Turbulent propagation of premixed flames in the presence of Darrieus–Landau instability

We investigate the role played by hydrodynamic instability in the wrinkled flamelet regime of turbulent combustion, where the intensity of turbulence is small compared to the laminar flame speed and the scale large compared to the flame thickness. To this end the Michelson–Sivashinsky (MS) equation for flame front propagation in one and two spatial dimensions is studied in the presence of uncorrelated and correlated noise representing a turbulent flow field. The combined effect of turbulence intensity, integral scale, and an instability parameter related to the Markstein length are examined and turbulent propagation speed monitored for both stable planar flames and corrugated flames for which the planar conformation is unstable. For planar flames a particularly simple scaling law emerges, involving quadratic dependence on intensity and a linear dependence on the degree of instability. For corrugated flames we find the dependence on intensity to be substantially weaker than quadratic, revealing that corrugated flames are more resilient to turbulence than planar flames. The existence of a threshold turbulence intensity is also observed, below which the corrugated flame in the presence of turbulence behaves like a laminar flame. We also analyze the conformation of the flame surface in the presence of turbulence, revealing primary, large-scale wrinkles of a size comparable to the main corrugation. When the integral scale is much smaller than the characteristic corrugation length we observe, in addition to primary wrinkles, secondary small-scale wrinkles contaminating the surface. The flame then acquires a multi-scale, self-similar conformation, with a fractal dimension, for one-dimensional flames, plateauing at 1.23 for large intensities. The existence of an intermediate integral scale is also found at which the turbulent speed is maximized. When two-dimensional flames are subject to turbulence, the primary wrinkling patterns give rise to polyhedral-cellular structures which bear a very close resemblance to those observed in experiments on hydrodynamically unstable expanding spherical flames.     

Laser diagnostics and their interplay with computations to understand turbulent combustion

Laser diagnostics for fundamental investigation of turbulent combustion are discussed in the context of collaborative research that has been conducted over the past decade to contribute toward the development and experimental validation of predictive science-based models for turbulent flames. The emphasis is on simultaneous application of multiple laser techniques in flames having relatively simple fuels and flow geometries, as well as separate application of complementary diagnostics in the same flames. Data needs and design considerations for turbulent combustion model-validation experiments are outlined. Examples are given of ways in which the interplay of experiments and computations on “standard” turbulent flames has led to better understanding of these flames and also a better understanding of the capabilities of laser diagnostics and models to accurately capture the effects of turbulence-chemistry interactions. Issues of spatial resolution, differential diffusion, and LES validation are discussed, and perspectives on current research challenges are offered.     

Simultaneous stereo‐PIV and OH×CH2O PLIF measurements in turbulent ultra lean CH4/H2 swirling wall‐impinging flames

We present experimental results from turbulent low-swirl lean H₂/CH₄ flames impinging on an inclined, cooled iso-thermal wall, based on simultaneous stereo-PIV and OH×CH₂O PLIF measurements. By increasing the H₂ fraction in the fuel while keeping Karlovitz number (Ka) fixed in a first series of flames, a fuel dependent near-wall flame structure is identified. Although Ka is constant, flames with high H₂ fraction exhibit significantly more broken reaction zones. In addition, these high H₂ fraction flames interact significantly more with the wall, stabilizing through the inner shear layer and well inside the near-wall swirling flow due to a higher resistance to mean strain rate. This flame-wall interaction is argued to increase the effective local Ka due to heat loss to the wall, as similar flames with a (near adiabatic) ceramic wall instead of a cooled wall exhibit significantly less flame brokenness. A second series of leaner flames were investigated near blow-off limit and showed complete quenching in the inner shear layer, where the mean strain rate matches the extinction strain rate extracted from 1D flames. For pure CH₄ flames (Ka ≈ 30), the reaction zone remains thin up to the quenching point, while conversely for the 70% H₂ flames (Ka ≈ 1100), the reaction zone is highly fragmented. Remarkably, in all near blow-off cases with CH₄ in the fuel, a large cloud of CH₂O persists downstream the quenching point, suggesting incomplete combustion. Finally, ultra lean pure hydrogen flames were also studied for equivalence ratios as low as 0.22, and through OH imaging, exhibit a clear transition from a cellular flame structure to a highly fragmented flame structure near blow-off.     

Scale-dependent nature of the surface fractal dimension for bi- and multi-disperse porous solids by mercury porosimetry

The surface fractal dimension was calculated by using a mathematical model and mercury intrusion data for a variety of bi- and multi-disperse porous solids including silica gels, alumina pellets, and building stones. The mathematical model was obtained by modifying the well-established scaling relation published previously [Ind. Eng. Chem. Res., 34 (1995) 1383-1386]. It was also verified by comparing with the theoretical surface fractal dimensions for regular fractal structures (Skerpinski tetrahedron and Menger sponge) and the calculated surface fractal dimensions for silica gel and alumina particles via the linear fitting method established previously. The calculation results for various bi- and multi-disperse porous solids have demonstrated that the scale-dependent nature of the surface fractal dimension is ubiquitous. The difference in the surface fractal dimension between pore size intervals usually exists. The estimation of the surface fractal dimension on an average stand may lead to erroneous results.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Surface fractal analysis of pore structure of high-volume fly-ash cement pastes

The surface fractal dimensions of high-volume fly-ash cement pastes are evaluated for their hardening processes on the basis of mercury intrusion porosimetry (MIP) data. Two surface fractal models are retained: Neimark's model with cylindrical pore hypothesis and Zhang's model without pore geometry assumption. From both models, the logarithm plots exhibit the scale-dependent fractal properties and three distinct fractal regions (I, II, III) are identified for the pore structures. For regions I and III, corresponding to the large (capillary) and small (C-S-H inter-granular) pore ranges respectively, the pore structure shows strong fractal property and the fractal dimensions are evaluated as 2.592-2.965 by Neimark's model and 2.487-2.695 by Zhang's model. The fractal dimension of region I increases with w/b ratio and hardening age but decreases with fly-ash content by its physical filling effect; the fractal dimension of region III does not evolve much with these factors. The region II of pore size range, corresponding to small capillary pores, turns out to be a transition region and show no clear fractal properties. The range of this region is much influenced by fly-ash content in the pastes. Finally, the correlation between the obtained fractal dimensions and pore structure evolution is discussed in depth.     

Turbulent diffusion of lines and circulations

We study material lines and passive vectors in a model of turbulent flow at infinite-Reynolds number, the Kraichnan–Kazantsev ensemble of velocities that are white-noise in time and rough (Hölder continuous) in space. It is argued that the phenomenon of “spontaneous stochasticity” generalizes to material lines and that conservation of circulations generalizes to a “martingale property” of the stochastic process of lines.     

Velocity of weakly turbulent flames of finite thickness

The velocity increase of a weakly turbulent flame of finite thickness is investigated using analytical theory developed in previous papers. The obtained velocity increase depends on the flow parameters: on the turbulent intensity, on the turbulent spectrum and on the characteristic length scale. It also depends on the thermal and chemical properties of the burning matter: thermal expansion, the Markstein number and the temperature dependence of transport coefficients. It is shown that the influence of the finite flame thickness is especially strong close to the resonance point, when the wavelength of the turbulent harmonic is equal to the cut off wavelength of the Darrieus–Landau instability. The velocity increase is almost independent of the Prandtl number. On the contrary, the Markstein number is one of the most important parameters controlling the velocity increase. The relative role of the external turbulence and the Darrieus–Landau instability for the velocity increase is studied for different parameters of the flow and the burning matter. The velocity increase for turbulent flames in methane and propane fuel mixtures is calculated for different values of the equivalence ratio. The present theoretical results are compared with previous experiments on turbulent flames. In order to perform the comparison, the theoretical results of the present paper are extrapolated to the case of a strongly corrugated flame front using the ideas of self-similar flame dynamics. The obtained theoretical results are in a reasonable agreement with the experimental data, taking into account the uncertainties of both the theory and the experiments. It is shown that in many experiments on turbulent flames the Darrieus–Landau instability is more important for the flame velocity than the external turbulence.     

湍流预混火焰传播速度的分形模型研究

本文利用激光层析技术和数字图像处理技术,在对Ｒｅｄ＝４３３５～１１１００范围内的Ｂｕｎｓｅｎ式湍流预混火焰热图像序列进行分形分析的基础上,提出了一种基于分形理论的湍流预混火焰传播速度模型,该模型将小尺度涡团在火焰锋面的强化湍流扩散效应归结为对锋面结构的改变上。结果表明：利用该模型预测的火焰传播速度与试验结果基本吻合。     

Turbulence/flame/wall interactions in non-premixed inclined slot-jet flames impinging at a wall using direct numerical simulation

In the present work, three-dimensional turbulent non-premixed oblique slot-jet flames impinging at a wall were investigated using direct numerical simulation (DNS). Two cases are considered with the Damköhler number (Da) of case A being twice that of case B. A 17 species and 73-step mechanism for methane combustion was employed in the simulations. It was found that flame extinction in case B is more prominent compared to case A. Reignition in the lower branch of combustion for case A occurs when the scalar dissipation rate relaxes, while no reignition occurs in the lower branch for case B due to excessive scalar dissipation rate. A method was proposed to identify the flame quenching edges of turbulent non-premixed flames in wall-bounded flows based on the intersections of mixture fraction and OH mass fraction iso-surfaces. The flame/wall interactions were examined in terms of the quenching distance and the wall heat flux along the quenching edges. There is essentially no flame/wall interaction in case B due to the extinction caused by excessive turbulent mixing. In contrast, significant interactions between flames and the wall are observed in case A. The quenching distance is found to be negatively correlated with wall heat flux as previously reported in turbulent premixed flames. The influence of chemical reactions and wall on flow topologies was identified. The FS/U and FC/U topologies are found near flame edges, and the NNN/U topology appears when reignition occurs. The vortex-dominant topologies, FC/U and FS/S, play an increasingly important role as the jet turbulence develops.     

Formation mechanism of “memory” phenomenon of microchannel plate image intensifier

A discrete resistance capacitance dynodes chain of channel multiplication model worked in a continuous variable dynode number described here is an attempt to explain the formation mechanism of “memory” phenomenon of microchannel plate image intensifier, wherein it was concluded conclusion that “memory” phenomenon of image intensifiers were the results of a silicon-rich layer, which existed between emission layer and conduction layer of channel inner wall of microchannel plate, having much higher resistance as compared with the conduction layer, and there are two distinct appearance ways of “negative memory” and “positive memory” only due to a difference in illumination and duration of the image intensifier suffered, and a strictly controlled MCP manufacture process would make considerable reduction of “memory” phenomenon occurrence ratio.     

High-speed observation of cavitation bubble clouds near a tissue boundary in high-intensity focused ultrasound fields

Cavitation bubble clouds generated near a tissue boundary by high-intensity focused ultrasound (HIFU) were studied using high-speed photography. In all, 171 image series were captured during the initial 100 ms of continuous HIFU exposure, which showed that cavitation bubble clouds at the tissue boundary organized into two structures - “cone-shape bubble cloud structure” recorded in 146 image series and “crown-shape bubble cloud structure” recorded in 18 image series. The remaining 7 image series showed the interchanging of these two structures. It was found that when cavitation bubbles first appeared at the tissue boundary, they developed to cone-shape bubble cloud. The cone-shape bubble cloud structure was characterized by a nearly fixed tip in front of the tissue boundary. When the cavitation bubbles initially appeared away from the tissue boundary they evolved into a crown-shape bubble cloud. Deformation of tissue boundary was shown in all the recorded image series.     

Parabolic drift towards homogeneity in large-scale structures of galaxies

To describe the progressive transition in large-scale structures of galaxies from a seemingly fractal behavior at small scales to a homogeneous distribution at large scales, we use a new geometrical framework called entropic-skins geometry which is based on a diffusion equation of scale entropy through scale space. In the case of an equipartition of scale entropy losses in scale space, it is shown that fractal dimension (varying from 0 to 3) depends linearly on the logarithm of scale from the average size l_c of galaxies until a characteristic length scale l₀ beyond which distribution becomes homogeneous. A simple parabolic expression for correlation function can be derived: ln(1+ξ_i)=(β/2)ln²(l_o/l_i) with β=3/ln(l₀/l_c)≈0.32 and . This law has been verified using correlation functions measured on several redshift surveys.     

CO2 addition and pressure effects on laminar and turbulent lean premixed CH4 air flames

An experimental study on CH₄–CO₂–air flames at various pressures is conducted by using both laminar and turbulent Bunsen flame configurations. The aim of this research is to contribute to the characterization of fuel lean methane/carbon dioxide/air premixed laminar and turbulent flames at different pressures, by studying laminar and turbulent flame propagation velocities, the flame surface density and the instantaneous flame front wrinkling parameters. PREMIX computations and experimental results indicate a decrease of the laminar flame propagation velocities with increasing CO₂ dilution rate. Instantaneous flame images are obtained by Mie scattering tomography. The image analysis shows that although the height of the turbulent flame increases with the CO₂ addition rate, the flame structure is quite similar. This implies that the flame wrinkling parameters and flame surface density are indifferent to the CO₂ addition. However, the pressure increase has a drastic effect on both parameters. This is also confirmed by a fractal analysis of instantaneous images. It is also observed that the combustion intensity S_T/S_L increases both with pressure and the CO₂ rate. Finally, the mean fuel consumption rate decreases with the CO₂ addition rate but increases with the pressure.     

Tomographic reconstruction of the OH*-chemiluminescence distribution in premixed and diffusion flames

A fast tomographic reconstruction device has been developed to detect the two-dimensional distribution of the chemiluminescence of OH^* in the reaction zones of flames. In the set-up, special emphasis was placed on the applicability of the technique to turbulent flames. A spatial resolution of the system, <1–2 mm, and an exposure time of 100–200 μs are required to resolve the chemiluminescence signal of OH^* originating from the folded flame front of a turbulent flame.     

Statistical dynamics of religion evolutions

A religion affiliation can be considered as a “degree of freedom” of an agent on the human genre network. A brief review is given on the state of the art in data analysis and modelization of religious “questions” in order to suggest and if possible initiate further research, after using a “statistical physics filter”. We present a discussion of the evolution of 18 so-called religions, as measured through their number of adherents between 1900 and 2000. Some emphasis is made on a few cases presenting a minimum or a maximum in the investigated time range—thereby suggesting a competitive ingredient to be considered, besides the well accepted “at birth” attachment effect. The importance of the “external field” is still stressed through an Avrami late stage crystal growth-like parameter. The observed features and some intuitive interpretations point to opinion based models with vector, rather than scalar, like agents.     

Un-graviton corrections to the Schwarzschild black hole

We introduce an effective action smoothly extending the standard Einstein–Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original “guess” of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and “dressing” the Newtonian potential with un-gravitons, we solve the “effective Einstein equations” including all order un-gravity effects. An unexpected “bonus” of accounting un-gravity effects is the fractalisation   of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension dU$d_U$.     

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a “typical” probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of “best strategy” (i.e., the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all “best” strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.     

Hysteresis loss subdivision

Assuming that different energy dissipation mechanisms are at work along hysteresis, a hysteresis loss subdivision procedure has been proposed, using the induction at maximum permeability (around 0.8 T, in electrical steels) as the boundary between the “low-induction” and the “high-induction” regions. This paper reviews the most important results obtained in 10 years of investigation of the effect of microstructure on these components of the hysteresis loss. As maximum induction increases, the “low-induction loss” increases linearly up to 1.2 T, while the “high-induction loss” is zero up to 0.7 T and then increases as a power law with n=5. Low-induction loss behavior is linearly related to H_c between 0.4 and 1.2 T. Grain size has a larger influence on low-induction losses than on high-induction losses. Texture has a much stronger influence on high loss than on low-induction loss, and it is related to the average magnetocrystalline energy. 6.5%Si steel shows smaller hysteresis loss at 1.5 T than 3.5%Si steel only because of its smaler high-induction component. The abrupt increase in hysteresis loss due to very small plastic deformation is strongly related to the high-induction loss component. These results are discussed in terms of energy dissipation mechanisms such as domain wall movement, irreversible rotation and domain wall energy dissipation at domain nucleation and annihilation.