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 - 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 - Vallem, Rishindra A1 - Klein, Marten A1 - Schmidt, Heiko T1 - Capabilities and limitations of smoothed particle hydrodynamics for the simulation of two‐phase flow instabilities T2 - Proceedings in Applied Mathematics and Mechanics N2 - 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 . KW - Smoothed Particle Hydrodynamics KW - two-phase flow KW - Kelvin-Helmholtz instability KW - rising bubble KW - growth rate Y1 - 2024 U6 - https://doi.org/10.1002/pamm.202400206 SN - 1617-7061 VL - 24/2024 PB - Wiley CY - Weinheim ER - TY - GEN A1 - Klein, Marten A1 - Kessler, Robert William A1 - Schmidt, Heiko T1 - Numerical investigation of drag reduction effects on a track bicycle fork using wings with a wavy leading edge T2 - Proceedings in Applied Mathematics and Mechanics N2 - 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. KW - sports aerodynamics KW - passive flow control KW - aerodynamic drag KW - drag reduction KW - computational fluid dynamics KW - turbulence modeling Y1 - 2024 U6 - https://doi.org/10.1002/pamm.202400178 SN - 1617-7061 VL - 24 SP - 1 EP - 14 PB - Wiley 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 - 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 - Parekh, Parshva Atulbhai A1 - Gschwander, Stefan A1 - Klein, Marten A1 - Gamisch, Sebastian T1 - CFD-based analysis and minimization of mixing during the charging phase of a thermal energy storage tank T2 - 1. Jahresfachtagung des Energie-Innovationszentrums (EIZ) Cottbus N2 - 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 KW - thermal energy storage tank KW - mixing KW - porous media KW - computational fluid dynamics Y1 - 2024 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_2024_EIZ1_abstract.pdf CY - Cottbus 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 - Investigating modifications of the heat transfer by velocity boundary conditions in turbulent thermal convection using an off-lattice Boltzmann method T2 - STAB Jahresbericht 2024 N2 - 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 Göttingen (project ID: bbi00022). KW - lattice Boltzmann method KW - thermal convection KW - hydrophilic and hydrophobic surfaces KW - Navier slip boundary condition Y1 - 2024 UR - https://bfm.rcbe.de/files/2024/11/2024_STAB-Jahresbericht.pdf SP - 40 EP - 41 PB - Deutsche Strömungsmechanische Arbeitsgemeinschaft, STAB CY - Regensburg [et al.] ER - TY - JOUR A1 - Delle Site, Luigi A1 - Hartmann, Carsten T1 - Scaling law for the size dependence of a finite-range quantum gas JF - Physical Review A Y1 - 2024 U6 - https://doi.org/10.1103/PhysRevA.109.022209 SN - 2469-9926 VL - 109 IS - 2 PB - American Physical Society (APS) ER -