A thermal formulation for single-wall quenching of transient laminar flames

Improving our knowledge of flame-wall interaction is of relevance to performing near-wall combustion calculations. Quenching distance is to be determined accordingly, as a major parameter of flame quenching. For this purpose, an equation describing the behavior of single-wall flame quenching has been derived from a simplified model of laminar flame-wall interaction. It allows evaluating quenching distance from wall heat flux and mixture properties; a significant advantage of this formula is the absence of any empirical coefficient. To assess its reliability, the results computed with this equation have been compared to experimental data concerning laminar flame-wall interaction. For this purpose, single-wall quenching parameters have been recorded in both head-on and sidewall configurations. Quenching distance and wall heat flux have been measured simultaneously, during the combustion of quiescent methane-air mixtures in a constant-volume vessel. Quenching distance is determined through direct visualization, whereas wall heat flux is processed from the time evolution of wall surface temperature. The equation has been verified over the pressure range 0.05-0.35 MPa in stoichiometric and lean mixtures. It shows good agreement with experimental data at first order, with less than 20% variation.     

The effects of hydrogen addition,inlet temperature and wall thermal conductivity on the flame-wall thermal coupling of premixed propane/air mixtures in meso-scale tubes

The effects of hydrogen addition, inlet temperature, wall thermal conductivity and wall thickness on the flame-wall coupling of the propane/air flames in a meso-scale tube are numerically investigated using a two dimensional model along with the detailed chemical mechanism. Higher wall thermal conductivity can result in preheating the fresh mixture uniformly in strongly flame-wall coupled system, which is vital to enhance the burning rate of fuel mixture. With the increase of wall thermal conductivity or hydrogen addition, the leading edge of the flame shifts from the wall to the axis, meanwhile the flame is more convex towards the unburned side near the leading edge. As the hydrogen addition and inlet temperature increase, the flame propagation speed increases significantly, while the maximum temperature and maximum total enthalpy decrease due to the reduced heat recirculation power. The flame propagation speed has a negative correlation with heat loss. The chemical reactions in preheat zone are enhanced at low wall thermal conductivity due to the higher inner wall temperature. Thinner combustor wall leads to higher flame speed and higher heat loss simultaneously. Results have implications on the choice of solid wall material and heat recirculation design in a stable meso-scale combustor for different fuels.     

湍流预混火焰结构的测度分形研究

本文利用图像可视化技术，在小型火焰试验台上获得了Ｒｅｄ＝４３３５～１１１００范围内的燃气预混火焰的湍流热图像序列，并对２维湍流结构参数进行了测量。结合基于测度分析的分形理论，研究了湍流火焰的分维特性，结果表明：湍流火焰的２维形状结构具有分数维特性，且维数在２．０５～２．２６范围内。在此基础上，得到维数与Ｒｅｄ、热释放率及１次风流量等燃烧控制因子的依变关系，并讨论了湍流火焰分维结构的内在机理。     

A numerical study of thermal and chemical effects in interactions of n-heptane flames with a single surface

The thermal and chemical effects of a one-dimensional, premixed flame quenching against a single surface are studied numerically. Fuels considered include n-heptane and molar-based mixtures of 95/5 and 70/30 percent n-heptane and hydrogen, respectively. A reduced gas-phase kinetic mechanism for n-heptane is employed. Wall boundary conditions investigated include both an adiabatic and an isothermal wall with temperatures ranging from 298 to 1200 K. The effects of equivalence ratio variations between 0.7 and 3 are investigated. The computations with n-heptane and n-heptane/hydrogen mixtures show that for wall temperatures greater than 400 K heat release rates have a higher value for the wall-interacting flame than for the freely propagating flame. It is also seen that the peak wall heat flux increases with increasing wall temperatures up to 1000 K. Chemical pathway analysis reveals the importance of radical recombination reactions at the surface to the heat release profiles of this study. The effect of H, O, and OH radical recombination near the inert wall is observed to lower the heat release spike on a 750 K isothermal boundary. The concentrations of intermediate hydrocarbons in the near-wall region are studied and related to unburned hydrocarbon formation in an engine cylinder. It is shown that a simple one-step global reaction rate expression for n-heptane fuel conversion cannot reproduce the flame-wall trends observed with the reduced n-heptane mechanism.     

A fractal analysis of dropwise condensation heat transfer

In this paper, a fractal model for dropwise condensation heat transfer is developed based on the fractal characteristics of drop size distributions on condensing surfaces. Expressions for the fractal dimension and area fraction of drop sizes are derived, which are shown to be a function of temperature difference between condensing surface and saturated vapor. The condensation heat transfer is found to be a function of the fractal dimension for drop sizes, maximum and minimum drop radii, the temperature difference, and physical properties of fluid. The predicted total heat flux from a condensing surface based on the present fractal model is compared with existing experimental data. Good agreement between the model predictions and experimental data is found, which verifies the validity of the present model.     

Modeling of heat transfer and differential diffusion in transported PDF methods

In order to model the conditional diffusive heat and mass fluxes in the joint probability density function (PDF) transport equation of the thermochemical variables, the diffusive fluxes are decomposed into their Favre mean and fluctuation. While the mean flux appears to be closed, the contributions of fluctuating fluxes are modeled with the interaction by exchange with the mean (IEM) model. Usually, the contribution of the Favre averaged diffusive fluxes is neglected at high Reynolds numbers. Here, however, this term is included to account for molecular mixing in regions, where turbulent mixing is negligible. This model approach is applied in steady state Reynolds Averaged Navier–Stokes (RANS)/transported PDF calculations to simulate the heat transfer of wall bounded flows as well as the stabilization of a hydrogen–air flame at the burner tip. For both flow problems it is demonstrated that molecular transport is recovered in regions where turbulent mixing vanishes. In wall bounded flows this is the case in the viscous sublayer. Heat transfer studies show, that “mixing models” based on the high Reynolds number assumption fail to compute correctly the temperature field and the heat flux close to the wall. A similar situation occurs at the flame root of the investigated turbulent hydrogen-air jet flame, where turbulent mixing is still too weak to achieve a fast mixing of reactants. In this area differential diffusion effects are observed in the experiment, i.e. superequilibrium temperatures and nonlinear relations between the elemental mixture fractions of hydrogen and oxygen. It will be shown, that the presented model can successfully reproduce these effects, which underlines the necessity to include Favre averaged molecular diffusive fluxes in transported PDF methods.     

Fractal structures of hydrodynamically unstable and diffusive-thermally unstable flames

This paper discusses the fractal structure of a hydrodynamically unstable flame with the background of the risk assessment of an explosion hazard. An accidental gas explosion usually occurs in a large-scale quiescent combustible mixture. A spherical flame outwardly propagates from the ignition point, and the flame accelerates owing to hydrodynamic instability. From the viewpoint of risk assessment, it is essential to consider such an increase in flame speed because the damage of an explosion is significantly influenced by the flame speed. Because hydrodynamically unstable flames have fractal structures and the flame area (and hence the flame speed) can be estimated using the fractal dimension, it is important to know the fractal dimension of the flame under the condition of a potential accidental explosion. Three methods (a box-counting method, a Fourier analysis, and a method based on the scale dependence of the flame speed) are tested to calculate the fractal dimension of a purely hydrodynamically unstable flame that is neutral in terms of diffusive-thermal instability. These methods are applied to the numerical solution of the Sivashinsky equation, but they can be also used to the result of an ordinary CFD calculation. The fractal structure of a purely diffusive-thermally unstable flame, which is neutral in terms of hydrodynamic instability, is also studied for comparison. The results show that all the three methods yield consistent fractal dimensions for the hydrodynamically unstable flame, whereas the diffusive-thermally unstable flame does not exhibit fractal characters. This is because the former flame has a hierarchical structure, whereas wrinkles of a specific wavelength mainly grow in the latter flame. The dependence of the fractal dimension on the thermal expansion ratio is also discussed.     

Investigation of heat transfer characteristics of hydrogen combustion process in cylindrical combustors from microscale to mesoscale

In the field of micro and mesoscale combustion, the feature of flame-wall thermal coupling is of great significance because of its small scale nature. Thus, this work provides a comprehensive heat transfer analysis in cylindrical combustors from the perspective of numerical simulation. The combustor has a fixed length-to-diameter aspect ratio of 10, and the channel diameter is scaling up from 1 mm to 11 mm to explore the influence of chamber dimension on heat transfer and flame structure. The distribution of convective and radiative heat flux on inner surface, contribution of thermal radiation are given. Moreover, the role of radiation in flame structure is analyzed, and the convective and radiative heat losses are quantitatively analyzed. We find that radiative heat flux is smaller compared to convective heat flux, and the proportion of radiative heat flux becomes larger with an increasing diameter. Thermal radiation does not change the flame structure when the diameter is less than 3 mm. When the diameter is greater than 5 mm, thermal radiation changes the location of flame front. The heat loss becomes larger at a smaller diameter, and heat loss ratio can reach approximately 73.6% in the combustor with diameter of 1 mm.     

Extinction conditions of a premixed flame in a channel

A local refinement method is used to numerically predict the propagation and extinction conditions of a premixed flame in a channel considering a thermodiffusive model. A local refinement method is employed because of the numerous length scales that characterize this phenomenon. The time integration is self adaptive and the solution is based on a multigrid method using a zonal mesh refinement in the flame reaction zone. The objective is to determine the conditions of extinction which are characterized by the flame structure and its properties. We are interested in the following properties: the curvature of the flame, its maximum temperature, its speed of propagation and the distance separating the flame from the wall. We analyze the influence of heat losses at the wall through the thermal conductivity of the wall and the nature of the fuel characterized by the Lewis number of the mixture. This investigation allows us to identify three propagation regimes according to heat losses at the wall and to the channel radius. The results show that there is an intermediate value of the radius for which the flame can bend and propagate provided that its curvature does not exceed a certain limit value. Indeed, small values of the radius will choke the flame and extinguish it. The extinction occurs if the flame curvature becomes too small. Furthermore, this study allows us to predict the limiting values of the heat loss coefficient at extinction as well as the critical value of the channel radius above which the premixed flame may propagate without extinction. A dead zone of length 2-4 times the flame thickness appears between the flame and the wall for a Lewis number (Le) between 0.8 and 2. For small values of Le, local extinctions are observed.     

Flame front surface characteristics in turbulent premixed propane/air combustion

The characteristics of the flame front surfaces in turbulent premixed propane/air flames were investigated. Flame front images were obtained using laser-induced fluorescence (LIF) of OH and Mie scattering on two Bunsen–type burners of 11.2-mm and 22.4-mm diameters. Nondimensional turbulence intensity, u′/S_L, was varied from 0.9 to 15, and the Reynolds number, based on the integral length scale, varied from 40 to 467. Approximately 100 images were recorded for each experimental condition. Fractal parameters (fractal dimension, inner and outer cutoffs) and corresponding standard deviations were determined by analysis of the flame front images using the caliper technique. The fractal dimensions derived from OH and Mie scattering images are almost identical. However, inner and outer cutoffs from OH images are consistently higher than those obtained from Mie scattering. The self-similar region of the flame front wrinkling is about a decade for all flames studied. In the nondimensional turbulence intensity range from 1 to 15, it was found that the mean fractal dimension is about 2.2 and it does not show any dependence on turbulence intensity. This contradicts the findings of the previous studies that showed that the fractal dimension asymptotically reaches to 2.35–2.37 when the nondimensional turbulence intensity u′/S_L exceeds 3. It is shown that the reason for this discrepancy is the image analysis method used in the previous studies. Examples are given to show the inadequacy of the circle method used in previous studies for extraction of fractal parameters from flame front images. The fractal parameters obtained so far, in this and previous studies, are not capable of correctly predicting the turbulent burning velocity using the available fractal area closure model.     

Flame speed predictions in planar micro/mesoscale combustors with conjugate heat transfer

An analytical model for flame stabilization in meso-scale channels is developed by solving the two-dimensional partial differential equations associated with heat transport in the gas and structure and species transport in the gas. It improves on previous models by eliminating the need to assume values for the Nusselt numbers in the pre and post-flame regions. The effects of heat loss to the environment, wall thermal conductivity, and wall geometry on the burning velocity and extinction are explored. Extinction limits and fast and slow burning modes are identified but their dependence on structure thermal conductivity and heat losses differ from previous quasi one-dimensional analyses. Heat recirculation from the post-flame to the pre-flame is shown to be the primary mechanism for flame stabilization and burning rate enhancement in micro-channels. Combustor design parameters like the wall thickness ratio, thermal conductivity ratio, and heat loss to the environment each influence the flame speed through their influence on the total heat recirculation. These findings are used to propose a simple methodology for preliminary micro-combustor design.     

Heat and mass transfer in a randomly packed hollow fiber membrane module: A fractal model approach

Hollow fiber membrane modules are widely used in various industries. The disordered nature of hollow fiber distributions in the module exhibits the existence of a fractal structure formed by the voids between the fibers. The area fractal dimension of the voids on the module cross section is obtained. Then the shell side flow distribution and convective heat and mass transfer are investigated based on the fractal theory developed. An experimental work where an air flow in the shell side is humidified by a water flow in the tube side is performed to validate the model. It is found that the model predicts the flow distribution and the heat and mass transfer deteriorations well with local data for a triangular array. With the model, friction factor and Sherwood number deteriorations which take into account of the degree of irregularity, in terms of fractal dimension, are analyzed. The results show that the higher the packing density is, the less the fractal dimension is, and the less the non-uniformity of the flow distribution is. The Sherwood and Nusselt numbers of a randomly distributed fiber module are only 1–5% of a uniformly spaced tube array. Correlations are proposed for the estimation of friction factor and Sherwood numbers considering the degree of irregularity. The predictions are also compared to the available mass transfer correlations in the literature.     

湍流预混火焰的分形特性

采用高速纹影摄影法获得了定容燃烧弹内预混湍流火焰的图像，分别用数盒子法和像素点覆盖法计算出了火焰图像的分形维数。湍流火焰的分形分析结果表明，定容燃烧弹内的预混湍流火焰结构具有分形特征，且属于非充分发展的湍流火焰。湍流火焰的分形维数反应了湍流脉动对火焰片的褶皱程度，湍流强度增大加剧湍流火焰前锋的褶皱，分形维数也随之增加。在相同湍流强度下，小尺度湍流对火焰前锋的褶皱作用更大。     

A petascale direct numerical simulation study of the modelling of flame wrinkling for large-eddy simulations in intense turbulence

A new set of petascale direct numerical simulations (DNS) modelling lean hydrogen combustion with detailed chemistry in a temporally evolving slot-jet configuration is presented as a database for the development and validation of models for premixed turbulent combustion. The jet Reynolds number is 10,000, requiring grid numbers up to nearly seven billion, which was achieved by computation on 120,000 processor cores. In contrast to many prior DNS studies, a mean shear exists that drives strong turbulent mixing within the flame structure. Three cases are simulated with different Damköhler numbers, while Reynolds number is held fixed. Basic statistics are presented showing that integrated burning rates up to approximately six times the laminar burning rate are obtained. It is shown that increased flame surface area accounts for most of the enhanced burning while increases in the burning rate per unit area also play an important contribution.The database is then used to assess a new model of flame wrinkling intended for large-eddy simulations (LES). The approach draws on concepts from fractal geometry, requiring the modelling of an inner cut-off scale representing the smallest scale of flame wrinkling, and the fractal dimension controlling the resolution dependence of the unresolved flame surface area. In contrast to previous modelling, it is argued that the inner cut-off should be filter-size invariant in an inertial range. Then, dimensional and physical reasoning together with Damköhler’s limiting scaling laws for the turbulent flame speed are used to infer the cut-off and fractal dimension in limiting regimes. Two methods of determining the fractal dimension are proposed: a static, algebraic expression or a dynamic approach exploiting a Germano-type identity. Finally the model is compared against the DNS in a priori tests and is found to give excellent results, quantitatively capturing the trends with time, space, filter size and Damköhler number.     

The coupling of turbulence and chemistry in a premixed bluff-body flame as studied by LES

In previous work a subgrid scale fractal model for large eddy simulation of turbulent combustion was developed and validated. In the present article the fractal model applicability is tested by simulating a bluff-body premixed flame anchored in a straight channel. The model assumes that chemical reactions take place only at the dissipative scales of turbulence, i.e., near the so-called “fine structures” (eddy dissipation concept). The model estimates the local spatial dissipative scale η, considering also the growth effect due to heat release, and turns itself automatically off where the local spatial filter Δ equals η. The premixed burner is simulated in 2 and 3 dimensions, both for cold flow and for reacting cases. Results are compared with experimental data and show three-dimensional vortex structures periodically shortening the recirculation zone downstream of the bluff body and entraining fresh mixture into the hot recirculating region. This physical mechanism is involved in flame anchoring. The effect of assuming periodic boundary conditions in the spanwise direction, instead of solid side walls, is also investigated. The analysis shows that periodic boundary conditions cannot capture various effects of side walls, such as the shortening of the recirculation zone and the flow acceleration downstream; furthermore, it also does not allow predictions of wall heat transfer. The 2D reactive case results are also compared with those using RANS κ−? and LES-Smagorinsky models. Finally, comparing kinetic energy spectral densities in the nonreacting and reacting cases it is shown that large-scale fluctuations are damped in the latter and that fast chemical reactions cause a high-frequency energy peak.     

Numerical studies of wall effects with laminar methane flames

Wall effects in the combustion of lean methane mixtures have been studied numerically using the CHEMKIN software. To gain a deeper understanding of the flame-wall interaction in lean burn combustion, and in particular the kinetic and thermal effects, we have simulated lean and steady methane/air flames in a boundary layer flow. The gas-phase chemistry is modeled with the GRI mechanism version 1.2. Boundary conditions include an inert wall, a recombination wall and catalytic combustion of methane. Different pressures, wall temperatures and fuel-air ratios are used to address questions such as which part of the wall effects is most important at a given set of conditions. As the results are analyzed it can be seen that the thermal wall effects are more significant at the lower wall temperature (600 K) and the wall can essentially be modeled as chemical inert for the lean mixtures used. At the higher wall temperature (1,200 K), the chemical wall effects become more significant and at the higher pressure (10 atm) the catalytic surface retards homogeneous combustion of methane more than the recombination wall because of product inhibition. This may explain the increased emissions of unburned fuel observed in engine studies, when using catalytic coatings on the cylinder walls. The overall wall effects were more pronounced for the leaner combustion case (φ = 0.2). When the position of the reaction zone obtained from the boundary layer calculations is compared with the results from a one-dimensional premixed flame model, there is a small but significant difference except at the richer combustion case (φ = 0.4) at atmospheric pressure, where the boundary layer model may not predict the flame position for the given initial conditions.     

Convective heat transfer from a partially premixed impinging flame jet. Part I: Time-averaged results

Axial and radial profiles of time-averaged local heat fluxes of methane-air jet flames impinging normal to a cooled plate are reported, as functions of equivalence ratio, Reynolds number, and nozzle-plate spacing. Time-resolved behavior for these conditions is examined in the companion paper, Part II. Flame structure was studied visually and photographed. Both premixed and diffusion flame behavior was observed. Nozzle-stabilized flames revealed a stable, axisymmetric flame structure at nozzle-plate spacings less than 14 diameters. At greater nozzle-plate spacings, buoyancy-induced instabilities caused the flame to oscillate visibly. Lifted flames exhibited varied flame structures dependent upon the Reynolds number, equivalence ratio, and nozzle-plate spacing, stabilizing in the free jet, at the stagnation zone, or downstream in the wall jet. Local heat flux measurements made in the stagnation zone and along the plate adjacent to the wall jet flame revealed correlation of the local heat flux to the flame structure. Negative heat fluxes resulted from cool gases impinging on the hotter plate. The magnitude of positive heat fluxes depended on the proximity of the flame to the sensor surface, the rate of heat release, and the local molecular and turbulent transport.     

Analysis of Evaporation Heat Transfer of Thin Liquid Film in a Capillary of Equilateral Triangular Cross—Section

IntroductionThe study on evaPoration heat transfer in caPillmpbodies is imPOrtant for design and development of higIilyefficient heat transfer equipment, such as heat pipe. P.C.W and Y.K. Kao[i] stUdied the interline heattransfer coefficients of an evaPorating wetting film.L.SoloVyev and S.A. KovalevI2l discussed the mechAnsmabout evaPoration of a liquld film from a porous sdse.A. Schonberg and P.C. Wayner['l developed Shae's(l953)['l evaPoration heat transfer model that based ontem…     

Experimental study of propane/air premixed flame dynamics with hydrogen addition in a meso-scale quartz tube

The combustion process of propane/air premixed flame in meso-scale quartz tubes with different hydrogen additions was investigated experimentally to explain the flame-wall interaction mechanism. The ranges of different flame regimes were obtained by changing the flow rates of propane and hydrogen. The effects of hydrogen addition, inlet velocity and equivalence ratio were analyzed. The results show that the hydrogen addition broadens the operation ranges of fast flame regime and slow flame regime significantly. The flame propagation speed is in the same order of the thermal wave speed in solid wall for the slow flames. In fast flame regime, the flame propagation speed has an inverse correlation with the inlet flow velocity irrespective of the equivalence ratio. With the increase of the equivalence ratio, the maximum flame speed in fast flame regime decreases gradually, while the maximum flame speed in slow flame regime increases continually. It indicates that rich fuel condition suppresses the fast flame and promotes the slow flame. In slow flame regime, the output thermal efficiency is dominated by the inlet velocity and equivalence ratio.