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Assessment of Large Eddy Simulation for the prediction of recessed inner tube coaxial flames

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Abstract

Large Eddy Simulations of recessed central-duct coaxial injectors under transcritical and two-phase conditions are detailed in this paper, with the objective of assessing the ability of recently develop models (Schmitt (Flow. Turbul. Combust. 105, 159–189, 2020), Pelletier et al. (Computers. Fluids. 206, 104588, 2020)) to recover the experimental observations of an augmentation of the flame expansion rate and its dynamics due to the recess. The simulated cases correspond to the LOx/GH\(_2\) Mascotte A10 and C10, both operating at 10 bar with two-phase flow conditions, and Mascotte C60, injected under transcritical conditions in a chamber at 60 bar (Habiballah et al. (Combust. Sci. Technol. 178, 101–128, 2006)). Cases A10 and C10 qualitatively reproduce the experimental visualizations. However, the simulation with recess for case C60 produces a more disrupted inner jet and a shorter flame than in the experiment. In addition, a fine grid resolution is necessary to capture the absolute instability in this case. Case C60 is then examined. It is observed in particular that heat release rate distribution is importantly modified once the LOx injector is recessed, nearly doubled up to 10 LOx injector diameters. This huge increase of heat release has two origins: (1) an enhanced turbulent mixing in the near injector region due to an increased injector exit velocity because of the thermal expansion in the recessed part, in line with the model proposed by Kendrick et al. (Combust. Flame. 118, 327–339, 1999); (2) a larger flame surface because of the quicker destabilization and larger spreading rate of the flame at the injector exit.

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Acknowledgements

This work was granted access to the HPC resources of TGCC (CEA) and CINES made available by GENCI (Grand Equipement National de Calcul Intensif) under the allocation A0102B06176. A part of this work was performed using HPC resources from the mésocentre computing center of Ecole CentraleSupélec and Ecole Normale Supérieure Paris-Saclay supported by CNRS and Région Ile-de-France.

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    Thomas Schmitt

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Appendices

A: Statistical convergence in the recess for cases A10-R2, C10-R2 and C60-R3

Radial profiles of temperature and axial velocity are plotted for different averaging times in Figs. 38, 39 and 40 for cases A10-R2, C10-R2 and C60-R3, respectively. For all the cases, the different profiles are close from each other, suggesting the simulation is properly statistically converged in the recess.

Fig. 38
figure 38

Case A10-R2, statistical convergence in the recess. Radial profiles of axial velocity. − mean profiles, \(--\) rms profiles

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Fig. 39
figure 39

Case C10-R2, statistical convergence in the recess. Radial profiles of axial velocity. − mean profiles, \(--\) rms profiles

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Fig. 40
figure 40

Case C60-R3, statistical convergence in the recess. Radial profiles of axial velocity. − mean profiles, \(--\) rms profiles

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B: Mean fields for cases A10 and C10

Longitudinal slices of average temperature, density and oxygen mass fraction for cases A10 and C10 are shown in Figs. 41 and 42. As could have been expected from the lowered annular injection velocity, the flame for cases C10 penetrates further into the chamber than for cases A10. The recess of the LOx tube leads to a reduction of the flame length, for both cases. This is similar to the observations made on case C60. This reduction is associated with a modification of the heat release rate distribution in the chamber, as depicted in Fig. 43. For both cases, the heat release rate is augmented up to x \(\approx\) 8d. Differences between recessed and non recessed cases are less noticeable further downstream. The change of heat release due to the recess is lower than the one obtained at 60 bar, but an important growth of 70% is however measured at x = 2d.

Fig. 41
figure 41

Cases A10-NR and A10-R. Longitudinal slices of average temperature, density, oxygen mass fraction and axial velocity. Blue: minimum, red: maximum

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Fig. 42
figure 42

Cases C10-NR and C10-R. Longitudinal slices of average temperature, density and oxygen mass fraction. Blue: minimum, red: maximum

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Fig. 43
figure 43

Longitudinal profiles transversely integrated heat release per unit length for a cases A10 and b cases C10

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C: Flame surface and heat release rate for cases A10 and C10

Following the procedure depicted in Sect. 7.3 and Eq. 4, resolved flame surfaces for cases A10 and C10 are plotted in Figs. 44a and 45a, respectively. Contrary to cases C60, the modification of the flame surface is here limited, and essentially corresponds to a one diameter shift of the curve once the injector is recessed. The change of heat release is thus provoked by a modification of the heat release per flame surface \(\dot{q}_s\). This is shown in Figs. 44b and 45b, where \(\dot{q}_s\) increases as the LOx injector is recessed. This is a consequence of the thermal expansion in the recess that augments velocity and turbulent mixing at the injector exit.

Fig. 44
figure 44

Cases A10-NR and A10-R. Longitudinal profile of a transversely integrated resolved flame surface per unit length and b transversely integrated heat release per resolved flame surface and per unit length

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Fig. 45
figure 45

Cases C10-NR and C10-R. Longitudinal profile of a transversely integrated resolved flame surface per unit length and b transversely integrated heat release per resolved flame surface and per unit length

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Schmitt, T. Assessment of Large Eddy Simulation for the prediction of recessed inner tube coaxial flames. CEAS Space J 16, 31–58 (2024). https://doi.org/10.1007/s12567-023-00485-0

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