TY - GEN A1 - Lignell, David O. A1 - Lansinger, Victoria B. A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Kerstein, Alan R. A1 - Schmidt, Heiko A1 - Fistler, Marco A1 - Oevermann, Michael T1 - One-dimensional turbulence modeling for cylindrical and spherical flows: model formulation and application T2 - Theoretical and Computational Fluid Dynamics N2 - The one-dimensional turbulence (ODT) model resolves a full range of time and length scales and is computationally efficient. ODT has been applied to a wide range of complex multi-scale flows, such as turbulent combustion. Previous ODT comparisons to experimental data have focused mainly on planar flows. Applications to cylindrical flows, such as round jets, have been based on rough analogies, e.g., by exploiting the fortuitous consistency of the similarity scalings of temporally developing planar jets and spatially developing round jets. To obtain a more systematic treatment, a new formulation of the ODT model in cylindrical and spherical coordinates is presented here. The model is written in terms of a geometric factor so that planar, cylindrical, and spherical configurations are represented in the same way. Temporal and spatial versions of the model are presented. A Lagrangian finite-volume implementation is used with a dynamically adaptive mesh. The adaptive mesh facilitates the implementation of cylindrical and spherical versions of the triplet map, which is used to model turbulent advection (eddy events) in the one-dimensional flow coordinate. In cylindrical and spherical coordinates, geometric stretching of the three triplet map images occurs due to the radial dependence of volume, with the stretching being strongest near the centerline. Two triplet map variants, TMA and TMB, are presented. In TMA, the three map images have the same volume, but different radial segment lengths. In TMB, the three map images have the same radial segment lengths, but different segment volumes. Cylindrical results are presented for temporal pipe flow, a spatial nonreacting jet, and a spatial nonreacting jet flame. These results compare very well to direct numerical simulation for the pipe flow, and to experimental data for the jets. The nonreacting jet treatment overpredicts velocity fluctuations near the centerline, due to the geometric stretching of the triplet maps and its effect on the eddy event rate distribution. TMB performs better than TMA. A hybrid planar-TMB (PTMB) approach is also presented, which further improves the results. TMA, TMB, and PTMB are nearly identical in the pipe flow where the key dynamics occur near the wall away from the centerline. The jet flame illustrates effects of variable density and viscosity, including dilatational effects. KW - Cylindrical ODT Y1 - 2018 U6 - https://doi.org/10.1007/s00162-018-0465-1 SN - 0935-4964 SN - 1432-2250 VL - 32 IS - 4 SP - 495 EP - 520 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 - Klein, Marten A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Transition to the ultimate regime in a stochastic model for thermal convection with internal sources Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_ipam21.pdf CY - IPAM Workshop: Transport and Mixing in Complex and Turbulent Flows (CTF2021), University of California, Los Angeles, CA, USA 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 - 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 - Klein, Marten A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection, 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. Y1 - 2021 UR - https://www-docs.b-tu.de/fg-stroemungsmodellierung/public/Klein_poster_ictam21.pdf UR - https://www.b-tu.de/media/video/Stochastic-modeling-of-transient-boundary-layers-in-high-Rayleigh-number-thermal-convection/f511d6b395472dc729543db3aa02dbc9 UR - https://www.ictam2020.org/assets/pdf/ICTAM2021-Fulllist-26-08.pdf ER - TY - GEN A1 - Klein, Marten A1 - Freire, Livia S. A1 - Lignell, David O. A1 - Kerstein, Alan R. A1 - Schmidt, Heiko T1 - Ein stochastischer Ansatz zur Modellierung fluktuierender Oberflächenflüsse in turbulenten Grenzschichten T2 - Kurzfassungen der Meteorologentagung DACH N2 - Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskräfte berücksichtigt werden können. Das Modell wird beispielhaft als unabhängiges, numerisches Werkzeug angewendet, um fluktuierende Oberflächenflüsse in turbulenten Kanalströmungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (poröse) Oberflächen betrachtet. Anhand neuer Ergebnisse wird demonstriert, dass der Modellansatz in der Lage ist, Referenzdaten zufriedenstellend zu reproduzieren und extrapolieren. Daneben werden aktuelle Arbeiten zur Kopplung des stochastischen Modellansatzes mit Large-Eddy-Simulationen vorgestellt. Es wird gezeigt, dass die stochastische Modellierung oberflächennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitterauflösung zu verringern. KW - one-dimensional turbulence KW - stochastic modeling KW - turbulent boundary layer KW - turbulent convection KW - rotating and stratified flows Y1 - 2021 UR - https://meetingorganizer.copernicus.org/DACH2022/DACH2022-22.html U6 - https://doi.org/10.5194/dach2022-22 VL - 2022 SP - 1 EP - 1 PB - Copernicus ER - TY - GEN A1 - Medina Méndez, Juan Ali A1 - Klein, Marten A1 - Peeters, Jurriaan W. R. A1 - Schmidt, Heiko T1 - Evaluating turbulent channel flows with rough walls : homogeneous roughness parameterization for use in a map-based turbulence model T2 - International journal of heat and fluid flow N2 - This work is focused on modeling the effects of homogeneous roughness on low-order velocity statistics in turbulent channel flows. Hydrodynamic effects due to the roughness are characterized on the basis of volume-averaging theory (VAT) and a discrete roughness element method. This theory exploits the homogeneous character of the roughness in order to reduce the complexity of the flow to its one-dimensional statistics. The formulated VAT-based roughness forcing is best suited for drag dominated surfaces. Turbulence modeling closure is achieved with a map-based turbulence model, the One-Dimensional Turbulence (ODT) model. This avoids the prescription of laws of the wall or other ad-hoc scalings, unlike in more traditional filter-based turbulence models. The modeling framework is applied on selected Reynolds number flows for likewise selected roughness topologies. Results are compared to direct numerical simulation (DNS) data available from the literature. Among others, model results are compared with those of a previously formulated parametric forcing approach (PFA) for roughness drag which involved a costly coefficient calibration linked to the roughness topology model. In ODT, the only calibration process required is the same one involved for the turbulence model parameters, i.e., similar to the ODT model application for smooth-wall flows. Despite all of the inherently implied shortcomings of a 1-D model, some appealing properties of ODT are discussed. Notably, the model is able to predict the roughness function, as well as the wall-normal profile of the Reynolds shear stress across the entire boundary layer thickness. KW - Turbulent channel KW - Roughness KW - ODT KW - Volume-averaging Y1 - 2026 UR - https://www.sciencedirect.com/science/article/pii/S0142727X25003716#d1e18585 U6 - https://doi.org/10.1016/j.ijheatfluidflow.2025.110113 VL - 117, Part B SP - 1 EP - 21 PB - Elsevier BV CY - Amsterdam ER -