A droplet transport model for channel and pipe flow based on particle kinetic theory and a stress–ω turbulence model

Suspensions in turbulent liquid pipe flow: Kinetic modelling and added mass effects

“…Algebraic relations between the particle and fluid stresses, including the stress redistribution terms can then be invoked, eliminating the need for stress boundary conditions. Only for larger particle/fluid density ratios are stress boundary conditions necessary (such as droplets in gas modelled by Skartlien, 2009, or solid particles in gas).…”

“…Another timescale that is frequently used is the eddy turnover time defined by the scalar diffusivity. Skartlien ( , 2009 showed that the wall normal particle diffusivity for vanishing Stokes number, and for drag only, limits to ð yy Þ h ¼ hu 0 y u 0 y is when the locally homogeneous form of the dispersion tensor k yy is invoked. If we impose consistency between the eddy diffusivity and the wall normal particle diffusivity for vanishing relaxation time, we obtain the following eddy turnover time:…”

“…In an accompanying paper, Skartlien (2009) addresses the modelling of droplets in a dense gas flow representative of conditions in pipelines. In the current paper, we discuss the modelling of solid particles suspended in a turbulent liquid.…”

“…These difficulties should however decrease for lower bulk velocity. In the droplet model of Skartlien (2009), the particle kinetic theory developed at the University of Newcastle by Reeks (1992Reeks ( , 1993, Swailes et al (1998) was adopted.…”