Particle concentration effects in bend erosion

Numerical Simulation of the Gas−Solid Flow in Three-Dimensional Pneumatic Conveying Bends

“…A ) area, m 2 c ) damping coefficient, dimensionless c d0 ) fluid drag coefficient, dimensionless d ) particle diameter, m E ) Young's modulus, Pa f c ) contact force, N f d ) damping force, N f pf ) particle-fluid interaction force, N F ) volumetric force, N/m 3 g ) gravity acceleration vector, 9.81 m/s 2 G ) gravity vector, N G s ) solid mass flow rate, kg/(m 2 s 1 ) I ) moment of inertia of a particle, k gm k c ) number of particles in a computational cell, dimensionless k i ) number of particles in contact with particle i, dimensionless k m ) number of contacts in a sample, dimensionless m ) mass of a particle, kg M ) rolling friction torque, N m n ) number of particles in a considered system, dimensionless n ) unit vector in the normal direction of two contact spheres, dimensionless P ) pressure, Pa ∆p ) pressure drop, Pa R ) radius vector (from particle center to a contact point), m R ) magnitude of R, m Re ) Reynolds number, dimensionless A ) the area of wall in a local cell, m 2 t ) time, s T ) total simulation time, s T ) driving friction torque, N m u ) fluid velocity, m/s V ) volume, m 3 V ) velocity vector, m/s ∆V c ) volume of a computational cell, m 3 Greek Letters R s ) solids concentration, dimensionless β ) empirical coefficient defined in Table 2, dimensionless δ ) vector of the particle-particle or particle-wall overlap, m δ ) magnitude of δ, m ε ) porosity, dimensionless µ ) fluid viscosity, kg/m/s µ r ) coefficient of rolling friction, m µ s ) coefficient of sliding friction, dimensionless ν ) Poisson's ratio, dimensionless F ) density, kg/m 3 τ ) viscous stress tensor, N/m 3 ω ) angular velocity, rad/s ω ) magnitude of angular velocity, rad/s ω ˆ) unit angular velocity Subscripts c ) contact d ) damping D ) drag f ) fluid phase ij ) between particle i and j i(j) ) corresponding to i(j)th particle max ) maximum n ) in normal direction p ) particle phase p-p ) between particle and particle p-w ) between particle and wall t ) in tangential direction…”

“…Particle−wall interaction force in bends attracts many research efforts since it closely relates to the wearing of transport pipes and the degrading of the conveyed product. ,,− In general, for a given bend, the extent of erosion on the wall depends on three factors: operational conditions, nature of target materials, and properties of impact particles. Of these factors, operational conditions, such as impinging velocity, impact angle, particle number density at impact, and properties of the carrier fluid, are the most important. ,, For dilute flow, Stokes number can be used to evaluate the impactability of particles on wall.…”

“…In the past, many experimental and numerical studies have been made to overcome the problem. [3][4][5][6][7][8][9][10][11] In recent years, numerical methods have been increasingly used to study gas-solid flow. The popular mathematical models proposed thus far can be grouped into two categories: the continuum approach at a macroscopic level represented by the two-fluid model (TFM), and the discrete approach at a microscopic level mainly represented by the so-called combined continuum and discrete model (CCDM).…”

“…The success of such a design varies, partially because of the limited understanding of the limited internal flow. In the past, many experimental and numerical studies have been made to overcome the problem. − …”

Numerical investigation of mass loading effects on elbow erosion

“…Based on four-waycoupled simulations of the gas-solid flow in the same geometry, a detailed analysis of the mass loading influence on particle motion and penetration rate was carried out. Unfortunately, a limited number of studies [14,15] have been conducted to understand the erosion rate as a function of mass loading and did not provide detailed information about particle-particle and particle-fluid interactions and their effects on erosive wear. In the present work, the finite-volume, unstructured code UNSCYFL3D, was used to solve the gas flow combined with a Lagrangian point-particle model for the particulate phase (EulerianLagrangian approach).…”