MEng Progress Report - M. Arnold

Mawaggali Arnold Noah - 011263

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MM4MPR MEng Individual Project

PROGRESS REPORT

Mawaggali Arnold Noah (8011263)


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Table of Contents Abstract ................................................................................................................................................... 4

INTRODUCTION .................................................................................................................................. 4

BODY AND LITERATURE REVIEW ................................................................................................. 5

SWIRL FLOW ........................................................................................................................................ 5

Figurative Illustration of swirl flow ................................................................................................. 6

Figure 1: Showing a half section of an industrial burner. ............................................................... 7

Figures 2: Visualisation of the PVC ............................................................................................... 7

Figure 3: shows a rough dimensional structure of an industrial burner. ......................................... 8

Vortex break-down ............................................................................................................................. 8

What is a Vortex break-down? ....................................................................................................... 8

Figure 4a: Vortex flow (Bubble Form) ........................................................................................... 9

Figure 4b: Vortex flow (Spiral Form) ............................................................................................. 9

METHODOLOGY/NUMERICAL REVIEW ............................................................................................. 10

Figure 5: Showing a one-dimensional application of the continuity equation which cannot be

applied in our calculations because the inlet and outlet points does not vary with time............... 11

The Eddy Viscosity model (EVM) ...................................................................................................... 12

Two 𝑘 − 휀 models. ............................................................................................................................ 13

Table 1: showing constants for the Abe-Kondoh-Nagano 𝐤 − 𝛆 model ....................................... 14

Other recommended 𝑘 − 휀 turbulence model ................................................................................. 14

Table 2: showing the constants in the RNG 𝑘 − 휀 model. ............................................................ 15

Analysis of Mass flow, Vorticity and Mesh Geometries ................................................................... 15

Table 3: showing some of the simulation/boundary conditions .................................................. 16

Table 4: showing some of the extracted data from the design iterations.................................... 17

Figure 6: Node-number against Mass flow Velocity in the X, and Y directions. ......................... 17

Figure 7: Node-number against Mass flow rate V. Z and a representation of the positions as lines.

...................................................................................................................................................... 17

Representation of contours, path lines and turbulence flow ........................................................... 18


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Figure 8, 9 and 10 respectively from left to right: showing the contours and path line turbulence

of the velocity flow of the air within the control system.............................................................. 19

Hexagonal Grid Mesh used. .............................................................................................................. 20

Figure 11: View of the Hexagonal Mesh applied. ......................................................................... 20

Velocity profiles created ................................................................................................................... 21

Figure 12: Showing a velocity profile alongside with the colour-scheme. ................................... 21

Figure 13: A close-up of the velocity profile ................................................................................. 21

Representation of the particle path lines ......................................................................................... 22

Figure 14: showing turbulent regions within the tube. ................................................................ 22

Path-lines ...................................................................................................................................... 23

Figure 15: Showing path-lines ....................................................................................................... 23

Figure 16: Showing path-lines with velocity profile 𝑚𝑠 − 1 .......................................................... 24

Figure 17: vector contours ............................................................................................................ 24

Figure 18: Velocity profile ............................................................................................................. 25

Figure 19: Path-line ....................................................................................................................... 25

Future work ........................................................................................................................................... 25

Figure 20: demonstrating variations of S, flow angle and flow rate ............................................. 27

Conclusion ............................................................................................................................................. 27

Possible targets ................................................................................................................................. 28

Limited resources .............................................................................................................................. 28

References ............................................................................................................................................ 28

Appendix ............................................................................................................................................... 30

Work done to date ............................................................................................................................ 30

Table 5: Summary of current completions ................................................................................... 30

Gantt chart ........................................................................................................................................ 31

Autumn Semester Gantt chart ...................................................................................................... 31

Whole Academic Year-round Gantt chart ..................................................................................... 31

Risk assessment and mitigation ........................................................................................................ 32


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Table 6: Showing the risk assessment. ......................................................................................... 32

STUDY OF GEOMETRICAL

BOUNDARIES ON SWIRL FLOW

Abstract Swirling flows are quite a complex phenomenon that require extensive experimentation and

research because they are widespread in nature as well as in industrial applications implying

that very many factors must be put into consideration whilst studying them. For example,

swirl flows can be naturally observed in tornados, which is in their rotational nature that

results into observable wind vortex. Swirling flows are also used in many engineering

applications, which is the focus of this research paper. An example of such applications is in

the instance of combustion e.g. in the aerospace industry as low NOx burner. The various

effects of swirl are flame stabilisation and a more intense mixing of air and fuel which helps

in utilisation of fuel and reduction in un-wanted emissions of mostly NOx (mono-nitrogen

oxides NO and NO2) which are produced from the reaction among nitrogen, oxygen and

even hydrocarbons (during combustion), especially at high temperatures. For this reason, a

lot of research based experimentation focusses swirling flows in a geometry resembling a

combustor, where only the cold swirling flow is studied; which is flow without combustion,

since understanding this flow is crucial in understanding the flow with combustion.

This article however is going to explore the implementation of CFD (Computational Fluid

Dynamics) technology in the design of a fuel powered industrial scale tube burner. An

exploitative analysis of vital aspects that are meant to aid in the acquisition of well calculated

results pertaining the analysis of swirl flow are going to be elaborated.

INTRODUCTION What is going to be observed in the article below is CFD, the coupling between flow field

and the combustion model is based on the eddy dissipation model. For turbulence flow, a

choice between the LES (Large Eddy Simulations) turbulence mover over standard RANS

(Reynolds Averaged Navier-Stokes) presents the possibility to improve the quality of the

combustion-flow field interaction.

RANS model is used as a Numerical tool which offers crucial information that cannot be

gathered by experimental investigations. Though the LESs have had an influence on the

industry as well as in combustion research, which offer additional information that is used in

the flame modelling, however the costs incurred from LES test are quite high, hence limiting

its usage in the industry.


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Boundary must be determined using Navier Stokes, putting into consideration the inlet and

outlet, wall, symmetry, periodic and axis boundaries, internal face boundaries and others as

will be elaborated in the report.

A sub-grid model like the Wall Adapting Local Eddy-Viscosity (WALE) is used since it’s

recommended for in application of complex geometries. (Kanjiras, et al. 2013)

Investigation of swirl flow as elaborated bellow has a various number of formulae approach

suggested by different researchers.

In the occurrence of Vortex breakdown, the swirl number S can be calculated depending on

the measurement platform that was initially used:

𝑆 =1

𝑅

(∫ 𝑤𝑢𝑟2𝑑𝑟∞

0)

(∫ 𝑢𝑟2𝑑𝑟∞

0)

(1)

(Influence of Axisymmetric Assumptions on Large Eddy Simulations of a Confined Jet and a Swirl Flow)

𝑆 =(∫ 𝑤𝑢𝑟2𝑑𝑟

𝑅𝑖𝑛0

)

𝑅𝑖𝑛(∫ 𝑢2𝑟𝑑𝑟∞

0 ) (2)

(Analysis of the Effect of the Swirl Flow Intensity on Combustion Characteristics in Liquid Fuel Powered Confined Swirling

Flames)

Equations above are very similar; (1) is integrated to from 0 to infinity whilst (2) is from 0 to

the tube inner radius.

However, the most renowned research in swirl flow is by N. Syred & J.M. BEER

They derived swirl flow as a characteristic that could be represented as angular momentum

𝐺∅ and axial flux of linear momentum𝐺𝑥.

Where 𝑆 =2𝐺∅

𝐺𝑥𝐷𝑒 (3)

𝐷𝑒 Is the diameter

Where 𝑮∅ - Axial flux of angular momentum

= ∫ (𝑤𝑟)𝜌𝑢2𝜋𝑟𝑑𝑟𝑅

0 (4)

And 𝑮𝒙 – Axial flux of linear momentum

= ∫ (𝑢𝑝𝑢2𝜋𝑟𝑑𝑟) + 𝑃. 2𝜋𝑟𝑑𝑟𝑅

0 (5)

BODY AND LITERATURE REVIEW

SWIRL FLOW

As mentioned earlier, swirl flows can be applied in very many situations, though capitalising

more on the industrial side, work on swirl flaws can be helpful with swirl combustors,

cyclone separators and flow over delta wigs.


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Figurative Illustration of swirl flow (An extract from Swirl Flow CFD - CAE images)

Since we are dealing with swirl flows, it is imperative that external influences are put into

consideration and this contributes to the complexity and strenuousness of the numerical

investigations.

Numerical calculations are pre-dominantly by RANS flow equations which aid in production

of a basic flow characterisation of the vortex break-down, plus other features like the

Precessing Vortex Cores (PVC).

Calculations with RANS are mostly used in swirl flow studies, though the use of LES can

also be employed. RANS and LES are different in certain aspects. The RANS model

calculations only give a time averaged mean value for velocity the velocity field, whereas the

LES is based on “filtering” as opposed to the RANS averaging. A filter size is picked, and all

velocity flows, both larger and smaller than the filter would be modelled. Slight accuracy

increment can be realized because of the smaller the filter size, the more exact the time

variation resolution of velocity vector will be.

A draw back to the LES is such that, a very high spatial discretization is required for the

computation process, which results into very high computational costs.

A diagrammatic extract showing a section of an industrial burner and the PVC in more visual

clarity.


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Figure 1: Showing a half section of an industrial burner. (40 years with Swirl, Vortex, Cyclonic

Flows, and Combustion)

Natural gas enters the system and is precisely premixed. The resulting pilot gas is carefully

mixed with Air (oxygen) and a spark is initiated by the burner which then results into the

combustion process within the combustion chamber, and the resulting gaseous residue is

expended through the exhaust.

Figures 2: Visualisation of the PVC (40 years with Swirl, Vortex, Cyclonic Flows, and Combustion)

Note: P.V.C frequency increases linearly with flowrate, and the PVC lies on the boundary of

central recirculation zone(CRV).

From left to right, we obverse a schematic, visualisation of burning and LES visualisation of

PVC.


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The swirl flow is investigated from initiation to final dispersion and therefore in

experimentation, the flow has different swirl numbers S, which are investigated using the

formula.

𝑆 =1

𝑅

(∫ 𝑤𝑢𝑟2𝑑𝑟∞

0 )

(∫ 𝑢𝑟2𝑑𝑟∞

0 ) (6)

The resulting LES computations in future work will be centred around two values.

1) Where there is no swirl at 𝑆 = 0

2) And at a strong swirl which is at 𝑆 = 0.6

The swirl values as above have been used in several swirl flow experiments because they

give a clear foundation of how the fluid flow starts, from point 0, up to the maximum 0.6, and

this aids to determining the Reynolds number at a given point in each turbulent or linear flow

scenario.

The effect of inlet swirl on the flow development and combustion dynamics in a lean-

premixed swirl-stabilized combustor has been numerically investigated using a large-eddy-

simulation (LES) technique. Results indicate that when the inlet swirl number exceeds a

critical value, a vortex-breakdown-induced central toroidal recirculation zone is established

in the downstream region. As the swirl number increases further, the recirculation zone

moves upstream and merges with the wake recirculation zone behind the centre-body.

Excessive swirl may cause the central recirculating flow to penetrate the inlet annulus and

lead to the occurrence of flame flashback. (Effect of swirl on combustion dynamics)

Figure 3: shows a rough dimensional structure of an industrial burner.

Vortex break-down

What is a Vortex break-down?

Vortex breakdown basically refers to a disturbance characterized by the formation of an

internal stagnation point on the vortex axis, followed by reversed flow in a region of limited

axial extent. (The structure of vortex breakdown)

Inlet Swirl


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Figure 4a: Vortex flow (Bubble Form)

Figure 4b: Vortex flow (Spiral Form)

The two figures above show vortex flow from left to right. Four distinct forms of vortex

breakdown are identified: The well documented bubble state, a new cone configuration in

which the vortex takes the form of an open conical sheet, and two associated asymmetric

bubble and asymmetric cone states, which are only observed at large Reynolds numbers. (Ref:

Billant et al (1998))

Though two forms are predominant, one called near-axisymmetric (axisymmetric or bubble-

like) and the other is spiral, as represented in figures 4a and 4b respectively. (REF: The structure of

vortex breakdown)

After the occurrence of a vortex breakdown phenomenon, two main flow states appear to

develop as follows;

a) High levels of turbulence are caused by a three-dimensional time dependent

instability of swirling flow referred to as Precessing Vortex Core.

b) Flows in which the amplitude of the PVC is damped by at least an order of

magnitude.

Note: Although the initial focus was on the Precessing vortex core (PVC) and its

characteristics, more recent work, especially with confined flows (i.e. combustion

chambers/furnaces) has shown the high susceptibility of the central recirculation zone

(CRZ) to deformation and its often time a dependant and deformed structure, which has more

effect on flame stability than the PVC.


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METHODOLOGY/NUMERICAL REVIEW

This review is mainly focusing on the velocity of air flowing into the tube burner. It’s a

stationary equipment though it can briefly be affiliated with Newton’s 3rd law ‘to every action

there is an equal but opposite reaction’. This law alone is applied in many circumstances of

the burner. However, boundary conditions will rotate around the application or RANS, which

is based on Newton’s 2nd Law.

The swirl burner to further elaborate, depends on the generation of an aerodynamically

formed central recirculation zone (CRZ), which essentially serves to recycle heat and pre-

existing chemical species to the root of the flame as well as providing low-velocity regions

where the flame speed can match the local flow velocity (evidently applying newtons third

law). The characteristics of the CRZ evidently depend heavily on the level of swirl (swirl

number), burner configuration, type of flow expansion (Will be in future work), Reynolds

number (i.e. flowrate) and equivalence ratio.

The above conditions are very essential in the observance of the swirl flow and prediction of

the pre-combustion and combustion chemical species.

Although it is not possible to physically solve the mathematical RANS equations, simulation

software like ANSYS-fluent©, has enabled researchers to model different possible outcomes

in swirl flow per varying structure changes in the tube burner. The computer software runs

while putting the principals mentioned below into consideration, and well considered

boundary conditions would result into accurate findings.

A simple overview of the numerical formulae required when calculating the boundary

conditions are as follows;

The instantaneous equations of motion


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Figure 5: Showing a one-dimensional application of the continuity equation which cannot be

applied in our calculations because the inlet and outlet points does not vary with time. (ref:

https://www.princeton.edu/~asmits/Bicycle_web/continuity.html)

However, the instantaneous equation of motion as shown below, show a representation of the

fluid motions where the continuum approximation is valid or governed by a set of dynamic

equations referred to as the continuity and momentum equations.

Note: It is apparent that the (U)RANS is applied in our assumptions. This is because we are

not assuming a steady state scenario i.e. Since in fluid dynamics, the continuity equation

states that, in any steady state process, the rate at which mass enters a system is equal to the

rate at which mass leaves the system, but we cannot make such assumptions since accuracy is

the reason as to why so much research is carried out and not to mention the space and time

variations with velocity as elucidated in the formulae below;

[𝜕�̃�

𝜕𝑡+ �̃�𝑗

𝜕�̃�

𝜕𝑥𝑗] + �̃�

𝜕�̃�

𝜕𝑥𝑗= 0 (7)

[𝜕𝑢𝑖

𝜕𝑡+ �̃�𝑗

𝜕𝑢𝑖

𝜕𝑥𝑗] += −

𝜕�̃�

𝜕𝑥𝑗+

𝜕�̃�𝑖𝑗(𝑣)

𝜕𝑥𝑗 (8)

Where �̃�𝑖 = �̃�𝑖(�⃗�, 𝑡), a function of space �⃗� and time t. 𝜕�̃�𝑖𝑗(𝑣)

(�⃗�, 𝑡) is referred to as the

viscous stress tensor. (Tensor used in continuum mechanics to model the part of the stress at a

point within a material that can be attributed to the strain rate and the rate at which it is

deforming around that point) this enables us to predict the potential weakness points in the

material used against factors like temperature and pressure.

Numerically it’s referred to as a fourth-order viscosity tensor (𝜇) such that 휀 = 𝜇𝐸. Where E

– strain rate, 휀-viscous stress (nomenclature)

The Newtonian closure for the viscous stress tensor relates it to the fluid motion using a

property of fluid, molecular viscosity (𝜇).

�̃�𝑖𝑗(𝑣)

= 2𝜇(�̃�𝑖𝑗 −1

3�̃�𝑘𝑘𝛿𝑖𝑗) (9)

Where �̃�𝑖𝑗 is the instantaneous strain rate tensor defined as;

�̃�𝑖𝑗 =1

2(

𝜕𝑢𝑖

𝜕𝑡+ �̃�𝑗

𝜕𝑢𝑖

𝜕𝑥𝑗) (10)

In the case for incompressible flows, the derivative of density following the fluid material is

zero

𝜕𝑢𝑖

𝜕𝑥𝑗= 0 (11)


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[𝜕𝑢𝑖

𝜕𝑡+ �̃�𝑗

𝜕𝑢𝑖

𝜕𝑥𝑗] = −

1

𝜌

𝜕�̃�

𝜕𝑥𝑖+

𝜕2𝑢𝑖

𝜕𝑥𝑗𝜕𝑥𝑗 (12)

We also use the URANS because as opposed to the detailed, very expensive and impractical

in industrial applications DNS (Direct Numerical Simulation), the URANS allows us to

analyse turbulent flow in two main parts.

�̃�𝑖 = �̅�𝑖 + 𝑢𝑖′ (13)

𝑝 = �̅� + 𝑝′ (14)

This approach is referred to as Reynolds Decomposition. These equations are inserted into

the instantaneous equations and hence averaging the results in the RANS equations.

𝜕�̅�𝑗

𝜕𝑥𝑗= 0 (15)

[𝜕𝑢𝑖

𝜕𝑡+ �̅�𝑗

𝜕�̅�𝑖

𝜕𝑥𝑗] = −

1

𝜌

𝜕�̅�

𝜕𝑥𝑖+

𝜕2�̅�𝑖

𝜕𝑥𝑗𝜕𝑥𝑗−

𝜕

𝜕𝑥𝑗{𝑢𝑖𝑢𝑗̅̅ ̅̅ ̅} (16)

Importantly noted: the averages are referred to as ensemble at times, and this basically states

that they are time-dependent. i.e. the time dependent variables in equation (16) are both a

function of space and time.

𝑈 = 𝑈𝑖(𝑥𝑖, 𝑡), 𝑃 = 𝑃(𝑥𝑖, 𝑡), 𝑢𝑖𝑢𝑗 = 𝑢𝑖𝑢𝑗(𝑥𝑖, 𝑡) (17)

The term “𝑢𝑖𝑢𝑗” defines the correlation between fluctuating velocities and is referred to as the

Reynolds stress tensor. When investigating the mean flow, all the turbulent fluid motion is

clustered into this single term by the (U)RANS process.

Further justification of using the (U)RANS model is that it provides us with ten unknowns in

total; 3-velocities, 1-pressure, 6-stresses and only and only four equations to tackle the whole

problem. 1=continuity, 3 components of Navier Stocks equation. This known as the

turbulence closure problem.

It is evident that the (Unsteady)RANS, gives us unsteady results, since we retain the transient

time response, 𝜕�̅�𝑖

𝜕𝑡 during the computation. The calculations are so time dependant that the

(U) is decomposed further into time dependant variables as shown below;

Time averaged part ⟨�̅�⟩, resolved fluctuation 𝑢′′, and the modelled turbulent fluctuation 𝑢′

Hence �̃� = �̅� + 𝑢′ = ⟨�̅�⟩ + 𝑢′′ + 𝑢′ (18)

The Eddy Viscosity model (EVM)

This model is use in the turbulence closure problem.


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There are a various number of EVMs, and this depends on the application at hand. As in the

Newtonian closure for the viscous stress tensor, we use a similar idea to apply for turbulence

closure problem.

So, to close the RANS equation, an analogy that tries to relate the Reynolds stresses to the

fluid motion through what is referred to as “turbulent” or “eddy” viscosity is introduced and

referred to as the “Boussinesq assumption”.

It’s represented in the equation as bellow;

𝜌𝑢𝑖𝑢𝑗̅̅ ̅̅ ̅ = −𝜇𝑡 (𝜕𝑈𝑖

𝜕𝑥𝑗+

𝜕𝑈𝑗

𝜕𝑥𝑖) +

2

3 𝜌𝛿𝑖𝑗𝑘 (19)

Basically, what this means is that the fluctuations are represented with a quantity that is kind

of averaged and then try to find out how the quantity is connected/coupled to the mean flow.

The EVM is a scalar quantity which is calculated using a turbulent velocity scale 𝒱, length

scale 𝑙, based on the dimensional analysis.

In the case of this projected length is one of the factors that would be varied in the future,

hence making it an appropriate fit for the numerical study.

𝑣𝑡 = 𝒱𝑙 (20)

In one EVM equation a solution for the turbulence quantity is probable and a second

turbulent quantity is derived from algebraic expression. These two quantities are what’s use

to describe “eddy” viscosity.

Two 𝑘 − 휀 models.

The k-epsilon model is one of the most used in CFD (Computational Fluid Dynamics). There

are a various number of these models used, though two are going to be talked about here. In

line with the above name formulae, the corresponding K-e model used was the Abe-Kondoh-

Nagano 𝒌 − 𝜺 model. 휀 appears naturally due to the dissipation rate of turbulent kinetic

energy and two equations for an EVM are most appropriate for the formation of 𝑣𝑡. Not to

mention the model is also a Low Reynolds Number (LRN) 𝒌 − 𝜺 model.

Equations are as follows;

𝜕𝑘

𝜕𝑡+ �̅�𝑗

𝜕𝑘

𝜕𝑥𝑗=

𝜕

𝜕𝑥𝑗[(𝑣 +

𝑣𝑡

𝜎𝑘)

𝜕𝑘

𝜕𝑥𝑗] + 𝑃𝑘 − 휀 (21)

𝜕𝜀

𝜕𝑡+ �̅�𝑗

𝜕𝜀

𝜕𝑥𝑗=

𝜕

𝜕𝑥𝑗[(𝑣 +

𝑣𝑡

𝜎𝜀)

𝜕𝜀

𝜕𝑥𝑗] + 𝐶𝜀1

𝜀

𝑘𝑃𝑘 − 𝐶𝜀2𝑓2

𝜀2

𝑘 (22)

Where,

𝑃𝑘 = [𝑣𝑡 (𝜕𝑈

𝜕𝑥𝑗+

𝜕�̅�𝑗

𝜕𝑥𝑗)]

𝜕�̅�𝑗

𝜕𝑥𝑗 (23)


14

𝑣𝑡 = 𝐶𝜇𝑓𝜇𝑘2

𝜀 (24)

Plus

𝑓𝜇 = [1 − exp (−𝑛∗

14)]

2

[1 +5

𝑅𝑡

34

exp {− (𝑅𝑡

200)

2

}] (25)

𝑓2 = [1 − exp (−𝑛∗

3.1)]

2

[1 + 0.3 exp {− (𝑅𝑡

6.5)

2

}] (26)

𝑛∗ =𝜀

14𝑛

𝑣34

(27)

Where ‘𝑛’ is the wall-normal distance between the node and the wall.

The constants in this model are as follows;

𝐶𝜇 = 0.09 𝐶𝜀1 = 1.5 𝐶𝜀2 = 1.9 𝜎𝑘 = 1.4 𝜎𝜀 = 1.4

Table 1: showing constants for the Abe-Kondoh-Nagano 𝐤 − 𝛆 model

Length scale for turbulence would be expressed as,

𝑙 =𝑘

32

𝜖 (28)

We have the time scale as well, which is obtained using velocity scale and the length scale as

expressed bellow;

𝒯 =𝑙

𝒱=

𝑙

𝐾12

=𝐾

32

𝜀𝐾12

=𝑘

𝜀 (29)

The wall boundary conditions on this model

�̅� = �̅� = 𝑘 = 0 (30)

And

휀𝑤𝑎𝑙𝑙 = 2𝑣 𝑘1/𝑛12 (31)

Where ‘𝑛1’ is the normal distance between the wall and the closest wall node.

Other recommended 𝑘 − 휀 turbulence model

This can be applied is as bellow; (ref: Numerical Simulation of Swirling Flows -Heat Transfer

Enhancement)

The 𝑘 − 휀 RNG model is dominated by swirl and since this report is mainly focused on swirl,

it is quite safe to say that it is recommended for the turbulent numerical calculations.


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The conservation equations for this model are as follows;

𝜕

𝜕𝑥𝑖(𝜌𝑘𝑢𝑖) =

𝜕

𝜕𝑥𝑗(𝛼𝑘𝜇𝑒𝑓𝑓

𝜕𝑘

𝜕𝑥𝑗 ) + 𝐺𝑘 − 𝜌휀 (32)

𝜕

𝜕𝑥𝑖(𝜌휀𝑢𝑖) =

𝜕

𝜕𝑥𝑗(𝛼𝜀𝜇𝑒𝑓𝑓

𝜕𝜖

𝜕𝑥𝑗 ) + 𝐶𝜀1

𝜀

𝑘𝐺𝑘 − 𝐶𝜀2𝑓𝜌

𝜀2

𝑘− 𝑅𝜀 (33)

Where,

𝑅𝜀 =𝐶𝜇𝜂3𝜌(1−

𝜂

𝜂𝑜)

1+𝛽𝜂3

𝜀2

𝑘 (34)

And

𝜂 = (2𝑆𝑖𝑗𝑆𝑖𝑗)0.5 𝑘

𝜀 (35)

Where ‘𝑘’ is the turbulent kinetic energy, ‘휀’ is the corresponding dissipation, u is the

averaged velocities and the density, 𝜌.

The term 𝑅𝜀 in equation 2 represents the rate of strain defined in equation 3 and 4, where S in

this case is the strain tensor also calculated based on “averaged” velocities.

Coefficient constant to this model are as below;

𝐶𝜇 = 0.0845 𝐶1𝜀 = 1.42 𝐶2𝜀 = 1.68 𝜂𝑜 = 4.38 𝛽 = 0.012

Table 2: showing the constants in the RNG 𝑘 − 휀 model.

The fluid Separations at the boundaries, and the recirculation zones affect and dominate the

flow fluid flow pattern quite a lot.

Analysis of Mass flow, Vorticity and Mesh Geometries

3Dimensional bar-charts were made using MATLAB – software to give a visual on the

velocity profile. This profile is plotted on a node-number vs X, Y and Z respectively on the

graphs as seen below.

The bar graphs represent the Velocity magnitude (𝑚−𝑠) derived from the mass flow rate

(𝑘𝑔−𝑠), plotted against the current position of the flowing air represented on X, Y, and Z

axes.

The mesh data calculated by the simulation software ranges from 1 to about 991700 meshes,

so the data plots were plotted from 1 to 100, to show the directional trend.


16

The results were recorded in the following conditions.

air mass flow rate (Inlet) 0.001626 (𝑘𝑔−𝑠 )

Swirl number 0.5,0.6,0.75

Average rotational angle -120° (all periodic zones)

Number of iterations 2000

Outlet - Pressure 0

Wall roughness constant 0.5

Table 3: showing some of the simulation/boundary conditions

Volume statistics: (𝑚3)

minimum volume: 1.019841e-11

maximum volume: 2.407020e-08

total volume: 2.825425e-03

Face area statistics: (𝑚2)

minimum face area: 4.995057e-09

maximum face area: 1.885111e-05

volume flow rate per area, 0.0013273469(𝑚3) at 0.00029037159(𝑚2)

The table below will show a sample of the data what the X, Y, and Z plains represent in terms

of position on a Cartesian plane including a 3rd dimension Z, with velocities u, v and w

respectively.

Node-number X

Axial

Y

Radial

Z

Azimuthal

1 2.058835700E-02 3.134277835E-02 1.300000101E-01

2 2.003933489E-02 3.050697036E-02 1.300000101E-01

3 1.923389733E-02 3.102107719E-02 1.300000101E-01

4 1.976085454E-02 3.187097237E-02 1.300000101E-01

5 1.949031092E-02 2.967116237E-02 1.300000101E-01

6 1.870694198E-02 3.017118573E-02 1.300000101E-01

7 1.894128881E-02 2.883535437E-02 1.300000101E-01

8 1.817998663E-02 2.932129242E-02 1.300000101E-01

9 1.839226671E-02 2.799954824E-02 1.300000101E-01

10 1.765302941E-02 2.847140096E-02 1.300000101E-01

11 1.784324087E-02 2.716374211E-02 1.300000101E-01

12 1.712607220E-02 2.762150951E-02 1.300000101E-01

13 1.841523871E-02 3.151395172E-02 1.300000101E-01

14 1.891976409E-02 3.237734735E-02 1.300000101E-01

15 1.791070960E-02 3.065055609E-02 1.300000101E-01

16 1.740618423E-02 2.978716046E-02 1.300000101E-01

17 1.690165699E-02 2.892376296E-02 1.300000101E-01

18 1.639712974E-02 2.806036733E-02 1.300000101E-01

19 1.758403145E-02 3.198518232E-02 1.300000101E-01


17

20 1.806578599E-02 3.286148980E-02 1.300000101E-01

Table 4: showing some of the extracted data from the design iterations

Figure 6: Node-number against Mass flow Velocity in the X, and Y directions.

Figure 7: Node-number against Mass flow rate V. Z and a representation of the positions as

lines.

As observed the axial velocity shows a deteriorating chart (a), which means that there are

many factors that influence the velocity particularly in this direction. The radial velocity is

seen to have a rigid and generally slightly incrementing graph (b), while the azimuthal chart

(c) direction is seen to have a consistently flat topography.

A lot of research is done about the flow nature of the air in the tube; for laminar flow, fluid

particles are observed to flow in a systematic and orderly manner along path-lines, whilst

momentum and energy are transferred across streamlines by what is known as molecular

diffusion. Whereas in turbulence/turbulent flow, there is an almost immediate creation of

swirling eddies which transport mass, momentum, and energy to other the other regions of

flow much more intensively and rapidly than molecular diffusion, hence enhancing mass,


18

momentum, and heat transfer by a rather large margin. Hence resulting into a clear

association of, turbulent flow with much greater friction, heat transfer, and mass transfer

coefficients values. (Ref: Pipe-flow introduction Chapter 8)

The intensity of these flow patterns is going to be even better understood from the figures and

explanations as will be seen next.

Boundary conditions applied in the simulation were as follows;

Pressure Velocity coupling - ‘simple’ and Discretization – ‘Second-Order Upwind Scheme’

and for turbulence, (U)RANS and 𝑘 − 휀 models were employed.

Representation of contours, path lines and turbulence flow


19

Figure 8, 9 and 10 respectively from left to right: showing the contours and path line

turbulence of the velocity flow of the air within the control system.

The colour schemes in the diagrams above are such that from red through to blue represent

intensity of the mass flow rate with red being the highest and blue the lowest.

Along the sides, especially right after the inlet, bubble like light blue structures can be seen

and this show the vorticity around those areas.

In figure 9 the swirl movements of air are observed through the tube.

To better elaborate the diagrams above.

First a grid mesh was created on the control design model used in the simulation software.


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Hexagonal Grid Mesh used.

Figure 11: showing the hexagonal mesh.

In table 2 a column that says node-number can be seen. This number represents the total

number of meshes that were applied on the tube, and in this case, there was a total of 991700

grid points.

An independent grid study was carried out to improve the simulated results.

Figure 11: View of the Hexagonal Mesh applied.

The mesh helps in defining which areas on the model would have a more intense of lighter

reaction with the swirl and mass flow rate a vector profile was created as shown in the figures

below to further illustrate the visualisation.

Then….,


21

Velocity profiles created

Figure 12: Showing a velocity profile alongside with the colour-scheme.

The colour scheme as observed, shows which areas experience the highest levels of air flow.

Form blue to red, the ferocity of the flow intensifies depending on the position of flow.

Figure 13: A close-up of the velocity profile

As briefly explained just below figure 7, we understand that mass flow rate violently occurs

close to the edges of the pipe, that’s why a proper mesh grid refinement is need to acquire

more accurate results.

It’s clearly seen arrow heads pointing us to the flow movement as air is flowing through the

tube.

The encircled and boxed areas show the formation of a resulting Precessing Vortex Core and

likely the recirculation zones created respectively within the tube burner.


22

Representation of the particle path lines

Figure 14: showing turbulent regions within the tube.

In all the 3 vector diagrams that the recirculation zones, PVC, and turbulence regions are

heavier at the root, and keep deteriorating as the flow moves towards the outlet.


23

Path-lines

Figure 15: Showing path-lines

The colour grid to the left in the diagram represents the rate of flow per area.

The arrow is pointing at the inlet point and the circled area shows how the air flows through

the tube in a swirly formation.

The same figure represented in terms of velocity would have a velocity profile as shown

below. Velocity magnitude (𝑚𝑠−1) can be read on the colour grid in the diagram below.


24

Figure 16: Showing path-lines with velocity profile (𝑚𝑠−1)

The path-lines are seen starting from the inlet and then moving through the tube in a swirl

formation.

On figure 15, the arrow shows the inlet, and the oval shows the swirl type movement of the

air within the tube.

Figures showing vector contours, vector profile and path-lines at a 0.01(𝑘𝑔𝑠−1)

Figure 17: vector contours


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Figure 18: Velocity profile

Figure 19: Path-line

When at a higher mass flow rate one would expect a more a more violent environment that

portrays very large vortices, high turbulence and generally a rougher pattern in the swirl flow,

contrary to expected results, many factors that affect the turbulence and movement of air

require a very extensive study to understand a more accurate understanding of how each

boundary condition varies with space and time at any given position from the fluid flow

process.

Future work Prospective future targets in this research project are a must and should be executed to get

close to perfect results that much some of the current findings. Some limitations will be stated

later in the conclusion section.

Future work plans will be in the line of what is stated below and they will be updated in

accordance with current and ongoing experimentation by larger and richer research

corporations expose their findings.

1) A Grid refinement study.

Mesh refinement is a core requirement in the generation of more accurate and better swirl

flow patterns within the tube burner. This will generally exploit the ‘nodal’ elements

dispersion as per the pre-existing boundary conditions. The refinement will most likely

elaborate a Low Reynolds Number mesh generated such that it is located around the near

wall node at 𝑌+ < 1


26

2) Vortex breakdown

This will exploit the various levels of vortex breakdown. It is a rather expansive field and

data will most likely be referenced from “N. Syred” past and current research. He is the most

renown researcher in Tube burner technology.

3) Fuel mixing.

Swirl flow is supplemented by the strategic fuel injection into the inlet of the tube burner.

Much research has been done in the line of how much fuel should be added per volume of air,

for this plays a big role in the combustion process and fuel conservation. Understanding the

plane where the missing occurs and at the same time putting into consideration the strong

rotational movement of the fluid brings to light the phase flow patterns that would result;

This in general betters the missing process. The mixture consistence which should occur from

the recirculation region all the way to the end of the combustion chamber is very key in

looking at aspects like Exhaust recirculation zones and how they can be exploited.

(Ref: Analysis of the Effect of the Swirl Flow Intensity on Combustion Characteristics in Liquid Fuel Powered Confined

Swirling Flames)

4) More investigation in the use of LES

LES (Large Eddy Simulation), as explained in the introduction is a strenuous and time

streaking procedure that is governed by a 3Dimensional detailed study is worth exploiting for

it gives noticeably more accurate results.

5) More detailed MATLAB representation

This will help in terms of given detailed graph that give a better visual when analysing grid

nodal positioning in the X, Y, and Z planes.

6) Geometry change

This will be done in many forms such as changing the physical geometry of the tube burner

in both length and width of tube burner. Another form will in terms of changing the geometry

flow angles, as this aids in understanding the positioning of the elements that initiate the

mixing process.


27

A figure below shows how the swirl number, S would vary with geometry and mass flow

rate.

Figure 20: demonstrating variations of S, flow angle and flow rate

7) Simulation of the entrainment process

This is intended to tackle mainly the aspect of pressure. Without entrainment, there is an

assumption that the pressure is constant, therefore eliminating this assumption is affiliated

with incorporating this aspect in fluid flow.

8) Animated path lines for even better clarity

Simulation of an animated path line aides in understanding the dynamics of the physical

layout of the structure and how it affects the fluid flow patterns.

9) Variation of the swirl flow number.

(REF: Central recirculation zone analysis in an unconfined tangential swirl burner with varying degrees of premixing)

Conclusion

The purpose of this research is to come up with an ideal design that puts into all factors into play.

Factors such as reduction in NOx emissions, and increased fuel mixing for economic reasons. The

rationale in the research entails understand the influence of fuel injectors as per CRZs produced by a

generic swirl burner operating at various varied boundary conditions like the swirl number, pressure

variations, and which control modules to apply under diffusive and partially premixed conditions.


28

As evident in the comparison of different mass flow rates, the different CRZs (Central Recirculation

Zones) were formed.

Possible targets

Exploitation of existing models like the (U)RANS and LES can provide close to good enough

results. This can be achieved through the exploitation of different proposed 𝒌 − 𝜺 and using

the one that simulates results closest to the current findings.

Limited resources

Results obtained generally are limited due to many factors that come into play when investing

swirl flow and similarly direct methods that would entail the creation of an environment to

simulate very detailed studies are impractical and heavily expensive. (ref: Central recirculation

zone analysis in an unconfined tangential swirl burner with varying degrees of premixing)

References

A. Valera-Medina, N. S. (2010). Central recirculation zone analysis in an unconfined tangential.

RESEARCH ARTICLE, 13.

Ahmed, M. G. (2013). Effect of the Variation of the Mixing Coefficient on a Turbulent Confined

Flame. Communication Science & technology, 8.

Ashraf Kotb, H. S. (2016). A comparison of the thermal and emission characteristics of co and

counter swirl inverse diffusion flames. International Journal of Thermal Sciences, 12.

Cheng, R. K. (n.d.). Low Swirl Combustion. Berkeley: Lawrence Berkeley National.

H. J. Sheen, W. J. (1996). Recirculation Zones of Unconfined and Confined. AIAA JOURNAL, 8.

Leibovich, S. (1978). The Structure of Vortex Breakdown. New York: Ann. Rev. Fluid Mech.

lucca-Negro, O. O. (2013). Vortex Breakdown: A Review. Wales: Cardiff University.

M. Klančišar1, T. S. (2015). Analysis of the Effect of the Swirl Flow Intensity on. Journal of Applied

Fluid Mechanics, 10.

M.E. Feyz, J. E. (2015). Effect of recess length on the flame parameters and combustion. (ELSEVIER)

Applied Thermal Engineering, 9.

N. SYRED, J. M. (1974). Combustion in Swirling Flows: A FReview. Sheffield England: Sheffield

University.


29

N. Tsioumanis, J. B. (2011). Flow processes in a radiant tube burner: Combusting flow. Energy

Conversion and Management, 9.

NARASIMHAMURTHY, V. D. (2004). Unsteady-RANS Simulation of Turbulent Trailing-Edge Flow.

Goteborg, Sweden: CHALMERS UNIVERSITY OF TECHNOLOGY.

O. Keck, W. M. (2002). Establishment of a Confined Swirling Natural gas/air flame as a standard

flame. Combustion Science and Technology, 36.

PAUL BILLANT, J.-M. (1998). Experimental study of vortex breakdown in swirling jets. Cambridge:

Cambridge University Press.

S. Archer, A. K. (8 January, 2004). Effect of Swirl on Flow Dynamics in Unconfined and Confined

Gaseous Fuel Flames. 42nd AIAA Aerospace Sciences Meeting and Exhibit, p. 10.

Schluter, J. (2001). Influence of Axisymmetric Assumptions on Large Eddy Simulations of a Confined

Jet and a Swirl Flow. paris: CERFACS.

Scribano.G, S. C. (2005). Pollutant emissions reduction and performance optimization of an industrial

radiant tube burner. ELSEVIER-Science Direct, 8.

Syred, N. (2011). 40 years with Swirl, Vortex, Cyclonic Flows, and Combustion. Orlando: oxford

university press.

Syred, N. (7 January, 2011). 40 years with Swirl, Vortex, Cyclonic Flows, and Combustion. 49th AIAA

Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p.

22.

T. Z. Shuguang Chen, K. K. (20116). Numerical simulation of the combustion characteristics and N

emission of a swirl burner: Influence of the structure of the burner outlet. Applied Thermal

Engineering, 12.

Teresa Parra, R. P. (2015). Numerical Simulation of Swirling Flows - Heat Transfer Enhancement.

Journal of Fluid Flow, Heat and Mass Transfer, 6.

WAHID, D. M. (2006). Studies on the effect of swirl intensity and fuel mixtures on combustion and

flame characteristics of swirl burner. Kuala lumpur: Fakulti Kejuruteraan Mekanikal,Universiti

Teknologi Malaysia.


30

Appendix

Work done to date

MM4MPR MEng year itinerary

Task Description Duration

(days) Expected outcome

Project Duration 40 credit Yearlong Project

182

Final report covering all expected fields of research of properly justifiable result outcomes

Book work station & literature review

Acquisition of a computer to carry out the necessary simulations with and studies

14

Attained a fully functional computer to carry out the necessary simulations with Ansys-Fluent© and literature review commenced

Geometry change & Progress report format

learning report format and geometrical variations in the design. 7 geometry change comparisons (future)

Numerical Methods & Progress Report

simulation of the model with boundary conditions

13

correctly set boundary conditions and use of the correct model to obtain accurate results

Grid generation & Periodic Flow

Meshing in Ansys workbench and creation of periodic zones on the tube surface. 7

successfully generated grid and periodic flow will aide in viewing the flow patterns and velocity contours

Numerical Modal & Meshing

More on mesh refinement. 15

this improves the mass flow patterns and describes boundary conditions more clearly

Contour & Path line study

review of obtained results 7 path lines in with a swirl movement.

Coupling between pressure & Velocity

review of obtained results 14 contours and velocity profiles

Velocity Profile & Mass Flow rate

variation of mass flow rate during different simulations 7

increase of decrease in the ferocity of the recirculation regions

Progress Report Submission

submission to university portal. 0.1 10-Dec

Table 5: Summary of current completions


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Gantt chart

Autumn Semester Gantt chart

Whole Academic Year-round Gantt chart

14-Oct 3-Dec 22-Jan 13-Mar 2-May 21-Jun

Project Duration

Book work station & literature review

Geometry change & Progress report…

Numerical Methods & Progress Report

Grid generation & Periodic Flow

Numerical Modal & Meshing

Contour & Pathline study

Coupling between pressure & Velocity

Velocity Profile & Mass Flow rate

Progress Report Submission

Resume Project & Refine Mesh

Run Simulation

Analysis of output results

Discussiong and analysis of findings

Review, Corrections and Final draft report

Submission of final report

MM4MPR MEng Individual Project

Start Date Duration (days)


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Risk assessment and mitigation

Task Risk Mitigation

Reading/Literature

review

Quite a lot of

information available

published by

different people.

Selection of data

from the most trusted

sources by looking at

work published by

renown researchers.

Methodology Some formulae like

the RANS model

cannot be physically

solved.

Extensive research

on how the equations

are explained and

applied by the

software used

Validation of results Results not tallying

with expected

outcomes.

Revision of input

boundary conditions

is key.

Progress report Possibility of

missing deadline

Time management

and comprehension

of data early enough.

Analysis and

discussion of results

Shallow

understanding of the

complex formulae

leads to

unsubstantial

analyses.

Very detailed

analysis of obtained

results to give a valid

explanation.

Referencing Incomplete and

shallow referencing.

Citing, quoting and

proper referencing of

all literature review

and obtained results.

Final report Cannot meet

deadline.

Well segmented and

properly written out

report with time left

for revision of the

contents

Table 6: Showing the risk assessment.

MEng Progress Report - M. Arnold

Documents

Transcript of MEng Progress Report - M. Arnold