Rayleigh–Taylor instability-induced turbulence in lean hydrogen/air premixed flames

Abstract

In the present work, direct numerical simulations (DNS) are employed to investigate Rayleigh–Taylor (RT) instability-induced turbulence in planar hydrogen/air premixed flames. Four cases with different values of body force are considered, where the body force in cases G0-L30, G10-L30, G30-L30 and G50-L30 is 0, 10, 30 and 50 times the normal gravity $g_0$, respectively. The effect of RT instability on flame morphology and flame speed was examined. It was found that the morphology of the flame front differs noticeably among the four cases. In case G0-L30, thermo-diffusive instability is evident, leading to small-scale cellular structures. In case G10-L30, RT instability becomes significant and finger structures of the flame develops. In cases G30-L30 and G50-L30, RT instability becomes dominant, resulting in the formation of bubble structures, while cellular structures due to thermo-diffusive instability are suppressed. The flame speed increases with increasing body force, primarily due to the increase in flame surface area, while the local reactivity remains largely unchanged. The characteristics of RT instability-induced turbulence in hydrogen/air flames are investigated. In cases G0-L30 and G10-L30, the weak turbulence first tends to be three-dimensional isotropic and subsequently evolves into one-component rod-like turbulence in the downstream region. In contrast, for cases G30-L30 and G50-L30 where RT instability has a dominant role, the RT instability-induced turbulence behind the flame is significant and predominantly rod-like, which then approximates three-dimensional isotropic in the downstream region. The analyses of turbulent kinetic energy spectra indicate that RT instability-induced turbulence follows the $k^{-5/3}$ power-law scaling of isotropic turbulence to some extent for all cases. It was shown that the vorticity magnitude is several times larger in cases G30-L30 and G50-L30 compared with that in cases G0-L30 and G10-L30. The budget of enstrophy transport equation is examined to understand the mechanism of vorticity generation. The dissipation term was found to be the primary sink, while the baroclinic term was the main source term in the region immediately behind the flame. Moreover, it was found that the baroclinic term is mainly determined by the magnitudes of the pressure gradient. For cases G30-L30 and G50-L30, the increase in vorticity magnitude causes a rise in the vortex-stretching term in the downstream region, which becomes the primary source of enstrophy. The effect of domain size on flame structures and RT instability-induced turbulence was investigated, revealing that the domain length in the transverse direction affects the flame morphology. The flame speed is correlated with the product of the normalized body force magnitude $g^{\ast }$ and the normalized domain length in the transverse direction $L^{\ast }$. Analysis of anisotropy invariant mapping suggests that the characteristics of RT instability-induced turbulence is influenced by $g^{\ast }{L}^{\ast }$.

Novelty and significance

In the present work, direct numerical simulations are employed to investigate Rayleigh–Taylor (RT) instability-induced turbulence in planar hydrogen/air premixed flames under different values of body force. For the first time, the characteristics of RT instability-induced turbulence in premixed flames are examined. It was found that the level of RT instability-induced turbulence increases with increasing values of body force. In the cases with small body force, the weak turbulence first tends to be three-dimensional isotropic immediately behind the flame and subsequently evolves into one-component rod-like turbulence in the downstream region. In contrast, for the cases with large body force, the RT instability-induced turbulence behind the flame is significant and predominantly rod-like, which then becomes three-dimensional isotropic in the downstream region. The budget analysis of enstrophy transport equation is performed to understand the mechanism of turbulence generation. Two main sources of enstropy production, i.e. the baroclinic and vortex-stretching terms, are identified, and their contributions are quantified.