EFFECTS OF RADIATION, WALL HEAT LOSS AND EFFUSION COOLING ON FLAME STABILI- SATION AND POLLUTANT PREDICTION IN LES OF GAS TURBINE COMBUSTION

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1 EFFECTS OF RADIATION, WALL HEAT LOSS AND EFFUSION COOLING ON FLAME STABILI- SATION AND POLLUTANT PREDICTION IN LES OF GAS TURBINE COMBUSTION P. Schmitt, B. Schuermans, K. P. Geigle 4 and T. Poinsot CERFACS - Toulouse, France IMFT - Toulouse, France Alstom Power Ltd. - Baden, Switzerland 4 DLR - Stuttgart, Germany Abstract Keywords The impact of heat transfer modelling on Large-Eddy Simulations of a laboratory scale gas turbine burner is shown. First, simple modelling strategies for heat transfer are presented: radiation is approximated by an optically thin model and convective heat transfer is modelled by wall functions. Then the configuration, a swirl stabilised, lean partially premixed burner including air cooling and fuel injections is detailed. Comparison of two simulations show, that air cooling modifies considerably local combustion temperature and flame shape. The radiative and convective heat transfer show equal impact on chamber temperature and therefore on nitric oxide formation. The simulation including all thermal aspects of the configuration matches significantly better the experimental data than the simulation without them. Large-Eddy Simulation, heat transfer, nitrous oxide, gas turbines INTRODUCTION Large-Eddy Simulations of reactive flows are becoming a frequently used approach for designing and understanding gas turbine combustion chambers []. Until today, the simulations were based on the general assumption that only the combustion process modifies the enthalpy balance of the process. Walls were assumed to be adiabatic, radiation was neglected and air cooling devices were not included. However, since these aspects can alter considerably flame stabilisation (and thus stability behaviour), pollutant formation and acoustic modes of the geometry, it is important to include these effects. In particular, the importance of heat transfer modelling becomes clear when looking at the mechanisms influencing nitrous oxide (NO X ) formation in lean partially premixed combustion (as used in modern gas turbines). Figure summarises all influencing factors. For combustion of a pure gaseous fuel such as methane, NO X is conveniently grouped into two parts: thermal and prompt NO X [,, 4]. Thermal NO X is produced if oxygen and nitrogen are

2 prompt (Fennimore) + Nitrous Oxide NO X fuel thermal (Zeldovich) exponential dependence on equivalence ratio X (gaseous fuel) exponential dependence on temperature equivalence ratio + augmentation + + equivalence ratio fluctuations + + turbulence instabilities + Chamber temperature + no radiation or convection heat loss Figure : Mechanisms that influence NO X production in a lean partially premixed combustion system. present and temperatures are sufficiently high. It has an exponential dependence on temperature. Prompt NO X is formed close to the flame front and has an exponential dependence on equivalence ratio. Consequently, NO X formation in gas turbine combustion is influenced by equivalence ratio, equivalence ratio fluctuations (due to the exponential dependence [5]) and chamber temperature (as shown in Figure ). The present paper does not explore the effects of different equivalence ratios, instabilities or other aspects related to mixing than cooling air injection. The main focus is laid on thermal processes which directly influence the global and/or local chamber temperature and therefore NO X emissions. In order to include detailed heat transfer, a transport equation for enthalpy (or an equivalent quantity) has to be solved. The question is how to introduce the different sink terms of this equation. In the following, simple heat transfer modelling strategies are recalled and their application to several simple cases

3 is shown. Finally, the impact of heat-transfer modelling will be shown using a laboratory scale, lean partially premixed gas turbine burner. HEAT TRANSFER MODELLING AND VALIDATION Radiative heat transfer modelling Radiative heat transfer modelling of gases (excluding particles) normally takes into account emitted radiation and re-absorption. The degree of importance of re-absorption is usually determined by the optical thickness τ = X/L P of the radiating gas, where X is a characteristic dimension of the enclosure and L P the burned-gas Planck mean absorption length [6]. For the considered configuration, τ is of the order of. This means that there is some re-absorption, but it is not the dominant process. Therefore it can be neglected. Furthermore, virtually no preheating of the fresh gases due to absorption occurs since it is assumed that they consist of undiluted air with small amounts of methane (lean conditions). Assuming that the gases are optically thin and that the cold surroundings have a constant temperature, the radiative heat loss per unit volume can be calculated as [7]: Q r = 4σ(T 4 Ts 4 ) (p i a p,i ) () i where σ = W/m K 4 is the Stefan-Boltzmann constant, T is the local gas temperature, T s is the temperature of the cool surroundings, p i is the partial pressure of species i, and a p,i is the Planck mean absorption coefficient for species i. This model requires the partial pressures of the involved species, which are either directly included in the simulation (for simulations using Arrhenius-type combustion models) or determined from the mixture fraction (for flamelet combustion models). For combustion of pure air and methane only H O andco in the burnt gases contribute considerably to radiation as they have high partial pressures and Planck mean absorption coefficients. Therefore, only those two species are included for the evaluation of the radiative heat loss. The Planck mean absorption coefficients can be calculated with the RADCAL programme [8]. Here the curve-fits provided by Gore et al. [9] are used. Note that including more detailed radiation predictions by taking into account spatially varying wall temperatures and/or absorption would necessitate computationally expensive models [].

4 -. GRI-Mech.!=.4!=.6!=.8 S_CH4_PS. x [cm] NO mass fraction Figure : Comparison of the reduced -step scheme to the GRI-Mech.. Temperature [K] with radiation adiabatic Temperature... x [cm] NO NO..x -.. Massfraction NO Figure : Comparison of a one-dimensional laminar flame with and without radiation. Radiative heat transfer validation In order to assess the impact of radiation modelling on the combustion process, one-dimensional laminar flames with and without radiation were computed. A -step reduced chemical scheme [], with Arrhenius coefficients fitted to match laminar flame speed and adiabatic combustion temperature of the GRI-Mech. [] was used. Additionally a third (non Arrhenius-type) reaction was added which accounts for thermal and prompt NO formation. The NO reaction rates were fitted to the GRI-Mech. for lean combustion. NO profiles for the simulation with the AVBP code [] using the described -step scheme are compared to PREMIX [] results using the GRI-Mech. in Figure. It is seen that at all three presented equivalence ratios, both schemes give very similar predictions for the NO mass-fraction. Figure compares a computation with radiative losses to the adiabatic one. The temperature at infinity for the radiation was set to K. It is seen how

5 radiation reduces considerably the temperature of the hot gases, thus largely affecting the production of thermal NO. However, neither flame thickness, speed or prompt NO production were considerably affected. Convective heat transfer modelling When sufficient spatial resolution near the solid boundaries is provided, turbulent convective heat transfer is resolved, and no modelling is necessary. However, in actual reactive LES of complex geometries, the resolution of the boundary layer region is computationally out of reach. Different strategies for the modelling of the turbulent boundary layer are possible [4]. Here, the computationally least expensive approach is chosen: applying the logarithmic law on velocity and temperature [5, 6]. In contrast to Grötzbach [6], who used mean temperature and velocity values, instantaneous values were used in this study. This assumes that the computational cells at the wall are sufficiently large to include several typical structures of near-wall turbulence. In order to apply a wall-function boundary condition, the classical no-slip condition at solid walls is abandoned and only the wall normal velocity is set to zero (AVBP is a cell-vertex type solver). Additionally, the wall shear stress and heat flux are imposed. The wall shear stress ρu τ is obtained by iteratively solving the logarithmic law of the wall: u u τ = κ ln ( E y u τ ν where ρ is density, u the velocity at the first interior grid node, u τ the friction velocity, κ =.4 the van Kármán constant, E = 9. an integration constant, y the distance of the first interior grid point, and ν the kinematic viscosity. As the logarithmic law of the wall was derived for the mean flow and considering that the biggest part of near wall turbulence is not resolved, the residual stress model should degenerate near the wall to a mixing-length type model. As this is the case for Smagorinsky s model [7], it is well-suited for this kind of simulations. Also, Cabot and Moin [8] have shown that in the near-wall region, the classic Smagorinsky model with wall functions gives better results than the dynamic model with wall functions. From the logarithmic law for temperature, the wall heat flux q wall is calculated: ρ wall u τ C p (T wall T ) q wall ) ( = κ ln F y u τ ν where C p is the heat capacity at constant pressure, T wall the wall temperature, T the temperature at the first interior grid point, and F =.96 an integra- ) () ()

6 u Log-law Wei et al.: Re! =655 W-F with WALE W-F with Smag. u'+, v'+ 5 4 u'+ Wei et al.: Re " =655 v'+ Wei et al.: Re " =655 u'+ W-F with WALE v'+ W-F with WALE u'+ W-F with Smag. v'+ W-F with Smag y y/!.6.8. Figure 4: Mean and fluctuating velocity profiles for the channel-flow simulations. tion constant. For flows with Prandtl numbers very different from one, more sophisticated formulations for the temperature law [9] may be used. It is known, that this approach gives only good results for attached flows [4]. This should not cause major errors in this case, since the heat transfer is mainly important in regions where the flow is locally attached (as downstream in the chamber or on the front plate). Convective heat transfer validation Validation of the convective heat transfer was done by periodic channel flow simulations. Quasi-isothermal simulations (only viscous heating at Ma =. present) as well as simulations involving temperature gradients (using a volume heat source term) comparable to those encountered in real combustion chambers were carried out. Figure 4 (left) shows the (non-dimensional) mean velocity profile of the quasi-isothermal simulation at Re τ = 5 (using Smagorinsky s model). It is compared to the logarithmic law ot the wall, measurements by Wei and Willmarth [] and a wall-function simulation using the WALE model [] as a representative for residual stress models with correct near-wall scaling of the turbulent viscosity. As expected, the wall-function simulation using Smagorinsky s model works best. Nonetheless, both simulations encounter difficulties in correctly predicting the velocity profile in the region near the wall where the simulations changes from a more RANS-type flow to a true LES. Figure 4 (right) shows axial and wall-normal velocity fluctuations. Both simulations show good behaviour far from the wall but near the wall, the simulation using Smagorinsky s model shows a clear superiority. The high values of turbulent viscosity tend to stabilise the flow and limit the axial veloc-

7 Nu Nu =. Re 4/5 Pr / under-res. WALE (! = -4 ) under-res. Smag. (! = -4 ) Smag. + W-F (! = -4 ) Smag. + W-F (! =.7) 6 7 Re 8 9 Figure 5: Nusselt numbers for different models and non isothermal channel flow. ity fluctuations. Nonetheless, simulations with the WALE model may provide good results when using different discretisation and/or schemes []. In order to verify the behaviour of the wall-function for high temperature gradients, a simulation which includes a volume heat source term was carried out. In order to classify these simulations, the non-isothermicity parameter ξ [] is used: q wall ξ = (4) ρ wall u τ C p T wall In reality it can reach values greater than. Figure 5 shows the Nusselt number, obtained by a simulation with ξ =.7. It is compared to an experimental correlation [4] and shows very good agreement. Figure 5 also shows the Nusselt numbers obtained by two quasi-isothermal simulations without wallfunction nor sufficient resolution in the boundary layer. The high turbulent viscosity values of Smagorinsky s model near the wall cause a strong overprediction of heat transfer. The WALE model gives the exact opposite result due to the under-prediction of turbulent viscosity near the wall. BURNER GEOMETRY General description The burner used for this study is a scaled industrial configuration [5]. It consists of two half-cones shifted in respect to each other in order to create a swirling flow. Figure 6 provides a schematic view of the burner and the combustion chamber. The hot gas flow is shown in the upper half, the cold gas flow in the lower half. Air and fuel enter the swirling unit on the left and mix rapidly. As the flow exits to the chamber, a recirculation zone is formed which stabilises the flame. The combustion products exit through a chimney on the

8 fuel injections Hot combustion products a b a: water cooling b: thin wall Preheating Cold air Figure 6: Schematic of the studied burner and chamber geometry. right. Thermal properties The lower half of Figure 6 presents the involved cooling precesses. Through the burner edge at the dump, cold air from the plenum is drawn through small holes in order to protect the burner from the flame. This was explicitly included in the computation by additional inlets which are larger in diameter (due to resolution constraints) but with the same mass-flux as in reality. At the edges between front plate and chamber walls additional cold air from the plenum is drawn through holes in order to protect the burner walls. This was included via one continuous low-speed inlet, which is a rather crude simplification. It is considered that the actual jets do not have a significant impact on the flow field and only their cooling impact had to be accounted for. Heat is evacuated from the combustion chamber by conduction through the chamber walls (and convection through the outlet). The amount of heat evacuated through conduction has two contributions: Hot gases from combustion radiate heat to the colder chamber walls. Turbulent convective processes exchange heat between the hot gases and the colder chamber walls. Since the combustion chamber serves as a preheating device for the combustion air, the chamber wall temperature is a result of a complex thermal process (see Figure 6). It would be possible to include modelling for the outside heatexchange, but as in our case the wall temperatures are approximately known,

9 .. OH Chemiluminescence Heat release in W/m e+8.e+8.e+8 4.4e+8 5e Figure 7: Left: OH chemiluminescence from experiment; right: Integrated heat release from the non-adiabatic LES. they were specified for the simulation. The temperature at the chamber walls was measured as approximately K (for the case with an adiabatic flame temperature of 85 K). The water cooled front plate has approximately the temperature of the fresh gases (7 K). Numerical Setup All simulations were carried out with the AVBP code []. It is a fully explicit cell-vertex type code that solves the compressible multi-species Navier- Stokes equations on unstructured meshes. In particular the presented simulations use Smagorinsky s LES model [7] and the Lax-Wendroff scheme with centred space discretisation. The chemistry modelling consists of the -step chemical kinetics presented in the radiation section and the thickened flame model [6] for taking into account flame-turbulence interactions. The computational grid contains.8 million tetrahedral cells. RESULTS Non-adiabatic simulation The simulation in this section includes cooling and heat-losses as described by using the models detailed above. From experiment, images of the OH radical are available. From LES, heat release is available, which should approximately correspond the OH radical [7]. As the experimental images integrate the entire OH chemiluminescence of the combustion process, the heat release from LES is integrated in the same line of sight. Both are compared in Figure 7 which represents a view of the combustion chamber. The burner exit is located

10 . Convection: -8.7 kw kw Radiation: -8.7 kw Figure 8: Integrated heat release from the non-adiabatic LES including thermal power of the flame. Additionally, convective and radiative losses are indicated. at =, where D is the burner exit diameter and x the axial coordinate. Experiment and simulation correspond relatively well: both show a flame, principally anchored by the central recirculation zone. In order to quantify the impact of the different thermal processes, heat release, radiation and wall heat flux are integrated over the whole domain. The obtained values are shown in Figure % of the thermal power of the combustion process is lost through the boundary layer at the cold walls and 7.8% through radiation. So, both processes are equally important and have a considerable impact on the temperature field as showed in the following. Figure 9: Cuts through the temperature and NO mass-fraction fields for the non-adiabatic simulation.

11 Figure 9 presents cuts through the burner and combustion chamber. In the upper half, temperature is shown, in the lower half NO mass-fraction. The adiabatic flame temperature (85 K) is not reached because of thermal losses. The temperature iso-contours show the temperature gradient in the boundary layer. NO is principally produced close to the flame. The main part of the burnt gases are not sufficiently hot in order to allow a significant amount of thermal NO to be produced. Additional validation is obtained via the comparison of axial and radial velocities. Figure presents measurements obtained by applying PIV to the reactive flow. The axial and radial velocity profiles match closely the predictions from the non-adiabatic LES. Also, the axial velocity fluctuations are nicely predicted. Only the radial velocity fluctuations show some disagreement. Close to the wall at =.75, the LES predicts strong fluctuations whereas in experiment, this is not observed. The heat release at this location (Figure 7) is also different from experiment and both results probably point to the same, still unknown problem.

12 Axial Mean Velocity /u ref RLN PIV reactive Radial Mean Velocity /u ref RLN PIV reactive Axial Rms Velocity /u ref RLN PIV reactive Radial Rms Velocity /u ref RLN PIV reactive Figure : Comparison of PIV measurements and the non-adiabatic LES (RLN).

13 .. OH Chemiluminescence Heat release in W/m e+8.e+8.e+8 4.4e+8 5e Figure : Left: OH chemiluminescence from experiment; right: Integrated heat release from the adiabatic LES. Adiabatic simulation In order to assess the impact of heat-transfer modelling and effusion cooling, a simulation without these models was carried out. The air that normally passes through the small air-cooling holes (of the order of 5% of the total mass flux) is diverted to the plenum. This ensures that both simulations have the same total combustion power and adiabatic flame temperature. A comparison between the integrated heat release and the chemiluminescence data already used for validation of the non-adiabatic case is shown in Figure. It is clearly seen that for the adiabatic simulation, the flame is not Figure : Cuts through the temperature and NO mass-fraction fields for the adiabatic simulation.

14 only anchored by the central recirculation zone, but also at the sudden expansion at the burner exit (the corner recirculation zones). This difference in flame anchoring is mainly attributed to the lack of cooling air at the burner exit. Figure shows cuts through the temperature and NO mass-fraction fields. It is seen that the adiabatic flame temperature is reached. This causes significant thermal NO production in the combustion chamber. Compared to the nonadiabatic case, the NO emissions at the chamber exit increase by one order of magnitude. Finally, velocity predictions for the adiabatic case are compared in Figure with the experimental data. Axial mean velocity and fluctuations do not match the experimental data as well as in the non-adiabatic case. Radial velocity is predicted with the same accuracy as for the non-adiabatic case. Again, the radial velocity fluctuations are too strong. CONCLUSION In order to evaluate the impact of heat transfer modelling on NO X predictions, simple modelling strategies for radiative and convective heat transfer modelling in LES have been detailed. Simulations, using these models reproduced NO X emission levels comparable to those found in literature [4]. Without the heat transfer modelling, NO X emission levels are over-predicted by one order of magnitude. It was also shown, that the inclusion of effusion cooling changes flame stabilisation from central and corner recirculation zone to central recirculation zone only. This certainly is an important aspect when the response of the burner to acoustic excitations becomes of interest. In summary, this paper shows that in order to obtain real insight into gasturbine combustion, including realistic heat transfer can be of of crucial importance. ACKNOWLEDGEMENTS This work was conducted in the framework of the FP5 EC-Project FuelChief. Part of the simulations have been carried out on computers of CEA s Research and Technology Computing Center (CCRT, Bruyères-le-Châtel, France) and the National Computer Centre of Higher Education (CINES, Montpellier, France).

15 Axial Mean Velocity /u ref RLN AD PIV reactive Radial Mean Velocity /u ref RLN AD PIV reactive Axial Rms Velocity /u ref RLN AD PIV reactive Radial Rms Velocity /u ref RLN AD PIV reactive Figure : Comparison of PIV measurements and the adiabatic LES (RLN AD).

16 NOMENCLATURE Latin symbols a p,i Planck mean absorption coefficient for species i C p heat capacity at constant pressure D burner exit diameter E integration constant (9.) F integration constant (.96) p i partial pressure of species i Q r radiative heat loss per unit volume q wall wall heat flux T local gas temperature T s temperature of the cool surroundings T wall temperature at wall u velocity u + non-dimensional velocity (u/u τ ) u +, v + non-dimensional velocity fluctuation (u /u τ, v /u τ ) u τ friction velocity u re f burner reference velocity x, y, z coordinates y + non-dimensional wall distance (yu τ /ν) Greek symbols δ channel half-height κ van Kármán constant (.4) ν kinematic viscosity ξ non-isothermicity parameter ρ density ρ wall density at wall σ Stefan-Boltzmann constant ( W/m K 4 ) REFERENCES [] L. Selle, G. Lartigue, T. Poinsot, R. Koch, K.-U. Schildmacher, W. Krebs, B. Prade, P. Kaufmann, and D. Veynante. Compressible Large-Eddy Simulation of turbulent combustion in complex geometry on unstructured meshes. Combustion and Flame, 7(4):489 55, 4. [] P. Glarborg, J.A. Miller, and R.J. Kee. Kinetic modeling and sensitivity analysis of nitrogen oxide formation in well-stirred reactors. Combustion and Flame, 65:77, 986.

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