Empirical description of granular flow inside a model silo with vertical walls

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.

► Velocity profiles of flowing material in the silo model obtained by the DPIV technique.
► Velocities using three types of empirical function (Gaussian, Modified Gaussian, Parabolic) made it possible to predict the flow rate in the model.
► Flow channel boundary described by parabolic and hyperbolic functions.