Flow fronts

A meld line is similar to a weld line except the flow fronts move in parallel rather than meet head. Usually the meld line is identified as a weld line. 

Opposite flow fronts produce a weld line that could also contain entrapped air. 

OS 95] [R 5] [P 75] Plugs of pyridine-2-azo-p-dimethylaniline were inserted in a continuous Ni ion stream. Thereafter, spatial concentration profiles were monitored in the micro channels as a result of interpenetrating flow fronts due to varying mobility of the species in an electrical field [17]. 

Figure 7.4 Representations of hydrodynamic flow, showing (a) laminar flow through a smooth pipe and (b) turbulent flow, e.g. as caused by an obstruction to movement in the pipe. The length of each arrow represents the velocity of the increment of solution. Notice in (a) how the flow front is curved (known as Poiseuille flow ), and in (b) how a solution can have both laminar and turbulent portions, with the greater pressure of solution flow adjacent to the obstruction.

Figure 5.3 Sample two-dimensional simulations of the RTM process. (Top) finite element mesh (bottom) flow front progression, Kyy — 3KXX, Kxy = 0.0...

Figure 5.6 Sample three-dimensional simulations of the IP process. (Top) Finite element mesh. Total length 30 cm (0 < X < 30), total height 1 cm (0 < Z < 1), total width 3 cm (0 < Y < 3). Fluid is injected from both sides through the thickness (i.e., in the Z-direction through a 1 cm x 1 cm square). (Bottom) Flow front progression at the midplane (i.e., Z — 0.5), Ka = Kzz = 2Kyy K, - = 0.0...

The permeability can be determined experimentally in several different ways (e.g., in a radial flow [19] or unidirectional flow experiment [20]). The experiments can also be done with either an advancing flow front (wetting flow) or a fully saturated reinforcement under steady-state conditions. There is some debate in the scientific community whether the... 

In this equation ut should be interpreted as the volumetric flux density (directional flow rate per unit total area). The indexes range from 1 to 3, and repetition of an index indicates summation over that index according to the conventional summation convention for Cartesian tensors. The term superficial velocity is often used, but it is in our opinion that it is misleading because n, is neither equal to the average velocity of the flow front nor to the local velocity in the pores. The permeability Kg is a positive definite tensor quantity and it can be determined both from unidirectional and radial flow experiments [20], Darcy s law has to be supplemented by a continuity equation to form a complete set of equations. In terms of the flux density this becomes ... 

The equations are normally solved with a control volume finite element method. With these methods no boundary conditions are necessary at the outlets (i.e., it is implicitly assumed that there will always be an outlet at the point where the flow front merges and fills the last part of the mold). For a further discussion of boundary conditions and details about the numerical solution of the field equations (Eqs. 12.5 and 12.6) see [15,21,22-24]. 

In the preceding example and point injection the flow front will develop as a circular front, starting at the inlet, until it meets the closest side. From then on the front will tend to move unidirectionally in both directions toward the far sides (if there is no leakage at the sides). A reasonable estimate of the fill time is somewhere between the time to fill radially and the time to fill unidirectionally to the far side (flow distance 1.5 m). For the radial flow case L in Equation. 12.10 is 3 m (the diameter of a circle touching the wall farthest away). With the assumed alternative with unidirectional flow from the center toward both shorter sides, L in Equation. 12.10 is 1.5 m. It is also necessary to estimate an effective inlet radius, in this case an inlet radius of 5 mm is chosen yielding e = 3.3 10-3 that was used in the formula in Table 12.2. The constant C in Equation 12.10 is 0.5 for the unidirectional flow case and 0.65 for the radial flow case. The upper and lower limit for the fill time in this case are then ... 

The flow instability can best be understood by looking at a case with unidirectional flow (see Fig. 12.7). There will always be some nonuniformity between the sides. This will result in the flow front moving faster on one side of the core than it does on the other. The net force on the core from the resin will be higher on the side where the flow front has moved the farthest and as a result the core will be pushed away from this side. The displacement of the core will increase the permeability more and the flow front will move even farther ahead on the fast side, and so on. The process will reach an equilibrium when the reaction force from the reinforcement becomes large enough to balance the fluid pressure on the other side of the core. 

The influence from the various process parameters on the void content at the flow front for a particular resin and fabric combination is summarized in Table 12.3. 

FEEDER (Vibratoryl. A mechanical device used to provide controlled hulk material flow front storage to processes, or to and fioni various processes. Generally, these feeders can be driven hydraulically, elcetrome-chanically. pneumatically, or eleetroniagnetically... 

The fulfillment of the two latter inequalities in parentheses is not necessary in practice. In Fig. 10 a, h(t) denotes the flow front which at the first approximation will be assumed to be flat, as elaborated in56>. This is known 57) to be valid under the conditions Re 1 and at the absence of the jet effect 57 60). 

In the region from a point gate (entrance) to a flow front, the equation of motion may be written as ... 

Since the influence of walls on the U and V flow components disappears upon the separation of the order of 8 from a solid wall, inaccuracy of the scheme cannot have an essential influence on the flow rate calculations. Equations (4.32) may have an explicit solution within some limited time interval when the flow from a point runner is still radial, while the flow front is circular. This filling pattern is realized up to the moment when the radius of a free boundary R(t) will become equal to B/2 (see Fig. 11). Such a filling regime we shall refer to as the first stage of filling the formulae of 4.2 with some minor corrections (for details see 36)) are applicable to this stage the corrections arise mainly due to the fact that the radial flow occurs in... 

Fig. 11a, b. Kinetic identification of the first stage of filling a flat mould through a round (point) runner a flow is purely radial during some limited time interval, flow front is approximately circular b the radius of free boundary becomes equal to half-width of the forming cavity R(t) = B/2... 

It should be kept in mind that two ultimate situations of filling through a short and long runner may be encountered in practice. Both cases were analysed in detail 36 53-54>. For the case of a short flat runner, the following expression for the coordinate of the flow front was obtained ... 

Finally, in calculating the pressure at the running point x (coordinate) within the forming cavity, the dimensionless time tx nesessary for the x point to be reached by the flow front may turn out to be of use (i.e. the time x is needed for pressure to become non-zero at the x point). According to Eqs. (6.7) and (6.7 a), this time is given by ... 

As in Sect. 6.1, let us consider the injection moulding of a long thin plate through a slit runner, neglecting the resistance of the runner. Then Eqs. (4.12), (5.11), (5.12) for pressure distribution P(z, t), the motion of the averaged flow front h(t), and filling time will have the form ... 

In order to predict the position of the flow front, r2, as a function of time, we first perform a simple mass (or volume) balance,... 

The above equations can now be used to plot the pressure requirement, or pressure at the gate, for a given flow rate as a function of time. They can also be used to plot for the pressure distribution within the disc at various points in time or flow front positions. In addition, the same equations can be used to solve for flow rates for given injection pressures. 

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