Probabilistic analysis of particle impact at a pipe bend in pneumatic conveying

A macro-scale model of the breakage of particles at a 90° bend during dilute phase pneumatic transport is presented. Breakage results if the impact force between the particle and pipe bend exceeds the intrinsic strength of the particle. The latter is taken to be distributed according to the Weibull distribution. Impact force depends on impact velocity and this relationship is obtained by a two-phase structural model of the particle, based on the widely used Kelvin–Voigt model. The impact velocity is distributed as a result of a distribution in particle velocity and in impact angle, though the variability in the latter is shown to be the significant component. The results of the theoretical analysis are confirmed by Monte Carlo simulations. For infant formula agglomerates with typical dimensions, slightly less than 2% of the infant formula agglomerates are predicted to fail when conveyed through a simple system containing one 90° bend (radius of 0.8 m) at a maximum superficial velocity of 20 m/s.

Illustration of a particle of radius rp colliding with a 90° bend of radius Rb at an angle θ. The pipe radius is R, and the particle is initially located at a distance of + y from the pipe centreline.Figure optionsDownload as PowerPoint slideHighlights
► A model of the breakage of IMF particles at a 90° bend during pneumatic transport is presented.
► Breakage results if the impact force exceeds the intrinsic strength of the particle.
► Impact force is calculated from particle velocity using a structural model.
► Particle strength and impact force are distributed quantities.
► Less than 2% of the agglomerates are predicted to fail when conveyed at a superficial velocity of 20 m/s.