One-dimensional Turbulence Research Articles

The Impact of Three-Dimensional Effects on the Simulation of Turbulence Kinetic Energy in a Major Alpine Valley

The correct simulation of the atmospheric boundary layer (ABL) is crucial for reliable weather forecasts in truly complex terrain. However, common assumptions for model parametrizations are only valid for horizontally homogeneous and flat terrain. Here, we evaluate the turbulence parametrization of the numerical weather prediction model COSMO with a horizontal grid spacing of Delta x = 1.1,hbox {km} for the Inn Valley, Austria. The long-term, high-resolution turbulence measurements of the i-Box measurement sites provide a useful data pool of the ABL structure in the valley and on slopes. We focus on days and nights when ABL processes dominate and a thermally-driven circulation is present. Simulations are performed for case studies with both a one-dimensional turbulence parametrization, which only considers the vertical turbulent exchange, and a hybrid turbulence parametrization, also including horizontal shear production and advection in the budget of turbulence kinetic energy (TKE). We find a general underestimation of TKE by the model with the one-dimensional turbulence parametrization. In the simulations with the hybrid turbulence parametrization, the modelled TKE has a more realistic structure, especially in situations when the TKE production is dominated by shear related to the afternoon up-valley flow, and during nights, when a stable ABL is present. The model performance also improves for stations on the slopes. An estimation of the horizontal shear production from the observation network suggests that three-dimensional effects are a relevant part of TKE production in the valley.

A Scale-Adaptive Turbulent Kinetic Energy Closure for the Dry Convective Boundary Layer

Abstract A pragmatic scale-adaptive turbulent kinetic energy (TKE) closure is proposed to simulate the dry convective boundary layer for a variety of horizontal grid resolutions: from 50 m, typical of large-eddy simulation models that use three-dimensional turbulence parameterizations/closures, up to 100 km, typical of climate models that use one-dimensional turbulence and convection parameterizations/closures. Since parameterizations/closures using the TKE approach have been frequently used in these two asymptotic limits, a simple method is proposed to merge them with a mixing-length-scale formulation for intermediate resolutions. This new scale-adaptive mixing length naturally increases with increasing grid length until it saturates as the grid length reaches mesoscale-model resolution. The results obtained using this new approach for dry convective boundary layers are promising. The mean vertical profiles of potential temperature and heat flux remain in good agreement for different resolutions. A continuous transition (in terms of resolution) across the gray zone is illustrated through the partitioning between the model-resolved and the subgrid-scale transports as well as by documenting the transition of the subgrid-scale TKE source/sink terms. In summary, a natural and continuous transition across resolutions (from 50 m to 100 km) is obtained, for dry convection, using exactly the same atmospheric model for all resolutions with a simple scale-adaptive mixing-length formulation.

Constant volume n-Heptane autoignition using One-Dimensional Turbulence

Constant volume premixed lean n-Heptane/air autoignition at high pressure is investigated using the One-Dimensional Turbulence (ODT) model. The configuration consists of a 1D fixed volume domain with a prescribed velocity spectrum and temperature fluctuations superimposed on an initial uniformly elevated scalar field. The sensitivity of the heat release rate and pressure evolution to the initial temperature distribution is studied by imposing different initial temperature fields while holding the mean, RMS and integral length scale of the field constant. Three detailed chemical mechanisms are employed for the prediction of autoignition and heat release rate. To mitigate the high computational cost associated with the calculation of the chemical source terms in the stiff complex mechanisms, an approach based on the Strang-Splitting method is presented. Finally, a study of the ODT model uncertainty is carried out. For validation, ODT results are compared to 2D DNS data from Yoo et al. (2011) for the temporal evolution of heat release rate, pressure and density-weighted displacement speed. Ensemble averaged ODT results show good agreement with the DNS data. ODT results generated from varying the initial temperature fields show that the ignition delay time is highly sensitive to the initial temperature field. The ODT model uncertainty study shows that dispersion due to the stochastic nature of the model is considerably smaller than the dispersion resulting from varying the initial temperature field. Overall, this study demonstrates that ODT accurately captures the evolution of complex chemistry reactive flows in constant volume autoignition simulations and that once validated, ODT is an efficient tool that can be used to carry out parametric studies not feasible by DNS.

A one-dimensional stochastic model of turbulence within and above plant canopies

The suitability of Kerstein's One-Dimensional Turbulence (ODT) model in the representation of atmospheric boundary layer (ABL) flows within and above plant canopies is investigated. The ODT model was adapted to represent a filtered version of flow and scalar fields, equipped with a Smagorinsky-like sub-grid scale model, a wall model, and a parameterization of the canopy effects on the flow. In the filtered ODT, the entire vertical extension of the ABL is modeled and the “resolved” vertical turbulent transport is represented by stochastic eddies that effectively mix fluid parcels across a path length, representing non-local turbulent fluxes that are a critical feature of the canopy roughness sublayer. Simulations for different canopies and stability conditions are performed and vertical profiles of turbulence and scalar statistics are compared with observational and large-eddy simulation data. This new filtered version of the ODT model yields grid-independent results. Model performance for plant canopies is consistent with previous results from ODT for all cases tested without any case-specific parameter adjustment, generating reasonable agreement in profiles of mean velocity, temperature and water vapor mixing ratio, as well as vertical fluxes of momentum and sensible and latent heat, despite the underestimation of all velocity variances. Non-local transport is intrinsic to the formulation of ODT, which represents a significant advantage compared to other reduced-model approaches employed for canopy flows.

Stochastic Modeling of Turbulent Scalar Transport at Very High Schmidt Numbers

AbstractA 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)

Application of ODT to constant volume autoignition problems

AbstractThe 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)

Modeling and numerical study of primary breakup under diesel conditions

A recently introduced stochastic model for reduced numerical simulation of primary jet breakup is evaluated by comparing model predictions to DNS results for primary jet breakup under diesel conditions. The model uses one-dimensional turbulence (ODT) to simulate liquid and gas time advancement along a lateral line of sight. This one-dimensional domain is interpreted as a Lagrangian object that is advected downstream at the jet bulk velocity, thus producing a flow state expressed as a function of streamwise and lateral location. Multiple realizations are run to gather ensemble statistics that are compared to DNS results. The model incorporates several empirical extensions of the original ODT model that represent the phenomenology governing the Weber number dependence of global jet structure. The model as previously formulated, including the assigned values of tunable parameters, is used here without modification in order to test its capability to predict various statistics of droplets generated by primary breakup. This test is enabled by the availability of DNS results that are suitable for model validation. Properties that are examined are the rate of bulk liquid mass conversion into droplets, the droplet size distribution, and the dependence of droplet velocities on droplet diameter. Quantities of greatest importance for engine modeling are found to be predicted with useful accuracy, thereby demonstrating a more detailed predictive capability by a highly reduced numerical model of primary jet breakup than has previously been achieved.

Chemical Explosive Mode Analysis for Local Reignition Scenarios in H2/N2 Turbulent Diffusion Flames

Local reignition scenarios in H2/N2 turbulent diffusion flames are investigated using a one-dimensional turbulence (ODT) model and chemical explosive mode analysis (CEMA). Through analogy with the flame fronts in homogeneous ignition and laminar premixed flames, four reignition scenarios are distinguished and analyzed by CEMA. Results show that the reignition scenario via premixed flame propagation corresponds to a high-temperature explosion index and the reignition process is segmentally dominated by the reactions related to the consumption and production of the hydrogen radical. While reignition mode through an independent flamelet corresponds to a high radical explosion index, the whole reignition process is dominated by the production reaction of the hydrogen radical. When these two reignition processes are terminated by turbulent eddies, a hybrid reignition process or reignition scenario through turbulent flame folding may occur, and the turbulent folding mode corresponds to a high dissipation rate a...

Comparison Between ODT and DNS for Ignition Occurrence in Turbulent Premixed Jet Combustion: Safety-Relevant Applications

Abstract This work investigates the ability of the one-dimensional turbulence model (ODT) to detect, in a predictive manner, occurrence of successful ignition or misfire in a reacting gas mixture subjected to turbulence. Since ODT is computationally very efficient, this significantly aids in the analysis of safety-relevant applications. ODT delivers fast predictions, while still capturing most relevant physicochemical processes controlling ignition. However, ODT contains some empirical parameters that must be set by comparison with reliable reference data. In order to determine these parameters and check the accuracy of resulting ODT predictions, they are compared in this work with reference data from direct numerical simulation (DNS). DNS is recognized as the most accurate numerical tool to investigate ignition in turbulent flows. However, it requires very high computational times, so that it cannot be used for practical safety predictions. It is demonstrated in this article that, thanks to validation and comparison with DNS, ODT realizations can be used to predict correctly the occurrence of ignition in turbulent premixed flames while saving more than 90% of the required computational time, memory and disk space.

Modelling the plankton groups of the deep, peri-alpine Lake Bourget

Predicting phytoplankton succession and variability in natural systems remains to be a grand challenge in aquatic ecosystems research. In this study, we identified six major plankton groups in Lake Bourget (France), based on cell size, taxonomic properties, food-web interactions and occurrence patterns: cyanobacterium Planktothrix rubescens, small and large phytoplankton, mixotrophs, herbivorous and carnivorous zooplankton. We then developed a deterministic dynamic model that describes the dynamics of these groups in terms of carbon and phosphorus fluxes, as well as of particulate organic phosphorus and dissolved inorganic phosphorus. The modular and generic model scheme, implemented as a set of modules under Framework for Aquatic Biogeochemical Models (FABM) enables run-time coupling of the plankton module an arbitrary number of times, each time with a prescribed position across the autotrophy/heterotrophy continuum. Parameters of the plankton groups were mainly determined conjointly by the taxonomic and allometric relationships, based on the species composition and average cellular volume of each group. The biogeochemical model was coupled to the one-dimensional General Ocean Turbulence Model (GOTM) and forced with local meteorological conditions. The coupled model system shows very high skill in predicting the spatiotemporal distributions of water temperature and dissolved inorganic phosphorus for five simulated years within the period 2004 to 2010, and intermediate skill in predicting the plankton succession. We performed a scenario analysis to gain insight into the factors driving the sudden disappearance of P. rubescens in 2010. Our results provide evidence for the hypothesis that the abundance of this species before the onset of stratification is critical for its success later in the growing season, pointing thereby to a priority effect.

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

ABSTRACTThe turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u∞ / v0 = 333, where u∞ and v0 are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.

Turbulence effects on the autoignition of DME in a turbulent co-flowing jet

Dimethyl ether (DME) autoignition in turbulent co-flowing jets with preheated air is studied using the one-dimensional turbulence (ODT) model. We investigate the effects of molecular and turbulent transport on the autoignition process at different jet Reynolds numbers and two air preheat conditions. Statistics for the cases considered show that the overall effects of turbulence and molecular transport can serve to delay or accelerate autoignition depending upon where ignition starts, the presence of 2-stage or single-stage ignition and the variations in ignition delay times in mixture fraction space. For the higher temperature air preheat cases, the classical view that autoignition is delayed by turbulence is established. For the lower preheat air temperature cases, we show that low-temperature chemistry associated with first-stage ignition can help accelerate the autoignition process and the transition to high-temperature chemistry. This acceleration can reduce the ignition delay time by as much as a factor of 2. Given this work and previous work by the authors based on a different fuel, n-heptane, we find that the ignition delay map based on homogeneous ignition for different mixture fractions can provide a preview of the ignition scenarios for the co-flowing jet configuration regardless of the choice of fuel considered.

State estimation and prediction using clustered particle filters

Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors.

Numerical investigation of turbulent-jet primary breakup using one-dimensional turbulence

Primary breakup to form droplets at liquid surfaces is an important fundamental process to study as it determines the initial properties of the dispersed phase, which affect mixing rates, secondary breakup, droplet collisions, and flow separation within the dispersed flow region. Primary breakup can be regarded as one of the least developed model components for simulating and predicting liquid jet breakup. However, it is of paramount importance in many technical applications, e.g. fuel injection in engines and spray painting. This paper presents a numerical investigation of primary breakup of a turbulent liquid jet in still air at standard conditions using the one-dimensional turbulence (ODT) modeling framework. ODT is a stochastic model that simulates turbulent flow evolution along a notional 1D line of sight by applying instantaneous maps to represent the effect of individual turbulent eddies on property profiles. An important feature of ODT is the resolution of all relevant scales, both temporal and spatial. The restriction to one spatial dimension in ODT permits affordable high resolution of interfacial and single-phase property gradients, which is key to capturing the local behavior of the breakup process and allows simulations at high Reynolds and Weber numbers that are currently not accessible to direct numerical simulations (DNS).This paper summarizes our extensions of the ODT model to simulate geometrically simple jet breakup problems, including representations of Rayleigh wave breakup, turbulent breakup, and shear-driven breakup. Each jet breakup simulation consists of a short temporal channel section to initialize a turbulent velocity profile at the nozzle exit followed by an adjacent jet section. The simulations are carried out for jet exit Reynolds number of 11,500, 23,000, 46,000 and 92,000 while the Weber number is varied within the range 102–107. We present results on breakup statistics including spatial locations of droplet release, droplet sizes and liquid core length. The results on primary breakup are compared to experimental results and models.

Evaluation of stochastic particle dispersion modeling in turbulent round jets

ODT (one-dimensional turbulence) simulations of particle-carrier gas interactions are performed in the jet flow configuration. Particles with different diameters are injected onto the centerline of a turbulent air jet. The particles are passive and do not impact the fluid phase. Their radial dispersion and axial velocities are obtained as functions of axial position. The time and length scales of the jet are varied through control of the jet exit velocity and nozzle diameter. Dispersion data at long times of flight for the nozzle diameter (7 mm), particle diameters (60 and 90 µm), and Reynolds numbers (10, 000–30, 000) are analyzed to obtain the Lagrangian particle dispersivity. Flow statistics of the ODT particle model are compared to experimental measurements. It is shown that the particle tracking method is capable of yielding Lagrangian prediction of the dispersive transport of particles in a round jet. In this paper, three particle-eddy interaction models (Type-I, -C, and -IC) are presented to examine the details of particle dispersion and particle-eddy interaction in jet flow.

Thermal radiation modeling using the LES–ODT framework for turbulent combustion flows

A novel multiscale Monte-Carlo Ray Tracing (MCRT) model in the large eddy simulation–one-dimensional turbulence (LES–ODT) framework for participating gray media is developed. LES–ODT is based on a hybrid simulation of the large scales within LES and 1D ODT fine-resolution solutions embedded in the LES. Radiation is solved within the ODT domain at the subgrid scale where a combination of stochastic and deterministic solutions allows the treatment of different processes governing the transport and chemistry for scalars and momentum. The MCRT model is implemented in a non-homogeneous auto-ignition isotropic turbulence simulation and compared to direct numerical simulations (DNS) of the same configuration. This configuration exhibits complex coupling between turbulent transport and molecular processes, diffusion, reaction and radiation, under highly transient conditions. Implementation in the LES–ODT framework is performed for different cases of optical thicknesses. Results of the simulations are compared to DNS statistics. The comparison of the different statistics shows a satisfactory agreement.

Non-periodic one-dimensional ideal conductors and integrable turbulence

To relate the motion of a quantum particle to the properties of the potential is a fundamental problem of physics, which is far from being solved. Can a medium with a potential which is neither periodic nor quasi-periodic be a conductor? That question seems to have been never addressed, despite being both interesting and having practical importance. Here we propose a new approach to the spectral problem of the one-dimensional Schrödinger operator with a bounded potential. We construct a wide class of potentials having a spectrum consisting of the positive semiaxis and finitely many bands on the negative semiaxis. These potentials, which we call primitive, are reflectionless for positive energy and in general are neither periodic nor quasi-periodic. Moreover, they can be stochastic, and yet allow ballistic transport, and thus describe one-dimensional ideal conductors. Primitive potentials also generate a new class of solutions of the KdV hierarchy. Stochastic primitive potentials describe integrable turbulence, which is important for hydrodynamics and nonlinear optics. We construct the potentials by numerically solving a system of singular integral equations. We hypothesize that finite-gap potentials are a subclass of primitive potentials, and prove this in the case of one-gap potentials.

Sensitivity of VOF simulations of the liquid jet breakup to physical and numerical parameters

In this paper the characteristics of the primary breakup of a liquid jet is analyzed numerically. We applied the Volumes of Fluids (VOF) approach utilizing the Direction Averaged Curvature (DAC) model, to estimate the interface curvature, and the Direction Averaged Normal (DAN) model, to propagate the interface. While being used for the first time to predict liquid atomization, this methodology showed a high accuracy. The influence of varying the fluid properties, namely liquid-gas density and viscosity ratio, and injection conditions is discussed related to the required grid resolution. Resulting droplet sizes are compared to distributions obtained through the One-Dimensional Turbulence (ODT) model.

One-Dimensional Modeling of Turbulent Premixed Jet Flames - Comparison to DNS

The one-dimensional turbulence (ODT) model, formulated in an Eulerian reference frame, is applied to a temporally-evolving premixed turbulent hydrogen plane-jet flame and results are compared with direct numerical simulation (DNS) data. This is the first published study to perform direct comparisons of ODT to DNS for premixed flames. The ODT model solves the full set of conservation equations for mass, momentum, energy, and species on a one-dimensional domain corresponding to the transverse jet direction. The effects of turbulent mixing are modeled via a stochastic process, while the full range of diffusive-reactive length and time scales are resolved directly on the one-dimensional domain. A detailed chemical mechanism for hydrogen combustion consisting of 9 species and 21 reactions and a mixture-averaged transport model are used (consistent with the DNS). Cases with two different Damkohler numbers are considered and comparisons between the ODT and DNS data are shown with respect to flow dynamics and thermochemistry. The ODT compared favorably with the DNS in terms of the overall entrainment as judged by the streamwise velocity profile and in terms of local flamelet structure as judged by progress-variable conditional reaction and scalar dissipation rates. While the ODT agreed qualitatively with the overall flame evolution, the net fuel consumption rate was somewhat over-predicted for a brief early period and under-predicted later on, leading to an overly long flame burnout time. It was demonstrated that adjusting a parameter controlling the selection of large eddies improved the prediction of the peak fuel consumption rate and overall reaction progress but worsened the prediction of jet entrainment. An analysis of the 1D nature of ODT is presented that suggests the FSD in ODT needs to be much higher than the FSD in the DNS in order to achieve the same overall burning rate, suggesting that the FSD is under-predicted by a significant fraction. While the success of the ODT in reproducing many of the salient features of nonpremixed flames has been demonstrated, the current study suggests that improvements are needed when applied to premixed flames. It is also important to note that the DNS required approximately 40×106 CPU hours while the ODT required approximately 103 CPU hours.

Lagrangian investigation and chemical explosive mode analysis of extinction and re-ignition in H2/CO/N2 syngas non-premixed flame

An investigation of the local flame extinction and re-ignition of hydrogen syngas non-premixed flame are carried out using one-dimensional turbulence (ODT) model with detailed chemistry. Based on the Lagrangian tracer method and chemical explosive mode analysis (CEMA), diagnostic tools have been defined to distinguish the different scenarios of local extinction and re-ignition. The results show that the extinction regime can be characterized by a large negative Damköhler number based on CEMA. From Lagrangian investigation, two scenarios of local extinction, i.e., severe extinction with lower temperature and moderate extinction with higher temperature, are shown. Meanwhile, two re-ignition mechanisms are distinguished by the explosion index of the process prior to re-ignition. It is found that re-ignition mechanism through premixed flame propagation corresponds to a rather long preheat period with thermal runaway and high temperature explosion index, while re-ignition mechanism via independent flamelet corresponds to a high radical explosion index and small temperature gradient.