Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910504272789504 |
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| author | Daou, Joel Rajamanickam, Prabakaran |
| author_facet | Daou, Joel Rajamanickam, Prabakaran |
| contents | The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number $Le$ and the flow Peclet number $Pe$. The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the $Le$-$Pe$ plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for $Le<1$, exists now for $Le>1$ but is absent when $Le<1$. In fact, the cellular instability identified for $Le>1$ is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I$_s$) or through a longwave stationary bifurcation (also known as type-II$_s$). The latter type-II$_s$ bifurcation leads in the weakly nonlinear regime to a Kuramoto--Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in $Le>1$ mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19093 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow Daou, Joel Rajamanickam, Prabakaran Fluid Dynamics The stability of a thick planar premixed flame, propagating steadily in a direction transverse to that of unidirectional shear flow, is studied. A linear stability analysis is carried out in the asymptotic limit of infinitely large activation energy, yielding a dispersion relation. The relation characterises the coupling between Taylor dispersion (or shear-enhanced diffusion) and the flame thermo-diffusive instabilities, in terms of two main parameters, namely, the reactant Lewis number $Le$ and the flow Peclet number $Pe$. The implications of the dispersion relation are discussed and various flame instabilities are identified and classified in the $Le$-$Pe$ plane. An important original finding is the demonstration that for values of the Peclet number exceeding a critical value, the classical cellular instability, commonly found for $Le<1$, exists now for $Le>1$ but is absent when $Le<1$. In fact, the cellular instability identified for $Le>1$ is shown to occur either through a finite-wavelength stationary bifurcation (also known as type-I$_s$) or through a longwave stationary bifurcation (also known as type-II$_s$). The latter type-II$_s$ bifurcation leads in the weakly nonlinear regime to a Kuramoto--Sivashinsky equation, which is determined. As for the oscillatory instability, usually encountered in the absence of Taylor dispersion in $Le>1$ mixtures, it is found to be absent if the Peclet number is large enough. The stability findings, which follow from the dispersion relation derived analytically, are complemented and examined numerically for a finite value of the Zeldovich number. The numerical study involves both computations of the eigenvalues of a linear stability boundary-value problem and numerical simulations of the time-dependent governing partial differential equations. The computations are found to be in good qualitative agreement with the analytical predictions. |
| title | Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2406.19093 |