Velocity distributions, pressure-control

Accuracy and repeatability of temperature/time/velocity/pressure controls of injection unit, accuracy and repeatability of clamping force, flatness and parallelism of platens, even distribution of clamping on all tie rods, repeatability of controlling pressure and temperature of oil, oil temperature variation minimized, no oil contamination (by the time you see oil contamination damage to the hydraulic system could have already occurred), machine properly leveled. 

Fig. 3.11 The cylinder on the left is filled with a gas at pressure p and bounded by two pistons that can move with velocity u. The long cylindrical annulus on the left is filled with a fluid. The center rod is fixed, but the outer cylindrical shell moves upward at a constant velocity. Under these circumstances a steady state-velocity distribution will develop in the fluid as illustrated u(r), with the zero velocity at the inner-rod wall and the wall velocity at the shell surface. A cylindrical control volume with its zrz shear stresses is illustrated.

Darcy s law describes fluid flux in porous media, and must be combined with the continuity equation to develop flow equations. From the flow equations, the spatial and temporal pressure and velocity distributions can be estimated that are needed for the transport equations. The derivation of flow equations starts with the continuity equation, which states that the change in mass or volume within a control volume equals the net flux across the control volume boundary, plus sources and sinks within the control volume. For water within porous media, the continuity equation on a mass basis is ... 

The parameter k is called the von Karman constant, and the value that fits most of the data is 0.41. The corresponding value of B is 5.0. Intermediate between these layers is the buffer layer, where both shear mechanisms are important. The essential feature of this data correlation is that the wall shear completely controls the turbulent boundary layer velocity distribution in the vicinity of the wall. So dominant is the effect of the wall shear that even when pressure gradients along the surface are present, the velocity distributions near the surface are essentially coincident with the data obtained on plates with uniform surface pressure [82]. Within this region for a flat plate, the local shear stress remains within about 10 percent of the surface shear stress. It is noted that this shear variation is often ignored in turbulent boundary layer theory. 

In general the net macroscopic pressure tensor is determined by two different molecular effects One pressure tensor component associated with the pressure and a second one associated with the viscous stresses. For a fluid at rest, the system is in an equilibrium static state containing no velocity or pressure gradients so the average pressure equals the static pressure everywhere in the system. The static pressure is thus always acting normal to any control volume surface area in the fluid independent of its orientation. For a compressible fluid at rest, the static pressure may be identified with the pressure of classical thermodynamics as may be derived from the diagonal elements of the pressure tensor expression (2.189) when the equilibrium distribution function is known. On the assumption that there is local thermodynamic equilibrium even when the fluid is in motion this concept of stress is retained at the macroscopic level. For an incompressible fluid the thermodynamic, or more correctly thermostatic, pressure cannot be deflned except as the limit of pressure in a sequence of compressible fluids. In this case the pressure has to be taken as an independent dynamical variable [2] (Sects. 5.13-5.24). 

Understanding the free surface flow of viscoelastic fluids in micro-channels is important for the design and optimization of micro-injection molding processes. In this paper, flow visualization of a non-Newtonian polyacrylamide (PA) aqueous solution in a transparent polymethylmethacrylate (PMMA) channel with microfeatures was carried out to study the flow dynamics in micro-injection molding. The transient flow near the flow front and vortex formation in microfeatures were observed. Simulations based on the control volume finite element method (CVFEM) and the volume of fluid (VOF) technique were carried out to investigate the velocity field, pressure, and shear stress distributions. The mesoscopic CONNFFESSIT (Calculation of Non-Newtonian How Finite Elements and Stochastic Simulation Technique) method was also used to calculate the normal stress difference, the orientation of the polymer molecules and the vortex formation at steady state. 

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