Time scale, engulfment

One of the principal difficulties faced when employing Lagrangian micromixing models is the determination of tm based on properties of the turbulent flow fields. Researchers have thus attempted to use the universal nature of high-Reynolds-number isotropic turbulence to link tm to the turbulence time scales. For example, in the E-model (Baldyga and Bourne 1989) the engulfment rate essentially controls the rate of micromixing and is defined by... 

Time constant ofmicromixing by engulfment Transitory vortex tubes are characteristic of turbulent flow. Small energetic vortices acting near Kolmogorov scale engulf the surround-... 

The lumped thermal mass equation also describes the heating-up process of flat face or clamp flanges, where the failure mode is, however, the loss of tightness and consequent secondary leak and fire. It should be noted that when the limped thermal mass heat transfer model was used for the calculation of time-to-failure of flanges engulfed by fire, the results agreed well with the full scale tests in Ref 4. 

The micro-mixing time may be equal to the diffusion time needed to equalize concentrations on the scale of the smallest eddies (in turbulent flow) or the striations (in laminar flow), see s. (4.8) and (4.16). However, with sufficiently intense turbulence, or in vigorously stirred viscous media, the micro-mixing times may be completely determined by rapid deformation of small liquid elements. The micro-mixing time may then be equal to the "engulfment time" in turbulent flow, or the "deformation time" in laminar flow see equations (4.10 and (4.19). Micro-mixing times in turbulent flow are generally on the order of 10 to 1 s, and in laminar flow they can be anywhere between 10 and 10 s. 

At the smallest scales, a micromixing time constant can be given by the reciprocal of the engulfment rate during mixing, Te- This is given (Baldyga and... 

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