Advancement of the Flow Front

The Lagrangian method is limited by the mesh distortion and the need for a time-consuming remeshing, and hence the Eulerian method is favored for our purpose. We will describe below three different approaches based on the Eulerian method. 

The entrance node is always treated as a filled node. After having obtained the nodal pressures, one calculates the net flow rates into each partially filled control 

The scheme has two major drawbacks. One is the dependence on the number and shape of the elements. The second is oscillation of the melt front. 

The Volume of Fluid (VOF) method, as introduced by Hirt and Nichols (1981), is based on the mass conservation principle. Similar to the control-volume method, in the VOF method, the whole domain can also be divided into control volumes, each of which is associated to an element node, and the volume fraction of fluid in each control volume is defined. The flow front is advanced by solving the following transport equation  

In this technique, the calculation domain is treated as a two-phase system. One phase consists of the liquid filled region, and the other consists of a void region. The flow front is regarded as the interface separating the two phases. The void is assumed to contain a virtual fluid, such as gas, with a set of virtual physical properties. Physical parameters in the governing flow equations are expressed using the mixture law weighed by F. for example, for the density, p, one has 

---

Fig. 8.3 Control-volume and node definition for advancement of the flow front...

The progression of the resin flow front is highly dependent on the mould geometry and the flow properties of the reinforcement placement of the inlet and vent ports is therefore crucial to obtain a good-quality manufactured part. Defects or material variation in the preform can also greatly affect the flow of resin. The inclusion of sensors built into the mould can help track the resin progression, and the use of multiple inlets and vents enables some control over the shape and advancement of the flow front. 

During processing, the operator usually has little control over the advancement of the flow front. In order to ease this problem, two approaches have been followed. On the one hand the physical parameters of the infusion process can be measured and controlled which is done in terms of resin viscosity by heating and the pressure difference [72,82-84], On the other hand the infusion process has been modeled extensively to avoid dry spots and to obtain optimal mechanical part properties [59,65,66,71,85,86]. 

Figure 4.52 Schematic representation of flow patterns during the injection filling of an endgated rectangular mold whose width is much greater than its thickness, (a) advancement of the flow front with fountain flow and...

At 10 MPa and 35 °C, C02 has a density of approximately 700kg/m3. Under these conditions, a cubic meter of sandstone with 10% porosity contains approximately 70 kg of C02 if the pore space is completely filled by C02. However, saturation of C02 is not complete, and some brine remains in the invaded pore spaces (Saripalli McGrail 2002 Pruess et al. 2003). In addition, non-uniform flow of C02 bypasses parts of the aquifer entirely. Darcy-flow based analytical and numerical solutions are used to evaluate some of these effects by simulating the advance of the C02 front over time-scales of decades to hundreds of years and over lateral distances of tens to hundreds of kilometers. To account for the extreme changes in density and viscosity of C02 with pressure and temperature, these models must incorporate experimentally constrained equations of state (Adams Bachu 2002). 

By far the most common and most practical approach to measure the rate of flame spread over a flat surface involves recording the location of the flame tip (wind-aided spread) or flame front (opposed-flow spread) as a function of time based on visual observations. However, in the case of wind-aided flame spread, it is very difficult to track propagation of the pyrolysis front (boundary between the pyrolyzing and nonpyrolyzing fuel) as it is hidden by the flame. This problem can be solved by attaching fine thermocouples to the surface at specified locations as ignition results in an abrupt rise of the surface temperature. This approach is very tedious and not suitable for routine use. An infrared video camera has been used to look through the flame and monitor the upward advancement of the pyrolysis front in a corner fire.62... 

In the direct flow variant, one and the same well is used both for the ignition of the oilbearing bed and for the subsequent oxidizer injection. Thus, the flow of the oxidizer and the advance of the burning front is in the same direction, namely from the injection well to the producing well. 

The wicking rate from an infinite liquid reservoir depends on the capillary dimensions of the substrate and the viscosity of the liquid [37,38]. For a theoretical treatment of capillary flow in fabrics, the fibrous assemblies are usually considered to consist of a number of parallel capillaries [39]. The advancement of the liquid front in a capillary occurs in small jumps. The advancing wetting line in a single capillary stretches the meniscus of the liquid until the elasticity of the... 

Its higher velocity 2) The finite pressure difference in the wave front 3) The increase in temperature and density of the medium thru the wave and 4) Physical flow of the material in the direction of advance of the wave. The rate of this flow, as well as that of wave propagation, and the magnitudes of the increases in density, tempera-... 

The unknown pressures are acquired by solving the system of algebraic equations, eqn. (8.144), after the boundary conditions are applied. With a known pressure field we can solve for the flow rates between the nodes and a the fill factor in the partially filled nodes can be updated using the smallest time step required to fill the next node. How to determine the appropriate time step is shown in Algorithm 3. The flow fronts are advanced in Algorithm 4. At that point, new boundary conditions are applied to the set of algebraic equations to solve for the new pressure and flow fields. This is repeated until all control volumes are full. 

Fig. 13.15 Schematic representation of the flow pattern in the central portion of the advancing front between two parallel plates. The coordinate system moves in the x direction with the front velocity. Black rectangles denote the stretching deformation the fluid particles experience. [Reprinted by permission from Z. Tadmor, Molecular Orientation in Injection Molding, J. Appl. Polym. Sci., 18, 1753 (1974).]...

The craze front velocity v can be governed by one of two distinct mechanisms of craze matter production. As Argon and Salama have discussed in detail, under the usual levels of service stresses or stresses under which most experiments are carried out, craze matter in single phase homopolymer is produced by the convolution of the free surface of the sohd polymer at the craze tip. This occurs by a fundamental interface instability present in the flow or deformation of all inelastic media when a concave, meniscus-like surface of the medium is being advanced locally by a suction gradient. This is the preferred mechanism of craze advance in homopolymers. In block copolymers with uniform distributions of compliant phases of a very small size, and often weaker interfaces than either of the two phases in bulk, craze advance can also occur by cavitation at such interfaces to produce craze matter as has been discussed by Argon et al. Both of these mechanisms of craze advance lead to very similar dependences of the craze front velocity on apphed stress and temperature that is of the basic form... 

The average flow velocity is a direct measure of the advancement of the mobile pha.se front in the empty capillary. Therefore, replacing (v) by dci/dr, we get an equation for r, - ... 

Special features of FF-TLC. Special advances of FF-TLC are related to its fundamentals the total elimination of the vapour phase and forcing the mobile phase by a pump. As the whole system (consisting of the stationary and mobile phases) is tightly closed, proper control of the mobile phase pump permits the adjustment and regulation of the flow rate of the mobile phase. Therefore, a new relationship characterises the movement of the mobile front ... 

---