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Large Eddy Simulation of Swirled Spray Flame Using Detailed and Tabulated Chemical Descriptions

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Abstract

Accurate characterization of swirled flames is a key point in the development of more efficient and safer aeronautical engines. The task is even more challenging for spray injection systems. On the one side, spray interacts with both turbulence and flame, eventually affecting the flame dynamics. On the other side, the structure of turbulent spray flame is highly complex due to equivalence ratio inhomogeneities caused by evaporation and mixing processes. The first objective of this work is to numerically characterize the structure and dynamics of a swirled spray flame. The target configuration is the experimental benchmark named MERCATO, representative of an actual turbojet injection system. Due to the complex nature of the flame, a detailed description of chemical kinetics is necessary and is here obtained by using a 24-species chemical scheme, which has been developed for numerical simulations of spray flames. The first Large Eddy Simulation (LES) of a swirled spray flame using such a detailed chemical description is performed here and results are analyzed to study the complex interactions between the spray, the turbulent flow and the flame. It is observed that this coupling has an effect on the flame structure and that flame dynamics are governed by the interactions between spray, precessing vortex core and flame front. Even if such a detailed kinetic description leads to an accurate characterization of the flame, it is still highly expensive in terms of CPU time. Tabulated techniques have been expressly developed to account for detailed chemistry at a reduced computational cost in purely gaseous configurations. The second objective is then to verify the capability of the FPI tabulated chemistry method to correctly reproduce the spray flame characteristics by performing LES. To do this, results with the FPI method are compared to the experimental database and to the results obtained with the 24-species description in terms of mean and fluctuating axial gas velocity and liquid phase characteristics (droplet diameter and liquid velocity). Moreover, the flame characterization obtained with the FPI approach is compared to the results of the 24-species scheme focusing on the flame structure, on major and minor species concentrations as well as on pollutant emissions. The potential and the limits of the tabulated approach for spray flame are finally assessed.

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Notes

  1. Experimental setup for investigation of air-breathing combustion using optical techniques.

  2. In the very dilute regime, the volume occupation of the liquid phase is negligible.

  3. To ensure consistency between the two chemical descriptions, the same definition of the sensor is used in both calculations. In the case of the detailed chemical description, the reaction rate of the progress variable is reconstructed from the transported species.

  4. Here the values for Schmidt and Prandtl numbers are Sc=0.7 and Pr=0.7, respectively [20].

  5. Monodisperse and monokinetic assumptions imply that at a given location all droplets have the same size and velocity, i.e. Dirac’s delta distributions in size and velocity phase spaces.

  6. The nozzle geometry has been modified according to this model.

  7. The random uncorrelated energy corresponds to the droplets velocity dispersion around the local mean velocity [49].

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Acknowledgments

This work was granted access to the HPC resources of CINES under the allocation x20152b6172 made by GENCI (Grand Equipement National de Calcul Intensif). CERFACS is also gratefully acknowledged for providing the AVBP code and the meshes for our computations.

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Appendix A: Performances of the FPI tabulation method on laminar counterflow spray flames

Appendix A: Performances of the FPI tabulation method on laminar counterflow spray flames

Franzelli et al. [21] investigated the adequacy of the FPI method to predict laminar counterflow spray flames by comparing in an a priori way the profiles of the tabulated quantities with the detailed variables. The present study completes the a priori analysis presented in [21] by evaluating the performance of the FPI method in a posteriori way on laminar counterflow spray flames (see Fig. 16). The same numerical configuration is considered in the present work. The system of equations describing the laminar spray flow as well as the evaporation model are given in details in [21].

Fig. 16
figure 16

Schematic of a laminar counterflow spray flame

Pure fresh air is injected from the left side (superscript o x) whereas spray fuel and pure air are injected from the right side (superscript f). Subscripts g and l denote the gas and the liquid phase respectively. The axial gas phase velocities are identical at both injection sides: \(v_{g}^{ox}=-{v_{g}^{f}}\). The axial velocities of the gas and liquid phases at the right injection are equal \({v_{g}^{f}}={v_{l}^{f}}\). Liquid and gas temperatures at injection are equal at both injection sides: \({T_{g}^{f}}=T_{g}^{ox}=T_{l}=400\) K. 1-D flame simulations are performed with the REGATH counterflow code using an Euler-Euler approach under the assumption of monodisperse liquid phase [46]. The reader is referred to [21] for more numerical details. Four spray flames, summarized in Table 1, have been investigated for the operating conditions representative of the observed values in the LES (liquid droplet diameter \({d_{l}^{f}}\), droplet number density \({n_{l}^{f}}\), injection velocity \({v_{l}^{f}}\) and liquid volume fraction \({\alpha _{l}^{f}}\)).

Table 1 Operating conditions of the different studied cases (value is in bold when the parameter is varied)

The look-up table is built from a collection of 100 adiabatic unstrained gaseous premixed flames for 100 and 500 different values of Y z and Y c , respectively, at T f=400 K and ambient pressure using the reference detailed chemical scheme [21]. Results obtained with the tabulated approach (lines) are compared to the multi-species description (symbols) in Fig. 17. In the left side of Fig. 17, the flame structure is represented by the mixture fraction and the progress variable profiles, together with the information of the liquid volume fraction α l . Temperature and C O mass fraction profiles are provided on the right side of Fig. 17.

Fig. 17
figure 17

Counterflow laminar spray flames of Table 1 (A-D from top to bottom). Comparison between the reference detailed model (symbols) and the tabulated description (line): axial profiles of mixture fraction, progress variable and liquid volume fraction (left), temperature and CO mass fraction (right)

The chemical structure of the counterflow spray flame is shown in Fig. 17a for case A in Table 1. Near the flame front, the gas temperature increases due to the thermal conductivity. Consequently, the evaporation source term drastically increases and the liquid volume fraction completely evaporates. The high temperature region (−5 mm < x < 3 mm) is characterized by the presence of intermediate species, such as CO, and products. A good agreement is observed between the detailed multi-species solution and the tabulated chemistry technique. The FPI method correctly localizes the flame front. However, as only a single flame archetype is used to generate the look-up table which does not account for strain rate and non-premixed effect, the temperature is slightly underestimated and the CO mass fraction is overestimated in rich regions [21].

In case B, the droplet diameter is increased keeping constant the liquid volume fraction at injection by decreasing the droplet number density (Fig. 17b). Since the droplets are bigger, evaporation is initially slower and fuel remains mainly in liquid phase before reaching the flame front, resulting in higher gradient of the mixture fraction in the high temperature region, where the liquid evaporates rapidly. Globally, the same agreement between the detailed description and the tabulated method discussed for case A is observed here.

The impact of the liquid volume fraction \({\alpha _{l}^{f}}\) on the flame structure and the performances of the tabulation method is investigated in case C (Table 1). The liquid volume fraction \({\alpha _{l}^{f}}\) is decreased keeping constant the droplet diameter, which means that the overall equivalence ratio is reduced. Evaporation is mainly localized before the flame front (Fig. 17c). As the combustion mainly occurs under premixed conditions, the FPI tabulation procedure is well adapted, leading to a good prediction of the temperature and CO mass fraction.

Finally, the injection velocity of both liquid and gas phases have been increased in case D (Table 1), keeping constant all other boundary conditions (Fig. 17d). The reaction zone is correctly located but the maximum value of the mixture fraction is overestimated. The temperature is correctly described in the near-injection zone as well as the liquid volume fraction. On the contrary, the CO mass fraction is overestimated by the tabulated methods. Globally, the FPI approach correctly reproduces the flame structure (i.e. Y c and Y z spatial evolution) for counterflow spray flames. However, a more sophisticated approach based on the tabulation of multiple manifold is necessary to obtain a good prediction of CO in laminar spray flames in order to account for the effect of strain rate and of the mixture fraction inhomogeneities on pollutant predictions.

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Franzelli, B., Vié, A., Boileau, M. et al. Large Eddy Simulation of Swirled Spray Flame Using Detailed and Tabulated Chemical Descriptions. Flow Turbulence Combust 98, 633–661 (2017). https://doi.org/10.1007/s10494-016-9763-0

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