TY - GEN A1 - Lignell, David O. A1 - Behrang, Masoomeh A1 - Kerstein, Alan R. A1 - Wheeler, Isaac A1 - Starick, Tommy A1 - Schmidt, Heiko T1 - Investigation of turbulent mixing of scalars with arbitrary Schmidt numbers using the stochastic Hierarchical Parcel Swapping Model T2 - 77th Annual Meeting of the Division of Fluid Dynamics, November 24–26, 2024; Salt Lake City, Utah N2 - 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. KW - turbulent mixing KW - variable Schmidt number KW - stochastic modeling KW - hierarchical parcel swapping Y1 - 2024 UR - https://meetings.aps.org/Meeting/DFD24/Session/X39.11 PB - American Physical Society ER - TY - GEN A1 - Starick, Tommy A1 - Behrang, Masoomeh A1 - Lignell, David O. A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Turbulent mixing simulation using the Hierarchical Parcel-Swapping (HiPS) model T2 - Technische Mechanik N2 - Turbulent mixing is an omnipresent phenomenon that permanently affects our everyday life. Mixing processes also plays an important role in many industrial applications. The full resolution of all relevant flow scales often poses a major challenge to the numerical simulation and requires a modeling of the small-scale effects. In transported Probability Density Function (PDF) methods, the simplified modeling of the molecular mixing is a known weak point. At this place, the Hierarchical Parcel-Swapping (HiPS) model developed by A.R. Kerstein [J. Stat. Phys. 153, 142-161 (2013)] represents a computationally efficient and novel turbulent mixing model. HiPS simulates the effects of turbulence on time-evolving, diffusive scalar fields. The interpretation of the diffusive scalar fields or a state space as a binary tree structure is an alternative approach compared to existing mixing models. The characteristic feature of HiPS is that every level of the tree corresponds to a specific length and time scale, which is based on turbulence inertial range scaling. The state variables only reside at the base of the tree and are understood as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub-trees at rates determined by turbulent time scales associated with the sub-trees. The mixing of adjacent fluid parcels is done at rates consistent with the prevailing diffusion time scales. In this work, a standalone HiPS model formulation for the simulation of passive scalar mixing is detailed first. The generated scalar power spectra with forced turbulence shows the known scaling law of Kolmogorov turbulence. Furthermore, results for the PDF of the passive scalar, mean square displacement and scalar dissipation rate are shown and reveal a reasonable agreement with experimental findings. The described possibility to account for variable Schmidt number effects is an important next development step for the HiPS formulation. This enables the incorporation of differential diffusion, which represents an immense advantage compared to the established mixing models. Using a binary structure allows HiPS to satisfy a large number of criteria for a good mixing model. Considering the reduced order and associated computational efficiency, HiPS is an attractive mixing model, which can contribute to an improved representation of the molecular mixing in transported PDF methods. KW - differential diffusion KW - hierarchical parcel-swapping KW - HiPS KW - mixing model KW - scalar mixing Y1 - 2023 U6 - https://doi.org/10.24352/UB.OVGU-2023-044 SN - 0232-3869 VL - 43 IS - 1 SP - 49 EP - 58 ER - TY - GEN A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Peeters, Jurriaan W. R. A1 - Schmidt, Heiko T1 - Evaluating turbulent channel flows with rough walls : homogeneous roughness parameterization for use in a map-based turbulence model T2 - International journal of heat and fluid flow N2 - This work is focused on modeling the effects of homogeneous roughness on low-order velocity statistics in turbulent channel flows. Hydrodynamic effects due to the roughness are characterized on the basis of volume-averaging theory (VAT) and a discrete roughness element method. This theory exploits the homogeneous character of the roughness in order to reduce the complexity of the flow to its one-dimensional statistics. The formulated VAT-based roughness forcing is best suited for drag dominated surfaces. Turbulence modeling closure is achieved with a map-based turbulence model, the One-Dimensional Turbulence (ODT) model. This avoids the prescription of laws of the wall or other ad-hoc scalings, unlike in more traditional filter-based turbulence models. The modeling framework is applied on selected Reynolds number flows for likewise selected roughness topologies. Results are compared to direct numerical simulation (DNS) data available from the literature. Among others, model results are compared with those of a previously formulated parametric forcing approach (PFA) for roughness drag which involved a costly coefficient calibration linked to the roughness topology model. In ODT, the only calibration process required is the same one involved for the turbulence model parameters, i.e., similar to the ODT model application for smooth-wall flows. Despite all of the inherently implied shortcomings of a 1-D model, some appealing properties of ODT are discussed. Notably, the model is able to predict the roughness function, as well as the wall-normal profile of the Reynolds shear stress across the entire boundary layer thickness. KW - Turbulent channel KW - Roughness KW - ODT KW - Volume-averaging Y1 - 2026 UR - https://www.sciencedirect.com/science/article/pii/S0142727X25003716#d1e18585 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2025.110113 VL - 117, Part B SP - 1 EP - 21 PB - Elsevier BV CY - Amsterdam ER - TY - CHAP A1 - Schmidt, J.-R. A1 - Egbers, Christoph A1 - Rath, H. J. T1 - Experiments on the isothermal flow in wide spherical gaps Y1 - 2001 ER - TY - GEN A1 - Braud, N. A1 - Wallander, H.J. A1 - Buß, L. A1 - Löfstrand, M. A1 - Blomqvist, J. A1 - Berschauer, C. A1 - Rodriguez, A. Morales A1 - Kofoed, P.M. A1 - Resta, A. A1 - Krisponeit, J.-O. A1 - Schmidt, T. A1 - Lundgren, E. A1 - Flege, J.I. A1 - Falta, J. A1 - Merte, L.R. T1 - Growth, structure, and morphology of ultra-thin tin oxide phases forming on Pt₃Sn(111) single crystals upon exposure to oxygen T2 - Surface science N2 - Here we report an investigation of ultrathin tin oxide films on Pt3Sn(111) using low-energy electron microscopy (LEEM), microspot low-energy electron diffraction (𝜇-LEED), scanning tunneling microscopy (STM), surface X-ray diffraction (SXRD), and high-resolution X-ray photoelectron spectroscopy (XPS). Oxidation at ∼390–410 ◦C produces triangular, two-dimensional oxide islands that nucleate rapidly and exhibit self-limited lateral growth, attributed to limited Sn diffusion from the subsurface of the crystal. 𝜇-LEED shows that the initially formed (4 × 4) Sn oxide is subsequently converted to a more oxygen-rich (2 × 2𝑛) ‘‘stripe’’ phase. At 630 ◦C, enhanced Sn mobility enables a closed (4 × 4) film. The (2 × 2𝑛) phase is shown to consist of a (2 × 2) Sn lattice modulated by 1D stripe defects with spacings of 𝑛 = 4–6 atomic rows; LEED and SXRD measurements show diffraction features corresponding to this striped superstructure. The two oxides can be distinguished in XPS by their O 1s lineshapes: the (4 × 4) phase shows a clear doublet attributable to distinct O species, whereas the (2 × 2𝑛) phase exhibits a broader envelope consistent with a distribution of O coordination environments. The Sn 3d5∕2 spectra are similar for both phases, reflecting closely related Sn bonding motifs. The spectra are consistent with those of previous near-ambient-pressure XPS measurements, suggesting that the surface oxides forming under CO oxidation conditions are similar to those studied here. KW - Tin oxide KW - Platinum-tin KW - LEEM KW - STM KW - SnOx KW - SXRD Y1 - 2026 U6 - https://doi.org/10.1016/j.susc.2025.122927 SN - 0039-6028 SN - 1879-2758 VL - 767 SP - 1 EP - 8 PB - Elsevier BV CY - Amsterdam ER -