Confined Granular Flow in Silos: Experimental and Numerical by Jacek Tejchman
By Jacek Tejchman
During limited circulation of bulk solids in silos a few attribute phenomena could be created, similar to: surprising and demanding bring up of wall stresses, assorted stream styles, formation and propagation of wall and inside shear zones, fluctuation of pressures and, powerful autogenous dynamic effects.
These phenomena haven't been defined or defined intimately but. the most purpose of the experimental and theoretical examine provided during this publication is to give an explanation for the above pointed out phenomena in granular bulk solids and to explain them with numerical FE types proven by means of experimental results.
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Extra info for Confined Granular Flow in Silos: Experimental and Numerical Investigations
114) where: pwf – symmetric wall shear stress after filling, pwe – symmetric wall shear stress during discharge, Cpf – local pressure filling coefficient (Eq. 92) i Cpe – local pressure discharge coefficient (Eqs. 104). 25dc), the silo belongs to the reliability class 2 and 3, and flow takes place close to the wall (Figs. 26). 60 3 Analytical and Standard Approaches to Silos a) b) Fig. 25 Flow channel and pressure system: a) side view, b) cross-section, 1 − static pressure, 2 − dead zone, 3 − local maximum pressure, 4 − flow channel, 5 − flow pressure (Eurocode 1 (2009)) For Silos in Reliability Class 2 The calculations are performed with one size of the flow channel determined by the angle θc=35°.
10) is the pressure parameter. The solution of Eq. 9 is the formula to calculate the mean vertical normal stress in the bulk solid σz = e − mM z a ( γa mM e mM z a + C) . 11) The integral constant C is determined by means of a boundary condition along the upper free surface. For the vertical coordinate z =0, the mean vertical normal stress is σ z = σ z0 . 13) mM and σz = γa mM + (σ − 0 z γa mM )e − mM z a . 15) the solution becomes σz = γa mM (1 − e − mM z a ). 16) 28 3 Analytical and Standard Approaches to Silos For a silo with an infinite height (z = ∞), Eq.
1) −dσ z − τ × dz a + γ × dz = 0 , dσ z τ + −γ = 0 . 4) dσ z 2τ + −γ = 0. 5) In general, the differential equation (Eq. 6) where the constant m=1 for planar silos and m=2 for cylindrical silos. Fig. 6 is an usual differential equation including two unknown quantities σz i τ. 8) wherein ϕw – wall friction angle between the bulk solid and wall, K – lateral pressure coefficient of the bulk solid. 10) is the pressure parameter. The solution of Eq. 9 is the formula to calculate the mean vertical normal stress in the bulk solid σz = e − mM z a ( γa mM e mM z a + C) .