Vessel flow field

A qualitative picture of the flow field created by an impeller in a mixing vessel in a single-phase liquid is useful in establishing whether there are stagnant or dead regions in the vessel, and whether or not particles are likely to be suspended. In addition, the efficiency of mixing equipment, as well as product quality, are influenced by the flow patterns prevailing in the vessel. 

Even if satisfactory equations of state and constitutive equations can be developed for complex fluids, large-scale computation will still be required to predict flow fields and stress distributions in complex fluids in vessels with complicated geometries. A major obstacle is that even simple equations of state that have been proposed for fluids do not always converge to a solution. It is not known whether this difficulty stems from the oversimplified nature of the equatiorrs, from problems with ntrmerical mathematics, or from the absence of a lamirrar steady-state solution to the eqrratiorrs. 

As a result, the turbulent-flow field in a stirred vessel may be far from isotropic and homogeneous. Some of the cornerstones of turbulence theory, however, start from the assumption that production and dissipation of turbulent kinetic energy balance locally. In many chemical engineering flows, this... 

Even nowadays, a DNS of the turbulent flow in, e.g., a lab-scale stirred vessel at a low Reynolds number (Re = 8,000) still takes approximately 3 months on 8 processors and more than 17 GB of memory (Sommerfeld and Decker, 2004). Hence, the turbulent flows in such applications are usually simulated with the help of the Reynolds Averaged Navier- Stokes (RANS) equations (see, e.g., Tennekes and Lumley, 1972) which deliver an averaged representation of the flow only. This may lead, however, to poor results as to small-scale phenomena, since many of the latter are nonlinearly dependent on the flow field (Rielly and Marquis, 2001). 

Yet (steady) RANS-based simulations are attractive as they relatively cheaply deliver a quick impression of the overall flow field in the vessel. Effects on the overall flow field of varying the position of impeller, feed pipe, withdrawal pipe, and/or heat coil can easily be explored. 

Whenever a free surface is present at some (mean) fixed position, most CFD codes assume it to be strictly flat, while in the direction normal to the free surface velocities and gradients of most variables are taken zero. Usually, this is accomplished by defining mirror cells at the free surface. It is not clear what the effect is of the use of such mirror cells on the flow field in the upper part of the vessel in comparison with real life where the surface is not necessarily flat. 

A second choice to be made relates to the size of the flow domain. It may be worthwhile to limit the calculational job by reducing the size of the flow domain, e.g., by identifying an axis or plane of symmetry, or, in a cylindrical vessel with baffles mounted on the wall, due to periodicity in the azimuthal direction. Commercial software accomplishes these choices by means of symmetry cells and cyclic cells, respectively although such choices reduce the size of the simulation, they may eliminate the possibility of finding the real (asymmetric, unstable, or transient) 3-D flow field. The presence of feed pipes or drain or withdrawal pipes may also make the use of symmetry or cyclic cells impossible. Again, this issue only plays a role in RANS-type simulations. 

Properly simulating a dissolution process of solid particles in a stirred vessel operated in the turbulent-flow regime urges for a very detailed simulation of the turbulent-flow field itself. Just reproducing the overall flow pattern by means of... 

One really may need an inherently transient LES to capture all these details. The finer the grid for such a LES, the more reliably the local transient conditions may be taken into account in reproducing this turbulent mass transfer process (while ignoring the issue of supplying the heat for the dissolution which may also depend on a proper representation of the turbulent-flow field). An additional important issue is how many particles have to be tracked for a proper representation of the transient spatial distribution of the particles over the vessel. 

This additional Eq. (18) was discretized at the same resolution as the flow equations, typical grids comprising 1203 and 1803 nodes. At every time step, the local particle concentration is transported within the resolved flow field. Furthermore, the local flow conditions yield an effective 3-D shear rate that can be used for estimating the local agglomeration rate constant /10. Fig. 10 (from Hollander et al., 2003) presents both instantaneous and time-averaged spatial distributions of /i0 in vessels agitated by two different impellers color versions of these plots can be found in Hollander (2002) and in Hollander et al. (2003). 

Mounting of the cloud water collectors on the aircraft is a critical issue because flow-field effects can easily distort the size distribution of drops. If at all possible, the collector should be mounted on a pylon so that the collector is in the free airstream. Substantially greater efficiencies can be achieved if the collector is mounted with a forward inclination of about 12° to 15° relative to a perpendicular from the aircraft longitudinal centerline. This kind of mounting accounts for the nose-up attitude at which most aircraft fly under cruise conditions and also provides a component of the airstream to drive impacted cloud droplets down the rod into the collection vessel, minimizing losses due to blow-off (28). 

Stirred tank. The simplest system to achieve droplet break-up is with a stirrer in a vessel. In this case, the flow field is not very intense, as the stirrer is usually not very close to the wall of the vessel, and therefore the droplets remain relatively large (>10 pm). The droplet size distribution is usually relatively wide, but will become smaller with longer treatment times. The power density that can be apphed is relatively small, so if one wants to produce droplets smaller than approximately 10 pm, this equipment does not suffice. 

Brucato, A., Ciofalo, M, Grisafi, F. and Micale, G. (1994), Complete numerical simulations of flow fields in baffled stirred vessels the inner-outer approach, I ChemE Symposium Series no. 136, 155. 

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