Radial flow profile determination

However, flow tube systems for use at much higher pressures, up to several hundred Torr, have also been designed and applied to reactions of atmospheric interest (e.g., see Keyser, 1984 Abbatt et al., 1990, 1992 Seeley et al., 1993 and Donahue et al., 1996a). At these higher pressures, the velocity and radical axial and radial concentration profiles are experimentally determined and the full continuity equation describing the concentration profiles is solved. 

An analysis of radial flow, fixed bed reactor (RFBR) is carried out to determine the effects of radial flow maldistribution and flow direction. Analytical criteria for optimum operation is established via a singular perturbation approach. It is shown that at high conversion an ideal flow profile always results in a higher yield irrespective of the reaction mechanism while dependence of conversion on flow direction is second order. The analysis then concentrates on the improvement of radial profile. Asymptotic solutions are obtained for the flow equations. They offer an optimum design method well suited for industrial application. Finally, all asymptotic results are verified by a numerical experience in a more sophisticated heterogeneous, two-dimensional cell model. 

The determination of the effective surface age is the key for comparison of results obtained by different experimental techniques. If for example the drop volume technique is used in its "classical" version, which is based on continuously growing drops, dynamic surface tensions are obtained as a function of drop formation time. It was shown in the previous chapter, that the process of adsorption at the surface of a growing drop is overlapped by a radial flow inside the drop, which changes the diffusion profile. In addition, the drop area increases and... 

The internals of the bubble column reactor may have a dramatic impact on the flow patterns of the bubbles and the liquid. Companies have not divulged details about the internals to date. Some details of the US DOE pilot plant (22.5 inch 0.57 m diameter) have been published [ 106]. In this report the dimensions of the cooling tubes, their location, and their number are provided. These cooling coils occupied about 10% of the total volume of their commercial reactors slurry volume. The gas holdup and bubble characteristics as well as their radial profiles were determined in a column that was about the size of the US DOE reactor [107-109]. Dense internals were found to increase the overall gas holdup and to alter the radial gas profile at various superficial gas velocities. The tube bundle in the column increased the liquid recirculation and eliminated the rise of bubbles in the wall region of the column. These results indicate that further studies of bubble column hydrodynamics are directed toward larger scale units equipped with heat exchange tubes. 

Here, we will apply the momentum balance to determine the steady-state radial velocity profile for the flow in a pipe of a Newtonian fluid. Figure 6.3 describes the system. 

Shown in Figure 12-4. By having six paths in the core block region the model can represent radial primary flow maldistribution as well as a radial power profile. TRACE heat structures (7) are used to model the core block between each ring of annular flow passages, This heat structure detail allows the model to determine core structural temperature profiles in both the axial and radial directions. 

Radial density gradients in FCC and other large-diameter pneumatic transfer risers reflect gas—soHd maldistributions and reduce product yields. Cold-flow units are used to measure the transverse catalyst profiles as functions of gas velocity, catalyst flux, and inlet design. Impacts of measured flow distributions have been evaluated using a simple four lump kinetic model and assuming dispersed catalyst clusters where all the reactions are assumed to occur coupled with a continuous gas phase. A 3 wt % conversion advantage is determined for injection feed around the riser circumference as compared with an axial injection design (28). 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Packed Beds. Data on liquid systems using a steady point source of tracer and measurement of a concentration profile have been obtained by Bernard and Wilhelm (B6), Jacques and Vermeulen (Jl), Latinen (L4), and Prausnitz (P9). Blackwell (B16) used the method of sampling from an annular region with the use of Eq. (62). Hartman et al. (H6) used a bed of ion-exchange resin through which a solution of one kind of ion flowed and another was steadily injected at a point source. After steady state conditions were attained, the flows were stopped and the total amount of injected ion determined. The radial dispersion coefficients can be determined from this information without having to measure detailed concentration profiles. 

One can analyze the Jeffery-Hamel flow using a nondimensional velocity scaled by the maximum velocity at a radial location [429]. This approach permits determination of the local shape of the velocity profiles but still requires an integral mass-flow constraint to determine the local maximum velocity and hence the specific velocity profiles (i.e., in m/s). Nevertheless, using this approach and the limit of small angle, but large Reynolds number, permits the determination of the separation point as a function of the combined parameter Rea2 alone. 

Recall that there is a fundamental scaling difference between the cylindrical wedge flow and the spherical inclined-disk flow. In the wedge flow, the Reynolds number is independent of r, whereas in the spherical case, the Reynolds number scales as /r. Thus, in the spherical case, there is a different Reynolds number at every radial position in the channel. In practice, a quantitative determination of the velocity profile is more complex in the spherical case. The nondimensional velocity profile must be determined at each radial position where the actual velocity profile is desired. 

Conditions C - Bonded cartridge. 8 mm 10 cm (Radial pak A. Waters Associates, Inc.) was used with a mobile phase of a linear gradient ofO-tuOtfc isopropyl alcohol-water (9 1, v/v) (solvent B) in acetonitrile-water (9 1, v/v) (solvent A) over a period of60 min at a flow rate of3 m Lj min. Both solvents contained 5 mM terrabutv/ammonium phosphate. For the determination of the radioactivity profile, fractions were collected at 3(fs intervals and assayed for radioactivity. 

In order to understand the profile of the pressure fluctuation over the volumetric space inside the reactor, multipoint measurement is carried out in each run with five probes. The measuring points are arranged according to the coordinate system shown in Fig. 11.3, where the x-z plane is the impingement plane, x-y is the horizontal plane, and y-z the vertical plane the values of the coordinates are in mm. The flow inside the SCISR is considered to have an approximately axial symmetry. For convenience, part of the data are interrelated in a pillar coordinate system, and the radial coordinate, r, is determined by... 

For a fixed spherical particle in a fully developed laminar pipe flow, determine the Saffinan force on the particle at various radial positions. Identify the location of the maximum Saffman force. Discuss the case if the flow is turbulent (using the 1/7 power law for the velocity profile). 

On the basis of the observations in the macroscale, the flow of a fast fluidized bed can be represented by the core-annulus flow structure in the radial direction, and coexistence of a bottom dense region and a top dilute region in the axial direction. Particle clusters are an indication of the heterogeneity in the mesoscale. A complete characterization of the hydrodynamics of a CFB requires the determination of the voidage and velocity profiles. There are a number of mathematical models accounting for the macro- or mesoaspects of the flow pattern in a CFB that are available. In the following, basic features of several types of models are discussed. 

S The velocity profile in fully developed laminar flow in a circular pipe, in m/s, is given by ii(i ) - 6(1 - 100/ ) where r is the radial distance from the centerline of the pipe in m. Determine (a) the radius of the pipe, (b) the mean velocity through the pipe, and (r) the maximum velocity in the pipe. 

This term may be determined in various ways from experimental data. A frequently used method for single-phase flow (S4) is to differentiate an experimental velocity profile graphically, and to obtain the kinematic viscosity from the velocity gradient with basic relations [e.g., Eqs. (3-1) and (3-2)]. The currently available data for velocity profile do not appear accurate enough to yield as a function of radial position. As an alternative, Hills (H9) has assumed a relation between the local vt and the radial position ... 

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