Taylor microscales

Although vortices of small scale, such as Kolmogorov scale or Taylor microscale, are significant in modeling turbulent combustion [4,6-9], vortices of large scale, in fhe order of millimeters, have been used in various experiments to determine the flame speed along a vorfex axis. 

These length scales characterize the larger eddies in the flow (hence the name integral ). Other widely used length scales are the Taylor microscales, which are determined by the... 

Likewise, the ratio of the transverse Taylor microscale and the turbulence integral scale can be expressed as... 

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 ... 

Like the velocity spatial correlation function discussed in Section 2.1, the scalar spatial correlation function provides length-scale information about the underlying scalar field. For a homogeneous, isotropic scalar field, the spatial correlation function will depend only on r = r, i.e., R,p(r, t). The scalar integral scale L and the scalar Taylor microscale >-,p can then be computed based on the normalized scalar spatial correlation function fp, defined by... 

Moreover, like the relationship between the turbulence Taylor microscale and the dissipation rate e, X t) is related to the scalar variance decay rate by17... 

The scalar Taylor microscale is thus related to the mixing time i.e., tmix = k /6r. 

In general, the scalar Taylor microscale will be a function of the Schmidt number. However, for fully developed turbulent flows,18 l.,p L and /, Sc 1/2Xg. Thus, a model for non-equilibrium scalar mixing could be formulated in terms of a dynamic model for Xassociated with working in terms of the scalar spatial correlation function, a simpler approach is to work with the scalar energy spectrum defined next. 

In a sense, the Taylor microscale is similar to an average of the other scales, /0 and Zk, but heavily weighted toward Zk. 

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 / ... 

The second length scale obtained from f t, x) is the longitudinal Taylor microscale, A/. 

The Taylor microscale Af is now defined as a length scale which for a very small X values gives ... 

The Taylor microscale does not represent any distinct group of eddies, but the ratios and are fair estimates of the rate of strain characterizing viscous dissipation of energy (e.g., [5], p. 148). 

The longitudinal macroscale A of turbulence can be expressed by the longitudinal Taylor microscale ... 

The micromixing term, the last one, involves, the Taylor microscale of the fluctuations (t>, which is also to be prescribed in turbulence of... 

In the lEM Model, the micromixing time (or exchange time) is a phenome-noiogicai parameter. It may actually represent various processes including molecular diffusion (and not only exchange in the Taylor microscale range). 

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