Asymptotic closure model for inertial particle transport in turbulent boundary layers

Transport equations for heavy inertial particles in turbulent boundary layers may be de-rived from an underlying phase-space probability density function (PDF) equation. These equations, however, are unclosed, and the standard closure approach is to use a quasinormal approximation (QNA) in which the fourth moments are approximated as behaving as if the velocities were Normally distributed. Except for particles with weak inertia, the QNA leads to large quantitative errors, and is not consistent with the known asymptotic predictions of [D. P. Sikovsky, Flow, Turbul. Combust. 92, 41 (2014)] for the moments of the PDF in the viscous sublayer. We derive a closure approximation based on an asymptotic solution to the transport equations in regions where the effect of particle inertia is significant. The closure is consistent with the asymptotic predictions of Sikovsky, but applies even outside the viscous sublayer. Comparisons with direct numerical simulations (DNSs) show that the closure gives similar results to the QNA (with the QNA results in slightly better agreement with the DNS) when the viscous Stokes number is St < 10, but for St > 10 our model is in far better agreement with the DNS than the QNA. While the predictions from our model leave room for improvement, the results suggest that our closure strategy is a very effective alternative to the traditional QNA approach, and the closure could be refined in future work.