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We examine the effects of the history force on the preferential concentration of small particles in homogeneous isotropic turbulence under a wide range of the particle-to-fluid mass density ratio γ (from 0 to 10000) by direct simulations of the Navier–Stokes equations. As to the history integral kernel, we introduce two expressions: i.e., the classical Basset kernel valid only in the limit of creeping flow conditions and for short times, and the Mei–Adrian kernel (Mei and Adrian, 1992) applicable for finite Reynolds numbers and large times. It is revealed that the presence of the history force weakens the level of preferential concentration to some extent, specifically under the conditions of the mass density ratio of around 1. 5 – 10 for heavy particles (e.g., solid particles in liquid) and smaller than 0.7 for light particles (e.g., bubbles in liquid) and that the overprediction of particle accumulation by neglecting the history force is much more remarkable for light particles. A comparison between the Basset kernel and the Mei–Adrian kernel has shown that the Basset kernel overestimates the history effect but only slightly. [ABSTRACT FROM AUTHOR]

The burning rate in a spherically expanding turbulent premixed flame is explored using direct numerical simulations, and a model of ordinary differential equations is proposed. The numerical dataset, from a previous work, is obtained from direct numerical simulations of confined spherical flames in isotropic turbulence over a range of Reynolds numbers. We begin the derivation of the model with an equation for the burning rate for the domain under consideration, and using a thin flame assumption and a two-fluid approach, we find the normalized turbulent burning rate to be controlled by the increase in flame surface area due to turbulent wrinkling, and correction factor that is observed to be consistently less than unity. A Reynolds scaling hypothesis for the flame turbulent wrinkling from a previous work using the same numerical dataset is used to model the term controlling the increase in flame surface area. The correction factor is hypothesized to reflect flame stretch effects, and hence this factor is modeled using Markstein theory applied to global averaged quantities. The ordinary differential equations are rewritten to reflect easily observable quantities such as the chamber pressure and mean flame radius, and then expressed in dimensionless form to assess dependence on various dimensionless parameters. The model predictions are found to be in good agreement with the numerical data within expected variances. Additionally, Markstein theory is found to be sufficient in describing the effects of flame stretch in the turbulent premixed flames under consideration. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to provide a comparison between several finitevolume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

The aim of the present paper is to provide a comparison between several finitevolume methods of different numerical accuracy: the second-order Godunov method with PPM interpolation and the high-order finite-volume WENO method. The results show that while on a smooth problem the high-order method performs better than the second-order one, when the solution contains a shock all the methods collapse to first-order accuracy. In the context of the decay of compressible homogeneous isotropic turbulence with shocklets, the actual overall order of accuracy of the methods reduces to second-order, despite the use of fifth-order reconstruction schemes at cell interfaces. Most important, results in terms of turbulent spectra are similar regardless of the numerical methods employed, except that the PPM method fails to provide an accurate representation in the high-frequency range of the spectra. It is found that this specific issue comes from the slope-limiting procedure and a novel hybrid PPM/WENO method is developed that has the ability to capture the turbulent spectra with the accuracy of a high-order method, but at the cost of the second-order Godunov method. Overall, it is shown that virtually the same physical solution can be obtained much faster by refining a simulation with the second-order method and carefully chosen numerical procedures, rather than running a coarse high-order simulation. Our results demonstrate the importance of evaluating the accuracy of a numerical method in terms of its actual spectral dissipation and dispersion properties on mixed smooth/shock cases, rather than by the theoretical formal order of convergence rate.

Over the years, many facilities have been developed to study turbulent flowin the laboratory. Homogeneous isotropic turbulence (HIT) with zero mean flow provides a unique environment for investigating fundamental aspects and specific applications of turbulent flow. We provide an extensive overview of laboratory facilities that generate incompressible zero-mean-flow HIT using different types of actuators and configurations. Reviewed facilities cover a variety of geometries and sizes, as well as forcing style (e.g. symmetric versus asymmetric and unsteady versus steady). We divide facilities into four categories, highlighting links between their geometries and the statistics of the flows they generate. We then compare published data to uncover similarities and differences among various turbulence-generation mechanisms. We also compare the decay of turbulence in zero-mean-flow facilities with that observed in wind and water tunnels, and we analyse the connections between flow characteristics and physical aspects of the facilities. Our results emphasize the importance of considering facility geometry and size together with the strength and type of actuators when studying zero-mean-flow HIT. Overall, we provide insight into how to optimally design and build laboratory facilities that generate zero-mean-flow HIT. [ABSTRACT FROM AUTHOR]

The concept of vortex is crucial in both understanding and modeling of turbulence. For large eddy simulation (LES), the effect of small-scale eddies onto the large scales or the resolved flow field is modeled by subgrid stress models. Even though the rotating motions of fluids, i.e., vortices or eddies are central in developing turbulent models, vortex identification methods are seldom used in these models. In this study, we develop a new subgrid model based on the Liutex vector, a new quantity introduced to decompose fluid motions into rigid rotation, pure shear and stretching, and thus identify vortices. The new model is then applied in a decaying homogeneous isotropic turbulence (DHIT) and a turbulent channel flow at Reynolds number Reτ = 180. It is shown that the new model can predict accurate energy spectra compared with experiments in DHIT and give a well-matched velocity profile in turbulent channel flow without changing the form of the model. Future directions include improvement of the Liutex based model, for example developing anisotropic subgrid models, and its applications in various turbulent flows. [ABSTRACT FROM AUTHOR]

Analysis and optimization of the hybrid upwind-central numerical methods for modern versions of large eddy simulations (LESs) are presented herein. Optimization was performed based on examination of the characteristics of the spatial and temporal finite-volume approximations of the convective terms of filtered Navier–Stokes equations. A method for selecting level of subgrid viscosity that corresponds to the chosen numerical scheme and makes it possible to obtain an extended inertial interval of the energy spectrum is proposed. A series of LESs of homogeneous isotropic turbulence decay were carried out, and the optimal values of the subgrid model constants included in the hybrid shear stress transport delay detached eddy simulation (SST-DDES) method were determined. A procedure for generating a consistent initial field of subgrid parameters for these simulations is described. The three-stage explicit Runge–Kutta method was demonstrated to be sufficient for stable time integration, while the popular explicit midpoint method was not. The slope of the energy spectrum was shown to be almost independent of the central-difference scheme order and of the mesh spacing when the correct numerical method was applied. Numerical viscosity was found to become much greater than subgrid viscosity when the upwind scheme contributed about 10% or more to the convective flux approximation. [ABSTRACT FROM AUTHOR]

This work is related to the investigation of innovative stator designs aiming to reduce the dominant interaction noise in aeroengines. The study of turbulent structures definition is crucial for the accurate prediction of broadband noise radiation from passive treatments, as leading-edge serrations studied here. A modified Fourier modes-based methodology is proposed to obtain a fully three-dimensional incompressible turbulence field, while taking into account periodic and wall-boundary conditions. A low-noise geometry is examined along with the reference profile on a rectilinear seven-vane cascade rig using a hybrid computational fluid dynamics/computational aeroacoustics method. Numerically assessed noise reductions from the serrated airfoils are favorably compared with an analytical solution and a semi-empirical law. An overall sound power-level reduction around 4 to 6 dB is obtained at three acoustic certification points. Finally, the aerodynamic performances are also evaluated through Reynolds-averaged Navier-Stokes computations, and an improved variant of the initial treatment is proposed, allowing for acceptable penalties at the aerodynamic design point. [ABSTRACT FROM AUTHOR]

Heat transfer of settling particles in homogeneous isotropic turbulence is investigated in one-way coupled Eulerian–Lagrangian direct numerical simulations. In the absence of gravity, our observations highlight that there was a correlation between particles concentration and temperature fronts, which are characterized by high-temperature gradients. The particle clustering is mainly influenced by the preferential concentration and the non-local effect, the latter being the memory of their interaction with the flow along their trajectories. Nevertheless, gravity significantly affects the clustering of particles, which further influence the heat transfer of particles with the fluid. We find that the heat transfer of particles is intricately related to particle dynamic inertia and thermal inertia, which can be quantified by the particle Stokes number S t and particle thermal Stokes number S t θ , respectively. In this study, we observe that the variance of particle temperature rate of change is independent of S t θ at small thermal inertia but inversely proportional to S t θ 2 for large thermal inertia. In the presence of gravity, the variance converges to S t θ − 1 for particles with negligible thermal inertia. Our findings reveal that the second-order structure function of the particle temperature, indicating the enhancement of Lagrangian scalar intermittency, adheres to a power-law behavior with limited thermal inertial particles in the dissipation region, denoted as r 2. However, as S t θ increases, the power law of the structure function of the particle temperature is disrupted leading to 'thermal caustics'. The present findings of the heat transfer behavior of settling particles advance the understanding of gravity effect, and are valuable for the modeling of heat transfer in particle-laden turbulent flows. • Particle clustering and temperature fronts are correlated. • Particle-induced thermal dissipation varies with thermal Stokes number. • The particle temperature structure function follows a power law. [ABSTRACT FROM AUTHOR]

The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. However, the correlations between energy transfer and strain are small, and point to complicated dynamics of energy transfer. By imposing a structure at large scales consisting of antiparallel vortex tubes in a statistically steady flow, we observed a picture qualitatively similar to what was observed for the transient flow, but the energy transfer statistics do not reproduce the type of triadic interactions seen in HIT. These results indicate that the specific properties of the large-scale vortical structures affect the way energy is transferred, and may not be fully representative of HIT.

Analysis and optimization of the hybrid upwind-central numerical methods for modern versions of large eddy simulations (LESs) are presented herein. Optimization was performed based on examination of the characteristics of the spatial and temporal finite-volume approximations of the convective terms of filtered Navier–Stokes equations. A method for selecting level of subgrid viscosity that corresponds to the chosen numerical scheme and makes it possible to obtain an extended inertial interval of the energy spectrum is proposed. A series of LESs of homogeneous isotropic turbulence decay were carried out, and the optimal values of the subgrid model constants included in the hybrid shear stress transport delay detached eddy simulation (SST-DDES) method were determined. A procedure for generating a consistent initial field of subgrid parameters for these simulations is described. The three-stage explicit Runge–Kutta method was demonstrated to be sufficient for stable time integration, while the popular explicit midpoint method was not. The slope of the energy spectrum was shown to be almost independent of the central-difference scheme order and of the mesh spacing when the correct numerical method was applied. Numerical viscosity was found to become much greater than subgrid viscosity when the upwind scheme contributed about 10% or more to the convective flux approximation.

A trend towards the increasing use of Adaptive Mesh Refinement (AMR) algorithms to simulate combustion processes is observed in the recent literature. AMR is attractive as it enables the physical phenomena of interest to be tracked by the numerical mesh, reducing the computational cost drastically. It is particularly efficient for combustion as small computational cells are needed very locally to resolve the flame structure. However, the questions arising from the coupling between AMR and the turbulent flame propagation have rarely been investigated so far. Indeed, the incomplete cascading of turbulent structures from a relatively coarse mesh used to solve the flow to a finer mesh solving the flame has implications on the turbulent combustion model which must be considered. In the present paper, a strategy for coupling AMR with the Thickened Flame Model (TFM) is proposed. It is shown that, under conditions relevant to industrial cases, the standard TFM model strongly under-estimates the turbulent flame propagation when the effects of AMR is not taken into account. A new model, AMR-E, is introduced to take this effect into account. The behavior of the model is first analyzed on an a priori 1D-study and is consequently validated on a 3-D turbulent flame propagation in Homogeneous Isotropic Turbulence (HIT). In particular, it is shown that the presented model has a similar behavior for different AMR refinement levels in the flame front. [ABSTRACT FROM AUTHOR]

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'. [ABSTRACT FROM AUTHOR]

A description of inverse energy cascade (from small scale to large scale) in homogeneous isotropic turbulence is introduced by using an eigenvalue method. We show a special isotropic turbulence, in which the initial condition is constructed by reversing the velocity field in space, i.e., the time-reversed turbulence. It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process. This description is consistent to the velocity derivative skewness Sk. However, compared with Sk, it is easier to be obtained, and it is expected to be extended to anisotropic turbulence. Furthermore, this description also works for the resolved velocity field, which means that it can be used in engineering turbulent flows. The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, S t K ~ 1 , occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles. [ABSTRACT FROM AUTHOR]

This work studies a stochastic method for the generation of artificial three-dimensional, divergence-free, homogeneous, and isotropic velocity fields. The technique is based on the randomized spectral method. The statistical and spectral properties of turbulent fields constructed by this generator are analyzed. A validation LES-based computation which uses the obtained turbulent fields as initial conditions, demonstrates good agreement of the results with the experimental data. [ABSTRACT FROM AUTHOR]

The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurate centered finite difference scheme is retained for the diffusive terms. One of the major findings of this analysis is that regions featuring strong rigid-body rotations or straining motions are highly spatially intermittent, while most of the flow regions exhibit moderately strong shearing motions in the absence of rigid-body rotations and straining motions. The majority of compressibility effects can be estimated if the scaling laws in the case of compressible turbulence are rescaled by only considering the solenoidal contributions.

• Clustering measured by 3D Voronoi diagrams and Minkowski functionals, among others. • Inter-particle collisions tend to re-disperse particles inside clusters. • Particle clustering behavior depends on local dilute or dense conditions. • In dilute flow clustering moderately enhances with growing void fraction. • In dense flow clustering reduces with void fraction because of particle collisions. This paper addresses the effect of inter-particle collisions on the segregation of non-settling inertial particles in homogeneous isotropic turbulence. For this purpose, direct numerical simulations of particles in statistically steady homogeneous isotropic turbulence have been performed by the lattice Boltzmann method considering inter-particle collisions. The preferential concentration of suspended particles is quantified using several clustering measures: segregation parameter, correlation dimension, radial distribution function, Voronoï diagrams and the topological tool of Minkowski functionals. Effects of particle inertia, inter-particle collisions and increasing volume fraction in the aforementioned measures are discussed. The obtained results show that collisions between particles have a remarkable influence on the formation of clusters. In particular, under locally dilute conditions, increasing particle volume fraction implies a moderate clustering intensification, but for locally dense conditions an increase of the mean inter-particle distance inside clusters can be envisaged as a consequence of the re-dispersing effect of inter-particle collisions. [ABSTRACT FROM AUTHOR]

In previous attempts of rational subgrid-scale (SGS) modeling by employing the Kolmogorov equation of filtered (KEF) quantities, it was necessary to assume that the resolved-scale second-order structure function is stationary. Forced isotropic turbulence is often used as a framework for establishing and validating such SGS models based on stationary restrictions, for it generates statistical stationary samples. However, traditional forcing method at low wavenumbers cannot provide an analytic form of forcing term for a complete KEF in physical space, which has been illustrated to be essential in the modeling of such SGS models. Thus, an alternative forcing method giving an analytic forcing term in physical space is needed for rational SGS modeling. Giving an analytic linear driving term in physical space, linearly forced isotropic turbulence should be considered an ideal theoretical framework for rational SGS modeling. In this paper, we demonstrate the feasibility of establishing a rational SGS model with stationary restriction based on linearly forced isotropic turbulence. The performance of this rational SGS model is validated. We, therefore, propose the use of linearly forced isotropic turbulence as a complement to free-decaying isotropic turbulence and low-wavenumber forced isotropic turbulence for SGS model validations. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical analysis of the particle inertia and volume fraction effects on colliding particle-pair velocity correlation immersed in an unsteady isotropic homogeneous turbulent flow. Such correlation function is required to build reliable statistical models for inter-particle collisions, in the frame of the Euler–Lagrange approach, to be used in a broad range of two-phase flow applications. Computations of the turbulent flow have been carried out by means of Direct Numerical Simulation (DNS) by the Lattice Boltzmann Method (LBM). Moreover, the dependence of statistical properties of collisions on particle inertia and volumetric fraction is evaluated and quantified. It has been found that collision locations of particles of intermediate inertia, StK~1, occurs in regions where the fluid strain rate and dissipation are higher than the corresponding averaged values at particle positions. Connected with this fact, the average kinetic energy of colliding particles of intermediate inertia (i.e., Stokes number around 1) is lower than the value averaged over all particles. From the study of the particle-pair velocity correlation, it has been demonstrated that the colliding particle-pair velocity correlation function cannot be approximated by the Eulerian particle-pair correlation, obtained by theoretical approaches, as particle separation tends to zero, a fact related with the larger values of the relative radial velocity between colliding particles.

Wind turbines are usually clustered in wind farms which causes the downstream turbines to operate in the turbulent wakes of upstream turbines. As turbulence is directly related to increased fatigue loads, knowledge of the turbulence in the wake and its evolution are important. Therefore, the main objective of this study is a comprehensive exploration of the turbulence evolution in the wind turbine’s wake to identify characteristic turbulence regions. For this, we present an experimental study of three model wind turbine wake scenarios that were scanned with hot-wire anemometry with a very high downstream resolution. The model wind turbine was exposed to three inflows: laminar inflow as a reference case, a central wind turbine wake, and half of the wake of an upstream turbine. A detailed turbulence analysis reveals four downstream turbulence regions by means of the mean velocity, variance, turbulence intensity, energy spectra, integral and Taylor length scales, and the Castaing parameter that indicates the intermittency, or gustiness, of turbulence. In addition, a wake core with features of homogeneous isotropic turbulence and a ring of high intermittency surrounding the wake can be identified. The results are important for turbulence modeling in wakes and optimization of wind farm wake control.

We report the direct numerical simulation of droplet breakup in forced homogeneous isotropic turbulence with a mass-conserving level set method. In particular, the effect of the Weber number on the interface morphology of droplet breakup and the interaction between vortical structures and the interface are addressed. The densities and viscosities are the same for both phases in the present simulations. It is found that with increasing the Weber number, the initially large-scale spherical droplet tends to break down into dispersed small droplets. Compared with the flow local topology in the carrier-phase turbulence, the local topology of the bi-axial strain is suppressed at the statistical stationary state inside the droplet. During the droplet breakup process, the vorticity tends to be tangent to the large-scale interface at the early stage, and subsequently the alignment is mitigated for large Weber numbers, because the small droplets with relatively strong surface tension and small local Weber numbers can resist the deformation induced by local turbulent straining motion in the statistically stationary state. [ABSTRACT FROM AUTHOR]

In this work, we investigate numerically the temporal evolution of Turbulent Kinetic Energy (TKE) of a chemically-reacting n-heptane and air mixture in statistically Homogeneous Isotropic Turbulence (HIT). Our specific focus is on the concurrent view of TKE evolution in both physical and scale (Fourier) spaces to identify the impact of reaction-induced heat release on turbulence. The simulation parameters are selected to represent the combustion characteristics of heavy hydrocarbon fuels under engine conditions. Results indicate that pressure dilatation work dominates the TKE evolution during the period of strong heat release and its dominance is attributed to the strong volumetric dilatation associated with the presence of reaction fronts in physical space. Viscous dissipation and viscous dilatation terms become much stronger with increasing heat release, primarily due to the increase in strain-rate and dilatation at the vicinity of the reaction fronts, but their magnitudes are still small compared to that of pressure dilatation work. In addition, the analysis in Fourier space shows that pressure dilatation work dominates the evolution of TKE not only in the mean, but also over a wide range of scales. The spectrum of pressure dilatation shows a power-law behavior, which is a direct consequence of the localized sheet-like reaction fronts in physical space. It is also shown that viscous dissipation spectrum initially removes kinetic energy at small scales when heat release is weak, but starts to remove kinetic energy at intermediate and later at large scales due to the presence of localized reaction fronts during the strong heat release period. More interestingly, it is observed that the inter-scale kinetic energy transfer spectrum moves energy from less dissipative scales (small scales) to scales where kinetic energy is more effectively removed by viscous dissipation work (large scales) during the period of strong heat release, which indicates possible up-scale kinetic energy transfer in Fourier space. [ABSTRACT FROM AUTHOR]