Radial velocity distribution

Fig. 3.3.9 Velocity encoded imaging (upper) and radial velocity distribution (lower) for a flow of water at 2.93 mm3 s- through the fixed bed reactor, taken in the same slice as for Figure 3.3.8. (a) Spherical glass beads of 2 mm in diameter and (b) cylindrical pellets with average equivalent diameter of 2.2 mm.

Fig. 1. HR diagram of NGC 2506 crosses are the data from [4]. The targets observed with FLAMES-GIRAFFE are indicated by circles (open circles are the outliers in the radial velocities distribution), and the blue stragglers observed with FLAMES-UVES are indicated by double circles.

Fig. 1 (left panel) shows the radial velocity distribution of selected stars. We estimate a main peak of Vr 220 7 km s 1, in good agreement with previous measurements based on RGB stars [2]. A secondary peak appears at Vr 180 7 km s-1. This dichotomy is shown in the right panel of Fig. 1, where the radial velocity is plotted as s function of the distance from the centre. 

Let us first consider the case when a flow passes through a single circular tube. The flow is assumed to be steady, incompressible, highly viscous, and fully developed. Thus, the radial velocity distribution can be obtained as (Problem 5.6)... 

The radial velocity distribution inside a bubble column has been given by Eq. (3-15). Differentiating this with respect to 4>, one finds the velocity gradient at the column wall, du/d(t>) i, to be zero, which means that peripherally descending liquid flow slides freely along the column wall. In other words, the column wall keeps the downflow in a cylindrical form at the periphery, but exerts only a negligible frictional force. 

The stream function and radial velocity distribution function for a low-Reynold.s-number flow around a sphere are given by the following expressions due to Stokes ... 

The radial velocity distribution in the monolith and the pressure drop across the converter depend on the shape of the divergent and of the monolith sections. Furthermore, mass and heat transfer and hydrodynamic properties depend on the shape of the monolith channels. Ceramic monoliths are generally made of square, circular or triangular channels. In metallic monoliths, channels are manufactured by rolling up a thin corrugated metal sheet. 

Muffler geometry and residence time distribution. The diameter of the converter is larger than the diameter of the exhaust pipe. In the exhaust pipe, flow is generally turbulent, and the turbulent fluid enters the converter trough a short divergent inlet. Due to the divergent flow and to the backpressure induced by the monolith a complicated flow pattern develops and results in a non-uniform radial velocity distribution at the monolith scale. Presently, it is not possible to calculate the velocity distribution, and experiments are required. 

Where can be calculated from correlations of fluid mechanics literature (Idelick (1979), Midoux (1985), Schlunder (1986), Shah and London (1978)). Due to the the lack of accurate data about the radial velocity distribution across the monolith, the pressure drop across the monolith is usually calculated assuming a uniform velocity distribution. Despite this assumption, experimental and theoretical results are in good agreement (Leclerc et al. (1989a, 1991). 

Zygourakis (1989), considered the same model and included a non-uniform radial velocity distribution. He concluded that this distribution may be at the origin of severe performance degradations. Although the various conclusions are coherent, the lack of reliable deactivation kinetics together with debatable rate expressions for the main reactions render these conclusions qualitative. 

To simulate a non-uniform radial velocity distribution, the monolith is assumed to be composed of several macrochannels placed in parallel where fluid velocity is uniform. Fluid velocity varies from one macrochannel to another. Since radial heat conduction is ignored, the full model is... 

A third assumption made in cyclone performance models is that the radial velocity is uniform over CS. The radial velocity is the smallest velocity component, and it is more difficult to measure with LDA than the other components. We can again resort to CFD to get an impression of the flow pattern. Figure 4.4.4 shows profile plots of the radial velocity distribution in both a cylindrical swirl tube and a cylinder-on-cone cyclone with slot inlet. 

Fig. 4.4.4. Profile plots from CFD simulations of the radial velocity distribution in a cylindrical swirl tube and a cylinder-on-cone cyclone. The main difference between the two is that the radial flow from the outer to the inner vortex is more uniformly distributed axially in the cyclone than in the swirl tube...

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