@misc{KersteinLignellSchmidtetal., author = {Kerstein, Alan R. and Lignell, David O. and Schmidt, Heiko and Starick, Tommy and Wheeler, Isaac and Behrang, Masoomeh}, title = {Using Hips As a New Mixing Model to Study Differential Diffusion of Scalar Mixing in Turbulent Flows}, series = {2021 AIChE Annual Meeting}, journal = {2021 AIChE Annual Meeting}, abstract = {Mixing two or more streams is ubiquitous in chemical processes and industries involving turbulent liquid or gaseous flows. Modeling turbulent mixing flows is complicated due to a wide range of time and length scales, and non-linear processes, especially when reaction is involved. On the other hand, in turbulent reacting flows, sub-grid scales need to be resolved accurately because they involve reactive and diffusive transport processes. Transported PDF methods use mixing models to capture the interaction in the sub-grid scales. Several models have been used with varying success. In this study, we present a novel model for simulation of turbulent mixing called Hierarchical Parcel Swapping (HiPS). The HiPS model is a stochastic mixing model that resolves a full range of time and length scales with the reduction in the complexity of modeling turbulent reacting flows. This model can be used as a sub-grid mixing model in PDF transport methods, as well as a standalone model. HiPS can be applied to transported scalars with variable Schmidt numbers to capture the effect of differential diffusion which is important for modeling scalars with low diffusivity like soot. We present an overview of the HiPS model, its formulation for variable Schmidt number flows, and then present results for evaluating the turbulence properties including the scalar energy spectra, the scalar dissipation rate, and Richardson dispersion. These model developments are an important step in applying HiPS to more complex flow configurations.}, language = {en} } @misc{LignellBehrangKersteinetal., author = {Lignell, David O. and Behrang, Masoomeh and Kerstein, Alan R. and Wheeler, Isaac and Starick, Tommy and Schmidt, Heiko}, title = {Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model}, series = {77th Annual Meeting of the Division of Fluid Dynamics, November 24-26, 2024; Salt Lake City, Utah}, journal = {77th Annual Meeting of the Division of Fluid Dynamics, November 24-26, 2024; Salt Lake City, Utah}, publisher = {American Physical Society}, abstract = {Hierarchical Parcel Swapping (HiPS) is a stochastic model of turbulent mixing. HiPS is based on a binary tree structure consisting of nodes emanating from the top of the tree and terminating in parcels at the base of the tree containing fluid properties. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent mixing is modeled by swapping subtrees at different tree levels. Swaps involving single parcels result in micromixing that changes scalar states. Swaps are implemented as a Poisson process at rates corresponding to level time scales. HiPS is extended to simulation of multiple scalars with arbitrary diffusivities, considering transport in the inertial, viscous-advective, and inertial-diffusive ranges. Fundamental analysis of particle dispersion is presented with comparisons to theoretical results and DNS data in the inertial and viscous ranges. Scalar energy spectra are analysed in the three ranges and reproduce known scaling exponents. Scalar dissipation statistics are analysed and reproduce the experimental and theoretical lognormal distribution with negative skewness represented by a stretched-exponential function. DNS data are used to evaluate empirical coefficients, facilitating quantitative applications. The physical fidelity demonstrated with HiPS suggests its use as a low-cost subgrid model for coarse-grained flow simulation, for which parcel-pair mixing is a common treatment.}, language = {en} } @misc{BehrangStarickWheeleretal., author = {Behrang, Masoomeh and Starick, Tommy and Wheeler, Isaac and Schmidt, Heiko and Kerstein, Alan and Lignell, David}, title = {Hierarchical parcel-swapping representation of turbulent mixing : part 4 : extension to the viscous range and to mixing of scalars with non-unity Schmidt numbers}, series = {Journal of fluid mechanics}, volume = {1020}, journal = {Journal of fluid mechanics}, publisher = {Cambridge University Press}, address = {Cambridge}, issn = {0022-1120}, doi = {doi:10.1017/jfm.2025.10512}, pages = {1 -- 39}, abstract = {Hierarchical parcel swapping (HiPS) is a multiscale stochastic model of turbulent mixing based on a binary tree. Length scales decrease geometrically with increasing tree level, and corresponding time scales follow inertial range scaling. Turbulent eddies are represented by swapping subtrees. Lowest-level swaps change fluid parcel pairings, with new pairings instantly mixed. This formulation suitable for unity Schmidt number Sc is extended to non-unity Sc. For high Sc, the tree is extended to the Batchelor level, assigning the same time scale (governing the rate of swap occurrences) to the added levels as the time scale at the base of the Sc=3 tree. For low Sc, a swap at the Obukhov-Corrsin level mixes all parcels within corresponding subtrees. Well-defined model analogues of turbulent diffusivity, and mean scalar-variance production and dissipation rates are identified. Simulations idealising stationary homogeneous turbulence with an imposed scalar gradient reproduce various statistical properties of viscous-range and inertial-range pair dispersion, and of the scalar power spectrum in the inertial-advective, inertial-diffusive and viscous-advective regimes. The viscous-range probability density functions of pair separation and scalar dissipation agree with applicable theory, including the stretched-exponential tail shape associated with viscous-range scalar intermittency. Previous observation of that tail shape for Sc=1, heretofore not modelled or explained, is reproduced. Comparisons to direct numerical simulation allow evaluation of empirical coefficients, facilitating quantitative applications. Parcel-pair mixing is a common mixing treatment, e.g. in subgrid closures for coarse-grained flow simulation, so HiPS can improve model physics simply by smarter (yet nearly cost-free) selection of pairs to be mixed.}, language = {en} }