Bulk flow isothermal conditions

Figure 19.7 Influence of swirl on antin-odal RMS pressure fluctuation flow arrangement with swirl bulk mean axial velocity of main flow in swirler, Um = 17 m/s, Reynolds number in swirler (for isothermal conditions). Res = UmD/v = 56,000 1 — Sw = 0.6 2 — 1.35 3 — 1.8 4 — 2.4 and 5 — 3.75...

Suppose that a gas reactant in a flowing fluid reacts on a nonporous catalyst at isothermal conditions. In steady state, the mass transfer rate of the reactant from the bulk of the fluid to the catalytic surface is equal to the reaction rate (nth order) ... 

Mkrostructured reactors (MSR) for heterogeneous catalytic processes mostly consist of a large number of parallel flow channels. At least one dimension of these channels is smaller than 1 mm, but rarely <100 pm. This leads to an increased heat transfer in the direction of the smallest dimension. The volumetric heat transfer performance in microstructured devices is several magnitudes higher than in conventional reactors. Therefore, even highly exothermic or endothermic reactions can be operated under near isothermal conditions and thermal runaway can be avoided (see Chapter 5). In addition, mass transfer between the bulk phase... 

The formation of gas bubbles bypasses reactant away from contact with the catalyst phase, although this effect is alleviated to some extent by exchange of reactant via mass transfer as well as bulk flow across the bubble surface. The bubbles coalesce to large sizes in their ascent through the bed. Our interest is in calculating the conversion in the reactor, which is assumed to occur under isothermal conditions. The following considerations are extremely important in the formulation of the population balance model. 

Assuming isothermal conditions and neglecting bulk flow, radial concentration gradients in the pore and external mass transfer resistance, the following dimensionless form of the pore plugging model is derived ( ). 

From the mechanism it can be seen that material is added to or depleted from the gas phase by adsorption/desorption with the exception of hydrogen which is assumed to be consumed directly from the gas phase. In formulating a theoretical model for the system it was assumed that the adsorption/desorption kinetics played an important role in the dynamics of the periodic operation and these kinetics were incorporated into the dynamic equations. Furthermore, it was assumed that there was neither bulk nor pore diffusional heat and mass transfer resistances, that the reactor was isothermal (both in the bulk gas phase and locally) and that the flow pattern in the reactor could be approximated by plug flow. Most of the above assumptions (i.e. plug flow, bulk isothermal conditions, no pore diffusion limitations) could be... 

We stress that Eq. (2.3.1) is the rigorous starting point for describing diffusion in porous media for isothermal conditions. Simplified forms of this equation are used frequently by neglecting both the bulk flow and the viscous flow terms. The bulk flow term may be neglected only for equimolar counterdiffusion or when the mole fraction of the transferred substance is small. 

First of all, let us consider the reaction of a porous solid with a reactant gas, such as discussed in Chapter 4. By assuming isothermal conditions, first-order kinetics, and the absence of bulk flow effects, the governing equations may be written as... 

Equation (5) signifies that the solution is restrained from bulk flow, a situation which always holds when the fluid is confined to a fixed closed vessel. Only isothermal conditions are considered - Equation (6) - and furthermore we suppose the absence of chemical reactions. A more complex situation would for instance be encountered if bound or condensed counter-ions were exchanging at a finite rate with atmospheric isotopic counter-ions [6]. 

Similar to the two previous cases (see Sections 9.5.2 and 9.5.3), the problem is solved numerically, whereas the liquid film region is discretized in a spatially uniform grid. The process is considered as an isothermal operation, assuming plug flow of both phases and constant flow rate values of both gas and liquid phases due to low solute concentrations [70]. In the bulk liquid, reaction equilibrium condition is used as a boundary condition for the film region. In order to describe film diffusion, the simple Fick s law is applied. 

In the jump-condition formulation the physical problem is generally decomposed into k bulk phase domains where the continuity and momentum equations for isothermal incompressible flows holds, and at the interface between these domains boundary conditions are specified using the interface jump conditions. That is, across the interface some quantities are required to be continuous, while others are required to have specific jumps. The discontinuous (singular) momentum jump condition can be derived by use of the surface divergence theorem (see e.g., [63] p 51 [26]). A rigorous derivation of the jump balances for the multi-fluid model is given in sect 3.3. 

Burghardt and Aerts [12] proposed a method for evaluation of the pressure change in an isothermal porous pellet within which a single chemical reaction takes place, accompanied by mass transfer by Knudsen diffusion, bulk diffusion and viscous convective flow of the reacting mixture. The pressure change did also depend on the reaction and on the mixture composition on the pellet surface. It was concluded that the pressure changes in a catalyst pellet under conditions normally encountered in industry are most likely so small that they can be neglected in process simulations. 

Additional simulation development is planned to correct any variances between the observations and predictions, and also to apply the simulation to highly dynamic, non-isothermal, and non-Newtonian flows. Accordingly, it is believed that a coupled field simulation may be required that interleaves the bulk deformation of the flow according to the Navier-Stokes equations with the morphology development predicted by the Cahn-Hilliard equation. Accordingly, the simulation should support the process development of appropriate boundary and initial conditions to enable polymer self-assembly. 

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