High order effects in one step reaction sheet jump conditions for premixed flames

Dold, J. W.; Thatcher, R. W.; Shah, Akeel A.

doi:10.1088/1364-7830/7/1/306

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…The assumptions underlying the two different approaches are therefore not compatible (most particularly that the one-step activation temperature is a large constant) and care is needed in interpreting results, such as flame-speed and stability boundaries, from one approach in the context of the other. Also, the close leading order connection between the models that arise from the different assumptions concerning the chemistry cannot be expected to extend to higher orders [32].…”

Section: Discussionmentioning

confidence: 99%

Premixed flames modelled with thermally sensitive intermediate branching kinetics

Dold

2007

Combustion Theory and Modelling

100

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The foundations of a relatively simple two-step kinetic scheme for flame chemistry are outlined, involving a model chain branching process that should adopt the activation temperature of a ratelimiting branching reaction in order to offer a broad approximation for hydrocarbon flames. A model energetic intermediate reactant then acts as a buffer between fuel consumption and the release of heat, as the intermediate is converted into products through a completion reaction step. By taking the rate of the latter reaction to be linear in the concentration of the intermediate, which is consistent with the final state being an equilibrium in a broader chemical system, a form of the model is arrived at which admits asymptotic solutions in a thermodiffusive context with constant coefficients. These are developed to second order for large values of the activation energy of the branching reaction and are found to involve the same trends that are seen for lean methane and hydrogen flames calculated using detailed chemical and transport models. Linear stability analysis identifies the ranges of Lewis numbers in which cellular or oscillatory instability can arise, with the latter form of instability disappearing above a threshold heat of reaction. These and the underlying flame solutions themselves depend on the heat of reaction and the degree of heat loss but not on the activation temperature of the branching reaction, to leading order. Near the limit of flammability a direct parallel arises with one-step kinetic models for premixed flames.

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Section: Discussionmentioning

confidence: 99%

Premixed flames modelled with thermally sensitive intermediate branching kinetics

Dold

2007

Combustion Theory and Modelling

100

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“…Hence, a number of models consider the evolution of the fireline instead. Combustion equations in the reaction sheet limit or large activation energy asymptotics reduce to a representation of the reaction zone (here, the fireline) as an evolving internal interface [17,21,24,35,56,77], though this reduction does not seem to have been done for exactly the same equations as here. The asymptotic models typically compute the speed of the movement of the reaction interface in the normal direction, often involving its curvature.…”

Section: Fireline Evolution Fire Spread and Empirical Modelsmentioning

confidence: 99%

A wildland fire model with data assimilation

Mandel

Bennethum

Beezley

et al. 2008

Mathematics and Computers in Simulation

141

107

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A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at selected points into running wildfire simulations. The assimilation technique is able to modify the simulations to track the measurements correctly even if the simulations were started with an erroneous ignition location that is quite far away from the correct one.

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“…At this stage, the solution closely resembles a solution that would arise if there was only a one-step chemical reaction F → P with F consumed and heat released entirely within a single narrow region where T ≈ 1. This property has been explored further in [41] and is discussed in [42].…”

Section: J W Dold Et Almentioning

confidence: 99%

“…Indeed, asymptotic and numerical predictions of some phenomena, such as the negative propagation speed of the flame edges [23][24][25][26] and the existence of stable flame balls [27][28][29][30][31][32][33], preceded and indeed motivated their observation experimentally [26,[31][32][33]. There is now a growing theoretical literature of flame-ball studies based on one-step chemistry [34][35][36][37][38][39][40][41][42], supplemented by numerical studies based on detailed chemical, transport and radiative models [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%