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Abstract:
In this paper we continue empirical description of eccentric granular flow registered by the DPIV (Digital Particle Image Velocimetry) technique. The first results concerning eccentric flow with the outlet located on the right were published in Sielamowicz et al. [30]. Here we present a methodology of empirical descriptions of velocities, flow rate and the flow channel boundary (FCB) in another eccentric case. The analysis is based on the experimental results (velocity profiles) obtained in the DPIV technique. Statistical analysis of the experimental results was also performed. We show how to fit the proper type of function to describe flow parameters in the silo model. The presented methodology is universal and can be applied in any case of eccentric flow of any granular material.

Keywords:
Universal methodology of empirical analysis, DPIV technique, Eccentric granular flow, Discharge on the left, Vertical model, Plexiglas, Velocity, Gaussian type function, Ch function, Multiple regression, “Joined functions”, Flow channel boundary (FCB)

Abstract:
DPIV (Digital Particle Image Velocimetry) is often used to record the flows in silo models and to recognise the flow in two-dimensional structures. Flow in a two-dimensional laboratory model with transparent walls was recorded using the DPIV technique. Recorded images were processed and the velocities of the flowing material were obtained. Statistical analysis of the readings taken from velocity profiles was also performed. To describe the flow the theoretical model of velocity presented in Choi, Kudrolli, and Bazant (2005) was modified. An empirical description of the flow rate was carried out. An analysis of the kinematic parameter b was carried out and compared to the solutions given by Medina, Córdova, Luna, and Treviño (1998) and Choi et al. (2005). Comparisons between the experimental measurements and the empirical descriptions are presented. Comparing the Gaussian based kinematic model of Choi et al. (2005) and a modified empirical kinematic model, a better description of velocity was obtained by using the latter. In further comparisons using the two aformentioned models and a parabolic description the best description of velocity was given by the parabolic function. Flow rate was analysed using the three types of functions. Both the Gaussian and modified empirical kinematic model gave almost the same values for calculated levels h = 5, 10 cm. Using the parabolic description the value of flow rates differed slightly. The flow channel boundary was analysed using parabolic and hyperbolic descriptions. Both descriptions were good because the correlation coefficients, had values ranging from 0.928 to 0.997.

Abstract:
The paper presents the methodology of empirical description and statistical analysis of velocity profiles that were depicted by the Digital Particle Image Velocimetry technique (DPIV). Experimental runs were recorded by the high resolution camera in the model with vertical walls. Here we analyze the eccentric discharge with the outlet located in the bottom close to the right vertical wall of the model. On the base of the experimental results we present an empirical analysis of velocities and calculation of the flow rate in two proposed descriptions of the flow. Velocity functions were presented by the exponential function (the modi fi ed Gauss type), by the multiple regression and by the ch function. Also the fl ow rate was calculated for two presented descriptions. Empirical calculations of the stagnant zone boundary was also presented using the readings from velocity profiles.

Keywords:
Particle Image Velocimetry, granular flow, Multiple regression