NUMERICAL STUDY OF FLAMEPROPAGATION IN BOUNDARY LAYERSMaria

An incompressible, reactive, viscous ow reaches a hot circular cylinder causing a reaction to start. We observe the progress of the reaction, concentrating in the transition towards turbulence within the boundary layer. The problem is divided into the uid dynamics eeects and the combustion eeects. The motion of the ow is resolved by the use of a hybrid vortex algorithm; the reactive part of the problem is modeled by a combination of a temperature equation and a ame ad-vection and propagation algorithm that mimics Huyghens' principle. The following paper will explain these methods, how to implement them, and will present the numerical results of the experiment. The motion of an incompressible, viscous ow is governed by the Navier-Stokes equations, which in vorticity transport form can be written as: @ t + (~ u ~ r) = Re ?1 div(~ u) = 0; (1) where ~ u = (u; v) is the velocity eld, = curl(~ u) = @ x v ? @ y u, Re is the Reynolds number associated with the ow, and is the Laplacian operator. To observe turbulent eeects we will choose the Reynolds number to be large. We will solve the Navier-Stokes equations in an indirect way, by using a stream function and a hybrid vortex algorithm. The stream function has the properties that u = @ y , v = ?@ x , and therefore = ?. The idea of the vortex blobs method is to solve for , given , and then by diierentiating obtain ~ u = (u; v). Near the boundary of the cylinder, the Navier-Stokes equations can be approximated by Pran-dlt's boundary layer equations, which in vorticity transport form can be written as: