Micromixing velocity

Note that we have used the fluid velocity U to describe convection of particles, which is valid for small Stokes number. In most practical applications, / is a highly nonlinear function of c. Thus, in a turbulent flow the average nucleation rate will depend strongly on the local micromixing conditions. In contrast, the growth rate G is often weakly nonlinear and therefore less influenced by turbulent mixing. 

Transported PDF methods combine an exact treatment of chemical reactions with a closure for the turbulence field. (Transported PDF methods can also be combined with LES.) They do so by solving a balance equation for the joint one-point, velocity, composition PDF wherein the chemical-reaction terms are in closed form. In this respect, transported PDF methods are similar to micromixing models. 

The composition PDF thus evolves by convective transport in real space due to the mean velocity (macromixing), by convective transport in real space due to the scalar-conditioned velocity fluctuations (mesomixing), and by transport in composition space due to molecular mixing (micromixing) and chemical reactions. Note that any of the molecular mixing models to be discussed in Section 6.6 can be used to close the micromixing term. The chemical source term is closed thus, only the mesomixing term requires a new model. 

An important piece of information that can be obtained from the measurement is that the impinging velocity is very small under normal conditions of SCISR operation, only of the order of magnitude of 10 1 m-s-1, implying very low power consumption, although the SCISR gives an excellent performance of promoting micromixing efficiently. 

As mentioned above, to determine one value for fM needs an experimental curve of X, versus u0 for the case where the impinging velocity m() is taken as the governing variable. The plot of a set of typical data is indicated in Fig. 10.12. From the curve the critical point at which Xs turns from a varying value to a small constant is found at u -0.184 m/s. With the known reaction rate constant at 298 K, the micromixing time can be calculated as... 

The reason for the decrease in the micromixing time with the increase in impinging velocity is clear a higher impinging velocity implies an increased energy dissipation rate and thus more efficient micromixing. 

Figure 10.13 Influence of impinging velocity on micromixing time at oe=] 5...

The reaction system, the experiment procedure, and the analytical method used for the determination of micromixing in the TIJ mixer are the same as those described in the last section of this book but Mahajan et al. correlated their experimental data not with impinging velocity w() but with the jet Reynolds number Re. Also, the researchers employed the measure of increasing both the initial concentration CBo and the reaction temperature to raise the sensitivity of the procedure. The characteristic reaction time constant tK = 200 ms at 25 °C and CBo = 2.5 mM, while rR = 65 ms at 35 °C and CB0 = 4.7 mM, which can be used to bound the micromixing times, rM, no greater than them, respectively. 

The dependences of the micromixing time upon the impinging velocity, tM versus... 

Similar to the case of the investigation on micromixing, the impinging velocity cannot be adjusted and controlled directly, but is done by changing the rotary speed of the propellers, N. Prior to all the measurements the curve describing the relationship between (> and N was calibrated with the same method as that used in Ref. [110], and the results are shown in Fig. 11.2, in which the curve is, in turn, used for conversion between the rotary speed and the impinging velocity in the data treatment. The curve in Fig. 11.2 is essentially the same as that shown in Fig. 10.9 but with some differences in specific data. The existence of such differences is natural, because the shape of the propeller paddle and particularly the width of the gap between the paddle of the propeller and the drawing tube have a fundamental influence on the flow rate drawn by the propeller, while errors in mechanical manufacture are also unavoidable.. 

Clear distinction between macromixing effects (large scale motions due to average velocities) and micromixing effects (turbulent fluctuations),... 

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