One-dimensional Turbulence Research Articles

Simulation of shock–turbulence interaction in non-reactive flow and in turbulent deflagration and detonation regimes using one-dimensional turbulence

The one-dimensional turbulence (ODT) methodology is extended to include an efficient compressible implementation and a model for capturing shock-induced turbulence is presented. Lignell et al. recently introduced a Lagrangian ODT implementation using an adaptive mesh. As the code operates in the incompressible regime (apart from constant-pressure dilatation) it cannot handle compressibility effects and their interactions with turbulence and chemistry. The necessary algorithmic changes to include compressibility effects are highlighted and our model for capturing shock–turbulence interaction is presented. To validate our compressible solver, we compare results for the Sod shock tube problem against a finite volume Riemann solver. To validate our model for shock–turbulence interaction, we present comparisons for a non-reactive and a reactive case. First, results of a shock traveling from light (air) to heavy (SF6) with reshock have been simulated to match mixing width growth data of experiments and turbulent kinetic energy results from LES. Then, for one-step chemistry calibrated to represent an acetylene/air mixture we simulate the interaction of a shock wave with an expanding flame front, and compare results with 2D simulation (2D-sim) data for flame brush formation and ensuing deflagration-to-detonation transitions (DDT). Results for the Sod shock tube comparison show that the shock speed and profile are captured accurately. Results for the non-reactive shock–reshock problem show that interface growth at all simulated Mach numbers is captured accurately and that the turbulent kinetic energy agrees in order of magnitude with LES data. The reactive shock tube results show that the flame brush thickness compares well to 2D-sim data and that the approximate location and timing of the DDT can be captured. The known sensitivity of DDT characteristics to details of individual flow realizations, seen also in ODT, implies that model agreement can be quantified only by comparing flow ensembles, which are presently unavailable other than in an ODT run-to-run sensitivity study that is reported herein.

A comparative study of thermochemistry models for oxy-coal combustion simulation

In this work, the One-Dimensional Turbulence (ODT) model is used to evaluate various thermochemistry models for capturing flame stand-off distance in oxy-coal combustion. In the gas phase, calculations made with detailed chemical kinetics are compared with results using an infinitely-fast (flame-sheet) chemistry model. Models for vaporization, devolatilization and char oxidation/gasification are incorporated for each Lagrangian coal particle. Two coal devolatilization models, namely a simple two-step Arrhenius and Chemical Percolation Devolatilization (CPD), are compared. The governing equations (mass, momentum and energy) are fully coupled between the particle and the gas phase. Flame stand-off distance determined by the simulation is compared with experimental results. Results show that the flame stand-off distance predicted by the infinitely-fast chemistry model is shorter than the prediction obtained by the detailed chemical kinetics model and that flame stand-off distance using two-step model is longer than the CPD model. Furthermore, it was observed that the minimum flame stand-off distance is determined by the devolatilization model and does not show sensitivity to the gas phase model. However, the shape of flame stand-off PDF is significantly altered by changing the gas-phase kinetic model.

Autoignition of n-heptane in a turbulent co-flowing jet

N-heptane autoignition in turbulent co-flowing jets with preheated air is studied using the one-dimensional turbulence (ODT) model. The simulations are designed to investigate the effects of molecular and turbulent transports on the process of autoignition. Both homogeneous and jet configuration simulations are carried out. The jet configurations are implemented at different jet inlet Reynolds numbers and for two air preheat conditions. Statistics for the cases considered show that, while the onset of autoignition may be delayed by turbulence, the eventual evolution of the volumetric heat release rate indicates that turbulence enhances the post-ignition stages. Since different regions of the mixture can have different ignition delays and may be characterized by one- or two-stage ignition, the autoignition process can be accelerated by ignition kernel propagation or the role of heat dissipation may be reduced through the prevalence of one-stage and two-stage ignitions in different regions of the mixture.

One-dimensional turbulence modeling of a turbulent counterflow flame with comparison to DNS

The one-dimensional turbulence (ODT) model is applied to a reactant-to-product counterflow configuration and results are compared with DNS data. The model employed herein solves conservation equations for momentum, energy, and species on a one dimensional (1D) domain corresponding to the line spanning the domain between nozzle orifice centers. The effects of turbulent mixing are modeled via a stochastic process, while the Kolmogorov and reactive length and time scales are explicitly resolved and a detailed chemical kinetic mechanism is used. Comparisons between model and DNS results for spatial mean and root-mean-square (RMS) velocity, temperature, and major and minor species profiles are shown. The ODT approach shows qualitatively and quantitatively reasonable agreement with the DNS data. Scatter plots and statistics conditioned on temperature are also compared for heat release rate and all species. ODT is able to capture the range of results depicted by DNS. However, conditional statistics show signs of underignition.

A numerical comparison of precipitating turbulent flows between large‐eddy simulation and one‐dimensional turbulence

This study presents the results of computational fluid dynamics simulations of a multiphase, reacting, turbulent mixing layer in an idealized geometry. The purpose is to compare large‐eddy simulation (LES) to one‐dimensional turbulence (ODT) and examine the trends of the flow under differing mixing conditions. Aqueous streams are mixed together to precipitate polymorphs of calcium carbonate. The polymorphs of calcium carbonate are tracked numerically using population balance equations (PBE). Each PBE contains all of the relevant physical models to track the particle evolution including nucleation, growth, and aggregation. A simple subgrid mixing model that is convenient for use with PBEs was implemented in the LES code. The higher spatial resolution achievable with ODT allowed an investigation on the effect of resolution on the mixing‐model error. The Reynolds number of the flow is varied and is shown to cause a decrease in average particle sizes with higher mixing rates. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3185–3197, 2015

Timestep Buffering to Preserve the Well-Mixed Condition in Lagrangian Stochastic Simulations

Using one or more physical time scales as a basis for timestep (\(\Delta t\)) selection is common in Lagrangian stochastic simulations of particle dispersion. This approach generally works well when the velocity statistics (and thus \(\Delta t\)) vary slowly but problems such as the \(\Delta t\) bias and imbalanced particle fluxes at interfaces can occur when the velocity statistics vary rapidly. These problems can result in violations of the well-mixed condition (WMC) and inaccurate predictions. An additional problem is that unrealistically high (or rogue) particle velocities can occur if \(\Delta t\) is too large. A small constant timestep can be used to reduce or eliminate these problems but incurs the penalty of considerable computational cost. A timestep-buffering technique that eliminates abrupt changes in a variable timestep through linear interpolation is demonstrated to be effective at satisfying the WMC and minimizing rogue velocities for particle dispersion in an idealized one-dimensional turbulence regime with a steep gradient. The technique is also shown to be effective when applied to a more realistic three-dimensional system.

Anomalous velocity fluctuation in one-dimensional defect turbulence.

In this paper various eccentric hole dynamics are presented in defect turbulence of the one-dimensional complex Ginzburg-Landau equation. Each hole shows coherent particlelike motion with nonconstant velocity. On the other hand, successive hole velocities without discriminating each hole exhibit anomalous intermittent motions being subject to multi-time-scale non-Gaussian statistics. An alternate non-Markov stochastic differential equation is proposed, by which all these observed statistical properties can be described successfully.

A new continuum approach for nonlinear kinetic simulation and transport analysis

A numerical code based on the I-transform approach is developed to solve the nonlinear Vlasov equation and carry out the transport analysis. The numerical results given by the I-transform approach agree with the conservative semi-Lagrangian approach in the Landau damping case and the bump-on-tail instability case. The diffusivities induced by the random fields and the quasilinear transport are also successfully demonstrated by using the new approach. It is found that the nonlinear transport in the one-dimensional Langmuir turbulence cannot be well-described by a simple diffusion model, due to the strong particle trapping at the nonlinear stage.

Principal component transport in turbulent combustion: A posteriori analysis

This paper presents a posteriori validation of the solution of a turbulent combustion problem based on the transport of principal components (PCs). The PCs are derived from a priori principal component analysis (PCA) of the same composition space. This analysis is used to construct and tabulate the PCs’ chemical source terms and diffusion coefficients in terms of the PCs using artificial neural networks (ANN). The a posteriori validation is implemented on a stand-alone one-dimensional turbulence (ODT) simulation of Sandia Flame F resulting in a very good reconstruction of the original thermo-chemical scalars profiles with 3 PCs at different downstream distances.

The reconstruction of thermo-chemical scalars in combustion from a reduced set of their principal components

We compare two reconstruction approaches for thermo-chemical scalars (TCSs) in turbulent combustion using principal component analysis. The first approach is based on the inversion of the linear relation between the TCSs and their principal components (PCs). The second is based on a regression of TCSs with a reduced set of the PCs using artificial neural networks. The study is based on one-dimensional turbulence simulation data of Sandia Flame F. We find that regression potentially offers superior reconstruction to the inversion expression when a truncated set of the original PCs is used.

Simulation of Ethylene Wall Fires Using the Spatially-Evolving One-Dimensional Turbulence Model

The mechanism of flame propagation in fuel beds of wildland fires is important to understand in order to quantify fire spread rates. Fires spread by radiative and convective heating and in some cases require direct flame contact to achieve ignition. The flame in an advancing fire is unsteady and turbulent, making study of intermittent flames in complex fuels difficult. A 1.83 m tall, 0.61 m wide vertical wall fire, in which ethylene fuel is slowly fed through a porous ceramic, is modeled to investigate unsteady turbulent flames in a controlled environment. Three fuel flow rates of 235, 390, and 470 L/min are considered. Simulations of this configuration are performed using a spatial formulation of the one-dimensional turbulence (ODT) model which is able to resolve individual flames (a key property of this model) and has been shown to provide turbulent statistics that compare well with experimental data for a number of flow configurations including wall fires. In the ODT model diffusion–reaction equations are solved along a notional line of sight perpendicular to the wall that is advanced vertically. Turbulent advection is modeled through stochastic domain mapping processes. A new Darrieus–Landau combustion instability model is incorporated in the ODT eddy selection process. The ODT model is shown to capture the evolution of the flame and describe the intermittent properties at the flame/air interface. Simulations include radiation and soot effects and are compared to experimental temperature measurements. Simulated mean temperatures differ from the experiments by an average of 63 K over all measurement points for the three fuel flow rates. Predicted root mean square temperature fluctuations capture the trends in the experimental data, but overestimate the raw experimental values by a factor of two. This difference is discussed using thermocouple response and heat transfer correction models. Simulated velocity, soot, and radiation properties are also reported.

Particle dispersion in homogeneous turbulence using the one-dimensional turbulence model

Lagrangian particle dispersion is studied using the one-dimensional turbulence (ODT) model in homogeneous decaying turbulence configurations. The ODT model has been widely and successfully applied to a number of reacting and nonreacting flow configurations, but only limited application has been made to multiphase flows. Here, we present a version of the particle implementation and interaction with the stochastic and instantaneous ODT eddy events. The model is characterized by comparison to experimental data of particle dispersion for a range of intrinsic particle time scales and body forces. Particle dispersion, velocity, and integral time scale results are presented. The particle implementation introduces a single model parameter βp, and sensitivity to this parameter and behavior of the model are discussed. Good agreement is found with experimental data and the ODT model is able to capture the particle inertial and trajectory crossing effects. These results serve as a validation case of the multiphase implementations of ODT for extensions to other flow configurations.

Prediction of oxy-coal flame stand-off using high-fidelity thermochemical models and the one-dimensional turbulence model

An Eulerian one-dimensional turbulence (ODT) model is applied to simulate oxy-coal combustion, with specific aim at predicting flame stand-off distances. Detailed gas-phase chemical kinetics based on the GRI3.0 mechanism are utilized. A high-fidelity model for devolatilization is considered that predicts evolution of several light gas species as well as char as products of devolatilization. The mass, momentum and energy governing equations are fully coupled between the particle and the gas phase. Likewise, char oxidation and gasification are both considered. Results indicate that char oxidation and gasification are both significant during the later stages of devolatilization. The impact of radiative temperature and mixing rate on oxy-coal flame is simulated and discussed where flame stand-off is used as a metric to compare the simulation prediction with experimental data. The data show evidence that there is kinetic limitation to the flame standoff distance. Finally, results show that ODT can provide quantitative agreement with experimental data in predicting flame standoff in oxy-coal jet flames.

Universality of Modal Time Correlation Functions in Medium Scale

We investigate the universality of modal time correlation functions using a closure equation for the normalized dimensionless time correlation function. As a candidate for a new universal function for turbulence, we propose a solution to the closure equation in the case of the critical value of the wavenumber, at which the decay form of the time correlation function changes from exponential to oscillatory exponential. The solution is compared with the normalized dimensionless time correlation functions obtained from numerical results for one-dimensional turbulence, such as the Kuramoto–Sivashinsky equation and that obtained from the direct interaction approximation for three-dimensional Navier–Stokes turbulence. As a result of the comparison, we provide evidence to show that the normalized dimensionless time correlation function is universal in the case of the critical value of the wavenumber.

New type of anomaly in turbulence.

The turbulent energy flux through scales, ε̅, remains constant and nonvanishing in the limit of zero viscosity, which results in the fundamental anomaly of time irreversibility. It was considered straightforward to deduce from this the Lagrangian velocity anomaly, ⟨du(2)/dt⟩=-4ε̅ at t=0, where u[over →] is the velocity difference of a pair of particles, initially separated by a fixed distance. Here we demonstrate that this assumed first taking the limit t→0 and then ν→0, while a zero-friction anomaly requires taking viscosity to zero first. We find that the limits t→0 and ν→0 do not commute if particles deplete (accumulate) in shocks backward (forward) in time on the viscous time scale. We compute analytically the resultant Lagrangian anomaly for one-dimensional Burgers turbulence and find it completely altered: ⟨du(2)/dt⟩ has different values forward and backward in time. For incompressible flows, on the other hand, we show that the limits commute and the Lagrangian anomaly is still induced by the flux law, apparently due to a homogeneous distribution of fluid particles at all times.

PRODUCTION OF FINE STRUCTURES IN TYPE III SOLAR RADIO BURSTS DUE TO TURBULENT DENSITY PROFILES

Magnetic reconnection events in the corona release energetic electron beams along open field lines, and the beams generate radio emission at multiples of the electron plasma frequency f{sub p} to produce type III solar radio bursts. Type III bursts often exhibit irregularities in the form of flux modulations with frequency and/or local temporal advances and delays, and a type IIIb burst represents the extreme case where a type III burst is fragmented into a chain of narrowband features called striae. Remote and in situ spacecraft measurements have shown that density turbulence is ubiquitous in the corona and solar wind, and often exhibits a Kolmogorov power spectrum. In this work, we numerically investigate the effects of one-dimensional macroscopic density turbulence (along the beam direction) on the behavior of type III bursts, and find that this turbulence produces stria-like fine structures in the dynamic spectra of both f{sub p} and 2 f{sub p} radiation. Spectral and temporal fine structures in the predicted type III emission are produced by variations in the scattering path lengths and group speeds of radio emission, and in the locations and sizes of emitting volumes. Moderate turbulence levels yield flux enhancements with much broader half-power bandwidths in f{submore » p} than 2 f{sub p} emission, possibly explaining the often observed type IIIb-III harmonic pairs as being where intensifications in 2 f{sub p} radiation are not resolved observationally. Larger turbulence levels producing trough-peak regions in the plasma density profile may lead to broader, resolvable intensifications in 2 f{sub p} radiation, which may account for the type IIIb-IIIb pairs that are sometimes observed.« less

Comparison of one-dimensional turbulence and direct numerical simulations of soot formation and transport in a nonpremixed ethylene jet flame

Accurate models of soot formation in turbulent flames are important for correctly predicting and simulating flames and fires. Modeling soot formation and transport is challenging due to the complex chemical formation processes, and differential diffusion of soot relative to a flame. Direct numerical simulations (DNS) have highlighted the importance of such transport on soot concentrations, however DNS is computationally expensive. The one-dimensional turbulence (ODT) model is able resolve a full range of length and timescales and solves the evolution of diffusive and reactive scalars in the natural physical coordinate. We present results of soot formation in ODT and compare the model to simulation results from DNS in a temporally-evolving planar ethylene jet flame where the same transport, thermodynamic, and kinetic models are applied. Good agreement is found for the jet evolution in terms of the mixture fraction profiles. Conditional soot statistics (mean and fluctuations) are presented, along with joint soot-mixture fraction PDFs that illustrate the location and motion of soot in the mixture fraction coordinate. Good qualitative agreement between the models is found and the soot behavior is similar. While the ODT cannot capture three-dimensional flow structures, the ODT simulations are less computationally expensive than the DNS suggesting its use in conjunction with DNS for parametric study, model validation, and investigation at parameter ranges not currently available to DNS.

On the application of a new formulation of nonlinear eddy viscosity based on anisotropy to numerical ocean models

The present paper explores the derivation of an alternative nonlinear eddy viscosity formulation based on Reynolds stress anisotropy and its implementation to numerical ocean models. This formulation takes into account the vorticity in addition to the mean strain rate. The proposed formulation does not include the stability function method which is a common approach in eddy viscosity calculations used in the present state-of-the-art numerical ocean models. Instead, it depends on the second invariant of anisotropy. Initially, the performance of the formulation is checked through a simple channel flow simulation. Consequently for model calibration, an idealised experiment of mixed-layer entrainment into stably stratified flow has been simulated and compared to empirical data. For sensitivity studies related to shear and stable stratification, concept of steady-state Richardson number is applied for homogeneous shear layer. Finally, the performance of the new formulation is tested by implementing it into one-dimensional General Ocean Turbulence Model. Furthermore, a realistic oceanic test case of a storm has been investigated considering different physical processes for the Fladenground Experiment (FLEX’ 76) in the northern North Sea and the results have been compared to the measured data. The main results signify that the overall performance of the nonlinear eddy viscosity model with a different value of steady-state Richardson number is as good as the Mellor–Yamada model in terms of predictability, and the eddy viscosity and diffusivity profiles follow the principle of law of the wall. Additionally, the present formulation does not require computing the stability functions and the ease of implementation into numerical ocean models gives the present formulation an upper hand over the existing formulations in the field of turbulence modelling in oceanography.

Multiscale eddy simulation for moist atmospheric convection: Preliminary investigation

A multiscale computational framework is designed for simulating atmospheric convection and clouds. In this multiscale framework, large eddy simulation (LES) is used to model the coarse scales of 100 m and larger, and a stochastic, one-dimensional turbulence (ODT) model is used to represent the fine scales of 100 m and smaller. Coupled and evolving together, these two components provide a multiscale eddy simulation (MES). Through its fine-scale turbulence and moist thermodynamics, MES allows coarse grid cells to be partially cloudy and to encompass cloudy–clear air mixing on scales down to 1 m; in contrast, in typical LES such fine-scale processes are not represented or are parameterized using bulk deterministic closures. To illustrate MES and investigate its multiscale dynamics, a shallow cumulus cloud field is simulated. The fine-scale variability is seen to take a plausible form, with partially cloudy grid cells prominent near cloud edges and cloud top. From earlier theoretical work, this mixing of cloudy and clear air is believed to have an important impact on buoyancy. However, contrary to expectations based on earlier theoretical studies, the mean statistics of the bulk cloud field are essentially the same in MES and LES; possible reasons for this are discussed, including possible limitations in the present formulation of MES. One difference between LES and MES is seen in the coarse-scale turbulent kinetic energy, which appears to grow slowly in time due to incoherent stochastic fluctuations in the buoyancy. This and other considerations suggest the need for some type of spatial and/or temporal filtering to attenuate undersampling of the stochastic fine-scale processes.

Effects of Fuel-Side N2, CO2, H2O Dilution on Combustion Characteristics and NOx Formation of Syngas Turbulent Nonpremixed Jet Flames

The effects of the three fuel-side diluents N2, CO2, and H2O on the accurate flame structure and NOx formation characteristics of the turbulent syngas nonpremixed flames are investigated using the one-dimensional-turbulence (ODT) model. For nonpremixed flames, the fuel mixtures consist of H2, CO and three diluents: N2, H2O, and CO2. The proportion of diluents is varied from 10% to 30% while the H2/CO ratio is kept as a constant at 0.75 all the time. Mass fraction of main species and temperature of 30% N2 basic dilution case predicted by the ODT model are compared with the tests measuring results obtained by International Workshop on Measurements and Computation of Turbulent Nonpremixed Flames, and it is found that the results are in good agreement. Numerical results indicate that the CO2 diluted flames have the largest reduction on flame temperature as well as the NOx emission, while H2O is more effective than N2. For CO2 and H2O dilution flames, flame structure becomes unstable with an obvious lift phenomenon. Since ODT captures the flame extinction process, flames added with CO2 and H2O not only have a lower extinction temperature but also the reignition process is slower.