TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schöps, Mark Simon A1 - Schmidt, Heiko A1 - Glawe, Christoph T1 - Towards physics-based nowcasting of the instantaneous wind velocity profile using a stochastic modeling approach T2 - STAB Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB, 13. - 14. November 2024, Regensburg N2 - 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. KW - atmospheric boundary layer KW - stochastic modeling KW - one-dimensional turbulence KW - wind energy KW - wind shear and veer Y1 - 2024 UR - https://bfm.rcbe.de/files/2024/11/2024_STAB-Jahresbericht.pdf SP - 162 EP - 163 PB - Deutsche Strömungsmechanische Arbeitsgemeinschaft, STAB CY - Regensburg [et al.] ER - TY - GEN A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Theoretical analysis and stochastic modeling of turbulent heat transfer in annular pipe flows T2 - 77th Annual Meeting of the Division of Fluid Dynamics, November 24–26, 2024; Salt Lake City, Utah N2 - 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. KW - heat transfer KW - boundary layer theory KW - stochastic modeling KW - one-dimensional turbulence KW - spanwise wall curvature KW - heated pipe flow Y1 - 2024 UR - https://meetings.aps.org/Meeting/DFD24/Session/T40.7 PB - American Physical Society ER - TY - GEN A1 - Klein, Marten A1 - Zenker, Christian A1 - Starick, Tommy A1 - Schmidt, Heiko T1 - Stochastic modeling of multi-stream mixing based on one-dimensional turbulence T2 - 77th Annual Meeting of the Division of Fluid Dynamics N2 - 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. KW - turbulent mixing KW - one-dimensional turbulence KW - coaxial jet KW - multi-stream mixing Y1 - 2024 UR - https://meetings.aps.org/Meeting/DFD24/Session/ZC40.4 PB - American Physical Society ER - TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Resolving the electrostatic boundary layer in a turbulent electrohydrodynamic flow with a map-based stochastic modeling approach T2 - 1st European Fluid Dynamics Conference - Daily Scientific Program N2 - 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. KW - EHD turbulence KW - electric double layer KW - boundary layer KW - Schmidt number effects KW - one-dimensional turbulence KW - stochastic modeling KW - skin friction drag Y1 - 2024 UR - https://www.conftool.org/efdc1/index.php?page=browseSessions&presentations=show&search=822+klein UR - https://www.aia.rwth-aachen.de/fileadmin/user_upload/Daily_Scientific_Program.pdf CY - Aachen ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Capturing features of transient boundary layers with a map-based stochastic modeling approach N2 - 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 KW - atmospheric boundary layer KW - stochastic modeling KW - one-dimensional turbulence KW - transient effects Y1 - 2024 U6 - https://doi.org/10.5194/egusphere-egu24-15560 PB - Copernicus GmbH ER - TY - GEN A1 - Polasanapalli, Sai Ravi Gupta A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Investigation of the impact of transient pressure gradients on turbulent channel flow dynamics T2 - Proceedings in Applied Mathematics and Mechanics N2 - 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. KW - turbulent heat transfer KW - turbulent drag KW - pumping power KW - one-dimensional turbulence KW - pulsating flow Y1 - 2024 U6 - https://doi.org/10.1002/pamm.202400183 SN - 1617-7061 VL - 24 SP - 1 EP - 12 PB - Wiley-VCH GmbH CY - Weinheim ER - TY - GEN A1 - Polasanapalli, Sai Ravi Gupta A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Towards stochastic subgrid-scale modeling of turbulent thermal convection in an under-resolved off-lattice Boltzmann method T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - 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. KW - thermal convection KW - heat transfer KW - lattice Boltzmann method KW - turbulence modeling KW - one-dimensional turbulence Y1 - 2023 UR - https://onlinelibrary.wiley.com/doi/10.1002/pamm.202300223 U6 - https://doi.org/10.1002/pamm.202300223 SN - 1617-7061 SP - 1 EP - 9 ER - TY - GEN A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Investigating Reynolds number effects in turbulent concentric coaxial pipe flow using stochastic one-dimensional turbulence modeling T2 - Proceedings in Applied Mathematics and Mechanics N2 - 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. KW - turbulent coaxial pipe flow KW - stochastic modeling KW - one-dimensional turbulence KW - spanwise curvature KW - turbulent boundary layer KW - high Reynolds number Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202300167 SN - 1617-7061 N1 - Proceedings of the GAMM Annual Meeting 2023, Dresden, Germany VL - 23 IS - 4 SP - 1 EP - 8 ER - TY - GEN A1 - Klein, Marten A1 - Zenker, Christian A1 - Starick, Tommy A1 - Schmidt, Heiko T1 - Stochastic modeling of multiple scalar mixing in a three-stream concentric coaxial jet based on one-dimensional turbulence T2 - International Journal of Heat and Fluid Flow N2 - 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. KW - map-based stochastic advection modeling KW - multiple passive scalars KW - one-dimensional turbulence KW - turbulent jet KW - turbulent mixing Y1 - 2023 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2023.109235 SN - 0142-727X N1 - This article is part of the "TSFP12 Special Issue". VL - 104 SP - 1 EP - 17 ER - TY - GEN A1 - Glawe, Christoph A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Stochastic deconvolution of wall statistics in Reynolds-averaged Navier–Stokes simulations based on one-dimensional turbulence T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - 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. KW - stochastic deconvolution KW - Reynolds-averaged Navier-Stokes simulation (RANS) KW - turbulent channel flow KW - turbulent boundary layer KW - one-dimensional turbulence Y1 - 2023 U6 - https://doi.org/10.1002/pamm.202300055 SN - 1617-7061 VL - 23 IS - 3 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Capturing features of turbulent Ekman–Stokes boundary layers with a stochastic modeling approach T2 - Advances in Science and Research N2 - 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. KW - turbulent boundary layer KW - stochastic modeling KW - periodic forcing KW - one-dimensional turbulence KW - rotating flow Y1 - 2023 UR - https://asr.copernicus.org/articles/20/55/2023/ U6 - https://doi.org/10.5194/asr-20-55-2023 SN - 1992-0636 SN - 1992-0628 N1 - This article is part of the special issue “EMS Annual Meeting: European Conference for Applied Meteorology and Climatology 2022”. N1 - This research is supported by the German Federal Government, the Federal Ministry of Education and Research and the State of Brandenburg within the framework of the joint project EIZ: Energy Innovation Center with funds from the Structural Development Act (Strukturstärkungsgesetz) for coal-mining regions. VL - 20 SP - 55 EP - 64 ER - TY - GEN A1 - Klein, Marten T1 - Map-based stochastic modeling of multiscale transfer processes in turbulent flows T2 - Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics N2 - 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. KW - stochastic modeling KW - one-dimensional turbulence KW - heat and mass transfer KW - boundary layer KW - turbulent mixing Y1 - 2023 UR - https://jahrestagung.gamm-ev.de/wp-content/uploads/2023/05/20230517_BookofAbstracts_final_red.pdf SP - 362 PB - GAMM e.V. CY - Dresden ER - TY - GEN A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Effects of Reynolds number on turbulent concentric coaxial pipe flow using stochastic modeling T2 - Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics KW - spanwise wall curvature KW - turbulent pipe flow KW - stochastic modeling KW - boundary layer theory KW - one-dimensional turbulence Y1 - 2023 UR - https://jahrestagung.gamm-ev.de/wp-content/uploads/2023/05/20230517_BookofAbstracts_final_red.pdf SP - 365 PB - GAMM e.V. CY - Dresden ER - TY - GEN A1 - Sharma, Sparsh A1 - Ayton, Lorna A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Estimation of ODT-resolved acoustic sources in high Reynolds number turbulent jets T2 - Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics KW - stochastic modeling KW - turbulent jet KW - turbulent acoustic sources KW - noise modeling KW - one-dimensional turbulence Y1 - 2023 UR - https://jahrestagung.gamm-ev.de/wp-content/uploads/2023/05/20230517_BookofAbstracts_final_red.pdf SP - 414 EP - 415 PB - GAMM e.V. CY - Dresden ER - TY - GEN A1 - Medina Méndez, Juan Alí A1 - Sharma, Sparsh A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Towards the use of a reduced order and stochastic turbulence model for assessment of far-field sound radiation: low Mach number jet flows T2 - Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics KW - turbulent noise sources KW - reduced-order modeling KW - one-dimensional turbulence KW - turbulent jet KW - stochastic modeling and simulation Y1 - 2023 UR - https://jahrestagung.gamm-ev.de/wp-content/uploads/2023/05/20230517_BookofAbstracts_final_red.pdf SP - 413 EP - 414 PB - GAMM e.V. CY - Dresden ER - TY - GEN A1 - Glawe, Christoph A1 - Klein, Marten A1 - Schmidt, Heiko T1 - ODT augmented RaNS T2 - Book of Abstracts of the 93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics KW - turbulence modeling KW - one-dimensional turbulence KW - Reynolds-averaged Navier-Stokes simulation KW - boundary layer KW - stochastic post-processing Y1 - 2023 UR - https://jahrestagung.gamm-ev.de/wp-content/uploads/2023/05/20230517_BookofAbstracts_final_red.pdf SP - 368 PB - GAMM e.V. CY - Dresden ER - TY - GEN A1 - Klein, Marten A1 - Schöps, Mark Simon A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Numerical simulation and analysis of transient Ekman boundary layers using a stochastic turbulence model T2 - EGU General Assembly 2023 KW - stochastic modeling KW - one-dimensional turbulence KW - turbulent Ekman flow KW - transient boundary layer Y1 - 2023 UR - https://meetingorganizer.copernicus.org/EGU23/EGU23-9116.html U6 - https://doi.org/10.5194/egusphere-egu23-9116 PB - EGU - European Geophysical Union CY - Vienna, Austria ER - TY - GEN A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow T2 - Proceedings in applied mathematics and mechanics : PAMM N2 - 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. KW - turbulent heat and mass transfer KW - heated pipe flow KW - one-dimensional turbulence KW - stochastic turbulence modeling KW - turbulent drag KW - spanwise curvature effects Y1 - 2023 UR - https://onlinelibrary.wiley.com/doi/10.1002/pamm.202200272 U6 - https://doi.org/10.1002/pamm.202200272 SN - 1617-7061 N1 - Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) VL - 22 IS - 1 ER - TY - GEN A1 - Gao, Tianyun A1 - Schmidt, Heiko A1 - Klein, Marten A1 - Liang, Jianhan A1 - Sun, Mingbo A1 - Chen, Chongpei A1 - Guan, Qingdi T1 - One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow T2 - Physics of Fluids N2 - 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. KW - supersonic turbulent channel flow KW - stochastic turbulence modeling KW - one-dimensional turbulence KW - compressibility effects KW - turbulent boundary layer Y1 - 2023 U6 - https://doi.org/10.1063/5.0125514 SN - 1089-7666 VL - 35 IS - 3 ER - TY - GEN A1 - Gao, Tianyun A1 - Schmidt, Heiko A1 - Klein, Marten A1 - Liang, Jianhan A1 - Sun, Mingbo A1 - Chen, Chongpei A1 - Guan, Qingdi T1 - One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock–turbulence interaction T2 - Physics of Fluids N2 - 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. KW - shock-turbulence interaction KW - stochastic turbulence modeling KW - one-dimensional turbulence KW - Richtmyer-Meshkov instability Y1 - 2023 U6 - https://doi.org/10.1063/5.0137435 SN - 1089-7666 VL - 35 IS - 3 ER - TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Stochastic modeling of electrohydrodynamically enhanced drag in one-way and fully coupled turbulent Poiseuille and Couette flow T2 - Technische Mechanik N2 - 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. KW - turbulent drag enhancement KW - electrohydrodynamic turbulence KW - high Schmidt number KW - multiphysical boundary layers KW - one-dimensional turbulence Y1 - 2023 U6 - https://doi.org/10.24352/UB.OVGU-2023-049 SN - 0232-3869 N1 - This article is part of the "Special Issue for CMFF’22". VL - 43 IS - 1 SP - 111 EP - 127 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model T2 - Advances in Science and Research N2 - Small-scale processes in atmospheric boundary layers are typically not resolved due to cost constraints but modeled based on physical relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed in the present study with the aid of the one-dimensional turbulence (ODT) model. ODT is applied as stand-alone column model to numerically investigate stratification effects in long-lived transient Ekman flows as canonical example of polar boundary layers by resolving turbulent winds and fluctuating temperature profiles on all relevant scales of the flow. We first calibrate the adjustable model parameters for neutral cases based on the surface drag law which yields slightly different optimal model set-ups for finite low and moderate Reynolds numbers. For the stably stratified cases, previously calibrated parameters are kept fixed and the model predictions are compared with various reference numerical simulations and also observations by an exploitation of boundary layer similarity. ODT reasonably captures the temporally developing flow for various prescribed stratification profiles, but fails to fully capture the near-surface laminarization by remaining longer in a fully developed turbulent state, which suggests preferential applicability to high-Reynolds-number flow regimes. Nevertheless, the model suggests that large near-surface turbulence scales are primarily affected by the developing stratification due to scale-selective buoyancy damping which agrees with the literature. The variability of the wind-turning angle represented by the ensemble of stratified cases simulated covers a wider range than reference reanalysis data. The present study suggests that the vertical-column ODT formulation that is highly resolved in space and time can help to accurately represent multi-physics boundary-layer and subgrid-scale processes, offering new opportunities for analysis of very stable polar boundary layer and atmospheric chemistry applications. KW - stochastic turbulence modeling KW - one-dimensional turbulence KW - stable stratification KW - atmospheric boundary layer KW - wind veering angle KW - Richardson number Y1 - 2022 UR - https://asr.copernicus.org/articles/19/117/2022/ U6 - https://doi.org/10.5194/asr-19-117-2022 SN - 1992-0636 N1 - This article is part of the special issue “21st EMS Annual Meeting – virtual: European Conference for Applied Meteorology and Climatology 2021”. VL - 19/2022 SP - 117 EP - 136 ER - TY - GEN A1 - Klein, Marten A1 - Zenker, Christian A1 - Starick, Tommy A1 - Schmidt, Heiko T1 - Stochastic modeling of three-scalar mixing in a coaxial jet using one-dimensional turbulence T2 - 12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022 N2 - Modeling complex mixing processes is a standing challenge for a number of applications ranging from chemical to mechanical and environmental engineering. Here, the gas-phase turbulent mixing in a three-stream concentric coaxial jet is investigated as a canonical problem. Reynolds-averaged Navier–Stokes simulations (RANS) suggest that the gas-phase mixing can be accurately modeled by air doped with passive scalars, for which small-scale resolving numerical simulations are performed with the one-dimensional turbulence (ODT) model as stand-alone tool. We show that both the spatial (S-ODT) and temporal (T-ODT) model formulations yield qualitatively similar results exhibiting reasonable to good agreement with available reference experiments, Reynolds-averaged and large-eddy simulations, as well as mixing models. This is demonstrated for low-order statistics, like the scalar variance and dissipation, but also the two-scalar joint probability density functions that can not be obtained with RANS. Our results suggest that S-ODT has better capabilities than T-ODT to model the mixing processes in the jet which we attribute to the account of local advective time scales. KW - stochastic modeling KW - one-dimensional turbulence KW - concentric coaxial round jet KW - multiple passive scalars KW - turbulent mixing KW - co-flow entrainment Y1 - 2022 UR - http://www.tsfp-conference.org/proceedings/2022/208.pdf UR - http://www.tsfp-conference.org/proceedings/proceedings-of-tsfp-12-2022-osaka.html N1 - Contribution No. 6 of 7 in Session 13C: Jets II SP - 1 EP - 6 ER - TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko ED - Vad, Janos T1 - Modeling electrohydrodynamically enhanced drag in channel and pipe flows using One-Dimensional Turbulenc T2 - Proceedings of the Conference on Modelling Fluid Flow (CMFF’22) N2 - The joint modeling of flow hydrodynamics and electrokinetics is a relatively unexplored area of turbulent flow research. We address a lack of available models for electrohydrodynamic (EHD) turbulent flow utilizing a lower-order approach, the stochastic One-Dimensional Turbulence (ODT) model. ODT is constructed on the principles of the direct energy cascade of Navier–Stokes turbulence, with key emphasis on the accurate resolution of the small molecular transport scales within a notional line-of-sight. We investigate two canonical flow configurations to demonstrate the applicability of the model in the simulation of EHD flows. First, we investigate EHD effects in zero-pressure-gradient turbulent boundary layers by two-way coupled model application to plane Couette flow of a dilute electrolyte. Second, we apply the one-way coupled model to EHD-enhanced gas flow through a vertical pipe with an inner concentric electrode, where electric fields are generated by means of a corona discharge and the corresponding effect of a continuum ionic charge density field. KW - EHD turbulence KW - multiphysical boundary layers KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent drag enhancement Y1 - 2022 UR - https://www.cmff.hu/pdf/CMFF22_Conference_Proceedings.pdf UR - https://www.cmff.hu/papers/CMFF22_Final_Paper_PDF_15.pdf SN - 978-963-421-881-4 SP - 82 EP - 91 PB - University of Technology and Economics, Department of Fluid Mechanics CY - Budapest, Hungary ER - TY - GEN A1 - Sharma, Sparsh A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Features of far-downstream asymptotic velocity fluctuations in a round jet: A one-dimensional turbulence study T2 - Physics of Fluids KW - stochastic modeling KW - turbulent round jet KW - one-dimensional turbulence KW - jet similarity KW - multi-scale fluctuation modeling Y1 - 2022 UR - https://aip.scitation.org/doi/10.1063/5.0101270 U6 - https://doi.org/10.1063/5.0101270 SN - 1089-7666 VL - 34 IS - 8 ER - TY - GEN A1 - Klein, Marten A1 - Medina Méndez, Juan Alí A1 - Schmidt, Heiko T1 - Modeling electrohydrodynamically enhanced drag in channel and pipe flows using one-dimensional turbulence T2 - Conference on Modelling Fluid Flow (CMFF’22) KW - stochastic modeling KW - one-dimensional turbulence KW - turbulent drag enhancement KW - electrohydrodynamic turbulence KW - multiphysical boundary layers Y1 - 2022 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_cmff22_abstract_EHDdrag.pdf UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_cmff22_paper_submitted_EHDdrag.pdf UR - https://www.cmff.hu/pdf/FinalProgramme.pdf SP - 1 EP - 8 CY - Budapest, Hungary ER - TY - GEN A1 - Klein, Marten A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko T1 - Stochastic modeling of heat and momentum transfer in annular pipe flow: A one-dimensional turbulence study with comparison to DNS and LES T2 - STAB Jahresbericht 2022 KW - stochastic modeling KW - one-dimensional turbulence KW - heat and mass transfer KW - turbulent Poiseuille flow KW - large-eddy simulation Y1 - 2022 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2022_STAB_abstract.pdf UR - https://www.dlr.de/as/desktopdefault.aspx/tabid-128/268_read-1678/ UR - https://www.dlr.de/as/Portaldata/5/Resources/dokumente/veranstaltungen/stab_workshop/Jahresbericht2022.pdf VL - 23 PB - Deutsche Strömungsmechanische Arbeitsgemeinschaft (STAB) CY - Göttingen, Germany ER - TY - GEN A1 - Tsai, Pei-Yun A1 - Schmidt, Heiko A1 - Klein, Marten T1 - Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow T2 - 92nd Annual Meeting of GAMM KW - stochastic modeling KW - one-dimensional turbulence KW - heat and mass transfer KW - skin friction drag KW - forced convection KW - spanwise wall curvature Y1 - 2022 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2022_coaxialPipe_GAMM_abstract.pdf UR - https://jahrestagung.gamm-ev.de/wp-content/uploads/2022/08/Daily_Program_Web.pdf PB - Gesellschaft für angewandte Mathematik und Mechanik e.V. CY - Aachen, Germany ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Stochastic modeling of transient Ekman flow at arbitrary Reynolds number driven by horizontal bottom wall oscillation T2 - EMS Annual Meeting 2022, Abstracts KW - stochastic modeling KW - one-dimensional turbulence KW - rotating boundary layers KW - intermittency Y1 - 2022 U6 - https://doi.org/10.5194/ems2022-617 VL - 19 PB - Copernicus CY - Bonn, Germany ER - TY - GEN A1 - Sharma, Sparsh A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Modelling turbulent jets at high-Reynolds number using one-dimensional turbulence T2 - AIAA AVIATION 2021 FORUM KW - stochastic modeling KW - turbulent round jet KW - one-dimensional turbulence Y1 - 2021 UR - https://arc.aiaa.org/doi/abs/10.2514/6.2021-2104 SN - 978-1-62410-610-1 U6 - https://doi.org/10.2514/6.2021-2104 PB - American Institute of Aeronautics and Astronautics, Inc. ER - TY - GEN A1 - Klein, Marten A1 - Maier, Roland Erich A1 - Schmidt, Heiko T1 - Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers T2 - Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) N2 - Neutral and stably-stratified Ekman boundary layers (EBLs) are numerically investigated with a stochastic one-dimensional turbulence (ODT) model. EBLs achieve the bulk-surface coupling in Earth's atmosphere. They are numerically challenging due to transient and non-universal turbulence properties even at small scales. ODT addresses this problem by distinguishing turbulent-advective from molecular-diffusive transport processes for a vertical column along which all relevant scales of the flow are resolved. We demonstrate the model's capabilities for economical, accurate, and stratification regime independent simulation of EBLs for the wind-turning angle. ODT reproduces and extrapolates reference direct numerical simulation results consistent with observations. We conclude that ODT may be useful for modeling of atmospheric surface layers. KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent Ekman flow KW - roating and stratified fluids KW - transition Y1 - 2021 U6 - https://doi.org/10.1002/pamm.202100146 VL - 21 SP - 1 EP - 3 PB - Wiley CY - Weinheim ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Investigating Schmidt number effects in turbulent electroconvection using one-dimensional turbulence T2 - Proc. Appl. Math. Mech. N2 - Turbulent electroconvection denotes a fluctuating multiphysical flow in which hydrodynamics and electrokinetics interact on multiple scales. The dynamical processes at work are entangled down to the molecular-diffusive scales that are determined by the Schmidt (Sc) and Reynolds (Re) number. Turbulence properties are generally nonuniversal which leads to high numerical resolution requirements. We address the numerical challenges associated with accuracy and feasibility by utilizing a stochastic one-dimensional turbulence (ODT) model. Here, ODT is applied to turbulent Couette flow of dilute electrolytes as canonical problem for turbulent electroconvection. For Sc ⩾ O(10), ODT predicts an increase of the skin friction drag due to electrohydrodynamically (EHD) enhanced small-scale eddy production once the flow is sufficiently turbulent. KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent Couette flow KW - electrohydrodynamic turbulence KW - Schmidt number effects KW - skin friction drag Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1002/pamm.202100147 VL - 21 SP - 1 EP - 3 PB - Wiley CY - Weinheim ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko ED - Wagner, Claus T1 - Stochastic modeling and simulation of turbulent boundary layers in annular channel flow using one-dimensional turbulence T2 - STAB Jahresbericht 2021 N2 - In our contribution to the STAB workshop we will present the ODT model formulation with an emphasis on turbulent eddy energetics and map-based advection modeling in radial direction. After that, we will address ODT’s capabilities for simulation of turbulent boundary layers in planar and annular channel flows in terms of conventional turbulence statistics and bulk quantities. Last, we will address the effects of radius ratio and Reynolds number variations. KW - one-dimensional turbulence KW - stochastic modeling KW - spanwise curvature effects KW - radial momentum transport KW - boundary layers KW - coaxial pipe flow Y1 - 2021 UR - https://www.dlr.de/as/desktopdefault.aspx/tabid-128/268_read-1678/ UR - https://www.dlr.de/as/Portaldata/5/Resources/dokumente/veranstaltungen/stab_workshop/STAB-Jahresbericht-2021.pdf VL - 2021 SP - 39 EP - 40 PB - Deutsche Strömungsmechanische Arbeitsgemeinschaft, STAB CY - Göttingen ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Lignell, David O. T1 - Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence T2 - International Journal of Heat and Fluid Flow N2 - Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt (Sc), Reynolds (Re), and Peclet (Pe) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood (Sh) number, self-consistently reproduces established scaling regimes and asymptotic relations. For high asymptotic Sc and Re, ODT results fall between the Dittus-Boelter, Sh ∼ Re^(4/5) Sc^(2/5), and Colburn, Sh ∼ Re^(4/5) Sc^(1/3), scalings but they are closer to the former. For finite Sc and Re, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, vol. 28, pp. 1204-1214, 2007) that yields locally steeper effective scalings than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic Sc ≪ Re_τ^(-1) (diffusive limit) with a functional form that has not been previously described. KW - one-dimensional turbulence KW - stochastic modeling KW - fluctuation modeling KW - passive scalar KW - scalar transfer KW - Schmidt number dependence KW - surface flux Y1 - 2021 UR - https://arxiv.org/abs/2111.15359 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2021.108889 SN - 0142-727X VL - 93 (2022) SP - 1 EP - 19 ER - TY - GEN A1 - Klein, Marten A1 - Lignell, David O. A1 - Schmidt, Heiko T1 - Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers T2 - EMS Annual Meeting 2021, online, 6–10 Sep 2021, EMS2021-79 N2 - Turbulence is ubiquitous in atmospheric boundary layers and manifests itself by transient transport processes on a range of scales. This range easily reaches down to less than a meter, which is smaller than the typical height of the first grid cell layer adjacent to the surface in numerical models for weather and climate prediction. In these models, the bulk-surface coupling plays an important role for the evolution of the atmosphere but it is not feasible to fully resolve it in applications. Hence, the overall quality of numerical weather and climate predictions crucially depends on the modeling of subfilter-scale transport processes near the surface. A standing challenge in this regard is the robust but efficient representation of transient and non-Fickian transport such as counter-gradient fluxes that arise from stratification and rotation effects. We address the issues mentioned above by utilizing a stochastic one-dimensional turbulence (ODT) model. For turbulent boundary layers, ODT aims to resolve the wall-normal transport processes on all relevant scales but only along a single one-dimensional domain (column) that is aligned with the vertical. Molecular diffusion and unbalanced Coriolis forces are directly resolved, whereas effects of turbulent advection and stratification are modeled by stochastically sampled sequence of mapping (eddy) events. Each of these events instantaneously modifies the flow profiles by a permutation of fluid parcels across a selected size interval. The model is of lower order but obeys fundamental conservation principles and Richardson's 1/4 law by construction. In this study, ODT is applied as stand-alone tool in order to investigate nondimensional control parameter dependencies of the scalar and momentum transport in turbulent channel, neutral, and stably-stratified Ekman flows up to (friction) Reynolds number Re = O(104). We demonstrate that ODT is able to capture the state-space statistics of transient surface fluxes as well as the boundary-layer structure and nondimensional control parameter dependencies of low-order flow statistics. Very good to reasonable agreement with available reference data is obtained for various observables using fixed model set-ups. We conclude that ODT is an economical turbulence model that is able to not only capture but also predict the wall-normal transport and surface fluxes in multiphysics turbulent boundary layers. KW - one-dimensional turbulence KW - stochastic modeling KW - Ekman flow KW - atmospheric boundary layer KW - roating and stratified fluids Y1 - 2021 UR - https://doi.org/10.5194/ems2021-79 UR - https://www.b-tu.de/media/video/Stochastic-modeling-of-transient-surface-scalar-and-momentum-fluxes-in-turbulent-boundary-layers/8c7baf58c040239649fb7c3b2212c1d5 U6 - https://doi.org/10.5194/ems2021-79 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Lignell, David O. T1 - Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers, EMS Annual Meeting 2021, online, 6–10 Sep 2021 KW - one-dimensional turbulence KW - stochastic modeling KW - Ekman flow KW - atmospheric boundary layer KW - roating and stratified fluids Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_ems21.pdf UR - https://www.b-tu.de/media/video/Stochastic-modeling-of-transient-surface-scalar-and-momentum-fluxes-in-turbulent-boundary-layers/8c7baf58c040239649fb7c3b2212c1d5 ER - TY - GEN A1 - Klein, Marten A1 - Zenker, Christian A1 - Schmidt, Heiko T1 - Map-based stochastic modeling of turbulent mixing in transient shear flows T2 - MATH+ CECAM Discussion Meeting on Generalized Langevin Equations N2 - Map-based stochastic modeling distinguishes molecular-diffusive from turbulent-advective transport processes in fluid flows. In the one-dimensional turbulence (ODT) model, a stochastic point process with energetically constrained rejection sampling of discrete eddy events is used to economically model the effects of turbulence on all relevant scales of the flow. Here I will discuss the model formulation and its application to passive scalar mixing in a confined jet. [1] M. Klein, C. Zenker, H. Schmidt (2019) Chem. Eng. Sci. 204:186-202 KW - one-dimensional turbulence KW - stochastic modeling KW - passive scalar KW - turbulent mixing Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_abstract_public_cecam21.pdf UR - https://www.b-tu.de/media/video/Map-based-stochastic-modeling-of-turbulent-mixing-in-transient-shear-flows/5f7312768f6bcce987ed801635dcdc07 UR - https://www.cecam.org/workshop-details/1086 UR - https://www.sciencedirect.com/science/article/pii/S0009250919303896?via%3Dihub ER - TY - CHAP A1 - Klein, Marten A1 - Schmidt, Heiko ED - Dillmann, Andreas ED - Heller, Gerd ED - Krämer, Ewald ED - Wagner, Claus T1 - Stochastic Modeling of Passive Scalars in Turbulent Channel Flows: Predictive Capabilities of One-Dimensional Turbulence T2 - New Results in Numerical and Experimental Fluid Mechanics XIII N2 - Numerical simulations of passive scalars in turbulent channel flows up to friction Reynolds number Reτ = 5200 and Schmidt number Sc = 2000 are performed by utilizing the stochastic one-dimensional turbulence (ODT) model as stand-alone tool. The model is calibrated once for the turbulent velocity boundary layer at Reτ = 5200 so that the passive scalar is a model prediction. ODT is able to reproduce with reasonable accuracy the scaling regimes of the scalar transfer and locally resolve the boundary layer structure. Albeit the model is unable to capture the emerging dissimilarity of near-wall scalar and momentum transport for high Sc, it can economically and accurately represent fluctuating wall-normal fluxes. KW - boundary layers KW - one-dimensional turbulence KW - passive scalar KW - turbulent channel flow Y1 - 2021 UR - https://link.springer.com/chapter/10.1007/978-3-030-79561-0_5 SN - 978-3-030-79561-0 U6 - https://doi.org/10.1007/978-3-030-79561-0_5 SP - 47 EP - 57 PB - Springer International Publishing CY - Cham ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Transition to the ultimate regime in a stochasticmodel for thermal convection with internal sources N2 - 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). KW - one-dimensional turbulence KW - turbulent thermal convection KW - heat transfer KW - high Rayleigh number Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_ictw21.pdf UR - https://www.b-tu.de/media/video/Transition-to-the-ultimate-regime-in-a-stochastic-model-for-thermal-convection-with-internal-sources/52aa69a52b8ab3ef29cc1d8bf9f20243 UR - https://pof.tnw.utwente.nl/ictw/schedule.html ER - TY - GEN A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Schmidt, Heiko T1 - The One-Dimensional Turbulence Aspects of Internal Forced Convective Flows T2 - 14th WCCM-ECCOMAS Congress 2020 N2 - We present an overview of issues for the modeling of internal forced convective flows with the One-Dimensional Turbulence (ODT) model. Results of recent research as well as prospective research issues are presented for statistically streamwise homogeneous flows and streamwise inhomogeneous mixed convective flows. The results illustrate the capabilities of the model to evaluate and bring insight into a wide range of physical phenomena in the field of convective flows. Nonetheless, as a model, ODT is best suited for the evaluation of asymptotically turbulent flows, i.e., away from laminar regimes. KW - one-dimensional turbulence KW - stochastic turbulence modeling KW - turbulent drag KW - internal flow KW - heat transfer Y1 - 2021 UR - https://www.scipedia.com/public/Mendez_et_al_2021a U6 - https://doi.org/10.23967/wccm-eccomas.2020.338 SP - 1 EP - 12 PB - Scipedia ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes T2 - 91st Annual Meeting of GAMM 2020@21 N2 - We investigate turbulent electrohydrodynamic (EHD) Couette flows of dilute electrolytes and how they are affected by a prescribed electric field. In this canonical problem, molecular diffusion and electric drift currents can interact with turbulence which yields intricate dynamics down to the Kolmogorov and Batchelor scales that need to be resolved. The electrolytes considered have neutral bulk charge and consist of two independent, positive and negative, ion species with the same valence and mobility. The top wall of the set-up is moving and held at a different voltage relative to the bottom one. Resolution requirements and numerical feasibility are addressed by utilizing the stochastic one-dimensional turbulence (ODT) model as stand-alone tool in order to resolve all relevant scales of the flow for a dimensionally reduced setting. Deterministic diffusion and charge-carrier drift are directly resolved, whereas the effects of turbulent advection and pressure fluctuations are modeled by a stochastic process that operates along the wall-normal ODT domain. For the hydrodynamic and low Schmidt number EHD regime, ODT reasonably captures and extrapolates relevant leading-order boundary-layer properties of reference direct numerical simulations (DNS). For the high Schmidt number EHD regime, the model predicts notable interactions between turbulence and elektrokinetics only for large enough Reynolds numbers that manifests itself by a significant increase of the turbulent drag. Present ODT results suggests that the origin of this effect is related to the time-scale separation of convective versus electric drift and molecular transport processes transport across the boundary layer. In the talk, we will address the model formulation and its application to EHD Couette flow. Additionally, we will comment on the representation of electrokinetics and hydro-dynamics for the selected set-up. Finally, we will discuss the flow regimes in terms of skin friction drag and flow profiles with an eye also on electric variables and time scales. KW - one-dimensional turbulence KW - stochastic turbulence modeling KW - EHD turbulence KW - channel flow KW - electrolyte flow Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2021_elco_GAMM_abstract.pdf UR - https://hessenbox.uni-kassel.de/dl/fi226HzF3AJV3g4LFWM4fWE6/daily_program_2020.pdf?inline ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Investigating Rayleigh-Bénard convection at low Prandtl numbers using one-dimensional turbulence modeling T2 - Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019 N2 - We numerically investigate the heat transfer in turbulent Rayleigh–Bénard convection at two Prandtl numbers, Pr = 0.021 and 0.7, respectively. Small-scale resolving simulations up to the Rayleigh numbers Ra = 10^(13) (Pr = 0.021) and 10^(16) (Pr = 0.7) are made feasible by utilizing the stochastic, one-dimensional turbulence (ODT) model. Present ODT simulations exhibit effective Nusselt number Nu scalings of the form Nu ∼ Ra^γ. At low Rayleigh numbers, ODT yields a scaling exponent of γ = 0.29 (Pr = 0.021) and 0.32 (Pr = 0.7), respectively. Both values are systematically, but just slightly, overestimating available reference data. At high Rayleigh numbers, present ODT results exhibit an increase of the exponent to γ = 0.32 (Pr = 0.021) and 0.36 (Pr = 0.7), respectively. Our preliminary results suggest that ODT might be able to capture a transition from the classical to the ultimate state of convection in terms of (i) critical Rayleigh number and (ii) increase of γ. KW - stochastic turbulence modeling KW - one-dimensional turbulence KW - turbulent thermal convection KW - high Rayleigh number Y1 - 2019 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2019_tsfp11_v2.pdf SP - 1 EP - 3 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Lignell, David O. T1 - Map-based modeling of high-Ra turbulent convection in planar and spherical geometries T2 - Conference on Modelling Fluid Flow 2018 (CMFF'18) N2 - Turbulent convection is important in many technological and geophysical applications. A model problem for such flows is Rayleigh-Bénard (RB) convection. The classical RB setup is a fluid- filled box with a heated bottom and cooled top. For geophysical applications, the spherical geometry of the confinement is sometimes important (e.g. in mantle convection). This is addressed by a spherical annulus configuration in which fluid is confined between an inner hot and an outer cold sphere. In this case, the gravity field is radial and its strength can also vary with the radius. Numerical simulations of RB convection are challenging because of the high Rayleigh numbers (Ra) observed in applications. 3-D direct simulations have been performed up to Ra ~ 10^(12), but even larger values of Ra are relevant. Hence modeling is needed if one wishes to increase the accessible Rayleigh number limit within the considerable future. The difficulty is that gradient-diffusion approaches do not allow for scale interactions, which can be crucial for the dynamics of the flow and the resulting heat transfer. In order to make such simulations feasible we make use of a different modeling strategy, the so-called One-Dimensional Turbulence (ODT). ODT resolves all scales of the flow along a notional line of sight, but reduces cost by assuming statistical homogeneity of the flow in the off-line directions. Along the line, turbulent advection is modeled by discrete mapping events, which mimic the effect of turbulent stirring. These events are stochastically sampled with highest probability where shear and buoyancy yield net available energy in analogy to real turbulence. In the talk, we evaluate ODT results against available reference data (e.g. flow statistics, heat transfer) using a new and fully adaptive version of ODT. This new version allows to simulate turbulent convection in spherical geometry. We address this by discussing the effects of radius ratio and radius-dependent gravity. KW - stochastic turbulence modeling KW - one-dimensional turbulence KW - heat transfer KW - high Rayleigh number KW - spherical shell convection KW - turbulent thermal convection Y1 - 2018 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_cmff18_abstract.pdf ER - TY - GEN A1 - Klein, Marten A1 - Zenker, Christian A1 - Hertha, Katja A1 - Schmidt, Heiko T1 - Modeling One and Two Passive Scalar Mixing in Turbulent Jets Using One-Dimensional Turbulence T2 - 14th WCCM-ECCOMAS Congress 2020 N2 - Turbulent mixing of two passive scalars is investigated in a constant-property jets using stochastic one-dimensional turbulence (ODT). Scalars are separately injected by a central round and a surrounding annular jet that issue into a uniform co-flow of low velocity. These scalars are transported downstream and dispersed in radial direction by turbulent advection and molecular diffusion. The jet as well as the turbulent inflow are numerically simulated with ODT as stand-alone tool using a temporal (T-ODT) and spatial (S-ODT) formulation. We show that ODT captures key properties of the turbulent mixing for one scalar by performing individual scalar statistics and for two scalars by computation of joint probabilities. Some limitations of the one-dimensional modeling approach are also discussed. KW - one-dimensional turbulence KW - stochastic turbulence modeling KW - turbulent mixing KW - round jet KW - passive scalars Y1 - 2021 UR - https://www.scipedia.com/public/Klein_et_al_2021a U6 - https://doi.org/10.23967/wccm-eccomas.2020.205 SP - 1 EP - 12 PB - Scipedia ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers T2 - 91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) - PAMM, Proceedings in Applied Mathematics and Mechanics N2 - Turbulence is a transient phenomenon in atmospheric boundary layers. These transients occur often due to surface temperature variations (e.g. due to diurnal forcing) that directly influence the near-surface flow by local stratification effects. Relevant dynamical and transport processes occur on a scale of meters near the surface which is a standing challenge for numerical weather and climate prediction. Here we investigate neutral and stably-stratified Ekman flows as a canonical problem for the night-time atmospheric boundary layer over flat terrain. The set-up used consists of an incompressible fluid over a smooth horizontal no-slip wall in a rotating frame of reference. The bulk flow is in geostrophic balance and acts as momentum source. In the case of stable stratification, temperature is prescribed as sudden cooling on a fully-developed turbulent neutrally-stratified Ekman boundary layer. When the stratification is weak, the temperature behaves like a passive scalar, but when it is strong, turbulence may locally disappear. Transient simulations across a relevant range of Reynolds and Froude numbers are made feasible by utilizing the stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve vertical (wall-normal) transport processes on all relevant scales for a one-dimensional domain. Deterministic molecular diffusion and Coriolis forces are directly resolved, whereas turbulent advection is modeled by a stochastic process. The model obeys several relevant physical principles as, for example, Richardson’s 1/4 law of stratified turbulence. Preliminary results suggest that the stand-alone model generally captures Reynolds (turbulence) and Froude number (stratification) effects when stratification is weak. For low Froude number (strong stratification), these results indicate that the model tends to overestimate turbulence effects near the surface unless stratification becomes so strong that near-surface turbulence is energetically prohibited. In the talk, we will address the model formulation and its application to Ekman flow. We will show and discuss model results for surface fluxes, boundary-layer profiles, and corresponding fluctuation statistics. In addition, we will discuss stratification effects and comment on their representation in the model. KW - one-dimensional turbulence KW - stochastic turbulence modeling KW - atmospheric boundary layer KW - rotating flow KW - stratified flow Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2021_Ekman_GAMM_abstract.pdf U6 - https://doi.org/10.1002/pamm.202000127 SN - 1617-7061 VL - 20 IS - 1 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Transition to the ultimate regime in a stochastic model for radiatively driven turbulent convection T2 - Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21 KW - stochastic turbulence modeling KW - turbulent thermal convection KW - one-dimensional turbulence KW - heat transfer Y1 - 2021 UR - https://www.dpg-verhandlungen.de/year/2021/conference/bpcppdysoe/part/dy/session/2/contribution/1?lang=en ER - TY - GEN A1 - Sharma, Sparsh A1 - Klein, Marten A1 - Schmidt, Heiko A1 - Sarradj, Ennes T1 - On a lower-order framework for jet noise prediction based on one-dimensional turbulence T2 - arXiv N2 - Noise prediction requires the resolution of relevant acoustic sources on all scales of a turbulent flow. High-resolution direct numerical and large-eddy simulation would be ideal but both are usually too costly despite developments in high performance computing. Lower-order modeling approaches are therefore of general interest. A crucial but standing problem for accurate predictive modeling is the estimation of missing noise from the modeled scales. In this paper we address this problem by presenting a novel lower-order framework that couples the one-dimensional turbulence model to the Ffowcs-Williams and Hawkings approach for prediction of the far-field noise of a subsonic turbulent round jet. KW - Ffowcs-Williams and Hawkings equation KW - jet noise KW - one-dimensional turbulence KW - turbulent mixing noise Y1 - 2020 UR - https://arxiv.org/abs/2010.11050 SP - 1 EP - 4 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes T2 - Proceedings in Applied Mathematics and Mechanics N2 - We investigate turbulent Couette flows of dilute, weakly-conducting electrolytes by utilizing the stochastic one-dimensional turbulence (ODT) model. The flow is driven by relative motion of the top and bottom wall and affected by an electric field between these walls that is prescribed by a voltage difference. The electrolytes considered have zero bulk charge and consist of two ion species with the same mobility, valence, and initial concentration. The stochastic model predicts a decrease of the mean streamwise velocity when an external voltage is applied provided that both Schmidt (Sc) and Reynolds (Re) numbers are sufficiently large, that is, Sc > 30 for Re = 12000 investigated. The effect observed is relevant for flow control, but the mechanism awaits clarification. Present ODT results may help to develop this understanding or design laboratory experiments. KW - one-dimensional turbulence KW - electroconvection KW - EHD turbulence KW - Couette flow KW - electrolyte flow Y1 - 2020 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2020_EHD-Couette_PAMM.pdf U6 - https://doi.org/10.1002/pamm.202000128 VL - 2020 IS - 20 SP - 1 EP - 2 PB - Wiley-VCH CY - Weinheim ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Stochastic modeling of passive scalars in turbulent channel flows T2 - Jahresbericht 2020 zum Band: Notes on Numerical Fluid Mechanics and Multidisciplinary Design - New Results in Numerical and Experimental Fluid Mechanics XIII KW - one-dimensional turbulence KW - passive scalar KW - channel flow Y1 - 2020 UR - https://www.dlr.de/as/Portaldata/5/Resources/dokumente/veranstaltungen/stab_workshop/STAB-Jahresbericht-2020.pdf VL - 2020 SP - 30 EP - 31 PB - Deutsche Strömungsmechanische Arbeitsgemeinschaft, STAB CY - Göttingen ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Predictive modeling of passive scalar transfer to a wall using stochastic one-dimensional turbulence T2 - arXiv N2 - Passive scalars in turbulent channel flows are investigated as canonical problem for heat and mass transfer in turbulent boundary-layer flows. The one-dimensional turbulence model is used to numerically investigate the Schmidt and Reynolds number dependence of the scalar transfer to a wall due to fluctuating wall-normal transport. First, the model is calibrated for low-order velocity statistics. After that, we keep the model parameters fixed and investigate low-order passive scalar statistics for a relevant Schmidt and Reynolds number range. We show that the model consistently predicts the boundary layer structure and the scaling regimes, for which it is close to asymptotic one-dimensional theory. KW - one-dimensional turbulence KW - passive scalar KW - turbulent channel flow KW - mass transfer coefficient KW - high Schmidt number Y1 - 2020 UR - https://arxiv.org/abs/2011.04818 ER - TY - GEN A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Modeling one and two passive scalar mixing in turbulent jets using one-dimensional turbulence T2 - 14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19–24 July 2020, Paris, France KW - one-dimensional turbulence KW - passive scalar KW - turbulent mixing KW - turbulent jet Y1 - 2020 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2020_scalars_in_jets_WCCM-abstract.pdf UR - https://www.wccm-eccomas2020.org ER - TY - GEN A1 - Klein, Marten A1 - Kerstein, Alan R. A1 - Schmidt, Heiko T1 - Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection T2 - 25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1) N2 - 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. KW - one-dimensional turbulence KW - thermal convection KW - turbulent boundary layer Y1 - 2020 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2020_ODT-RBC_ICTAM20+1.pdf ER - TY - GEN A1 - Rakhi, Rakhi A1 - Klein, Marten A1 - Medina Méndez, Juan Ali A1 - Schmidt, Heiko T1 - One-dimensional turbulence modelling of incompressible temporally developing turbulent boundary layers with comparison to DNS T2 - Journal of Turbulence N2 - The incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range 250 ≤ Reb ≤ 2000 using fixed model parameters. The influence of the model parameters is analysed for Reb = 1000 and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows. KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent boundary layers Y1 - 2019 U6 - https://doi.org/10.1080/14685248.2019.1674859 SN - 1468-5248 VL - 20 IS - 8 SP - 506 EP - 543 ER -