The equations of motion for thermally driven, buoyant flows

Rehm, Ronald G.; Baum, Howard R.

doi:10.6028/jres.083.019

Cited by 345 publications

(231 citation statements)

References 17 publications

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“…The details of the model have been described previously [1,2] and will not be repeated here. A full description can be found in Ref.…”

Section: Hydrodynamic Modelmentioning

confidence: 99%

Numerical Modeling Of Pool Fires Using Les And Finite Volume Method For Radiation

Hostikka¹,

McGrattan²,

Hamins³

2003

Fire Saf. Sci.

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The thermal environment in small and moderate-scale pool flames is studied by Large Eddy Simulation and the Finite Volume Method for radiative transport. The spectral dependence of the local absorption coefficient is represented using a simple wide band model. The predicted radiative heat fluxes from methane/natural gas flames as well as methanol pool burning rates and flame temperatures are compared with measurements. The model can qualitatively predict the pool size dependence of the burning rate, but the accuracy of the radiation predictions is strongly affected by even small errors in prediction of the gas phase temperature.

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“…The details of the model have been described previously [1,2] and will not be repeated here. A full description can be found in Ref.…”

Section: Hydrodynamic Modelmentioning

confidence: 99%

Numerical Modeling Of Pool Fires Using Les And Finite Volume Method For Radiation

Hostikka¹,

McGrattan²,

Hamins³

2003

Fire Saf. Sci.

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“…Generalizations that incorporate variations in density include the Boussinesq approximation (Boussinesq 1903), which allows heating-induced buoyancy in a constant-density background, and the anelastic atmospheric (Batchelor 1953;Ogura & Phillips 1962;Dutton & Fichtl 1969;Gough 1969;Lipps & Hemler 1982, 1985Lipps 1990;Wilhelmson & Ogura 1972) and stellar ( Latour et al 1976;Gilman & Glatzmaier 1981;Glatzmaier 1984) approximations that include the effect of large-scale background stratification in the fluid density and pressure but assume small thermodynamic perturbations from the background. Low Mach number models for chemical combustion (Rehm & Baum 1978;Majda & Sethian 1985;Day & Bell 2000) and nuclear burning (Bell et al 2004) incorporate large compressibility effects due to chemical nuclear reactions and thermal processes with a spatially constant background pressure.…”

Section: Introductionmentioning

confidence: 99%

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics

Almgren

Bell

Rendleman

et al. 2006

ApJ

126

135

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We introduce a low Mach number equation set for the large-scale numerical simulation of carbon-oxygen white dwarfs experiencing a thermonuclear deflagration. Since most of the interesting physics in a Type Ia supernova transpires at Mach numbers from 0.01 to 0.1, such an approach enables both a considerable increase in accuracy and a savings in computer time compared with frequently used compressible codes. Our equation set is derived from the fully compressible equations using low Mach number asymptotics, but without any restriction on the size of perturbations in density or temperature. Comparisons with simulations that use the fully compressible equations validate the low Mach number model in regimes where both are applicable. Comparisons to simulations based on the more traditional anelastic approximation also demonstrate the agreement of these models in the regime for which the anelastic approximation is valid. For low Mach number flows with potentially finite amplitude variations in density and temperature, the low Mach number model overcomes the limitations of each of the more traditional models and can serve as the basis for an accurate and efficient simulation tool.

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“…The ideal software for this purpose is that described by Day and Bell [27], based on the low-Mach-number formulation of the reacting-flow equations of Rehm and Baum [28], for which the Courant-Fredericks-Levy condition [29] does not require the very small time steps that would be needed for numerical stability in the presence of acoustic waves. Thus the dynamics of the fronts can be observed over long durations.…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

A hypothetical burning-velocity formula for very lean hydrogen–air mixtures

Williams¹,

Grcar²

2009

Proceedings of the Combustion Institute

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Very lean hydrogen-air mixtures experience strong diffusive-thermal types of cellular instabilities that tend to increase the laminar burning velocity above the value that applies to steady, planar laminar flames that are homogeneous in transverse directions. Flame balls constitute an extreme limit of evolution of cellular flames. To account qualitatively for the ultimate effect of diffusive-thermal instability, a model is proposed in which the flame is a steadily propagating, planar, hexagonal, close-packed array of flame balls, each burning as if it were an isolated, stationary, ideal flame ball in an infinite, quiescent atmosphere. An expression for the laminar burning velocity is derived from this model, which theoretically may provide an upper limit for the experimental burning velocity.

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The equations of motion for thermally driven, buoyant flows

Cited by 345 publications

References 17 publications

Numerical Modeling Of Pool Fires Using Les And Finite Volume Method For Radiation

Numerical Modeling Of Pool Fires Using Les And Finite Volume Method For Radiation

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics

A hypothetical burning-velocity formula for very lean hydrogen–air mixtures

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