Reynolds number Taylor-scale

Note that at high Reynolds number Xg lies at scales between L and 77, and thus cannot be given a clear physical interpretation in terms of eddies in the flow. Nevertheless, the Taylor microscale is often used to define the Taylor-scale Reynolds number ... 

V / oX / )]" a relationship that enables lines of constant values of Ri to be plotted, as shown. Turbulence Reynolds numbers quoted in the literature are often based on the Taylor scale, equation (31), instead of the integral scale these are directly related to and are denoted by in Figure 10.5. In addition to the ratio IJd) of the smallest turbulence scale to the laminar-flame thickness, the ratio of the largest scale (the integral scale) to the flame thickness, //<5, is a relevant parameter. Lines of constant values of //(5, generated from equation (30), also are shown in Figure 10.5. 

Earlier it was stated that the structure of a turbulent velocity field may be presented in terms of two parameters—the scale and the intensity of turbulence. The intensity was defined as the square root of the turbulent kinetic energy, which essentially gives a root-mean-square velocity fluctuation U. Three length scales were defined the integral scale /q, which characterizes the large eddies the Taylor microscale X, which is obtained from the rate of strain and the Kolmogorov microscale 1, which typifies the smallest dissipative eddies. These length scales and the intensity can be combined to form not one, but three turbulent Reynolds numbers Ri = U lo/v, Rx. = U X/v, and / k = U ly/v. From the relationship between Iq, X, and /k previously derived it is found that / ... 

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