%0 Journal Article %1 oberlack2000stochastic %A Oberlack, Martin %A Arlitt, Raphael %A Peters, Norbert %D 2000 %J Combustion Theory and Modelling %K prev %N 4 %P 495-509 %T On stochastic Damkohler number variations in a homogeneous flow reactor %V 4 %X For combustion in a homogeneous flow reactor stochastic fluctuations of the Damköhler number are analysed. The chemistry is described by a one-step first-order reaction with Arrhenius kinetics. The case of an adiabatic system is studied allowing for a reduction to a single equation for the temperature. A parameter of that equation is the Damköhler number which is separated into a mean and a stochastic term carrying white noise characteristics. This allows for an exact treatment of the probability density function in terms of a Fokker-Planck equation. In the case of steady statistics the Fokker-Planck equation is solved exactly in terms of exponential integrals. It is shown that the probability density function usually admits mono- and bi-modal behaviour but even tri-modal behaviour is observed depending on the activation energy, the heat of combustion, the mean Damköhler number and the variance of the Damköhler number. The most common features are mono-modal characteristics, which indicate that the system is strongly attracted either to the unburned or the burned state. Two cases of Damköhler number variations are studied. The first one corresponds to the classical combustion situation, where two steady states exist and transitions between them can be triggered by Damköhler number fluctuations. The other corresponds to a new mode of combustion, called `mild' combustion, where the steady-state solution depends monotonically on the Damköhler number, such that ignition and extinction events are suppressed.

@article{oberlack2000stochastic, abstract = {For combustion in a homogeneous flow reactor stochastic fluctuations of the Damköhler number are analysed. The chemistry is described by a one-step first-order reaction with Arrhenius kinetics. The case of an adiabatic system is studied allowing for a reduction to a single equation for the temperature. A parameter of that equation is the Damköhler number which is separated into a mean and a stochastic term carrying white noise characteristics. This allows for an exact treatment of the probability density function in terms of a Fokker-Planck equation. In the case of steady statistics the Fokker-Planck equation is solved exactly in terms of exponential integrals. It is shown that the probability density function usually admits mono- and bi-modal behaviour but even tri-modal behaviour is observed depending on the activation energy, the heat of combustion, the mean Damköhler number and the variance of the Damköhler number. The most common features are mono-modal characteristics, which indicate that the system is strongly attracted either to the unburned or the burned state. Two cases of Damköhler number variations are studied. The first one corresponds to the classical combustion situation, where two steady states exist and transitions between them can be triggered by Damköhler number fluctuations. The other corresponds to a new mode of combustion, called `mild' combustion, where the steady-state solution depends monotonically on the Damköhler number, such that ignition and extinction events are suppressed. }, added-at = {2013-03-21T15:13:41.000+0100}, author = {Oberlack, Martin and Arlitt, Raphael and Peters, Norbert}, biburl = {https://www.bibsonomy.org/bibtex/2478ce67faf850c503578a2c705cec73d/itv}, interhash = {530f9d59f9081c92c0b2219326099845}, intrahash = {478ce67faf850c503578a2c705cec73d}, journal = {Combustion Theory and Modelling}, keywords = {prev}, number = 4, pages = {495-509}, timestamp = {2014-07-31T07:46:38.000+0200}, title = {On stochastic Damkohler number variations in a homogeneous flow reactor}, volume = 4, year = 2000 }