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Fundamentals of Computational Fluid Dynamics Modeling and Its Applications in Food Processing
Published in C. Anandharamakrishnan, S. Padma Ishwarya, Essentials and Applications of Food Engineering, 2019
C. Anandharamakrishnan, S. Padma Ishwarya
The initial conditions are the conditions at the time, t = 0. The boundary and initial conditions are required to solve the governing equation for a particular physical situation. In general, boundary conditions can be classified into four types: no-slip, axisymmetric, inlet–outlet, and periodic. Consider the example of a pipe in which the fluid is flowing from left to right (Figure 16.11). While the left part represents the input, the right part shows the output of the system. As the fluid enters the pipe from the inlet located at the left, the velocity can be set manually. Nevertheless, the outlet (on the RHS) boundary condition may be used to keep all the properties constant, implying that all the gradients are zero. In the no-slip boundary condition, the velocity at the wall of the pipe is set at zero. In other words, the no-slip boundary condition implies that the velocity of a fluid which is in contact with the wall of the pipe is equal to the velocity of the wall. But at the center of the pipe, the axisymmetric boundary condition is used as the geometry and the pattern of flow solution, having mirror symmetry (Figure 16.11). The asymmetric boundary condition can be defined by a zero flux of all quantities across the symmetric boundary. Since there is no convective flux across a symmetry plane, the normal velocity component at the symmetry plane is zero. Also, due to the absence of diffusion flux across a symmetry plane, the normal gradients of all flow variables are zero at the symmetry plane.
Investigation of interfacial slippage on filler reinforcement in carbon-black filled elastomers
Published in Per-Erik Austrell, Leif Kari, Constitutive Models for Rubber IV, 2017
J.J.C. Busfield, V. Jha, A.A. Hon, A.G. Thomas
2D models were investigated to validate the critical shear stress friction model at the filler rubber interface. A typical 2D quarter symmetry model used is shown in Figure 1. The boundary conditions were established to model a repetitive symmetric geometry, which represents a uniform packing of the filler, by ensuring that each side of the model is a mirror symmetry plane.
Practical Considerations and Applications
Published in Steven M. Lepi, Practical Guide to Finite Elements, 2020
Mirror symmetry is employed when both the geometry of the structure and the loading are symmetrical about a plane. Boundary conditions are then invoked on the nodes that lie on the plane(s) of symmetry to simulate the effects of having the entire structure present.
A new reconstruction core of the 30° partial dislocation in silicon
Published in Philosophical Magazine, 2019
Lili Huang, Rui Wang, Shaofeng Wang
The fully discrete dislocation equation satisfied by the mismatch field (j = x, y, z) (see Figure 2) was proposed in Ref [35]where Ω is a matrix, is the component of the nonlinear interaction force (per unit area) between two half-infinite crystals, σ is the area volume of the primitive cell of the slip plane that is a two-dimensional lattice. In study of the dislocation structure, the coordinates system is generally chosen that the slip plane is the x–y plane and the dislocation line is the y-axis. The coordinates system given in this way will be called the natural coordinates system. If a crystal possesses the mirror symmetry with regard to the y–z plane, i.e. the left and right of dislocation are symmetric, the matrix Ω is diagonal in the natural coordinates systemFor the partial dislocation in semiconductor silicon, the mirror symmetry cannot be proved simply from its lattice geometry. However, the symmetry break is weak and it can be neglected in the first-order approximation.