Particle Reynolds stress model for wall turbulence with inertial particle clustering

Abstract

The modification of Zaichik particle Reynolds stress transport model for turbulent particle-laden flows is developed taking into account the clustering phenomenon of inertial particles. The main novelty is the new boundary condition for the particle Reynolds stress, which is posed at some distance from the wall in the viscous sublayer and is consistent with the power-law singularity of particle concentration at the wall. The modified model avoids the spurious bifurcation of the solution, which observed for non-modified Zaichik model with the near-equilibrium wall boundary condition.

Asymptotic closure model for inertial particle transport in turbulent boundary layers

“…The predictions of the new closed model are compared with DNS data and we find that while the new model is not always in full quantitative agreement with the DNS, it does provide far superior predictions compared to the QNA when the particle inertia is moderate to strong. Moreover, even when there are quantitative discrepancies, the predictions are qualitatively consistent with the DNS data, unlike the QNA model whose solutions also feature a spurious bifurcation near the wall as the Stokes number is increased beyond a threshold value [17]. Therefore, while there is still room for improvement, the results suggest that the new closure approach is promising, and could be further refined in future work.…”

“…This is similar to the approach described in [17] to specify ∇ z W 2 | za as an alternative boundary condition for the QNA model. However, we found that za dz = 1 in the case where the interval [z a , z b ] spans the height of the whole flow.…”

“…The second issue is that the QNA equation for W 2 given by ( 11) predicts a bifurcation in the solution as St exceeds a threshold value [17], which through (12) also leads to a bifurcation in the solution for . This predicted bifurcation is not supported by DNS data and is argued to be unphysical [17], and will be illustrated in §III.…”

“…Since (17) explicitly contains , then (17) must be solved simultaneously with the equation governing , namely (12). However, we have found that the numerical stability of solutions to the coupled equations for and M 2 is improved if instead a second-order ODE is solved for .…”

“…where u is the vertical fluid velocity at a fixed position (in contrast to u p (t) which is the vertical fluid velocity along a particle trajectory). In the results that follow, the DNS data for the fluid wall-normal Reynolds stress uu is used, while the model discussed in [17] for the fluid Lagrangian timescale seen by the particle τ L was used. We begin by comparing the QNA and ACA model predictions with each other, in order to highlight their key differences.…”