@misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for radiatively driven turbulent convection}, series = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, journal = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochasticmodel for thermal convection with internal sources}, pages = {1}, abstract = {It is well established that heat transfer in turbulent Rayleigh-Bénard convection and angular momentum transfer in turbulent Taylor-Couette flow are similar in nature. This similarity manifests itself by isomorphic scaling laws for corresponding flow regimes. However, it is not clear at present if this similarity extends to flows with internal sources and different types of boundary conditions. Internal sources may occur, for example, due to radiative heating in dry or condensation in moist convection, or due to internal wave breaking and mean flow excitation in rotating Taylor-Couette-like flows. In this study, heat transfer in radiatively-driven turbulent Rayleigh-Bénard convection is investigated using the stochastic one-dimensional-turbulence model (ODT). A Boussinesq fluid of Prandtl number 1 is confined between two horizontal adiabatic no-slip walls that are located at z = 0 and H, respectively. The fluid is exposed to constant background gravity that points in vertical (-z) direction. A flow is driven by radiative heating from below yielding the local heating rate Q(z) = (P/l) exp(-z/l), where P is the prescribed mean total heat flux and l the absorption length that controls the thermal boundary layer thickness. ODT resolves all relevant scales of the flow, including molecular-diffusive scales, along a vertical one-dimensional domain, whereas stochastically sampled eddy events represent the effects of turbulent advection. ODT results reproduce and extrapolate available reference experiments of Lepot et al. (Proc. Natl. Acad. Sci. USA, 115, 2018, pp. 8937-8941) and Bouillaut et al. (J. Fluid Mech., 861, 2019, R5) in particular capturing the turbulent transition from the classical to the 'ultimate' regime. For these regimes, the exponent values in N u ∼ Ra^p scaling are found to be p ≈ 0.33 and p ≈ 0.55, respectively, in agreement with measured values. Joint probabilities of turbulent eddy size and location suggest that the regime transition is associated with a suppression of small-scale near-wall turbulent motions. The latter observation is found consistent with recent direct numerical simulations of heat transfer between permeable walls (Kawano et al., J. Fluid Mech., 914, 2021, A13).}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection, 25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {1}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinFreireLignelletal., author = {Klein, Marten and Freire, Livia S. and Lignell, David O. and Kerstein, Alan R. and Schmidt, Heiko}, title = {Ein stochastischer Ansatz zur Modellierung fluktuierender Oberfl{\"a}chenfl{\"u}sse in turbulenten Grenzschichten}, series = {Kurzfassungen der Meteorologentagung DACH}, volume = {2022}, journal = {Kurzfassungen der Meteorologentagung DACH}, publisher = {Copernicus}, doi = {10.5194/dach2022-22}, pages = {1 -- 1}, abstract = {Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskr{\"a}fte ber{\"u}cksichtigt werden k{\"o}nnen. Das Modell wird beispielhaft als unabh{\"a}ngiges, numerisches Werkzeug angewendet, um fluktuierende Oberfl{\"a}chenfl{\"u}sse in turbulenten Kanalstr{\"o}mungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (por{\"o}se) Oberfl{\"a}chen betrachtet. Anhand neuer Ergebnisse wird demonstriert, dass der Modellansatz in der Lage ist, Referenzdaten zufriedenstellend zu reproduzieren und extrapolieren. Daneben werden aktuelle Arbeiten zur Kopplung des stochastischen Modellansatzes mit Large-Eddy-Simulationen vorgestellt. Es wird gezeigt, dass die stochastische Modellierung oberfl{\"a}chennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitteraufl{\"o}sung zu verringern.}, language = {de} } @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{BoehlerRosencrantzWolfetal., author = {B{\"o}hler, Stefan and Rosencrantz, Sophia and Wolf, Karina and Heinemann, Robert and Schmidt, Peer and Ganster, Johannes and B{\"u}sse, Thomas and Balko, Jens and Rosencrantz, Ruben R.}, title = {Active protease formulation in commodity polymers withstands melt processing into compounds and blown films}, series = {Materials Today Communications}, volume = {34}, journal = {Materials Today Communications}, issn = {2352-4928}, doi = {10.1016/j.mtcomm.2022.105018}, pages = {1 -- 9}, abstract = {Integrating enzymes into thermoplastic polymers is challenging due to their lack of robustness with respect to temperature and shear fields during conventional melt processing. In the present study, blown films from low-density polyethylene (LDPE) were prepared containing a technical protease from Bacillus sp. First, LDPE/protease compounds were produced followed by blown film extrusion, both processes at melt mass temperatures of 130 °C or higher. Enzyme activity was proven, both for the LDPE/protease compound and the blown film. The highest enzyme activity in the compound was determined for processing at 132 °C and a screw speed of 75 rpm. The influence of melt temperature and shear fields was studied in detail. Enzyme activities were determined for melt temperatures up to 160 °C and for screw speeds ranging from 75 to 300 rpm during compounding by twin-screw extrusion. The process was also applied for biobased and biodegradable polyesters, where similar protease activity after compounding was verified. Electron microscopy, X-ray diffraction, nuclear magnetic resonance spectroscopy and differential scanning calorimetry served to analyze components and morphology of the enzyme formulation used here. It is proposed that the porous morphology of the protease particles is beneficial for the enzyme to remain active after processing. Additionally, the polymer matrix surrounding the particles protects the protease at elevated temperatures, which can be attributed to thermal insulation. Thus, the right combination of a suited technical enzyme formulation with appropriate mild melt compounding conditions allows enzymes to be incorporated into thermoplastics and retain their activity. This opens the way to use the abundant biological functions of enzymes in thermoplastic applications.}, language = {en} } @misc{StarickBehrangLignelletal., author = {Starick, Tommy and Behrang, Masoomeh and Lignell, David O. and Schmidt, Heiko and Kerstein, Alan R.}, title = {Turbulent mixing simulation using the Hierarchical Parcel Swapping (HiPS) model}, series = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, publisher = {Department of Fluid Mechanics, University of Technology and Economics}, address = {Budapest, Hungary}, isbn = {978-963-421-881-4}, pages = {1 -- 7}, 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{StarickBehrangLignelletal., author = {Starick, Tommy and Behrang, Masoomeh and Lignell, David O. and Schmidt, Heiko and Kerstein, Alan R.}, title = {Turbulent mixing simulation using the Hierarchical Parcel-Swapping (HiPS) model}, series = {Technische Mechanik}, volume = {43}, journal = {Technische Mechanik}, number = {1}, issn = {0232-3869}, doi = {10.24352/UB.OVGU-2023-044}, pages = {49 -- 58}, abstract = {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.}, language = {en} } @misc{MedinaMendezKleinPeetersetal., author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Peeters, Jurriaan W. R. and Schmidt, Heiko}, title = {Evaluating turbulent channel flows with rough walls : homogeneous roughness parameterization for use in a map-based turbulence model}, series = {International journal of heat and fluid flow}, volume = {117, Part B}, journal = {International journal of heat and fluid flow}, publisher = {Elsevier BV}, address = {Amsterdam}, doi = {10.1016/j.ijheatfluidflow.2025.110113}, pages = {1 -- 21}, abstract = {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.}, language = {en} } @inproceedings{SchmidtEgbersRath, author = {Schmidt, J.-R. and Egbers, Christoph and Rath, H. J.}, title = {Experiments on the isothermal flow in wide spherical gaps}, language = {en} } @misc{BraudWallanderBussetal., author = {Braud, N. and Wallander, H.J. and Buß, L. and L{\"o}fstrand, M. and Blomqvist, J. and Berschauer, C. and Rodriguez, A. Morales and Kofoed, P.M. and Resta, A. and Krisponeit, J.-O. and Schmidt, T. and Lundgren, E. and Flege, J.I. and Falta, J. and Merte, L.R.}, title = {Growth, structure, and morphology of ultra-thin tin oxide phases forming on Pt₃Sn(111) single crystals upon exposure to oxygen}, series = {Surface science}, volume = {767}, journal = {Surface science}, publisher = {Elsevier BV}, address = {Amsterdam}, issn = {0039-6028}, doi = {10.1016/j.susc.2025.122927}, pages = {1 -- 8}, abstract = {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.}, language = {en} }