cfd course work 3rd year sam mailer

8/2/2019 CFD Course Work 3rd Year Sam Mailer

1/12

Samuel Mailer

200943702

Analysis of Airflow through a

Duct

Mechanical Engineering

3rd

Year

Semester 2


2/12

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

cfd course work 3rd year sam mailer

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