A combustible mixture of air and fuel is ignited at the point O at time t-0...

 

  

Transcribed Image Text:

A combustible mixture of air and fuel is ignited at the point O at time t-0 by a spark, which initiates a spherical flame front moving outwards from the point O at a constant velocity Vr. The combustible mixture, which has constant density pu ahead of the flame front, is converted in the very thin flame front to products of combustion, which has a much lower density pp. Because the volume of a fluid element is increased as it is enveloped by the flame front, the combustible mixture is pushed radially outward, although the combustion products remain stationary (up = 0). Determine the radial outflow velocity u,(r,t) of the combustion mixture at r for any time t<r/Vf. Problem 3. Vf Flame front Pu u;(r,t) Combustion r products Pp Vf Vf A combustible mixture of air and fuel is ignited at the point O at time t-0 by a spark, which initiates a spherical flame front moving outwards from the point O at a constant velocity Vr. The combustible mixture, which has constant density pu ahead of the flame front, is converted in the very thin flame front to products of combustion, which has a much lower density pp. Because the volume of a fluid element is increased as it is enveloped by the flame front, the combustible mixture is pushed radially outward, although the combustion products remain stationary (up = 0). Determine the radial outflow velocity u,(r,t) of the combustion mixture at r for any time t<r/Vf. Problem 3. Vf Flame front Pu u;(r,t) Combustion r products Pp Vf Vf