The Radial Flow Method

Since the longest flow path may exceed the radius of the projected area that causes mold separating pressures, we must also find the radius of equivalent projected area, Rp, to compute a more accurate mold clamping force. However, to perform the calculations to predict velocities and pressure fields, we assume a disc geometry of radius R and thickeness h, schematically depicted in Fig. 8.41. 

As a constitutive model for the momentum balance, Stevenson chose a temperature dependent power law model represented by 

Temperature distributions across the thickness of the channel for various Brinckman 

The energy balance for the geometry represented in Fig. 8.41 results in transient and convective terms, conduction through the thickness and viscous dissipation caused by the through-the-thickness shear components 

Assuming a characteristic viscosity of fj = me aTlA/n, where the characteristic rate of deformation is taken as 7 = u/b, where t f is the fill time and u = i 2/t / the characteristic velocity, we can write the viscosity in dimensionless form as 

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Sample application of the radial flow method. In this sample application, we are to determine the maximum clamping force and injection pressure required to mold an ABS suitcase shell with a filling time, tf=2.5 s. For the calculation we will use the dimensions and geometry schematically depicted in Fig. 8.49, an injection temperature of 227°C (500 K), a mold temperature of 27°C (300 K) and the material properties given in Table 8.8. 

Experimental measurements remain the most reliable way to determine permeability. The two most widely used techniques for measurement of the in-plane permeability are the rectilinear flow method and the radial flow method. In a rectilinear flow experiment the reinforcement is usually placed in a rectangular mould and resin is injected fiem a side gate and allowed to permeate the reinforcement in only one direction. 

It is interesting to note that the measurements of Price [7] now appear in a new light. Price devided the exit crossection of the packed bed into concentric circles and measured flow velocities within the radially shielded segments. By this method he suppressed the radial flow components above the bed and obtained profiles similar to the calculated ones (Figure 3 ). In particular Price also found the maximum very close to the wall. 

In practical cell culture applications, fluid flow methods of estimating cell adhesion have been most useful. In particular, the radial flow chamber shown in Fig. 12.14 was developed to study both deposition and removal of cells at surfaces. The apparatus has been used to measure adhesion of many cell types to different surfaces, including diatoms and pseudomonas fluorescens. ... 

Heardman et al. [11] described a radial flow method to measure permeability under transient flow, where neither the pressure nor the flow-rate is considered constant. They obtained good agreement with experiments using the normal constant pressure setup for assemblies of woven fabrics. They also showed that, using error analysis on the equation used to calculate permeability, the estimated error due to the parameters used to determine permeability (e g. pressure, viscosity and time) is in the range of 8-16%. However, they did not quantify the range of measured permeability values for their reinforcements and hence did not compare it to the estimated error. 

Beckman Elutriation Method. The Beckman elutriation method uses a chamber designed so that the centrifugal effect of the radial inward fluid flow is constant (Fig. 3). The separation chambers are made of transparent epoxy resin which faciUtates observation of the movements of the cell boundary in strobe light illumination. This enables detection of the radius at which the cells are separating. When a mixture of cells, eg, mononuclear white cells, enters the chamber, separation can be achieved by fine tuning centrifuge speed and inward fluid flow to the specific cell group. This is a laboratory method suitable for relatively small numbers of cells. Chambers are available in sizes to handle 2-3 x 10 , 1 2 x 10 , and 1 x 10 ° cells. The Beckman chambers can be appHed to collect mononuclear cells from bone marrow aspirates. 

Boyce, M.P., and Bale, Y.S., A New Method for the Calculation of Blade Loadings in Radial-Flow Compressors, ASME Paper No. 71-GT-60, June 1971. 

Vortex formation leads to a considerable drop in mixing efficiency and should be suppressed as much as possible in practical applications to increase the homogenizing effects of mixers. The preferable method of vortex suppression is to install vertical baffles at the walls of the mixing tank. These impede rotational flow without interfering with the radial or longitudinal flow. Figure 11 illustrates such a system. 

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. 

Rotary motion (and surface vortex) can always be slopped by inserting projections in the body of the fluid when these are at the side if the tank they are called baffles, and this is the method most commonly used to obtain good mixing in large industrial equipment. The propeller with baffles will produce an axil flow pattern, Fig. 3, and the paddle and turbine will produce radial flow, Fig 4. 

The space velocity for a given conversion is often used as a ready measure of the performance of a reactor. The use of equation 1.25 to calculate reaction time, as if for a batch reactor, is not to be recommended as normal practice it can be equated to VJv only if there is no change in volume. Further, the method of using reaction time is a blind alley in the sense that it has to be abandoned when the theory of tubular reactors is extended to take into account longitudinal and radial dispersion and other departures from the plug flow hypothesis which are important in the design of catalytic tubular reactors (Chapter 3, Section 3.6.1)... 

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