Anisotropic second-order moment method of particles for dense gas-solid flow

A second-order moment model of particles is proposed in the dense gas-solid flow based on the kinetic theory of granular flow and kinetic theory of gases. The constitutive model of solid phase is closed with the approximated third-order moment enclosure equation of particle velocity from the elementary transport theory. The boundary conditions of velocity and fluctuating velocity energy of particles are proposed with the consideration of the energy transfer and dissipations by collisions between the wall and particles. Interaction between gas phase and solid phase is modeled by Koch (1999) mode. Flow behavior of particles is simulated in a riser. Numerical simulations indicate the distinct anisotropy behavior of the turbulent particles in the riser. Simulated particle velocities, concentration and second-order moments are in agreement with measurements by Tartan and Gidaspow (2004) in a riser. Predicted axial fluctuating energy of particles is on average 1.5 times the mean fluctuating energy of particles, and the axial fluctuating energy is 3.0 times the lateral fluctuating energy of particles.