@misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of passive scalars in turbulent channel flows}, series = {Jahresbericht 2020 zum Band: Notes on Numerical Fluid Mechanics and Multidisciplinary Design - New Results in Numerical and Experimental Fluid Mechanics XIII}, volume = {2020}, journal = {Jahresbericht 2020 zum Band: Notes on Numerical Fluid Mechanics and Multidisciplinary Design - New Results in Numerical and Experimental Fluid Mechanics XIII}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {G{\"o}ttingen}, pages = {30 -- 31}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes}, series = {Proceedings in Applied Mathematics and Mechanics}, volume = {2020}, journal = {Proceedings in Applied Mathematics and Mechanics}, number = {20}, publisher = {Wiley-VCH}, address = {Weinheim}, doi = {10.1002/pamm.202000128}, pages = {1 -- 2}, abstract = {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.}, language = {en} } @misc{SharmaKleinSchmidtetal., author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko and Sarradj, Ennes}, title = {On a lower-order framework for jet noise prediction based on one-dimensional turbulence}, series = {arXiv}, journal = {arXiv}, pages = {1 -- 4}, abstract = {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.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Predictive modeling of passive scalar transfer to a wall using stochastic one-dimensional turbulence}, series = {arXiv}, journal = {arXiv}, pages = {8}, abstract = {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.}, language = {en} } @misc{SchmidtMedinaMendezKlein, author = {Schmidt, Heiko and Medina M{\´e}ndez, Juan Ali and Klein, Marten}, title = {EHD turbulence in channel flows with inhomogeneous electrical fields: a one-dimensional turbulence study}, series = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, journal = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, doi = {10.23967/wccm-eccomas.2020.131}, pages = {12}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Modeling one and two passive scalar mixing in turbulent jets using one-dimensional turbulence}, series = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, journal = {14th World Congress on Computational Mechanics (WCCM) ; ECCOMAS Congress 2020, 19-24 July 2020, Paris, France}, pages = {1}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {MS404: Map-based stochastic methods for accurate modeling of turbulent heat and mass transfer}, series = {14th World Congress on Computational Mechanics (WCCM XIV) ; 8th European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2020), July 19-24, 2020, Paris, France}, journal = {14th World Congress on Computational Mechanics (WCCM XIV) ; 8th European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS 2020), July 19-24, 2020, Paris, France}, pages = {1}, language = {en} } @misc{KleinKersteinSchmidt, author = {Klein, Marten and Kerstein, Alan R. and Schmidt, Heiko}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection}, series = {25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, journal = {25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {2}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for thermal convection with internal sources}, address = {IPAM Workshop: Transport and Mixing in Complex and Turbulent Flows (CTF2021), University of California, Los Angeles, CA, USA}, pages = {1}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Map-based stochastic methods for accurate modeling of turbulent transport: towards poly-dispersed engineering flows}, series = {Jahrestreffen der ProcessNet Fachgruppen Mehrphasenst{\"o}mung (MPH) und Computational Fluid Dynamics (CFD)}, journal = {Jahrestreffen der ProcessNet Fachgruppen Mehrphasenst{\"o}mung (MPH) und Computational Fluid Dynamics (CFD)}, address = {Cottbus}, pages = {2}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Map-based modeling of high-Ra turbulent convection in planar and spherical geometries}, series = {Conference on Modelling Fluid Flow 2018 (CMFF'18)}, journal = {Conference on Modelling Fluid Flow 2018 (CMFF'18)}, pages = {1}, abstract = {Turbulent convection is important in many technological and geophysical applications. A model problem for such flows is Rayleigh-B{\´e}nard (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.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating Rayleigh-B{\´e}nard convection at low Prandtl numbers using one-dimensional turbulence modeling}, series = {Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019}, journal = {Proc. of the 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP11), Southampton, UK, July 30 to August 2, 2019}, pages = {1 -- 3}, abstract = {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.}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {The One-Dimensional Turbulence Aspects of Internal Forced Convective Flows}, series = {14th WCCM-ECCOMAS Congress 2020}, journal = {14th WCCM-ECCOMAS Congress 2020}, publisher = {Scipedia}, doi = {10.23967/wccm-eccomas.2020.338}, pages = {1 -- 12}, abstract = {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.}, language = {en} } @misc{KleinZenkerHerthaetal., author = {Klein, Marten and Zenker, Christian and Hertha, Katja and Schmidt, Heiko}, title = {Modeling One and Two Passive Scalar Mixing in Turbulent Jets Using One-Dimensional Turbulence}, series = {14th WCCM-ECCOMAS Congress 2020}, journal = {14th WCCM-ECCOMAS Congress 2020}, publisher = {Scipedia}, doi = {10.23967/wccm-eccomas.2020.205}, pages = {1 -- 12}, abstract = {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.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Towards a stochastic model for electrohydrodynamic turbulence with application to electrolytes}, series = {91st Annual Meeting of GAMM 2020@21}, journal = {91st Annual Meeting of GAMM 2020@21}, pages = {1}, abstract = {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.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers}, series = {91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) - PAMM, Proceedings in Applied Mathematics and Mechanics}, volume = {20}, journal = {91st Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) - PAMM, Proceedings in Applied Mathematics and Mechanics}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.202000127}, pages = {3}, abstract = {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.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochastic model for radiatively driven turbulent convection}, series = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, journal = {Verhandlungen der Deutschen Physikalischen Gesellschaft - BPCPPDYSOE21}, language = {en} } @incollection{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic Modeling of Passive Scalars in Turbulent Channel Flows: Predictive Capabilities of One-Dimensional Turbulence}, series = {New Results in Numerical and Experimental Fluid Mechanics XIII}, booktitle = {New Results in Numerical and Experimental Fluid Mechanics XIII}, editor = {Dillmann, Andreas and Heller, Gerd and Kr{\"a}mer, Ewald and Wagner, Claus}, publisher = {Springer International Publishing}, address = {Cham}, isbn = {978-3-030-79561-0}, doi = {10.1007/978-3-030-79561-0_5}, pages = {47 -- 57}, abstract = {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.}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Transition to the ultimate regime in a stochasticmodel for thermal convection with internal sources}, pages = {1}, abstract = {It is well established that heat transfer in turbulent Rayleigh-Bénard convection and angular momentum transfer in turbulent Taylor-Couette flow are similar in nature. This similarity manifests itself by isomorphic scaling laws for corresponding flow regimes. However, it is not clear at present if this similarity extends to flows with internal sources and different types of boundary conditions. Internal sources may occur, for example, due to radiative heating in dry or condensation in moist convection, or due to internal wave breaking and mean flow excitation in rotating Taylor-Couette-like flows. In this study, heat transfer in radiatively-driven turbulent Rayleigh-Bénard convection is investigated using the stochastic one-dimensional-turbulence model (ODT). A Boussinesq fluid of Prandtl number 1 is confined between two horizontal adiabatic no-slip walls that are located at z = 0 and H, respectively. The fluid is exposed to constant background gravity that points in vertical (-z) direction. A flow is driven by radiative heating from below yielding the local heating rate Q(z) = (P/l) exp(-z/l), where P is the prescribed mean total heat flux and l the absorption length that controls the thermal boundary layer thickness. ODT resolves all relevant scales of the flow, including molecular-diffusive scales, along a vertical one-dimensional domain, whereas stochastically sampled eddy events represent the effects of turbulent advection. ODT results reproduce and extrapolate available reference experiments of Lepot et al. (Proc. Natl. Acad. Sci. USA, 115, 2018, pp. 8937-8941) and Bouillaut et al. (J. Fluid Mech., 861, 2019, R5) in particular capturing the turbulent transition from the classical to the 'ultimate' regime. For these regimes, the exponent values in N u ∼ Ra^p scaling are found to be p ≈ 0.33 and p ≈ 0.55, respectively, in agreement with measured values. Joint probabilities of turbulent eddy size and location suggest that the regime transition is associated with a suppression of small-scale near-wall turbulent motions. The latter observation is found consistent with recent direct numerical simulations of heat transfer between permeable walls (Kawano et al., J. Fluid Mech., 914, 2021, A13).}, language = {en} } @misc{KleinZenkerSchmidt, author = {Klein, Marten and Zenker, Christian and Schmidt, Heiko}, title = {Map-based stochastic modeling of turbulent mixing in transient shear flows}, series = {MATH+ CECAM Discussion Meeting on Generalized Langevin Equations}, journal = {MATH+ CECAM Discussion Meeting on Generalized Langevin Equations}, pages = {1}, abstract = {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}, language = {en} } @misc{KleinSchmidtKerstein, author = {Klein, Marten and Schmidt, Heiko and Kerstein, Alan R.}, title = {Stochastic modeling of transient boundary layers in high-Rayleigh-number thermal convection, 25th International Congress of Theoretical and Applied Mechanics (ICTAM 20+1)}, pages = {1}, abstract = {One-dimensional turbulence (ODT) modeling is used to investigate the boundary layer in high-Rayleigh-number thermal convection for a notionally infinite horizontal layer of fluid. The model formulation distinguishes between turbulent advection, which is modeled by a stochastic process, and deterministic molecular diffusion to capture relevant vertical transport processes (including counter-gradient fluxes). For this study, statistical homogenization is applied to the two horizontal dimensions so that we use ODT as stand-alone tool. We show that the model yields mean and fluctuation temperature profiles that are in several respects consistent with available reference data. Furthermore, the profile of a surrogate for the fluctuation velocity is reminiscent of canonical wall turbulence.}, language = {en} } @misc{KleinLignellSchmidt, author = {Klein, Marten and Lignell, David O. and Schmidt, Heiko}, title = {Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers}, series = {EMS Annual Meeting 2021, online, 6-10 Sep 2021, EMS2021-79}, journal = {EMS Annual Meeting 2021, online, 6-10 Sep 2021, EMS2021-79}, doi = {10.5194/ems2021-79}, abstract = {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.}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Stochastic modeling of transient surface scalar and momentum fluxes in turbulent boundary layers, EMS Annual Meeting 2021, online, 6-10 Sep 2021}, pages = {1}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling and simulation of turbulent boundary layers in annular channel flow using one-dimensional turbulence}, series = {STAB Jahresbericht 2021}, volume = {2021}, journal = {STAB Jahresbericht 2021}, editor = {Wagner, Claus}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {G{\"o}ttingen}, pages = {39 -- 40}, abstract = {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.}, language = {en} } @misc{KleinSchmidtLignell, author = {Klein, Marten and Schmidt, Heiko and Lignell, David O.}, title = {Stochastic modeling of surface scalar-flux fluctuations in turbulent channel flow using one-dimensional turbulence}, series = {International Journal of Heat and Fluid Flow}, volume = {93 (2022)}, journal = {International Journal of Heat and Fluid Flow}, issn = {0142-727X}, doi = {10.1016/j.ijheatfluidflow.2021.108889}, pages = {1 -- 19}, abstract = {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.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Investigating Schmidt number effects in turbulent electroconvection using one-dimensional turbulence}, series = {Proc. Appl. Math. Mech.}, volume = {21}, journal = {Proc. Appl. Math. Mech.}, publisher = {Wiley}, address = {Weinheim}, doi = {https://doi.org/10.1002/pamm.202100147}, pages = {1 -- 3}, abstract = {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.}, language = {en} } @misc{KleinMaierSchmidt, author = {Klein, Marten and Maier, Roland Erich and Schmidt, Heiko}, title = {Stochastic modeling of transient neutral and stably-stratified Ekman boundary layers}, series = {Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, volume = {21}, journal = {Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)}, publisher = {Wiley}, address = {Weinheim}, doi = {10.1002/pamm.202100146}, pages = {1 -- 3}, abstract = {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.}, language = {en} } @misc{KleinFreireLignelletal., author = {Klein, Marten and Freire, Livia S. and Lignell, David O. and Kerstein, Alan R. and Schmidt, Heiko}, title = {Ein stochastischer Ansatz zur Modellierung fluktuierender Oberfl{\"a}chenfl{\"u}sse in turbulenten Grenzschichten}, series = {Kurzfassungen der Meteorologentagung DACH}, volume = {2022}, journal = {Kurzfassungen der Meteorologentagung DACH}, publisher = {Copernicus}, doi = {10.5194/dach2022-22}, pages = {1 -- 1}, abstract = {Im Konferenzbeitrag wird auf die Formulierung des stochastischen Modells eingegangen und gezeigt, dass neben Scherspannungen auch Druck-, Coriolis- und Auftriebskr{\"a}fte ber{\"u}cksichtigt werden k{\"o}nnen. Das Modell wird beispielhaft als unabh{\"a}ngiges, numerisches Werkzeug angewendet, um fluktuierende Oberfl{\"a}chenfl{\"u}sse in turbulenten Kanalstr{\"o}mungen sowie stabilen und konvektiven Grenzschichten zu untersuchen. Es werden sowohl glatte, als auch raue bzw. bewachsene (por{\"o}se) Oberfl{\"a}chen betrachtet. Anhand neuer Ergebnisse wird demonstriert, dass der Modellansatz in der Lage ist, Referenzdaten zufriedenstellend zu reproduzieren und extrapolieren. Daneben werden aktuelle Arbeiten zur Kopplung des stochastischen Modellansatzes mit Large-Eddy-Simulationen vorgestellt. Es wird gezeigt, dass die stochastische Modellierung oberfl{\"a}chennaher, subgitterskaliger Schwankungen in der Lage ist, wandnahe Turbulenzspektren zu reproduzieren und den filterbasierten Modellfehler bei ansonsten fester Gitteraufl{\"o}sung zu verringern.}, language = {de} } @misc{SharmaKleinSchmidt, author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko}, title = {Modelling turbulent jets at high-Reynolds number using one-dimensional turbulence}, series = {AIAA AVIATION 2021 FORUM}, journal = {AIAA AVIATION 2021 FORUM}, publisher = {American Institute of Aeronautics and Astronautics, Inc.}, isbn = {978-1-62410-610-1}, doi = {10.2514/6.2021-2104}, language = {en} } @misc{SharmaKleinSchmidt, author = {Sharma, Sparsh and Klein, Marten and Schmidt, Heiko}, title = {Features of far-downstream asymptotic velocity fluctuations in a round jet: A one-dimensional turbulence study}, series = {Physics of Fluids}, volume = {34}, journal = {Physics of Fluids}, number = {8}, issn = {1089-7666}, doi = {10.1063/5.0101270}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Stochastic modeling of transient Ekman flow at arbitrary Reynolds number driven by horizontal bottom wall oscillation}, series = {EMS Annual Meeting 2022, Abstracts}, volume = {19}, journal = {EMS Annual Meeting 2022, Abstracts}, publisher = {Copernicus}, address = {Bonn, Germany}, doi = {10.5194/ems2022-617}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow}, series = {92nd Annual Meeting of GAMM}, journal = {92nd Annual Meeting of GAMM}, publisher = {Gesellschaft f{\"u}r angewandte Mathematik und Mechanik e.V.}, address = {Aachen, Germany}, language = {en} } @misc{KleinTsaiSchmidt, author = {Klein, Marten and Tsai, Pei-Yun and Schmidt, Heiko}, title = {Stochastic modeling of heat and momentum transfer in annular pipe flow: A one-dimensional turbulence study with comparison to DNS and LES}, series = {STAB Jahresbericht 2022}, volume = {23}, journal = {STAB Jahresbericht 2022}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft (STAB)}, address = {G{\"o}ttingen, Germany}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Modeling electrohydrodynamically enhanced drag in channel and pipe flows using one-dimensional turbulence}, series = {Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Conference on Modelling Fluid Flow (CMFF'22)}, address = {Budapest, Hungary}, pages = {1 -- 8}, language = {en} } @misc{KleinMedinaMendezSchmidt, author = {Klein, Marten and Medina M{\´e}ndez, Juan Al{\´i} and Schmidt, Heiko}, title = {Modeling electrohydrodynamically enhanced drag in channel and pipe flows using One-Dimensional Turbulenc}, series = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, journal = {Proceedings of the Conference on Modelling Fluid Flow (CMFF'22)}, editor = {Vad, Janos}, publisher = {University of Technology and Economics, Department of Fluid Mechanics}, address = {Budapest, Hungary}, isbn = {978-963-421-881-4}, pages = {82 -- 91}, abstract = {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.}, language = {en} } @misc{KleinZenkerStaricketal., author = {Klein, Marten and Zenker, Christian and Starick, Tommy and Schmidt, Heiko}, title = {Stochastic modeling of three-scalar mixing in a coaxial jet using one-dimensional turbulence}, series = {12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022}, journal = {12th International Symposium on Turbulence and Shear Flow Phenomena (TSFP12), Osaka, Japan (Online), July 19-22, 2022}, pages = {1 -- 6}, abstract = {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.}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Exploring stratification effects in stable Ekman boundary layers using a stochastic one-dimensional turbulence model}, series = {Advances in Science and Research}, volume = {19/2022}, journal = {Advances in Science and Research}, issn = {1992-0636}, doi = {10.5194/asr-19-117-2022}, pages = {117 -- 136}, abstract = {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.}, language = {en} } @misc{SchmidtKlein, author = {Schmidt, Heiko and Klein, Marten}, title = {Chair of Numerical Fluid and Gas Dynamics}, pages = {1}, language = {en} } @misc{HartmannKoehlerSchmidtetal., author = {Hartmann, Carsten and K{\"o}hler, Ekkehard and Schmidt, Heiko and Klein, Marten}, title = {Scientific computing LAB (SCL)}, series = {"Get Into Energy", BTU Cottbus-Senftenberg, ZHG Building, 1 Feb. 2023}, journal = {"Get Into Energy", BTU Cottbus-Senftenberg, ZHG Building, 1 Feb. 2023}, address = {Cottbus}, pages = {1}, abstract = {KEY COMPETENCE AND FOCUS • Development of numerical methods and algorithms for multi-energy systems • Multiscale and multiphysics modeling and simulation of P2X technologies • Stochastic simulation and efficient optimization of complex energy networks}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling of heated turbulent coaxial pipe flow prescribing different thermal boundary conditions}, series = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, journal = {18th European Turbulence Conference (ETC18), 4-6 September 2023, Valencia}, address = {Valencia}, pages = {1}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Al{\´i} and Klein, Marten and Schmidt, Heiko}, title = {Fractal roughness representation in a stochastic one-dimensional turbulence modeling approach}, series = {Book of Abstracts 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montr{\´e}al, Canada, June 25-28, 2024}, journal = {Book of Abstracts 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montr{\´e}al, Canada, June 25-28, 2024}, address = {Montr{\´e}al, Canada}, pages = {3}, language = {en} } @misc{NaikBuryeMedinaMendezKleinetal., author = {Naik Burye, Nishidh Shailesh and Medina M{\´e}ndez, Juan Al{\´i} and Klein, Marten and Schmidt, Heiko}, title = {Revisiting near-wall modeling of fully developed turbulent flow in concentric annuli}, series = {Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB 13.-14. November 2024, Regensburg}, journal = {Jahresbericht 2024 zum 24. DGLR-Fachsymposium der STAB 13.-14. November 2024, Regensburg}, publisher = {Deutsche Str{\"o}mungsmechanische Arbeitsgemeinschaft, STAB}, address = {Regensburg}, pages = {174 -- 175}, language = {en} } @misc{PolasanapalliKleinSchmidt, author = {Polasanapalli, Sai Ravi Gupta and Klein, Marten and Schmidt, Heiko}, title = {Numerical study on the effects of transient pressure gradients on isothermal and heated pipe flows}, series = {94th Annual Meeting of the Association of Applied Mathematics and Mechanics March 18th-March 22nd, 2024 Magdeburg (Germany) : Book of Abstracts}, journal = {94th Annual Meeting of the Association of Applied Mathematics and Mechanics March 18th-March 22nd, 2024 Magdeburg (Germany) : Book of Abstracts}, address = {Magdeburg (Germany)}, pages = {227 -- 228}, language = {en} } @misc{JoshiMedinaMendezKleinetal., author = {Joshi, Abhishek and Medina Mendez, Juan Ali and Klein, Marten and Schmidt, Heiko}, title = {Simulating homogenous isotropic turbulence with deterministic and stochastic forcings using a one-dimensional turbulence model}, pages = {1}, abstract = {To understand the intermittency present in scalar fields we need to address the expense of current start-of-art DNS to probe the higher-order structure functions. These higher order moments become increasingly sensitive to increasing Reλ and much more prone to extreme events. Here, in this work, we investigate using a Reduced order model(ODT) to simulate Homogenous Isotropic turbulence as an initial step towards that goal by employing a linear forcing [1] proposed by Lundgren that is proportional to local and instantaneous velocity.}, language = {en} } @misc{MarinkovićMedinaMendezSchmidtetal., author = {Marinković, Pavle and Medina M{\´e}ndez, Juan Ali and Schmidt, Heiko and Klein, Marten}, title = {Ongoing development of a hybrid reduced order stochastic/LES solver for turbulent flows}, address = {Cottbus}, pages = {1}, language = {en} } @misc{MedinaMendezKleinSchmidt, author = {Medina M{\´e}ndez, Juan Al{\´i} and Klein, Marten and Schmidt, Heiko}, title = {Fractal roughness representation in a stochastic one-dimensional turbulence modeling approach}, series = {Proceedings of the 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montr{\´e}al, Canada, June 25-28, 2024}, journal = {Proceedings of the 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montr{\´e}al, Canada, June 25-28, 2024}, pages = {1 -- 6}, language = {en} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Stochastic modeling and theoretical analysis of heated concentric coaxial pipes at low Prandtl number}, series = {94rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Book of Abstracts}, journal = {94rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, Book of Abstracts}, publisher = {GAMM e.V.}, address = {Magdeburg}, pages = {11}, language = {en} } @misc{KleinSchmidt, author = {Klein, Marten and Schmidt, Heiko}, title = {Time-resolved simulations of wind speed fluctuations across atmospheric boundary layers using a stochastic forward model}, series = {Verhandlungen der DPG Fr{\"u}hjahrstagung SMuK 2023}, journal = {Verhandlungen der DPG Fr{\"u}hjahrstagung SMuK 2023}, publisher = {Deutsche Physikalische Gesellschaft (DPG)}, address = {Dresden}, abstract = {Atmospheric boundary layers (ABLs) govern the atmosphere-surface coupling and are therefore of fundamental relevance for Earth's weather and climate system. Time-resolved numerical simulations of ABLs are challenging due to intricate interactions of inertial, Coriolis, buoyancy, and viscous forces on all relevant scales of the turbulent flow. Small-scale processes, albeit potentially nonuniversal, are typically not resolved due to cost constraints but modeled based on physically justified relations with the resolved scales, neglecting expensive backscatter. This lack in modeling is addressed here by utilizing a dimensionally reduced stochastic modeling approach. The model aims to reproduce turbulent cascade phenomenology by a stochastic process, respecting fundamental physical conservation principles. Momentary wind velocity and temperature profiles evolve autonomously in time for an ensemble of initial conditions. By comparison with available high-fidelity reference numerical simulations, reanalysis, and observations, it is shown that the model captures various relevant flow properties, exhibiting limitations mainly in a delayed relaminarization under very stable conditions. Forthcoming research aims to contribute to a better understanding of polar boundary layers, requiring predictive modeling capabilities, high resolution, and numerical efficiency to perform long-time simulations.}, language = {de} } @misc{TsaiSchmidtKlein, author = {Tsai, Pei-Yun and Schmidt, Heiko and Klein, Marten}, title = {Modeling simultaneous momentum and passive scalar transfer in turbulent annular Poiseuille flow}, series = {Proceedings in applied mathematics and mechanics : PAMM}, volume = {22}, journal = {Proceedings in applied mathematics and mechanics : PAMM}, number = {1}, issn = {1617-7061}, doi = {10.1002/pamm.202200272}, abstract = {Simultaneous momentum and passive scalar transfer in weakly heated pressure-driven turbulent concentric annular pipe flow is numerically investigated using the cylindrical formulation of the stochastic one-dimensional turbulence (ODT) model,which is utilized here as standalone tool. In the present study, we focus on the model calibration for heated annular pipes based on recent reference direct numerical simulations (DNS) from Bagheri and Wang (Int. J. Heat Fluid Flow 86, 108725,2020; Phys. Fluids 33, 055131, 2021). It is shown that the model is able to individually capture scalar and momentum transfer, but not both equally well at the same time. We attribute this to less dissimilar scalar and momentum transport in the model at the low Reynolds number investigated. It is argued that the model prefers a fully developed turbulent state due to its construction. Nevertheless, it is demonstrated that ODT is able to reasonably capture the radial inner-outer asymmetry of the scalar and momentum boundary layers which yields better predictive capabilities than wall-function-based approaches.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows. I. Conservative Eulerian formulation and application to supersonic channel flow}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0125514}, abstract = {Accurate but economical modeling of supersonic turbulent boundary layers is a standing challenge due to the intricate entanglement of temperature, density, and velocity fluctuations on top of the mean-field variation. Application of the van Driest transformation may describe well the mean state but cannot provide detailed flow information. This lack-in modeling coarse and fine-scale variability is addressed by the present study using a stochastic one-dimensional turbulence (ODT) model. ODT is a simulation methodology that represents the evolution of turbulent flow in a low-dimensional stochastic way. In this study, ODT is extended to fully compressible flows. An Eulerian framework and a conservative form of the governing equations serve as the basis of the compressible ODT model. Computational methods for statistical properties based on ODT realizations are also extended to compressible flows, and a comprehensive way of turbulent kinetic energy budget calculation based on compressible ODT is put forward for the first time. Two canonical direct numerical simulation cases of supersonic isothermal-wall channel flow at Mach numbers 1.5 and 3.0 with bulk Reynolds numbers 3000 and 4880, respectively, are used to validate the extended model. A rigorous numerical validation is presented, including the first-order mean statistics, the second-order root mean square statistics, and higher-order turbulent fluctuation statistics. In ODT results, both mean and root mean square profiles are accurately captured in the near-wall region. Near-wall temperature spectra reveal that temperature fluctuations are amplified at all turbulent scales as the effects of compressibility increase. This phenomenon is caused by intensified viscous heating at a higher Mach number, which is indicated by the steeper profiles of viscous turbulent kinetic energy budget terms in the very near-wall region. The low computational cost and predictive capabilities of ODT suggest that it is a promising approach for detailed modeling of highly turbulent compressible boundary layers. Furthermore, it is found that the ODT model requires a Mach-number-dependent increase in a viscous penalty parameter Z in wall-bounded turbulent flows to enable accurate capture of the buffer layer.}, language = {en} } @misc{GaoSchmidtKleinetal., author = {Gao, Tianyun and Schmidt, Heiko and Klein, Marten and Liang, Jianhan and Sun, Mingbo and Chen, Chongpei and Guan, Qingdi}, title = {One-dimensional turbulence modeling of compressible flows: II. Full compressible modification and application to shock-turbulence interaction}, series = {Physics of Fluids}, volume = {35}, journal = {Physics of Fluids}, number = {3}, issn = {1089-7666}, doi = {10.1063/5.0137435}, abstract = {One-dimensional turbulence (ODT) is a simulation methodology that represents the essential physics of three-dimensional turbulence through stochastic resolution of the full range of length and time scales on a one-dimensional domain. In the present study, full compressible modifications are incorporated into ODT methodology, based on an Eulerian framework and a conservative form of the governing equations. In the deterministic part of this approach, a shock capturing scheme is introduced for the first time. In the stochastic part, one-dimensional eddy events are modeled and sampled according to standard methods for compressible flow simulation. Time advancement adjustments are made to balance comparable time steps between the deterministic and stochastic parts in compressible flows. Canonical shock-turbulence interaction cases involving Richtmyer-Meshkov instability at Mach numbers 1.24, 1.5, and 1.98 are simulated to validate the extended model. The ODT results are compared with available reference data from large eddy simulations and laboratory experiments. The introduction of a shock capturing scheme significantly improves the performance of the ODT method, and the results for turbulent kinetic energy are qualitatively improved compared with those of a previous compressible Lagrangian ODT method [Jozefik et al., "Simulation of shock-turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence," Combust. Flame 164, 53 (2016)]. For the time evolution of profiles of the turbulent mixing zone width, ensemble-averaged density, and specific heat ratio, the new model also yields good to reasonable results. Furthermore, it is found that the viscous penalty parameter Z of the ODT model is insensitive to compressibility effects in turbulent flows without wall effects. A small value of Z is appropriate for turbulent flows with weak wall effects, and the parameter Z serves to suppress extremely small eddy events that would be dissipated instantly by viscosity.}, language = {en} }