Scalar Dissipation Research Articles

Large Eddy Simulation of a turbulent lifted flame using multi-modal manifold-based models: Feasibility and interpretability

A general model for multi-modal turbulent combustion is achievable with two-dimensional manifold equations that use the mixture fraction and a generalized progress variable as coordinates. Information about the underlying mode of combustion is encoded in three scalar dissipation rates that appear as parameters in the two-dimensional equations. In this work, Large Eddy Simulation (LES) of a multi-modal turbulent lifted hydrogen jet flame in a vitiated coflow is performed using this new turbulent combustion model, leveraging both convolution-on-the-fly and In-Situ Adaptive Tabulation for computational tractability. The simulation predicts a lifted flame consistent with observations from past experiments. The feasibility of such a model implemented in LES is examined, and the cost per timestep is found to be comparable to conventional one-dimensional manifold-based models describing one asymptotic mode of combustion. Additionally, the model provides clear interpretability, allowing for combustion mode analysis to be performed with ease by evaluating the scalar dissipation rates and generalized progress variable source term. This analysis is used to show that the flame is stabilized by autoignition and has a trailing nonpremixed flame. Furthermore, transport of progress variable from the most reactive mixture fraction towards richer mixtures at the centerline is found to be important.

Single-shot imaging of major species and OH mole fractions and temperature in non-premixed H2/N2 flames at elevated pressure

Simultaneous, single-shot imaging of all major species (N2, O2, H2, and H2O), OH, temperature, and mixture fraction is demonstrated for the first time in H2N2 non-premixed jet flames at 12 bar. The spatial distribution of mole fraction is obtained for the four major species by recording images of Raman scattering on four separate back-illuminated CCD cameras. The available field-of-view is 25(H) × 8(V) mm2. Temperature and mixture fraction are derived from Raman scattering images. Images of OH fluorescence intensity are recorded using OH-PLIF and are converted into OH mole fraction by calculating the Boltzmann population distribution and the quenching rate accurately for each pixel. Precision and accuracy are assessed by comparing 2-D Raman/OH-PLIF measurements in laminar flames to 1-D flame computations accounting for differential diffusion. Single-shot precision on N2, O2, H2, and temperature is better than 5%. It is better than 6% and 10% for H2O and OH, respectively. Accuracy lies within these values, except for H2O with 10%. Such good performance of Raman imaging is attributed to (a) the use of non-intensified CCD cameras, (b) wavelet adaptive thresholding (WATR) image denoising, (c) rejection of flame luminosity by a Pockels cell electro-optical shutter with 500 ns gating, and (d) elevated pressure that boosts the Raman signal intensity. Measurements in a turbulent flame (3.6N2:H2 by vol. and Re = 29,000) show that most of the flame's thermochemical structure is accurately captured by unity Lewis number computations, suggesting that effects of differential diffusion are less important above some Reynolds number. This is consistent with expectations and it engenders confidence in the Raman imaging technique. Because images of both mixture fraction and OH mole fraction are available, it is also possible to reconstruct a more accurate scalar dissipation rate by projection onto the 2-D flame front normal.

A shock-stable modification of the HLLC Riemann solver with reduced numerical dissipation

The purpose of this paper is twofold. First, the application of high-order methods in combination with the popular HLLC Riemann solver demonstrates that the grid-aligned shock instability can strongly affect simulation results when the grid resolution is increased. Beyond the well-documented two-dimensional behavior, the problem is particularly troublesome with three-dimensional simulations. Hence, there is a need for shock-stable modifications of HLLC-type solvers for high-speed flow simulations.Second, the paper provides a stabilization of the popular HLLC flux based on a recently proposed mechanism for grid aligned-shock instabilities Fleischmann et al. (2020) [8]. The instability was found to be triggered by an inappropriate scaling of acoustic and advection dissipation for local low Mach numbers. These low Mach numbers occur during the calculation of fluxes in transverse direction of the shock propagation, where the local velocity component vanishes. A centralized formulation of the HLLC flux is provided for this purpose, which allows for a simple reduction of nonlinear signal speeds. In contrast to other shock-stable versions of the HLLC flux, the resulting HLLC-LM flux reduces the inherent numerical dissipation of the scheme.The robustness of the proposed scheme is tested for a comprehensive range of cases involving strong shock waves. Three-dimensional single- and multi-component simulations are performed with high-order methods to demonstrate that the HLLC-LM flux also copes with latest challenges of compressible high-speed computational fluid dynamics.

Conditional scalar dissipation rate modeling for turbulent spray flames using artificial neural networks

Machine learning techniques have been used for the closure of the conditional scalar dissipation rate in turbulent spray flames. Statistical data are extracted from carrier-phase direct numerical simulation (CP-DNS) results for the generation of artificial neural networks that are trained to predict the conditional scalar dissipation rate such that they could serve as a sub-grid model for large eddy simulations of spray combustion. A quantitative error assessment suggests that predictions of the conditionally averaged dissipation rate are in excellent agreement with CP-DNS data. Further comparison with commonly used models for the unconditionally filtered dissipation rate promises significant improvements if ANNs are used for closure. The artificial neural networks also help to identify the important features that affect the local dissipation rates. The results suggest that few - mostly droplet related - parameters suffice as input features for accurate ANNs. This is in contradiction to standard modeling techniques that are solely based on gas phase properties and highlights the need to revisit scalar dissipation rate modeling for spray flames if analytical expressions are to be used.

Effects of Fuel Lewis Number on the Near-wall Dynamics for Statistically Planar Turbulent Premixed Flames Impinging on Inert Cold Walls

ABSTRACT The flame-wall interaction in a quasi-steady configuration, where a statistically planar premixed flame is pushed by the inflow of unburned reactants and stabilizes at a distance away from the wall, has been analyzed for different fuel Lewis numbers and inlet turbulence intensities. The extent of flame-wall interaction has been found to increase with increasing inlet turbulence intensity and increasing fuel Lewis number due to the greater extent of flame wrinkling and smaller flame stabilization distance from the wall, respectively. The increasing trend of turbulent flame speed with decreasing fuel Lewis number and increasing inlet turbulence intensity act to increase the wall heat flux magnitude. However, the quenching distance remains comparable to the quenching distance predicted by one-dimensional conventional head-on quenching simulations. It has been found that the wall Stanton number and the skin friction coefficient are of the same order of magnitude, but the Reynolds-Colburn analogy does not remain strictly valid in the case of flame-wall interaction in this configuration. For a given value of bulk mean inlet velocity to laminar burning velocity ratio, the flames with smaller stabilize further away from the wall due to their higher turbulent flame speed and thus the flame-wall interaction events are less frequent for small values of . The drops in temperature and reaction rate magnitude lead to reductions in the values of dilatation rate, normal strain rate, and flame displacement speed in the flame quenching zone; with the increased likelihood of finding negative values for these quantities in the near-wall region. The decrease in displacement speed with decreasing wall-normal distance leads to predominantly positive normal strain rates induced by flame propagation in the quenching zone. These behaviors act to reduce the magnitude of the reaction progress variable gradient in the quenching zone, which has implications on the behaviors of the Flame Surface Density and scalar dissipation rate in the near-wall region.

Investigation of the ignition processes of a multi-injection flame in a Diesel engine environment using the flamelet model

In this work, the first flamelet analysis is conducted of a highly resolved DNS of a multi-injection flame with both auto-ignition and ignition induced by flame-flame interaction. A novel method is proposed to identify the different combustion modes of ignition processes using generalized flamelet equations. The state-of-the-art DNS database generated by Rieth et al. (US National Combustion Meeting, 2019) for a multi-injection flame in a Diesel engine environment is investigated. Three-dimensional flamelets are extracted from the DNS at different time instants with a focus on auto-ignition and interaction-ignition processes. The influences of mixture field interactions and the scalar dissipation rate on the ignition process are investigated by varying the species composition boundary conditions of the transient flamelet equations. Budget analyses of the generalized flamelet equations show that the transport along the mixture fraction iso-surface is insignificant during the auto-ignition process, but becomes important when interaction-ignition occurs, which is further confirmed through a flamelet regime classification method.

Hierarchical model form uncertainty quantification for turbulent combustion modeling

All models invoke assumptions that result in model errors. The objective of model form uncertainty quantification is to translate these assumptions into mathematical statements of uncertainty. If each assumption in a model can be isolated, then the uncertainties associated with each assumption can be independently assessed. In situations where a series of assumptions leads to a hierarchy of models with nested assumptions, physical principles from a higher-fidelity model can be used to directly estimate a physics-based uncertainty in a lower-fidelity model. Turbulent nonpremixed combustion models fall into a natural hierarchy from the full governing equations to Conditional Moment Closure to flamelet-like models to thermodynamic equilibrium, and, at each stage of the hierarchy, a single assumption can be isolated. In this work, estimates are developed for the uncertainties associated with each assumption in the hierarchy. The general method identifies a trigger parameter that can be obtained with information only from the lower-fidelity model that is used to estimate the error in the lower-fidelity model using only physical principles from the higher-fidelity model. Starting from the lowest fidelity model, the trigger parameters identified in this work are the product of a chemical time scale and the scalar dissipation rate for the equilibrium chemistry model, which characterizes the errors associated with neglecting finite-rate chemistry and transport; the reciprocal of the product of a generalized Lagrangian flow time and the scalar dissipation rate for the steady flamelet model, which characterizes the errors associated with neglecting flow history effects; and the relative magnitude of the conditional fluctuations for Conditional Moment Closure. The approach is applied in LES to a turbulent nonpremixed simple jet flame to quantify the errors associated with the equilibrium chemistry model and the steady flamelet model. The results indicate that errors associated with neglecting finite-rate chemistry and transport in the equilibrium chemistry model are dominant upstream while errors associated with neglecting flow history in the steady flamelet model become more important downstream.

High-resolution velocity measurements in turbulent premixed flames using wavelet-based optical flow velocimetry (wOFV)

Wavelet-based optical flow velocimetry (wOFV) is used to estimate two-dimensional velocity fields from tracer particle images acquired simultaneously with CH PLIF imaging within two highly turbulent premixed methane-air flames. Unlike conventional correlation-based PIV approaches, the current wOFV approach yields a dense (i.e. one vector per pixel) estimation of the velocity field which offers the possibility of greatly enhanced spatial resolution as compared to correlation-based PIV. Results from the wOFV method and correlation-based PIV are directly compared in terms of instantaneous fields, flow statistics, energy spectra, and derived gradient quantities such as vorticity and 2D strain rate. An assessment of the results indicates an increase in spatial resolution and dynamic range of almost one order-of-magnitude when using wOFV as compared to high-resolution PIV. In fact, the use of wOFV permits resolution of the smallest dissipative scales within the premixed flames with turbulent Reynolds numbers of O(104). A particular focus concerns velocity measurements near and within the CH layers, which are excellent markers of the local flame front but are spatially narrow and intermittent. The high-resolution velocity results from the wOFV method provide an opportunity for improved velocity estimations, derivative quantities, and their statistical characterization at and near the flame front.

Large eddy simulations of the UMD line burner with the conditional moment closure method

The conditional moment closure (CMC) method is applied in combination with large eddy simulations (LES-CMC) to the UMD line burner configuration. This corresponds to a low-strain, buoyant diffusion flame. The low strain rate conditions are representative of fire conditions and the aim of the study is to evaluate LES-CMC results, including radiative effects. Only conditions far from extinction are studied. The weighted sum of grey gases model (WSGGM) for radiation is applied in mixture fraction space. Results are compared to what is obtained when radiation is taken into account as a local loss term in the conditional heat release rate, with prescribed radiative fraction. It is shown that the conditional scalar dissipation rate (CSDR) profile in mixture fraction space and the spatial terms in the transport equations for the conditional quantities have a major impact with the non-local WSGGM approach, while this is not the case in adiabatic simulations, nor in the radiative fraction approach. In the latter, only the value of the CSDR at stoichiometric is important, making this approach less sensitive. However, the latter are not well suited for extinction simulations.

Near-interface flow modeling in large-eddy simulation of two-phase turbulence

The smallest hydrodynamic length scales in two-phase turbulence are located at the interface between phases, or fluids, as a result of two-way coupling phenomena. Typically, these interface-generated scales are several times smaller than the dissipative scales in the surrounding bulk flow identified by Kolmogorov’s 1941 theory. Consequently, to properly capture these interface-generated small scales with sufficiently fine resolutions, the computational cost of performing large-eddy simulations of two-phase turbulent flow increases significantly from its (single-phase) theoretical optimum and toward values on the order of the direct numerical simulation of turbulence. Therefore, to maintain the cost of scale-resolving approaches linear with respect to the Reynolds number, this work investigates the modeling of the small-scale fluid motions in the vicinity of the viscous near-interface region of two-phase turbulent flows. Given the resemblance between the flow structures in the near-interface regions and those found in the boundary layers of turbulent wall-bounded flow, the modeling methodology proposed is inspired by ideas developed for turbulent flows interacting with solid walls, but modified to capture slip-velocity effects between phases. The performance of the approach is a priori assessed by utilizing data from direct numerical simulations of decaying isotropic turbulence laden with droplets of super-Kolmogorov size, demonstrating its computational feasibility and potential for reducing the cost of large-eddy simulation studies of two-phase turbulence.

Effects of Solar Activity on Taylor Scale and Correlation Scale in Solar Wind Magnetic Fluctuations

Abstract The correlation scale and the Taylor scale are evaluated for interplanetary magnetic field fluctuations from two-point, single time correlation function using the Advanced Composition Explorer (ACE), Wind, and Cluster spacecraft data during the time period from 2001 to 2017, which covers over an entire solar cycle. The correlation scale and the Taylor scale are respectively compared with the sunspot number to investigate the effects of solar activity on the structure of the plasma turbulence. Our studies show that the Taylor scale increases with the increasing sunspot number, which indicates that the Taylor scale is positively correlated with the energy cascade rate, and the correlation coefficient between the sunspot number and the Taylor scale is 0.92. However, these results are not consistent with the traditional knowledge in hydrodynamic dissipation theories. One possible explanation is that in the solar wind, the fluid approximation fails at the spatial scales near the dissipation ranges. Therefore, the traditional hydrodynamic turbulence theory is incomplete for describing the physical nature of the solar wind turbulence, especially at the spatial scales near the kinetic dissipation scales.

Large Eddy Simulation of soot evolution in turbulent reacting flows: Strain-Sensitive Transport Approach for Polycyclic Aromatic Hydrocarbons

Polycyclic Aromatic Hydrocarbons (PAH) are confined to spatially intermittent regions of low scalar dissipation rates due to their slow formation chemistry. The length scales of these regions are on the order of the Kolmogorov scale or smaller, where molecular diffusion dominates over turbulent mixing irrespective of the large-scale turbulent Reynolds number. A strain-sensitivity parameter is proposed to identify such species. A Strain-Sensitive Transport Approach (SSTA) is then developed to model this differential transport in the nonpremixed flamelet equations. Specifically, the strain-sensitive species are modeled with their non-unity molecular effective Lewis numbers, while the remaining species are modeled with unity effective Lewis numbers. An a priori analysis of nonpremixed flamelet solutions reveals that the flame temperature and strain-insensitive species (e.g., major products of combustion, acetylene, etc.) profiles from the proposed SSTA closely match those from the unity effective Lewis number approach, but the mass fractions of strain-sensitive species (e.g., naphthalene) are significantly modified compared to the unity effective Lewis number approach and are consistent with Direct Numerical Simulation (DNS) data. This new SSTA model is implemented within a Large Eddy Simulation (LES) framework, applied to a series of laboratory-scale turbulent nonpremixed sooting jet flames, and validated via comparisons with experimental measurements of temperature and soot volume fraction. Both the unity effective Lewis number approach and SSTA model provide temperature predictions in good agreement with the experimental data, but the non-unity molecular effective Lewis number approach overpredicts the flame length. Compared to the unity effective Lewis number approach, the spatial distribution of soot volume fraction predicted by SSTA is in better agreement with the experimental measurements in terms of the upstream growth of the soot volume fraction and the location of its peak value along the centerline, both of which strongly depend on accurate predictions of the PAH mass fraction. The maximum soot volume fraction is minimally influenced and in good agreement with the experimental measurements. Finally, with this new SSTA model, the influence of global strain rate on turbulent nonpremixed sooting jet flames is analyzed to find that, even though PAH is inversely proportional to the global strain rate, the soot volume fraction may not be inversely proportional to the global strain rate due to an increase in the acetylene surface growth rate coefficient with global strain rate.

Fast Mixing in Heterogeneous Media Characterized by Fractional Derivative Model

This study aims at investigating non-Fickian temporal scaling of fast mixing processes using fractional advection dispersion equation (FADE) model in Indiana carbonate, multi-lognormal hydraulic conductivity field, self-affine fractures and cemented porous media, in which the fundamental solution of the FADE model is a standard symmetric Levy stable distribution. The temporal scaling of the scalar dissipation rate (SDR) induced by the FADE model is a function of fractional derivative order $$\alpha$$ , $$\chi (t) \sim t^{{ - \frac{\alpha + 1}{\alpha }}}$$ ( $$1 \le \alpha \le 2$$ ), and it reduces to the Fickian scaling $$t^{{ - \frac{3}{2}}}$$ when $$\alpha = 2$$ . Smaller values of $$\alpha$$ reflect more efficient and a better mixing state at early time. The fitted results show that the FADE model is much more accurate than the traditional model, which can also well interpret the fast mixing scaling from clearer physical mechanism than the empirical power law fitting line. The fitted values of $$\alpha$$ capture the complexity of the heterogeneous media, which are consistent with the existing empirical results. Thus, the SDR of the FADE model is feasible to describe the temporal scaling of the fast mixing for the tracer transport in heterogeneous media.

Automated identification and characterization method of turbulent bursting from single-point records of the velocity field

A new automated method capable of accurately identifying bursting periods in single-point turbulent velocity field records is presented. Manual selection of the method sensitivity and threshold are necessary for effective discrimination between burst periods and the background turbulent flow fluctuations (burst-free periods). The flow characteristic used for identification is the normalized ‘instantaneous’ TKE dissipation rate levels, calculated using sliding window averaging. Use of the record root mean square and average values for normalization eliminates the need for definition of a physics-based flow-specific threshold. Instead, the suitable sensitivity range and the threshold parameters are selected based on preliminary examination of the velocity records. This, potentially, makes the method applicable for use across various flow fields, especially as it does not require resolving the burst-generation mechanism. The method performance is examined using a field obtained dataset of buoyancy driven turbulent boundary layer flow. Here, the selection of a two-fold increase is used and the sensitivity of the method is examined. Spectral shapes of non-bursting periods show distinguished similarity to those of the Kolmogorov theory, while the bursting period spectral shapes vary significantly. Low-resolution records of temperature fluctuations were observed to exhibit a significant decrease in temperature (scalar) dissipation rate during bursting periods. Based on this observation and additional processing, a statistical examination of temperature (scalar) dissipation rate is presented along with a normalization procedure. Future examination of additional scalar variations, i.e. particulate matter and/or gaseous pollutant concentrations, in connection with turbulent bursting periods can assist in further understanding of bursting generation and scalar transfer processes.

Shot noise multifractal model for turbulent pseudo-dissipation

Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully discussed in the literature. Here a causal lognormal stochastic process is built to represent the dynamics of pseudo-dissipation in a Lagrangian trajectory. It is introduced as the solution of a stochastic differential equation, driven by a source of noise which has sudden jumps at periodic intervals, its period being the dissipative time scale of the flow. This random field has scale invariance for a continuum of scales, and displays discontinuous jumps in time, with a smooth time evolution below the Kolmogorov scale. Its multifractal and correlation properties are demonstrated numerically.

Dynamics of a long chain in turbulent flows: impact of vortices.

We show and explain how a long bead-spring chain, immersed in a homogeneous isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of three-dimensional (3D) turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In the 3D case on the contrary, the chain is extended even in vortical regions, which suggests that the chain follows axially stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly flexible, inextensible chain also shows preferential sampling in three dimensions, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in two dimensions is considerably reduced. In three dimensions, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Analytical and numerical study of near-field ignition of H2/air by injection of hot gas

Ignition initiation by a turbulent hot jet involves complex transport and chemical processes with disparate and sensitive time scales. Its understanding is important for improved ignition in advanced and novel combustion engines and in ignition avoidance for explosion safety measures. This study is aimed at the modeling of turbulent hot jet ignition of stoichiometric hydrogen-air mixture with fast chemistry and short chemical time scales relative to the large-scale mixing time scales. The evolution of jet mixture fraction in the near-field shear layer of a suddenly-starting turbulent jet is analytically modeled and calibrated by large-eddy simulation of the reacting fluid. When integrated with a correlation for instantaneous chemical induction time, the model estimates the radial location and the timing of ignition as the jet travels in the streamwise direction. The estimation includes accounting for the role of the scalar dissipation rate in the suppression of ignition. The radial location of ignition migrates towards the jet centerline with time, migrating faster for higher injection temperatures and much slower for leaner ambient fuel-air ratios. The limitations of the present model are investigated by assessing the regions of mixing layer where strong diffusive transport collocates with the high production rate of active radicals. To complete the perspective into analytic modeling of transient jet ignition, other limitations associated with turbulent fluctuations and jet composition are discussed, as well as the role of near-field ignition relative to ignition at the jet tip or head vortex ring.

On dissipative gradient effect in higher-order strain gradient plasticity: the modelling of surface passivation

The phenomenological flow theory of higher-order strain gradient plasticity proposed by Fleck and Hutchinson (J. Mech. Phys. Solids, 2001) and then improved by Fleck and Willis (J. Mech. Phys. Solids, 2009) is used to investigate the surface-passivation problem and micro-scale plasticity. An extremum principle is stated for the theory involving one material length scale. To solve the initial boundary value problem, a numerical scheme based on the framework of variational constitutive updates is developed for the strain gradient plasticity theory. The main idea is that, in each incremental time step, the value of the effective plastic strain is obtained through the variation of a functional in regard to effective plastic strain, provided the displacement or deformation gradient. Numerical results for elasto-plastic foils under tension and bending, thin wires under torsion, are given by using the minimum principle and the numerical scheme. Implications for the role of dissipative gradient effect are explored for three non-proportional loading conditions: (1) stretch-passivation problem, (2) bending-passivation problem, and (3) torsion-passivation problem. The results indicate that, within the Fleck–Hutchinson–Willis theory, the dissipative length scale controls the strengthening size effect, i.e. the increase of initial yielding strength, while the surface passivation gives rise to an increase of strain hardening rate.

LES/PDF modeling of swirl-stabilized non-premixed methane/air flames with local extinction and re-ignition

Turbulent non-premixed flames with local extinction and re-ignition exhibit multiple combustion modes including ignition waves, diffusion flames, partially premixed flames, and ignition-assisted partially premixed flames. The mechanisms of local extinction and re-ignition are not well understood and numerical modeling of multi-mode combustion is a challenging task. In this work, a specially designed swirl-burner was used to study local extinction and re-ignition of non-premixed turbulent methane/air flames. High speed Particle Image Velocimetry (PIV) and laser induced fluorescence of OH radicals (OH-PLIF) measurements along with Large Eddy Simulation (LES) were carried out to investigate the mechanisms of extinction and re-ignition processes in the burner. LES is based on a transported probability density function model within the framework of Eulerian Stochastic Fields (PDF-ESF). It is found that local extinction occurs when the scalar dissipation rate around the stoichiometric mixture fraction is high. The characteristic time scale for local extinction and re-ignition in the present flames is an order of magnitude longer than the characteristic time scale of diffusion/extinction of laminar flamelets. There are two mechanisms for flame hole re-ignition in the present flames. First, under low degree of local extinction conditions (i.e., for small flame holes surrounded by flames) the flame hole re-ignition is due to the mechanism of turbulent flame folding. Second, under high degree of extinction conditions (i.e., with large regions of extinction and lifted flames), re-ignition of the locally extinguished flame is due to the mechanism of ignition assisted partially premixed flame propagation. The results show that the PDF-ESF model is capable of simulating the quenching and re-ignition process found in the experiments.

Small-Scale Analysis of Hydrodynamical Helicity Suppression in the Mean-Field Dynamo-Model

We compare the classical mean-field dynamo model proposed by Steenbeck, Krause, and Radler to describe the generation of large-scale magnetic fields and the Kazantsev model that describes the small-scale dynamo in an unbounded homogeneous and isotropic flow. We consider the subcritical regime of small magnetic Reynolds numbers whereby there is no rapid generation. The same regime can also be understood as a process in which the small-scale generation is stopped due to its intrinsic mechanisms. Within both approaches we examine what distinguishes the spectra of the linear and nonlinear processes under the suppression of hydrodynamic (kinetic) helicity or, in other words, compare the alpha-quenchings. We check whether averaging the induction equation over scales larger than the velocity field correlation length leads to the loss of any features in the spectrum near the dissipative scale. We study the various types of dynamo stabilization using which seems more justified physically than the standard alpha-quenching, but more difficult within large-scale models containing limited information about the random velocity field. In particular, we compare the integral suppression whereby the total energy is conserved and the spectral suppression that suggests the conservation of energy and helicity in each spectral shell without assuming their redistribution over the spectrum.