231 Inlet

For any model representing a flow process, the inlet boundary is a boundary through which the surrounding environment communicates with the solution domain. Generally, at such inlet boundaries, information about the velocity (or pressure), temperature and composition of the incoming fluid stream is assumed to be known. When the velocity components at the inlet are known, the inlet boundary conditions simply become:

where subscript 'set' indicates known values. <p represents all the scalar variables of interest (temperature, species concentrations, physical properties and so on) except pressure. When the normal component of the velocity is known at the boundary, the boundary condition for pressure is not required since the velocity field depends on the pressure gradient and not on the absolute value of pressure.

It must be noted here that in most reactor simulations, the solution domain is restricted to the vessel, and generally flow within the feed pipes is not modeled. This means, that although volumetric flow rates are known accurately, the velocity distribution at the inlet is seldom known accurately. The most widely used practice is to use a knowledge of fully developed flow in pipes to specify the inlet velocity distribution. Thus, for laminar flow through a cylindrical inlet pipe, one can specify a parabolic velocity profile as a boundary condition at the inlet. However, if feed pipes have complex shapes, it will be necessary to develop an additional model to formulate appropriate inlet boundary conditions. Even with simple geometry like cylindrical pipes, in many reactor engineering applications the specification of inlet boundary conditions based on fully developed profiles may not be appropriate. To illustrate this, consider a simple example of a reactor vessel with a bottom inlet. In most cases, such an inlet pipe will have a bend very near to the entry in the reactor vessel (Fig. 2.2). Such a bend or any other pipe fitting will significantly change the velocity profile at the inlet defined at the vessel boundary. In such cases, either one has to include a significant portion of the feed pipe in the reactor simulation model or develop a separate model for the inlet pipe and use the results obtained from such a model to specify inlet boundary conditions near the vessel boundary.

When velocity components at the inlet boundary are not known, it is necessary to specify the pressure at the inlet boundary. Simplified equations can then be used (such as Bernoulli's equation) to calculate velocity at the inlet boundary (Fig. 2.3). For incompressible flow, if the specified total pressure at the inlet boundary is po, the

Possible inlet locations

Not appropriate to use fully developed profile: It is necessary to use experimental data or a separate model to specify inlet boundary conditions at this location

Possible inlet locations

Fully developed profile may be used

FIGURE 2.2 Typical arrangement of feed pipe to reactor vessel and location of inlet boundaries.

Pressure Inlet -►

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