Cellpose-SAM: Transformer-based segmentation for cellular instability analysis of spherical hydrogen-air premixed flames

Research on cellular instabilities in outwardly propagating spherical hydrogen-air flames

The cellular flame area continues to increase with the development of cells on the spherical flame surface, which will greatly promote the flame burning rate and propagation speed. This work mainly focuses on a new three-dimensional (3D) reconstruction method of the cellular structure on the flame surface, attempting to quantitatively characterize the real flame area. Initially, the visualization investigation of hydrogen-air premixed spherical flames within a constant volume vessel was conducted using the Schlieren optical technique under room temperature and atmospheric pressure conditions. In parallel, the Cellpose 2.0 graphical user interface was used for the preliminary training of the cell segmentation model. Subsequently, this pre-trained model was applied in the image post-processing, enabling the quantitative characteristics extraction of the cellular structure, such as the cells number, area, and the flame radius, etc. Additionally, a concept of peak height h on the flame profile was proposed to characterize the fluctuation degree of flame profile. A new flame equivalent radius ru was defined by the average value of valid distance from flame centroid to flame profile pixel by pixel. Based on the comparison of cell equivalent radius r and average peak height h¯, an innovative 3D reconstruction concept was proposed for the quantitative characterization of flame area. Finally, cellularity factor ξ was introduced to evaluate the cellularization degree on spherical flames surface. Results show that the appearance of secondary cracks marks the formal onset of flame cellularization, accompanied by an increase in the h¯. In the later stages of flame development, cellularization will eventually tend to a stable value of about 0.4, indicating the occurrence of “saturated state”. After 3D reconstruction, the average cell area stable at around 26 mm2 in this stage. The results of this study provide data support for the construction of combustion models in the field of premixed hydrogen-air combustion.

The composite flux method described by Dixon-Lewis, Goldsworthy &amp; Greenberg (1.975 a )for the computation of detailed temperature and composition profiles in suitable flames has been applied to the simulation of the properties of a number of fuel-rich and fuel-lean hydrogen-oxygen-nitrogen flame systems. The reaction mechanism proposed by Day, Dixon-Lewis &amp; Thompson (1972), extended to include all the reverse reactions, has been used in the simulation, together with assumed sets of reaction rate and transport parameters. The computed profiles have then been compared with published measurements in flames, covering a wide range of experimental conditions, in order to arrive iteratively at an optimum, self-consistent set of rate parameters which also takes full account of the available elementary reaction rate data from sources other than flames. The flame properties considered in this part of the investigation were ( a ) radical recombination profiles in both fuel-rich and fuel-lean flames, and ( b ) the burning velocities and properties of the main reaction zones of several low temperature, slow burning, fuel-rich flames. Three sets of rate parameters which satisfy all the constraints, and which differ only in detail, are given as sets 1, 2 and 3 in table 4 of the paper. Measurements by Kaskan (1958 b ) of radical recombination in the hydrogen-lean systems have used the (0, 0) band ultraviolet absorption of the hydroxyl radical in order to measure its concentration. The interpretation of the measurements so as also to be consistent with the remaining flame measurements by other methods additionally allows a determination of the oscillator strength associated with the transition. A band oscillator strengths f 00 — 9.5 x 10 -4 was found. Following the establishment of the reaction rate parameters, one set of these (table 9) was used to calculate the expected properties of the whole composition range of hydrogen-air premixed flames. In these cases, as well as in the calculations already summarized, either partial equilibrium or kinetic quasi-steady state assumptions must be used in conjunction with the composite flux method. Partial equilibrium assumptions on the reactions <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">OH</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mo stretchy="false">⇌</mml:mo> <mml:mspace width="thinmathspace" /> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mspace width="1em" /> <mml:mspace width="1em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">i</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mspace width="thinmathspace" /> <mml:mo stretchy="false">⇌</mml:mo> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mi mathvariant="normal">OH</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:mspace width="1em" /> <mml:mspace width="1em" /> <mml:mspace width="1em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">ii</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> <mml:mspace width="thinmathspace" /> <mml:mo stretchy="false">⇌</mml:mo> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mi mathvariant="normal">OH</mml:mi> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mo>+</mml:mo> </mml:mrow> <mml:mspace width="thinmathspace" /> <mml:mrow> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> <mml:mspace width="1em" /> <mml:mspace width="1em" /> <mml:mspace width="1em" /> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="normal">iii</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> may be employed to relate the concentrations of H, OH, O and O 2 in calculations where only the concentration profiles in the recombination regions of the flames are required. In the calculation of complete flame properties, quasi-steady state assumptions must be used to relate the concentrations either of O, OH and HO 2 with that of H (rich flame formulation), or of H, O and HO 2 with that of OH (lean flame formulation). Subsequent investigation showed that the quasi-steady state assumptions were not completely valid for oxygen atoms everywhere in the flames. Nevertheless, further calculations on several flames by the completely different approach of implicit finite difference solution of the time-dependent flame equations, which does not involve any quasi-steady state assumptions, led to results essentially identical with the original computations. The departures from the quasi-steady state do not therefore significantly affect the flame properties computed by the composite flux method. The general pattern of flame structure which emerges from the complete flame calculations is one in which radicals are produced by chain branching reactions in the hotter regions of the flames, while the major heat releasing reactions occur at lower temperatures. Ahead of the heat release zone there is only a very small preheat zone where heating occurs purely by thermal conduction. This behaviour is different from that of flame models which assume a large preheat zone coupled with a single global exothermic reaction of high activation energy. Comparison of the results of calculations which employed respectively the partial equilibrium and quasi-steady state assumptions showed that the former were valid in the ‘recombination zones’ of the flames for predicting the concentrations of those species which are present in significant amounts. Except in lower temperature flames, for example the 15% hydrogen-air flame and to some extent the 70% hydrogen-air flame, the ‘recombination zones’ extend almost back from the hot boundaries of the flames to the maxima in the hydrogen atom mole fraction profiles. On continuing the flame integrations back from the recombination zones into the main reaction zones, the quasi-steady state overall radical concentrations, represented by X H + 2 X O + X OH , where X</jats:

• Quenching distances of laminar CH 4 -air and H 2 -air premixed flames are determined numerically and engineering correlations presented. • Quenching distance sensitivity to final velocity is investigated and reported, which is neglected in literature before. • The setup geometry effects the quenching distance measurement, and contact surface area with the wall has a primary effect on it. • Quenching distance decreases almost linearly with increasing wall temperature for hydrogen-air premixed flames. • H 2 flames has significantly lower non-dimensionalized quenching distance than CH 4 flames. The quenching behavior of laminar premixed hydrogen-air and methane-air flames is studied in two-dimensional configurations with detailed chemistry. Quenching distances are determined by simulating an initially stationary flame and then decreasing the inlet speed, allowing upstream flame propagation in a converging duct. The quenching distance is then defined as the distance between the cold surfaces where the flame extinguishes due to heat loss to the walls. The results for methane-air and hydrogen-air mixtures at various equivalence ratios are compared with experimental data, showing good agreement. The effects of flow inlet velocity, geometry, and wall temperature on quenching distance are investigated. The quenching distance is found to be sensitive to the inlet speed and decreases with decreasing inlet speed. The quenching distance is shown to decrease linearly with increasing wall temperature in hydrogen-air flames. In addition, the quenching distance depends on the geometry of the setup. Slit and annular ducts result in similar quenching distances, whereas circular ducts have higher quenching distances compared to the others. The study highlights the importance of considering these factors in burner design and flashback prevention devices.

A comparison between head-on quenching of stoichiometric methane-air and hydrogen-air premixed flames using Direct Numerical Simulations

Some aspects of ignition by localized sources, and of cylindrical and spherical flames

A theoretical and numerical study was conducted on expanding spherical flames in order to understand how stationary flame ball (SFB) can be attained. Numerical simulation of the full unsteady problem was first performed for mixtures with low Lewis numbers. Depending on the order of magnitude of the heat loss, three typical regimes were found: (i) when the heat loss is very small, the spherical flame expands outwardly and transforms asymptotically to a planar flame; (ii) when the heat loss is moderately large, the planar flame does not exist and the expanding flame quenches; and (iii) when the heat loss is large, the expanding spherical flame transforms to a stationary flame ball. A quasi-steady nonlinear relation between the instantaneous flame radius R and its velocity U was obtained via asymptotic analysis and numerical computations with constant density and one-step Arrhenius kinetics. It was found that there is a continuous variation of the flame velocity from zero to the planar flame velocity. When the heat loss is larger than a critical value, the velocity-radius relation exhibits a turning point which may correspond to either flame extinction or reversal of the direction of propagation. Introduction Studies have been performed on spherical flames with emphasis on different aspects of the phenomena, such as: i) Relation between the flame velocity, stretch, and curvature; ii) stationary flame balls (SFB); and iii) spherical flame ignition. Multi-dimensional instability of spherical flames and spherical turbulent flames have also been investigated. For an outwardly propagating spherical flame, both the curvature and the flow field characterized by stretch modify the propagation velocity. The linear velocity-stretch-curvature relation determined for the one-dimensional spherical flame [l] is similar to that determined in multi-dimensional instability analysis [2]. In fact, small-amplitude cellular flames can be approximated locally to a one-dimensional spherical flame surface. A recent study with detailed chemistry on this problem, together with a review of related studies, can be found in Ref. 3. The work mentioned above concerns spherical flames whose radius is much larger than the flame thickness such that both the structure and flame velocity are only slightly different from those of the planar flame. The structure of the SFB, however, is very different. For SFB, which was first proposed by Zeldovich [4] to explain certain existing experimental phenomena, convective transport is absent while the product and heat release are transported radially outward into the ambient via diffusion. Stability analyses subsequently carried out by Zeldovich et al. [5] and by Deshaies and Joulin [6] with a thermal-diffusion model show that the adiabatic SFB is unconditionally unstable at its equilibrium radius, either collapsing inwardly for a negative initial perturbation of the flame position, or propagating outwardly for a positive initial perturbation. Based on such an unstable nature of SFB, Zeldovich et al. [5] pointed out that the critical condition for flame ignition should be controlled by the radius of SFB. To explain phenomena similar to the SFB observed in experiments (see Ref. 5 and the references therein), it was [5] also suggested that heat loss could play a stabilizing role because the extent of heat loss increases with increasing flame -* Copyright

The extraction of cellular structure feature on the spherical premixed flame surface faces accuracy challenges. The Schlieren technique was employed to obtain the hydrogen-air premixed spherical flames images in a constant volume vessel at room temperature and atmospheric pressure under an equivalent ratio of 0.8 in this work. A bio-inspired Cellpose 2.0, driven by deep learning, is innovatively introduced to train the cell segmentation model in the combustion field. After labeling and training cells of different shapes and sizes, an efficient and accurate model suitable for cell feature extraction was finally obtained to identify and quantify various cells characteristics, such as number, size, and distribution. Results show that the average precision (AP) during the model online pre-training process reaches 0.625. Meanwhile, the critical flame radius of transition acceleration obtained is 36 mm and the crack length tends to grow linearly after the flame radius exceeds this critical point. Additionally, the average cell area gradually converges to a stable value after the flame radius exceeds the uniform cellularity critical radius. The cell segmentation model obtained in this work can be further used to train different spherical flames under various conditions, helping to develop hydrogen combustion and explosion modelling.

Experimental study on self-acceleration in expanding spherical hydrogen-air flames

Buoyant unstable behavior in initially spherical lean hydrogen-air premixed flames within a center-ignited combustion vessel have been studied experimentally under a wide range of pressures (including reduced, normal, and elevated pressures). The experimental observations show that the flame front of lean hydrogen-air premixed flames will not give rise to the phenomenon of cellular instability when the equivalence ratio has been reduced to a certain value, which is totally different from the traditional understanding of the instability characteristics of lean hydrogen premixed flames. Accompanied by the smoothened flame front, the propagation mode of lean hydrogen premixed flames transitions from initially spherical outwardly towards upwardly when the flames expand to certain sizes. To quantitatively investigate such buoyant instability behaviors, two parameters, “float rate (ψ)” and “critical flame radius (Rcr)”, have been proposed in the present article. The quantitative results demonstrate that the influences of initial pressure (Pint) on buoyant unstable behaviors are different. Based on the effects of variation of density difference and stretch rate on the flame front, the mechanism of such buoyant unstable behaviors has been explained by the competition between the stretch force and the results of gravity and buoyancy, and lean hydrogen premixed flames will display buoyant unstable behavior when the stretch effects on the flame front are weaker than the effects of gravity and buoyancy.

Spherical flame initiation and propagation in particle-laden mixtures are investigated theoretically in this work. Within the framework of constant density, large activation energy and quasi-steady assumptions, a correlation describing spherical flame propagation speed as a function of flame radius is derived. This correlation is used to assess the influence of gas and particle properties on initiation and propagation of premixed spherical flames. Spherical flame initiation and propagation are shown to be influenced noticeably by the appearance of inert solid particles. It is found that the flame propagation speed and temperature both decrease with increased particle heat capacity and thermal relaxation time. A non-monotonic change of the flame propagation speed with flame radius is observed when there are particles with large heat capacity. Furthermore, the bifurcation of flame propagation speed is observed for particles with large heat capacity and thermal relaxation time. Within a certain flame radius range, there are both strong and weak flame solutions. The abrupt jump from the strong flame to weak flame results from the excessive heat loss caused by the solid particles and the energy balance is re-established along the weak flame branch. The Lewis number strongly affects the flame propagation speed, particularly for small thermal response time and high particle heat capacity. Additionally, the minimum ignition energy of the particle-laden spherical flames is found to increase with the Lewis number. At higher Lewis number, the difference of minimum ignition energy between gaseous and particle-laden situations becomes larger. To validate the theoretical results, one-dimensional transient simulations of particle-laden spherical flames with detailed chemistry have been conducted. Qualitative agreement is achieved for results from numerical simulations and theoretical analysis.

Effects of hydrocarbon substitution on atmospheric hydrogen–air flame propagation

Effects of thermodiffusive instability on the spherical premixed flames anchored to a porous-plug burner

This paper reports results of an experimental study and numerical simulation of the effect of the equivalence ratio (φ = 0.6–1.6) on the burning velocity of laminar, premixed atmospheric methane-air and propane-air flames without additives and with 0.06% trimethylphosphate (TMP). The effect of the equivalence ratio (φ = 0.7–4.5) on the burning velocity of hydrogen-air flames without additives and with 0.1% TMP was studied by simulation. The experimental and simulation results show that, in hydrocarbon flames doped with TMP, the inhibition effectiveness decreases sharply with a growth in φ from 1.2–1.3 to 1.4–1.6 and in hydrogen-air flames, the inhibition effectiveness increases with a rise in φ from 1.5 to 4.5. The reactions determining the dependence of the inhibition effectiveness on the equivalence ratio were found by analyzing the flame velocity sensitivity coefficients to changes in reaction rate constants.

Statistically spherical expanding turbulent premixed flames are computed using an unsteady Reynolds-averaged Navier–Stokes (URANS) approach. Mean reaction rate is closed using strained and unstrained flamelet models and an algebraic model. The flamelets are parametrized using the scalar dissipation rate in the strained flamelet model. It is shown that this model is able to capture the measured growth rate of methane–air turbulent flame ball, which is free of thermo–diffusive instability. The spherical flames are observed to accelerate continuously. The flame brush thickness grows in time and the role of turbulent diffusion on this growth seems secondary compared to the convection due to the fluid velocity induced by the chemical reaction. The spherical flames have larger turbulent flame speed, the leading-edge displacement speed st, compared to the planar flames for a given turbulence and thermochemical condition. The computational results suggest with 0.57 ≤ n ≤ 0.58, where Re t is the turbulence Reynolds number and is the unstrained planar laminar flame speed, for both spherical and planar flames.