Rheological and solid wall boundary condition characterization of unvulcanized elastomers and their compounds

1982 ◽  
Vol 27 (8) ◽  
pp. 3171-3184 ◽  
Author(s):  
Shigeyuki Toki ◽  
James L. White
Author(s):  
Habib Khazaei ◽  
Ali Madadi ◽  
Mohammad Jafar Kermani

Boundary condition is one of the major factors to influence the numerical stability and solution accuracy in numerical analysis. One of the most important physical boundary conditions in the flow field analysis is the wall boundary condition imposed on the body surfaces. To solve a three-dimensional compressible Euler equation (with five coupled PDE’s), totally five boundary conditions at the body surfaces should be prescribed. The momentum equation in the direction normal to the inviscid solid wall provides the pressure at the surface of the wall. For the cases with no-heat source or sink, the total temperature at the wall and the incoming flow should remain constant, when the steady condition is prevailed. The no-penetration condition through the solid wall and slip condition provides an equation relating the three velocity components. Assuming identical flow direction at the wall with the adjacent node, the last thing is the velocity magnitude that should be cast in such a way to give accurate, stable and robust solution. In this paper, four different methods for calculation of the wall velocity magnitude are proposed and applied to an identical test case of subsonic and supersonic flows such as: (1) Inviscid flow in a 3D converging-diverging nozzle, (2) Inviscid subsonic flow in a single 90° elbow, (3) Inviscid supersonic flow over a wedge, and (4) Inviscid flow through a compressor blade geometry of NACA 65410. A recently implemented 3D in-house CFD code (based on the flux difference splitting scheme of Roe (1981)) is used to compute compressible flows in generalized coordinates. It is found that the way to specify the additional numerical wall boundary condition strongly affects the overall stability and accuracy of the solution. It is concluded that there is no best boundary condition to cover all of the test cases, but the best wall boundary condition should be introduced very carefully for each type of flow.


2014 ◽  
Vol 31 (1) ◽  
pp. 55-68 ◽  
Author(s):  
S.-Y. Lin ◽  
Y.-H. Chin ◽  
F.-L. Yang ◽  
J.-F. Lin ◽  
J.-J. Hu ◽  
...  

AbstractA unified wall-boundary condition for the pressure-based lattice Boltzmann method (LBM) is proposed. The present approach is developed from the direct-forcing technique in the immersed boundary method and is derived from the equilibrium pressure distribution function. The proposed method can handle many kinds of wall boundaries, such as fixed wall and moving wall boundaries, in the same way. It is found that the new method has the following advantages: (1) simple in concept and easy to implement, (2) higher-order accuracy, (3) mass conservation, and (4) a stable and good convergence rate. Based on this wall-boundary condition, if a solid wall is immersed in a fluid, then by applying Gauss's theorem, the formulas for computing the force and torque acting on the solid wall from fluid flow are derived from the volume integrals over the solid volume instead of from the surface integrals over the solid surface. Based on the pressure-based LBM, inlet and outlet boundary conditions are also proposed. The order of accuracy of the proposed boundary condition is demonstrated with the errors of the velocity field, wall stress, and gradients of velocity and pressure. The steady flow past a circular cylinder is simulated to demonstrate the efficiency and capabilities of the proposed unified method.


Author(s):  
P Spijker ◽  
H M M ten Eikelder ◽  
A J Markvoort ◽  
S V Nedea ◽  
P A J Hilbers

Thin film and nano-tube manufacturing, micro-channel cooling, and many other similar interesting techniques demand the prediction of heat transfer characteristics at the nanometre scale. In this respect, the transport properties at gas—solid and liquid—solid interfaces are very important. The processes at these interfaces can be studied in detail with molecular dynamics (MD) simulations. However, the computational cost involved in simulating the solid wall currently restrains the size of channels, which can be simulated. Therefore, the solid wall is sometimes replaced by boundary conditions, which often compromise on macroscopic quantities, such as density, temperature, pressure, and heat flux. In the current paper, a new particle wall boundary condition is presented, which is in good agreement with existing boundary conditions, but allows for the pressure calculation. This new boundary condition is based on averaging the contributions of an explicit solid wall and is derived using knowledge on common practices in MD algorithms, such as truncation and shifting. Moreover, it allows for different crystal lattices to be included in the new potential. The applicability of the new method is demonstrated by MD simulations of a gas between two parallel plates at different temperatures and densities. Furthermore, these simulations are compared with explicit wall simulations and existing boundary conditions.


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