Calculations for the preliminary design of the combustors

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CHAPTER 7. DESIGN REFINEMENT 187

Figure 7.61: Reaction rate at the entire flame of model 41, isometric view

Model 44 - Increased injector housing area. Based on model 40

Model 44 is similar to model 40 but with wider injector annulus having an area equal to model 39.

Results No substantial improvement in premixing performance was observed. The model 43 is preferred in order to continue the optimization process, since the top intake row penetration was more evenly distributed (Figure 7.63).

Model 45 - Lengthened injector. Based on model 40

Aiming at increasing the effects brought by model 43, using model 40 as basis, the convergent cone at outlet has been lengthened by 20 mm, while the straight portion of injector has been placed 20 mm outwards; he distances between top, intermediate and bottom air intake rows were kept unchanged.

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(a) Velocity field at plane γds, mod. 40 (b) Velocity field at plane γds, mod. 42

(c) Total pressure at γds, model 40 (d) Total pressure at γds, model 42

Figure 7.62: Projected velocity and total pressure fields at plane γds of models 40 and 42

Results In comparison to model 43, it was observed that premixing performance has worsened. In addition, total pressure losses have increased in injector housing.

The cause is that probably the third air intake row which previously was favoured by a more direct flow coming from combustor annulus now face additional obstruction since its flow has to go deeper inside the injector annulus than before.

Model 46 - Doubled fuel inlets, same fuel inlet overall area. Based on model 43

The injectors of this combustor are equal to the injectors of model 43, the difference lies on the number and size of fuel inlets, it now has eight holes (previously there

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(a) Φ at ωtop,ds, model 43 (b) Φ at ωtop,ds, model 44

Figure 7.63: Equivalence ratio (Φ) at downstream injector top transverse plane (ωtop,ds) of models 43 and 44 for comparison of dilution jets penetration

were four fuel inlets in each injector) but with the same overall area of model 43 which means that each of the new hole has the diameter equal to 71% of model 43.

Naturally, since the fuel flow rate is imposed as a boundary condition, the fuel inlet velocity has been maintained at 163 m/s.

Model 47 - Doubled fuel inlets, doubled fuel inlet overall area. Based on model 43

The injectors of this combustor are equal to the injector of model 43, the difference lies on the number of fuel inlets, instead of four there are present eight fuel inlet per injector, while maintaining the same fuel inlet diameter of model 43. Naturally, since the fuel flow rate is imposed as a boundary condition, the velocity has reduced to its half, now 82 m/s.

Results After observing both models 46 and 47 it was noted that the fuel velocity difference between the two models play little importance on pre-mixing performance (σphi). In addition, it was observed that using eight fuel injector holes worsen slightly σ_phi in both cases. Model 46 is thus preferred to model 47.

Model 48 - All primary air flow passages scaled down with cooled primary zone. Based on model 40

Model 48 is equal to model 40 (reduced primary air flow passages) but with the liner modifications of model 32, including the provision of eight additional splash rings

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for film cooling in the preliminary zone (four on the inner liner, other four in the outer liner).

Results The analysis of cold flow premixing performance shows increased total pressure loss in injector annulus. From the reactive simulation, results show that CH4 and CO emissions increase due to flame quenching. Both flames of models 48 and 49 touch the inner liner film cooling. Liner hot spots (Figure 7.64a) show that a conjugated heat transfer analysis across the liner walls might be necessary in future simulations. Nonetheless, Figure 7.64a shows that inner liner film cooling are more effective than outer liner film cooling. Since the flame of model 48 is locally quenched by inner liner film cooling, this issue is a concern and should be tackled in next models.

Model 49 - All primary air flow passages scaled down with cooled primary zone. Based on model 43

Model 49 is equal to model 43 with the provision of eight additional splash rings for film cooling in the primary zone (four on the inner liner, other four in the outer liner).

Results from model 49 shows slightly lower total pressure loss than model 48, however its premixing performance is slightly worse than the 48 case. The reactive simulation showed that the flame touches the inner liner film cooling as in model 48.

We consider model 48 as the reference case for model 50 since it has given better overall results (specially lower σΦ).

Model 50 - Four additional splash rings in outer liner in primary zone and reduction of cooling passages. Based on model 48

We consider model 48 as the reference case since it has given better overall results.

After analyzing hot spots in the inner liner, the modification brought by model 50 consists in adding four additional splash rings in the outer liner in the primary zone and reducing all the cooling holes diameter in the combustor from 2.72 mm to 2 mm, the height of splash rings passages is also reduced from 2.5 mm to 2 mm.

Results Despite having reduced cooling holes’ area to half the value of model 48, cooling mass flow rate reduced less than its half value (cooling flow rate of model 48 was 3.262 kg/s), now the cooling flow rate of model 50 is 2.334 kg/s, i.e. a decrease of 28.5%, this is not an issue however.

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(a) Hot spots model 48 (b) Hot spots model 50

Figure 7.64: Hot spots on liner (gas side) of models 48 and 50 for comparison of liner splash rings cooling

Premixing performance of model 50 is on average (considering upstream and downstream injectors) the same as model 48 since in both cases sσΦ = 0.10; injectors of model 50 perform more similar to each other than in case 48 which is an advantage in favor of this.

Pattern factor is considerably lower (0.27) than 48 case (0.40). Since now the number of flow obstructions has increased (additional cooling holes) the total pressure loss has increased slightly, as expected. CO emissions have decreased an order of magnitude. The same is true for CH4 emissions.

The flame of model 50 touches but it is not interrupted by inner liner film cooling.

Recall that model 48 has presented a worse result with its flame being interrupted by inner liner film cooling. This reduced quenching justifies why CO and CH4emissions of model 50 are lower.

Noting liner hot spots (Figure 7.64b), the added film cooling splash rings in the outer liner are indeed beneficial, however, the reduction in cooling holes’ diameter caused less cooling air to be directed to inner liner where new hot-spots have arisen, this area may receive further attention. Another area that should receive attention in next models is the dome whose hot spots temperature has increased. These improvements however should be considered after trying to reallocate the flame to the center of liner channel, therefore the next model will present injector axes that touch the mean diameter.

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(a) Reaction rate at plane β2 (b) Reaction rate at flame

Figure 7.65: Flame - cooling slots interference in model 51

Model 51 - Injector axis tangent to liner mean diameter. Based on model 50

Same as model 50 but with the injector axes tilted outwards 5 degrees, now tangent to liner mean diameter. The objective if to reallocate the flame to the center of liner channel.

Results The reaction rate in plane β2 shows a very deformed flame (Figure 7.65), this model does not perform well. The complete figure is evident observing the reaction rate at the flame: downstream flame impacts against the outer liner cooling rings and is drastically quenched. The repositioning of injector axis did not bring the desired results and we need to consider model 50 as a basis for model 52.

Model 52 - Increased liner thickness. Based on model 50

Same as model 50 but with the liner thickness equal to 2 mm instead of the 1.5 mm used up to now. The objective is to start performing conjugate heat transfer analysis allowing for more cells to be created in the solid mesh since we have opted for a coarse mesh (see Section C).

Results The reaction rate in the flame showed that the flame interacts drastically with the film cooling in the outer liner. Given this unsatisfactory result, the conjugate heat transfer analysis was aborted and is was decided to move back to a 1.5 mm thickness liner.

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Model 53 - First conjugate heat transfer analysis. Based on model 50 This is a milestone design, configuring the first conjugate heat transfer analysis.

It is the same as model 50 but includes a solid mesh in the liner and premixing duct for a conjugate heat transfer through the walls and fluid dynamic analysis. As presented before, the mesh criteria in this and following conjugate analysis are the same used in previous models:

• Quality: Target Skewness: 0.8

• Match control: Combustion Chamber, Annulus and Liner periodicity (120^◦)

• Inflation (aimed at y⁺ = 40 at various Boundary Layers):

– Growth rate: 1.2 (when not specified) – Maximum Layers: 5

– First Layer Thicknesses (mm):

∗ 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

Results Non-reactive simulation shows good numerical results agreement with the non-reactive simulation of the base model 50 (that has absence of solid meshes), considering an already improved mesh around the dome for a better resolution of thermal gradients.⁸

Three types of reactive simulations were prepared for model 53 (all of them have the mesh close to the dome improved in order to better resolve thermal gradients):

1. reactive (non-conjugate, i.e. adiabatic walls);

2. reactive conjugate;

8From model 53 onward, non-conjugate, reactive simulations numerical results shown in Ap- pendix D will represent a simulation where the solid walls in contact with the fluid are set to adiabatic; the walls will allow heat transfer only in the "conjugate reactive cases".

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3. reactive conjugate with refinement of cells for which total temperature gradient exceeded 10% of maximum gradient found at ‘reactive conjugate’ simulation for better flame resolution;

In all reactive simulations, the temperature of flow zones present a substantial change in the meridian planes (α) particularly in the dome region, which in the case of simulated adiabatic walls (type 1) was in contact with a considerably hotter flow but in the conjugate case (types 2 and 3) the heat transfer to the annulus region created a layer of cooler flow in proximity to the wall (Figure 7.66). Besides the type 3 simulation showed that this layer might be thin, its actual thickness is still questionable, a feature that might be observed in the next models.

The reactive simulation with conjugated heat transfer through liner walls demon- strated in addition that the outer and inner liner in this heat transfer conjugate analysis are cooled considerably better than non-conjugate 53 case (Figure 7.67), i.e. type 1. Liner temperatures of model 53, type 1, are almost identical to case 50.

The type 3 simulation, is considerable the most appropriate setting for subsequent conjugate analysis.

Despite the conjugate analysis having showed that the combustor annulus indeed receive part of the heat produced in the combustor chamber and as a consequence the liner temperatures results now more moderate, the next three models 54, 55 and 56 will aim at cooling the dome directly with additional cooling flow as we’re going to explain next.

Models 54, 55 and 56 - Trials of direct cooling the dome. Based on model 53

After we have observed that the dome in model 53 could be further cooled (despite its temperature distribution not being considerably high), we decided to proceed with three modifications in the dome for providing more cooling air in this region:

• Model 54 has a shielded dome (1.5 mm plate located 4 mm from the dome, Figure 7.68b), which was perforated (three circumferential rows containing 102, 117 and 129 - total of 348, 2mm holes from the inner radius to the outer radius) to allow air enter and provide film cooling with augmented convection (Figure 7.68a);

• Model 55 contains the perforated dome of model 54 (Figure 7.68a) but does not contain the shield;

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(a) Reactive simulation (non-conjugate, i.e. adiabatic walls), type 1, 23 million cells (solid cells inactive)

(b) Reactive conjugate simulation, type 2, 23 million cells

(c) Reactive conjugate refined simulation, type 3, 30 million cells

Figure 7.66: Total temperature field at plane α1 of model 53 with superimposed mesh, showing the difference between simple and conjugate heat transfer analysis

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(a) Hot spots model 53, type 1 (b) Hot spots model 53, type 3

Figure 7.67: Hot spots on mid-layer of liner of model 53 in type 1 and type 3 simulations for comparison between the adiabatic case and conjugate analysis case, respectively

(a) Back view of one third of combustor liner with perforated dome (used in mod-

els 54, 55 and similar to model 56) (b) Detail of dome shield used in Model

54

Figure 7.68: Perforated and shielded dome used in the trials of direct cooling the dome

• Model 56 does not contain a shield and the hole rows in the dome are now four (from inner to outer radius: 66, 81, 93 and 105, total: 345 holes) the flow passage area is intended to be the same as model 55.

Results model 54 Figure 7.69 indicates that despite the shield vane being at moderate temperatures could not protect the liner dome from contact with unac- ceptable hot spots of stagnated flow (considered above 1150 K). This concept should

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be better improved to remove stagnation points and could work fine if the shield were to be made with a more refractory alloy than the liner (common nickel alloy).

The added cooling flow results 0.17 kg/s which could be acceptable (the total mass flow rate in the combustor passes from 7.162 kg/s (model 53) to 7.294 kg/s). We put aside these considerations and evaluate Model 55, without the heat shield.

Results model 55 Figure 7.70 shows that without the heat shield the cooling jets in the dome don’t remain attached to the liner wall and mix with the main flow, not the desired behavior, since it provides poor cooling. Model 56 was drawn but its simulation was aborted given that the results would be as unsatisfactory as those of its base model, 55.

Model 57 - end portion of the liner enclosed by annulus & radial inlet.

Based on model 53

Looking at the end portion of the liner of model 53 (Figure 7.71b) we can note the presence of considerable hot spots with temperatures higher than 1150 K. That’s due partially to the fact that up to now the end portion of the liner is not in contact with annulus air flow, so the external side of these wall were imposed to be adiabatic while their internal side could assume the flow temperature, resulting in hot spots.

Model 57 brings the following modification: it encloses the end portion of the liner with annulus extensions to aid the cooling of this area. In addition, model 57 has a second and independent feature that we wanted to analyze: the combustor inlet is radial instead of axial, the inlet area is kept unchanged (Figure 7.71a).

Results The extended annulus indeed aided at cooling the final portion of the liner, as can be seen comparing Figures 7.71b and 7.71c. The modification of streamlines at inlet did not brought significant effects on annulus flow and almost no effect on main flow inside the combustion chamber.

Model 58 - Removal of last dilution row in the inner liner. Based on model 57

Same as model 57 but the last dilution row (located in the inner liner) has been removed, since it was seen that it worsened the pattern factor. The dilution flow area of the twenty one holes that comprised the removed row was maintained after inclusion of nine dilution holes in the second dilution row in each side (outer and inner liner).

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(a) Detail in the vane between shield and dome, plane α1

(b) At shield surface

(c) At liner (mid-layer)

Figure 7.69: Temperature distribution after the provision for a heat shield (model 54)

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(a) Detail of the jets in the dome, plane α₁

(b) Hot spots (mid-liner)

Figure 7.70: Ineffective jets in the dome of model 55, liner temperatures don’t differ substantially from model 53, Figure 7.67b

Results It was observed that indeed, the last dilution row in the inner liner did not contributed to a lower pattern factor which still results 0.20, a low satisfactory value (NASA standard is PF=0.21). However the curved end portion of the inner liner is still to be cooled, the curved end portion of the outer liner is already cooled by a film cooling.

Model 59 - Cooled end portion of the inner liner, last Natural Gas simulation. Based on model 58

It was noted in model 58 that the end portion of the inner liner still had to be cooled, therefore, model 59 includes a splash ring for film cooling in this region.

This represents the final combustor geometry which is shown in Figure 7.72, technical drawings showing mainly the position of dilution rows, splash rings for film cooling and the position of injectors and the updated reference planes drawing are presented in Appendix E.

Mesh The mesh of model 59 has been refined twice: the cells in proximity to the dome have been firstly refined to better capture temperature gradients in this zone, then the cells for which total temperature gradient exceeded 10% of maximum gradient found at ‘reactive conjugate’ simulation were refined for better flame resolution.

The resulting mesh is shown in Figures 7.73 where its possible to see that the cells comprising the flame are finer and 7.74 where it’s possible to see not only some re-

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(a) New annulus of model 57 fully encloses the end portion of liner, inlet is radial

(b) Temperatures at end portion of liner (model 53)

(c) Temperatures at end portion of liner (model 57)

Figure 7.71: Model 57 and differences in hot spots at the end portion of liner with respect to model 53

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(a) Isometric view (b) Back view

Figure 7.72: Rendered CAD model of combustor #59, final model

fined cells in the flame region, but also some refined cells in the dilution jet zone and the refined cells in the dome region.

Figure 7.73: Mesh detail view, plane β1, model 59

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Figure 7.74: Mesh detail view, plane α2, model 59

Results The steady-state simulation of reactive flow with conjugated heat transfer of model 59 is shown in this section.

Figures 7.75 and 7.76 give an overview of the general flow in the combustor, after air enters the injectors it acquires a strong tangential velocity component that predominates in the flow inside the combustion chamber.

Figures 7.77, 7.78, 7.87a, show fuel pre-mixing performance which is fairly good with Φus = 0.527 and σΦ,us = 0.119 in the upstream injector and Φds = 0.533 and σ_Φ,us = 0.073 in the downstream injector.

Figures 7.79, 7.80, 7.81, 7.82, 7.83 and 7.84 illustrate the temperature distribu- tion in the various meridian planes α, putting in evidence: 1) good flame positioning that does not touch the liner neither interacts with film cooling, 2) proper liner film cooling (see also Figure 7.85, where the temperature does not exceed 1150 K in most of the liner) that works in conjunction with one another and 3) proper gases dilution resulting in a low pattern factor of 0.16 (see also Figure 7.86 for a view of the outlet passage), the mass weighted average total temperature in this model is 1221 K and the maximum temperature in the outlet is 1334 K. The fuel flow rate required is

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Figure 7.75: General flow of model 59, isometric view

Table 7.10: Biogas composition considered for the models 60 and 61 Component Molar fraction

CH4 0.6

CO2 0.4

Model 60 - Enlarged fuel inlet holes, first Biogas simulation. Based on model 59

We are going to discuss here what actually changes for a simulation using biogas instead of natural gas. Recall that the composition of the natural gas considered in all the simulations up to now is given in Table 6.3. The biogas composition considered is given in Table 7.10 and a discussion of its thermodynamic properties is given in Appendix A.

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Figure 7.76: General flow of model 59, back view

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Figure 7.77: Equivalence ratio distribution in plane β1, model 59

Useful parameters The first useful parameter that can be calculated based on biogas composition is its Lower Heating Value. The appendix section A.1.1 demon- strates how this calculation is done. The LHV of biogas results 17 692 kJ kg⁻¹.

The required fuel flow rate to raise the total temperature of the targeted air flow rate 7.62 kg/s entering the combustor at 527 K to 1223 K (the target outlet total temperature) can be calculated performing an energy balance on the combustor (see Equation A.1 on Appendix sectionA.2). Two additional parameters related to the fuel are required by Eq. A.1, the injection temperature Tinj and the specific heat at constant pressure at the injection temperature (cp,f), their determination is described in section A.1.3. Furthermore, an estimate of the exhaust gases specific heat at

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Figure 7.78: Equivalence ratio distribution in plane β1 and the originated flames, model 59

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Figure 7.79: Flames and the temperature fields created in the meridian planes of model 59

Figure 7.80: The temperature fields created in the meridian planes of model 59

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Figure 7.81: Total temperature field at plane α1, model 59

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Figure 7.85: Liner temperature distribution of model 59, most of it lies below the safety value of 1150 K

constant pressure (cp,g) is also required, it can be calculated using the procedure showed in section 6.7.3 together with section A.4.

Following the aforementioned procedure for the 1500 kW MGT combustor, some useful parameters can be calculated and summarized in Table 7.11 which incorporates data from Table 6.8.

Modification of model 59 necessary for biogas utilization It is desired to test the same injectors and combustor dimensions (including cooling and dilution holes disposition) for biogas. However since the mass flow rate of biogas estimate is 0.425 kg/s, roughly three times more than natural gas case, if the fuel injector nozzle holes were kept the same the fuel jet could be too fast and problems of poor pre-mixing perfomance or supersonic flow could arise. Therefore model 60 considers the velocity of natural gas jet 170.25 m/s of case 59 and modifies the holes diameter to obtain such velocity, naturally, the difference in fuel specific mass is considered in

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Figure 7.86: Total temperature field at outlet section, model 59, pattern factor results low: 0.16

this calculation.

Using this approach, the hole diameter for model 60 results 5.3 mm while for model 59 it was 3.8 mm. The expected Mach number at fuel nozzle is 0.411, fairly subsonic; in model 59 it was 0.321.

Results The fuel flow rate estimated to raise 7.62 kg/s of air flow rate initially at 527 K to 1223 K is 0.425 kg/s of biogas. The simulation required 0.356 kg/s to 7.26 kg/s of air flow rate to 1222 K; the total flow rate leaving the combustor results 7.617 kg/s, therefore, the estimation and the simulation are in agreement.

The average equivalence ratio at injectors outlet passes from 0.53 (model 59) to 0.55; the pre-mixing performance is quite good as before since σphi < 0.1 for both upstream and downstream injectors (see Table D.2).

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CHAPTER 7. DESIGN REFINEMENT 212 Table 7.11: Useful fuel parameters prior to biogas simulation (models 60 and 61) and Natural Gas data (all other models) in the order they are calculated

Description Biogas Natural Gas Unit

Lower Hetaing Value, LHV¹ 17692 49127 kJ/kg

Molecular Weight, MWf 27.23 16.18 g/mol

Gas constant, Rf 0.305 0.514 kJ/kg.K

Injection temperature, Tinj 437.3 438.5 K

Specific heat at constant pressure, cp,f2 1.578 2.677 kJ/kg.K

Mass flow rate, mf2,3 0.425 0.143 kg/s

Specific mass, ρf2 4.636 2.748 kg/m3

1 At standard reference state.

2 At Tinj.

3 Estimated values. The actual flow rate required by model 59 is 0.124 kg/s of natural gas and the actual value required by models 60 and 61 is 0.355 kg/s of biogas.

Pattern factor is 0.22 which is yet fairly good.

Total pressure losses are still low: 1.58%.

Methane emissions are practically the same and low. The same is true for CO emissions (see Table D.3).

Average bulk velocity at injectors outlet increases slightly, passing from 51.6 m/s to 52.6 m/s due to increased fuel flow rate. This increased velocity could worsen the stability condition of the flame since it’s known that the biogas flame speed is lower than natural gas flame speed and the risk of blowout (read Section 4.5.1) could increase. Nonetheless, the simulation (in steady state conditions) shows that the biogas flame is sustained by these injectors.

Figures 7.87a and 7.87b illustrate that the biogas flame (at least one of its ramifi- cations) is longer than the natural gas flame. This was expected from the theoretical analysis of fuel shift from natural gas to biogas, chapter 4. Recall from this chapter that biogas has lower adiabatic flame temperature than natural gas and thus lower flame speed, which combined with a slightly higher bulk velocity produces a longer flame.

Liner temperatures are rather contained to 1150 K in the dome in both models (59 and 60). Also, the temperature around the splash rings and dilution holes in the outer liner are very similar in both cases. The same is true for the inner liner and the outlet walls. Temperature profiles in the meridian planes α are similar.

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(a) Model 59, natural gas shorter flame (b) Model 60, biogas longer flame

Figure 7.87: Equivalence ratio distribution at injectors outlet sections and the originated flames, models 59 and 60

Model 61 - Doubled fuel inlet holes, second Biogas simulation. Based on model 59

This model presents eight fuel injection nozzles per injector instead of four (model 59). This may distribute the increased fuel flow rate of biogas though the nozzles in order to still have contained jet velocities. If this model works satisfactorily, model 59 can be substitute by it and only four injector holes per injector can be active while using natural gas. Better pre-mixing performance is expected than model 60 since in model 61 each fuel injector holes is aligned with an air intake in the topmost row of the injector.

Results Despite having on fuel injector hole aligned with each air intake hole, the pre-mixing performance of model 61 has worsened (σφ,us = 0.158; σφ,ds = 0.127).

Probably the reduced momentum of the fuel jets cause them to be directed towards the periphery of the premixing duct when they interact with air intake jets, this can be seen in Figure 7.4.2 where we compare pre-mixing of models 60 and 61.

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(a) Model 60, σφ,us = 0.112 (b) Model 61, σφ,us= 0.158

Figure 7.88: Equivalence ratio distribution in plane β1, models 60 and 61

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215

Chapter 8 Conclusions

The Anaerobic Digestion process which produces biogas and its the typical composition for a Micro Gas Turbine combustor utilization were clearly understood upon reading chapter 2.

Combustion book references, articles in literature, and industrial best practices were used for the preliminary design of the reverse flow combustor using spreadsheets and parametric CAD softwares (Chapter 6).

The Computational Fluid Dynamic software Ansys Fluent was used to perform the various simulation steps aimed at refining the preliminary design (Chapter 7).

Such simulations were at steady state and turbulent conditions which justified the use of Reynolds-Averaged Navier-Stokes equations with k − turbulence models. In particular, realizable k− turbulence models were used to better deal with the nature of the overall flow whose presence of many secondary flows is significant.

At first, the flow fields simulated were non-reactive involving solely species trans- port (diffusion and convection), afterwards reactive simulations were carried out using finite-rate/eddy-dissipation model (7.1.2) and finally conjugated heat transfer analysis through the liner were carried out in order to capture more realistically not only the flow field but also the liner temperatures.

Detailed post processing analysis including temperature, velocity, total pressure, reaction rate and equivalence ratio fields in the various meridian planes (α) and orthogonal planes (β) of the combustor either for natural gas or biogas were carried out.Combustor models 59 and 60 represent the final models for natural gas and biogas, respectively, with the only modification between them being the fuel nozzle diameter; this means that the combustor and injector itself can be maintained the same while only the change of the back plate that hoses the fuel nozzle is necessary.

Some features of models 59 (60 for biogas) can be highlighted:

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CHAPTER 8. CONCLUSIONS 216

• The flames are well centered not touching the liner and barely interacting with film cooling;

• Each film cooling is integrated with each other;

• In the dilution zone a satisfactory dilution is provided with the resulting low patter factor 0.16;

• Outlet mass weighted average total temperature is close to the target value of 1223 K;

• Total mass flow rate is closer to the target of 7.62 kg/s, therefore the combustor allows for an approx. 1500 kW Micro Gas Turbine;

• Total pressure drop (including hot and cold losses) results low: 1.6%;

• Liner temperatures lie bellow the safety threshold of 1150 K;

• Regarding the flame structure,

– biogas flame (model 60) in slightly longer than natural gas flame (model 59), a result that is in agreement with pre-mixed flame theory;

– in addition, both flames are well anchored and are generated from a well mixed fuel-air mixture, low σphi;

– combustor air partioning, dilution and cooling division, are substantially the same in either models, 59 and 60;

• Combustor emissions either operating with biogas or natural gas presents low CH4 and CO emissions.

The novelty feature of this study may consist in the design of a simple yet well- performing tangential injector for a reverse flow annular combustor. Furthermore, the provision of film cooling also has been done using easy to manufacture technologies, i.e., splash rings.

There are few published design procedures in literature, even fewer with a conjugate heat transfer fluid dynamic analysis. Notwithstanding, there are further studies that could be carried on using this thesis content as a starting point, these include:

• Futher investigation of the approximation regarding the turbine-compressor matching mentioned in Chapter 3;

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CHAPTER 8. CONCLUSIONS 217

• Study of utilization of other fuel mixtures (syngas originated from biomass for example) in the combustor;

• Study of off-design performance and emissions since most micro gas turbines operate in partial load quite often;

• Improvement of pollutants’ formation model, specially regarding NO formation considering the discussion of Section 5.3.

• Multidisciplinary design optimization of the combustor aerodynamic performance and thermo-mechanical resistance using Genetic Algorithm, Artificial Neural Networks and an integrated Python script that is able to manage MS Excel, AutoCAD Inventor, Ansys FLUENT and Ansys Mechanical;

• Realization of unsteady RANS (uRANS) simulations in order to identify the possible vortexes creation/destruction time-scales, aiding in subsequent exper- imental analysis.

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218

Part IV

Appendix

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219

Appendix A

Calculations for the preliminary design of the combustors

Here we show all the useful calculations and additional information that can aid the comprehension of discussed topics.

A.1 Biogases and natural gases thermodynamic properties

Biogas can be defined by its quality which is meant by the percentage of methane (in a volume basis) in the mixture. The remaining of the fuel is assumed to be carbon dioxide, even though hydrogen sulfide is present in the dry biogas and may be reduced to avoid corrosion in downstream components, the respective amount is very little, ranging from 0 % to 0.5 % in a volume basis [49], and is thus disregarded here.

Since both methane and carbon dioxide in a typical biogas application, such as compression in a boosting system and burning in a combustion chamber of a micro gas turbine apparatus, are at relatively high temperatures and low pressures, they behave as ideal gases. For this reason a biogas with a quality 60% mean not only that 60 per cent of mixture is methane but also that 60 per cent of the moles in it are composed by methane molecules (CH4). Disregarding nitrogen (N2) in the biogas¹, the remaining moles in the mixture can be assumed to be carbon dioxide

1There are some cases where the percentage of nitrogen in the biogas may not be small enough to be neglected, as in the case where air in injected at the top of reactor during the rough hydrogen sulfide removal (See Section 2.5.2)

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APPENDIX A. CALCULATIONS FOR THE PRELIMINARY DESIGN OF THE

COMBUSTORS 220

(CO2). Therefore, in this case, one could say that the mole fraction of methane (χCH4) equals 0.6 and that χCO2 = 0.4.

On the other hand both nitrogen and carbon dioxide are present in natural gases in small but similar concentrations. Therefore, it is a good practice to account for both in the determination of LHV of natural gases (which we assume to be a mixture of CH4, CO2 and N2) and on subsequent calculations.

A.1.1 Lower Heating Value “LHV”

Consider 1 mole of gaseous fuel which behaves as an ideal gas at 25 °C and 1atm, in such conditions, this amount of gas occupies 0.0245 m³. Consider that this amount of fuel contains 60% in a mole (or volume) basis of methane whose molecular weight is 16.042 g mol⁻¹ and the remaining is carbon dioxide whose molecular weight is 44.011 g mol⁻¹. The mass of methane in the mixture is given by 0.6×16.042 = 9.625 g and the mass of the mixture is given by 0.6 × 16.042 + 0.4 × 44.011 = 27.230 g. Since the only fuel in the mixture is methane (being carbon dioxide an inert) and its Lower Heating Value (LHV ) at 25 °C and 1atm is 50 050 kJ kg⁻¹ [29], the LHV of the mixture can be calculated by 9.625×50050

27.230 = 17 692 kJ kg⁻¹.

Proceeding analogously to what described in previous paragraph but considering the presence of nitrogen gas, a typical natural gas, which we refer as one whose χ_CH₄ = 0.9902, χCO2 = 0.0015 and χN2 = 0.0083 has LHV = 49 127 kJ kg⁻¹.

A.1.2 Molecular weight and gas constant “R”

The molecular weight of the fuel mixture containing 60% of methane is simply given by MWf = 27.230 g mol⁻¹, calculated above. This value is used in the determination of the fuel gas constant (R) that is used in its ideal gas law. It is given by dividing the universal gas constant by the molecular weight of the biogas mixture: R = ^8.31447_27.230 = 0.305 kJ kg⁻¹K⁻¹.

The natural gas whose composition is indicated in Table 6.3 has R = 0.514 kJ kg⁻¹K⁻¹.

A.1.3 Fuel specific mass “ρ_f”

Before reaching the injection nozzles, the fuel needs to be compressed to a pressure slightly higher than the combustion chamber pressure in the combustion zone. Since, for the 100 kW MGT, the inlet total pressure in the combustor is 430 000 Pa, we can assume, for the purpose of this section, that the pressure at injection nozzles outlet could be set as 435 000 Pa, i.e. setting the boosting system to operate with pressure ratio of 4.29. Being the fuel compressed from atmospheric pressure (101 325 Pa).

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COMBUSTORS 221

In order to use the ideal gas law to determine the specific mass of fuel at injec- tion conditions (ρf), besides the pressure (456 975 Pa) and the gas constant (R = 0.305 kJ kg⁻¹K⁻¹), we need to know the temperature at injection (Tinj). The sim- plest approach to determine Tinj is assuming an isentropic compression of the fuel with a pressure ratio of 4.29 and initial (ambient) temperature of 298.15 K. The average specific heat ratio of the fuel (γf) for the given temperature range is also necessary to calculate the injection temperature after compression and is determined iteratively knowing:

the isentropic compression formula²:

T_inj = 298.15 × 4.29^{γf −1}^γf

the calculation of the average specific heat ratio (the bar denotes here average in the temperature range):

¯

γ_f = γ_f(298.15) + γf(Tinj) 2

the definition of the specific heat ratio:

γf(T ) ≡ c_p,f(T ) c_p,f(T ) − R

and that the specific heat of the fuel (¯cp,f), an ideal gas mixture, similar to the approach adopted to determine the LHV is a weigthed average in a mole basis of the specific heats of methane and carbon dioxide, both functions of temperature solely (as any ideal gas) and can be described by polynomials [29]:

¯cp,f(T ) = χCH4 ·¯cp,CH4(T ) +χCO2 ·¯cp,CO2(T )

¯cp,CH4(T ) = 19.89 + 5.024 81 × 10⁻²T + 1.269 × 10⁻⁵T²+

−11.01 × 10⁻⁹T³

¯cp,CO2(T ) = 22.26 + 5.981 × 10⁻²T −3.501 × 10⁻⁵T²+ +7.469 × 10⁻⁹T³

2For the design of the 1500 kW MGT the boosting system pressure ratio is set as 6.11.

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COMBUSTORS 222

where the bar over the variables denotes here that the specific heat is in mole basis³. Dividing by the MWf we obtain the specific heat in kilogram basis:

c_p,f(T ) = ¯cpf(T ) M W_f

For the natural gas, after some iterations: Tinj = 408.82K. Using the ideal gas law, it is possible to obtain ρf = 2.071 kg m⁻³. Considering the biogas specified, it results that Tinj = 407.71K and ρf = 3.494 kg m⁻³.

A.2 Fuel flow rate required in the combustion chamber “ ˙ m

_f

”

Using the nomenclature of Figure 6.1, we now recall that the combustion chamber (CC) is a steady-flow device in which the stream of compressed air ( ˙m1) after passing the regenerator enters with an inlet total temperature (T05) participates in a com- bustion process requiring a fuel flow ( ˙mf) and the resulting exhaust gases exits with a specified outlet total temperature (T03). Fuel entering the CC can provide sensible heat if its temperature (Tinj) is higher than 298 K and will provide theoretically the full amount of the energy designated by its LHV during combustion. Considering the averaged values of specific heats of air cp,a and product gases cp,g the energy balance in the combustion chamber is given by:

( ˙mf+ ˙m1)cp,g(T03−298)− ˙mfLHV − ˙mfc_p,f(Tinj−298)− ˙m1c_p,a(T05−298) = 0 (A.1) Note that the flow of product gases is equal to the sum of fuel and air flows and that the reactive form of energy equation with one inlet, one outlet in steady flow has been used. Usually the ratio of fuel to combustor air flow is designated by f, i.e.

˙ mf

˙

m1 = f. Considering the inputs in the Natural gas case: cp,a = 1.123 kJ kg⁻¹K⁻¹, c_p,g = 1.218 kJ kg⁻¹K⁻¹, T05 = 893.15 K, T03 = 1223.15 K, LHV = 49 127 kJ kg⁻¹, T_inj = 408.82 K and cp,f = 2.577 kJ kg⁻¹K⁻¹, the balance in the CC results in f = 0.0095. For the biogas with χCH4 = 0.6, f results equal to 0.0275, approximately three times the fuel required in natural gas case.

A.2.1 Combustion efficiency “η_b”

If the residence time of fuel in the combustion zone is not long enough for the completion of combustion, the fuel to air ratio necessary to raise the temperature in

3kJ kmol⁻¹K⁻¹

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COMBUSTORS 223

the CC may be slightly higher than the theoretical value calculated previously. For the case of gaseous fuels, this residence time may be enough for chemical reactions completion. The combustion efficiency is defined as

ηb = f f_actual

where factual is the actual fuel to air ratio necessary to raise the temperature from T05to T03. Notwithstanding, ηb will be in correspondence to NASA combustion efficiency of 100%. The results remain unchanged, factual = 0.0275 for biogas and f_actual= 0.0095 for natural gas. The fuel flow rate can be calculated with

˙mf = ˙m1 × f_actual.

A.3 Combustion air fraction “α”

In Section A.2 we determined the fuel flow to be injected in the combustion chamber per unit of air mass flow rate entering it to guarantee a certain overall raise in temperature. In this section we focus on the region of the combustion chamber where the chemical reactions actually take place, i.e. the combustion zone. All the fuel injected in the CC is injected in this zone and the amount of air directed to it serves for combustion purposes; not for cooling or dilution purposes. Such amount of air depends on the equivalence ratio chosen and the fuel quality⁴as shown below.⁵ The global reaction of combustion between the fuel mixture (valid either for biogases and natural gases) and air is given by (as indicated in Section 6):

CH4+ (^χ_χ^CO_CH²

4)CO2+ (_χ^χ_CH^N²

4)N2+_Φ²(O2+ 3.76 N2) −−→

(1^{+ χ}_χ^CO_CH²

4)CO2+ 2 H2O + 2 (^1-Φ_Φ )O2+ (^7.52_Φ ^{+ χ}_χ_CH^N²

4)N2. The fuel is represented by CH4+(^χ_χ^CO_CH²

4)CO2+(_χ^χ_CH^N²

4)N2(with χCH4+χCO2+χN2 = 1), the oxidant (in this case the air) is represented by _Φ²(O2 + 3.76 N2) and the

4As explained in Section A.1.

5The choice of the equivalence ratio (Φ) can be done after knowing the fuel quality and the resulting maximum temperature of products after combustion (adiabatic flame temperature) and nitrogen oxide mechanism reaction rates since both control, at least, the thermal NOx formed. In simple terms, decreasing the fuel quality reduces the adiabatic flame temperature and NOx reaction rates of formation such that a higher Φ could be chosen for nominal operation when using biogas.

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COMBUSTORS 224

products are represented by the right side of the reaction. The stoichiometric air-to- fuel ratio (AF Rst) is calculated by setting the equivalence ratio Φ = 1 and dividing the mass of oxidant by the mass of fuel required:

AF R_st = (2 × 32 + 7.52 × 28)/(1 × 16.042 +χ_CO₂ χ_CH₄

×44.011 + χ_N₂ χ_CH₄

×28) AF R_st results 6.05 for the biogas (χCH4 = 0.6; χCO2 = 0.4) and AF Rst = 16.80 for the natural gas (χCH4 = 0.9902; χCO2 = 0.0015).

When Φ is set, the air-to-fuel ratio (AF R) to be adopted in the combustion zone of the combustion chamber can be determined by:

AF R= AF R_st Φ

Choosing Φ = 0.50 either for the biogas and for the natural gas, the AF R to be used result 12.10 and 33.60, respectively.

Noting that factual is the actual fuel to air ratio referred to the whole CC, that AF R is the air to fuel ratio to be adopted in the combustion zone and that the whole fuel injected in the CC is injected in the combustion zone (through holes in the swirlers), the calculation of the the combustion air fraction (α) is simply done by:

α= factual× AF R

Where the denominator of factual and the numerator of AF R have cancelled out each other, both denoting the entire air mass flow that enters the CC. For the biogas α= 0.333, while for the natural gas α = 0.319.

A.4 Mole flow rate leaving combustor

The mass flow rate of air that does not participate in combustion (excess air) is given by ˙m1(1−α). The mole flow rate of excess air is given by dividing it by the molecular weight of dry air⁶ (^m^˙_{M W}¹^(1−α)_air ). Analogously, the mass flow rate that participates on combustion is α ˙m1. The mole flow rate of combustion air is _{M W}^{α ˙}^m_air¹ . According to the global reaction, when ²/_Φ·4.76 moles of air react, there is production of

(1 + ^χ_χ^CO2

CH4) + 2 + 2(^1−Φ_Φ ) + (^7.52_Φ + _χ^χ^N2

CH4)

6M Wair= 28.840g/mol.

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COMBUSTORS 225

moles of products.

Therefore, the total mole flow rate leaving the combustor is given by:

m˙1(1−α)

M Wair + _{M W}^{α ˙}^m_air¹ _2.76^Φ (1 + ^χ_χ^CO2

CH4) + 2 + 2(^1−Φ_Φ ) + (^7.52_Φ + _χ^χ^N2

CH4)= 25.387mol/s

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226

Calculations for the preliminary design of the combustors

Chapter 8 Conclusions

Part IV

Appendix

Appendix A

Calculations for the preliminary design of the combustors

A.1 Biogases and natural gases thermodynamic properties

A.2 Fuel flow rate required in the combustion chamber “ ˙ m

”

A.3 Combustion air fraction “α”

A.4 Mole flow rate leaving combustor

Appendix B

Quoted drawing of the combustor

for the 1500 kW micro gas turbine

- preliminary design