Turbulent mixing simulation of variable Sc flows using the Hierarchical Parcel Swapping (HiPS) model

The Heirarchical Parcel Swapping (HiPS) model is a minimal reduced-order stochastic model for simulating turbulent mixing. HiPS is structured as a binary tree consisting of nodes that branch to fluid parcels at the base of the tree. The tree levels have a geometric progression of length scales, with timescales corresponding to inertial-range scaling. Simulations consist of swapping subtrees and repairing of fluid parcels that can then be mixed in several ways. HiPS can be used as a mixing model in PDF transport-type fluid simulations. Computational costs are similar to other popular methods, e.g., the Modified Curl's model, but with mixing that contains a range of length scales that reproduces key turbulent scalings, is local in scale space, and maintains plausible "closeness" in state space. We extend the HiPS model to treat mixing with scalars of arbitrary Sc. This is important in applications requiring differential diffusion, such as in metallic flows, combustion, or aerosol mixing. We present scalar energy spectra for mixing in the low and high Sc regimes and show that the HiPS model is able to recover the theoretical scalings. We also present results of the scalar dissipation rate including probability density functions and show that a nominally lognormal profile is recovered, with negative skewness that is consistent with detailed numerical and experimental studies. This is significant given the relative simplicity of the HiPS model, and provides insights that can be difficult to discern in high-fidelity experiments or simulations. We also present results of the Richardson dispersion and show that the model recovers the cubic power law. Discussion of the model and further application to reactive flows are discussed.