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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. [ABSTRACT FROM AUTHOR]

Turbulent mixing is an omnipresent phenomenon that constantly affects our everyday life and plays an important role in a variety of industrial applications. The simulation of turbulent mixing poses great challenges, since the full resolution of all relevant length and time scales is associated with an immense computational effort. This limitation can be overcome by only resolving the large‐scale effects and completely model the sub‐grid scales. The development of an accurate sub‐grid mixing model is therefore a key challenge to capture all interactions in the sub‐grid scales. At this place, the hierarchical parcel‐swapping (HiPS) model formulated by A.R. Kerstein [J. Stat. Phys. 153, 142–161 (2013)] represents a computationally efficient and scale‐resolving turbulent mixing model. HiPS mimics the effects of turbulence on time‐evolving, diffusive scalar fields. In HiPS, the diffusive scalar fields or a state space is interpreted as a binary tree structure, which is an alternative approach compared to the most common mixing models. Every level of the tree represents a specific length and time scale, which is based on turbulence inertial range scaling. The state variables are only located at the base of the tree and are treated as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing only takes places between adjacent fluid parcels and at rates consistent with the prevailing diffusion time scales. In this work, the HiPS model formulation for the simulation of passive scalar mixing is detailed first. Preliminary results for the mean square displacement, passive scalar probability density function (PDF) and scalar dissipation rate are given and reveal the strengths of the HiPS model considering the reduced order and computational efficiency. These model investigations are an important step of further HiPS advancements. The integrated auxiliary binary tree structure allows HiPS to satisfy a large number of criteria for a good mixing model. From this point of view, HiPS is an attractive candidate for modeling the mixing in transported PDF methods. [ABSTRACT FROM AUTHOR]

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)$(\eta ={R}_{i}/{R}_{o}=0.1,0.04,0.02)$. 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 spanwise 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. Combust., 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. [ABSTRACT FROM AUTHOR]

This work presents a novel framework for the evaluation of far‐field sound radiation, specializing to a low Mach number jet flow. The framework comprises an analytical and a numerical part. In the analytical part, a low Mach number asymptotic analysis is presented to obtain the spectral sources of sound radiation starting from a pressure wave equation that is directly obtained from the Navier–Stokes equations. The derivation procedure is based on the fundamental premise of Lighthill's acoustic analogy. In the numerical part, a reduced‐order model for turbulent flow, the one‐dimensional turbulence model, is used to simulate the velocity field of a low Mach number turbulent round jet, assumed fully developed and statistically steady, hence homogeneous in the azimuthal direction and for a cross‐sectional slab assumed locally homogeneous in axial direction, too. The generated velocity field is used for the calculation of the spectral pressure sources, and consequently, to estimate the far‐field sound pressure level (SPL) of the jet. The results of the analysis are compared against available experimental SPL measurements from a subsonic jet. A reasonable agreement is obtained for the SPL. Furthermore, the analysis sheds light into the different contributions of the subsonic flow to sound radiation. The framework is readily extendable for any kind of low Mach number flow, including variable density flows and jet flames. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Turbulent mixed convection in an air‐water system is evaluated with a novel numerical solver implementing the stochastic One‐Dimensional Turbulence (ODT) model in a turbulent air flow surrounded by a laminar cocurrent water falling film in a cylindrical geometry. The ODT model is used as a reduced order surrogate model for the effects of turbulent advection, turbulent heat flux, and turbulent mass‐flux within a one‐dimensional domain. An ad‐hoc temporal‐to‐spatial transformation relying on the bulk flow gas velocity is used to obtain streamwise‐dependent statistics of the flow. The ODT simulation results are compared to simulations obtained with the assumption of a quasi‐laminar one‐dimensional gas flow, and to Reynolds‐Averaged Navier‐Stokes (RANS) reference data for a cocurrent water falling film evaporator [1]. The results show that the turbulent transport plays a decisive role in the estimation of interface gradients of temperature and vapor mass fraction. Although ODT predicts global quantities such as the interface temperature in a reasonable way, the model falls short of successfully predicting streamwise‐dependent radial profiles. Despite the shortcomings, the framework presented here is the first stepping stone towards the evaluation of complex multiphase momentum, mass, and heat transfer couplings with full scale resolution on potential evaporative devices. The model, thus, provides valuable information with minimal empiricism on the dynamics of the small scales for pioneering engineering applications. [ABSTRACT FROM AUTHOR]

Turbulent mixing plays an important role in a variety of applications ranging from astrophysics to combustion and even pollutant dispersion. The Direct Numerical Simulation (DNS) that resolves all scales is not feasible for most engineering applications since the flow has a wide range of length and time scales, which yields extremely high resolution requirements. Large Eddy Simulations (LES) overcome this limitation by modeling the sub‐grid scale effects. In transported Probability Density Function (PDF) methods, the key challenge is to develop an accurate mixing model. At this point, the Hierarchical Parcel‐Swapping (HiPS) model, introduced by A.R. Kerstein [J. Stat. Phys. 153, 142‐161 (2013)], is an attractive candidate. It is characterized by a computationally efficient representation of the effects of turbulence on a time‐evolving structure of diffusive scalar fields. The interpretation of the diffusive scalar fields or a state space as a binary tree structure is an alternative approach compared to the most common mixing models. The characteristic feature of HiPS is that every level of the tree corresponds to a specific length and time scale, which is based on turbulence inertial range scaling. The state variables only reside at the base of the tree and are understood as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by prevailing turbulent time scales associated with the sub‐trees. The mixing of adjacent fluid parcels is done either instantaneously or at rates consistent with the corresponding diffusion time scales. In this work, HiPS is detailed for the simulation of passive scalar mixing first. Preliminary results for the scalar power spectra, mean square displacement and scalar dissipation rate are shown and reveal a reasonable agreement with experimental findings. Furthermore, the integrated binary tree structure allows to satisfy a large number of criteria for a good mixing model. Considering the reduced order and computational efficiency, HiPS is an attractive candidate for modeling the mixing in transported PDF methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The One‐Dimensional Turbulence (ODT) model framework for the simulation of particle‐laden wire‐tube electrostatic precipitators is detailed in this work by specifying initial conditions, governing equations, and the mechanism for two‐way coupling between the electrostatic fields and the hydrodynamic flow. Unlike in a previous investigation [1], a two‐way coupling is required due to the low electrical mobility of aerosol particles, making flow motion responsible for the appearance of electrical convective currents. The ultimate goal of this framework is to develop a method which is able to investigate the precipitation phenomenon in wire‐tube precipitators, e.g., the collection efficiency, while relying on highly resolved physics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This preliminary numerical study investigates a lifted methane/air jet flame in a vitiated coflow by means of the One‐Dimensional Turbulence (ODT) model. In the considered Cabra Burner configuration [Combust. Flame 143 491‐506 (2005)], a jet flame issues from a central nozzle into a vitiated coflow of hot combustion products from lean premixed hydrogen/air flames. ODT is a map‐based model for turbulent flow simulations which uses a stochastic formulation for the turbulent advection. The diffusion and reaction effects along the one‐dimensional domain are considered by temporally advancing deterministic evolution equations. ODT simulations are performed with a representation of the methane/air chemistry by a reduced 19‐species mechanism with 15 reactions and a detailed 53‐species mechanism with 325 reactions. In this work, we present centerline profile of temperature and species concentrations obtained from ODT simulations using a cylindrical ODT‐formulation. Additionally, two‐dimensional renderings of the temperature distribution are shown. Although the simulation of reactive jet configurations by means of ODT is not novel, the complex stabilization region depending on the flow conditions represents a challenge for the model. Considering the reduced order of the model, ODT is able to predict the flow characteristics and reasonably matches the existing experimental data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We numerically investigate stable and intermittently unstable Ekman–Stokes boundary layers (ESBLs) as canonical problem for oscillatory near‐surface flows in Earth's ocean and atmosphere. The configuration is given by a neutrally‐stratified Newtonian fluid above a horizontal wall that resides in a rotating frame of reference. A flow is excited relative to this frame by lateral wall oscillations with prescribed amplitude and frequency. We utilize the stochastic one‐dimensional turbulence (ODT) model and investigate it's capabilities for time‐resolved numerical simulations from the laminar to the turbulent flow regime. The results obtained so far suggest that the model is able to capture the leading‐order transient dynamics of the laminar and turbulent ESBL. We conclude that ODT is an economical and reasonably accurate tool for studying transient boundary layers. [ABSTRACT FROM AUTHOR]

The One‐Dimensional Turbulence (ODT) model is applied for the evaluation of internal pipe flows subject to electrohydrodynamic (EHD) forces. The ODT formulation presented here incorporates the effects of the electrostatic potential energy transfer to the kinetic energy of the flow due to EHD instabilities in the presence of a corona discharge. Results for integral quantities such as the skin friction coefficient Cf and the Nusselt number Nu are obtained from ODT simulations and compared to available experimental data [1,2]. The results demonstrate the capabilities of ODT for simulating EHD flows. [ABSTRACT FROM AUTHOR]

We investigate incompressible temporally developing turbulent boundary layers for the first time using the One‐Dimensional Turbulence (ODT) model. ODT is spatially fully resolved along the 1D domain, only turbulent advection is represented by stochastic mapping events. We compare the mean and root mean square velocity profiles with the Direct Numerical Simulations (DNS) results for bulk Reynolds numbers, Reb = 500 and 1000 (Reb = Ubd/ν, where ν is the kinematic viscosity, Ub is the velocity provided at the bottom wall and d is the trip wire diameter for experiments). The study demonstrates that ODT has the capability to systematically investigate developing boundary layers. [ABSTRACT FROM AUTHOR]

We numerically investigate the Reynolds number dependency of the transport of a passive scalar in incompressible, fully‐developed turbulent channel flows. The stochastic one‐dimensional turbulence (ODT) model is used to make such numerical simulation feasible up to the friction Reynolds number Reτ = uτ δ/ν ≈ 5200 (channel half‐height δ, friction velocity uτ, kinematic viscosity ν) in the Schmidt number range 1 ≤ Sc = ν/Γ = 400 (mass diffusion coefficient Γ). The ODT simulations exhibit a turbulent boundary layer for which we show that the simulated mass transfer coefficient K+ follows the functional dependency suggested by Schwertfirm and Manhart, Int. J. Heat Fluid Flow 28, 1204–1214 (2007). The agreement is good for Sc ≤ 25 but a different scaling is obtained for Sc ≥ 49 investigated. [ABSTRACT FROM AUTHOR]

One‐dimensional turbulence (ODT) based models are able to generate good results for canonical flow problems compared to Direct Numerical Simulations. ODT has been successfully implemented as a sub‐grid scale model for LES problems (ODTLES) delivering promising results. However, due to the computational cost of the ODT model in this scope, there is a need for an even faster model for real world parameter regimes. The Hierarchical Parcel Swapping (HiPS) algorithm used in combination with the ODT model to simulate a channel flow recently provided results with an acceptable quality in a fraction of the time of an ODT simulation. HiPS uses a binary tree to define the fluid domain, and stochastic eddy events are sampled in this tree. A local instantaneous and complete mixing of the cells is performed when an eddy event happens at the Kolmogorov scale. The biggest limitation of this model is that the viscosity of the solution is implicitly defined by the number of cells in a mesh. Further development of HiPS is planned in order to create a computationally cheaper alternative for the ODT model to be used in ODTLES flow simulations. [ABSTRACT FROM AUTHOR]

Cylindrical pipe‐flow is evaluated by means of the One‐Dimensional Turbulence (ODT) model applying both an incompressible and a low Mach number variable density framework. In the variable density formulation, the velocity field is decomposed into density‐related (non‐divergence‐free) and density‐unrelated (divergence‐free) contributions, as detailed in Medina et al. [Combust. Flame 190 (2018) 388‐401]. Both contributions to the velocity field are subject to the effects of diffusion and turbulent transport, as it is normally the case for the incompressible velocity field in traditional ODT formulations. The turbulent transport is implemented by means of stochastic eddy events. These are influenced by the available kinetic energy given by the divergence‐free velocity contribution. An eddy may arise from the different regions of shear caused by varying velocity gradients in the 1‐D domain, but also as a consequence of the temperature‐varying dynamic viscosity. The cylindrical low Mach number variable density formulation is tested in a very low heat transfer regime and compared to the passive scalar results of the incompressible pipe‐flow formulation. ODT model parameters are assumed equal for both formulations. ODT results are compared to DNS results from Satake and Kunugi [Int. J. Numer. Methods Heat Fluid Flow 12 (2002) 958‐1008]. The passive scalar and variable density results show very good agreement with each other as well as with DNS data, respectively, thus suggesting new possible applications for ODT. [ABSTRACT FROM AUTHOR]

Hierarchical Parcel‐Swapping (HiPS) developed by A.R. Kerstein [J. Stat. Phys. 153, 142‐161 (2013)] is a computationally efficient and novel model for the effects of turbulence on time‐evolving, diffusive scalar fields. The characteristic feature of HiPS is the interpretation of the one‐dimensional flow domain or a state space as a binary tree structure. Every tree level corresponds to a specific length and time scale, which is based on a turbulence inertial range scaling. The state variables reside at the base of the tree and are interpreted as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing of adjacent fluid parcels is done at rates consistent with the prevailing diffusion time scales. In this work, we investigate the influence of turbulent time scale variations on an isothermal series‐parallel reaction scheme. The production of a desired chemical species is evaluated by means of a defined selectivity and is strongly affected by the underlying mixing time scales. [ABSTRACT FROM AUTHOR]

The stochastic One‐Dimensional Turbulence (ODT) model is used in combination with a Large Eddy Simulation (LES) approach in order to illustrate the potential of the fully coupled model (ODTLES) for highly turbulent flows. In this work, we use a new C++ implementation of the ODTLES code in order to analyze the computational performance in a classical incompressible turbulent channel flow problem. The parallelization potential of the model, as well as its physical and numerical consistency are evaluated and compared to Direct Numerical Simulations (DNSs). The numerical results show that the model is capable of reproducing a representative part of the DNS data at a cheaper computational cost. This advantage can be enhanced in the future by the implementation of a straightforward parallelization approach. [ABSTRACT FROM AUTHOR]

Abstract: The One‐Dimensional Turbulence (ODT) model is applied to a constant volume configuration by means of a periodic, one‐dimensional domain subject to randomized ensemble members with initial inhomogeneous temperature fields and homogeneous mass fraction profiles. The multidimensional turbulent interactions in the flow are modeled by the separate implementation of turbulent advection and the diffusion‐reaction processes, neglecting the mean advection of the system. On one hand, turbulent advection is modeled by means of the eddy events defined within the framework of ODT; on the other hand, the diffusion‐reaction system is solved by means of the Zero‐Mach limit conservation equations discretized with a 1D Finite Volume Method (FVM). The treatment is specialized in this work to constant volume systems. Due to the inherent stiffness of the diffusion‐reaction system, an operator splitting approach is also included in the formulation. Results for n‐Heptane chemistry comprising the temporal evolution of the heat release rate, pressure and normalized density‐weighted displacement speed are shown and compared to DNS results from Yoo et al. [Combust. Flame 158 (2011) 1727‐1741], in terms of individual ensemble members and mean ensemble behavior. The results show that it is possible to obtain reasonably good results in comparison to the DNS if an appropriate set of initial conditions is used. Furthermore, it is shown that the model uncertainty is negligible in comparison to the ensemble standard deviation introduced by randomized initial conditions. Overall, this work introduces the framework for constant volume autoignition in ODT and shows its efficiency for complex chemistry simulations. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Abstract: A stochastic modeling approach, the so‐called One‐Dimensional Turbulence (ODT), is used to study passive scalar transport in incompressible, fully‐developed, turbulent channel flows up to very high Schmidt numbers Sc = ν/Γ ∼ 104 (kinematic viscosity ν, scalar diffusivity Γ). Good agreement is obtained between ODT and Direct Numerical Simulation (DNS) results with respect to the mean, the fluctuation statistics, and the dimensionless mass transfer coefficient K+. ODT yields the mass transfer coefficient to become independent of the Reynolds number at high Schmidt numbers, which is similar to reference laboratory measurements and DNS. The present ODT results exhibit the power law K+ ∝ Sc−0.65 with a scaling exponent that is only slightly larger than in the reference laboratory measurements and DNS. The results obtained suggests that ODT can be a versatile tool for turbulent transport modeling in a wide range of physical parameters. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Abstract: The one‐dimensional turbulence model (ODT) is applied to study turbulent asymptotic suction boundary layers for a Reynolds number of Re = u∞/v0 = 333, where u∞ and v0 are the free stream and suction velocity, respectively. In here we will demonstrate that a large eddy suppression mechanism may reduce the influence of ODT model parameters, such as the viscous cut‐off parameter Z. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We summarize the group's progress in applying, analyzing, and improving ODT and ODT-based stochastic turbulence models like ODTLES. Compared to DNS these models span a wider range of scales while compared to RANS/LES (i) the molecular effects are retained and (ii) no assumption of scale separation is made. In this regard ODTLES has more properties of DNS than of standard LES. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]