Cellular Fronts Research Articles

From graph theory and geometric probabilities to a representative width for three-dimensional detonation cells

We present a model for predicting a representative width for the three-dimensional irregular patterns observed on the front views of cellular detonation fronts in reactive gases. Its physical premise is that the cellular combustion process produces the same burnt mass per unit of time as the average planar steady Zel’dovich-von Neuman-Döring (ZND) process. The transverse waves of irregular cells are described as a stochastic system subject to a stationary ergodic process, considering that the distributions of the patterns should have identical temporal and statistical average properties. Graph theory then defines an ideal cell whose grouping is equivalent to the actual 3D cellular front, geometric probabilities determine the mean burned fraction that parameterizes the model, and ZND calculations close the problem with the time-position relationship of a fluid element in the ZND reaction zone. The model is limited to detonation reaction zones whose only ignition mechanism is adiabatic shock compression, such as those of the mixtures with H2, C3H8 or C2H4 as fuels considered in this work. The comparison of their measured and calculated widths shows an agreement better than or within the accepted experimental uncertainties, depending on the quality of the chemical kinetic scheme used for the ZND calculations. However, the comparison for CH4:O2 mixtures shows high overestimates, indirectly confirming that the detonation reaction zones in these mixtures certainly include other ignition mechanisms contributing to the combustion process, such as turbulent diffusion. In these situations, the cell widths on longitudinal soot recordings have a very large dispersion, so a mean width may thus not be a relevant detonation characteristic length. The model is easily implementable as a post-process of ZND profiles and provides rapid estimates of the cell width, length and reaction time.

The Normal Velocity of the Population Front in the “Predator–Prey” Model

The propagation of one and two-dimensional waves of populations are numerically investigated in the framework of the “predator-prey” model with the Arditi - Ginzburg trophic function. The propagation of prey and predator population waves and the propagation of co-existing populations’ waves are considered. The simulations demonstrate that even in the case of an unstable quasi-equilibrium state of the system, which is established behind the front of a traveling wave, the propagation velocity of the joint population wave is a well-defined function. The calculated average propagation velocity of a cellular non-stationary wave front is determined uniquely for a given set of problem parameters. The estimations of the wave propagation velocity are obtained for both the case of a plane and cellular wave fronts of populations. The structure and velocity of outward propagating circular cellular wave are investigated to clarify the local curvature and scaling effects on the wave dynamics.

Simulation of the self-propagating hydrogen-air premixed flame in a closed-vessel by an open-source CFD code

ABSTRACT The three-dimensional simulations of the combustion of self-propagating hydrogen-air premixed flame are performed by an open-source CFD code. The characteristics of the flame such as flame propagation behavior, flame radius, temperature, and pressure are analysed by varying the initial laminar flame speed and grid size. When the initial laminar speed increases, the thermal expansion effects become strong which leads the increase of flame radius along with the increase of flame surface area, flame temperature, and pressure. The fluctuation of pressure appears and it leads the temperature to fluctuate further. The increase in flame radius is directly related to the flame temperature. A new laminar flame speed model derived previously from the results of experiment is also introduced to the code and the obtained flame radii are compared with those from the experiments. The formation of cellular flame fronts is captured by simulation and the cell separation on the flame surface vividly appears when the grid resolution becomes sufficiently higher. The propagation behavior of cellular flame front and the flame radius obtained from the simulations have the reasonable agreement with the previous experiments.

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Abstract In this paper, the behavior of liquid and solid inclusions at advancing planar and cellular solid fronts during the solidification of steels was investigated through in situ visualization with a confocal scanning laser microscope. In the case of the liquid spherical Al2O3–CaO–MgO inclusions, theoretical prediction models agree with the experimental observations with respect to the critical front velocity required for engulfment. For the irregular solid Al2O3 inclusions, the prediction models underestimate the critical velocities. At very low growth velocities, the inclusions were found to slide along the front and get entrapped in the intercellular regions. Once entrapped, it was found that liquid inclusions appeared to be more readily engulfed at the intercellular regions than at the planar fronts. This was not observed for the large solid inclusion clusters.

Propagation of Cellular Modes of Titanium-Powder Layer Combustion in Air Channels, Allowing for the Effect of Natural Convection of Gas

In this paper, we have studied the effect of impurity and inert gases on the formation and propagation of cellular-combustion regimes for their inhomogeneous distribution above the surface of the reacting metal layer. The gas-dynamic aspects of the formation and steady propagation of inhomogeneous wave structures in the combustion of a titanium powder layer in through and semi-closed inclined air canals and in channels with uneven loading are considered. The gas composition heterogeneity over the reaction zone and the gas stratification, i.e., the stratification of a gas mixture of different densiies above the reacting layer, are shown to lead to the formation of inclined non-uniform and cellular fronts under conditions of a lack of active gas in the reaction zone and the loss of stability of the planar front.

Cellular combustion of Ti powder in air ducts: Influence of convection currents

Influence of gas convection on cellular combustion of Ti powder in slit-like reactors was studied experimentally. Heterogeneous combustion in inclined and dead-ended reactors was accompanied by diffusional and convective mass exchange between gaseous reactant and metal powder. Free convection of the gases evolved during combustion was found to favor the formation of inclined and cellular combustion fronts.

Outward propagation velocity and acceleration characteristics in hydrogen-air deflagration

Propagation characteristics of hydrogen-air deflagration need to be understood for an accurate risk assessment. Especially, flame propagation velocity is one of the most important factors. Propagation velocity of outwardly propagating flame has been estimated from burning velocity of a flat flame considering influence of thermal expansion at a flame front; however, this conventional method is not enough to estimate an actual propagation velocity because flame propagation is accelerated owing to cellular flame front caused by intrinsic instability in hydrogen-air deflagration. Therefore, it is important to understand the dynamic propagation characteristics of hydrogen-air deflagration. We performed explosion tests in a closed chamber which has 300 mm diameter windows and observed flame propagation phenomena by using Schlieren photography. In the explosion experiments, hydrogen-air mixtures were ignited at atmospheric pressure and room temperature and in the range of equivalence ratio from 0.2 to 1.0. Analyzing the obtained Schlieren images, flame radius and flame propagation velocity were measured. As the result, cellular flame fronts formed and flame propagations of hydrogen–air mixture were accelerated at the all equivalence ratios. In the case of equivalent ratio φ = 0.2, a flame floated up and could not propagate downward because the influence of buoyancy exceeded a laminar burning velocity. Based upon these propagation characteristics, a favorable estimation method of flame propagation velocity including influence of flame acceleration was proposed. Moreover, the influence of intrinsic instability on propagation characteristics was elucidated.

水素-空気混合気における球状伝播火炎の動的挙動及び火炎加速

From the perspective of safety, it is necessary to assess the risk of hydrogen-air deflagration accurately. Especially, flame propagation velocity is one of the most important factors. Propagation velocity of outwardly expanding flame has been estimated from burning velocity of a flat flame considering influence of thermal expansion at a flame front; however, this conventional method is not enough to estimate an actual propagation velocity because flame propagation is accelerated owing to cellular flame front caused by intrinsic instability in hydrogen-air deflagration. Therefore, the dynamic propagation characteristics of hydrogen-air deflagration need to be understood. We performed explosion tests in a closed chamber which has 300mm diameter windows at atmospheric pressure and room temperature and in the range of equivalence ratio from 0.2 to 1.0. In the explosion tests, dynamic behaviors of flame propagation were observed by using high speed Schlieren photography. Analyzing the obtained Schlieren images, flame radius and flame propagation velocity were measured. As the result, cellular flame fronts formed and flame propagations of hydrogen-air mixture were accelerated in the range of equivalence ratio from 0.3 to 1.0. At the equivalence ratio of 0.2, a flame floated up and could not propagate downward because the influence of buoyancy exceeded a laminar burning velocity. In the range of smooth flame at small radius, considering the correlation of flame propagation velocity with flame stretch, flame propagation velocity of flat flame and Markstein length were obtained and critical flame radius was found. In the range of cellular flame at large radius, flame propagation velocity was fitted well by using a regression equation which including a logarithm of flame radius and characteristics of flame acceleration was discussed based upon the regression equation. Based upon these considerations, we propose this regression equation as simple model of flame propagation velocity.

Irregular and cellular wave structures in the combustion of porous media under conditions of natural gas infiltration

The experimental results on the unsteady propagation of cellular waves during the infiltration-controlled combustion of a titanium powder layer are presented. The modes of frontal combustion of a porous medium with a nonuniform thermal structure that arise because of the loss of stability of the front under conditions of controlled gas transport into the exothermic reaction zone are examined. The conditions of transformation of an irregular combustion front into a cellular combustion wave are determined. The effects of the key thermal parameters of the heterogeneous system on the structure of the irregular and cellular fronts and on the characteristics of the oscillatory dynamics of their propagation are examined.

Cellular instabilities of non-adiabatic laminar flat methane/hydrogen oxy-fuel flames highly diluted with CO2

Cellular instability of non-adiabatic laminar premixed flat methane/hydrogen oxy-fuel flames highly diluted with CO2 was studied systematically. The CH4/H2/CO2/O2 flames were stabilized on a McKenna burner at atmospheric pressure. The CH4/H2/CO2/O2 flames with varied equivalence ratios and hydrogen mole fractions were investigated. Quantitative structure parameters of the cellular flame fronts were obtained with OH-PLIF technique. On the basis of experimental results, theoretical analysis was made to clarify the effect of mixture properties and heat loss on flame cellular instability. Results showed that cellular flame structure appeared near the lean limit combustion condition. Cell number of flame and its hydrodynamic factor, ωDL, present a positive correlation. The average stand-off distance, L, is well identified to characterize the cellular flames. Average cell amplitude, A, and wavelength, λ, increased with the increase of L. A good indicator of instability level, A·λ, was defined. The RS model was used in a linear stability analysis, and the onset of cellular flames was found to be governed by both hydrodynamic and thermal-diffusive instability mechanisms, while the heat loss made the flame more stable. The RS model is not an appropriate model to predict critical wavenumber for the non-adiabatic flame.

Phase-field simulations and geometrical characterization of cellular solidification fronts

The structure and dynamics of cellular solidification fronts produced during the directional solidification of dilute binary alloys are studied by phase-field simulations. A quantitative phase-field model in conjunction with a multi-scale simulation algorithm allows us to simulate arrays with 10–40 cells in three dimensions on time scales that are long enough to allow for a significant reorganization of the array. We analyze the geometry of the complex two-phase structure (mushy zone) and extract the fraction of solid and the connectivity of the two phases as a function of depth. We find a transition from stable arrays at high values of the crystalline anisotropy to unsteady arrays at low anisotropy that continuously exhibit tip splitting and cell elimination events.

Instability of CH<sub>4</sub>/O<sub>2</sub>/CO<sub>2</sub> Premixed Flames (Front Shape and Fluctuation of Cellular Flames)

To investigate the front shape and fluctuation of cellular flames on a flat burner, we treated CH4/Air mixtures and two types of CH4/O2/CO2 mixtures. We obtained the front shape of cellular flames, i.e. the cell width and cell depth, by the planar laser-induced fluorescence of CH radicals (CH-PLIF) and measured the light emission to clarify the characteristics of fluctuation of premixed flames. As the flow rate of methane decreased, the cell width and cell depth became larger, and the size of attractors increased. Compared with CH4/Air mixtures, cellular fronts were observed at large flow rates of methane in CH4/O2/CO2 mixtures, and the trajectory of attractors was complicated. These were because of high intensity of diffusive-thermal instability resulting from the replacement of N2 with CO2.

Modal decomposition and normal form for hydrodynamic flows: Examples from cellular flame patterns

Spatio-temporal complexity of hydrodynamic flows may be reduced through modal decomposition, especially in systems with symmetries. The symmetries of the most significant modes can then be used to deduce normal form equations associated with the observed state. In turn, the normal form equations can be used to deduce bifurcations to and from the given state. We illustrate this process using two spatio-temporal cellular states on a circular flame front. The first example contains a pair of uniformly rotating cells. Principle component analysis shows that two coherent structures capture most of the dynamics and suggests that the state is a broken-parity traveling mode. Other experimentally observed states, such as modulated rotating states and a heteroclinic cycle between two spatially orthonormal states result from secondary bifurcations from the rotating state. The second example, referred to as the hopping mode, visually appears to have significantly more complicated dynamics. However, modal decomposition shows that it consists of two parity broken states moving at different angular velocities. The corresponding normal form contains a codimension-three steady-state bifurcation leading to a homoclinic cycle whose spatio-temporal characteristics are similar to those of hopping states. We use these examples to propose a methodology to combine coherent structures that form a single, possibly time-dependent entity which we refer to as a generalized coherent structure. The process can reduce the number of entities needed to expand complex spatio-temporal states. The paper is dedicated to the memory of Michael Gorman, whose experiments on cellular flame fronts and relentless demands for better theoretical understanding of the patterns motivated the study.

Pattern formation in the iodate–sulfite–thiosulfate reaction–diffusion system

Sodium polyacrylate-induced pH pattern formation and starch-induced iodine pattern formation were investigated in the iodate-sulfite-thiosulfate (IST) reaction in a one-side fed disc gel reactor (OSFR). As binding agents of the autocatalyst of hydrogen ions or iodide ions, different content of sodium polyacrylate or starch has induced various types of pattern formation. We observed pH pulses, striped patterns, mixed spots and stripes, and hexagonal spots upon increasing the content of sodium polyacrylate and observed iodine pulses, branched patterns, and labyrinthine patterns upon increasing the starch content in the system. Coexistence of a pH front and an iodine front was also studied in a batch IST reaction-diffusion system. Both pH and iodine front instabilities were observed in the presence of sodium polyacrylate, i.e., cellular fronts and transient Turing structures resulting from the decrease in diffusion coefficients of activators. The mechanism of multiple feedback may explain the different patterns in the IST reaction-diffusion system.

Analysis of Schwann-astrocyte Interactions Using <em>In Vitro</em> Assays

Schwann cells are one of the commonly used cells in repair strategies following spinal cord injuries. Schwann cells are capable of supporting axonal regeneration and sprouting by secreting growth factors 1,2 and providing growth promoting adhesion molecules 3 and extracellular matrix molecules 4. In addition they myelinate the demyelinated axons at the site of injury 5. However following transplantation, Schwann cells do not migrate from the site of implant and do not intermingle with the host astrocytes 6,7. This results in formation of a sharp boundary between the Schwann cells and astrocytes, creating an obstacle for growing axons trying to exit the graft back into the host tissue proximally and distally. Astrocytes in contact with Schwann cells also undergo hypertrophy and up-regulate the inhibitory molecules 8-13. In vitro assays have been used to model Schwann cell-astrocyte interactions and have been important in understanding the mechanism underlying the cellular behaviour. These in vitro assays include boundary assay, where a co-culture is made using two different cells with each cell type occupying different territories with only a small gap separating the two cell fronts. As the cells divide and migrate, the two cellular fronts get closer to each other and finally collide. This allows the behaviour of the two cellular populations to be analyzed at the boundary. Another variation of the same technique is to mix the two cellular populations in culture and over time the two cell types segregate with Schwann cells clumped together as islands in between astrocytes together creating multiple Schwann-astrocyte boundaries. The second assay used in studying the interaction of two cell types is the migration assay where cellular movement can be tracked on the surface of the other cell type monolayer 14,15. This assay is commonly known as inverted coverslip assay. Schwann cells are cultured on small glass fragments and they are inverted face down onto the surface of astrocyte monolayers and migration is assessed from the edge of coverslip. Both assays have been instrumental in studying the underlying mechanisms involved in the cellular exclusion and boundary formation. Some of the molecules identified using these techniques include N-Cadherins 15, Chondroitin Sulphate proteoglycans(CSPGs) 16,17, FGF/Heparin 18, Eph/Ephrins19. This article intends to describe boundary assay and migration assay in stepwise fashion and elucidate the possible technical problems that might occur.

Analysis of Schwann-astrocyte Interactions Using <em>In Vitro</em> Assays

Schwann cells are one of the commonly used cells in repair strategies following spinal cord injuries. Schwann cells are capable of supporting axonal regeneration and sprouting by secreting growth factors (1,2) and providing growth promoting adhesion molecules (3) and extracellular matrix molecules (4). In addition they myelinate the demyelinated axons at the site of injury (5). However following transplantation, Schwann cells do not migrate from the site of implant and do not intermingle with the host astrocytes (6,7). This results in formation of a sharp boundary between the Schwann cells and astrocytes, creating an obstacle for growing axons trying to exit the graft back into the host tissue proximally and distally. Astrocytes in contact with Schwann cells also undergo hypertrophy and up-regulate the inhibitory molecules (8-13). In vitro assays have been used to model Schwann cell-astrocyte interactions and have been important in understanding the mechanism underlying the cellular behaviour. These in vitro assays include boundary assay, where a co-culture is made using two different cells with each cell type occupying different territories with only a small gap separating the two cell fronts. As the cells divide and migrate, the two cellular fronts get closer to each other and finally collide. This allows the behaviour of the two cellular populations to be analyzed at the boundary. Another variation of the same technique is to mix the two cellular populations in culture and over time the two cell types segregate with Schwann cells clumped together as islands in between astrocytes together creating multiple Schwann-astrocyte boundaries. The second assay used in studying the interaction of two cell types is the migration assay where cellular movement can be tracked on the surface of the other cell type monolayer (14,15). This assay is commonly known as inverted coverslip assay. Schwann cells are cultured on small glass fragments and they are inverted face down onto the surface of astrocyte monolayers and migration is assessed from the edge of coverslip. Both assays have been instrumental in studying the underlying mechanisms involved in the cellular exclusion and boundary formation. Some of the molecules identified using these techniques include N-Cadherins 15, Chondroitin Sulphate proteoglycans(CSPGs) (16,17), FGF/Heparin (18), Eph/Ephrins(19). This article intends to describe boundary assay and migration assay in stepwise fashion and elucidate the possible technical problems that might occur.

Growth Detection: A Novel Role for CD4 T-cells (87.20)

Abstract One of the central goals of immunology has been to understand the cellular and molecular mechanisms of immune regulation. Progress on the cellular front has developed rapidly with the identification of distinct CD4 T-cell populations with unique functions and patterns of cytokine production. Similarly, the discovery of TLRs in the late 1990s resulted in rapid advances towards an understanding of the molecular mechanisms of immune regulation. Despite the progress being made on both the cellular and molecular fronts, however, many aspects of immune regulation remain unexplained. Two Th-cell populations - induced regulatory T-cells (iTreg) and Th17 cells have recently been characterized. How iTreg and Th17 cells integrate with other Th populations remains an active area of research. Recently, we proposed a novel mechanism of immune regulation based on detection of pathogen growth (Bewick et. al, PLoS ONE, 2009). We then showed how growth detection can arise naturally as a result of signaling interactions and maturation kinetics of iTreg and Th17 cells. Building off of the basic premise of this growth detection model, we now extend the iTreg/Th17 system to include additional immune effector cells. This allows us to show how the immune system is organized in such a way that it can accurately and robustly classify different pathogens based on growth rate.

Enhanced Cellular Mobility Guided by TiO2 Nanotube Surfaces

The in vitro endothelial response of primary bovine aortic endothelial cells (BAECs) was investigated on a flat Ti surface vs a nanostructured TiO2 nanotube surface. The nanotopography provided nanoscale cues that facilitated cellular probing, cell sensing, and especially cell migration, where more organized actin cytoskeletal filaments formed lamellipodia and locomotive morphologies. Motile cell protrusions were able to probe down into the nanotube pores for contact stimulation, and focal adhesions were formed and disassembled readily for enhanced advancement of cellular fronts, which was not observed on a flat substrate of titanium. NOx and endothelin-1 functional assays confirmed that the nanotubes also up-regulated an antithrombic cellular state for maintaining vascular tone. The enhanced endothelial response to TiO2 nanotubes is significant for a potential modification of vascular stent surfaces in order to increase the rate and reliability of endothelialization and endothelial cell migration onto the stent for repairing arterial injury after activation.

Lateral instability induced by an inhomogeneous electric field

We have studied the pattern formation in a planar reaction-diffusion front driven by an inhomogeneous electric field to maintain a constant current density parallel to the direction of propagation. Our experiments and modeling calculations show that in the selected reaction lateral instability is favored for field orientation where the mixing of the reactants and the autocatalyst is enhanced by ionic migration. Cellular fronts develop when the drift velocity of reactant anions ahead of the front sufficiently exceeds that of the autocatalyst cation behind the front, which is achieved by the differential acceleration of the reactants.

Theory of gaseous detonations.

The objective of the present paper is to review some developments that have occurred in detonation theory over the last ten years. They concern nonlinear dynamics of detonation fronts, namely patterns of pulsating and/or cellular fronts, selection of the cell size, dynamical self-quenching, direct (blast) or spontaneous initiation, and transition from deflagration to detonation. These phenomena are all well documented by experiments since the sixties but remained unexplained until recently. In the first part of the paper, the patterns of cellular detonations are described by an asymptotic solution to nonlinear hyperbolic equations (reactive Euler equations) in the form of unsteady (sometime chaotic) and multidimensional traveling-waves. In the second part, turning points of quasi-steady solutions are shown to correspond to critical conditions of fully unsteady problems, either for (direct or spontaneous) initiation or for spontaneous failure (self-quenching). Physical insights are tentatively presented rather than technical aspects. The challenge is to identify the physical mechanisms with their relevant parameters, and more specifically to explain how the length-scales involved in detonation dynamics are larger by two order of magnitude (at least) than the length-scale involved in the steady planar traveling-wave solution (detonation thickness).