meshes are much finer meshes than the overall face mesh but this is
obviously need to give the more detailed analysis in the specified areas as previously discussed. Each
edge required a different grading of mesh to give the desired results. The upper and lower walls
were Bi-exponent meshes, with a ratio of 0.4 and an interval count of 50. The inlet and outlet were
also Bi-exponent meshes with a ratio 0.6 and an interval count of 30. The mesh around the cylinder
was slightly different as it was a Successive ratio mesh with a ratio of 1 and an interval count of 50.
After all of this had been applied, the final face mesh could be applied to the whole
model, using pave type tri elements. The final face mesh is shown in figure 2, and is ready to be
exported to fluent after the boundary conditions of all the edges, domain fluid and solver had all
been set.
2.3 Exporting the Mesh and Fluent Analysis
Now the mesh could be exported into the CFD programme fluent and analysis of the fluid
flow through the duct could be carried out. Firstly the correct solver parameters had to be set to
ensure appropriate results are yielded, but in this case the desired settings were in fact the default
Fluent settings. Then after a few more setting within the programme had been checked to ensure
things like the turbulence for the model were specified. The material properties of the air flowing
through the duct also had to be checked, and the operating conditions were set, so that the system
was operating at atmospheric pressure, and gauge and vacuum pressure could be measured against
it.
figure 2
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After the boundary conditions had been set at the inlet (velocity = 0.005m/s) and the outlet
(gauge pressure = 0, operating at atmospheric pressure), the model could now start to be solved.
2.4Solving the Model In Fluent
Firstly the solution scheme is checked and the relaxation parameters are set, which for this
problem are also the default settings in Fluent. Then the programme was told to initialize the
solution from the inlet of the duct. After this, as part of the desired solution was for the residuals to
be displayed as part of the results, the correct parameters had to be entered to give the correct
graph. This meant that all the convergence criteria had to be set to 1e-5. Now the settings had to be
entered to give the correct graphs and results for the lift and drag forces on the cylinder. For this to
work, Fluent again had to be told to compute all of these from the inlet of the duct, which once
selected gave all criteria and characteristics of the fluid at the duct entry. Finally the number of
iterations that was needed for each of the graphs of the results was the final piece of informationFluent needed before solving the model. In this case 300 was an appropriate figure, but the solution
could be interrupted and stop at a value before this to check certain values if needed by clicking
cancel on the working form. While the solution is being carried out, a plot of thee residuals is shown
at the same time, with each of the three plots on the graph steadily decreasing until 1e-5 is reached,
which is the point where the solution should have converged. The residuals graph is shown in the
results section asfigure 10along with both the cylinder drag and lift graphs which arefigures 8and
9 respectively.
2.5Obtaining Vector and Contour Plots for the Solution
Another useful part of the result was to use Fluent to give colour vector and contour plots of
both the velocity in different areas of the moving air, and the pressure on the inside of different
parts of the duct. The velocity vectors were given by using the display and then vector function and
setting the processor to velocity. The result of this is shown infigure 4. The contour plots for both
velocity and pressure were gained by using the display and then the contour function and selecting
either velocity or pressure depending on which information was needed. The images displaying the
results of this analysis are shown infigure 6 for velocity andfigure 7for pressure.
2.6Changing the Flow Velocity
As part of the investigation, a new velocity had to be chosen which would provide a new
Reynolds number for which the Strouhal number was a constant value of 0.21. To get the new
velocity, the relationship between the Reynolds number and the Strouhal number could be used.
This relationship is shown below infigure 3, which is the graph of Reynolds v Strouhal numbers.
From the graph, it isnt very clear but looking very closely it looks that for a Stouhal number of 0.21,
the corresponding Reynolds number value is roughly 400. Now that the Reynolds number is known,
this can be used to gain the desired velocity of the air. This is shown in the formula below;
, where is the density of the air (1.225), u is the velocity of the air which
the equation is to be solved for, d is the diameter of the cylinder (0.1m) and Re is the new Reynolds
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number which from the graph is shown as 400. Rearranging this formula and solving gives the new
velocity of the air as 0.05843.
Now this new value for velocity could be used to run the Fluent Analysis again for the model.
This was done using exactly the procedure as discussed previously to obtain the wanted results,
graphs and plots. (A point to note is that between the values of 400 and 6000 the graph of Reynolds
v Strouhal number levels out, with the corresponding Stouhal number being 0.21. 400 was chosen
for the analysis as smaller Reynolds numbers tend to generate better results for the way the Fluent
has been set up for analysis of this model).
3.0 Results
From the
initial analysis with
the velocity set at
0.005m/s an
interesting set of
results we obtained.
Firstly, from the
velocity vector plot in
figure 4, we can see
how the velocity of
the air is changing as
it passes through the
duct. From the index
at the side of the
figure, blue signifies
slow moving air while moving up the scale towards red indicates that the air is moving faster. From
the image we can see that fluid is moving fastest as it goes past the top side of the cylinder. This is to
Reynolds number of 400
Intersection point
Strouhal number of 0.21
Figure 3, Reynolds v Strouhal numbers
Figure 4
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be expected though as from basic fluid dynamics knowledge, it is known that with a decreasing
throat area, the velocity of the fluid will increase. The diagram also shows that there are three areas
where the air is either very slow moving or has completely stopped. This occurs at the very front of
the cylinder, as at the very front of the cylinder the air cannot move around so it comes to a
complete stop. This is known as the stagnation point. It is better shown infigures 6 and 7, which are
the velocity and pressure contour plots respectively. The second area where the fluid becomes very
slow moving is against the walls of the duct. This is due to friction between the fluid and the walls
causing a big decrease in velocity. This is shown well by the results from fluent as the walls and
around the cylinder had to be individually meshed to give there frictional effects. Another area of
interest from the results is in the flow wake of the cylinder. From a closer look atfigure 4, infigure
5, an interesting phenomenon is shown. The fluid is seen to be recalculating behind the cylinder in a
vortices. This is
due to the flow
separating over
the cylinder andcausing a
turbulent area
behind the
cylinder. This
leads to an
effect called von
Karmen vortex
shedding. This
vortex shedding
as the air re-
circulates is due
to separation of the boundary layer over the cylinder. This effect is again also shown in the velocity
contour plot infigure 6, shown below.
Re-circulation zone, causing multiple
vortices.
Turbulent wake
Stagnation Point
Boundary Layer
Figure 5
Figure 6
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After the general analysis of the duct with coloured plots, Fluent can also be used to
generate graphs of how the coefficients of drag and lift vary on the cylinder. Figures 8 and 9, show
the graphs generated of the drag and lift coefficient respectively on the cylinder. Firstly looking the
graph of the coefficient of drag we can see that at the start the coefficient of drag is infinitely high as
this is at the stagnation point. The graph the
rapidly decreases as the air moves quickly
round the cylinder before fluctuating slightly
and levelling off at the stagnation point. The
graph here shows that the cylinder develops a
coefficient of drag of just below one.
Comparing this tofigure 9, showing the
coefficient of lift, we can see some
similarities. Firstly the coefficient of lift is
infinitely high right at the start at thestagnation point again as lift is immeasurable
here. It then also drops sharply as the air
moves around the cylinder generating lift
before also fluctuating and levelling off at the
separation point where the air is flowing in a level steady state. Another important graph generated
by fluent is the graph of the residuals as shown infigure 10. This shows that all the desired criteria
have converged to the desired value as stated in the original set up ().
Stagnation Point Figure 7
Figure 8
Figure 9 Figure 10
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As we as these graph of the general analysis of the duct, Fluent can also be used to gain
graphs of what is happening to the static pressure and velocity through the duct in the X and Y
directions separately. First of all, looking at how the static pressure varies in the X and Y direction in
figures 11 and 12 respectively. Looking atfigure 11, it shows how the pressure starts of steady and
then sharply increases as it hits the front of
the cylinder and the stagnation point is
generated. There is then a gap in the graph
where a new low pressure reading appears in
the wake of the cylinder. The graph then
steadily increases as the fluid moves down
the pipe as the flow effects begin to have
more of an input. Figure 12 then shows the
vertical static pressure within the duct. It
shows that the highest pressures occurring at
the walls of the duct, with the absolutehighest pressure being above the cylinder,
which follows as the smallest space is
bound to have the highest pressure. The
pressure then quickly decreases around
the walls of the cylinder, and the part of
the graph where there is no reading is
where the cylinder is positioned in the duct
so there will clearly be no reading there.
As mentioned previously, Fluentcan also be used to also give graphs of
how velocity changes in the X and Y
directions within the duct. Figure 13,
shows how the velocity varies on the Y
axis. This graph shows how the fastest
moving fluid occurs exactly half way
between the edge of the cylinder and its
corresponding wall. We can also see
that the slowest moving air occurs at the
walls of the duct and edges of the
cylinder. This is to be expected though
at frictional effects will cause the air to
slow down quickly.
These were the final results generated for air at a speed of 0.005 so as mentioned
section2.6of the methodology the speed was then changed in the Fluent set up to the new
calculated speed of 0.05834 and the analysis was run again using the same process outlined in
Figure 11
Figure 12
Figure 13
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Much larger turbulent wake
the methodology. Firstly looking at the velocity vector graph shown infigure 14 and comparing it to
the original the one generated in the original analysis (figure 4), some very distinctive differences
are shown. It is shown that now the air is moving much more quickly above the cylinder than below.
This has possibly been
caused in this analysis
due to a much higher
velocity of the air
passing through the
duct, and from the
laws of fluid dynamics
it is known that the
velocity of a fluid will
increase with a
decrease in the throat
area. The realdifference in the two
systems comes when a
closer look is taken at
the wake of the
cylinder. Comparingfigures 4 and14, it shows that in the wake of cylinder infigure14 that the flow
has become much more turbulent, and the vortex shedding effects in the wake continue much
further down the duct as a much bigger wake is created. This is also due to the much higher velocity
of the fluid from the
original set-up. There
are still some similarities
between the two
though as the flow
effects at both the walls
and edges of the
cylinder look relatively
similar. These effects
are better shown in the
velocity and pressure
contour plots shown in
figures16 and17
respectively. The much
larger turbulent wake is
well demonstrated in
Figure16 as it shows the wake extending much further down the duct and tailing off. The larger
difference in velocities above and below the cylinder is shown more clearly as well. Comparing
figures 7 and17we can see how the pressure contour plots are very similar for both systems, with
the only real difference coming in the fact that much narrower area of very low pressure is cause
behind the cylinder with the air moving at a higher velocity.
Figure 14
Figure 15
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Comparing the graphs of the drag and lift coefficients, shown infigures18 and19 respectively,
similarities and differences can also be drawn up here. Firstly looking at the graph of the drag
coefficient for the new system we can see how the actual shape of both the graphs infigures 8 and
18is almost identical, but the difference comes in what the actual coefficient of drag finally levelsout at. In figure 8we can see that the final coefficient of drag for the cylinder ends up at roughly just
below one, while infigure18it shows a coefficient of drag at just below 0.5. The interesting
difference comes when the graphs of lift coefficients are compared. Fromfigure 19 it is shown that
the coefficient of lift never actually settles a constant value and is constantly fluctuating. This may
highlight a problem doing this kind of analysis in fluent as with this new speed, we are dealing with a
turbulent flow around the cylinder and from
the methodology it is stated that fluent hasbeen set up to model and analyse laminar
flow. Turbulent flows are complex and difficult
to do calculations on though. This point
enforced when the graph of the residuals,
shown infigure20, is examined. From this we
can see that none of the solutions actually
converge to, but instead level off at a
value much higher than this. This means that a
much less accurate solution has been
calculated but this may be due to the reason discussed previously.
Figure 16 Figure 17
Figure 18 Figure 19
Figure 20
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From the new analysis at the new speed of 0.05834m/s, graphs of static pressure and velocity in the
X and Y axis separately were also generated. Comparingfigures21 and22 of the static pressure at
0.005m/s to the static pressure graphs infigues11 and12 we can see that there is very little
diffenreces apart form the actual values of the pressures.
The graphs that show a real difference in the two systems are the ones showing how the velocity
changes on both the X and Y axis along the duct. Fromfigure23 and24, we can see that when it
comes to calculating the velocity along the X axis, a problem occurs in the area directly behind the
pipe and Fluent cannot get an accurate reading on what the velocity is actually supposed to be. This
again is probably down to the fact that the flow has gone turbulent at this point and Fluent has been
set to only work with laminar flows.
4.0 Conclusions
From this Fluent analysis of this duct we can see how changing the velocity of the fluid
passing through the duct can generate very different results. When it comes to pressure areas within
the duct, everything stays pretty similar regardless of velocity, but looking at velocity vector and
contour plots, it is proved that increasing the inlet velocity has major effects on what happens inside
the pipe and how a phenomenon called vortex shedding can be achieved. It seems that increasing
the velocity increases the frequency of vortex shedding, and from the formula we can see that as the
inlet velocity is increased to 0.05834m/s, the frequency of vortex shedding is 0.36Hz.
Figure 21Figure 22
Figure 23
Figure 24