Control volume method

The axial pressure and temperature distributions for the molten resin in the melt-conveying channel are calculated using the control volume method outlined in Section 7.7.5. For this method, the change in pressure and temperature are calculated using the local channel dimensions, HJ z) and FK (z), and the mass flow rate in the channel using Eq. 7.54 for flow and the methods in Section 7.7.5.1 for energy dissipation and temperature. The amount of mass added to the melt chan-... 

Equation 7.84 assumes that the viscosity is not a function of temperature. It is presented here to describe the method. In Section 7.7.5, a control volume method will be described that allows the temperature to vary in the down-channel direction. 

The temperature increase calculation in Sections 7.7.1 and 7.7.2 was based on the viscosity using the temperature at the entry to the metering section. Because the temperature of the resin increases as it flows downstream, the shear viscosity continuously decreases. A better method to calculate the temperature of the resin in the channel is to divide the channel into many Az or Az increments, and then for each increment, perform an energy balance on each control volume [67]. A schematic of the control volume is shown in Fig. 7.36. The energy balance includes convection into and out of the volume, dissipation due to rotation and pressure flows, and energy conduction through the barrel wall and the root of the screw. This section will describe a control volume method for temperature calculation for both screw rotation and barrel rotation. 

The simplified method for calculation of the temperature profile using the control volume method and screw rotation is shown by Eq. A7.20f. The simplified calculation under-predicts the energy dissipation. 

Control volume method Finite element method Boundary element method and analytic element method Designed for conditions with fluxes across interfaces of small, well-mixed elements - primarily used in fluid transport Extrapolates parameters between nodes. Predominant in the analysis of solids, and sometimes used in groundwater flow. Functions with Laplace s equation, which describes highly viscous flow, such as in groundwater, and inviscid flow, which occurs far from boundaries. 

The model uses an irregular mesh of trihedral prisms for the presentation of filtration properties and supplementary thereto - a mesh of hexagonal prisms for the approximation of filtration and heat transfer equations by the finite difference control volume method. Numerous foundations of hexagonal right angle prisms (additional planar mesh) are presented in Fig. 4. Nodes of the basic planar mesh are geometric centers of hexahedral cells of the additional planar mesh. Fig.4 shows that the boundaries of the area modeled and the mesh of faults is accurately approximated by planar mesh subdivision. The faults are assumed to be strictly vertical. 

Computational fluid dynamics (CFD) Control volume method Control volume-based finite difference method... 

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 ... 

Both models can be solved by different numerical schemes. The boundary element method has the advantage that the velocity gradient can be obtained more accurately than the finite-element method, which is important for predicting the fiber orientation (Barone and Caulk, 1986 Osswald and Thcker, 1988). However, it is restricted to single charge, flat parts and cases of uniform thickness. Hence, many simulation efforts have converged to the use of the finite-element/control-volume method (Erwin and Thcker, 1995 Osswald and Tucker, 1990) coupled with the volume of fluid (VOF) method to track the position of flow front (Hirt and Nichols, 1981). 

Commercially available discretization methods for solving complex real-world physical systems are predominantly based on finite volume method and finite element method. The most widely used commercial software tools, such as ANSYS Fluent , STAR-CD , and STAR-CCM+ , are based on finite volume method, whereas ANSYS CFX uses finite element-based control volume method. On the other hand, COMSOL Multiphysics is based on finite element method. Both methods have advantages and disadvantages, but nevertheless they give enough comparable computational results with real-world physical systems. 

Since, as discussed, it is Justifiable to assume 3T/30 = 0, the rotor can be modelled as a 2D axisynmietrlc domain. A non uniform grid is quite easy to arrange if the control volume method is used. Sinks can be specified to model rotor cooling, and Irregular shapes can be used if necessary to allow (for example) for cooling at the inner radius of a rotor plate as well as at the outer radius. 

If using the box method [16] or perhaps the finite volume method (also called control volume method [17, 18]), fluxes might be just what is needed. If, however, the point method is to be used, Eq (13.1) is converted into a time-dependent concentration form, using... 

Krylov, D. A., Sidnyaev, N. I., Control volume method in problems of temperature forecasting in three-dimensional areas Abstracts of papers. University research conference Student spring-2011. Moscow, BMSTU, 2011. Vol. XI, part l,pp. 125-127. 

The boundary conditions are essentially the same for all the methods reviewed above. However, the multiphase and multi-domain methods need extra boundary conditions due to the additional equations solved. Therefore the general boundary conditions employed in control volume methods and FEMs are discussed together and additional boundary conditions required for other methods are given in subsequent sections. 

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