Reactor design Navier-Stokes

The permeate is continuously withdrawn through the membrane from the feed sueam. The fluid velocity, pressure and species concentrations on both sides of the membrane and permeate flux are made complex by the reaction and the suction of the permeate stream and all of them depend on the position, design configurations and operating conditions in the membrane reactor. In other words, the Navier-Stokes equations, the convective diffusion equations of species and the reaction kinetics equations are coupled. The transport equations are usually coupled through the concentration-dependent membrane flux and species concentration gradients at the membrane wall. As shown in Chapter 10, for all the available membrane reactor models, the hydrodynamics is assumed to follow prescribed velocity and sometimes pressure drop equations. This makes the species transport and kinetics equations decoupled and renders the solution of... 

In addition to the Navier-Stokes equations, the convective diffusion or mass balance equations need to be considered. Filtration is included in the simulation by preventing convection or diffusion of the retained species. The porosity of the membrane is assumed to decrease exponentially with time as a result of fouling. Wai and Fumeaux [1990] modeled the filtration of a 0.2 pm membrane with a central transverse filtrate outlet across the membrane support. They performed transient calculations to predict the flux reduction as a function of time due to fouling. Different membrane or membrane reactor designs can be evaluated by CFD with an ever decreasing amount of computational time. 

Physical modeling of CVD processes means solving the Navier-Stokes equations, partial differential equations for mass and heat transport in fluids given the constant boundary conditions of the reactor. These processes affect the uniformity of the deposit in all parts of the reactor. The proper name for CVD reactor physics is chemical vapor technology (CVT) and it is a subject of some significance for industrial reactor design. (This branch of continuum physics is outside the scope of this book, which is concerned with materials rather than machinery.)... 

Fluid dynamics, especially hydrodynamics (the study of moving liquids), is of major importance in the design of chemical plant. The hydrodynamics largely determine the energy consumption of the total plant, the separation performance of columns, and the residence-time behavior of reactors turbulent flow can even destroy pipes. The classical equations for describing the state of flow (= velocity field in space and time) of a fluid are due to Navier and Stokes and date back to the 1800s (Equation 2.4-1) ... 

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