@misc{NaikBuryeMedinaMendezKleinetal., author = {Naik Burye, Nishidh Shailesh and Medina M{\´e}ndez, Juan Al{\´i} and Klein, Marten and Schmidt, Heiko}, title = {Revisiting near-wall modeling of fully developed turbulent flow in concentric annuli}, series = {Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB 13.-14. November 2024, Regensburg}, journal = {Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB 13.-14. November 2024, Regensburg}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {Regensburg}, pages = {174 -- 175}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Numerical study on the effects of transient pressure gradients on isothermal and heated pipe flows}, series = {94th Annual Meeting of the Association of Applied Mathematics and Mechanics March 18th-March 22nd, 2024 Magdeburg (Germany) : Book of Abstracts}, journal = {94th Annual Meeting of the Association of Applied Mathematics and Mechanics March 18th-March 22nd, 2024 Magdeburg (Germany) : Book of Abstracts}, address = {Magdeburg (Germany)}, pages = {227 -- 228}, language = {en} } @misc{JoshiMedinaMendezKleinetal., author = {Joshi, Abhishek and Medina Mendez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Simulating homogenous isotropic turbulence with deterministic and stochastic forcings using a one-dimensional turbulence model}, pages = {1}, abstract = {To understand the intermittency present in scalar fields we need to address the expense of current start-of-art DNS to probe the higher-order structure functions. These higher order moments become increasingly sensitive to increasing Reλ and much more prone to extreme events. Here, in this work, we investigate using a Reduced order model(ODT) to simulate Homogenous Isotropic turbulence as an initial step towards that goal by employing a linear forcing [1] proposed by Lundgren that is proportional to local and instantaneous velocity.}, language = {en} } @misc{MarinkovićMedinaMendezSchmidtetal., author = {Marinković, Pavle and Medina M{\´e}ndez, Juan Ali and Schmidt, Heiko and Klein, Marten}, title = {Ongoing development of a hybrid reduced order stochastic/LES solver for turbulent flows}, address = {Cottbus}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling and theoretical analysis of heated concentric coaxial pipes at low Prandtl number}, series = {94rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Book of Abstracts}, journal = {94rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Book of Abstracts}, publisher = {GAMM e.V.}, address = {Magdeburg}, pages = {11}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Time-resolved simulations of wind speed fluctuations across atmospheric boundary layers using a stochastic forward model}, series = {Verhandlungen der DPG Fr{\"u}hjahrstagung SMuK 2023}, journal = {Verhandlungen der DPG Fr{\"u}hjahrstagung SMuK 2023}, publisher = {Deutsche Physikalische Gesellschaft (DPG)}, address = {Dresden}, abstract = {Atmospheric boundary layers (ABLs) govern the atmosphere-surface coupling and are therefore of fundamental relevance for Earth's weather and climate system. Time-resolved numerical simulations of ABLs are challenging due to intricate interactions of inertial, Coriolis, buoyancy, and viscous forces on all relevant scales of the turbulent flow. Small-scale processes, albeit potentially nonuniversal, are typically not resolved due to cost constraints but modeled based on physically justified relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed here by utilizing a dimensionally reduced stochastic modeling approach. The model aims to reproduce turbulent cascade phenomenology by a stochastic process, respecting fundamental physical conservation principles. Momentary wind velocity and temperature profiles evolve autonomously in time for an ensemble of initial conditions. By comparison with available high-fidelity reference numerical simulations, reanalysis, and observations, it is shown that the model captures various relevant flow properties, exhibiting limitations mainly in a delayed relaminarization under very stable conditions. Forthcoming research aims to contribute to a better understanding of polar boundary layers, requiring predictive modeling capabilities, high resolution, and numerical efficiency to perform long-time simulations.}, language = {de} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {22}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.202200272}, abstract = {Simultaneous momentum and passive scalar transfer in weakly heated pressure-driven turbulent concentric annular pipe flow is numerically investigated using the cylindrical formulation of the stochastic one-dimensional turbulence (ODT) model,which is utilized here as standalone tool. In the present study, we focus on the model calibration for heated annular pipes based on recent reference direct numerical simulations (DNS) from Bagheri and Wang (Int. J. Heat Fluid Flow 86, 108725,2020; Phys. Fluids 33, 055131, 2021). It is shown that the model is able to individually capture scalar and momentum transfer, but not both equally well at the same time. We attribute this to less dissimilar scalar and momentum transport in the model at the low Reynolds number investigated. It is argued that the model prefers a fully developed turbulent state due to its construction. Nevertheless, it is demonstrated that ODT is able to reasonably capture the radial inner-outer asymmetry of the scalar and momentum boundary layers which yields better predictive capabilities than wall-function-based approaches.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0125514}, abstract = {Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock-turbulence interaction}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0137435}, abstract = {One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock-turbulence interaction cases involving Richtmyer-Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., "Simulation of shock-turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence," Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity.}, language = {en} } @misc{KleinSchoepsMedinaMendezetal., author = {Klein, Marten and Sch{\"o}ps, Mark Simon and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Numerical simulation and analysis of transient Ekman boundary layers using a stochastic turbulence model}, series = {EGU General Assembly 2023}, journal = {EGU General Assembly 2023}, publisher = {EGU - European Geophysical Union}, address = {Vienna, Austria}, doi = {10.5194/egusphere-egu23-9116}, language = {en} } @misc{GlaweKleinSchmidt, author = {Glawe, Christoph and Klein, Marten and Schmidt, Heiko}, title = {ODT augmented RaNS}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {368}, language = {en} } @misc{MedinaMendezSharmaSchmidtetal., author = {Medina M{\´e}ndez, Juan Al{\´i} and Sharma, Sparsh and Schmidt, Heiko and Klein, Marten}, title = {Towards the use of a reduced order and stochastic turbulence model for assessment of far-field sound radiation: low Mach number jet flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {413 -- 414}, language = {en} } @misc{SharmaAytonKleinetal., author = {Sharma, Sparsh and Ayton, Lorna and Klein, Marten and Schmidt, Heiko}, title = {Estimation of ODT-resolved acoustic sources in high Reynolds number turbulent jets}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {414 -- 415}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {SGS modeling in lattice Boltzmann method for non-fully resolved turbulent flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {363 -- 364}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Effects of Reynolds number on turbulent concentric coaxial pipe flow using stochastic modeling}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {365}, language = {en} } @misc{Klein, author = {Klein, Marten}, title = {Map-based stochastic modeling of multiscale transfer processes in turbulent flows}, series = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, journal = {Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics}, publisher = {GAMM e.V.}, address = {Dresden}, pages = {362}, abstract = {The detailed modeling of turbulent mixing has remained a numerical challenge for a number of applications, ranging from chemically reacting flows to noise prediction in technical flows, and encompassing convection on multiple scales in the geophysical context, among others. Complications arise from the dynamical complexity of turbulence that manifests itself by emergent small-scale flow features, scaling cascades, and intermittency due to prescribed forcings, boundary and initial conditions. In order to robustly predict, for example, the occurrence of catalytic reactions, generation of mixing noise, or the heat transfer across a layer of fluid, it is crucial to represent the physical redistribution processes in the flow with a proper account of participating time and length scales. This yields scale-locality and causality constraints that can usually only be fully addressed by direct numerical simulation (DNS) based on the discretized three-dimensional (3-D) Navier-Stokes equations, which is a very costly undertaking and limited to moderate or low turbulence intensities. In order to over- come the fundamental limitations of statistical turbulence models and numerical cost of DNS, so-called map-based stochastic turbulence models have been developed and increasingly applied to various mutiphysical flows over the last couple of decades. These models utilize onedimensional (1-D) generalized Baker's maps in order to distinguish advective filamentation from molecular diffusion processes, resolving all relevant scales of the flow along a single physical coordinate. Baker's maps are probabilistically sampled with respect to size, location, and time of occurrence which introduces dynamical complexity into the bottom-up modeling approach. When the sampling is based on the evolving flow state, a self-contained reduced- order model with predictive capabilities for turbulent flows can be formulated. In the talk, I will summarize the map-based stochastic modeling strategy with an emphasize on the so-called One-Dimensional Turbulence (ODT) model. After that, I will discuss some recent advances in the field, demonstrating the applicability of the approach across flow configurations. I will address in more detail the flow physics representation by means of entrainment and passive scalar mixing in turbulent jets, as well as heat flux and wall shear stress fluctuations in heated channels and stably-stratified atmospheric boundary layers.}, language = {en} } @misc{GlaweKleinSchmidt, author = {Glawe, Christoph and Klein, Marten and Schmidt, Heiko}, title = {Stochastic deconvolution of wall statistics in Reynolds-averaged Navier-Stokes simulations based on one-dimensional turbulence}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {23}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {3}, issn = {1617-7061}, doi = {10.1002/pamm.202300055}, pages = {9}, abstract = {Reynolds-averaged Navier-Stokes simulation (RaNS) is state-of-the-art for numerical analysis of complex flows at high Reynolds number. Standalone RaNS may yield a reasonable estimate of the wall-shear stress and turbulent drag if a proper wall-function is prescribed, but detailed turbulence statistics cannot be obtained, especially at the wall. This lack in modeling is addressed here by a stochastic deconvolution strategy based on a stochastic one-dimensional turbulence (ODT) model. Here, a one-way coupling strategy is proposed in which a forcing term is computed from the balanced RaNS solution that is in turn utilized in the ODT model. The temporally developing ODT solution exhibits turbulent perturbations but relaxes toward the local RaNS solution due to resolved molecular-diffusive processes. It is demonstrated that the approach is able to recover the distribution of positive wall-shear stress fluctuations in turbulent channel flow. When formulated as post-processing tool, it is suggested that RaNS can be enhanced by ODT providing economical means for local high-fidelity numerical modeling based on a low-fidelity flow solution.}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Investigating dissipative roughness effects on turbulent drag using a stochastic turbulence model}, series = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, journal = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, address = {Valencia}, pages = {1}, language = {en} } @misc{MedinaMendezSharmaSchmidtetal., author = {Medina M{\´e}ndez, Juan Ali and Sharma, Sparsh and Schmidt, Heiko and Klein, Marten}, title = {Toward the use of a reduced-order and stochastic turbulence model for assessment of far-field sound radiation: Low Mach number jet flows}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {3}, issn = {1617-7061}, doi = {10.1002/pamm.202300186}, pages = {9}, language = {en} } @misc{KleinKesslerSchmidt, author = {Klein, Marten and Kessler, Robert William and Schmidt, Heiko}, title = {On the influence of a wavy leading edge on the aerodynamic drag of a wing: A numerical parameter study}, series = {STAB Jahresbericht 2023}, volume = {21/2023}, journal = {STAB Jahresbericht 2023}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, pages = {110 -- 111}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating heat transfer properties of tubular heat exchangers with a stochastic turbulence model}, series = {1st EIZ (Energie-Innovationszentrum) Annual Meeting, 24-25 April 2024, Cottbus, Germany}, journal = {1st EIZ (Energie-Innovationszentrum) Annual Meeting, 24-25 April 2024, Cottbus, Germany}, address = {Cottbus, Germany}, pages = {2}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Features of turbulent boundary layers in heated concentric coaxial pipe flow at high Reynolds and low Prandtl numbers}, series = {ICTAM 2024}, journal = {ICTAM 2024}, address = {Daegu, South Korea}, doi = {10.13140/RG.2.2.30075.12323}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating Prandtl number effects in heated concentric coaxial pipe flow at high Reynolds number}, series = {1st European Fluid Dynamics Conference (EFDC1), 16-20 September 2024, Aachen, Germany}, journal = {1st European Fluid Dynamics Conference (EFDC1), 16-20 September 2024, Aachen, Germany}, address = {Aachen, Germany}, pages = {1}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Theoretical analysis and stochastic modeling of turbulent heat transfer in annular pipe flows}, 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 = {Heat transfer in annular pipes is determined by the thermal and momentum boundary layer at the cylindrical inner and outer walls, respectively. The relative contributions are expressed by a local Nusselt number that depends on the radius ratio, the Prandtl number, and the Reynolds number. Direct numerical simulation (DNS) has been used previously to infer closure relations constrained to weakly turbulent flow due to numerical resource requirements. Here, stochastic one-dimensional turbulence (ODT) is utilized as a standalone tool as an alternative to DNS. ODT offers full-scale resolution along a representative radial domain, providing predictive capabilities relative to a calibrated reference case at a radically reduced cost. On average, ODT obeys radial balance equations compatible with the Navier-Stokes equations. Separating the boundary layer into a diffusion and a mixing-length dominated region in cylindrical geometry yields wall-curvature corrections at the inner wall. The proposed expressions can be used to enhance prescribed wall functions, for example, in Reynolds-averaged Navier-Stokes simulations.}, language = {en} } @misc{KleinZenkerStaricketal., author = {Klein, Marten and Zenker, Christian and Starick, Tommy and Schmidt, Heiko}, title = {Stochastic modeling of multi-stream mixing based on one-dimensional turbulence}, series = {77th Annual Meeting of the Division of Fluid Dynamics}, journal = {77th Annual Meeting of the Division of Fluid Dynamics}, publisher = {American Physical Society}, abstract = {Measurements of multiple scalar mixing in a turbulent jet show a strong location dependence of the scalar fluctuations and mixing processes. Mixing is quantitatively described by the state space of scalar fluctuations in terms of a joint probability density function (JPDF). The JPDF evolves in the downstream and radial directions and has non-Gaussian shape which is a burden for mixing modeling since factoring into marginal distribution functions is not permissible. Stochastic simulations based on one-dimensional turbulence (ODT) are able to reasonably reproduce the JPDF and its spatial evolution by a parabolic marching problem that circumvents constraints of the underlying elliptic problem. The model reproduces the inertial-advective range (exponent -5/3) and predicts the emergence of the viscous-advective range (exponent -1) at higher wavenumbers as the Schmidt number increases. The model offers full-scale resolution at affordable cost providing means to reasonably capture state-space statistics of turbulent mixing.}, language = {en} } @misc{KleinMedinaMendezSchoepsetal., author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Sch{\"o}ps, Mark Simon and Schmidt, Heiko and Glawe, Christoph}, title = {Towards physics-based nowcasting of the instantaneous wind velocity profile using a stochastic modeling approach}, series = {STAB Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB, 13. - 14. November 2024, Regensburg}, journal = {STAB Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB, 13. - 14. November 2024, Regensburg}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {Regensburg [et al.]}, pages = {162 -- 163}, abstract = {The primary objective of this contribution is to provide an overview of the regime-spanning forward modeling capabilities offered by the stochastic one-dimensional turbulence model. The focus is on the applicability of the model and its validation for neutral and stable atmospheric boundary layer flows as a prerequisite for future applications to challenging atmospheric conditions.}, language = {en} } @misc{VallemKleinSchmidt, author = {Vallem, Rishindra and Klein, Marten and Schmidt, Heiko}, title = {Capabilities and limitations of smoothed particle hydrodynamics for the simulation of two-phase flow instabilities}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {24/2024}, journal = {Proceedings in Applied Mathematics and Mechanics}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.202400206}, pages = {15}, abstract = {Smoothed particle hydrodynamics (SPH) is a mesh-free, Lagrangian particle-based method that is able to simulate multiphase flows in an economical manner. However, its ability to capture the flow regimes and regime transitions in two phase (liquid-gas) internal flows, such as pipe or channel flows is not yet generally established. To address this lack in understanding, we first examine a laminar rising bubble case in order to evaluate the fluid-fluid interface representation and transient interface evolution by the solver. With a focus towards the transition mechanism from a stratified flow regime to a slug flow regime, we investigate the Kelvin-Helmholtz instability (KHI) both qualitatively and quantitatively, initially focusing on a low density ratio () and then extending it to a high density ratio (). For the low density ratio, we conduct an analysis of the temporal evolution and demonstrate that the SPH solver captures the initial exponential growth in qualitative agreement with inviscid linear stability theory (LST) and reference numerical data for shear-dominated flow with Richardson number . By conducting eight additional simulations for various for the high density ratio, we demonstrate that the numerically obtained parameter value for instability is around , which is in reasonable agreement with the theoretically expected value of . Based on the SPH results obtained for the range , we suggest a simple parameterization of the reduction of the effective growth rate proportional to .}, language = {en} } @misc{KleinKesslerSchmidt, author = {Klein, Marten and Kessler, Robert William and Schmidt, Heiko}, title = {Numerical investigation of drag reduction effects on a track bicycle fork using wings with a wavy leading edge}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {24}, journal = {Proceedings in Applied Mathematics and Mechanics}, publisher = {Wiley}, issn = {1617-7061}, doi = {10.1002/pamm.202400178}, pages = {1 -- 14}, abstract = {Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES) of the flow around wings with a wavy leading edge (WLE) are conducted in order to assess the capabilities of a passive flow control strategy for drag reduction. The intended application is indoor track cycling with controlled flow conditions. A section of a single fork rod is investigated in order to make the numerical simulations feasible. The present study reveals that net drag reduction is possible by a nonsinusoidal modification of the leading edge of the wing. However, the drag reduction effect remains limited to a few percent. While RANS and LES yield the same drag coefficient for a reference case, RANS underestimates the drag reduction effect for a longer wing and the WLE cases, but exhibits otherwise a qualitatively similar trend as the LES. With the aid of RANS, an optimal geometry is obtained defined by the wavelength-to-chord length ratio of and the amplitude-to-chord length ratio of . Corresponding LES results give an indication of the origin of drag reduction by a hampered vortex shedding. The generation of smaller and more streamwise oriented vortical flow structures at the trailing edge and behind the WLE wing is correlated with significantly reduced lift fluctuations and drag reduction.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Capturing features of transient boundary layers with a map-based stochastic modeling approach}, publisher = {Copernicus GmbH}, doi = {10.5194/egusphere-egu24-15560}, pages = {2}, abstract = {Atmospheric boundary layers (ABLs) exhibit transient processes on various time and length scales, with a scale separation between the large-scale forcing and the small-scale response. Some crucial but standing challenges in modeling and simulation of ABL flows lie in the detailed representation of boundary layer turbulence (e.g. [1]). This includes intermittent and transient processes and the resulting turbulent and laminar response mechanisms. State-of-the-art subgrid-scale models utilize statistical closures for an averaged resolved flow state on the basis of the Monin-Obhukov similarity theory (MOST) to represent scalar fluxes and momentum fluxes (e.g. [2]). Fluctuations are not resolved in MOST. Instead, their ensemble effect is parameterized by the resolved large scales, neglecting backscatter from the unresolved small scales. Data-driven stochastic approaches aim to incorporate fluctuations and the spontaneous occurrence of instabilities, but at the expense of ad hoc forcings (e.g. [3]). The mentioned limitations can be removed by a physically compatible representation of turbulent fluctuations. This is addressed here by utilization of a map-based stochastic approach that is based on the one-dimensional turbulence (ODT) model [4]. ODT autonomously evolves vertical flow profiles for prescribed initial and boundary conditions, and physical forcings. The model captures turbulent cascade phenomenology and aims to resolve all relevant turbulent scales along a physical coordinate. Turbulent advection is modeled by a stochastically sampled sequence of spatial mapping events that punctuate the deterministic advancement due to viscous and Coriolis forces. The offered dynamical complexity removes the need for artificial forcings. In the contribution, key results from recent and ongoing studies related to the reduced-order modeling of ABL flows will be presented. First, surface scalar and momentum fluxes in turbulent channels are discussed emphasizing the correctly predicted inapplicability of the Reynolds analogy [5]. Second, the influence of system rotation and stratification is discussed for low-order velocity statistics and the participating turbulent scales [6,7]. Third, results for nonequilibrium conditions are presented for a transient ABL that exhibits turbulent bursts in response to an oscillatory geostrophic forcing [8]. Last, some preliminary results on the stochastic deconvolution of averaged data [9] will be presented focusing on the additional physical insight that is offered by the model. References [1] L. Mahrt. Annu. Rev. Fluid Mech. 46:23-45, 2014. [2] I. Stiperski, and M. Calaf. Phys. Rev. Lett. 130:124001, 2023. [3] V. Boyko, and N. Vercauteren. Q. J. R. Meteorol. Soc. 149(755):2125-2145, 2023. [4] A. R. Kerstein, and S. Wunsch. Bound.-Lay. Meteorol. 118:325-356, 2006. [5] M. Klein, H. Schmidt, and D. Lignell. Int. J. Heat Fluid Flow 93:108889, 2022. [6] M. Klein, and H. Schmidt. Adv. Sci. Res. 19:117-136, 2022. [7] L. S. Freire. Bound.-Lay. Meteorol. 184:25-43, 2022. [8] M. Klein, and H. Schmidt. Adv. Sci. Res. 20:55-64, 2023. [9] C. Glawe, M. Klein, and H. Schmidt. Proc. Appl. Math. Mech. 23:e202300055, 202}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Resolving the electrostatic boundary layer in a turbulent electrohydrodynamic flow with a map-based stochastic modeling approach}, series = {1st European Fluid Dynamics Conference - Daily Scientific Program}, journal = {1st European Fluid Dynamics Conference - Daily Scientific Program}, address = {Aachen}, pages = {1}, abstract = {Electrohydrodynamically (EHD) enhanced wall-bounded turbulent flows are encountered in various technical applications ranging from air-cleaning devices (like precipitators) to electrolyte flows (like redox flow batteries). The multi-physical processes governing the flow properties, however, are not yet very well understood. This is due the inaccessibility to and limitations of measurement equipment and numerical resolution requirements imposed by the electrostatic charge boundary layer that interacts on different time scales with the turbulent boundary layer. Recent advances in measurement techniques allow to resolve the exponential electrostatic charge boundary layer in a charged particle-ladden, weakly turbulent gas flow [1], which is qualitatively compatible with direct numerical simulation (DNS) results for a weakly turbulent flow of an electrolyte [2] at low Reynolds (Re) number. The challenge that remains is the extrapolation to highly turbulent flow conditions. Charged particles are heavy compared with fluid molecules and can be treated as a high Schmidt (Sc) number scalar, which is a burden for DNS. In this contribution, it is demonstrated that this burden can be overcome for the transient boundary layer evolution by utilizing a radically reduced, map-based stochastic one-dimensional turbulence (ODT) model. The model predicts a significant enhancement of the skin friction drag due to turbulence-induced screening layer depletion [3], as summarized in Fig. 1. In the talk, features of the instantaneous and mean velocity and electrostatic boundary layer will be presented. The plausibility of the model prediction is evaluated on a physical basis, encompassing details of the model formulation and the emerging hydrodynamic and electrokinetic properties of the boundary layer. References [1] W. Xu, S. Jantaˇc, T. Matsuyama, and H. Grosshans. arXiv:2306.06970, 2023. (Accepted for publication by Exp. Fluids.) [2] R. Ostilla-M´onico, and A. A. Lee. Faraday Discuss., 199:159-173, 2017. [3] M. Klein, J. A. Medina M´endez, and H. Schmidt. Tech. Mech., 43:111-127, 2023.}, language = {en} } @misc{ParekhGschwanderKleinetal., author = {Parekh, Parshva Atulbhai and Gschwander, Stefan and Klein, Marten and Gamisch, Sebastian}, title = {CFD-based analysis and minimization of mixing during the charging phase of a thermal energy storage tank}, series = {1. Jahresfachtagung des Energie-Innovationszentrums (EIZ) Cottbus}, journal = {1. Jahresfachtagung des Energie-Innovationszentrums (EIZ) Cottbus}, address = {Cottbus}, pages = {2}, abstract = {Transient numerical simulations are performed for a cuboidal storage tank in order to resolve the transient features of the charging phase in a feasible manner. A diffuser is utilized for the inflow of water in order avoid large-scale overturning fluid motions in order to establish a thermal stratification. It is demonstrated that the thermal stratification can be furrther enhanced by introducing a layer of a porous medium at the top of the storage tank based on computational fluid dynamics (CFD) simulations using COMSOL Multiphysics®. Initially, a storage tank configuration without a porous medium is simulated in order to establish a baseline understanding. Subsequent simulations are performed systematically varying various parameters of the porous medium, such as porosity, location, and inclination. The inclined placement of the porous sheet yields a reduction of the thermocline thickness by approximately 38\% compared to the reference case, thereby significantly enhancing the thermal stratification. As next step, the results obtained will be verified in an experimental apparatus at Fraunhofer ISE. In the talk, the set-up of the numerical model, including the treatment of the porous sheet, the thermocline evolution together with the governing fluid flow, and the effect of an additionally installed porous sheet will be discussed}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Investigation of the impact of transient pressure gradients on turbulent channel flow dynamics}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {24}, journal = {Proceedings in Applied Mathematics and Mechanics}, publisher = {Wiley-VCH GmbH}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.202400183}, pages = {1 -- 12}, abstract = {The effect of transient pressure gradients, or transient pumping in turbulent channel flow configuration, is investigated. Employing a cost-efficient reduced-order stochastic method known as one-dimensional turbulence (ODT) modeling, simulations explore different signal shapes for the modulation of the prescribed pressure gradient forcing, including sinusoidal modulation, step-like modulation, and piecewise sinusoidal beating. Various cycle periods and active pumping times are investigated. The simulations are conducted at a frictional Reynolds number of \$Re_\tau = 395\$ and a molecular Prandtl number of \$Pr = 1\$. The study adopts a passive scalar formulation to investigate heat transfer properties. The study quantifies the effects of transient pressure gradients on heat transfer rate, drag, and pumping power. Preliminary ODT predictions suggest that all transient cases exhibit lower heat transfer rates and a higher pumping power requirement than the constant pressure gradient case, with the step-like modulation yields superior skin-friction drag and heat transfer rate reductions relative to other signals.}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Investigating modifications of the heat transfer by velocity boundary conditions in turbulent thermal convection using an off-lattice Boltzmann method}, series = {STAB Jahresbericht 2024}, journal = {STAB Jahresbericht 2024}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {Regensburg [et al.]}, pages = {40 -- 41}, abstract = {In our contribution to the STAB workshop, we will present the effect of different surfaces on flow and heat transfer characteristics, taking into account the no-slip, free-slip, and finite-slip lengths of the walls. Following that, the impact of different walls, such as horizontal or side walls, will be discussed separately. Finally, the influence of finite slip length on turbulent characteristics will also be addressed. The work was supported by the North- German Supercomputing Alliance (HLRN) and numerical simulations were carried out on HLRN high-performance computing facilities at Berlin and G{\"o}ttingen (project ID: bbi00022).}, language = {en} } @incollection{KleinTsaiSchmidt, author = {Klein, Marten and Tsai, Pei-Yun and Schmidt, Heiko}, title = {Stochastic Modeling and Large-Eddy Simulation of Heated Concentric Coaxial Pipes}, series = {New Results in Numerical and Experimental Fluid Mechanics XIV, STAB/DGLR Symposium 2022}, booktitle = {New Results in Numerical and Experimental Fluid Mechanics XIV, STAB/DGLR Symposium 2022}, editor = {Dillmann, Andreas and Heller, Gerd and Kr{\"a}mer, Ewald and Wagner, Claus and Weiss, Julien}, publisher = {Springer}, address = {Cham}, isbn = {978-3-031-40482-5}, issn = {1612-2909}, doi = {10.1007/978-3-031-40482-5_41}, pages = {435 -- 444}, abstract = {Turbulent concentric coaxial pipe flows are numerically investigated as canonical problem addressing spanwise curvature effects on heat and momentum transfer that are encountered in various engineering applications. It is demonstrated that the wall-adapting local eddy-viscosity (WALE) model within a large-eddy simulation (LES) framework, without model parameter recalibration, has limited predictive capabilities as signalized by poor representation of wall curvature effects and notable grid dependence. The identified lack in the modeling of radial transport processes is therefore addressed here by utilizing a stochastic one-dimensional turbulence (ODT) model. A standalone ODT formulation for cylindrical geometry is used in order to assess to which extent the predictability can be expected to improve by utilizing an advanced wall-modeling strategy.}, language = {en} } @misc{Klein, author = {Klein, Marten}, title = {Map-based stochastic simulation data of a transient Ekman boundary layer}, abstract = {A journal paper in Advances in Science and Research details the numerical modeling approach used to create the data. Here, the model input files, the raw data, processed data, and plot scripts are provided that support the research. The code used to generate the data is an extended version of the one-dimensional turbulence (ODT) model. The current model implementation utilizes an adaptive grid that further increases numerical efficiency. A reduced version of the adaptive ODT code used in this work is available free of charge at: https://github.com/BYUignite/ODT The bash script makePlot.sh is the top-level driver and contains all additional information about the cases. Some other Details are provided by low-level README files. Python-3.8 is required to run the scripts.}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Towards stochastic subgrid-scale modeling of turbulent thermal convection in an under-resolved off-lattice Boltzmann method}, series = {Proceedings in applied mathematics and mechanics : PAMM}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, issn = {1617-7061}, doi = {10.1002/pamm.202300223}, pages = {1 -- 9}, abstract = {A characteristic-based Off-Lattice Boltzmann Method (OLBM) and a stochastic One-Dimensional Turbulence (ODT) model is utilized for numerical simulation of turbulent thermal convection. Standalone ODT results for low-order statistics are compared with those from various eddy-viscosity-based subgrid-scale models utilized in Large-Eddy Simulations (LES) with OLBM. The predictive capabilities of both approaches are discussed by comparison with available reference Direct Numerical Simulation (DNS) results. All turbulence models are able to predicted the mean temperature, but fail to fully capture fluctuations. While the OLBM aims to represent large-scale structures, it misses some constitutional small-scale fluctuations. By contrast, the reduced-order ODT model captures small-scale fluctuations in the vicinity of the wall, but cannot resolve the organized bulk flow. Here, the modeling capabilities of both OLBM and ODT as standalone tools are discussed. On this basis, a strategy for the incorporation of ODT as wall model in OLBM is suggested.}, language = {en} } @misc{KleinZenkerStaricketal., author = {Klein, Marten and Zenker, Christian and Starick, Tommy and Schmidt, Heiko}, title = {Stochastic modeling of multiple scalar mixing in a three-stream concentric coaxial jet based on one-dimensional turbulence}, series = {International Journal of Heat and Fluid Flow}, volume = {104}, journal = {International Journal of Heat and Fluid Flow}, issn = {0142-727X}, doi = {10.1016/j.ijheatfluidflow.2023.109235}, pages = {1 -- 17}, abstract = {Modeling turbulent mixing is a standing challenge for nonpremixed chemically reacting flows. Key complications arise from the requirement to capture all relevant scales of the flow and the necessity to distinguish between turbulent advective transport and molecular diffusive transport processes. In addition, anisotropic mean shear, variable advection time scales, and the coexistence of turbulent and nonturbulent regions need to be represented. The fundamental issues at stake are addressed by investigating multi-scalar mixing in a three-stream coaxial jet with a map-based stochastic one-dimensional turbulence model. ODT provides full-scale resolution at affordable costs by a radical reduction of complexity compared to high-fidelity Navier-Stokes solvers. The approach is partly justified by an application of the boundary-layer approximation, but neglects fluctuating axial pressure gradients. It is demonstrated that low-order scalar statistics are reasonably but not fully captured. Despite this shortcoming, it is shown that the model is able to reproduce experimental state-space statistics of multi-stream multi-scalar mixing. The model therefore offers physics-compatible improvements in multi-stream mixing modeling despite some fundamental limitations that remain from unjustified assumptions.}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Investigating Reynolds number effects in turbulent concentric coaxial pipe flow using stochastic one-dimensional turbulence modeling}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {23}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {4}, issn = {1617-7061}, doi = {10.1002/pamm.202300167}, pages = {1 -- 8}, abstract = {The present study numerically investigates turbulent momentum transfer in concentric coaxial (annular) pipe flow with small radius ratios (𝜂 = 𝑅𝑖∕𝑅𝑜 = 0.1,0.04,0.02). To model the flow, a stochastic one-dimensional turbulence (ODT) model formulated for cylindrical geometry is used that provides full-scale resolution along a representative radial coordinate. The present investigation extends the model validation by Tsai et al. (PAMM,22:e202200272, 2023), to radius ratios smaller than 0.1 and addresses boundary layers with strong span-wise curvature effects. The focus is on the assessment and analysis of statistical flow features in the vicinity of the inner cylinder wall, particularly in cases with small radius ratios. Following Boersma \& Breugem (Flow Turbul. Com-bust.,86:113-127, 2011), classical boundary-layer and mixing-length theory is utilized to analyze the model predictions. The results demonstrate that the ODT model captures leading-order curvature and mixing-length effects by its physics-compatible construction. Utilizing the model for extrapolation to high Reynolds numbers inaccessible to conventional high-fidelity numerical approaches shows that curvature effects persist and nonlocally affect the entire boundary layer. The model results provide support for a spanwise-curvature-modified wall function.}, language = {en} } @misc{KleinStarickZenkeretal., author = {Klein, Marten and Starick, Tommy and Zenker, Christian and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Reduced order stochastic modeling of turbulent mixing based on conservative baker's maps}, series = {Proceedings of the 14th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM-14)}, journal = {Proceedings of the 14th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements (ETMM-14)}, publisher = {ERCOFTAC}, address = {Barcelona, Spain}, pages = {613 -- 618}, abstract = {The detailed numerical representation of turbulent mixing processes is a standing challenge for non-premixed chemically reacting flows. The full range of relevant flow scales needs to be captured and it is also necessary to distinguish turbulent advective from molecular diffusive processes in order to represent Reynolds and Schmidt number effects. These requirements are addressed here by utilizing two different map-based stochastic turbulence modeling strategies. The one-dimensional turbulence (ODT) model utilizes event-based turbulence modeling, whereas the hierarchical parcel-swapping (HiPS) model is a fully event-based mixing model. ODT provides full-scale resolution at affordable costs by dimensional model reduction based on the boundary-layer approximation to shear flow. HiPS is far less costly than ODT but currently limited to locally homogeneous isotropic turbulence. The physics-compatible modeling capabilities with respect to phase-space representation of turbulent mixing are demonstrated for two canonical cases using standalone model formulations.}, language = {en} } @misc{VallemKleinSchmidt, author = {Vallem, Rishindra and Klein, Marten and Schmidt, Heiko}, title = {Numerical modeling and simulation of two-phase internal flow instabilities using Smoothed Particle Hydrodynamics (SPH)}, series = {STAB Jahresbericht 2023}, volume = {21/2023}, journal = {STAB Jahresbericht 2023}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, pages = {158 -- 159}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling of asymmetric turbulent boundary layers in annular pipe flow}, doi = {10.13140/RG.2.2.18789.78567}, pages = {1}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Stochastic modeling of electrohydrodynamically enhanced drag in one-way and fully coupled turbulent Poiseuille and Couette flow}, series = {Technische Mechanik}, volume = {43}, journal = {Technische Mechanik}, number = {1}, issn = {0232-3869}, doi = {10.24352/UB.OVGU-2023-049}, pages = {111 -- 127}, abstract = {Joint predictive modeling of hydrodynamics and electrokinetics is a standing numerical challenge but crucial for various applications in electrochemistry and power engineering. The present lack in modeling of electrohydrodynamic (EHD) turbulent flows lies in the treatment of small-scale processes and scale interactions. To overcome these limitations, a stochastic one-dimensional turbulence (ODT) model is utilized. The model aims to resolve all scales of the flow, but only on a notional line-of-sight, modeling turbulent advection by a stochastically sampled sequence of eddy events that punctuate deterministic molecular diffusive advancement. In this study, two canonical flow configurations are investigated that address different coupling strategies and flow physics. First, EHD effects in a variable-density vertical pipe flow of an ideal gas with an inner concentric electrode are investigated with a one-way coupled model formulation. Electric fields are generated by means of a corona discharge and the corresponding effect of a fixed ionic charge density field. Second, in order to reduce physical complexity, EHD effects the turbulent boundary layers in plane Couette flow of an isothermal univalent ionic liquid are investigated with a fully coupled model formulation. Both application cases demonstrate that ODT has predictive capabilities due to multiscale resolution of transport processes. Present results suggest that more expensive fully than one-way coupling of electrokinetics is crucial when charge relaxation times are significantly larger than the mean advection time scale.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Capturing features of turbulent Ekman-Stokes boundary layers with a stochastic modeling approach}, series = {Advances in Science and Research}, volume = {20}, journal = {Advances in Science and Research}, issn = {1992-0636}, doi = {10.5194/asr-20-55-2023}, pages = {55 -- 64}, abstract = {Atmospheric boundary layers (ABLs) exhibit transient processes on various time scales that range from a few days down to seconds, with a scale separation of the large-scale forcing and the small-scale turbulent response. One of the standing challenges in modeling and simulation of ABLs is a physically based representation of complex multiscale boundary layer dynamics. In this study, an idealized time-dependent ABL, the so-called Ekman-Stokes boundary layer (ESBL), is considered as a simple model for the near-surface flow in the mid latitudes and polar regions. The ESBL is driven by a prescribed temporal modulation of the bulk-surface velocity difference. A stochastic one-dimensional turbulence (ODT) model is applied to the ESBL as standalone tool that aims to resolve all relevant scales of the flow along a representative vertical coordinate. It is demonstrated by comparison with reference data that ODT is able to capture relevant features of the time-dependent boundary layer flow. The model predicts a parametric enhancement of the bulk-surface coupling in the event of a boundary layer resonance when the flow is forced with the local Coriolis frequency. The latter reproduces leading order effects of the critical latitudes. The model results suggest that the bulk flow decouples from the surface for high forcing frequencies due to a relative increase in detached residual turbulence.}, language = {en} } @misc{MedinaMendezKleinSchoepsetal., author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Sch{\"o}ps, Mark Simon and Schmidt, Heiko}, title = {Predicting volatile wind energy: Stochastic forward modeling and machine learning}, series = {86. Jahrestagung der DPG (86th Annual Conference of the DPG), DPG-Fr{\"u}hjahrstagung 2023, (DPG Spring Meeting 2023 of the Matter and Cosmos Section (SMuK), 20-24 March 2023, Technische Universit{\"a}t Dresden}, journal = {86. Jahrestagung der DPG (86th Annual Conference of the DPG), DPG-Fr{\"u}hjahrstagung 2023, (DPG Spring Meeting 2023 of the Matter and Cosmos Section (SMuK), 20-24 March 2023, Technische Universit{\"a}t Dresden}, publisher = {Deutsche Physikalische Gesellschaft}, address = {Bad Honnef}, issn = {2751-0522}, pages = {S. 343}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling and theoretical analysis of weakly heated concentric coaxial pipe flows at low prandtl number}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {25}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {1}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.70006}, pages = {1 -- 7}, abstract = {Heated concentric coaxial (annular) pipe flows are numerically investigated by a stochastic one-dimensional turbulence (ODT) model. The main objective of this work is to more accurately predict the heat transfer in tubular heat exchangers at low Prandtl numbers by extending the analysis for weak temperature fluctuations as recently introduced in Tsai et al., Proceedings in Applied Mathematics and Mechanics, 23:e202300167, 2023. The ODT model offers the required predictive capabilities at affordable cost by providing full-scale resolution of viscous, conductive, and turbulent advective transport processes along a representative radial coordinate. The Prandtl numbers and are considered for which the radius ratio of the annular pipe and the Reynolds number are varied. Numerical results demonstrate that the geometry (radius ratio) has a significant influence on the thermal boundary layer that emerges over the inner and outer curved wall, respectively. Application of boundary layer theory and mixing length arguments yield an analytical expression that includes both Reynolds number and curvature effects. Unknown closure coefficients are estimated with ODT, providing a physically based correlation for the Nusselt number.}, language = {en} } @misc{MarinkovićMedinaSchoepsetal., author = {Marinković, Pavle and Medina, Juan A. and Sch{\"o}ps, Mark Simon and Klein, Marten and Schmidt, Heiko}, title = {Experiences from the bottom-up development of an object-oriented CFD solver with prospective hybrid turbulence model applications}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {25}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {1}, publisher = {Wiley}, issn = {1617-7061}, doi = {10.1002/pamm.202400190}, abstract = {In this work, we discuss recent experiences related to the development and enhancement of a hybrid stochastic computational fluid dynamics (CFD) solver, the C++ version of the Implicit/Explicit (IMEX) time-advancement algorithm used in the one-dimensional turbulence-based (ODT) large eddy simulation (LES) model, abbreviated as ODTLES. After being ported from Fortran 90, the current capabilities of the C++ code are restricted to the reproducibility of turbulent channel flow simulations with respect to the former Fortran code version that was able to achieve reasonable agreement with available reference direct numerical simulation (DNS) for low to moderate Reynolds number turbulent channel flows. This is far from satisfactory so that current efforts are centered on improving the solver code structure through comprehensive refactoring, robust unit testing, and strict adherence to code style guides, following the principles of Clean Code. We focus the discussion on a methodology to balance unit, regression, and integration testing, here for the LES component of the code. The objective is to frame a starting point that is relevant also for other CFD codes, irrespective of whether they utilize conventional or novel discretization or flow modeling approaches.}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Simulating Volatile Wind Energy: Stochastic Forward Modeling and Machine Learning}, publisher = {Innovation Hub 13, TH Wildau}, address = {Wildau}, pages = {1}, abstract = {The transformation of the energy sector is based on the integration of various renewable sources, such as wind and solar energy. One of the key challenges for the integration of these sources into the existing power grid is their erratic and sometimes discontinuous availability (volatility). Wind energy is one of the most relevant sources of CO2 neutral electric energy, but volatile due to fluctuating wind fields on multiple scales. This has already been realized so that senors provide real-time information on the scale of individual wind turbines. However, fore- casting remains an unresolved problem since numerical weather prediction models cannot provide the necessary level of detail. New modeling strategies are required that integrate turbine-scale and meso-scale information for accurate site-specific short-term prediction. Present and forthcoming research aims to incorporate fluctuations on multiple levels of fidelity, depending on the abstraction layer}, language = {en} } @misc{LiKleinSchmidt, author = {Li, Hanchen and Klein, Marten and Schmidt, Heiko}, title = {Simulation of radiatively driven mixing in a smoke cloud using "one-dimensional turbulence"}, doi = {10.5194/egusphere-egu25-9491}, pages = {1}, abstract = {Large-eddy simulations (LESs) are known to significantly overestimate entrainment in cloud-topped boundary layers, negatively impacting predictions on cloud mass and cover. This overestimation stems from coarse model resolutions that lead to numerical broadening of the entrainment layer. While it has been shown in direct numerical simulations (DNSs) that down-to-centimetre-scale resolutions can mitigate this issue, such high resolutions are not viable for most applications in the atmospheric sciences. The one-dimensional turbulence model (ODT), introduced by Kerstein [1], offers a computationally efficient alternative that provides full-scale resolution along a 1-D vertical domain. Molecular diffusion is explicitly resolved, while turbulent advection is modelled through a stochastically sampled sequence of spatial mappings, known as eddy events. Physically plausible eddy events are selected based on their current kinetic and potential energy. This allows an accurate representation of local turbulence properties and their dynamical complexity by evolving instantaneous property profiles. This study applies ODT to investigate cloud-top turbulent mixing processes driven by radiative cooling in a smoke cloud, benchmarking the results against DNS. Building on the preliminary findings by Meiselbach [2], we demonstrate improvements in mean profiles and turbulent fluxes of buoyancy and smoke concentration, showing ODT's ability to reproduce salient features observed in DNSs. In addition, we explore convective boundary layer scalings at extended Reynolds and Richardson numbers beyond those accessible in DNS studies. References: [1] A. R. Kerstein, Journal of Fluid Mechanics 392, 277334 (1999). [2] F. T. Meiselbach, Application of ODT to Turbulent Flow Problems, doctoral thesis, BTU Cottbus-Senftenberg (2015).}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating cutoff scales in turbulent Ekman flow with a map-based stochastic modeling approach}, publisher = {Copernicus GmbH}, address = {G{\"o}ttingen}, doi = {10.5194/egusphere-egu25-13495}, pages = {1}, abstract = {The Ozmidov scale marks the cutoff scale above which overturning fluid motions in stably stratified shear flows are energetically prohibited. A recent study of a turbulent shear layer demonstrates that the Corrsin scale provides an intrinsic cutoff scale when stratification is absent [1]. For the neutral boundary layer, it is proposed by analogy to the mixing layer that the cutoff scale is linked to the Corrsin scale rather than the unbounded Ozmidov scale. The claim is numerically investigated for turbulent Ekman flow with the aid of Kerstein's one-dimensional turbulence (ODT) model [2], utilizing the case setup described in [3]. ODT offers full-scale resolution along a vertical coordinate by autonomously evolving the instantaneous property profiles. Molecular diffusion is directly resolved, whereas turbulent advection is modeled by a stochastic process that is formulated with the aid of spatial mapping events, which are sampled based on the local available energy. In this model formulation, a cutoff scale is economically prescribed by limiting the sampling range of turbulent scales. Model results in terms of low-order and detailed turbulence statistics will be presented and compared to available reference data and theoretical analysis. References [1] F. G. Jacobitz and K. Schneider. Phys. Rev. Fluids 9:044602, 2024. [2] A. R. Kerstein and S. Wunsch. Bound.-Lay. Meteorol. 118:325-356, 2006. [3] M. Klein and H. Schmidt. Adv. Sci. Res. 19:117-136, 2022.}, language = {en} } @misc{MarinkovicMedinaKleinetal., author = {Marinkovic, Pavle and Medina, Juan and Klein, Marten and Schmidt, Heiko}, title = {Application of extended large-eddy simualtion (XLES) to turbulent channel flow}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {25 : special issue : 95th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {2}, publisher = {Wiley}, address = {Weinheim}, issn = {1617-7061}, doi = {10.1002/pamm.70010}, pages = {1 -- 7}, abstract = {Extended large-eddy simulation (XLES) offers a promising middle ground between computational efficiency and predictive accuracy in turbulent flow simulations. By integrating the one-dimensional turbulence model as a stochastic subgrid-scale approach, XLES autonomously resolves turbulent microscales in a dimensionally reduced setting. Our implementation employs a coarse grid solely for pressure calculations, while three specialized high-resolution grids handle the turbulence dynamics. This multi-scale architecture reduces computational requirements by approximately two orders of magnitude compared to direct numerical simulation while maintaining comparable accuracy. Our results for turbulent channel flow at Reynolds number 395 demonstrate that XLES with a base resolution of just cells closely matches DNS reference data, vastly outperforming implicit LES using identical resolution and discretization schemes. This updated implementation of XLES, though still under active development, demonstrates significant potential for accurately simulating wall-bounded turbulent flows while substantially reducing computational requirements compared to traditional high-fidelity approaches.}, language = {en} } @misc{MarinkovicMedinaMendezKleinetal., author = {Marinkovic, Pavle and Medina M{\´e}ndez, Juan A. and Klein, Marten and Schmidt, Heiko}, title = {ODTLES : large-eddy simulation with autonomous stochastic subgrid-scale modeling applied to turbulent duct flow}, series = {Proceedings of the Conference on Modelling Fluid Flow CMFF'25}, journal = {Proceedings of the Conference on Modelling Fluid Flow CMFF'25}, publisher = {Budapest University of Technology and Economics}, address = {Budapest}, isbn = {978-615-112-002-6}, pages = {8}, abstract = {In this work, we discuss the application of the One-Dimensional Turbulence-based (very) Large-Eddy Simulation model, abbreviated as ODTLES, to turbulent duct flow. ODTLES is a multi-scale flow model in which an autonomous stochastic One-Dimensional Turbulence (ODT) model, capable of simulating the full bandwidth of time and length-scales in a 1-D domain, is supplemented with large-scale 3-D information coming from a very large eddy simulation (VLES) grid. ODTLES is more expensive than any other VLES, but could be cheaper than highly resolved LES or, naturally, than Direct Numerical Simulation (DNS). Unlike Reynolds-Averaged Navier-Stokes (RANS) and VLES, ODTLES does neither need a wall model, nor a damping function. The correct near-wall behavior is naturally obtained from one SGS ODT domain that is locally wall-normal. The proposed hybrid (3-D/1-D) approach allows the resolution of all relevant scales, modeling certain aspects of 3-D turbulence on the SGS scale. Here, turbulent duct flow is considered as an example, which poses a moderate challenge for traditional LES due to emerging secondary flows that manifest themselves by corner vortices that crucially depend on the accurate capturing of small and large scale motions. Preliminary results indicate a reasonable match with DNS for mean velocity profiles, although capturing secondary flow structures remains a challenge at this stage. Further refinements of the solver and modeling approach are ongoing to improve accuracy and predictive capabilities.}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Effects of wall slip on large-scale flow in turbulent Rayleigh-B{\´e}nard convection}, series = {Proceedings of the Conference on Modelling Fluid Flow CMFF'25}, journal = {Proceedings of the Conference on Modelling Fluid Flow CMFF'25}, publisher = {Budapest University of Technology and Economics}, address = {Budapest}, isbn = {978-615-112-002-6}, pages = {8}, abstract = {The current study investigates the effects of surface boundary conditions—no-slip, free-slip, and finite-slip-on flow dynamics and heat transfer inturbulent Rayleigh-B{\´e}nard (RB) convection for different Prandtl numbers. Using a three-dimensional lattice Boltzmann method (LBM) solver in direct numerical simulation (DNS) mode, simulations are performed for three Prandtl numbers Pr = 0.786, 4.38, 10 and two Rayleigh numbers Ra = 2 ×10^6 , 10^7 . The aim is to understand how surface conditions influence flow patterns, thermal mixing, and heat transfer efficiency in a cubic cavity with heated bottom and cooled top walls. Results show that free-slip conditions significantly enhance heat transfer, yielding higher Nusselt numbers due to thinner thermal boundary layers and stronger convective currents. In contrast, finite-slip conditions produce results similar to no-slip cases, indicating minimal impact for the slip lengths considered. The results demonstrate that surface boundary conditions play a role in modulating flow dynamics and heat transfer in RB convection.}, language = {en} }