Radial liquid velocity

Figs 8.12 and 8.13 show simulated and experimental results with superficial gas velocity, Vg = 8 (cm/s). Fig 8.12 shows the axial and radial liquid velocity components, the axial gas velocity component and the gas fraction 2.0 (m) above the column inlet. Fig 8.13 shows the number density in each class 2.0 (m) above the inlet. 

The pressure force term is treated in the same way as described for the radial liquid velocity component. 

Though velocity drop leads not only to a decrease of inertia forces, but also to a decrease of radial liquid velocity at any point close to the surface. The first effect is quadratic and dominates over the second which is linear. 

Collision efficiency was calculated by the method proposed for the first time by Dukhin Derjaguin (1958). To calculate the integral in Eq. (10.25) it is necessary to know the distribution of the radial velocity of particles whose centre are located at a distance equal to their radius from the bubble surface. The latter is presented as superposition of the rate of particle sedimentation on a bubble surface and radial components of liquid velocity calculated for the position of particle centres. Such an approximation is possibly true for moderate Reynolds numbers until the boundary hydrodynamic layer arises. At a particle size commensurable with the hydrodynamic layer thickness, the differential of the radial liquid velocity at a distance equal to the particle diameter is a double liquid velocity which corresponds to the position of the particle centre. Such a situation radically differs from the situation at Reynolds numbers of the order of unity and less when the velocity in the hydrodynamic field of a bubble varies at a distance of the order ab ap. At a distance of the order of the particle diameter it varies by less than about 10%. Just for such conditions the identification of particle velocity and liquid local velocity was proposed and seems to be sufficiently exact. In situations of commensurability of the size of particle and hydrodynamic boundary layer thickness at strongly retarded surface such identification leads to an error and nothing is known about its magnitude. 

In the case of slurry flow in a rotary drum, turbulent suspension of the solids can occur due to the axial liquid velocity coupled with the radial liquid velocity due to the drum rotation and mixing action created by the drum internals. Typically, the peripheral drum velocity is much higher than the slurry axial velocity, and, consequently, the drum rotational speed becomes very important for solids turbulent suspension and, hence, transport. 

Figure 3 shows the radial profile of the gas holdup in the riser with increasing superficial gas velocity under different solid holdups. The gas holdup increases with increasing superficial gas velocity at the different solid holdups. At a low superficial gas velocity, the liquid velocity... 

Various correlations for mean droplet size generated by plain-jet, prefilming, and miscellaneous air-blast atomizers using air as atomization gas are listed in Tables 4.7, 4.8, 4.9, and 4.10, respectively. In these correlations, ALR is the mass flow rate ratio of air to liquid, ALR = mAlmL, Dp is the prefilmer diameter, Dh is the hydraulic mean diameter of air exit duct, vr is the kinematic viscosity ratio relative to water, a is the radial distance from cup lip, DL is the diameter of cup at lip, Up is the cup peripheral velocity, Ur is the air to liquid velocity ratio defined as U=UAIUp, Lw is the diameter of wetted periphery between air and liquid streams, Aa is the flow area of atomizing air stream, m is a power index, PA is the pressure of air, and B is a composite numerical factor. The important parameters influencing the mean droplet size include relative velocity between atomization air/gas and liquid, mass flow rate ratio of air to liquid, physical properties of liquid (viscosity, density, surface tension) and air (density), and atomizer geometry as described by nozzle diameter, prefilmer diameter, etc. 

When the radial distances from the rotational axis of a centrifuge to the liquid surface and the bowl wall are /q and respectively, the axial liquid velocity u (m s" ) is given by... 

Fig. 8 shows the time and azimuthally averaged radial liquid saturation profiles at varying superficial gas and liquid velocities at the middle axial position (2.5D). The figure shows that liquid saturation is nearly flat, which suggests a fair uniformity of liquid distribution. Moreover, with increasing liquid velocities, liquid saturation increases. Similar trends were obtained at all scan heights. 

Fig. 8. Effect of superficial gas and liquid velocities on the liquid saturation Fig. 9 Effects of gas and liquid superficial velocities on the cross-radial profile at axial position of 2.5D. sectionally averaged liquid saturation.

Small bubbles and flow uniformity are important for gas-liquid and gas-liquid-solid multiphase reactors. A reactor internal was designed and installed in an external-loop airlift reactor (EL-ALR) to enhance bubble breakup and flow redistribution and improve reactor performance. Hydrodynamic parameters, including local gas holdup, bubble rise velocity, bubble Sauter diameter and liquid velocity were measured. A radial maldistribution index was introduced to describe radial non-uniformity in the hydrodynamic parameters. The influence of the internal on this index was studied. Experimental results show that The effect of the internal is to make the radial profiles of the gas holdup, bubble rise velocity and liquid velocity radially uniform. The bubble Sauter diameter decreases and the bubble size distribution is narrower. With increasing distance away from the internal, the radial profiles change back to be similar to those before contact with it. The internal improves the flow behavior up to a distance of 1.4 m. 

Liquid mixing time decreases sharply for an initial increase in the gas sparging rate and approach an asymptotic value that is determined by the height and diameter of the downcomer and the liquid properties [5]. A higher liquid velocity shortens the gas residence time and results in a decrease of gas holdup and interfacial area. The radial profile of the liquid is parabolic. These are disadvantageous for mass transfer. The mounting of internals in a fixed bed is often used to improve the radial profile of the liquid velocity. This motivates us to mount internals in an EL-ALRs to improve the radial profile of the gas holdup and the liquid velocity and to intensify turbulence. 

Fig. 12 shows the radial profile of the liquid velocity at different axial positions. Due of the baffles, the liquid is redistributed in the radial direction and the turbulent intensity is increased. The radial profile of the liquid velocity is almost uniform after passing the internal. Liquid velocity is lower at the center and higher near the wall as compared with that below the internal. With increasing distance from the internal, the turbulence intensity diminishes and the wall effect becomes more apparent, that is, the liquid velocity increases at the center and decreases near the wall. The radial profile obtained at the position of 114 cm from the internal is similar to that obtained below the internal and is the same as that at the position of 144 cm. 

Mass transfer is essential in EL-ALRs. Smaller bubbles and a uniform gas holdup radial distribution increase the interfacial area and improve mass transfer. Intensified turbulence increases the surface renewal frequency and decreases bubble size. A novel internal to improve mass transfer and the hydrodynamic behavior in a gas-liquid system is reported. Experiments were carried out to study the effect of the internal on the bubble behavior and liquid velocity in an EL-ALR. 

Turbulence is intensified after passing through the internal. The radial profile of the liquid velocity becomes flatter. liquid velocity 114 cm above the internal is the same as that below, that is, the internal affects the liquid velocity up to about 110 cm above the internal. 

Figure 16c is a sample flow map of the liquid velocity profile 221. The gas phase occupies more than 50% of the cross-sectional area of the pipe, and it is not symmetrically distributed above the liquid phase. Figure 16c also shows a higher liquid velocity near the center of the pipe that decreases radially. The lighter (yellow) lines in the lower part of the pipe and near the wall correspond to the liquid velocity values obtained from the power law equation the darker lines (dark gray) above the power law equation values correspond to the near field effect of the transducer. 

Fig. 8.11 Diffusion of volatiles into a growing bubble of radius R. The pressure inside the bubble is Pv, the pressure in the liquid far from the bubble surface is P,x the bubble surface is moving radially at velocity R.

Fig. 1. Schematic diagram of a centrifugal impeller bioreactor (5 1). 1 Magnetic stirring device 2 gas in 3 head plate 4 agitator shaft 5 measurements of the liquid velocity profiles of the discharge flow were performed in the vertical direction across the width of the blades (the vertical dashed line) and at various radial distances from the impeller tip 6 sintered stainless sparger 7 centrifugal blade 8 draft tube 9 DO probe 10 centrifugal rotating pan...

The above analysis can be applied for the case of bubble columns. From Figure I it can be seen that, near the wall the axial component of the liquid velocity is downwards, whereas the radial component of the liquid velocity is towards the wall in the top half of the circulation cell and away from the wall in the lower half of the circulation cell. As a result, for one circulation cell the enhancement factor is given by the following equation ... 

---