Abstract
We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.
Full Text
Topics from this Paper
Cellular Flow
Bulk Burning Rate
Periodic Shear Flow
Shear Flow
Quenching
+ Show 5 more
Create a personalized feed of these topics
Get StartedSimilar Papers
Combustion Theory and Modelling
Sep 1, 2003
Physical Review E
Apr 29, 2013
Social Work
Jan 1, 2016
Physics Letters A
Oct 1, 2011
Sep 18, 2022
arXiv: Analysis of PDEs
Feb 22, 2000
Aug 16, 2019
Journal of Physics: Condensed Matter
May 11, 2011
arXiv: Statistical Mechanics
Jul 3, 2008
Jan 1, 2018
Journal of Fluid Mechanics
Apr 22, 2020
Journal of The Electrochemical Society
Oct 1, 1995
Jan 1, 2009
arXiv: Astrophysics
Aug 4, 2001
arXiv: Fluid Dynamics
arXiv: Fluid Dynamics
May 13, 2021
arXiv: Fluid Dynamics
Apr 27, 2021
arXiv: Fluid Dynamics
Apr 22, 2021
arXiv: Fluid Dynamics
Apr 11, 2021
arXiv: Fluid Dynamics
Apr 7, 2021
arXiv: Fluid Dynamics
Mar 31, 2021
arXiv: Fluid Dynamics
Mar 31, 2021
arXiv: Fluid Dynamics
Mar 30, 2021