Initial Turbulence Research Articles

A 2-D DNS study of the effects of nozzle geometry, ignition kernel placement and initial turbulence on prechamber ignition

A parametric direct numerical simulation study was conducted to investigate the effects of the initial flow field (quiescent or turbulent), nozzle inlet sharpness and width, main chamber composition (lean and stoichiometric), and ignition kernel placement in a two-dimensional prechamber (PC) ignition system. The strongly coupled operating and geometric parameters determine the time at which the flame exits the prechamber, the transient structure and penetration of the initially cold and subsequently hot reactive jet and their impingement on the lower main chamber (MC) wall, affecting the combustion mode and the fuel consumption rate. The temperature of the flame reaching and crossing the nozzle is affected by the flame exit time and is significantly lower than the adiabatic flame temperature of the planar flame, although no quenching is observed. Interaction with the flow field (strong small scale vortices for narrow and sharp entry nozzles, large vortices for wide nozzles) generated close to the exit increases the surface area of the flame and its interaction with the MC mixture. Jet penetration and impingement on the lower MC wall is determined by combustion in the PC and the flow field it generates in the main chamber. Impingement results in large scale vortical structures, which further contribute to the flame area increase and accelerate the consumption of the MC charge at later times. For the conditions studied, budget analysis shows that the main combustion mode is premixed deflagration with locally enhanced or reduced reactivity. Local flame–flame interactions which are more pronounced close to the nozzle exit and the lower MC wall can increase the propagation speed up to six times compared to the planar flame. The evolution of the probability density functions of different quantities is used to characterize the strongly transient process.

Experimental study of overpressure and temperature field behaviors of a methane-air mixture with different ignition positions, solid structure obstacles and initial turbulence levels

For gas explosion accidents occurring in buildings, the explosion characteristics may be affected by the presence of the equipment and furniture, and the temperature produced by the vented explosion threatens the safety of surrounding personal and buildings. To investigate the internal overpressure and external temperature behaviors, explosion venting tests of methane-air mixtures were conducted in a self-designed 4.5-m3 square chamber, by changing the solid obstacles, ignition positions, and initial turbulence levels. The results showed that P1 is generated due to the venting rate exceeding the volume growth rate of products after vent opening; with increasing flame propagation, flame front increases and more folds are present on the surface during venting, when the rate of combustion product exceeds the venting rate again, then P2 forms. Ignition position and obstacles have little effect on P1, but affect the Helmholtz oscillation and high-frequency pressure oscillation (P4). Front ignition leads to the longest duration of Helmholtz oscillation and central ignition results in the largest P4. In the presence of obstacles, P4 is eliminated and strengthened in the cases of rear and front ignitions, respectively. P4 decreases and then increases as a function of the number of obstacles. Front ignition leads to the lowest temperature peak, rear and central ignition results in the same temperature peak. The length of the high-temperature field is the shortest under four obstacles and front ignition, respectively. Under strong initial turbulence, the overpressure peak, length and duration of the high-temperature field are the largest.

Modeling and nonlinear analysis of chaotic wave processes in electrochemically active neuronal media based on matrix decomposition

A general model of the origin and evolution of chaotic wave processes in electrochemically active neuronal media based on the proposed method of matrix decomposition of operators of nonlinear systems has been developed. The mathematical models of Hodgkin – Huxley and FitzHugh – Nagumo of an electrochemically active neuronal media are considered. The necessary conditions for self-organization of chaotic self-oscillations in the FitzHugh – Nagumo model are determined. Computer modeling based on the matrix decomposition of chaotic wave processes in electrochemically active neuronal media has shown the interaction of higher-order nonlinear processes leading to stabilization (to a finite value) of the amplitude of the chaotic wave process. Mathematically, this is expressed in the synchronous “counteraction” of nonlinear processes of even and odd orders in the general vector-matrix model of an electrochemically active neuronal media being in a chaotic mode. It is noted that the state of hard self-excitation of nonlinear oscillations in an electrochemically active neuronal media leads to the appearance of a chaotic attractor in the state space. At the same time, the proposed vector-matrix model made it possible to find more general conditions for the appearance and evolution of chaotic wave processes in comparison with the initial Landau turbulence model and, as a result, to explain the occurrence of consistent nonlinear phenomena in an electrochemically active neuronal media.

Speckle characteristics of vortex beams scattered from rough targets in turbulent atmosphere

In this study, the echo speckle characteristics of the Laguerre-Gauss (LG) vortex beams scattered from random rough surface targets were examined based on the Rytov Approximation Theory. In addition, the expressions of the intensity correlation and coherence functions, along with the normalized intensity variances of the speckle fields, were derived. The coherent lengths and scintillation indexes of the speckle fields were then numerically simulated, and the speckle characteristics of the Laguerre-Gauss vortex beam were compared with those of the Gaussian beams. The effects of the topological charges, rough target radii, initial beam radii, turbulence intensities, and roughness degrees of the targets on the speckle characteristics of the LG vortex beams were analyzed. This study's results showed that in the weak turbulence regions, the target characteristics were the main influencing factors of the speckle fields. Meanwhile, in the strong turbulence regions, the turbulence effects were the main influencing factors of the speckle fields. The influence effects of turbulent atmosphere and target characteristics on the coherent lengths and scintillation effects of the vortex beam echoes were observed to be less than those of the Gaussian beams. In addition, the influence effects of the turbulent atmosphere on coherent lengths and scintillation effects of the vortex beams echoes with small topology were found to be minimal. Therefore, this study's results can potentially provide theoretical and technical guidance for the future applications of laser target detection, target recognition, and speckle measurement processes in space.

Flame self-interactions in globally stoichiometric spherically expanding flames propagating into fuel droplet-mists

A three-dimensional Direct Numerical Simulation (DNS) database of statistically spherical flames propagating into the mono-sized droplet-laden mixtures for an overall (i.e. gaseous + liquid phases) equivalence ratio of unity has been considered to investigate the distribution of flame topologies associated with flame self-interaction events. The analysis has been carried out for different values of initial droplet diameters and turbulence intensities to demonstrate their influences on the statistics of flame self-interactions. Spherically expanding stoichiometric premixed gaseous flames have also been additionally considered for the same initial burned gas radius and turbulence intensities for the purpose of comparison with the cases propagating into droplet-laden mixtures. It has been found that the topologies associated with flame self-interaction predominantly occur close to burned gas side of the flame front for turbulent premixed flames and also for droplet cases with small turbulence intensities, although tunnel closure/formation topologies are prevalent in premixed flames in contrast to unburned mixture pocket type topologies in the droplet cases. The distribution of the flame topologies has been observed to be influenced by both turbulence intensity and droplet diameter. The flame self-interaction events have mostly been found in the preheat zone for highly turbulent spray flames. It has been found that the occurrence of tunnel formation and closure topologies dominates over the availability of the unburned and burned mixture pockets in all cases except for the droplet cases under low turbulence intensities. The frequency of flame self-interaction events increases with increasing turbulence intensity and droplet diameter. The differences in the nature and distributions of flame self-interaction events between turbulent premixed and droplet cases are likely to have important implications on the possible extension of flame surface based modelling methodologies for simulating turbulent combustion in droplet-laden mixtures.

The role of collision speed, cloud density, and turbulence in the formation of young massive clusters via cloud–cloud collisions

ABSTRACT Young massive clusters (YMCs) are recently formed astronomical objects with unusually high star formation rates. We propose the collision of giant molecular clouds (GMCs) as a likely formation mechanism of YMCs, consistent with the YMC conveyor-belt formation mode concluded by other authors. We conducted smoothed particle hydrodynamical simulations of cloud–cloud collisions and explored the effect of the clouds’ collision speed, initial cloud density, and the level of cloud turbulence on the global star formation rate and the properties of the clusters formed from the collision. We show that greater collision speed, greater initial cloud density and lower turbulence increase the overall star formation rate and produce clusters with greater cluster mass. In general, collisions with relative velocity ≳ 25 km s−1, initial cloud density ≳ 250 cm−3, and turbulence of ≈2.5 km s−1 can produce massive clusters with properties resembling the observed Milky Way YMCs.

GOTHIC simulations of OECD/NEA THAI multi-vessel hydrogen deflagration tests

This paper presents GOTHIC analyses of hydrogen deflagration tests performed in the framework of the OECD/NEA THAI program. The experiments were performed in one or two interconnected vessels under similar conditions, including cases with forced convection loops and both upward- and downward-propagating burns. To capture the influence of initial turbulence and flame wrinkling, a global burn enhancement factor was employed in the calculations. The simulations captured the overall propagation of the hydrogen burns and the pressurization rate. Overall agreement was reasonably good for the upward-propagating flames, but some dynamics in the second interconnected vessel were more challenging for GOTHIC to replicate, as the flame propagation speed was generally over-predicted with the global burn enhancement model. The benchmark exercise has helped to better understand the requirements for modeling hydrogen deflagrations in multiple interconnected volumes with initial turbulence, and can be used to improve guidance on hydrogen issues in nuclear safety analysis.

Comparative experimental investigation on combustion pressure of pure methane and natural gas with elevated initial pressure

In this study, the combustion pressure of pure methane-air mixture, with 99.99% purity, and a mixture of air with Natural Gas (NG) consisted of 84.2% Methane, 9.5% Ethane, and 3.7% Propane was investigated, while both mixtures had an initial pressure of 10 bar. In this study, the combined effect of initial turbulence, pressure, and ignition energy on the combustion characteristics of each mixture was investigated. The fuel concentration in the methane-air and NG-air mixture varied between 4.98% and 17.3%. The flammability limits of the NG were 4.41% and 14.47%, whereas they were 5% and 15% for pure methane. To investigate the effect of rich or lean mixture on the combustion pressure, experiments were conducted with equivalence ratios of 0.50, 0.75, 1.00, 1.50, and 2.00. For both sets of experiments, the maximum combustion pressure occurred at the equivalence ratio of 1.00. The results showed that the lower methane concentration and the presence of other hydrocarbons such as Ethane and Propane in NG, do not cause the maximum combustion pressure to occur in a ratio other than the equivalence ratio of 1.00. Also, the study showed that the igniter energy had a significant effect on the combustion pressure, where an increase in the spark energy dramatically increased the combustion pressure for both pure methane and NG. The experiments were expended to demonstrate the effect of initial turbulence created via the mixer, on the combustion pressure for both fuels. The results suggest that the use of the mixer has a significant effect on the combustion pressure, so that experiments performed with the mixer significantly increased the combustion pressure in both fuels. Also, the study showed that the combustion pressure is influenced more than initial turbulence rather than ignition energy. The results of this study can be used in different fields from preventing unwanted combustion and detonation in engines or at places with High-risk environments such as mines and storage facilities for these gases.

A Numerical Investigation of the Minimum Ignition Energy Requirement for Forced Ignition of Turbulent Droplet-laden Mixtures

ABSTRACT The effects of droplet diameter, overall (i.e. liquid and gaseous phases) equivalence ratio, and turbulence intensity on the variation of the Minimum Ignition Energy (MIE) for localized forced ignition of uniformly dispersed mono-sized n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on Direct Numerical Simulation (DNS) data. The MIE was evaluated just for (i) obtaining thermal runway irrespective of the fate of the resulting flame kernel, and (ii) also for a successful self-sustained flame propagation without the assistance of an external energy source following the energy deposition by the ignitor. It has been found that the MIE requirement increases with increasing turbulence intensity and this trend for the MIE increase is especially significant for large values of turbulence intensity. The MIE requirement increases with increasing initial droplet diameter and with decreasing overall equivalence ratio. The MIE requirements for droplet-laden mixtures have been found to be greater than the corresponding value for homogeneous mixture with the same nominal values of initial turbulence intensity and equivalence ratio for the parameter range considered here. This behavior arises due to the deposited energy being partially utilized to supply the latent heat of evaporation and also due to the predominantly fuel-lean composition of the gaseous flammable mixture. This tendency of obtaining fuel-lean mixture strengthens with increasing (decreasing) initial droplet diameter (overall equivalence ratio). It has also been demonstrated that combustion takes place predominantly in the fuel-lean premixed mode although there is a finite probability of having non-premixed combustion in all cases. Moreover, there is a small probability of fuel-rich combustion occurring for small droplets, especially under fuel-rich overall equivalence ratios. The stochastic nature of the ignition event has been demonstrated by considering different realizations of statistically similar turbulent flow fields. The conditions giving rise to a successful thermal runaway/self-sustained flame propagation have been identified by a detailed analysis of the energy budget.

Fast Acceleration of Transrelativistic Electrons in Astrophysical Turbulence

Abstract Highly energetic, relativistic electrons are commonly present in many astrophysical systems, from solar flares to the intracluster medium, as indicated by observed electromagnetic radiation. However, open questions remain about the mechanisms responsible for their acceleration, and possible reacceleration. Ubiquitous plasma turbulence is one of the possible universal mechanisms. We study the energization of transrelativistic electrons in turbulence using a hybrid particle-in-cell method, which provides a realistic model of Alfvénic turbulence from MHD to subion scales, and test particle simulations for electrons. We find that, depending on the electron initial energy and turbulence strength, electrons may undergo a fast and efficient phase of energization due to the magnetic curvature drift during the time they are trapped in dynamic magnetic structures. In addition, electrons are accelerated stochastically, which is a slower process that yields lower maximum energies. The combined effect of these two processes determines the overall electron acceleration. With appropriate turbulence parameters, we find that superthermal electrons can be accelerated up to relativistic energies. For example, with heliospheric parameters and a relatively high turbulence level, rapid energization to megaelectronvolt energies is possible.

What determines the formation and characteristics of protoplanetary discs?

Context. Planets form in protoplanetary discs. Their masses, distribution, and orbits sensitively depend on the structure of the protoplanetary discs. However, what sets the initial structure of the discs in terms of mass, radius and accretion rate is still unknown. Aims. It is therefore of great importance to understand exactly how protoplanetary discs form and what determines their physical properties. We aim to quantify the role of the initial dense core magnetisation, rotation, turbulence, and misalignment between rotation and magnetic field axis as well as the role of the accretion scheme onto the central object. Methods. We performed non-ideal magnetohydrodynamics numerical simulations using the adaptive mesh refinement code Ramses of a collapsing, one solar mass molecular core to study the disc formation and early, up to 100 kyr, evolution. We paid particular attention to the impact of numerical resolution and accretion scheme. Results. We found that the mass of the central object is almost independent of the numerical parameters such as the resolution and the accretion scheme onto the sink particle. The disc mass and to a lower extent its size, however heavily depend on the accretion scheme, which we found is itself resolution dependent. This implies that the accretion onto the star and through the disc are largely decoupled. For a relatively large domain of initial conditions (except at low magnetisation), we found that the properties of the disc do not change too significantly. In particular both the level of initial rotation and turbulence do not influence the disc properties provide the core is sufficiently magnetised. After a short relaxation phase, the disc settles in a stationary state. It then slowly grows in size but not in mass. The disc itself is weakly magnetised but its immediate surrounding on the contrary is highly magnetised. Conclusions. Our results show that the disc properties directly depend on the inner boundary condition, i.e. the accretion scheme onto the central object. This suggests that the disc mass is eventually controlled by a small-scale accretion process, possibly the star-disc interaction. Because of ambipolar diffusion and its significant resistivity, the disc diversity remains limited and except for low magnetisation, their properties are weakly sensitive to initial conditions such as rotation and turbulence.

Effects of concentration and initial turbulence on the vented explosion characteristics of methane-air mixtures

The testing of vented explosion of methane-air mixtures was conducted in a custom-designed 4.5-m3 steel chamber. Methane concentrations in the mixed gas varied between 7 and 13 vol% and the static hysteresis time was set as 0, 1, and 5 min to characterize strong, medium and weak turbulence levels. The effects of concentration and initial turbulence on pressure characteristics and flame development were investigated. It is found that the quasi-static pressure in the chamber during vented explosion can be divided into three stages: pressure release, Helmholtz oscillation, and acoustic oscillation. The Helmholtz oscillation at a frequency of about 20–40 Hz is produced after the peak pressure P1 caused by the pressure release at all concentrations; however, the acoustic oscillation at a frequency of about 300 Hz only occurs after Helmholtz oscillation when the concentration is near the optimum. In the early stage of internal flame development, the cellular structure is generated due to hydrodynamic instability and diffusive-thermal instability, and the flame front is distorted owing to the instability caused by venting. Initial turbulence distorts the flame front, significantly increases the peak pressure, and stimulates the generation of acoustic oscillation at the upper and lower limits of concentration. Under the influence of initial high turbulence, the internal flame propagation distance has a power function relationship with time, and the turbulence acceleration factor and distance also show a power function relationship.

Influence of jet exit conditions on mixing and statistics of flow fine structures

Mixing in a coaxial jet mixer was investigated at variable initial conditions simultaneously using PIV and PLIF methods. Velocity and concentration fields were measured at two spatial resolutions: across the mixer and in a small area at its axis resolving Kolmogorov's scale. Jet exit conditions were modeled by varying flow rate (3⋅103 ≤ Red ≤ 1.78⋅104) and by applying vortex generators (tabs) at the jet exit. The study was executed within a transition flow region. Nevertheless, it is possible to claim that in the self-similarity flow region mean flow parameters do not depend on the initial conditions but turbulence does. The influence of the initial conditions is manifested in turbulent characteristics measured at a high spatial resolution and in the size of fine structures of the studied flows.

Turbulent burning velocity of stoichiometric syngas flames with different hydrogen volumetric fractions upon constant-volume method with multi-zone model

Syngas has been widely concerned and tested in various thermo-power devices as one promising alternative fuel. However, little is known about the turbulent combustion characteristics, especially on outwardly propagating turbulent syngas/air premixed flames. In this paper, the outwardly propagating turbulent syngas/air premixed flames were experimentally investigated in a constant-volume fan-stirred vessel. Tests were conducted on stoichiometric syngas with different hydrogen volumetric fractions (XH2, 10%–90%) in the ambience with different initial turbulence intensity (u'rms, 0.100 m/s~1.309 m/s). Turbulent burning velocity was taken as the major topic to be studied upon the multi-zone model in constant-volume propagating flame method. The influences of initial turbulent intensity and hydrogen volumetric fraction on the turbulent flame speed were analysed and discussed. An explicit correlation of turbulent flame speed was obtained from the experimental results.

Surface Density Function Evolution in Spherically Expanding Flames in Globally Stoichiometric Droplet-laden Mixtures

ABSTRACT The statistical behaviors of the magnitude of the reaction progress variable gradient (alternatively known as the Surface Density Function (SDF)) and the strain rates, which affect the SDF evolution, have been analyzed using three-dimensional Direct Numerical Simulations (DNS) of spherically expanding flames in globally stoichiometric initially mono-sized droplet-laden mixtures for different initial turbulence intensities and droplet diameters. It has been found that gaseous phase combustion predominantly takes place under fuel–lean mode and this tendency strengthens for large droplets and high turbulence intensities. The mean values of flame displacement speed, dilatation rate and normal strain rate decrease with increasing turbulence intensity and droplet diameter. By contrast, the mean tangential strain rate increases with increasing turbulence intensity for all droplet diameters. The mean normal strain rate induced by flame propagation remains negative but its magnitude decreases with increasing droplet size and turbulence intensity. The mean tangential strain rate induced by flame propagation (alternatively curvature stretch rate) assumes negative values except for the laminar flame with small droplets. The mean effective normal strain rate has been found to assume predominantly positive values and increases with increasing turbulence intensity for the droplet cases considered here. The mean effective tangential strain rate (alternatively stretch rate) is found to assume mostly negative values except for the laminar case with small droplets. The mean effective tangential strain rate decreases with increasing droplet size, which leads to a smaller extent of flame surface area generation for flames with larger droplets.

Disc formation in magnetized dense cores with turbulence and ambipolar diffusion

ABSTRACT Discs are essential to the formation of both stars and planets, but how they form in magnetized molecular cloud cores remains debated. This work focuses on how the disc formation is affected by turbulence and ambipolar diffusion (AD), both separately and in combination, with an emphasis on the protostellar mass accretion phase of star formation. We find that a relatively strong, sonic turbulence on the core scale strongly warps but does not completely disrupt the well-known magnetically induced flattened pseudo-disc that dominates the inner protostellar accretion flow in the laminar case, in agreement with previous work. The turbulence enables the formation of a relatively large disc at early times with or without AD, but such a disc remains strongly magnetized and does not persist to the end of our simulation unless a relatively strong AD is also present. The AD-enabled discs in laminar simulations tend to fragment gravitationally. The disc fragmentation is suppressed by initial turbulence. The AD facilitates the disc formation and survival by reducing the field strength in the circumstellar region through magnetic flux redistribution and by making the field lines there less pinched azimuthally, especially at late times. We conclude that turbulence and AD complement each other in promoting disc formation. The discs formed in our simulations inherit a rather strong magnetic field from its parental core, with a typical plasma-β of order a few tens or smaller, which is 2–3 orders of magnitude lower than the values commonly adopted in magnetohydrodynamic simulations of protoplanetary discs. To resolve this potential tension, longer term simulations of disc formation and evolution with increasingly more realistic physics are needed.

Nanopowders explosion: Influence of the dispersion characteristics

This work aims to study the influence of the dispersion conditions in a standard 20L sphere on the explosibility of a nanopowder. Even more than for micropowders, the dispersion conditions have a strong impact on the dust cloud homogeneity and its particle size distribution (PSD). Due to their high surface energy, nanoparticles are prone to agglomeration, but such structures can be broken during the dispersion process. Varying the dispersion procedure, the ignition delay time and even the nozzle type (rebound or symmetric) leads to modifications of the dust specific surface area, and thus of its reactivity. Tests were performed on aluminum and carbon black nanopowders. They were characterized before and during their dispersion in the sphere, notably using in situ laser PSD measurement. The initial turbulence level of the dust cloud was determined by particle image velocimetry. A lower shear stress is exerted on the agglomerates by using the symmetric nozzle, which causes less fragmentation and decreases the explosion severity. However, the results obtained with this nozzle are more reproducible than with the rebound nozzle.Because pre-ignition phenomenon was observed for aluminum nanopowders during their injection through the electrovalve, the dust dispersion by dust lifting was experimented. With regard to the standard procedure, the maximum rate of pressure rise decreased by approximately 30% whereas the maximum overpressure remains nearly unchanged. It means that the same amount of dust reacts in both kinds of experiments but that less fragmentation occurs, which is confirmed by PSD measurements. This work brings some questions about the interpretation of the explosivity results related to nanopowders and highlights the potential need to introduce recommendations in the current standards.

The Transition from a Lognormal to a Power-law Column Density Distribution in Molecular Clouds: An Imprint of the Initial Magnetic Field and Turbulence

Abstract We introduce a theory for the development of a transitional column density ΣTP between the lognormal and the power-law forms of the probability distribution function in a molecular cloud. Our turbulent magnetohydrodynamic simulations show that the value of ΣTP increases as the strength of both the initial magnetic field and turbulence increases. We develop an analytic expression for ΣTP based on the interplay of turbulence, a (strong) magnetic field, and gravity. The transition value ΣTP scales with , the square of the initial sonic Mach number, and β 0, the initial ratio of gas pressure to magnetic pressure. We fit the variation of ΣTP among different model clouds as a function of or, equivalently, the square of the initial Alfvénic Mach number . This implies that the transition value ΣTP is an imprint of cloud initial conditions and is set by turbulent compression of a magnetic cloud. Physically, the value of ΣTP denotes the boundary above which the mass-to-flux ratio becomes supercritical and gravity drives the evolution.

Effects of the external turbulence on centrally-ignited spherical unstable Ch4/H2/air flames in the constant-volume combustion bomb

In the present study, we conducted experiments to investigate the effects of external turbulence on the development of spherical H2/CH4/air unstable flames developments at two different equivalence ratios associated with different turbulent intensities using a spherical constant-volume turbulent combustion bomb and high speed schlieren photography technology. Flame front morphology and acceleration process were recorded and different effects of weak external turbulent flow field and intrinsic flame instability on the unstable flame propagation were compared. Results showed the external turbulence has a great influence on the unstable flame propagation under rich fuel conditions. For fuel-lean premixed flames, however, the effects of external turbulence on the morphology of the cellular structure on the flame front was not that obvious. Critical radius decreased firstly and then kept almost unchanged with the augment of the turbulence intensity. This indicated the dominating inhibiting effect of flame stretch on the turbulent premixed flame at the initial stage of the flame front development. Beyond the critical radius, the acceleration exponent was found increasing with the enhancement of initial turbulence intensity for fuel-lean premixed flames. For fuel-rich conditions, however, the initial turbulence intensity had little effect on acceleration exponent. In order to evaluate the important impact of the intrinsic flame instability and external turbulent flow field for spherical propagating premixed flames, intrinsic flame instability scale and average diameter of vortex tube were calculated. Intrinsic flame instability scale decreased greatly and then stayed unchanged with the propagation of the flame front. The comparison between intrinsic flame instability scale and average diameter of vortex tube demonstrated that the external turbulent flow filed will be more important for the evolution of wrinkle structure in the final stage of the flame propagation, when the turbulence intensity was more than 0.404 m/s.

Scalings of Inverse Energy Transfer and Energy Decay in 3-D Decaying Isotropic Turbulence with Non-rotating or Rotating Frame of Reference

Energy development of decaying isotropic turbulence in a 3-D periodic cube with non-rotating or rotating frames of reference is studied through direct numerical simulation using GPU accelerated lattice Boltzmann method. The initial turbulence is isotropic, generated in spectral space with prescribed energy spectrum E(κ)~κm in a range between κmin and κmax. The Taylor microscale Reynolds number Reλ and Rossby number Ro are introduced to characterize the inertial, viscous, and rotational attributes of the system. The focus of this study is on the scalings of early inverse energy transfer and late energy decay in the development of turbulent energy under various conditions through combinations of m, κmin, κmax, Reλ and Ro. First, we demonstrate the validity of the simulation by confirming the quantitative dependence of the decay exponent n on the initial energy spectrum exponent m, at Reλ =255 and Ro=∞, varying the values of m, κmin and κmax. Second, at relatively low Reλ, the decay exponent for different initial spectra statistically fall in respective ranges, all of which agree well with the corresponding analytical predictions. Third, we quantitatively investigate the 3-D inverse energy transfer. Our findings include (i) the exponent of inverse energy transfer spectrum E(κ)~κσ depends on the initial spectrum exponent E(κ) ~ κm: if m<4, σ=m while if m≥4, σ=4; (ii) rotation alters the inverse energy transfer rate when Reλ≤255 and Ro≥0.8; (iii) the energy increase in large scale during inverse energy transfer exhibits a bell shape, the peak of which varies with Reλ and Ro.