The reaction rates, as exemplified in Equation 4.14, that appear as source terms are computed in ANSYS Fluent, for turbulent flows, by one of three approaches [22]:

The CFD sotware we are using, ANSYS Fluent, can model the mixing and transport of chemical species by solving the conservation equations (4.1 - continuity, 4.10 - species, 4.19 - momentum and 4.27 - energy) that describes convection, diffusion, and reaction sources for each component species.

The reaction rates, as exemplified in Equation 4.14, that appear as source terms are computed in ANSYS Fluent, for turbulent flows, by one of three approaches [22]:

1. Direct use of finite-rate kinetics: The effect of turbulent fluctuations on kinetic rates are neglected and reaction rates are determined by general finite-rate chemistry directly; i.e. there is no turbulence-chemistry interaction;

2. Eddy-Dissipation Model: Reaction rates are assumed to be controlled by the turbulence, ignoring the effect of chemistry timescales, which avoids expensive Arrhenius chemical kinetic calculations. The model is computationally cheap, but, for realistic results, only one or two step heat-release mechanisms should be used. This approach should be used only when the chemistry timescales of interest are known to be fast relative to the turbulence timescales throughout the domain;

3. Eddy-Dissipation-Concept (EDC) model: Detailed chemical kinetics can be incorporated in turbulent flames, considering timescales of both turbulence and kinetics. Ansys Fluent manual notes that detailed chemical kinetic calculations can be computationally expensive.

The generalized finite-rate formulation is suitable for a wide range of applica- tions including laminar or turbulent reaction systems, and combustion systems with premixed, non-premixed, or partially premixed flames [22].

The Eddy-Dissipation Model

Under some combustion conditions, fuels burn quickly and the overall rate of reaction is controlled by turbulent mixing. In certain premixed flames, the turbulence slowly convects/mixes cold reactants and hot products into the reaction zones, where reac- tion occurs rapidly. In such cases, one approximation is to assume the combustion is mixing-limited, allowing neglect of the complex chemical kinetic rates and instead assuming instantaneous burn upon mixing [23].

In the equations of the Eddy-Dissipation model, the chemical reaction rate is

governed by the large-eddy mixing time scale, ^k / _ , as in the eddy-breakup model

of Spalding [52] (p. 1020). Combustion proceeds whenever turbulence is present

( ^k /  > 0), and an ignition source is not required to initiate combustion. This is usually acceptable for non-premixed flames, but in premixed flames, the reactants will burn as soon as they enter the computational domain, upstream of the flame stabilizer. To remedy this, ANSYS Fluent provides the finite-rate/eddy-dissipation model, where both the finite-rate model reaction rates, and eddy-dissipation model rates are calculated. The net reaction rate is taken as the minimum of these two rates. In practice, the finite-rate kinetics acts as a kinetic “switch”, preventing reaction before the flame holder. Once the flame is ignited, the eddy-dissipation rate is generally smaller than the Arrhenius rate, and reactions are mixing-limited [23].

We presume that the large-eddy mixing time scale governs the reaction rate in the flame zone, but due to the presence of the pre-mixing duct wherein fuel and air mixes before the flame is stabilized, the model that is recognized as the most suitable for the reactive simulations of the entire flow domain of this combustor is the finite-rate/eddy-dissipation model.

The justification for a two-step methane air mechanism in the simulations Although ANSYS Fluent allows multi-step reaction mechanisms (number of reac- tions > 2) with the eddy-dissipation and finite-rate/eddy-dissipation models, these will likely produce incorrect solutions. The reason is that multi-step chemical mech- anisms are typically based on Arrhenius rates, which differ for each reaction. In the eddy-dissipation model, every reaction has the same, turbulent rate, and there- fore the model should be used only for one-step (reactant → product), or two-step (reactant → intermediate, intermediate → product) global reactions. The model cannot predict kinetically controlled species such as radicals. To incorporate multi- step chemical kinetic mechanisms in turbulent flows it would be necessary to use the Eddy-Dissipation-Concept (EDC) Model [23].

This justifies our choice for a two-step methane-air combustion mechanism, de- tailed in Section 7.4.1.

7.2 Mesh criteria

The non-structured mesh criteria adopted in all combustor models (1 to 61) are:

• Quality: Target Skewness: 0.8;

• Match control: Combustion Chamber, Annulus and Liner periodicity;

• Inflation (aimed at y

= 40 at various Boundary Layers, each viscous layer is based

on local parameters):

– Maximum Layers: 5

7.2.1 Mesh sensitivity

Initially, for the non reactive simulations, where the main objective was to attain the desired flow partitioning between dilution, cooling and primary air, despite the combustor geometry varied considerably, the previous mesh criteria were maintained for all the simulations from 1 to 19, except from minimal considerations regarding the inflation layers which were consistently based on local parameters.

During the reactive design phase, ranging from combustor models 20 to 61, the same mesh criteria described above were utilized. However, since the main geometric parameters (diameters and lengths) did not vary substantially and it was desirable to determine the mesh fineness that could yield reliable yet not too time consum- ing calculations, a reasonable mesh sensitivity was devised for combustor model 20 where global results such as average temperature and mass flow rate at outlet were compared for three different mesh sizes. No significant differences were observed in the average temperature nor the mass flow rate at outlet, for the three cases whose total cells count were approximately 13, 23 and 30 million cells. However calcula- tion time for the 30 million cell combustor was considered relatively high; the best compromise being the mesh setup that results in 23 million cells, yielding reasonable computational time and consistent results.

It is noted that, the first layer thicknesses (in mm) for models 20 to 61, respecting y

= 40 at various Boundary Layers were:

• Combustor casing adiabatic: 0.28

• Injector casing adiabatic and Injector air side: 0.11

• Liner air side: 0.27

• Liner gas side and dome: 0.31 (Growth rate: 1.15)

• Injector fuel side and Injector fuel side adiabatic: 0.17

• Injector air intakes and cooling holes: 0.18

• Dilution holes: 0.07

• Injector skirt adiabatic: 0.2

A second combustor mesh sensitivity was tackled in the occasion of simulation of combustor model 53, where it was observed that further refinement in the grid was only necessary in regions where the total temperature gradient exceeded 10% of maximum gradient in order to better simulate conjugate heat transfer through liner walls, for further details on this analysis please read Section 7.4.2.

7.3 Steady flow non-reactive multi-species simulations

7.3.1 Attaining the desired flow rate partition

In order to study if cooling air films are actually eliminating eventual hot spots zones, if dilution jets are able to mix the burned gases so that pattern factor at outlet is as minimum as possible and allow for the desired air flow rate in the injectors such that the desired equivalence ratio (0.5) is attained, the flow rate dedicated to each of these zones initially must respect the preliminary design (Table 6.10).

Table 7.1 shows the results from this first refinement phase of the preliminary design (refer to Section 6.10 and Appendix B) and how they were reached.

The modifications applied on the reference designs leading to the current designs marked by an identification number in Table 7.1 are listed below, they represent all the trials undertaken to reach the flow rate targets in this first refinement phase:

1. All passage diameters were increased by an arbitrary factor of 1.2;

2. Injector distribution plate has been removed;

3. A third row of injector intake holes has been provided between the two existing rows;

4. Injector has been shortened by a factor equal to 0.75;

5. Injector annular channel width has been increased by a factor of 1.5;

6. Injector annular channel width has been increased by a factor of 2;

7. Injector axis has been shifted towards the liner dome, in a position that cor-

responds to the middle of the presumed primary zone, i.e. the zone comprised

between the dome extremity and the exit of first liner cooling splash ring. In

previous designs such axis was a located slightly forwards. It is intended that

by doing so, air intake from the back portion of the injector is facilitated;

Table 7.1: Flow rate partitioning (in kg/s) - first refinement phase of preliminary design for 1500 kW MGT combustor. In parenthesis the % contribution of total air.

Design

identification # Reference design #

Primary air and

fuel Cooling Dilution Total

outlet Preliminary

design

(target) 4.891 (64.2) 1.29 (16.9) 1.44 (18.9) 7.621

1 Preliminary

design 0.582 (12.8) 1.000 (21.9) 2.974 (65.3) 4.556

2 1 0.768 (16.3) 0.970 (20.6) 2.979 (63.2) 4.716

3 2 0.767 (16.3) 0.968 (20.6) 2.973 (63.2) 4.707

4 2 0.793 (16.7) 0.967 (20.4) 2.978 (62.8) 4.738

5 4 0.843 (17.6) 0.968 (20.2) 2.986 (62.2) 4.797

6 4 0.863 (17.9) 0.967 (20.0) 2.995 (62.1) 4.825

7 6 0.870 (18.0) 0.967 (20.0) 2.995 (62.0) 4.832

8 7 0.878 (18.1) 0.980 (20.2) 2.988 (61.7) 4.846

9 8 0.887 (18.3) 0.969 (19.9) 3.000 (61.8) 4.856

10 8 0.897 (18.4) 0.973 (20.0) 3.002 (61.6) 4.873

11 10 0.905 (18.5) 0.981 (20.1) 3.005 (61.4) 4.891

12 11 0.907 (18.5) 0.979 (20.0) 3.019 (61.6) 4.905

13 12 0.906 (18.5) 0.979 (20.0) 3.018 (61.6) 4.903

14 12 1.860 (32.0) 0.957 (16.5) 2.993 (51.5) 5.810

15 14 2.588 (39.9) 0.941 (14.5) 2.957 (45.6) 6.486

16 15 3.455 (47.2) 0.926 (12.7) 2.932 (40.1) 7.313

17 16 4.641 (55.5) 0.865 (10.4) 2.851 (34.1) 8.357

18 17 5.037 (65.5) 1.109 (14.4) 1.547 (20.1) 7.693

19 18 5.070 (64.4) 1.331 (16.9) 1.475 (18.7) 7.876

8. The injector external back plate has been approximated to the first intake holes in order to minimize flow dead zones in the injector annulus. In addition the first and second intake holes rows were staggered circumstantially with respect to injector axis in order to facilitate penetration of air in both rows;

9. The combustor annulus widths have been modified: before the injector the width has been increased by a factor of 10% while after the injector the width has been decreased by a factor of 10%. By doing this, the pressure upstream the injector increases and thus more air flows through the annulus of the injectors, while the pressure downstream the injectors decreases and thus less air would enter dilution and cooling holes in the inner liner of the combustor. This approach would require a decrease in dilution and cooling holes diameter in the outer liner and, probably also a slight increase in cooling holes diameter in the inner liner; the dilution air need to be reduced and therefore the dilution holes in the inner liner will not be increase. These modifications are to be done next;

10. The combustor annulus widths have been modified: before the injector the width has been increased by a factor of 20% while after the injector the width has been decreased by a factor of 20%. By doing this, the pressure upstream the injector increases and thus more air flows through the annulus of the injectors, while the pressure downstream the injectors decreases and thus less air would enter dilution and cooling holes in the inner liner of the combustor. This approach would require a decrease in dilution and cooling holes diameter in the outer liner and, probably also a slight increase in cooling holes diameter in the inner liner; the dilution air need to be reduced and therefore the dilution holes in the inner liner will not be increase. These modifications are to be done next;

11. The annulus width before the injectors has been increased by a factor of 25%;

12. The second row of air intake holes of the injector has been approximated to the injector tip by a factor of 25%;

13. Provision for a baffle in the annulus downstream the injector; the objective is to favor air intake through the aft-most part of the injector;

14. The injector has been scaled up by a factor 1.5; the primary air zone has been lengthened 20 mm to accommodate the larger injector;

15. The injector has been scaled up by a factor 1.2; the primary air zone has been

lengthened 20 mm to accommodate the larger injector;

in a plane close to the dome and four in a plane located downstream;

17. The injectors have been scaled up by a factor 1.2;

18. All three typologies of flow passages were scaled up or down in order to attain the desired flow rate; the injectors were scaled up by a factor of 1.0266; the cooling holes were scaled up by a factor of 1.22 and the dilution holes were scaled down by a factor of 0.71;

19. The dilution row close to the outlet has been moved upstream to eliminate recirculation, and thus backflow, close to the outlet. In addition, all three typologies of flow passages were scaled up or down in order to attain the desired flow rate; the injectors were scaled down by a factor of 0.985; the cooling holes were scaled up by a factor of 1.078 and the dilution holes were scaled down by a factor of 0.965. The simulation has been carried out with limited production term in the turbulence equation, because simulation was unstable.

The injector used in all designs simulated is not axially mounted and located at the dome as Appendix B may suggest, instead we adopted a tangentially (with respect to the inner liner) mounted injector located close to the dome. Such typology is adopted by the industry as can be seen after reading Patent [35]. Apparently the advantage of such typology is the small amount of injectors required (six as indicated in Article [8] or three as indicated in the Patent [35]) if compared to axially mounted injectors (recall that Appendix B suggested the utilization of eighteen injectors), that’s due to the larger available space at the casing of the combustor.

Designs 1 to 13 all use three tangential injectors, however do to the necessity of allowing for more primary air designs 14 to 19 present six tangential injectors.

Referring the later combustors, similarly to Reference [8] two of the injectors are located in proximity of the combustor dome and would operate at all conditions and the four remaining are located in a downstream plane and would operate at design power and not at start up or at partial loads, where only the upstream injectors operate. This configuration would allow for a future load partialization study. Design 19 tri-dimensional model is presented in Figure 7.3.1, the quoted drawing is of little interest at this stage since the design is to be further refined, specifically with respect to the injector passages and internal features.

Interesting to note the absolute velocity scalar flow field in the meridian plane

(Figure 7.2) and in two injectors plane (upstream and downstream, relative to the

dome) of combustor 19 (Figures 7.3 and 7.4), which indicate that the injector accel-

(a) Isometric view showing the filleted in- jector dome

(b) Front view showing injectors’ tangen- tial mounting

(c) Detail view of injector pre-mixing

tube (to be modified for dual-fuel usage) (d) Cross-sectional view of upstream in- jector’s plane

(e) Cross-sectional view of meridional plane

(f) Generic detail view indicating injec- tors (upstream and downstream), cooling passages and dilution holes

Figure 7.1: Half combustor views for the 1500 kW MGT, model 19, prior to injector

design refinement

circumferential neighboring injector. They refer to a non-reactive simulation.

Figure 7.2: Absolute velocity scalar field in meridian plane of combustor 19 (non- reactive)

Figure 7.3: Absolute velocity scalar field in the injector planes of combustor 19 (non-reactive) - Upstream plane

Also note the CH 4 mole fraction scalar field at the injectors plane (Figures 7.5

and 7.6).

Figure 7.4: Absolute velocity scalar field in the injector planes of combustor 19 (non-reactive) - Downstream plane

Figure 7.5: Methane (CH 4 ) mole-fraction scalar field in the injector planes of com-

bustor 19 (non-reactive) - Upstream plane

Figure 7.6: Methane (CH 4 ) mole-fraction scalar field in the injector planes of com- bustor 19 (non-reactive) - Downstream plane

Further quantitative analysis of injectors from combustor design 19 It’s opportune to verify some data resulted from the flow field generated by the injectors present on combustor model 19. We are interested at knowing some values at their outlet, in particular: the average velocity magnitude (V avg ), the mass flow rate ( ˙m), the average equivalence ratio (¯Φ) and the standard deviation of the equivalence ratio (σ Φ ) which we consider as the mixing performance indicator ¹ .

These data are obtained in CFD post-processing phase. The averages refer to mass-weighted averages. Recall from Section A.3 that the air-to fuel ratio (AFR) and the equivalence ratio are relate by the definition:

Φ = AF R _st

AF R (7.1)

Recall yet that for our global equation, the stoichiometric air-to-fuel ratio for natural gas results AF R st,N G = 16.80.

Each cell in the injector outlet may present an actual AFR that can be calculated by:

AF R = ˙m air

˙m f (7.2)

1

The sample space in this case is the set of cells in the downstream or upstream injectors outlet.

Table 7.2: Quantitative results obtained for each injector of combustor model 19

Injector

id. V _avg (m/s) ˙m (kg/s) ¯Φ σ _Φ

US 54.93 0.875 0.457 0.131

DS 51.79 0.820 0.488 0.099

which, for each cell at injector outlet in any single moment is simply the ratio of mass of air to the mass of fuel

AF R = m _air

m _f (7.3)

or, in a mole basis,

AF R = χ _air M W _air

χ f M W f (7.4)

The molecular weights are known based on the composition (see Section A.1):

M W air = 28.840g/mol and MW f,N G = 16.18g/mol. The fuel mole fraction (χ f ) can be determined by knowing the actual mole fraction of methane (χ ⁰ CH

) at injector outlet, which is obtained in CFD post-processing phase, the mole fraction of methane in the fuel (χ CH

), which is imposed as boundary condition at fuel inlet (see Table 6.3), and knowledge that no methane is present in the air, such that

χ _CH

χ f = χ ⁰ CH

(7.5)

The air mole fraction is given by

χ _air = 1 − χ f (7.6)

Table 7.2 presents the quantitative results obtained for each of two upstream (US) and four downstream injectors (DS) of combustor model 19.

Note that the equivalence ratio is close to the target — Φ = 0.5 — however the relatively high σ Φ indicate poor mixing performance; it is intended that it should remain as low as σ Φ = 0.02. Next section will be dedicated to the evaluation of mixing performance and comparison among different injectors concept with reactive CFD simulations.

In order to give insights on the direction of injector optimization, it is interest-

ing to show the equivalence ratio distribution simulated at the upstream (US) and

(a) Upstream injector

(b) Downstream injector 1 (c) Downstream injector 2

Figure 7.7: Equivalence ratio distribution simulated at the upstream (US) and down- stream injectors (DS 1 and DS 2 ) of combustor model 19.

downstream injectors (DS 1 and DS 2 ) of combustor model 19 (Figure 7.7). These images show that fuel tend to concentrate at one side of the injector outlet.

7.4 Steady flow reactive simulations

In the following reactive simulations we are going to adopt the 2 Step Methane- Air Mechanism for the reaction of Natural Gas with air described bellow. The justification for this simplified mechanism involves some considerations regarding the Eddy-Dissipation Model 7.1.2.

7.4.1 The 2 Step Methane-Air Mechanism

First reaction is

CH 4 + 3 2 O 2

k

−−→ CO + 2 H 2 O (7.7)

for which the reaction rate determining the rate methane is consumed is

ν ₁ = − d [CH 4 ]

dt = k 1 [CH 4 ] ^0.7 [O 2 ] ^0.8 (7.8) the respective reaction rate coefficient is given by the following Arrhenius law:

k ₁ = 5.012 · 10 ¹¹ e ⁽

^/

⁾ (7.9) The second reaction is

CO + 1 2 O 2

k

−−→ CO 2 (7.10)

for which the reaction rate determining the rate carbon monoxide is oxidized is given by

ν ₂ = − d [CO]

dt = k 2 [CO][O 2 ] ^0.25 (7.11) the respective reaction rate coefficient is given by

k ₂ = 2.239 · 10 ¹² e ⁽

^/

⁾ (7.12) Note that from the pre-exponential factor that reaction 1 is the slowest step, and therefore its reaction rate may be used as an indicator of flame locus, together with low methane mass fraction (we may consider 0.005) since in a premixed flame the concentration of the fuel passes from its mixture value before the thin flame region to theoretically zero in the post flame zone ² .

Note also that under certain conditions (contact with cold flow coming from film cooling, or dilution jets) if the flame is still present it may be partially quenched.

This may affect the CH 4 and CO consumption rates (Equations (7.8) and (7.11)) and cause increased emissions. The other type of emmisions are nitrogen oxides emissions, in particular NO emission, the mechanisms are rather complex and are discussed in Chapter 5.

2

The eddy-dissipation model requires products to initiate reaction. When the solution for steady

flows is initialized, ANSYS Fluent sets all species mass fractions to a maximum in the user-specified

initial value and 0.01. This is usually sufficient to start the reaction. However, if a mixing solution

is firstly converged, which is the case in this thesis, where all product mass fractions are zero, it is

necessary to patch products into the reaction zone to ignite the flame.

For each model from 20 to 61, Table 7.3 presents the geometric modifications adopted (based on a reference model). The full data set of quantitative results generated during this phase is given in various tables of Appendix D).

Below we describe the resulting main flow characteristics and the main quantita- tive results that have raised our attention. Some designs have presented more than one beneficial feature, these are called milestone designs and correspond to models 28, 34, 38, and 53.

Table 7.3: Geometric modifications that leads (marked with an asterisk) to the final combustor design. In parenthesis, the base models are reported. Legend: BAC:

Better Accomodate Flame; MFMG: Modify Flame Main Geometry; IC: Improve Cooling; IPM: Improve Pre-Mixing; FCA: Facilitate Conjugate Analysis; ID: Improve Dilution; TB: Test Biogas.

target Main Model

Id. Description

BAF * 20 (19) Modification of injector axis angle, from inner liner tan- gency to liner mean diameter tangency

“ 21 (20) Using three injectors upstream, three downstream

“ 22 (21) Tilting injectors axes forward 15 ^◦

“ * 23 (20) Injector planes approximated

“ 24 (23) Injectors tilted inwards 10 ^◦

“ * 25 (23) Injectors tilted inwards 5 ^◦

“ * 26 (25) Upstream injector tilted inwards further 5 ^◦

“ * 27 (26) Annulus and liner heights increased

“ * 28 (27) Using three injectors upstream, three downstream ³

“ 29 (27) Using two injectos upstream, two downstream MFMG 30 (29) Increased air intake holes

“ 31 (28) Reduced injector outlet area

IC 32 (28) Addition of 8 splash rings in primary zone

“ 33 (32) Reduction of cooling holes’ diameter MFMG * 34 (28) Removal of injectors tip ⁴

IPM 35 (34) Removal of bottom injector intake row and using rect- angular air intake passages in the top row

3

Milestone: Better flame distribution with three injectors upstream, three downstream.

4

Milestone design: Reduces flow obstruction and may increase injector safety while reducing

flashback risk.

target Main Model

Id. Description

“ 36 (34) Using rectangular air intake passages in the injector

“ * 37 (34) Reduced injector outlet area (increased convergent)

“ * 38 (37) Provision for injector housing skirts ⁵

“ * 39 (38) Provision for a third air intake row in the injectors BAF * 40 (39) All primary air flow passages scaled down

MFMG 41 (40) Intake rows shifted upwards; increased injector housing area; provision for a pre-mixing duct skirt

IPM 42 (40) Intake rows shifted upwards; increased injector housing

“ 43 (40) Intake rows shifted upwards area

“ 44 (40) Increased injector housing area

“ 45 (40) Lengthened injector

“ 46 (43) Doubled fuel inlets, same fuel inlet overall area

“ 47 (43) Doubled fuel inlets, doubled fuel inlet overall area IC * 48 (40) All primary air flow passages scaled down with cooled

primary zone

“ 49 (43) “

“ * 50 (48) Four additional splash rings in outer liner in primary zone and reduction of cooling passages

BAF 51 (50) Injector axis tangent to liner mean diameter FCA 52 (50) Increased liner thickness

IC * 53 (50) First conjugate heat transfer analysis ⁶

“ 54 (53) Trial of direct cooling the dome

“ 55 (53) “

“ 56 (53) “

“ * 57 (53) End portion of the liner enclosed by annulus & radial inlet

ID * 58 (57) Removal of last dilution row in the inner liner

IC * 59 (58) Cooled end portion of the inner liner, last Natural Gas simulation

TB * 60 (59) Enlarged fuel inlet holes, first Biogas simulation

“ 61 (59) Doubled fuel inlet holes, second Biogas simulation

5

Milestone: Improves pre-mixing, reduces combustor total pressure loss.

6

Milestone: Improves cooling simulation.

Calculation of actual equivalence ratio in the combustor, either for nat- ural gas or biogas Section A.3 describes well the determination of the stoichio- metric air-to-fuel ratio (AF R st ) either for biogas AF R st = 6.05 and for natural gas AF R _st = 16.80 based on fuel composition and the global reaction. This was part of the calculation in the preliminary design phase that aimed at the determination of the combustion air fraction (α) necessary for the initial simulations where the equivalence ratio was pre-determined to be 0.5.

For a proper understanding of the pre-mixing performance during non-reactive or reactive flows in the combustor, the actual equivalence ratio must be determined in every point in the domain.

For this scope, recall the definition of the equivalence ratio Φ = AF R _st

AF R (7.13)

where the air-to-fuel ratio is given by

AF R = χ _air M W _air

χ _f M W _f (7.14)

Since we may find χ CH

= 0.9902 in a cell with solely natural gas and no air and χ CH

= 0.6 in a cell with solely biogas and no air, the actual mole fraction of methane χ ⁰ _CH

resulting from a simulation can be used to determine the fuel mole fraction in the cell by

χ _f = χ ⁰ _CH

χ _CH

(7.15)

finally, noting that

χ _air = 1 − χ f (7.16)

we substitute Equations (7.14), (7.15) and (7.16) into Equation (7.13) to obtain Φ = χ ⁰ _CH

4

χ _CH

− χ ⁰ _CH

· M W _f

M W _air · AF R _st (7.17)

it results that

Φ ng = 9.4252 ^ χ ⁰ _CH

0.9902 − χ ⁰ _CH

 (7.18)

Table 7.4: Flow rate partitioning (in kg/s) - combustor model 20. In parenthesis the

% contribution of total air.

Design

identification Reference design

Primary air and

fuel Cooling Dilution Total

outlet Preliminary

design

(target) 4.891 (64.2) 1.29 (16.9) 1.44 (18.9) 7.621

20 19 4.928 (63.7) 1.356 (17.5) 1.456 (18.8) 7.739

gives the equivalence ratio for natural gas simulation and Φ biogas = 5.7123 ^ χ ⁰ _CH

0.6 − χ ⁰ _CH

 (7.19)

gives the equivalence ratio for biogas simulations (models 60 and 61).

Model 20 - Modification of injector axis angle, from inner liner tangency to liner mean diameter tangency. Based on model 19

Observing the flow in the primary zone of combustor model 19 (Figures 7.3 and 7.4), it’s possible to note that the injectors outlet flow impinges on the surface of the inner liner before mixing with the flow from the neighboring injector and flowing downstream; that’s because the injector axis of model 19 is tangent to the inner liner (Figure 7.8).

In order to promote the mixing of hot gases (after the flame has been stabilized) from one injector with its neighboring injector outflow and also to reduce viscous losses and hot spots created when flow swipes the inner liner it’s a good practice to move the injector axis outwards; making it tangent to the mean liner diameter it’s a better option, such modification is illustrated in Figure 7.9) and defines the combustor model 20.

Results. Mass flow rate partitioning and equivalence ratio at injectors

outlet. The mass flow rate partitioning and equivalence ratio at injectors outlet of

combustor 20 are indicated in Tables 7.4 and 7.5.

Figure 7.8: Injector axis configuration in combustor model 19: inner liner tangent.

(Note: circumferential angle between injectors is 45 ^◦ )

Table 7.5: Quantitative results obtained for each injector of combustor model 20

Injector

id. V _avg (m/s) ˙m (kg/s) ¯Φ σ _Φ

US 53.00 0.821 0.492 0.139

DS 52.04 0.818 0.495 0.111

Figure 7.9: Injector axis configuration in combustor model 20: mean liner diameter tangent. (Note: circumferential angle between injectors is still 45 ^◦ )

Conclusions about model 20 Despite the modification of injector axis orienta- tion, a reactive flow could not sustain itself in the combustor 20 ⁷ . The reasons are yet unclear, however the outlet flow from each injector is essentially axial (with re- spect to the injector), the velocity is about 50 m/s which if compared to a turbulent pre-mixed natural gas flame speed is clearly high, this may denote that the flame might have been extinguished due to blow off (see Section 4.5.1).

In addition, the hypothesis that the jet coming out from an injector would be able to heat the jet from its neighbor injector and thus sustain its flame are yet to be verified.

Figures 7.10 and 7.11 define the planes of interest for this model.

The planes indicated in Figure 7.10 are labeled α i with the subscript denoting

7

In CFD the ignition of a combustible - air mixture can be done by patching specific regions

(usually spheres) of the flow domain in proximity of the injectors outlet such that a certain temper-

ature be assigned to the corresponding cells; usually this temperature is well above the adiabatic

flame temperature (which is related to the actual ignition energy), the patches is this thesis are of

3000 K.

Figure 7.10: Meridian planes (six) of interest in the full combustor aimed to analyze

recirculation and other features (frontal view), model 20

Figure 7.11: Ortogonal planes (seven) of interest in the full combustor aimed to

analyze recirculation and other features (half-sectional view at plane α 6 ), model 20

injector outlet while α 6 is the furthest. By doing so, one can observe how the outlet flow from the injectors develop downstream. Also of note is that α 1 and α 2 intersect the first dilution rows while α 4 and α 5 intersect the second dilution rows; the flow field on these planes may indicate the influence of dilution jets on the injector’s outflow.

The planes indicated in Figure 7.11 are labeled β i with the subscript denoting the relative position to the combustor dome; β 1 and β 3 are the US and DS injector planes, β 2 is the plane in between them. In addition, β 4 , β 5 , β 6 and β 7 correspond to the combustion chamber control sections (1), (2.1), (2.2) and (2.3) respectively, as indicated in Appendix B. Recall that control section (1) marks the end of the presumed primary zone, that control sections (2.1) and (2.2) are in correspondence to the first and second dilution rows respectively and control section (2.3) is located where the liner has its lowest width. Also note that the primary zone has been lengthened to accommodate a second row of injectors.

Figures 7.12 and 7.13 show the plane projected velocity vectors resulted from a CFD simulation of combustor model 20 in absence of reactions in planes α 6 and β ₁ . Note that in the ortogonal plane only the radial and tangential components of velocity are represented while in the meridian plane only the radial and axial components are shown. The figures give an idea of how the injector jets whose velocity is predominantly tangential conform themselves and recirculate due to an eventual partial blockage from dilution jets prior to entering the actual dilution zone, where the bulk of reactions have already taken place and the flow simply mixes with fresh air from the compressor before exiting to the turbine.

Observe also that actual fuel velocity at nozzle resulted about 195 m/s, i.e. M ≈ 0.35, the range of velocities in the figures has been reduced from 0 to 70 m/s for easy of flow visualization inside the combustion chamber where the maximum velocity magnitude is bellow 70 m/s.

It is interesting to show the contour plots of velocity magnitude in planes β 5

(Figure 7.14) and β 6 (Figure 7.15) because indicate not only the dilution jets pene- tration but also that the flow momentum in tangential direction is sufficiently large to deflect the dilution jets.

Model 21 - Using three injectors upstream, three downstream. Based on model 20

Injectors plane were approximated and three injectors are located upstream, other

three downstream (Figure 7.23)

Figure 7.12: Meridian plane α 6 projected velocity vectors in combustor model 20, non-reactive flow

Results. Mass flow rate partitioning and equivalence ratio at injectors outlet. The mass flow rate partitioning and equivalence ratio at injectors outlet of combustor 21 are indicated in Tables 7.6 and 7.7.

Model 22 - Tilting injectors axes forward 15 ^◦ . Based on model 21

Results. Mass flow rate partitioning and equivalence ratio at injectors

outlet. The mass flow rate partitioning and equivalence ratio at injectors outlet of

combustor 22 whose injectors axes were tilted forward 15 ^◦ are indicated in Tables

7.8 and 7.9.

Figure 7.13: Ortogonal plane β 1 (US injector plane) projected velocity vectors in combustor model 20, non-reactive flow

Table 7.6: Flow rate partitioning (in kg/s) - combustor model 21. In parenthesis the

% contribution of total air.

Design

identification Reference design

Primary air and

fuel Cooling Dilution Total

outlet Preliminary

design

(target) 4.891 (64.2) 1.29 (16.9) 1.44 (18.9) 7.621

21 20 4.832 (63.9) 1.333 (17.6) 1.398 (18.5) 7.564

Figure 7.14: Contour plot of velocity magnitude in plane β 5 of model 20

Table 7.7: Quantitative results obtained for each injector of combustor model 21

Injector

id. V _avg (m/s) ˙m (kg/s) ¯Φ σ _Φ

US 53.21 0.815 0.488 0.128

DS 50.12 0.793 0.523 0.073

Figure 7.15: Contour plot of velocity magnitude in plane β 6 of model 20

Table 7.8: Flow rate partitioning (in kg/s) - combustor model 22. In parenthesis the % contribution of total air.

Design

identification Reference design

Primary air and

fuel Cooling Dilution Total

outlet Preliminary

design

(target) 4.891 (64.2) 1.29 (16.9) 1.44 (18.9) 7.621

22 21 5.085 (64.5) 1.347 (17.1) 1.446 (18.4) 7.878

Figure 7.16: Meridian plane position relative to the combustors that have three injectors upstream and three injectors downstream (models: 21, 22, 28 onwards)

Table 7.9: Quantitative results obtained for each injector of combustor model 22

Injector

id. V _avg (m/s) ˙m (kg/s) ¯Φ σ _Φ

US 53.09 0.842 0.482 0.076

DS 53.28 0.854 0.474 0.166

Model 23 refers to model 20, therefore, it has two injectors upstream and four down- stream. The injectors plane in this case were approximated. This modification is due to a longer flame upstream if compared to the flame downstream. As with the model 20, the number of injectors upstream is two while four injectors are located downstream. The orthogonal planes positions are the same of 21. The NO forma- tion model assumes the temperature and species fluctuations due to turbulence to be modeled by a BETA distribution; with the absence of OH radicals in this sim- ulation. In this simulation we have raised a concern about how the NO-formation model considers the temperature and species fluctuates due to turbulence. There are two possible Probability Distribution Functions that can be used to describe the variability, beta and normal. We have also tested the relevance of the third equation in the extended Zeldovich reaction mechanism for thermal-NO formation by choos- ing or not to consider the OH radical formation, the third equation considers the formation of OH (see Chapter 5 for details.)

Modification in boundary conditions - model 23.1 Same as c23 but with outlet flow rate resulting 6.21% lower.Fuel flow rate was reduced to 0.1186 kg/s (the previous value was 0.141 kg/s).

Modification in boundary conditions - model 23.2 The model 23.2 is the same as 23.1 but during the NO-formation simulation, the temperature and species fluctuations due to turbulence were modeled using a NORMAL distribution with the absence of OH radicals.

Modification in boundary conditions - model 23.3 Same as model 23.1 but with the NO formation modeled using a BETA distribution with the presence of OH radicals.

Modification in boundary conditions - model 23.4 Same as model 23.1 but with the NO formation modeled with the NORMAL distribution and presence of OH radicals.

Modification in boundary conditions - model 23.5 Same as model 23 but with Fuel flow rate was reduced to 0.1078 kg/s as a consequence the outlet flow rate reduced 25.3%.

For the results concerning the NO-formation, please refer to the Table D.3.

Model 24 - Injectors tilted inwards 10 ^◦ . Based on model 23

Referring to model 23.5, the reaction rate scalar field on plane β 2 allows us to see that the flame of Model 23.5, despite showing that the combustion chamber should be increased to sustain the target flow rate (air and fuel) and hence the power output, shows that the flame would be better distributed in the liner if the injector axis were tilted inwards about 10 ^◦ ; this configures the modification presented by model 24. In addition, this modification reduces the obstruction that the injectors cause inside the liner, thus reducing stagnation of reactive flow coming from neighboring injectors and therefore the concentration of reaction rate and temperature, but also it could aid in the process of reduce the flame extension that in model 23.5 extends downstream in a spiral (meridian plane α 2 shows that there is still reaction near the combustor outlet). Notably this spiral flame is induced considerably more by the downstream injectors whose flow are intensified by the upstream injectors.

Model 25 - Injectors tilted inwards 5 ^◦ . Based on model 23

With respect to the design 23.5, there was still a considerable amount of methane further downstream on combustor model 25. The tilt of 10 degrees of downstream injectors caused a slight reduction in flow impingement behind the outlet tip of injector tubes, however the flame was shown to squeeze against the inner liner causing excessive reaction in the proximity of where the flow contacts the liner, this could also compromise the liner durability. Therefore, the tilt angle for downstream injectors was changed from 10 to 5 degrees in order to reduce reaction concentration either where flow impinges in the successive injector tube tip or against the liner. Upstream injectors tilt showed a detrimental effect with respect to the case where the axis was tangent to the liner mean diameter, so their tilt was completely removed. Also, since a considerable amount of methane and reaction were still present further downstream both injector planes were moved 25 mm towards the dome occupying a region that was dominated by recirculation zones of low intensity.

Model 26 - Upstream injector tilted inwards further 5 ^◦ . Based on model 25

Upstream injector angle was tilted further 5 degrees inwards in order to reduce flame concentration in outer liner as shown in plane β 1 of model 25 (Figure 7.17).

Results In the reactive simulation, results show good overall improvements on

flame configuration (reaction rate at plane β 1 , Figure 7.18), it does not touch anymore

Figure 7.17: Reaction rate at plane β 1 of model 25

the outer liner but now it touches slightly the inner liner. However, now, plane β 4

indicates that there is still reaction from downstream injectors (Figure 7.19).

Model 27 - Annulus and liner heights increased. Based on model 26 With respect to its reference model (26), the model 27 differs in that its flame tube and annulus passages had their area increased 40% in order to better accommodate the flame which in the previous cases touched either the outer liner (model 25) or the inner liner (model 26). The liner axial velocity to annulus axial velocity ratio is kept unchanged so that to not interfere with dilution jets penetration.

Results suggest that indeed the increased dimensions favor flame development;

the reduced axial velocity in the liner could present a problem since the flame could

touch the tip of the neighboring injector (the tangential velocity of injector outflow

Figure 7.18: Reaction rate at plane β 1 of model 26

is kept substantially unchanged given that the pressure drop and flow passages are all the same).

In addition, comparing to model 26, reaction rate in plane α 3 indicates that flame is not squeezed against inner liner anymore and is more centered (Figures 7.20 and 7.21).

Regarding the temperature, its global maximum has decreased substantially from 1933 K to 1780 K thanks to a reduced equivalence ratio (0.50 versus 0.55 in the previous case, model 26).The temperature field in the meridian planes show that the dome is occupied by a thermal gradient which justifies the decision to keep its shape.

The penetration of dilution jets, evident in temperature profiles of planes β 4 and β ₅ (Figure 7.4.2), are substantially the same as in the previous case, indicating that indeed, the liner axial velocity to annulus axial velocity ratio has been maintained.

Next modifications aim still at eliminating flame contact of one injector to its

Figure 7.19: Reaction rate at plane β 4 of model 26

neighboring injector tip, such that model 28 will present three injectors up- stream and three downstream . In alternative, model 29 will present two injec- tors upstream and two downstream with an addition of a third intake row inside each injector to compensate the reduced number of injectors and increased fuel inlet passages to allow for same Mach number of fuel jet.

Model 28 - Using three injectors upstream, three downstream. Based on model 27

This is a milestone design, it promoted better flame distribution. It is based on

model 27, in comparison to which, this model presents three injectors upstream and

three injectors downstream. The objective is to distribute the flames more evenly

and avoid that the flame of downstream injectors touch the tip of their neighbors as

happened in model 27. The meridian plane position relative to the combustors that

have this three injectors upstream and three injectors downstream is represented in

Figure 7.23.

Figure 7.20: Reaction rate at plane α 3 of model 26

Figure 7.21: Reaction rate at plane α 3 of model 27

(a) Total temperature at β 4 , model 26 (b) Total temperature at β 5 , model 26

(c) Total temperature at β 4 , model 27 (d) Total temperature at β 5 , model 27 Figure 7.22: Total temperature fields at orthogonal planes β 4 and β 5 of models 26 and 27 for penetration of dilution jets comparison

Results Compare Figures 7.24 and 7.25 and note that the problem of the flame touching the neighbor injector tip has been resolved. The next modifications may change flame configuration and this issue may be readdressed.

Modification in boundary conditions - model 28.1 Same as model 28 (reac- tive case), buth with reduced fuel flow rate to 0.1029 kg/s in order to have equivalence ratio equal to 0.5 given the combustion air remains 3.457kg/s. This measure was taken in order to reduce the average outlet temperature.

Model 29 - Using two injectos upstream, two downstream. Based on model 27

Still, this model is based on model 27. In comparison to model 27, this model

presents two injectors upstream and two downstream, with an addition of a third

intake row inside each injector to compensate the reduced number of injectors and

increased fuel inlet passages to allow for same Mach number of fuel jet.

Figure 7.23: Meridian plane position relative to the combustors that have three injectors upstream and three injectors downstream (models: 21, 22, 28 onwards)

Results The expected mass flow rate in the injectors in cold flow is that of model 28 at cold flow, i.e. 3.821 kg/s, however results show that the diameter of air intake holes must be increased by a factor of 1.18 in order to attain this target. This modification configures model 30.

Model 30 - Increased air intake holes. Based on model 29

This model based on model 29. Injector air intakes were increased by a factor of

1.18.

Figure 7.24: Reaction rate at plane β 2 of model 27

Results Injector outlets (either upstream or downstream) present considerable ob- struction since they remained unchanged and the 18% increase in air intakes didn’t cause the 39% increase expected in primary air flow rate. We proceed with modifi- cations in the boundary conditions.

Modification in boundary conditions - model 30.1 Same as model 30 but with targeted mass flow at outlet of 5.938 kg/s, i.e. that of model 28. Static pressure at outlet resulted 601854.8 Pa.

Modification in boundary conditions - model 30.2 Further modification in the targeted mass flow rate at outlet which is now 6.85 kg/s in order to attain a primary and fuel flow of 3.821 kg/s (the same of model 28).

Modification in boundary conditions - model 30.3 Aiming at an increased

equivalence ratio equal to the average of model 28 for comparison (0.5355), the fuel

Figure 7.25: Reaction rate at plane β 2 of model 28

flow rate has been increased from 0.1617 kg/s to 0.1812 kg/s. The total temperature at outlet rose as expected.

Results show that due to the increase in fuel flow rate, and given the consequent increased hot losses of total pressure, the outlet flow could be maintained after a reduction in outlet static pressure.

Model 31 - Reduced injector outlet area. Based on model 28

Same as model 28 but with the injector outlet area reduced 5%. The objective of this simulation is to understand if injector bulk velocity increases or decreases and to see what happens to mass flow rate after a reduction in injector outlet area. Results show that after a restriction in the injector outlet diameter the velocity increases 2.18%

on average (instead of remaining unaltered, as in the case of isentropic flow). The

increased velocity in turn causes increased viscous losses that shows up as increased

total pressure losses that ultimately causes the mass flow rate across the injectors

to reduce 3.72% (in case of isentropic flow, the reduction of mass flow rate could be

to model 32 which is based on model 28 but with added cooling in primary zone.

Model 32 - Addition of 8 splash rings in primary zone. Based on model 28

To be compared with model 28 since both have approximately equivalence ratio equal to 0.55. The geometry is the same as model 28 but with the addition of 8 splash rings for added film cooling in the primary zone to reduce hot spots. Such measure could be taken because average total temperature at outlet of the reference combustor (model 28), 1339 K, is still higher than the target of 1223 K. Four of the new splash rings are located in the outer liner, the other four in the inner liner, all of them were equally distributed along the liner. The geometry has been regenerated in the CAD software to allow for future modifications.

Results Pattern Factor has worsened (it increased from 0.23 in model 28 to 0.50 in the current design), that’s because after increased air addition through wall cooling, the average outlet temperature has decrease but the maximum temperature at outlet still reflects poor dilution (an aspect that will be tackled later on).

The added film cooling in primary zone has caused some detrimental effects on flame however, mass fraction of methane at outlet has increased two orders of mag- nitude due to localized flame quenching, Figures 7.26 and 7.27 show partial flame quenching by the film cooling. The modification adopted for the next design includes reducing the hole diameter of the film cooling from 2.7 mm to 2.2 mm through-out all the combustor, in order to understand better which zones need more cooling and which zones were more affected by flame quenching.

Model 33 - Reduction of cooling holes’ diameter. Based on model 32 Based on model 32. The modification adopted for this design includes reducing the hole diameter of the film cooling from 2.7 mm to 2.2 mm through-out all the combustor, in order to understand better which zones need more cooling and which zones were more affected by flame quenching.

Results Numerical results show that mass flow rates of model 33 are similar to

those of model 28 since film cooling from model 32 has been restrained. Equivalence

ratios (downstream and upstream injectors) of model 33 are approximately equal to

that of model 28 (0.54). Pattern factor has improved; CO and CH 4 (most notably)

Figure 7.26: Total temperature at plane α 1 of model 32

Figure 7.27: Reaction rate at plane α 1 of model 32

restrained flame quenching that in model 32 was excessive.

Hotspots in the liner (Figure 7.28) indicate moderate film cooling; hot spots around downstream injector tip indicate the presence of a stagnation zone (see also Figure 7.29) from the upstream flame that finds its way downstream after surround- ing downstream injectors tip. This observation allowed us to come with the following modification: removal of injectors tip that protrudes inside the liner in order to check if stagnation zones are minimized.

Figure 7.28: Hot spots on liner (gas side) of model 33

Model 34 - removal of injectors tip. Based on model 28

This is a milestone design, it promoted reduced flow obstruction, and may increase

injector safety and reduce flashback risk. [capstone_report] Same as model 28

but with removal of injectors tip that protrudes inside the liner in order to check if

Figure 7.29: Total temperature at plane β 1 of model 32

stagnation zones and localized recirculation bubbles in the liner are minimized and perhaps more important to check if stagnation hot zones behind the injectors tips are removed. This latter feature will be evident from model 48 on, when we will re-install the added cooling slots in primary zone as we did with models 32 and 33 and compare models 48 and 33.

Results After the removal of injector’s tip, the bulk velocity of mixture reduces and the flame occupies a larger volume of the liner (Figures 7.30 and 7.31); the flame is still present in plane β 3 (Figures 7.32 and 7.33) and this justifies the high concen- tration of CO and CH 4 at outlet, this observation suggests the future adoption of a convergent injector outlet even if not protruding inside the liner. The recirculation bubbles in the proximity of the dome are altered significantly also (compare Figures 7.34 and 7.35).

The next modification involves improving the pre-mixing performance upon re-

moving the bottom air intake rows (the row closer to the liner) and modifying the

Figure 7.30: Reaction rate at plane β 1 of model 28

top air intake rows (the row closer to the fuel inlets), providing rectangular openings instead of circular ones. The area of the rectangular openings is initially set equal to the top and bottom circular openings from model 32 combined.

Model 35 - Removal of bottom injector intake row and using rectangular air intake passages in the top row. Based on model 34

This design, based on model 34, is aimed at testing effects on pre-mixing performance after removing the bottom air intake rows (that closer to the liner) and modifying the top air intake rows (that closer to the fuel inlet), providing rectangular openings instead of circular ones. The area of the rectangular openings is initially set equal to the top and bottom circular openings from model 34 combined.

Results Intermediate results show that despite the area of the rectangular openings

being equal to the previous circular opening rows combined, the primary air and fuel

(which includes fuel flow rate 0.1287 kg/s) results slightly lower (4.333 kg/s) than

Figure 7.31: Reaction rate at plane β 1 of model 34

the flow rate of model 34 (4.434 kg/s) at non-reactive conditions. The area of the

rectangular openings were then increased by a factor equal to ^4.434 / _4.333 = 1.0233; the

opening width is kept the same (22 mm), while its length passes from 50 mm to 52

mm. Results from a reactive simulation show that pre-mixing performance has wors-

ened (standard deviation of the equivalence ratio has roughly doubled), that’s be-

cause the penetration of air intakes jets remain substantially the same (note that the

pressure drop across the injector tube hasn’t changed) which is still low (see equiv-

alence ratio distribution of at the top intake holes at upstream injectors in Figures

7.36 and 7.37) and the bottom row of air intake holes actually played an important

role in disrupting the fuel rich jet that forms inside the injector and tends to remain

unmixed (compare Figures 7.38 and 7.39). Observe that the planes named omega

cross the injector axis perpendicular and intend to show the flow, equivalence ra-

tio, pressures etc. inside the injector. The bottom row of air intake holes aids at

redistributing the fuel inside the premixing duct, after momentum and mass transfer.

Figure 7.32: Reaction rate at plane β 3 of model 28

Model 36 - Using rectangular air intake passages in the injector. Based on model 34

Same as model 34, but in the place of circular air intakes passages, the injectors present rectangular passages keeping same area as before. The objective of this simulation is to check if pre-mixing performance is eventually altered upon the change of typology of the passage geometry, but also to allow for a passage geometry whose area could be modified upon altering its height while maintaining the solidity of the wall by not changing its width.

Results Premixing performance results actually worse than in model 34; upstream injector premixing performance has worsened more than downstream injector pre- mixing performance, as can be indicated by observing the standard deviations of equivalence ratio (Table D.2).

In both injectors, the modification of shape of intakes passages causes the flow

in the injector housing to change, creating different recirculation zones and different

Figure 7.33: Reaction rate at plane β 3 of model 34

Figure 7.34: Axial velocity contours at plane α 2 of model 28

Figure 7.35: Axial velocity contours at plane α 2 of model 34

Figure 7.36: Equivalence ratio contours at plane ω top,us of upstream injector of model

34, non-reactive flow

Figure 7.37: Equivalence ratio contours at plane ω top,us of upstream injector of model 35, non-reactive flow

levels of total pressure losses, that in turn affects the penetration of air intake jets.

That is evident by looking at upstream injector total pressure fields in the combustor orthogonal plane beta 1 (compare Figures 7.40 and 7.41), compare also the projected velocity fields in Figures 7.38 and 7.42 and notice the presence of localized low speed zones in model 36.

Recall that for good jet penetration it is desirable relatively high local total pressure at upstream and low static pressure at downstream of intake passages.

From the observation of the aforementioned figures and Figures 7.43 and 7.44, it

was concluded that the rectangular passages presented deficient penetration, the

circular openings are thus preferred to rectangular ones.

Figure 7.38: Projected velocity field at plane β 1 of model 34, non-reactive flow

Model 37 - Reduced injector outlet area (increased convergent). Based on model 34

Same as model 34, but with the injector outlet cone having a semi-angle of 8 ^◦ in- stead of 4.3 ^◦ . The objective of this simulation is to observe effects on premixing performance due to increased speed caused by the more convergent outlet.

Results It’s noted that the convergent outlet, despite helping to uniform the flow (upon accelerating it) does not improve fuel pre-mixing performance (see Table D.2).

Figure 7.52c shows the position where the recirculation in the upstream injector

housing has caused the total pressure to drop more drastically, this in turn is the

main cause of poor penetration of some intake jets from the top row. The mod-

ification proposed is the provision for injector housing skirts such that air coming

from the combustor annulus has a facilitated entry at injector annulus and create

less recirculation, thus less total pressure drop (mainly in the combustor inlet side)

and consequently make the top air intake jets penetration more even. Figure 7.51a

Figure 7.39: Projected velocity field at plane β 1 of model 35, non-reactive flow

shows an uneven jet penetration at the top air intake row in the upstream injector of model 37.

Model 38 - Provision for injector housing skirts. Based on model 37 This is a milestone design, it improved pre-mixing and reduced combustor total pressure loss. Same as model 37, but with the provision for injector housing skirts (fillets with 40 mm radius that connects combustor housing and injector housing) such that air coming from combustor annulus has a facilitated entry at injector annulus and create less recirculation, thus less total pressure drop (mainly in the combustor inlet side) and consequently made the first intake jets (those at the top) penetration more even, besides other improvements (Figure 7.45).

Non-reactive flow results Regarding pre-mixing efficiency, it was observed that the mixture jet is more centered in the injector (Figures 7.46, 7.47, 7.48 and 7.49).

However in the plane perpendicular to β 1 containing the combustor axis (γ us ) it’s

Figure 7.40: Total pressure field at plane β 1 of model 34, non-reactive flow

possible to see that air streaks persist in upstream (US) injector outlet (Figure 7.50.

Indeed, at US injector the σ phi is larger than in DS injector (Table D.2). Despite fewer air streaks being visible in downstream injector outlet in plane γ ds , this problem should be addressed in both injectors;

The projected velocity vector fields in the planes perpendicular to the injector axis (ω planes) show that the air intake jet penetration of US injectors which were the most problematic in model 37 are now more even (Figures in 7.51). These figures also show that the intake jets maintain their angular momentum in clockwise direction inside the premixing duct.

In general, both US and DS injectors have more even penetration either in the

top or bottom rows when compared to previous models; the improvement in reducing

recirculation zones in the injector annulus at its short side and at combustor inlet

side after the provision for the injector housing skirts can be seen in the total pressure

fields at planes β 1 and γ us (Figures in 7.52). The reduction of total pressure loss

Figure 7.41: Total pressure field at plane β 1 of model 36, non-reactive flow

when compared to model 37 is the main cause for increased air intake jet penetration in the top rows, where there was previously a deficiency; this in turn favors a more even penetration.

Reactive flow results Regarding the flame configuration, Figure 7.53a shows the effect of still poor pre-mixing performance that can be further improved; in the downstream injector, Figure 7.53b shows a better flame configuration (because DS injector pre-mixes better the fuel); A positive aspect of model 38 is that at plane β 4

no reactions take place anymore, this reflects in low CO and CH 4 emissions.

It was possible to note that inside the premixing duct, at its intermediate plane

between the top and bottom air intake rows, an external lean flow is created which

has slightly higher axial velocity (referring to injector axis), while the core has lower

axial speeds and is richer (Figures 7.54a and 7.54b). This suggests the provision for

an intermediate air intake row that therefore might have facilitated entrainment and

Figure 7.42: Projected velocity field at plane β 1 of model 36, non-reactive flow

might promote via jet penetration that such lean external flow mixes with the richer inner core.

Model 39 - Provision for a third air intake row in the injectors. Based on model 38

Same as model 38, but with the provision for a third air intake row in the middle

of first and second air intake rows in order to promote better premixing. It was

observed that the core of injectors of model 38 had lower axial speeds and is richer

(recall Figures 7.54a and 7.54b). This suggested the provision for an intermediate

air intake row that therefore might have facilitated entrainment and might promote

via jet penetration that such lean external flow mixes with the richer inner core. The

fuel flow rate, inlet total pressure and outlet static pressure being the same as model

38 causes the equivalence ration in primary zone to decrease since more air is drawn

Figure 7.43: Equivalence ratio contours at plane ω bottom,us of upstream injector of

model 34, non-reactive flow

Figure 7.44: Equivalence ratio contours at plane ω bottom,us of upstream injector of

model 36, non-reactive flow

Figure 7.45: Section (120 ^◦ ) of the combustor model 38 showing in green its injector housing skirts for facilitated air intake

be the injectors air intakes. However the equivalence ratio is still over the acceptable minimum (0.475).

Results Despite the fact of working with a slightly lower equivalence ratio, the flame in plane β 1 demonstrates that the better premixing performance indeed con- tributes to an uniform flame geometry that does not deviate too much neither to the outer liner nor to the inner liner (compare Figures 7.55 and 7.53a). The third air intake row is therefore considered beneficial. The flame is entirely contained between the dome and plane β 4 (where dilution starts), therefore causing low CH 4 and CO emissions.

The tridimensional flame geometry visualization is a feature learned while work-

ing in this model, it will be shown in this case (Figure 7.56) and in future models

as necessary. Basically, the flame geometry is the set of nodes where the methane

mass fraction equals 0.005 (Y CH

,f lame = 0.005), each node is colored according to

the reaction rate (for reaction 1 in the simplified mechanism) using the same scale

currently used in other flame visualizations. The flames seems to bifurcate in two

jets that maintain attached almost along the entire flame length. Such bifurcated

geometry is probably caused by the fact that the mixture stream needs to conserve