@article{Starick_Behrang_Lignell_Schmidt_Kerstein_2023, title={Turbulent mixing simulation using the Hierarchical Parcel-Swapping (HiPS) model}, volume={43}, url={https://journals.ub.ovgu.de/index.php/techmech/article/view/2115}, DOI={10.24352/UB.OVGU-2023-044}, abstractNote={<p><span dir="ltr" role="presentation">Turbulent mixing is an omnipresent phenomenon that permanently affects our everyday life. Mixing processes also</span><br role="presentation"><span dir="ltr" role="presentation">plays an important role in many industrial applications. The full resolution of all relevant flow scales often poses a major challenge </span><span dir="ltr" role="presentation">to the numerical simulation and requires a modeling of the small-scale effects. In transported Probability Density Function (PDF) </span><span dir="ltr" role="presentation">methods, the simplified modeling of the molecular mixing is a known weak point. At this place, the Hierarchical Parcel-Swapping </span><span dir="ltr" role="presentation">(HiPS) model developed by A.R. Kerstein [J. Stat. Phys. 153, 142-161 (2013)] represents a computationally efficient and novel </span><span dir="ltr" role="presentation">turbulent mixing model. HiPS simulates the effects of turbulence on time-evolving, diffusive scalar fields. The interpretation </span><span dir="ltr" role="presentation">of the diffusive scalar fields or a state space as a binary tree structure is an alternative approach compared to existing mixing </span><span dir="ltr" role="presentation">models. The characteristic feature of HiPS is that every level of the tree corresponds to a specific length and time scale, which </span><span dir="ltr" role="presentation">is based on turbulence inertial range scaling. The state variables only reside at the base of the tree and are understood as fluid </span><span dir="ltr" role="presentation">parcels. The effects of turbulent advection are represented by stochastic swaps of sub-trees at rates determined by turbulent time </span><span dir="ltr" role="presentation">scales associated with the sub-trees. The mixing of adjacent fluid parcels is done at rates consistent with the prevailing diffusion </span><span dir="ltr" role="presentation">time scales. In this work, a standalone HiPS model formulation for the simulation of passive scalar mixing is detailed first. The </span><span dir="ltr" role="presentation">generated scalar power spectra with forced turbulence shows the known scaling law of Kolmogorov turbulence. Furthermore, </span><span dir="ltr" role="presentation">results for the PDF of the passive scalar, mean square displacement and scalar dissipation rate are shown and reveal a reasonable </span><span dir="ltr" role="presentation">agreement with experimental findings. The described possibility to account for variable Schmidt number effects is an important </span><span dir="ltr" role="presentation">next development step for the HiPS formulation. This enables the incorporation of differential diffusion, which represents an </span><span dir="ltr" role="presentation">immense advantage compared to the established mixing models. Using a binary structure allows HiPS to satisfy a large number of </span><span dir="ltr" role="presentation">criteria for a good mixing model. Considering the reduced order and associated computational efficiency, HiPS is an attractive </span><span dir="ltr" role="presentation">mixing model, which can contribute to an improved representation of the molecular mixing in transported PDF methods.</span></p>}, number={1}, journal={Technische Mechanik - European Journal of Engineering Mechanics}, author={Starick, Tommy and Behrang, Masoomeh and Lignell, David O. and Schmidt, Heiko and Kerstein, Alan R.}, year={2023}, month={Feb.}, pages={49–58} }