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Model flames in the Boussinesq limit: The case of pulsating fronts



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PHYSICAL REVIEW E 71 067303 2005 Model flames in the Boussinesq limit The case of pulsating fronts N Vladimirova and R Rosner ASC Flash Center Department of Astronomy and Astrophysics The University of Chicago Chicago Illiuois 60637 USA Received 28 September 2004 published 29 June 2005 We extend earlier work on the nonlinear behavior of premixed flames in a gravitationally stratified medium subject to the Boussinesq approximation in two dimensions The main result is that the nature of the traveling burning front is largely determined by the form of the adopted boundary conditions on the side walls while symmetric boundary conditions lead to stably scalloped traveling wave solutions loss of symmetry leads to the development of pulsating fronts However despite differences in geometrical features the symmetric and asymmetric systems obey the same scaling behavior for the average effective flame speed DOI 10 1103 PhysRevE 71 067303 PACS number s 47 70 Fw 47 20 Bp 47 55 Hd 44 25 f The Boussinesq model is the simplest system exhibiting buoyancy effects without introducing the complexities associated with the presence of sound waves and gravitational stratification of the ambient medium In our earlier article 1 we have studied flames in the Boussinesq limit in a two dimensional Rayleigh Taylor configuration see also 2 The heavier reactant was placed on top of the lighter product with the interface between the reactant and the product slightly perturbed The reaction front becomes RayleighTaylor unstable increasing the length of the interface and consequently the bulk burning rate Eventually the front stabilizes in a scalloped shape which propagates as a twodimensional traveling wave The shape of the interface and the traveling wave speed are determined by the maximum allowable wavelength and in the limit of large wavelengths are independent of the laminar flame speed The focus of 1 was on a comparison with classic singlemode Landau Darrieus and Rayleigh Taylor instabilities



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