Hexahedral cells

The aspect ratio of hexahedral cells should be not too high, typically below 20-100. If high-aspect ratio cells are used, the accuracy and possible convergence problems depend greatly on the flow direction. 

Later, Polyakov and Tarakanov modified the model by presenting if of a hexahedral cell having an initial curvature (eccentricity) near the rods disposed in two perpendicular directions. This model, which makes allowance for the initial anisotropy of the plastic foam, satisfactorily describes the elastic properties of flexible foams under considerable strains, but generally predicts unduly high values of the elastic properties of foamed plastics. 

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. 

Numerical implementation of the boundary conditions is conducted by the use of the IN-FORM tool in PHOENICS 2008, which increases the simulation time, as higher computational effort is demanded. On the other hand, it represents a simpler and more intuitive manner of dealing with complex initial or boundary conditions. A point-history object is used to track the plume concentration reached on a location at a distance of about 750 meters far from the source point. A lighter-than-air gas is considered and a single density calculation is conducted for the whole domain, as a fimction of the gas fraction (mixture air and gas). A monitoring time of 30 minutes is simulated by the use of adequate time and space grids 9000 time steps (0.2 s for each) and about 18,000 hexahedral cells. 

The initial mesh consists of uniform hexahedral cells. Mesh dependency tests have been performed, which exhibit that the simulation results are reasonably grid independent when the cube width (a) is resolved by at least ten cells. The left of Fig. 18.44 exhibits the variation of the particle velocity during penetration while the right displays the temporal evolution of the penetration process. For the rough mesh resolution (a/A = 5), the simulation collapsed at the moment of 5 ps. 

A grid is a decomposition of some volume, 1 , into a finite set of subvolumes, such that (i) the union of the subvolumes is approximately equal to the parent volume and (ii) most of the intersection of the surfaces of any pair of subvolumes is included in the intersection of their respective volumes. The subvolumes are called cells or blocks. Thus one is allowing some finite volume of overlap between subvolumes and also some holes provided that the offending volumes are small. Ideally the volume of overlap and of holes will be zero, but in complicated geometries and with the possible constraint to hexahedral cells this is not always practical. 

Highly skewed cells should be avoided. The angles between the grid lines of a hexahedral mesh should be 90°. Angles < 40° or > 140° often imply a reduced accuracy or numerical instabilities. 

The modeling considered 1.25 mm of the channel before the confluence and 3 mm of the channel after the confluence with a plane of symmetry at half the channel depth. The computational domain was discretized with structured hexahedral meshes, the size of the cells being 10 pm long. Diffusion was modeled. 

All the fuel handling equipment of V-392 reactor plant (in-plant transport packing set for fresh and spent fuel, leak-tight bottles, bottles of defective assembly detection system) have the cells for fuel assemblies made of hexahedral tubes. This measure provides for improvement of nuclear safety under accident situations and also prevents mechanical damage of fuel assembly during its installation and withdrawal from the fuel handling equipment. 

In laminar flows, the grid near boundaries should be refined to allow the solution to capture the boundary layer flow detail. A boundary layer grid should contain quadrilateral elements in 2D and hexahedral or prism elements in 3D, and should have at least five layers of cells. For turbulent flows, it is customary to use a wall function in the near-waU regions. This is due to the fact that the transport equation for the eddy dissipation has a singularity at the wall, where k [in the denominator in the source terms in eq. (5-14)] is zero. Thus, the equation for e must be treated in an alternative manner. Wall functions rely on the fact... 

QUICK Differencing Scheme. The QUICK differencing scheme (Leonard and Mokhtari, 1990) is similar to the second-order upwind differencing scheme, with modifications that restrict its use to quadrilateral or hexahedral meshes. In addition to the value of the variable at the upwind cell center, the value from the next neighbor upwind is also used. Along with the value at the node P, a quadratic function is fitted to the variable at these three points and used to compute the face value. This scheme can offer improvements over the second-order upwind differencing scheme for some flows with high swirl. 

Figure 5-36 shows the flow pattern in the vertical plane of a vessel equipped with a helical ribbon. A fully structured hexahedral mesh with approximately 100 000 cells was used. The structured 3D mesh was created by extruding and twisting a 2D planar mesh. The fluid is viscous and the impeller Reynolds number is approximately 10. The velocity vectors show that the impeller pumps down at the wall and up in the center. Contours of velocity magnitude on the tank bottom show that there are low velocities in the center and higher velocities near the outside wall. Small circulation loops form between the impeller blades and the vessel wall, as discussed in the general literature. These indicate the need for an even larger D/T or the use of wall scrapers if optimum heat transfer is to be obtained. 

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