Stability of a planar flame front in the slow-combustion regime

Liberman, M. A.; Vv, Bychkov; Sm, Golberg; Dl, Book

doi:10.1103/physreve.49.445

Cited by 46 publications

(39 citation statements)

References 11 publications

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“…214,[369][370][371][372][373] These models confirmed Kull's conclusion 368 that the most-important parameter characterizing the instability is the Froude number Fr ¼ V 2 a =ðgL 0 Þ (which is the inverse of Kull's parameter C), where L 0 ¼ v=V a is the characteristic width of the ablation region. When Fr is large, the unstable spectrum consists of only long-wavelength modes…”

Section: Hydrodynamic Stabilitysupporting

confidence: 62%

Direct-drive inertial confinement fusion: A review

et al. 2015

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The direct-drive, laser-based approach to inertial confinement fusion (ICF) is reviewed from its inception following the demonstration of the first laser to its implementation on the present generation of high-power lasers. The review focuses on the evolution of scientific understanding gained from target-physics experiments in many areas, identifying problems that were demonstrated and the solutions implemented. The review starts with the basic understanding of laser–plasma interactions that was obtained before the declassification of laser-induced compression in the early 1970s and continues with the compression experiments using infrared lasers in the late 1970s that produced thermonuclear neutrons. The problem of suprathermal electrons and the target preheat that they caused, associated with the infrared laser wavelength, led to lasers being built after 1980 to operate at shorter wavelengths, especially 0.35 μm—the third harmonic of the Nd:glass laser—and 0.248 μm (the KrF gas laser). The main physics areas relevant to direct drive are reviewed. The primary absorption mechanism at short wavelengths is classical inverse bremsstrahlung. Nonuniformities imprinted on the target by laser irradiation have been addressed by the development of a number of beam-smoothing techniques and imprint-mitigation strategies. The effects of hydrodynamic instabilities are mitigated by a combination of imprint reduction and target designs that minimize the instability growth rates. Several coronal plasma physics processes are reviewed. The two-plasmon–decay instability, stimulated Brillouin scattering (together with cross-beam energy transfer), and (possibly) stimulated Raman scattering are identified as potential concerns, placing constraints on the laser intensities used in target designs, while other processes (self-focusing and filamentation, the parametric decay instability, and magnetic fields), once considered important, are now of lesser concern for mainline direct-drive target concepts. Filamentation is largely suppressed by beam smoothing. Thermal transport modeling, important to the interpretation of experiments and to target design, has been found to be nonlocal in nature. Advances in shock timing and equation-of-state measurements relevant to direct-drive ICF are reported. Room-temperature implosions have provided an increased understanding of the importance of stability and uniformity. The evolution of cryogenic implosion capabilities, leading to an extensive series carried out on the 60-beam OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)], is reviewed together with major advances in cryogenic target formation. A polar-drive concept has been developed that will enable direct-drive–ignition experiments to be performed on the National Ignition Facility [Haynam et al., Appl. Opt. 46(16), 3276 (2007)]. The advantages offered by the alternative approaches of fast ignition and shock ignition and the issues associated with these concepts are described. The lessons learned from target-physics and implosion experiments are taken into account in ignition and high-gain target designs for laser wavelengths of 1/3 μm and 1/4 μm. Substantial advances in direct-drive inertial fusion reactor concepts are reviewed. Overall, the progress in scientific understanding over the past five decades has been enormous, to the point that inertial fusion energy using direct drive shows significant promise as a future environmentally attractive energy source.

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Section: Hydrodynamic Stabilitysupporting

confidence: 62%

Direct-drive inertial confinement fusion: A review

et al. 2015

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“…Note that the Pr = 0 case investigated by Liberman et al (1994) is a singular limit of (17). For Pr = 0, u 1 and v 1 do not appear in the problem, and the corresponding version of (17) is reduced to a 6 × 6 problem.…”

Section: Linearized Equationsmentioning

confidence: 99%

“…Mukunda & Drummond (1993) used a spectral collocation scheme with a simple model for hydrogen-oxygen involving four species and variable transport properties, but only give results for a couple of parameter sets. Liberman et al (1994) examined the problem using a shooting method, ignoring viscosity and for unit Lewis number, and hence did not take into account thermal-diffusive effects. Lasseigne, Jackson & Jameson (1999) used the CDA model with finite activation temperature, which ignores the hydrodynamics.…”

Section: Introductionmentioning

confidence: 99%

Linear stability of planar premixed flames: Reactive Navier–Stokes equations with finite activation energy and arbitrary Lewis number

Sharpe

2003

Combustion Theory and Modelling

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Abstract. A numerical shooting method for performing linear stability analyses of travelling waves is described and applied to the problem of freely propagating planar premixed flames. Previous linear stability analyses of premixed flames either employ high activation temperature asymptotics or have been performed numerically with finite activation temperature, but either for unit Lewis numbers (which ignores thermal-diffusive effects) or in the limit of small heat release (which ignores hydrodynamic effects). In this paper the full Reactive NavierStokes equations are used with arbitrary values of the parameters (activation temperature, Lewis number, heat of reaction, Prandtl number), for which both thermal-diffusive and hydrodynamic effects on the instability, and their interactions, are taken into account. Comparisons are made with previous asymptotic and numerical results. For Lewis numbers very close to or above unity, for which hydrodynamic effects caused by thermal expansion are the dominant destablizing mechanism, it is shown that slowly varying flame analyses give qualitatively good but quantitatively poor predictions, and also that the stability is insensitive to the activation temperature. However, for Lewis numbers sufficiently below unity for which thermal-diffusive effects play a major role, the stability of the flame becomes very sensitive to the activation temperature. Indeed, unphysically high activation temperatures are required for the high activation temperature analysis to give quantitatively good predictions at such low Lewis numbers. It is also shown that state-insensitive viscosity has a small destabilizing effect on the cellular instability at low Lewis numbers.

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“…Finite activation energy linear stability results have been achieved more recently, by Lasseigne et al (1999) for the CDM, by Liberman et al (1994) for the purely hydrodynamic case (Lewis number of unity) and by Sharpe (2003) for the full Reactive Navier-Stokes model with arbitrary Lewis numbers. The works of Lasseigne et al (1999) and Sharpe (2003) showed that for Lewis numbers less than unity (for which thermal-diffusive effects have a major role in the cellular instability) unphysically high activation energies are required for the high activation energy asymptotics to give quantitatively accurate results.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Sharpe

Falle

2006

Combustion Theory and Modelling

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Abstract. Two-dimensional compressible Reactive Navier-Stokes numerical simulations of intrinsic planar, premixed flame instabilities are performed. The initial growth of a sinusoidally perturbed planar flame is first compared with the predictions of a recent exact linear stability analysis, and it is shown the analysis provides a necessary but not sufficient test problem for validating numerical schemes intended for flame simulations. The long-time nonlinear evolution up to the final nonlinear stationary cellular flame is then examined for numerical domains of increasing width. It is shown that for routinely computationally affordable domain widths, the evolution and final state is, in general, entirely dependent on the width of the domain and choice of numerical boundary conditions. It is also shown that the linear analysis has no relevance to the final nonlinear cell size. When both hydrodynamic and thermal-diffusive effects are important, the evolution consists of a number of symmetry breaking cell splitting and re-merging processes which results in a stationary state of a single very asymmetric cell in the domain, a flame shape which is not predicted by weakly nonlinear evolution equations. Resolution studies are performed and it is found that lower numerical resolutions, typical of those used in previous works, do not give even the qualitatively correct solution in wide domains. We also show that the long-time evolution, including whether or not a stationary state is ever achieved, depends on the choice of the numerical boundary conditions at the inflow and outflow boundaries, and on the numerical domain length and flame Mach number for the types of boundary conditions used in some previous works.

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Stability of a planar flame front in the slow-combustion regime

Cited by 46 publications

References 11 publications

Direct-drive inertial confinement fusion: A review

Direct-drive inertial confinement fusion: A review

Linear stability of planar premixed flames: Reactive Navier–Stokes equations with finite activation energy and arbitrary Lewis number

Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

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