Timing grid size, effect

Thin sections may readily be examined with TEM-EDXA or SEM-EDXA in the transmission mode (STEM-EDXA). However, to use conventional SEM-EDXA, some modifications of the equipment are required. As shown in Fig. 4.4.3, the electrons transmitted through a thin specimen impinge upon the carbon plate underneath. This causes the emission of a strong continuous spectrum of white X-rays. To minimize this problem, a carbon grid holder with a Faraday cup should be used. If the depth of the cylinder in the Faraday cup is more than 20 times the size of aperture, the electrons can be effectively collected (Grubb 1971, Howitt et al. 1976), thus reducing a large portion of the white X-rays emitted. 

The size effect can be demonstrated nicely using different size film squares As shown in Fig. 33 a, the breakdown probability for the crazes in a small grid square that is 9 times smaller in area than a larger grid square is much lower at a given... 

In numerical models, the grid size and time step have a direct effect on the convergence and accuracy of the output data. 

The time step At is chosen as 3 s, and the actual grid size Aa slowly varies in the range of 1312-1556 m. The dispersion-correction parameters 7 calculated by given conditions such as time step At, actual spatial grid Aa , and local depth h, give the values between —2.93 and 0.08 in the whole computational domain. As mentioned above, the minimum value of 7 is restricted to —0.125 to maintain the stabihty for the deep areas of the East Sea. Due to this limitation, the dispersion effects are underestimated in the numerical solutions. However, the present scheme gives more accurate solutions than the conventional models which use a uniform 7 value, i.e., 7 = 0.0, everywhere. 

The finite element grid should be validated for any specific load case to be represented. Short duration loads (typical in explosions) often require dedicated models, different, for example, from the traditional dynamic models used for seismic analysis. Particularly, in order to avoid spurious filtering effects, a dense finite element grid should be used to represent the vibration field in the structure at high frequencies (above 20 Hz). Moreover, limitations to the finite element grid size should be adopted in expUdt time integration schemes to avoid numerical instabilities. 

Rock core permeability (darcies) Rock core porosity (decimal nbr) Viscosity of invading fluid (op) Viscosity, displaced fluid (op) Pressure at well boundary (psi) Pressure, effective radius (psi) Radius of the bore hole (ft) Reservoir effective radius (ft) Initial "Rfront" position (feet) Integration space step size (ft) Integration time step size (sec) Maximum allowed number of steps Number spatial DR grids selected... 

Figure 5 Effect of grid resolution (A.) on the time-averaged dimensionless slip velocity (us/uT). Geldart group A particles are used. The ordinate is scaled with the terminal velocity of single particles (uT 21.84 cm/s) and the abscissa is scaled with the particle diameter dp. The domain size is 1.5 x 6 cm2, comparable to the coarse-grid used in normal simulations.

In all such computations, it can be expected that the accuracy of the calculated results will generally improve with an increase in the size of the basis set and in the level of the calculation. However, this improvement often comes at considerable increase in computation time, so explorations of basis set and level effects are probably best done as class projects, with each student responsible for one or two calculations. The grid below gives a... 

Optimum size distribution is important for a fluid bed reactor (Bergoug-nou). Models based on bubbles are not yet capable of predicting the wall effect (Wen). Vertical baflles are most effective in breaking up large bubbles (Volk). The height of the bottom ends of vertical tube bundles above the grid will set the attainable bubble size at the bottom of the bundle. The bundles then essentially maintain the bubble size (Zenz). Horizontal perforated baflle plates reduce the mean residence time of elutriable fine particles in a fluidized bed (Buckham). Observations on attrition in cyclones indicate that it is an exponential function of velocity (Tenney). 

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