Turbulent—laminar flow system

This equation, which is called the Deutsch equation, has been shown to be a useful tool for estimating the performance of electrostatic precipitators. An interesting detail in the Deutsch equation is the exponent, which is equal to the collection efficiency of a laminar flow system. The equations based on laminar flow and turbulent flow can be assumed to be the extreme conditions, and the true situation is somewhere in between these two cases (see Fig. 13.1,5). 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

In the absence of diffusion, all hydrodynamic models show infinite variances. This is a consequence of the zero-slip condition of hydrodynamics that forces Vz = 0 at the walls of a vessel. In real systems, molecular diffusion will ultimately remove molecules from the stagnant regions near walls. For real systems, W t) will asymptotically approach an exponential distribution and will have finite moments of all orders. However, molecular diffusivities are low for liquids, and may be large indeed. This fact suggests the general inappropriateness of using to characterize the residence time distribution in a laminar flow system. Turbulent flow is less of a problem due to eddy diffusion that typically results in an exponentially decreasing tail at fairly low multiples of the mean residence time. 

Many experimental results have been published, which deal with shear stress in biological systems. Most of them use laminar flow systems such as viscosimeters, flow channels or flasks and very small agitated vessels which are not relevant to technical reactor systems with fully developed turbulent flow. On the other hand the geometric and technical parameters are often not sufficiently described. Therefore it is not possible to explain the complex mechanism of force in bioreactors only on the basis of existing results from biological systems. 

Finally, we can also mention that laminar-flow systems with non-Newtonian fluids often require special numerical algorithms that are usually not available in CFD codes designed mainly for turbulent flows. 

At low Re, the viscous effects dominate inertial effects and a completely laminar flow occurs. In the laminar flow system, fluid streams flow parallel to each other and the velocity at any location within the fluid stream is invariant with time when boundary conditions are constant. This implies that convective mass transfer occurs only in the direction of the fluid flow, and mixing can be achieved only by molecular diffusion [37]. By contrast, at high Re the opposite is true. The flow is dominated by inertial forces and characterized by a turbulent flow. In a turbulent flow, the fluid exhibits motion that is random in both space and time, and there are convective mass transports in all directions [38]. 

The most important use of residence time theory is its application to equipment that is already bnilt and operating. It is usually possible to find a tracer together with injection and detection methods that will be acceptable to a plant manager. The RTD is measnred and then analyzed to understand system performance. In this section we focns on such uses. The washout function is assumed to have an experimental basis. Calculations using it will be numerical in nature or will be analytical procednres applied to a model that reproduces the data accurately. Data fitting is best done by nonlinear least squares using untransformed experimental measurements of W(t), F(t), or f(t) versus time, t. Eddy diffusion in a turbulent system justifies exponential extrapolation of the integrals that define the moments in Table 1-2. For laminar flow systems, washout experiments should be continued until at least five times the estimated valne for t. The dimensionless variance has limited usefnlness in laminar flow systems. 

If the system is badly fouled, m - 0, and increasing or decreasing flow at constant pressure has httle effect on flux. However, raising the pressure may raise flux. For an unfouled system in laminar flow 0.33 [Pg.2041]

Pressure drop in catalyst beds is governed by the same principles as in any flow system. Consequently, at very low flow, pressure drop is directly proportional to velocity, and at very high flow, to the square of velocity. These conditions correspond to the laminar and turbulent regimes of the flow. 

While designers of fluid power equipment do what they can to minimize turbulence, it cannot be avoided. For example, in a 4-inch pipe at 68°F, flow becomes turbulent at velocities over approximately 6 inches per second (ips) or about 3 ips in a 6-inch pipe. These velocities are far below those commonly encountered in fluid power systems, where velocities of 5 feet per second (fps) and above are common. In laminar flow, losses due to friction increase directly with velocity. With turbulent flow, these losses increase much more rapidly. 

Fluid flow is also critical for proper operation of a hydraulic system. Turbulent flow should be avoided as much as possible. Clean, smooth pipe or tubing should be used to provide laminar flow and the lowest friction possible within the system. Sharp, close radius bends and sudden changes in cross-sectional area are avoided. 

As a general rule, scaled-down reactors will more closely approach isothermal operation but will less closely approach ideal piston flow when the large reactor is turbulent. Large scaledowns will lead to laminar flow. If the large system is laminar, the scaled-down version will be laminar as well and will more closely approach piston flow due to greater radial diffusion. 

The dimensionless variance has been used extensively, perhaps excessively, to characterize mixing. For piston flow, a = 0 and for a CSTR, a = l. Most turbulent flow systems have dimensionless variances that lie between zero and 1, and cr can then be used to fit a variety of residence time models as will be discussed in Section 15.2. The dimensionless variance is generally unsatisfactory for characterizing laminar flows where > 1 is normal in liquid systems. 

Figure 11 shows the reference floe diameter for viscometers as a function of shear stress and also the comparison with the results for stirred tanks. The stress was determined in the case of viscosimeters from Eq. (13) and impeller systems from Eqs. (2) and (4) using the maximum energy density according to Eq. (20). For r > 1 N/m (Ta > 2000), the disintegration performance produced by the flow in the viscosimeter with laminar flow of Taylor eddies is less than that in the turbulent flow of stirred tanks. Whereas in the stirred tank according to Eq. (4) and (16b) the particle diameter is inversely affected by the turbulent stress dp l/T, in viscosimeters it was found for r > 1.5 N/m, independently of the type (Searle or Couette), the dependency dp l/ pi (see Fig. 11). 

Many results with model systems and also biological particle systems indicate that the stress in technical bioreactors, in which turbulent flow conditions exist, could not be simulated by model studies in small bioreactors, where no fully turbulent flow exists, and especially with laminar flow devices such as viscosimeters, tubes or channels. 

Similar kinetics have been observed for some [91] but not all [116] animal/insect lines. Trials conducted over a range of average shear stresses (Fig. 2) clearly indicate a higher degree of suspension sensitivity to turbulent, rather than laminar, flow conditions. Similar effects have been reported by other workers for plant [57] and mammalian [86,114,122] systems. From these... 

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