Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

“…The particle phase is computed by advancing (2) with a second-order Runge-Kutta method, using trilinear interpolation to compute the fluid velocity at particle locations. Higher-order Lagrange interpolation schemes are tested and resulted in little change to the quantities of interest in this paper (Johnson et al, 2019). Particlewall collisions are computed using a unity restitution coefficient.…”

“…The first term is the average wall-normal force on all particles at a particular distance from the wall. Using Stokes drag to illustrate the basic idea, a y |y = τ −1 p u y |y (recall that v y |y = 0 at steady-state), where u y |y > 0 as inertial particles tend to preferentially sample ejection events (Johnson, 2018;Johnson et al, 2019). This biased sampling of the flow leads to a net force on particles away from the wall.…”

“…At St + = 2, the biased sampling force is comparable in magnitude to turbophoresis, attenuating the large nearwall concentrations seen at higher St + . In fact, it can be shown analytically that the biased sampling term exactly cancels turbophoresis in the St + → 0 limit (Johnson, 2018;Johnson et al, 2019). As St + increases, both turbophoresis and biased sampling decrease in magnitude, though turbophoresis decreases much more slowly.…”

“…Particle-particle collisions are known to effect particle dynamics in wall-bounded turbulent flows as volume fractions become high enough (Li et al, 2001;Yamamoto et al, 2001;Caraman et al, 2003;Kuerten andVreman, 2015, 2016;Johnson et al, 2019). In fact, the volume fraction at which collisions have a significant effect on the concentration profile can be quite 'low', as shown in Figure 2.…”

“…Thus, the wall-normal mixing of particles near the wall is greatly enhanced, flattening the concentration profiles even at relatively low bulk volume fractions ∼ 10 −4 (Yamamoto et al, 2001;Kuerten and Vreman, 2015). The quadratic scaling of collision rate with particle number density creates the scenario in which the particle concentration profile, as a function of wall-normal distance, is very sensitive to the bulk volume fraction of the particle-laden flow (Johnson, 2018;Johnson et al, 2019).…”