Computational fluid dynamics mass balance

Finite Volume Methods Finite volume methods are utilized extensively in computational fluid dynamics. In this method, a mass balance is made over a cell, accounting for the change in what is in the cell, and the flow in and out. Figure 3-52 illustrates the geometry of the ith cell. A mass balance made on this cell (with area A perpendicular to the paper) is... 

If one wants to model a process unit that has significant flow variation, and possibly some concentration distributions as well, one can consider using computational fluid dynamics (CFD) to do so. These calculations are very time-consuming, though, so that they are often left until the mechanical design of the unit. The exception would occur when the flow variation and concentration distribution had a significant effect on the output of the unit so that mass and energy balances couldn t be made without it. 

For the coarse estimation of extruder size and screw speed, simple mass and energy balances based on a fixed output rate can be used. For the more detailed design of a twin-screw extruder configuration it is necessary to combine implicit experience knowledge with simulation techniques. Theses simulation techniques cover a broad range from specialized programs based on very simple models up to detailed Computational Fluid Dynamics (CFD) driven by Finite Element Analysis (FEA) or Boundary Element Method (BEM). 

Significant progress is being made in fundamental approaches. The current powerful computational fluid dynamics (CFD) tools (e.g., FLUENT and CFX software)—based on the solution of differential mass and momentum balances—have made it possible to allow simulations of the flow patterns within the crystallizer. Both physical and mathematical modeling add to our knowledge and understanding of the nature of high-concentration suspension flows. 

Under steady-state conditions in a plug-flow tubular reactor, the onedimensional mass transfer equation for reactant A can be integrated rather easily to predict reactor performance. Equation (22-1) was derived for a control volume that is differentially thick in all coordinate directions. Consequently, mass transfer rate processes due to convection and diffusion occur, at most, in three coordinate directions and the mass balance is described by a partial differential equation. Current research in computational fluid dynamics applied to fixed-bed reactors seeks a better understanding of the flow phenomena by modeling the catalytic pellets where they are, instead of averaging or homogenizing... 

The time-averaged velocities and gas holdups in the compartments, as well as the fluid interactions between the zones, are first calculated by computational fluid dynamics (CFD). Then, balance equations for heat and mass transfer and for chemical reactions are evaluated and solved using appropriate software. First results from a simulation of a cumene oxidation reactor on an industrial scale were impressive, as they matched real temperature and concentration fields. 

Carry out heat and mass balances, airflow rate for drying, heater capacity. Computational fluid dynamics (CFD) simulations for such a spray dryer may be performed to determine trends as accuracy of CID models are still not well defined. 

Two basic approaches are often used for fluidized bed reactor modeling. One approach is based on computational fluid dynamics developed on the basis of the mass, momentum, and energy balance or the first principle coupled with reaction kinetics (see Chapter 9). Another approach is based on phenomenological models that capture the main features of the flow with simplifications by assumption. The flow patterns of plug flow, CSTR (continuous-stirred tank reactor). 

Numerical simulations allowed the reproduction of the reactor s dynamic behavior, mainly the thermal balance. Despite the differences between the models, both models reproduced almost in the same way in terms of the reactor and coolant fluid temperature dynamic profiles. Regarding the use of a specific model, the authors advise to take into account some points if the internal heat and mass-transfer coefficients of the catalyst particles are significant. Dynamic Model I is more suitable to represent the reactor dynamic behavior in case of difficulties in the measurement of such parameters. Dynamic Model II must be chosen. For design and simulation studies, where computational time and numeric difficulties for model solution are not limiting factors. Dynamic Model I is the most reliable however, if the same factors are limiting. Dynamic Model II should be the best alternative. 

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