Reynolds’ splitting

Turbulent Exchange Model Reynolds Splitting Model Vertical Turbulent Diffusion... 

The technique developed in Section 22.2 (Reynolds splitting) to describe transport by turbulent diffusion can also be applied to dispersion. By analogy to Eq. 22-28, the... 

The Kenics mixer, Figure 10.14(a), for example, consists of a succession of helical elements twisted alternately in opposite directions. In laminar flow for instance, the flow is split in two at each element so that after n elements the number of striations becomes 2". The effect of this geometrical progression is illustrated in Figure 10.14(b) and points out how effective the mixing becomes after only a few elements. The Reynolds number in a corresponding empty pipe is the major discriminant for the size of mixer, one manufacturer s recommendations being... 

Reynolds, P.H.S., Boland, M.J., McNaughton, G.S., More, R.D. Jones, W.T. (1990). Induction of ammonium assimilation leguminous roots compared with nodules using split root system. Physiologia Plantarum 79, 359-67. 

A number of micro mixers use secondary or rotational flows, which are, e.g., created by in-channel flow structures, to stretch and fold fluids. The mixing approach here superposes the rotation by a break-up step, which basically is a splitting step [146], This was done based on the analysis of elementary mixing steps and their corresponding transfer to low Reynolds number mixing. 

Reynolds [127] provided the fundamental ideas about averaging and was the first to accomplish the formulation of the governing equations for turbulent flows in terms of mean and fluctuating flow quantities rather than instantaneous quantities. Reynolds stated the mathematical rules for forming mean values. That is, he suggested splitting a turbulent velocity field into its mean and fluctuating components, and wrote down the equations of motion for these two velocity quantities. 

If the. system is operated such that the main flow and the individual small jet flows have the same Reynolds numbers, Rej = Re , then d /di = Un/d = 1 /n and f nim/f i = 1 / -The ratio of particle number concentrations in the two systems is also equal to I / . By splitting a large jet flow into 10 smaller jets, in the case of constant Reynolds number and total mass flow, the overall particle formation rate should be decreased by a factor of 100. Stream. splitting leads to a decrease in particle formation because the condensable vapor has a shorter residence time in the shear layer, or nucleation zone of the smaller jets, and the residence time in the shear layer is proportional to d/tta, which is smaller in the split streams. For the analysis to hold, both the large and small jets must be turbulent. The scaling relationships hold in jets with low nucleation rates, in the region downstream of the shear layer, where no new particles form. 

The stream splitting concept was tested experimentally by measuring the particle concentration in jets with two different nozzle diameters and the same Reynolds number. The results are shown in Fig. 10.12. For a given axial position and vapor concentration, the aerosol concentration measured on the Jet centerline was proportional to the nozzle diameter. For example, at 20 nozzle diameters, for Re = 4700, the concentration in the Jet with d = 0.375 cm was 5400/cm, and the one with d = 0.235 cm was 2I00/cm . The ratio of the two mea.sured particle concentrations was close to the theoretically predicted value (0.375/0.235) = 2.6. The stream splitting correlation held for the entire range of vapor concentrations tested in the experimenLs. 

Schonfeld, E., Theoretical and experimental characterization of a low-Reynolds number split-and-recombine mixer, Micrqfluidics Nanofluidics 2(3)... 

REYNOLDS NUMBER MAIN FLOW (SCFH) SAMPLE FLOW (SCFH) SPLIT... 

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