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Abstract:
This paper is a third of a series of the three where eccentric cases of flow in silo models recorded by the DPIV technique are presented and discussed in detail. The methodology of empirical descriptions of velocities, flow rate and stagnant zone boundaries on the base of registered velocity fields in eccentric filling and discharge in 2D silo model was discussed. In previous two papers [1] and [2] we analyzed also eccentric flows but with different locations of the outlet. It was stated that in practice even tiny eccentricity of filling or discharge processes may lead to quite an unexpected behavior of the silo structure. During asymmetrical processes, flow patterns and wall stresses may be quite different. It is therefore crucial to identify how flow patterns developed in the material during eccentric filling or discharge and to determine both the flow rate and wall stresses occurring under such state of loads. Thus, we discuss here the third case of discharge — located in the center of the silo bottom. A comparison of these three cases of discharge mode will be presented in the next paper. Empirical descriptions of eccentric flow velocities in silo model by the linear and nonlinear regressions are presented here with specific functions like the Gaussian function and “the double logarithmic function”. In both methods the velocity was also descripted by linearization and in the Gaussian method also by the nonlinear method of Gauss–Newton and in the case of the method of double logarithm — the nonlinear method of Levenberg–Marquardt was applied. Velocities were predicted by using interpolation due to the nonlinear model of the Gaussian type and to the nonlinear function of “the double logarithm”.

Keywords:
Eccentric granular flow, Silo model, Empirical description, Linear and nonlinear regression, Gaussian description, Double logarithm