Mixers Reynolds number

The pumping number is a function of impeller type, the impeller/tank diameter ratio (D/T), and mixing Reynolds number Re = pND /p.. Figure 3 shows the relationship (2) for a 45° pitched blade turbine (PBT). The total flow in a mixing tank is the sum of the impeller flow and flow entrained by the hquid jet. The entrainment depends on the mixer geometry and impeller diameter. For large-size impellers, enhancement of total flow by entrainment is lower (Fig. 4) compared with small impellers. 

The constant depends on the hydraulic diameter of the static mixer. The mass-transfer coefficient expressed as a Sherwood number Sh = df /D is related to the pipe Reynolds number Re = D vp/p and Schmidt number Sc = p/pD by Sh = 0.0062Re Sc R. ... 

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

In most proeess piping applieations, the required Kenies mixer diameter is the same as the existing proeess line diameter. The K-faetor for a speeifie proeess applieation is determined by the Reynolds number as follows [35] ... 

Li et al. [36] performed an extensive study on AP in a Sulzer SMX statie mixer with both Newtonian and non-Newtonian fluids. They showed that AP inereased by a faetor of 23 in a SMX statie mixer in the laminar flow regime. Figure 7-24 shows their eorrelation between the Fanning frietion faetor and the Reynolds number for experimental points under various operating eonditions. 

Fig ure 7-24. Friotion faotor versus Reynolds number in Sulzer SMX Statio Mixer. (Source Li et a ., Trans. IChemE, Vol. 75, Part A, pp. 792-798, 1997. Reproduced with permission of the Trans. IChemE.)... 

Figure 5-11 [28] presents an analysis of pumping number versus Reynolds Number for various vessel dimensional relationships, for turbine mixers. 

Figure 7.7. Power number as a function of Reynolds number for a turbine mixer...

Figure 2.40 Zigzag micro mixer with concentration field (left) and flow stream lines (right) obtained from a CFD simulation for a Reynolds number of 38. In [135] a sawtooth geometry of larger amplitude was considered and distinctive recirculation zones were found only at Reynolds numbers larger than 80.

Figure 2.45 Design of a multilamination mixer with hydrodynamic focusing (upper left) and flow pattern in such a mixer for a total volume flow of 10 ml h of water (lower left), taken from [141. The right side of the figure shows the orientation of liquid lamellae over a cross-section of the constriction for different Reynolds numbers [142].

If the Newton number, Ne, in relation to the Reynolds number, Re, of the mixer is known from experiments and the rotor speed, n, the mixer diameter, dji and the mass density pc of the continuous liquid are given. 

Figure 34. Ratio of fluxes (with and without a static mixer) as a function of the Reynolds number (1% polymer latex) (13)...

The second method uses dimensionless numbers to predict scale-up parameters. The use of dimensionless numbers simplifies design calculations by reducing the number of variables to consider. The dimensionless number approach has been used with good success in heat transfer calculations and to some extent in gas dispersion (mass transfer) for mixer scale-up. Usually, the primary independent variable in a dimensionless number correlation is Reynolds number ... 

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... 

The empty-pipe Reynolds number is based on the inner pipe diameter and superficial fluid velocity [Eq. (1)]. If the pipe contains a motionless mixer, Eq. (1) needs to be modified to take into account the metal in the mixer, which reduces the effective diameter but increases the fluid velocity (because it blocks part of the cross section). The theoretically sound characteristic dimension for a motionless mixer is the hydraulic diameter, given by... 

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. 

Electric-force mixing is adequate for mixing flows at very low Reynolds number (-1). By lamination of two fluids with different electric conductivity and/or permittivity in a micro mixer, a steep cross-sectional gradient of the respective properties can be established [91]. The electric field may be parallel or perpendicular to the fluid interface, which is also a boundary where electric properties abruptly... 

M 4] [P 3] Using the improved EKI mixer device, bulk-averaged flow velocities in the outlet channel and in the mixing chamber were 0.5 and 0.16 mm s 1, respectively [25]. The corresponding Reynolds number (Re) is 1.5. 

Channel width, depth (fan) Hydraulic diameter of the micro mixer (fan) Reynolds number Mixing time (ms)... 

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. 

Figure 1.142 A kind of flow-pattern map for zig-zag micro mixers of various dimensions correlating their Reynolds numbers with their hydrodynamic regimes as a function of their ratio of bend length to hydraulic diameter [151]...

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