A new closure for PDF-based transport equations for inertial particles in turbulent boundary layers

Transport equations for inertial particles in turbulent boundary layers may be derived from an underlying phase-space, probability density function (PDF) equation. However, these equations are unclosed, and the standard closure approach is to use a quasi-Normal 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 asymptotic predictions of Sikovsky (Flow, Turb. and Comb. 92, 2014) for the moments of the PDF in the viscous sublayer. We derive a new closure approximation based on an asymptotic solution to the transport equations in regions where the effect of particle inertia is significant. The new closure is consistent with the asymptotic predictions of Sikovsky, but is valid even outside the viscous sublayer, and captures the strong non-Gaussianity of the particle velocities. Comparisons with DNS show that the new closure performs much better than the QNA, and while the predictions leave room for improvement, the results suggest that this new closure approach is promising.