TY - JOUR

T1 - Flame enhancement and quenching in fluid flows

AU - Vladimirova, Natalia

AU - Constantin, Peter

AU - Kiselev, Alexander

AU - Ruchayskiy, Oleg

AU - Ryzhik, Leonid

N1 - Funding Information:
This research is supported in part by the ASCI Flash center at the University of Chicago under DOE contract B341495. PC was supported partially by NSF DMS-0202531. AK has been supported by NSF grants DMS-0102554 and DMS-0129470 and an Alfred P Sloan Fellowship. LR was supported partially by NSF grant DMS-0203537 and by an Alfred P Sloan Research Fellowship.

PY - 2003/9

Y1 - 2003/9

N2 - We perform direct numerical simulations 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 the 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 ∼ aU + 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 ∼ U1/4. We also study the 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 size W can be typically quenched by a flow with amplitude U ∼ αW. The constant α 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 ∼ W4 if the cell size is smaller than a critical value.

AB - We perform direct numerical simulations 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 the 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 ∼ aU + 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 ∼ U1/4. We also study the 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 size W can be typically quenched by a flow with amplitude U ∼ αW. The constant α 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 ∼ W4 if the cell size is smaller than a critical value.

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U2 - 10.1088/1364-7830/7/3/303

DO - 10.1088/1364-7830/7/3/303

M3 - Article

AN - SCOPUS:0142156219

VL - 7

SP - 487

EP - 508

JO - Combustion Theory and Modelling

JF - Combustion Theory and Modelling

SN - 1364-7830

IS - 3

ER -