Regimes of turbulent reacting flows

The previous example epitomizes how the reacting media can be affected by a turbulent field. To understand the detailed effect, one must understand the elements of the field of turbulence. When considering turbulent combustion systems in this regard, a suitable starting point is the consideration of the quantities that determine the fluid characteristics of the system. The material presented subsequently has been mostly synthesized from Refs. [48] and [49], Most flows have at least one characteristic velocity, U, and one characteristic length scale, L, of the device in which the flow takes place. In addition there is at 

Even though the Reynolds number gives some measure of turbulent phenomena, flow quantities characteristic of turbulence itself are of more direct relevance to modeling turbulent reacting systems. The turbulent kinetic energy q may be assigned a representative value 7o at a suitable reference point. The relative intensity of the turbulence is then characterized by either q()KH2 U2) or (77(7, where (/ = (2q0)m is a representative root-mean-square velocity fluctuation. Weak turbulence corresponds to U /U 1 and intense turbulence has (77(7 of the order unity. 

The second length scale characterizing turbulence is that over which molecular effects are significant it can be introduced in terms of a representative rate of dissipation of velocity fluctuations, essentially the rate of dissipation of the turbulent kinetic energy. This rate of dissipation, which is given by the symbol e0, is 

This rate estimate corresponds to the idea that the time scale over which velocity fluctuations (turbulent kinetic energy) decay by a factor of (He) is 

This length is representative of the dimension at which dissipation occurs and defines a cut-off of the turbulence spectrum. For large A) there is a large spread of the two extreme lengths characterizing turbulence. This spread is reduced with the increasing temperature found in combustion of the consequent increase in v(). 

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