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 − 𝜀 models.............................................................................................................................13
Table 1: showing constants for the Abe-Kondoh-Nagano 𝐤 − 𝛆 model.......................................14
Other recommended 𝑘 − 𝜀 turbulence model.................................................................................14
Table 2: showing the constants in the RNG 𝑘 − 𝜀 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
(∫ 𝑤𝑢𝑟2 𝑑𝑟
∞
0
)
(∫ 𝑢𝑟2 𝑑𝑟
∞
0
)
(1)
(Influence of Axisymmetric Assumptions on Large Eddy Simulations of a Confined Jet and a Swirl Flow)
𝑆 =
𝑅𝑖𝑛
0
)
𝑅𝑖𝑛(∫ 𝑢2 𝑟𝑑𝑟
∞
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∅
𝐺 𝑥 𝐷𝑒
(3)
𝐷𝑒 Is the diameter
Where 𝑮∅ - Axial flux of angular momentum
= ∫ (𝑤𝑟)𝜌𝑢2𝜋𝑟𝑑𝑟
𝑅
0
(4)
And 𝑮 𝒙 – Axial flux of linear momentum
= ∫ (𝑢 𝑝 𝑢2𝜋𝑟𝑑𝑟) + 𝑃. 2𝜋𝑟𝑑𝑟
𝑅
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
∞
0
)
(∫ 𝑢𝑟2 𝑑𝑟
∞
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;
[
𝜕𝜌̃
𝜕𝑡
+ 𝑢̃𝑗
𝜕𝜌̃
𝜕𝑥 𝑗
] + 𝜌̃
𝜕𝜌̃
𝜕𝑥 𝑗
= 0 (7)
[
𝜕𝑢̃ 𝑖
𝜕𝑡
+ 𝑢̃𝑗
𝜕𝑢̃𝑖
𝜕𝑥 𝑗
] += −
𝜕𝜌̃
𝜕𝑥 𝑗
+
𝜕𝑇̃ 𝑖𝑗
(𝑣)
𝜕𝑥 𝑗
(8)
Where 𝑢̃ 𝑖 = 𝑢̃ 𝑖(𝑥⃗, 𝑡), a function of space 𝑥⃗ and time t. 𝜕𝑇̃𝑖𝑗
(𝑣)
(𝑥⃗, 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 𝜀 = 𝜇𝐸. Where E
– strain rate, 𝜀-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).
𝑇̃𝑖𝑗
(𝑣)
= 2𝜇(𝑠̃𝑖 𝑗 −
1
3
𝑠̃ 𝑘 𝑘 𝛿̃𝑖𝑗) (9)
Where 𝑠̃ 𝑖 𝑗 is the instantaneous strain rate tensor defined as;
𝑠̃𝑖 𝑗 =
1
2
(
𝜕𝑢̃ 𝑖
𝜕𝑡
+ 𝑢̃𝑗
𝜕𝑢̃ 𝑖
𝜕𝑥 𝑗
) (10)
In the case for incompressible flows, the derivative of density following the fluid material is
zero
𝜕𝑢̃𝑖
𝜕𝑥 𝑗
= 0 (11)

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[
𝜕𝑢̃ 𝑖
𝜕𝑡
+ 𝑢̃𝑗
𝜕𝑢̃𝑖
𝜕𝑥 𝑗
] = −
1
𝜌
𝜕𝜌̃
𝜕𝑥 𝑖
+
𝜕2 𝑢̃𝑖
𝜕𝑥 𝑗 𝜕𝑥 𝑗
(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.
𝑢̃ 𝑖 = 𝑈̅𝑖 + 𝑢𝑖
′
(13)
𝑝̃ = 𝑃̅ + 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.
𝜕𝑈̅ 𝑗
𝜕𝑥 𝑗
= 0 (15)
[
𝜕𝑢̃ 𝑖
𝜕𝑡
+ 𝑈̅𝑗
𝜕𝑈̅𝑖
𝜕𝑥 𝑗
] = −
1
𝜌
𝜕𝑃̅
𝜕𝑥 𝑖
+
𝜕2 𝑈̅ 𝑖
𝜕𝑥 𝑗 𝜕𝑥 𝑗
−
𝜕
𝜕𝑥 𝑗
{𝑢𝑖 𝑢𝑗̅̅̅̅̅} (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), 𝑢𝑖 𝑢𝑗 = 𝑢𝑖 𝑢𝑗(𝑥𝑖, 𝑡) (17)
The term “𝑢𝑖 𝑢𝑗” 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,
𝜕𝑈̅𝑖
𝜕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 〈𝑈̅〉, resolved fluctuation 𝑢′′
, and the modelled turbulent fluctuation 𝑢′
Hence 𝑢̃ = 𝑈̅ + 𝑢′
= 〈𝑈̅〉 + 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;
𝜌𝑢𝑖 𝑢𝑗̅̅̅̅̅ = −𝜇 𝑡 (
𝜕𝑈𝑖
𝜕𝑥 𝑗
+
𝜕𝑈 𝑗
𝜕𝑥 𝑖
) +
2
3
𝜌𝛿𝑖𝑗 𝑘 (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 − 𝜀 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. 𝜀 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
+ 𝑈̅𝑗
𝜕𝑘
𝜕𝑥 𝑗
=
𝜕
𝜕𝑥 𝑗
[(𝑣 +
𝑣 𝑡
𝜎 𝑘
)
𝜕𝑘
𝜕𝑥 𝑗
] + 𝑃𝑘 − 𝜀 (21)
𝜕𝜀
𝜕𝑡
+ 𝑈̅𝑗
𝜕𝜀
𝜕𝑥 𝑗
=
𝜕
𝜕𝑥 𝑗
[(𝑣 +
𝑣 𝑡
𝜎 𝜀
)
𝜕𝜀
𝜕𝑥 𝑗
] + 𝐶𝜀1
𝜀
𝑘
𝑃𝑘 − 𝐶𝜀2𝑓2
𝜀2
𝑘
(22)
Where,
𝑃𝑘 = [𝑣𝑡 (
𝜕𝑈
𝜕𝑥 𝑗
+
𝜕𝑈̅ 𝑗
𝜕𝑥 𝑗
)]
𝜕𝑈̅ 𝑗
𝜕𝑥 𝑗
(23)

14
𝑣𝑡 = 𝐶𝜇 𝑓𝜇
𝑘2
𝜀
(24)
Plus
𝑓𝜇 = [1 − exp (−
𝑛∗
14
)]
2
[1 +
5
𝑅 𝑡
3
4
exp {− (
𝑅 𝑡
200
)
2
}] (25)
𝑓2 = [1 − exp (−
𝑛∗
3.1
)]
2
[1 + 0.3 exp {− (
𝑅 𝑡
6.5
)
2
}] (26)
𝑛∗
=
𝜀
1
4 𝑛
𝑣
3
4
(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
3
2
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
𝐾
1
2
=
𝐾
3
2
𝜀𝐾
1
2
=
𝑘
𝜀
(29)
The wall boundary conditions on this model
𝑈̅ = 𝑉̅ = 𝑘 = 0 (30)
And
𝜀 𝑤𝑎𝑙𝑙 = 2𝑣 𝑘1/𝑛1
2
(31)
Where ‘𝑛1’ is the normal distance between the wall and the closest wall node.
Other recommended 𝑘 − 𝜀 turbulence model
This can be applied is as bellow; (ref: Numerical Simulation of Swirling Flows -Heat Transfer
Enhancement)
The 𝑘 − 𝜀 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.

15
The conservation equations for this model are as follows;
𝜕
𝜕𝑥𝑖
(𝜌𝑘𝑢𝑖) =
𝜕
𝜕𝑥𝑗
(𝛼 𝑘 𝜇 𝑒𝑓𝑓
𝜕𝑘
𝜕𝑥𝑗
) + 𝐺𝑘 − 𝜌𝜀 (32)
𝜕
𝜕𝑥𝑖
(𝜌𝜀𝑢𝑖) =
𝜕
𝜕𝑥𝑗
(𝛼 𝜀 𝜇 𝑒𝑓𝑓
𝜕𝜖
𝜕𝑥𝑗
) + 𝐶𝜀1
𝜀
𝑘
𝐺 𝑘 − 𝐶𝜀2𝑓 𝜌
𝜀2
𝑘
− 𝑅 𝜀 (33)
Where,
𝑅 𝜀 =
𝐶 𝜇 𝜂3 𝜌(1−
𝜂
𝜂 𝑜
)
1+𝛽𝜂3
𝜀2
𝑘
(34)
And
𝜂 = (2𝑆𝑖𝑗 𝑆𝑖𝑗)
0.5 𝑘
𝜀
(35)
Where ‘𝑘’ is the turbulent kinetic energy, ‘𝜀’ is the corresponding dissipation, u is the
averaged velocities and the density, 𝜌.
The term 𝑅 𝜀 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 𝜂 𝑜 = 4.38 𝛽 = 0.012
Table 2: showing the constants in the RNG 𝑘 − 𝜀 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 − 𝜀 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.

20
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

25
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

31
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)

32
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

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