**3. Laboratory burners**

appropriate in several works (see for example [20, 32–36]). The beta function requires the first and second moments, thus the SGS joint PDF is expressed as

progress variable and mixture fraction respectively. Note that here the two PDFs are treated independently, which is usually acceptable in LES with an appropriate grid size [37]. The SGS variances obtained using their transport equations are better than using algebraic expressions since convective and diffusive processes are

*<sup>c</sup>* and *σ*<sup>2</sup>

� 2*ρ*~*εξ* þ 2*ρ*

for the SGS variance of progress variable. From left to right the various terms in the above equations represent total derivative, effective diffusion, scalar dissipation, turbulent production and source term. The evaporation of droplets contributes

expression consistent with Eq. (4). The evaporation and the spray model in general are out of the scope of this section. For the specific simulations to be presented in Section 4, a Lagrangian approach is used for the two-phase flow, with parcel sampled using a Rosin-Rammler distribution and the Sattelmayer correlation for the initial Sauter mean diameter (SMD) [38]. Only secondary breakup is considered using the process described in [39], and a rapid mixing formulation for the droplet

The scalar dissipation rate (SDR) terms in Eqs. (5) and (6) need closure. The

works have suggested that this constant is to be revised in case of liquid fuel due to the evaporation source term in Eq. (5) [27]. For the progress variable SGS variance, it is shown in [20] that the reactive term in this equation is of leading order at least for Δ of sizes comparable or larger than the flame thickness, and thus the SDR has to balance the sources coming from reaction and turbulence. Hence, the linear relaxation model is unsuitable on physical grounds. To justify the use of linear relaxation model, a delta or three-delta function is used sometimes instead of the Beta function in Eq. (4) so that *<sup>c</sup>ω*\_ � <sup>~</sup>*cω*\_ <sup>¼</sup> 0 in Eq. (6). This, however, creates a conflict since

flamelet modelling in the context of LES to take into account the correct reactionturbulence-diffusion balance led to appearance of more sophisticated, yet simple, model for the SDR of progress variable. One recent development in this sense is the SDR closure of Dunstan et al. [41], which approaches the linear relaxation concept in the limiting behaviour of non-reactive mixture and is thus more recommended. This model has been used in many past studies for different combustion regimes

The set of equations shown above is used in conjunction with the LES equations for mass and momentum, which are the same for reacting and non-reacting flows, see for example [2, 3] for a more detailed explanation. In principle, the temperature and density fields can be also computed *a priori* using an equation consistent to (4) and accessed in runtime using the controlling variables. In order to account for possible non-adiabatic

*<sup>c</sup>* changes without the reactive term. More recently, revision of the

*νt Sct*

*νt Sct*

*<sup>ξ</sup>* are the SGS variances of the

<sup>∇</sup>~*<sup>ξ</sup>* � <sup>∇</sup>~*ξ*Þ þ *<sup>ρ</sup>S,* (5)

<sup>∇</sup>~*<sup>c</sup>* � <sup>∇</sup>~*c*Þ þ <sup>2</sup> *<sup>c</sup>ω*\_ � <sup>~</sup>*cω*\_ (6)

*<sup>ξ</sup>*, with *C<sup>ξ</sup>* ≈ 2, is well accepted [5]. Recent

*<sup>c</sup>*. The latter is closed with an

, where *σ*<sup>2</sup>

*ξ* 

*Environmental Impact of Aviation and Sustainable Solutions*

*Dt* <sup>¼</sup> <sup>∇</sup> � <sup>D</sup>*eff*∇*σ*<sup>2</sup>

for the mixture fraction variance, and

*Dt* ≈ ∇ � <sup>D</sup>*eff*∇*σ*<sup>2</sup>

important at subgrid scales [20]. These equations are written as:

*c* � <sup>2</sup>*ρ*~*ε<sup>c</sup>* <sup>þ</sup> <sup>2</sup>*<sup>ρ</sup>*

*<sup>ξ</sup>* and the subgrid reaction processes contribute to *σ*<sup>2</sup>

evaporation. More details can be found in [23, 27, 40].

linear relaxation model, <sup>~</sup>*εξ* <sup>¼</sup> *<sup>C</sup><sup>ξ</sup> <sup>ν</sup>t=*Δ<sup>2</sup> *<sup>σ</sup>*<sup>2</sup>

[20, 22, 24, 36] (see also Sections 3 and 4).

*ξ* 

*<sup>P</sup>*ð Þ¼ *<sup>ζ</sup>; <sup>η</sup> β ζ*;~*c; <sup>σ</sup>*<sup>2</sup>

*c β η*j*ζ*; <sup>~</sup>*ξ; <sup>σ</sup>*<sup>2</sup>

> *ρ Dσ*<sup>2</sup> *ξ*

*ρ Dσ*<sup>2</sup> *c*

the meaning of *σ*<sup>2</sup>

**50**

to *σ*<sup>2</sup>

For practical jet engines, it is technically difficult and very costly to conduct measurements inside the combustion chamber due to the extremely hostile conditions and complex geometry. Therefore, laboratory burners not only play a crucial role in experimental combustion research but also serve as a main source for CFD model validation. In the past, the majority of the modelling efforts were devoted to flames in simple geometry such as jet flames and bluff-body or swirl stabilised flames in an open environment. Many of these flames have been benchmarked as standard model validation cases documented in the well-known TNF Workshop [43]. Over the last few decades, a large number of combustion models including most of those discussed earlier in Section 2 have been tested using the TNF benchmark flames [44]. Despite the different models used, the computational results converge to a similar level of very satisfactory accuracy when compared with measurements for the main flow and flame statistics. For example, the transient ignition of a lifted methane-air jet flame [45] was simulated using FlaRe [46], conditional moment closure (CMC) [47], thickened flame (TF) [48] and transported PDF with Eulerian stochastic fields (TPDF/ESF) [49] approaches, all showing comparably good agreement with the measurements for the flame upstream propagation. However, this level of general agreement among different models is yet to be achieved for more complex engine-relevant geometry and conditions. Therefore, this section focuses on the state-of-the-art laboratory gas turbine model combustors (GTMCs). In order to demonstrate the current CFD capabilities of tackling the various issues in these combustors, two cases, for single and multiple burner configurations, are considered.

#### **3.1 Single burner with dual swirlers**

The dual-swirl GTMC experimentally investigated by Meier et al. [50, 51] at the German Aerospace Center (DLR) is of interest. The schematic of this GTMC

#### **Figure 1.**

*The DLR dual-swirl combustor: (a) schematic of the experimental setup and (b) typical flame surface marked using ω*\_ ∗ *<sup>c</sup> = 200 kg/m<sup>3</sup> /s, coloured by temperature.*

[50, 51] and a typical computed flame surface using LES [24] are shown in **Figure 1**. This burner has a single nozzle head with dual-swirl air passages, which is a common design in modern jet engines to achieve fast fuel-air mixing. The methane gas injector was modified from a practical air-blasting liquid fuel injector mounted on the wall in between the two air nozzles. The experiments were conducted at atmospheric pressure and the operating range investigated was from 5 to 35 kW with the equivalence ratio varying from 0.5 to 1.2, which are typical jet-engine relevant conditions [1].

reaction zone shape (represented by CH radials), temperature and fuel concentration distributions in the combustion chamber. It can be seen that the overall behaviours of these quantities are captured quantitatively in the simulation, suggesting the accuracy of these CFD calculations has reached a sufficient level for practical design purposes. Here it is of particular practical importance that the change in the

*Typical comparison between LES results and measurements for flames A and B: (a) mid-plane mean concentration of CH radials, mean radial variation of (b) temperature and (c) fuel mass fraction.*

*The Role of CFD in Modern Jet Engine Combustor Design*

*DOI: http://dx.doi.org/10.5772/intechopen.88267*

To obtain the experimental time-averaged statistics shown in **Figure 2**, a 5-Hz laser system was used [50, 51] and no time-resolved measurement was available at the time. High-speed laser facilities have advanced rapidly in recent years allowing for measurements taken at a repetition rate up to several tens of kilo-Hertz. This hardware advancement has a significant impact on turbulent combustion experiments because the large-scale structures can now be readily resolved by the measurements in both physical space and time. From a modelling perspective, these measurements largely enrich the validation data and make it possible to assess the model capabilities of capturing transient behaviours. For the present combustor, for example, the dynamic motion of the coherent vortical structure, the so-called

flame shape from a V-form in flame A to a flat shape in flame B is correctly reproduced by the LES because the location and distribution of the flame dictates many design factors such as combustor cooling and pollutant emission control, etc. The underlying physical mechanism for this flame shape change involves a fine interplay between the fluid dynamics of the fuel/air inflows and the combustor acoustics under the operating conditions of flame B [55]. This mechanism introduces a different fuel-air mixing pattern at the nozzle exit, and this is also reflected in the downstream temperature and fuel mass fraction distributions shown in **Figure 2(b)** and **(c)**. Such mutually-interacting flow and flame dynamics cannot be captured by the conventional RANS modelling paradigm, which highlights the important role that LES can potentially play in jet engine combustor design and

development.

**53**

**Figure 2.**

Within the range of conditions operated, a variety of phenomena were observed including flame-vortex interaction [52], self-excited thermo-acoustic oscillations [53] and lean blow-out (LBO) dynamics [54] in the experiments. Three cases detailed in **Table 1** were chosen for experimental study: a thermo-acoustically stable flame, designated as flame A, an unstable flame showing self-excited thermoacoustic oscillations, called flame B, and flame C exhibiting periodic blowout and re-ignition. To investigate the rich physics exhibited in these flames, stateof-the-art laser diagnostic techniques including stereoscopic particle image velocimetry (stereo-PIV), Raman spectroscopy, laser Doppler velocimetry (LDV), OH\* /CH\* chemiluminescence and OH/CH/CH2O planar laser-induced fluorescence (PLIF), were performed and highly repetitive results were obtained. Hence, these measurements constitute a comprehensive database for rigorous combustion model assessment.

As noted earlier, only typical results are presented here for a brief demonstration of the model performance. **Figure 2** compares the measured and computed mean


#### **Table 1.** *Summary of operating conditions.*

*The Role of CFD in Modern Jet Engine Combustor Design DOI: http://dx.doi.org/10.5772/intechopen.88267*

**Figure 2.**

[50, 51] and a typical computed flame surface using LES [24] are shown in **Figure 1**. This burner has a single nozzle head with dual-swirl air passages, which is a common design in modern jet engines to achieve fast fuel-air mixing. The methane gas injector was modified from a practical air-blasting liquid fuel injector mounted on the wall in between the two air nozzles. The experiments were conducted at atmospheric pressure and the operating range investigated was from 5 to 35 kW with the equivalence ratio varying from 0.5 to 1.2, which are typical jet-engine relevant

*The DLR dual-swirl combustor: (a) schematic of the experimental setup and (b) typical flame surface marked*

*/s, coloured by temperature.*

*Environmental Impact of Aviation and Sustainable Solutions*

Within the range of conditions operated, a variety of phenomena were observed including flame-vortex interaction [52], self-excited thermo-acoustic oscillations [53] and lean blow-out (LBO) dynamics [54] in the experiments. Three cases detailed in **Table 1** were chosen for experimental study: a thermo-acoustically stable

thermoacoustic oscillations, called flame B, and flame C exhibiting periodic blowout and re-ignition. To investigate the rich physics exhibited in these flames, stateof-the-art laser diagnostic techniques including stereoscopic particle image

velocimetry (stereo-PIV), Raman spectroscopy, laser Doppler velocimetry (LDV),

/CH\* chemiluminescence and OH/CH/CH2O planar laser-induced fluorescence (PLIF), were performed and highly repetitive results were obtained. Hence, these measurements constitute a comprehensive database for rigorous combustion model

As noted earlier, only typical results are presented here for a brief demonstration of the model performance. **Figure 2** compares the measured and computed mean

**Flame** *ϕ***glob** *Z***glob** *m*\_ <sup>p</sup> **[g/s]** *m*\_ <sup>j</sup> **[g/s] Swirl number** *Pth* **[kW]** A (stable) 0.65 0.037 18.25 0.697 0.9 34.9 B (unstable) 0.75 0.042 4.68 0.205 0.55 10.3 C (approaching LBO) 0.55 0.031 4.68 0.15 0.55 7.6

flame, designated as flame A, an unstable flame showing self-excited

conditions [1].

**Figure 1.**

*<sup>c</sup> = 200 kg/m<sup>3</sup>*

*using ω*\_ ∗

OH\*

assessment.

**Table 1.**

**52**

*Summary of operating conditions.*

*Typical comparison between LES results and measurements for flames A and B: (a) mid-plane mean concentration of CH radials, mean radial variation of (b) temperature and (c) fuel mass fraction.*

reaction zone shape (represented by CH radials), temperature and fuel concentration distributions in the combustion chamber. It can be seen that the overall behaviours of these quantities are captured quantitatively in the simulation, suggesting the accuracy of these CFD calculations has reached a sufficient level for practical design purposes. Here it is of particular practical importance that the change in the flame shape from a V-form in flame A to a flat shape in flame B is correctly reproduced by the LES because the location and distribution of the flame dictates many design factors such as combustor cooling and pollutant emission control, etc. The underlying physical mechanism for this flame shape change involves a fine interplay between the fluid dynamics of the fuel/air inflows and the combustor acoustics under the operating conditions of flame B [55]. This mechanism introduces a different fuel-air mixing pattern at the nozzle exit, and this is also reflected in the downstream temperature and fuel mass fraction distributions shown in **Figure 2(b)** and **(c)**. Such mutually-interacting flow and flame dynamics cannot be captured by the conventional RANS modelling paradigm, which highlights the important role that LES can potentially play in jet engine combustor design and development.

To obtain the experimental time-averaged statistics shown in **Figure 2**, a 5-Hz laser system was used [50, 51] and no time-resolved measurement was available at the time. High-speed laser facilities have advanced rapidly in recent years allowing for measurements taken at a repetition rate up to several tens of kilo-Hertz. This hardware advancement has a significant impact on turbulent combustion experiments because the large-scale structures can now be readily resolved by the measurements in both physical space and time. From a modelling perspective, these measurements largely enrich the validation data and make it possible to assess the model capabilities of capturing transient behaviours. For the present combustor, for example, the dynamic motion of the coherent vortical structure, the so-called

precessing vortex core (PVC), and the thermo-acoustic oscillation (TAO) were both identified using 10-kHz PIV measurements [52, 56]. **Figure 3** shows a typical comparison of measured and computed axial velocity spectra for two representative monitoring points (marked in **Figure 1a**) in flames A and B. These two points are located in the swirling jet and inner shear layer (between the jet and inner recirculation zone) respectively. The velocity spectra show strong dependence on the location and also behave quite differently in the two flames. The pronounced peaks correspond to the dominant frequencies for the PVC and TAO. These frequencies with their respective amplitudes are captured reasonably well in the simulation despite a considerable under-estimation of the PVC frequency for flame A. This suggests that the LES modelling framework and the FlaRe combustion submodel described in Section 2 are adequate to capture the complex flow/flame/ acoustic dynamics in this dual-swirl combustor, which are similar to those occurring in real gas turbine combustors.

As modern jet engines operate at fuel lean conditions to achieve low emissions, the flame is prone to local extinctions or even complete blow-off in the worst scenario. Such events are disastrous when occurring at high altitudes, where the engine is difficult to relight due to the low temperature, pressure and O2 level environment. Therefore, the physical mechanism driving flame blow-off deserves a better understanding, which helps to develop not only control strategies but also predictive CFD tools for the engine design. To this end, the approaching blow-off flame C in **Table 1** was investigated experimentally by Stöhr et al. [54]. It was observed that the flame was highly unstable exhibiting sudden lift-off events with vanished flame root. Recently, this flame has been tackled using LES with FlaRe [57] and CMC [58] subgrid combustion closures, both showing a good agreement between the simulation and experiment for the flow and flame statistics. Although the flame root dynamics associated with the PVC motion was captured by both combustion models, the extreme lift-off event was only shown in the study using FlaRe [57]. This is probably due to the limitation of non-premixed CMC with a single conditioning variable-mixture fraction, while the flame root experiences strong partially premixing effects during lift-off [59]. To illustrate this lift-off event in a clear manner, **Figure 4** depicts the typical computed (using FlaRe [57]) and measured [54] flame roots for a stable instant at *t* ¼ 0 ms and an extinguished instant at *t* ¼ 40 ms. Despite the qualitative nature of this comparison, the simulated flame root behaviour agrees quite well with that measured using high-speed OH-PLIF and details can be found in [57]. Remarkably, the flame root extinction is successfully captured by an unstrained flamelet model, which suggests that the subgrid straining effect is not of leading order in the extinction process. This has a further implication that the cost-effective flamelet models can be used for

prediction of blow-off, which itself is a slow (usually hundreds of ms) and hence computationally expensive process to simulate for practical combustor conditions.

*illustrated by filtered reaction rate contours and OH-PLIF images respectively.*

*The Role of CFD in Modern Jet Engine Combustor Design*

*DOI: http://dx.doi.org/10.5772/intechopen.88267*

*LES [57] and experimental [54] snapshots of flame root overlaid by velocity arrows (coloured by magnitude) for typical stable (lower row) and extinguished (upper row) instants. The computed and measured flame is*

In most modern jet engines, multiple burners are aligned circumferentially to achieve high thermal power within a compact volume. As a result, the unsteady heat release of these individual flames interact with the annular geometry of the combustion chamber, which gives rise to self-excited azimuthal instabilities [60]. Compared to longitudinal modes observed for a single flame, e.g., flame B of the DLR dual-swirl burner discussed earlier in this section, azimuthal modes are more dominant and destructive in practical applications because the circumference is usually shorter than the longitudinal length of the combustor resulting in higher resonant frequencies [61]. Thus, azimuthal instability is recognised as a primary

Due to the complexity and high cost, only few laboratory model annular combustors have been studied experimentally so far, e.g., [62, 63], and the numerical works are scarce. To bridge this gap and gain physical insight into azimuthal instabilities, the annular burner of Worth et al. [62, 64] is simulated using the FlaRe model in this subsection. A photograph along with the schematic of this burner is shown in **Figure 5**. Fully premixed ethylene-air mixture was supplied at the bottom of the plenum and then passed through a honeycomb flow straightener before splitting into 12 bluff-body tubes by a hemispherical flow divider. Both swirling [62] and non-swirling [64] cases were investigated with and without the swirlers below the bluff-bodies. The experiments were operated at room temperature and atmospheric pressure. A bulk mean velocity evaluated at the bluff-body exit was kept constant at 18 m/s for all cases and pronounced azimuthal instability was observed for equivalence ratio ranging from *ϕ* ¼ 0*:*8 to 1.0. Three pressure transducers, denoted as P1, P2 and P3, were mounted on the tube wall 45 mm upstream of the bluff-body exit and they were separated by 120° to measure the azimuthal

The typical computed flame structures of the non-swirling and swirling cases for *ϕ* ¼ 0*:*8 are presented in **Figure 6** using volumetric rendering of the reaction rate for the 12 burners. The instantaneous axial velocity field is also shown for the mid-

**3.2 Multi-burner annular combustor**

**Figure 4.**

issue for jet engine manufacturers.

pressure waves travelling in the *θ*-direction.

**55**

#### **Figure 3.**

*Comparison of axial velocity spectra for two monitor points (marked in Figure 1a) located in: (a) swirling jet and (b) inner shear layer near the nozzle exit.*

**Figure 4.**

precessing vortex core (PVC), and the thermo-acoustic oscillation (TAO) were both identified using 10-kHz PIV measurements [52, 56]. **Figure 3** shows a typical comparison of measured and computed axial velocity spectra for two representative monitoring points (marked in **Figure 1a**) in flames A and B. These two points are located in the swirling jet and inner shear layer (between the jet and inner recirculation zone) respectively. The velocity spectra show strong dependence on the location and also behave quite differently in the two flames. The pronounced peaks correspond to the dominant frequencies for the PVC and TAO. These frequencies with their respective amplitudes are captured reasonably well in the simulation despite a considerable under-estimation of the PVC frequency for flame A. This suggests that the LES modelling framework and the FlaRe combustion submodel described in Section 2 are adequate to capture the complex flow/flame/ acoustic dynamics in this dual-swirl combustor, which are similar to those occur-

As modern jet engines operate at fuel lean conditions to achieve low emissions,

the flame is prone to local extinctions or even complete blow-off in the worst scenario. Such events are disastrous when occurring at high altitudes, where the engine is difficult to relight due to the low temperature, pressure and O2 level environment. Therefore, the physical mechanism driving flame blow-off deserves a better understanding, which helps to develop not only control strategies but also predictive CFD tools for the engine design. To this end, the approaching blow-off flame C in **Table 1** was investigated experimentally by Stöhr et al. [54]. It was observed that the flame was highly unstable exhibiting sudden lift-off events with vanished flame root. Recently, this flame has been tackled using LES with FlaRe [57] and CMC [58] subgrid combustion closures, both showing a good agreement between the simulation and experiment for the flow and flame statistics. Although the flame root dynamics associated with the PVC motion was captured by both combustion models, the extreme lift-off event was only shown in the study using FlaRe [57]. This is probably due to the limitation of non-premixed CMC with a single conditioning variable-mixture fraction, while the flame root experiences strong partially premixing effects during lift-off [59]. To illustrate this lift-off event in a clear manner, **Figure 4** depicts the typical computed (using FlaRe [57]) and measured [54] flame roots for a stable instant at *t* ¼ 0 ms and an extinguished instant at *t* ¼ 40 ms. Despite the qualitative nature of this comparison, the simulated flame root behaviour agrees quite well with that measured using high-speed OH-PLIF and details can be found in [57]. Remarkably, the flame root extinction is successfully captured by an unstrained flamelet model, which suggests that the subgrid straining effect is not of leading order in the extinction process. This has a

further implication that the cost-effective flamelet models can be used for

*Comparison of axial velocity spectra for two monitor points (marked in Figure 1a) located in: (a) swirling jet*

ring in real gas turbine combustors.

*Environmental Impact of Aviation and Sustainable Solutions*

**Figure 3.**

**54**

*and (b) inner shear layer near the nozzle exit.*

*LES [57] and experimental [54] snapshots of flame root overlaid by velocity arrows (coloured by magnitude) for typical stable (lower row) and extinguished (upper row) instants. The computed and measured flame is illustrated by filtered reaction rate contours and OH-PLIF images respectively.*

prediction of blow-off, which itself is a slow (usually hundreds of ms) and hence computationally expensive process to simulate for practical combustor conditions.
