Research Article  Open Access
Ali Cemal Benim, Sohail Iqbal, Franz Joos, Alexander Wiedermann, "Numerical Analysis of Turbulent Combustion in a Model Swirl Gas Turbine Combustor", Journal of Combustion, vol. 2016, Article ID 2572035, 12 pages, 2016. https://doi.org/10.1155/2016/2572035
Numerical Analysis of Turbulent Combustion in a Model Swirl Gas Turbine Combustor
Abstract
Turbulent reacting flows in a generic swirl gas turbine combustor are investigated numerically. Turbulence is modelled by a URANS formulation in combination with the SST turbulence model, as the basic modelling approach. For comparison, URANS is applied also in combination with the RSM turbulence model to one of the investigated cases. For this case, LES is also used for turbulence modelling. For modelling turbulencechemistry interaction, a laminar flamelet model is used, which is based on the mixture fraction and the reaction progress variable. This model is implemented in the open source CFD code OpenFOAM, which has been used as the basis for the present investigation. For validation purposes, predictions are compared with the measurements for a natural gas flame with external flue gas recirculation. A good agreement with the experimental data is observed. Subsequently, the numerical study is extended to syngas, for comparing its combustion behavior with that of natural gas. Here, the analysis is carried out for cases without external flue gas recirculation. The computational model is observed to provide a fair prediction of the experimental data and predict the increased flashback propensity of syngas.
1. Introduction
Modern gas turbines are to provide high efficiency, reliability, and stability, while meeting strict low emission requirements, with emerging additional requirements such as fuel flexibility. In that respect, the combustor is obviously a core component, and a detailed understanding of the complex flow, heat, and mass transfer processes in the flame is of great importance. Experimental investigation of gas turbine combustion is difficult and can provide only limited information due to practical limitations. Numerical simulations can provide detailed insight and reduce the number of costly experiments. Nevertheless, the highly complex processes in the combustor are difficult to model and the simulations are afflicted with inaccuracies. Thus, development of mathematical and numerical models for GTC and their experimental validation have been a continuous endeavor, to which the present work is aimed to provide a contribution.
Fureby [1] applied an EDCtype combustion model in combination with LES to analyze GTC. Lörstad et al. [2] analyzed the reacting flow in the Siemens SGT800 burner experimentally and numerically applying RANS and LES approaches, along with an EDCtype combustion model, a focus of the work being on the effect of burner fuel distribution on flame dynamics. A recent study on URANS and LES modelling of GTC for a Siemens scaled combustor was presented by Goldin et al. [3] using the flamelet generated manifold model as combustion model in combination with LES and turbulent flame speed models in combination with URANS. They found that LES predictions of the mean and RMS axial velocity, mixture fraction, and temperature fields do not show an improvement over the RANS. Again recently, ALSTOM’s reheat combustor was successfully analyzed by Kulkarni et al. [4] applying a novel combustion model based on a composite reaction progress variable, along with a tabulated chemistry approach and the stochastic fields turbulencechemistry interaction model.
In the simulation of GTC, one of the main challenges is turbulence modelling. This is caused by the highly nonisotropic turbulence structure, which is created by the high swirl levels applied to induce a flamestabilizing vortex breakdown. In the previous work of present authors [5–7], it was shown that a threedimensional and unsteady formulation that can resolve the unsteadiness of coherent structures is necessary for achieving sufficient accuracy in such flows (as also confirmed by the recent work of other authors [1–4]). This requirement is fulfilled (at different levels) by URANS and LES approaches. In the present application, a URANS formulation is used, as the basic modelling approach, in combination with a twoequation turbulence model. In modelling turbulent swirling flows, the RSM has generally been found to be more accurate compared to twoequation turbulence models (while convergence difficulties may impede its application in some cases). We have found, however, that this superiority of the RSM is given basically for the RANS, that is, steadystate formulations. In an unsteady formulation such as URANS, we quite often observed that twoequation models perform similarly well. In this case, the use of a twoequation turbulence model is reasonable, since the additional computational overhead of the RSM (5 additional transport equations and less superior convergence behavior) does not seem to be justified. Still, for comparison, URANS is applied also in combination with the RSM to one of the investigated cases. For this case, LES is also used for turbulence modelling.
Modelling of the turbulencechemistry interaction is the further main challenge, of course. A method, which is found to be adequate in modelling turbulencechemistry interaction is the EDC [8], as successfully applied to GTC by several authors [1]. A drawback of EDC is, however, that an individual transport equation needs to be solved for each species, which increases the computational demand proportionally with the considered number of species. For meeting the current demands of combustion technology, reaction mechanisms with always increasing level of sophistication are required that incorporate a rather large number of species. In combination with computationally demanding turbulence modelling approaches such as URANS and LES, which are necessary for achieving sufficient accuracy as discussed above, the computational costs become extremely high, especially for real applications in the industrial development environment. On the other hand, the laminar flamelet method (LFM) [9] provides a very efficient way of considering detailed reaction kinetics in turbulent combustion, where a completely detailed reaction mechanism can be incorporated via a few variables that describe flamelet characteristics. Although the validity of the LFM for GTC was questioned in the past, based on Damköhler number arguments, it was shown, later on [10, 11], that purely dimensional arguments neglecting the transient effects may be misleading and typical GTC operation conditions are rather in the validity range of the LFM. Thus, the LFM is used as the turbulent combustion model in the present study. It is argued that a mixture fractionreaction progress variable characterization of the flamelets is convenient for the present partially premixed flame, as will be described in more detail below.
The computational model is applied to predict turbulent combustion in a model gas turbine combustor firing natural gas (NG) and syngas (SG). First, a validation study is performed for the NG flame with flue gas recirculation (FGR). Numerical results are compared with the experimental data, where a reasonably fair agreement is observed. Then, the validated model is applied to predict the combustion behavior of SG, in comparison to NG, without FGR.
The motivation of the present work has been the assessment of the performance of the advocated laminar flamelet method in predicting gas turbine swirl flames considering the realistic fuel injection configuration of an industrial swirl burner. Moreover, the assessment of the predictive capability of the approach for the CO and NO emissions under flue gas recirculation and using syngas as fuel (instead of natural gas) has been a further motivation. The coherent consideration of the all abovementioned aspects on the same rig and within the same modelling framework is a novelty of the present investigation.
2. The Test Case
Experiments were performed at the Turbomachinery Laboratory of Helmut Schmidt University, Hamburg. The CAD drawing of the atmospheric model combustor, which is equipped by a single swirl burner with 12 channels, is illustrated in Figure 1. The oxidizer stream passes through a hood (not displayed in the figure) and enters radially into the channels of the radial swirler.
Fuel is injected into the crossflowing air by 12 injection holes, each located at the wall of each swirler channel. After passing through the swirler channels, each of which having an inclination of 45°, the fuelair mixture enters the central convergingdiverging burner nozzle and, subsequently, into the octagonal main combustion chamber. A converging exhaust gas nozzle is attached to the combustor exit to avoid reverse flow. Based on the local unburnt bulk axial velocity and the diameter at the exit of the convergingdiverging burner nozzle, the Reynolds number turns out to be about 34,000. Assuming a perfect guidance by the swirler channels and conservation of angular momentum within the burner, and defining the swirl number as the ratio of the maximum swirl velocity to the bulk axial velocity, a swirl number of about 0.9 can be estimated at the burner nozzle outlet. A detailed description of the setup and measurement methods are provided in [12].
The combustor was designed for premixed/partially premixed operation. In the experiments [12], different fuel compositions were considered. The compositions of the NG and SG that are considered in the present work are presented in Table 1.

The measurements [12] were performed for investigating the effect of external flue gas recirculation (FGR). Thus, different oxidizer compositions were investigated [12]. The oxidizer compositions that are considered in the present study are shown in Table 2 (FGR0 corresponding to “zero” flue gas ratio, i.e., to pure air).

In the present analysis, totally three cases are analyzed: NG with FGR (NGFG20), NG without FGR (NGFGR0), and SG without FGR (SGFGR0). For the NGFG20 case, the mixture composition was adjusted to have an adiabatic flame temperature of about 1525 K (corresponding to an equivalence ratio of about 0.5, fuel and oxidizer mass flow rates being 0.0009217 kg/s and 0.03575 kg/s, and combustor inlet temperature 573 K). For SGFGR0 case, an operation point was chosen corresponding to a slightly lower adiabatic temperature of 1450 K.
3. Modelling
3.1. Grid, Boundary Conditions, and Outline of the Mathematical Model
A block structured mesh, consisting of 1.2 million cells, is used. A detailed view of the surface mesh is illustrated in Figure 2. At the fuel and oxidizer inlets, constant profiles are prescribed for velocities, temperature, and mass fractions that result from the global combustor data. At the outlet, zerogradient boundary conditions are applied for convectivediffusively transported variables, along with a constant static pressure. The noslip walls are assumed to be adiabatic. Near solid walls, the turbulence modelling is augmented by the use of standard, logarithmic wallfunctions. The nearwall grid resolution was such that the values [13] were not exceeding 120 and had an average value of approx. 50 in the burner. Although the applied nearwall resolution is not very fine (to resolve the wall boundary layers), we assume that this would not lead to a serious deterioration of the predictive capability, since the governing processes of the problem such as jet mixing or vortex breakdown are of rather freeshear layer type and, thus, not much affected by the wall boundary layers.
For the computational investigation, the finite volume method based open source CFD code OpenFOAM [13] is used, where a pressurecorrection scheme (PIMPLE, which is a combination of PISO and SIMPLE schemes) was applied for treating the velocitypressure coupling. As turbulence model, the Shear Stress Transport (SST) model [13] is applied within a URANS context as the main approach. For scalars, a gradientdiffusion approximation is used, along with the assumption of constant turbulent Schmidt numbers of value 0.7. For comparison, the Reynolds Stress Model (RSM) [14] is also used in comparison with URANS, for one of the cases. Additionally, the Large Eddy Simulation (LES) [15] approach is also employed as turbulence modelling strategy for this case, using the SmagorinskyLilly subgridscale model [15].
A secondorder upwind scheme was applied to discretize the convective terms in the transport equations for all the variables. A firstorder Euler scheme was used for time stepping, since stability problems were quite often encountered with a secondorder time discretization. The time step size is chosen in such a way that cell Courant numbers do not exceed unity. Starting from an initial field, the numerical simulations were performed for a time period, which is long enough to allow the development of a quasiperiodic flow field that is no more dependent on the initial conditions. After this state, the timeaveraging of the results was started, which was continued until the timeaveraged fields did not show any substantial change in time.
Along with the three momentum equations, the pressurecorrection equation, and two equations for the turbulence model, three additional differential transport equations (four equations, if NO is included) are solved for combustion modelling which are discussed in the following section.
3.2. The Combustion Model
The turbulencechemistry interactions necessitate the use of a combustion model, if flow turbulence is not directly simulated but modelled. In the present work, the laminar flamelet method (LFM) is used. According to the usual assumptions of the LFM [9], for a steady, onedimensional, adiabatic, laminar diffusion flame, all thermochemical dependent variables () can be expressed as unique functions of the mixture fraction and the stoichiometric value of the scalar dissipation rate asThe mixture fraction represents the mass fraction of fuel stream locally in the unburnt mixture. For , an assumed functional dependence on (e.g., as the one suggested by Peters [9]) is quite commonly used. Such functional relationships (see (1)) are obtained by performing 1D laminar flame calculations, once for all, and made available in tabulated form (flamelet libraries) for the subsequent CFD analysis. Note that the laminar flame extinguishes for a sufficiently large value of the scalar dissipation rate. This is the socalled “quenching limit.” For a quenched laminar flame, relationships of type (1) describe the nonburning state. In the turbulent flow, the average values of the thermochemical dependent variables such as the species mass fractions and the static mixture temperature can be obtained by the following expression, utilizing presumed PDFs (the expression is written for a Favreaveraged quantity but holds analogously for a Reynoldsaveraged quantity).In the above expression, a statistical independence of and is assumed along with the assumption of a singledelta PDF for . The presumed PDF for is typically controlled by its two moments, that is, the average value and the variance . The modelled timeaveraged differential transport equations of these variables [16] arewhere is a model constant ( is used). The “steady” LFM outlined above is known to perform successfully for a large class of nonpremixed flames. However, it is known [9] that it cannot accurately describe phenomena such as local extinction, reignition, and flame liftoff. Thus, it is principally not adequate for premixed/partially premixed flames like the present one.
Therefore, in the present study, a flamelet model based on the mixture fraction and the reaction progress variable () is adopted, which is more suitable for premixed/partially premixed flames. The model was originally proposed by Pierce and Moin [17] within an LES framework, who suggested a parameterization of the flamelets based on the reaction progress variable instead of the scalar dissipation rate. The complete locus of solutions of the flamelet equations results in a so called Sshaped curve, an example of which is shown in Figure 3, for the NGFGR20 case. The upper branch represents the stable burning flamelets till the turning point, which corresponds to the quenching limit. After the quenching limit the curve continues to decrease scalar dissipation rate and describes the unstable flamelets whereas the lower branch corresponds to nonburning flamelets. Pierce and Moin [17] parameterized the flamelets based on the socalled reaction progress variable by projecting the flame states horizontally along the Sshaped curve (Figure 3).
The reaction progress variable can be defined in different ways. In the present work, a temperaturebased definition is preferred (the alternative speciesbased definitions are rather difficult to handle in the present case with FGR due to the existence of combustion products at the oxidizer inlet)In (5), is the maximum static temperature locally prevailing within the stretched 1D laminar flame. and denote the unburnt and burnt equilibrium temperatures of the mixture. Please note that also depends on the scalar dissipation rate, incorporating its effect indirectly. Thus, within this concept, the laminar flamelet functional relationships are established asAssuming and are independent, with the help of presumed PDFs, the average values of the thermochemical variables are obtained in a similar fashion to (2). In the present work, a singledelta PDF is assumed for (as it was commonly assumed in the previous applications of the model including the original work of Pierce and Moin [17]). For , a beta PDF () is used. Thus, the average values of the static mixture temperature and all species mass fractions (except that of NO) are obtained fromWhat remains is the field information on the averaged progress variable to close the system. For this, a differential transport equation is solved, which is derived following Bray’s approximation [18] of the chemical source term reading asIn (8) is defined aswhere and denote volumetric heat release rate and the mean isobaric heat capacity, respectively. The volumetric heat release rate is obtained from the 1D laminar flame libraries.
Since NO reactions are very slow compared to the main combustion reactions, the extraction of NO mass fractions out of the flamelet data (see (6)) is inappropriate. Thus for NO, an additional transport equation is solved. This approach does not create a serious conflict with the detailed combustion mechanism underlying the LFM, due to the extremely small NO mass fractions having negligibly small effects on the transport processes and heat release in the flame. The modelled NO transport equation reads asThe critical issue here is the determination of the source term (). As previously demonstrated [11], a quite effective means for this purpose is the extraction of its instantaneous value out of the flamelet libraries, like many other thermochemical variables (via (6)) and obtaining the timeaveraged value (for closing (10)) by means of PDFs (see (7)). Since the source term stems from a detailed reaction mechanism, all NO formation paths are simultaneously considered, whereas the thermal NO formation is expected to be the dominating one in the present application.
The flamelet libraries (see (6)) are constructed by 1D steady, adiabatic laminar flame calculations using the FlameMaster code [19], before the field calculations of the turbulent reacting flow by means of CFD. As the underlying reaction mechanism, the GRI Mech 3.0 [20] is used, assuming a Lewis number of unity for all species. Within the subsequent CFD calculations, the local values of the Favreaveraged species mass fractions and temperature are obtained from (7), which relies on the solution of three differential transport equations for (see (3)), (see (4)), and (see (8)). If NO prediction is required, (10) is additionally solved for . The abovedescribed combustion model is implemented in OpenFOAM [13].
3.3. On the Adequacy of the Grid Resolution
A formal grid independence study was not performed. The grid is constructed based on our previous experience on similar flames [6, 7]. The following analysis of the turbulent scales of the present results indicates that the applied grid resolution is reasonably fine, based on the suggestions of Celik et al. [21] and our previous experience [6, 7]. Within the framework of LES, different measures were proposed for assessing the grid resolution, such as the Grid Index (GI) defined as ratio of the local grid size (assumed to be given by the third root of the cell volume) to the Kolmogorov length scalewithAccording to Celik et al. [21], GI should be smaller than 25, for achieving sufficient accuracy for LES. In our previous LES modelling work [7] on swirling flows, we found that the results obtained for GI ≤ 50 do not remarkably differ from those obtained for GI ≤ 25. This led to the conclusion that the criterion GI ≤ 50 was sufficient for good accuracy, at least for the present class of flow problems. In the present work, besides the URANS approach as the main turbulence modelling strategy, LES is also used. We assume that the LES grid resolution criteria can be regarded to be useful for URANS too, since URANS principally has less stringent grid resolution requirements compared to LES. Figure 4 presents the distribution of GI (see (11)) in a plane through the swirler (at the channel midheight) and in a plane through the middle of the combustor, at a time step (for the NGFGR20 flame).
(a)
(b)
One can see that there are large regions fulfilling GI < 25. In the remaining regions, the values remain mostly within the band 25 < GI < 50. Thus, the calculated GI values (Figure 4) can be interpreted to indicate a sufficiently fine grid for the present purposes.
4. Results and Discussion
The results will be presented in two parts; in the first part, the results for the NG flame with FGR (NGFGR20) will be discussed. In the second part, the results for the NG and SG flames without FGR (NGFGR0, SGFGR0) will be presented.
4.1. NG Flame with FGR
The present combustor is designed to operate in premixed/partially premixed mode [12]. The fuel jets mix into the oxidizer in the swirler channels and then along the convergingdiverging burner nozzle (Figure 1). Given the high swirl level of the flow, the sudden area expansion at the exit of the burner nozzle induces a vortex breakdown, that is, an inner recirculation zone, which shall act as an aerodynamic flame holder at which the flame front shall be anchored. Depending on the degree of mixing achieved in the burner, a premixed or partially premixed flame can result.
Although it was obvious that the LFM based on the mixture fraction and the scalar dissipation rate (see (1)–(4)) is not convenient for the present case, it was still applied to see its performance in the specific application and to demonstrate the improvement of the method by the introduction of the reaction progress variable (see (3)–(9)). Figure 5 displays the predicted temperature field at a time step in a plane through the combustor, which was calculated using the mixture fractionscalar dissipation rate based LFM (see (1)–(4)), for the NGFGR20 flame. The predicted flame burns in diffusion mode (Figure 5), and a flame liftoff could not be predicted. The rather low temperatures (<1000 K) in the swirler channels are caused by locally high strain rates and quenching effects in the close vicinity of fuel injection holes. Downstream the swirler channels, where the local strain rate is lower, locally nearstoichiometric combustion leads to high flame temperatures about 2100 K.
In the present work, the LFM based on the mixture fraction and the reaction progress variable (see (5)–(9)) is used as the combustion model. In the following, the results obtained by this model will be presented.
Distributions of the axial velocity predicted by the mixture fractionreaction progress variable LFM for the NGFGR20 flame, at two different time steps, in a plane through the combustor are presented in Figure 6, using URANSSST, URANSRSM, and LES approaches. The predicted inner recirculation zone due to vortex breakdown can be seen in Figure 6, which exhibits a quite unsteady and threedimensional structure. As expected, LES (Figure 6(c)) resolves finer structures compared to URANS (Figures 6(a) and 6(b)), whereas URANSRSM (Figure 6(b)) also seems to capture finer structures than URANSSST (Figure 6(a)). It is interesting to note that the recirculation zone is attached to the burner back plate. In the present plots in a twodimensional plane (Figure 6), the extension of the threedimensional recirculation zone to the burner back plate cannot directly be seen but deduced, for example, from Figure 6(a).
(a)
(b)
(c)
Timeaveraged predictions of the axial velocity component and the velocity magnitude, as predicted by URANSSST, URANSRSM, and LES, for the NGFGR20 flame, are shown in a plane through the combustor in Figure 7. One can see that the timeaveraged axial velocity field exhibits a bubbleshaped vortex breakdown recirculation zone (Figures 7(a), 7(c), and 7(d)). The slender negative axial velocity regions that were precessing inside the burner (Figure 6(a)) disappear in the time averaging for URANSSST (Figure 7(a)). URANSRSM predicts a quite intensive inner recirculation zone with higher negative axial velocities and a deeper extension of the timeaveraged recirculation zone into the burner, practically up to the burner back plate (Figure 7(c)). The velocity magnitude plot (Figure 7(b)) indicates the very strong vortex core in the burner, which expands downstream and extends along the combustor length.
(a)
(b)
(c)
(d)
As an indication of the flow turbulence, the distribution of the representative RMS value of the velocity fluctuations () normalized by a reference velocity () is presented in Figure 8, for a plane through the combustor. The LES results are used for this purpose. The representative is obtained from the calculated turbulence kinetic energy () from . Doing so, the turbulence kinetic energy is calculated from , where , , and represent the RMS of the three velocity components resolved by LES. As the reference velocity, the bulk axial velocity at the throat of the burner nozzle is used ( = 23 m/s). One can see that quite high turbulence intensities prevail especially in the burner nozzle and in its downstream, where the vortex breakdown occurs.
The predicted timeaveraged fields of temperature and CO mass fraction for the NGFGR20 flame resulting from URANSSST, URANSRSM, and LES calculations are displayed in Figure 9. As it can be deduced from the distributions given in Figure 9, the predictions indicate that the flame is now anchored at the burner nozzle exit, as confirmed by the experiments, and no high temperature zones exist near burner walls (Figure 5), which is important for the integrity of the hardware. One can also observe that URANSSST (Figure 9(a)) and LES (Figure 9(b)) predict a flame front, which is practically positioned just downstream the burner nozzle, whereas URANSRSM indicates a more strongly inclined flame front, reaching deeper into the burner on its axis (Figure 9(c)). LES (Figure 9(d)) predicts a slightly thicker flame brush than the both URANS solutions (Figures 9(a) and 9(c)). The combustion takes place in the premixed mode, where a maximum temperature of about 1500 K is achieved behind the curved flame brush (Figures 9(a), 9(c), and 9(d)). The CO mass fraction quickly attains a local maximum in the reaction zone (Figure 9(b)) and gets depleted downstream.
(a)
(b)
(c)
(d)
The predicted and measured profiles of timeaveraged temperature along the “combustor axis” and along the “evaluation line” (Figure 1) are compared in Figure 10. Note that the displayed domain in Figure 10 covers the combustor domain downstream the burner nozzle exit (, Figure 1).
(a)
(b)
Both experiments and predictions show (Figure 10) a quite rapid increase of the temperature across the relatively thin flame front, as already indicated by the temperature plot presented in Figure 9. The evaluation line touches the edge of the burner nozzle exit at (Figure 1). Since the flame front is curved and rather thick near the edge of the burner nozzle exit, especially for URANSSST and LES (Figure 9), the evaluation line (Figure 1) crosses through the whole reaction zone. On the combustor axis, the displayed part in Figure 10(a) () covers the rather thin reaction zone of URANSSST and LES only partially (only the rear part, since the flame brush is located slightly within the burner nozzle). The reaction zone of URANSRSM is not covered at all on the combustor axis shown in Figure 10(a), since the flame is located at a substantially upstream position compared to . Thus, the temperature increase observed along the evaluation line (Figure 10(b)) is larger and takes place in a larger distance compared to the temperature rise along the combustor axis (Figure 10(a)). This trend is qualitatively the same in all predictions as well as in the experiments. On the evaluation line, which encompasses the whole flame front, the measured temperatures exhibit a local maximum (Figure 10(b)). Calculations agree quite well with the measurements in predicting this temperature peak in the flame zone (Figure 10(b)). This is predicted slightly better by LES compared to the other models. URANSSST predictions are quite close to those of LES. The temperature gradient predicted by URANSRSM occurs at a slightly upstream position compared to the experiments and other predictions (Figure 10(b)), due to the difference in the predicted flame front shape as discussed above. Similar trends are generally observed for the combustor axis (Figure 10(a)). Due to the quite upstream position of the flame front predicted by URANSRSM on the combustor axis, as discussed above, the URANSRSM results do not exhibit a temperature gradient for the profile shown in Figure 10(a), for the combustor axis. Downstream the initial peak, the measured temperatures decline, whereas the predicted values do not decrease. The burnt gas temperature is overpredicted by about 100–150 K (Figure 10). This may be due to the assumption of no heat loss to the environment (adiabatic combustor walls) in the predictions.
The predicted and measured profiles of timeaveraged CO mass fraction along the combustor axis and along the “evaluation line” (Figure 1) are compared in Figure 11. The evaluation line displayed in Figure 11(b) cuts through the whole flame front (as discussed in the preceding paragraph). Thus, peak values produced in the flame zone are well captured. One can see in Figure 11(b) that quite large CO mass fractions are predicted by all models at the beginning of the evaluation line, which agree quite well with the measurements. LES seems to predict even higher maximum values compared to URANSSST and URANSRSM (Figure 11(b)). Downstream of this peak, the measurements show a quite sharp decay. The calculations agree well with this gradient only for a short distance (for ≤ approx. 0.05 m). Beyond this region, the measured values continue to decay sharply up to approx. m, where the predictions exhibit a rather milder decay, which may be due to an underprediction of the CO burnout rate in this region (Figure 11(b)). This results in a local overprediction of the CO mass fractions beyond the initial region ( m) (Figure 11(b)). Compared to the other models, the decay of the CO mass fractions is predicted at best by URANSRSM, which, however, overpredicts the exit value (Figure 11(b)). URANSSST and LES agree better with the experiments at the exit (Figure 11(b)). For the combustor axis (Figure 11(a)), the predicted peak values occur at a more upstream position compared to Figure 11(b), due to the curved shape of the flame front. Due to similar effects, an overprediction of the CO mass fractions for a region along the centreline is observed (Figure 11(a)). The predicted combustor outlet values are quite close to the measurements (Figure 11(a)). For the evaluation line (Figure 11(a)) and especially for the combustor axis (Figure 11(a)), the shape of the experimental curve is predicted at best by URANSRSM. In comparison, LES generally predicts a quite gradual decay (instead of an initial sharp decay followed by a rather flat curve, as observed in experiments), whereas URANSSST results may be seen to be qualitatively between those of URANSRSM and LES (Figure 11).
(a)
(b)
The predicted and measured profiles of timeaveraged NO mass fraction along the combustor axis and along the “evaluation line” (Figure 1) are compared in Figure 12. For NO mass fraction, the calculations overpredict the experiments throughout (Figure 12). However, the discrepancy is not too large, and this is at least partially due to the overpredicted temperature field (Figure 10). The relative performance of the different models correlates with the temperature predictions. LES seems to perform slightly better than the other models in the initial parts, where the NO mass fractions sharply increase. URANSSST also shows a rather good agreement there. The URANSRSM predictions show a slight upstream shift compared to the other results, since the flame front was predicted at a slightly upstream position in comparison (Figure 9). Overall, a fair agreement between the predictions and the measurements is observed (Figure 12).
(a)
(b)
4.2. NG and SG Flames without FGR
All results presented in this section are obtained by URANSSST. The predicted timeaveraged temperature fields for the NGFGR0 and SGFGR0 flames are displayed in Figure 13.
(a)
(b)
As seen in Figure 13, the NGFGR0 case exhibits a shorter, less curved flame brush (Figure 13(a)) compared to NGFGR20 (Figure 9(a)). In the central part of the burner, the flame front shows a slightly higher penetration into the burner nozzle for NGFGR0 (Figure 13(a)) compared to NGFGR20 (Figure 9(a)). However, there is no “flashback” as the burner walls are not exposed to high temperatures. On the contrary, in the SGFGR0 flame, although the adiabatic flame temperature is lower, a flashback tendency is predicted (Figure 13(b)) as the flame propagates deep upstream into the burner with an accompanying overheating of the burner walls around the edges of the nozzle exit. There are several mechanisms that can trigger a flashback [22]. Flashback due to combustion induced vortex breakdown is less likely to be the cause, since the expansion ratio, which is observed to correlate to this phenomenon [22], is even smaller for the SG (where the flashback occurs) compared the NG flame. Thus, it likely that the flashback is due to flame propagation in the core or in the boundary layers due to increased laminar flame speed by the higher hydrogen content of SG. The test rig was not designed to make detailed measurements in the burner. Thus, it is not clear how well the predicted flashback tendency corresponds to the experiments, for this operation point. However, although not quantified and documented, a generally strong flashback propensity of the used SG fuel was observed during the experimental investigation [12].
Figure 14 shows the contours of the timeaveraged mixture fraction with respect to the flame front for both (NGFGR0 and SGFGR0) flames. The flame front is characterized by the = 0.5 isoline of the reaction progress variable, which is indicated by the thick red line in the figure. Thinner black lines indicate the isolines of the mixture fraction, where the corresponding values are typed nearby. The fully premixed values of are 0.025 and 0.065 for the NGFGR0 and SGFGR0 flames, respectively. One can see that the NGFGR0 flame burns in fully premixed regime (similar to NGFGR20). For the SGFGR0 flame, the mixture fraction varies within the range about 0.035–0.075 indicating a partially premixed combustion (Figure 14).
(a)
(b)
For NGFGR0 and SGFGR0 cases, measurements were not available within the combustor but at the combustor outlet. Tables 3 and 4 compare the predicted and measured CO and NO mass fractions at the combustor outlet, for NGFGR0 and SGFGR0 flames, respectively.


For CO, the prediction for the SGFGR0 flame is quite close to the measurement (Table 3). For the NGFGR0 flame, the deviation between the prediction and measurement is larger but still not too large (Table 4). For NO, there is a moderate overprediction for both flames (Tables 3 and 4). This is affected by the overprediction of the flame temperature due to the assumption of adiabatic walls, as discussed in the previous section. Overall, a fair agreement of the predictions with experiments can be observed (Tables 3 and 4).
5. Conclusions
Turbulent flames in a generic swirl gas turbine combustor designed to operate in premixed/partially premixed mode are investigated numerically. Turbulence is modelled by a URANS formulation, using the SST turbulence model, as the basic modelling approach. For comparison, URANS is applied also in combination with the RSM to one of the investigated cases. For this case, LES is also used for turbulence modelling. For modelling the turbulencechemistry interaction, a laminar flamelet model based on the mixture fraction and reaction progress variable is used, coupled with a presumed probability density function approach. Natural gas and syngas flames with and without external flue gas recirculation are investigated. Comparing the predictive performances of different turbulence models for one of the cases (NGFGR20), it was observed that LES predicts a slightly thicker flame brush compared to URANSSST, while URANSRSM predicts a slightly sharper and more inclined flame front compared to URANSSST, extending deeper into the burner on the axis. The numerical results obtained by different turbulence models are observed to show a comparable overall performance and a fair overall agreement with the experimental data. The slight overprediction of the combustor exit temperature is assumed to be affected by the assumption of adiabatic walls in the mathematical model. The model will be improved in the future to include nonadiabatic effects, which is also expected to lead to a more accurate prediction of NO emissions. For syngas, an increased flashback propensity could be predicted, which qualitatively agrees with the experimental observations.
Nomenclature
:  Reaction progress variable (—) 
:  Mean specific heat capacity at constant pressure (J ) 
:  Turbulence kinetic energy ( ) 
:  Kolmogorov length scale (m) 
:  Static pressure (Pa) 
:  Favre or Reynolds probability density function (—) 
:  Volumetric heat release rate (J ) 
:  Source term of transport equation for species (kg ) 
:  Time (s) 
:  Static temperature (K) 
:  Space coordinates (m) 
:  Velocity vector () 
:  Axial velocity () 
:  Velocity magnitude () 
:  Mass fraction of species (—) 
:  Dimensionless wall distance (—) 
:  Mixture fraction (—). 
:  Beta probability density function (Favre or Reynolds) (—) 
:  Local finite volume cell size (m) 
:  Dissipation rate of () 
:  Source term for progress variable equation (kg ) 
:  Viscosity (kg ) 
:  Density (kg ) 
:  Schmidt number (—) 
:  Thermochemical variable to be extracted from flamelet libraries (—) 
:  Scalar dissipation rate () 
:  Turbulence eddy frequency (). 
~:  Favreaveraged value 
Reynoldsaveraged value  
:  Favre fluctuational value. 
:  Burnt 
st:  Stoichiometric 
:  Turbulent 
:  Unburnt. 
EDC:  Eddy dissipation concept 
FGR:  Flue gas recirculation 
GI:  Grid Index 
GT:  Gas turbine 
GTC:  Gas turbine combustion/combustor 
LES:  Large Eddy Simulation 
LFM:  Laminar flamelet method 
NG:  Natural gas 
PDF:  Probability density function 
RANS:  Reynolds Averaged Numerical Simulation 
RMS:  Root Mean Square 
RSM:  Reynolds Stress Model 
SG:  Syngas 
URANS:  Unsteady RANS 
SST:  Shear Stress Transport. 
Competing Interests
The authors declare that they have no competing interests.
References
 C. Fureby, “Large eddy simulation modelling of combustion for propulsion applications,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 367, no. 1899, pp. 2957–2969, 2009. View at: Publisher Site  Google Scholar
 D. Lörstad, A. Lindholm, N. Aklin et al., “Experimental and LES investigation of a SGT800 burner in a combustion rig,” in Proceedings of the ASME Turbo Expo 2010: Power for Land, Sea, and Air, Paper no GT201022688, Glasgow, UK, June 2010. View at: Google Scholar
 G. Goldin, F. Montana, and S. Patil, “A comparison of RANS and LES of an industrial lean premixed burner,” in Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Paper No GT201425352, Düsseldorf, Germany, June 2014. View at: Google Scholar
 R. Kulkarni, B. Bunkute, F. Biagioli, M. Duesing, and W. Polifke, “Large eddy simulation of ALSTOMs reheat combustor using tabulated chemistry and stochasticfields combustion model,” in Proceedings of the Turbo Expo 2014: Turbine Technical Conference and Exposition, Paper no GT2014 26053, Düsseldorf, Germany, June 2014. View at: Google Scholar
 A. C. Benim, A. Nahavandi, and K. J. Syed, “URANS and LES analysis of turbulent swirling flows,” Progress in Computational Fluid Dynamics, vol. 5, no. 8, pp. 444–454, 2005. View at: Publisher Site  Google Scholar
 A. C. Benim, M. P. Escudier, A. Nahavandi, A. K. Nickson, K. J. Syed, and F. Joos, “Experimental and numerical investigation of isothermal flow in an idealized swirl combustor,” International Journal of Numerical Methods for Heat & Fluid Flow, vol. 20, no. 3, pp. 348–370, 2010. View at: Publisher Site  Google Scholar
 A. C. Benim, S. Iqbal, A. Nahavandi, W. Meier, A. Wiedermann, and F. Joos, “Analysis of turbulent swirling flows in an isothermal gas turbine combustor model,” in Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Paper No GT201425008, Düsseldorf, Germany, June 2014. View at: Publisher Site  Google Scholar
 B. F. Magnussen, “On the structure of turbulence and generalized eddy dissipation concept for chemical reactions in turbulent flow,” in Proceedings of the 19th Aerospace Sciences Meeting, Aerospace Sciences Meetings, pp. 1–6, St. Louis, Mo, USA, January 1981. View at: Publisher Site  Google Scholar
 N. Peters, Turbulent Combustion, Cambridge University Press, Cambridge, UK, 2002.
 T. Poinsot, D. Veynante, and S. Candel, “Diagrams of premixed turbulent combustion based on direct simulation,” Symposium (International) on Combustion, vol. 23, no. 1, pp. 613–619, 1991. View at: Publisher Site  Google Scholar
 A. C. Benim and K. J. Syed, “Laminar flamelet modelling of turbulent premixed combustion,” Applied Mathematical Modelling, vol. 22, no. 12, pp. 113–136, 1998. View at: Publisher Site  Google Scholar
 S. Fischer, D. Kluss, and F. Joos, “Experimental investigation of a fuel flexible generic gas turbine combustor with external flue gas recirculation,” in Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Paper No GT201425388, Düsseldorf, Germany, June 2014. View at: Publisher Site  Google Scholar
 http://www.openfoam.com/.
 B. E. Launder, G. J. Reece, and W. Rodi, “Progress in the development of a Reynoldsstress turbulent closure,” Journal of Fluid Mechanics, vol. 68, no. 3, pp. 537–566, 1975. View at: Publisher Site  Google Scholar
 M. Lesieur, O. Métais, and P. Comte, LargeEddy Simulations of Turbulence, Cambridge University Press, New York, NY, USA, 2005. View at: Publisher Site  MathSciNet
 T. Poinsot and D. Veynante, Theoretical and Numerical Combustion, R. T. Edwards Inc., Philadelphia, Pa, USA, 2nd edition, 2005.
 C. D. Pierce and P. Moin, “Progressvariable approach for largeeddy simulation of nonpremixed turbulent combustion,” Journal of Fluid Mechanics, vol. 504, pp. 73–97, 2004. View at: Publisher Site  Google Scholar  MathSciNet
 K. N. C. Bray, “The interaction between turbulence and combustion,” in Proceedings of the 17th International Symposium on Combustion, pp. 223–233, The Combustion Institute, Pittsburgh, Pa, USA, 1978. View at: Google Scholar
 H. Pitsch, “A C++ computer program for 0D and 1D laminar flamelet calculations,” Tech. Rep., RWTH, Aachen, Germany, 1998. View at: Google Scholar
 http://combustion.berkeley.edu/grimech/.
 I. B. Celik, Z. N. Cehreli, and I. Yavuz, “Index of resolution quality for large eddy simulations,” Journal of Fluids Engineering, vol. 127, no. 5, pp. 949–958, 2005. View at: Publisher Site  Google Scholar
 A. C. Benim and K. J. Syed, Flashback Mechanisms in Lean Premixed Gas Turbine Combustion, Academic Press, New York, NY, USA, 2015.
Copyright
Copyright © 2016 Ali Cemal Benim et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.