Stretch Rate Research Articles

Shear layer flame stabilization sensitivities in a swirling flow

A variety of different flame configurations and heat release distributions exist in high swirl, annular flows, due to the existence of inner and outer shear layers as well a vortex breakdown bubble. Each of these different configurations, in turn, has different thermoacoustic sensitivities and influences on combustor emissions, nozzle durability, and liner heating. This paper presents findings on the sensitivities of the outer shear layer- stabilized flames to a range of parameters, including equivalence ratio, bulkhead temperature, flow velocity, and preheat temperature. There is significant hysteresis for flame attachment/detachment from the outer shear layer and this hysteresis is also described. Results are also correlated with extinction stretch rate calculations based on detailed kinetic simulations. In addition, we show that the bulkhead temperature near the flame attachment point has significant impact on outer shear layer detachment. This indicates that understanding the heat transfer between the edge flame stabilized in the shear layer and the nozzle hardware is needed in order to predict shear layer flame stabilization limits. Moreover, it shows that simulations cannot simply assume adiabatic boundary conditions if they are to capture these transitions. We also show that the reference temperature for correlating these transitions is quite different for attachment and local blow off. Finally, these results highlight the deficiencies in current understanding of the influence of fluid mechanic parameters (e.g. velocity, swirl number) on shear layer flame attachment. For example, they show that the seemingly simple matter of scaling flame transition points with changes in flow velocities is not understood.

Multiple Cracks Propagate Simultaneously in Polymer Liquids in Tension

Understanding the mechanism of fracture is essential for material and process design. While the initiation of fracture in brittle solids is generally associated with the preexistence of material imperfections, the mechanism for initiation of fracture in viscoelastic fluids, e.g., polymer melts and solutions, remains an open question. We use high speed imaging to visualize crack propagation in entangled polymer liquid filaments under tension. The images reveal the simultaneous propagation of multiple cracks. The critical stress and strain for the onset of crack propagation are found to be highly reproducible functions of the stretch rate, while the position of initiation is completely random. The reproducibility of conditions for fracture points to a mechanism for crack initiation that depends on the dynamic state of the material alone, while the crack profiles reveal the mechanism of energy dissipation during crack propagation.

Extinction limit and near-limit kinetics of lean premixed stretched H2-CO-air flames

The extinction limit of laminar lean premixed stretched H2-CO-air flames was investigated with particular attention to the chemical kinetic characteristics under near-limit conditions. The extinction stretch rates were determined by the digital particle image velocimetry measurement using the Counterflow Twin-Flame method. Corresponding numerical simulations were conducted using CHEMKIN II with detailed chemical kinetic mechanisms. The simulation results generally agreed well with the experimental data. It was found that increasing H2 ratio restrained the flame from being extinguished, and this restraining effect was more profound low H2 ratios. Further analyses of the flame speed, temperature and elementary reaction sensitivities revealed that H2 addition played a crucial role in flame extinction by changing the competition between chain branching and termination reactions. To quantitatively measure the kinetic effect of H2 addition, a dimensionless extinction exponent (β) defined as the ratio between the relative sensitivities of termination (ωT) and branching (ωB) reaction rates, i.e., β = ∂lnωT/∂lnωB, was proposed. For a given syngas, β rapidly increased to a certain constant, defined as the critical extinction exponent, when the flame extinction was approached, despite variations in the stretch rate and changes in the loss mechanism. The chemical kinetic characteristics and loss mechanism jointly determined the extinction limit of lean premixed H2-CO-air flames.

New insights into the use of multi-mode phenomenological constitutive equations to model extrusion film casting process

This article is concerned with the effect of the individual viscoelastic relaxation modes of a polymer melt on its behavior in polymer melt extrusion film casting process. We compare the predicted versus experimentally obtained film necking or neck-in profile as a function of draw ratio. The predicted necking profile was obtained using well-established one-dimensional isothermal flow kinematics and consisted of using two different phenomenological constitutive equations, upper convected Maxwell and Phan-Thien–Tanner, with a discrete spectrum of relaxation times. The numerical simulations, containing the two different phenomenological constitutive equations, provided an insight into the effect of the slow and the fast relaxing modes on the stresses, strains, and strain/extensional rates that develop in the molten polymer film as it is stretched from the die exit to the chill-roll. The slow relaxing modes follow trends that are directly proportional to strain (similar to Hookean solids), whereas the fast relaxing modes follow trends that are directly proportional to the stretch rate (in accordance with Newton’s law of viscosity). Comparing the numerical predictions with the experiments showed that predictions using the upper convected Maxwell constitutive equation best described the long-chain branched polymers (like low-density polyethylene, which shows extensional strain hardening) in the extrusion film casting process. On the other hand, predictions using the Phan-Thien–Tanner constitutive equation best described the linear polymers (like linear low-density polyethylene, which does not show noticeable extensional strain hardening) in the extrusion film casting process.

The turbulent flame speed for low-to-moderate turbulence intensities: Hydrodynamic theory vs. experiments

This paper, dedicated to Norbert Peters, follows his lead in developing theoretical understanding of the complex flow-turbulence interactions occurring in the propagation of premixed flames. The work is based on the asymptotic hydrodynamic model of premixed flames, where the flame is modeled by a surface that separates unburned and burned gases and propagates relative to the incoming flow at a speed that depends locally on the flame stretch rate. As such the work may be categorized as corresponding to the “flamelet regime”, based on the turbulent combustion regimes diagram. The results at the present are limited to mixtures corresponding to positive Markstein lengths, and to “two-dimensional turbulent flows”. In this parametric study, the different factors affecting the turbulent flame speed have been examined and scaling laws for the turbulent flame speed are proposed for low-to-moderate turbulence intensities that highlight the dependence on physically measurable quantities. Comparison to various empirical correlations suggested in the literature is presented. The results, devoid of turbulence-modeling assumptions and/or ad-hoc coefficients, can help explaining the influence of varying the system parameters individually and collectively, and formulating physically-based small-scale models for large-scale numerical simulations of turbulent flames.

Impact of the bluff-body material on the flame leading edge structure and flame–flow interaction of premixed CH4/air flames

In this paper we investigate the interaction between the flame structure, the flow field and the coupled heat transfer with the flame holder of a laminar lean premixed CH4/air flame stabilized on a heat conducting bluff body in a channel. The study is conducted with a 2-D direct numerical simulation with detailed chemistry and species transport and with no artificial flame anchoring boundary conditions. Capturing the multiple time scales, length scales and flame-wall thermal interaction was done using a low Mach number operator-split projection algorithm, coupled with a block-structured adaptive mesh refinement and an immersed boundary method for the solid body. The flame structure displays profiles of the main species and atomic ratios similar to previously published experimental measurements on an annular bluff body configuration for both laminar and turbulent flow, demonstrating generality of the resolved flame leading edge structure for flames that stabilize on a sudden expansion. The flame structure near the bluff body and further downstream shows dependence on the thermal properties of the bluff body. We analyze the influence of flow strain and heat losses on the flame, and show that the flame stretch increases sharply at the flame leading edge, and this high stretch rate, together with heat losses, dictate the flame anchoring location. By analyzing the impact of the flame on the flow field we reveal that the strong dependence of vorticity dilatation on the flame location leads to high impact of the flame anchoring location on the flow and flame stretch downstream. This study sheds light on the impact of heat losses to the flame holder on the flame–flow feedback mechanism in lean premixed flames.

Study on the combustion limit, near-limit extinction boundary, and flame regimes of low-Lewis-number CH4/O2/CO2 counterflow flames under microgravity

To obtain an accurate and comprehensive understanding on the fuel-lean combustion limit, near-limit extinction boundary and flame regimes, experimental and numerical investigations using premixed counterflow flames were conducted for low-Lewis-number mixtures. Counterflow flame experiments were conducted under microgravity (2.2≦a≦12.9s−1) and under normal gravity (35≦a≦150s−1) using fuel-lean CH4/O2/CO2 mixtures (Le=0.75) where a is the stretch rate. The mole fraction ratio of O2 to CO2 in the mixtures was 0.40. Microgravity experiments at a=2.7–3.2s−1 showed that transitions from planar flames to ball-like flames occurred near extinction for the investigated mixture. In addition to planar flames and ball-like flames, multi-dimensional flames such as cellular flames and twin-curved flames were also observed at a=2.2–5.5s−1 in microgravity experiments. In conjunction with experimental results under normal gravity, experimental flame regimes for overall stretch rates were obtained for the first time and the region where ball-like flames were observed showed a qualitative agreement with our previous study based on the 3-D transient computations with the diffusive-thermal model. Extinction points obtained by microgravity experiments were found to scatter at very low stretch rates where multi-dimensional flames such as ball-like flames and cellular flames were observed, indicating the existence of a flame regime at lower stretch rates leaner than the planar counterflow flame extinction boundary. In addition, flame bifurcation at low stretch rates and at ϕ=0.58 and 0.60 were experimentally observed for the present low-Lewis-number mixture, indicating the validity of the previous computational and theoretical studies on the G-shaped extinction curve of planar counterflow flames.

Flamelet budget and regime analysis for non-premixed tubular flames

A recently developed flamelet model for non-premixed combustion accounting for curvature effects is examined. The work focusses on the curvature-induced differential diffusion in flame-tangential direction that is not included in classical flamelet formulations. Non-premixed tubular hydrogen and hydrocarbon counterflow flames are computed in physical and in composition space for various stretch rates. These flames were studied experimentally in previous works (Hu et al., 2007; Hu and Pitz, 2009) and allow a detailed investigation of stretch and curvature effects, while retaining a well-defined one-dimensional flame structure. First, the influence of curvature effects on the flame structure of a non-premixed tubular hydrogen flame is assessed by comparing flamelet solutions with and without curvature to the physical space solution. For the selected flame configuration, curvature-induced differential diffusion leads to a flame temperature deviation of 11% compared to a planar counterflow flame with the same scalar dissipation rate profile. Thereafter, the curvature terms are examined in a budget analysis of the flamelet equations. Finally, hydrogen and hydrocarbon tubular flames are placed in an extended regime diagram that allows non-premixed flame structures to be characterized with respect to curvature effects. The regime diagram contains the classical flamelet regime (Regime I) and the curvature-affected flamelet regime (Regime II) enclosing a novel transition zone, where curvature effects are not dominant, but already influence the flame structure significantly. It is shown that the hydrogen flames (Lef=0.34) fall into the transition zone while the hydrocarbon flames (Lef=0.88−1.49) reside in the classical flamelet regime with negligible curvature influence.

Effect of reduced pressures on the combustion efficiency of lean H2/air flames in a micro cavity-combustor

The effect of reduced pressures (i.e., p = 1.0 atm, 0.8 atm and 0.5 atm) on the combustion efficiency of lean H2/air flames in a micro-combustor was investigated in this work. We found that the combustion efficiency increases as the pressure is reduced from 1.0 atm to 0.8 atm, and then decreases when the pressure is further reduced from 0.8 atm to 0.5 atm. Numerical analyses reveal that when the pressure is reduced to 0.8 atm, the laminar burning velocity, the heat release rate and the effective Lewis number are increased, while the stretch rate is decreased. The combined effects of these aspects retard the occurrence of “flame tip opening” and lead to a higher combustion efficiency. When the pressure is further reduced to 0.5 atm, the fuel supply and heat release amount are significantly reduced, resulting in much lower temperature level and weaker reaction intensity. Meanwhile, the heat-loss ratio is almost doubled. Therefore, the combustion is completely extinguished in the downstream channel and a large amount of fuel leaks out without burning. As a consequence, the combustion efficiency decreases drastically.

Effect of inlet temperature on combustion efficiency of lean H2/air mixtures in a micro-combustor with wall cavities

Micro-combustors with wall cavities can achieve a large flame blowout limit. However, the combustion efficiency is sharply decreased at high inlet velocities for relatively lean H2/air mixtures (equivalence ratio, ϕ=0.3–0.5) due to the occurrence of “flame tip opening phenomenon”. In the present work, the effect of inlet mixture temperature (Tin) on flame tip opening and combustion efficiency was investigated. It is demonstrated that for ϕ=0.5, flame tip opening is negligible even at Tin=300K, while for ϕ=0.3 and 0.4, this phenomenon becomes serious. As a result, a great amount of fuel leaks out and the combustion efficiency is sharply decreased. Nevertheless, if the inlet temperature is increased by around 50–100K for ϕ=0.4 and 150–200K for ϕ=0.3, the flame tip opening phenomenon can be notably improved and the combustion efficiency is significantly increased. Theoretical analysis reveals that an appropriate increment in the inlet mixture temperature can bring about favorable effects on the effective Lewis number, flame stretch rate and combustion intensity.

Experimental investigation and theoretical modelling of induced anisotropy during stress-softening of rubber

The Mullins effect refers to a stress-softening phenomenon of rubber-like materials during cyclic loading. Anisotropy of the material behaviour is generally observed after stretching. In this paper, a large set of original suitable experiments are reported to characterise this effect under several deformation conditions. Then, a phenomenological model is derived to capture the anisotropic distribution. For that, the affine micro-sphere model (Miehe et al., 2004) is amended with a directional network alteration in order to describe anisotropy. The alteration process, involving the breakage and the slippage of the links embedded in the macromolecular network, is modelled by the evolution of the average number of monomer segments per chain during stretching. The average chain length and the chain density are incrementally described by functions to allow both softening and stiffening, depending to the maximum and the minimum stretch rates and levels endured in each direction. The good capacity of the model to reproduce experimental observations validates the above assumptions.

Lift-off and blow-off of methane and propane subsonic vertical jet flames, with and without diluent air

The paper seeks to increase understanding of subsonic jet flame blow-off phenomena, through experimental studies that include the controlled introduction of air into the fuel jet. As the molar concentration of air in the jet flame gas, Aj, is increased the reaction zone becomes leaner, and the flame lift-off distance increases. Eventually, flame oscillations develop and are followed by flame blow-off. A jet mixing analysis enables the extent of the leaning-off of the mixture to be estimated. From this, the reduced mean flamelet burning velocity, ua, is found at the location of the pure fuel jet flame. The conditions for blow-off are correlated with the last measured stable values of the dimensionless flow number, Ub∗, for methane and propane jet flames, with and without added air. Values of Ub∗ decline as the proportion of added air increases, more markedly so with methane. This is attributed to the leaning-off of the flame, and the associated decrease in the flame extinction stretch rate. As Ub∗ declines in value, with increasing air dilution, the emissions of unburned hydrocarbons just prior to blow-off increase. An underlying generality of the findings is revealed when ua is introduced into the expression for Ub∗, and Aj is normalised by the moles of air required to burn a mole of fuel.

Diffusive-thermal instability of stretched low-Lewis-number flames of slot-jet counterflow burners

Characteristics and spatial structure of premixed low-Lewis-number flames in stretched flow of two slot burners are studied numerically and theoretically in the frame of thermo-diffusive model with one-step chemical reaction. Three different combustion regimes are distinguished: twin planar flames, twin wrinkled flames and multiple flame tubes. In the multiple flame tube case the continuous flame front surface does not exist and combustion wave is represented by the set of separate reacting spots of tube-like form. The regions of existence of different combustion regimes in fuel concentration / stretch rate plane were determined. It was found that continuous flames (i.e. wrinkled and planar twin flames) exist inside the C-shape extinction limit curve obtained in the frame of one-dimensional model, while flame tubes appear beyond this limit in the entire range of stretch rates. Investigations of Lewis number effect allow to conclude that extension of low-Lewis-number counterflow flame flammability limits is related with the possibility of formation of non-planar flame tube structure caused by the effect of diffusive-thermal instability. Similarities and differences in regime diagrams and spatial flame structure of stretched premixed flames in conventional axisymmetric configuration and in slot-jet arrangement are discussed. Besides that, theoretical and numerical results are compared with experimental data available in a literature.

Formation of a cool diffusion flame and its characteristics

Low-temperature (∼700 K) “cool” flames formed with n-heptane fuel were observed in the experiments conducted under microgravity. Recently, Won et al. demonstrated experimentally that such “cool” flames could be established under normal gravity. However, as ozone was added to air for supporting the flames in that experiment, the fundamental question on the formation of a self-supported n-heptane/air “cool” flame remained unanswered. A numerical investigation is conducted for (1) finding an answer to this question and (2) determining a procedure for establishing a “cool” flame. A standard opposing-jet burner is considered. Investigations are performed using a well-tested CFD code. A reduced mechanism that successfully captured the “cool” flames in microgravity is used. Calculations have demonstrated that a “cool” diffusion flame can be established with n-heptane under normal gravity without resorting to flame-speed promoters such as ozone, pressure or temperature. Using velocities of 4 and 7 cm/s and temperatures of 400 and 300 K for the fuel and air jets, respectively, a stable “cool” flame was obtained. Flame was ignited through increasing the temperature of the air jet to a value >724 K and then a self-sustained “cool” flame was obtained by decreasing the temperature back to 300 K. Parametric studies are performed on the applied gravitational force such that the heavy n-heptane flowed upward from the bottom nozzle or downward from the top nozzle. In general, flame remained flat with or without the gravity. However, when the fuel jet was at the bottom, it expanded faster and moved the flame closer to the fuel nozzle. “Cool” flame could not be stabilized for the same velocity and temperature conditions when fuel flowed from the top. “Cool” and normal diffusion flames obtained with identical flow conditions are compared. Limiting stretch rate for extinguishing the “cool” flame is determined.

Biomechanical behavior of bovine periodontal ligament: Experimental tests and constitutive model

A viscohyperelastic constitutive model with the use of the internal variables approach was formulated to evaluate the nonlinear elastic and time dependent anisotropic mechanical behavior of the periodontal ligament (PDL). Since the relaxation response was found to depend on the applied stretch, the adoption of the nonlinear viscous behavior in the present model was necessary. In this paper, Helmholtz free energy function was assigned to the material as the sum of hyperelastic and viscous terms which is based on the physical concept of internal variables. The constitutive model parameters were evaluated from the comparison of the proposed model and experimental data. For this purpose, tensile response of the bovine PDL samples under different stretch rates was obtained. The good correspondence between the proposed model and the experimental results confirmed the capability of the model to interpret the stretch rate behavior of the PDL. Moreover, the validity of structural model parameters was checked according to the results of the stress relaxation tests.

Laminar Burning Velocities of Fuels for Advanced Combustion Engines (FACE) Gasoline and Gasoline Surrogates with and without Ethanol Blending Associated with Octane Rating

ABSTRACTLaminar burning velocities of fuels for advanced combustion engines (FACE) C gasoline and of several blends of surrogate toluene reference fuels (TRFs) (n-heptane, iso-octane, and toluene mixtures) of the same research octane number are presented. Effects of ethanol addition on laminar flame speed of FACE-C and its surrogate are addressed. Measurements were conducted using a constant volume spherical combustion vessel in the constant pressure, stable flame regime at an initial temperature of 358 K and initial pressures up to 0.6 MPa with the equivalence ratios ranging from 0.8 to 1.6. Comparable values in the laminar burning velocities were measured for the FACE-C gasoline and the proposed surrogate fuel (17.60% n-heptane + 77.40% iso-octane + 5% toluene) over the range of experimental conditions. Sensitivity of flame propagation to total stretch rate effects and thermo-diffusive instability was quantified by determining Markstein length. Two percentages of an oxygenated fuel of ethanol as an additive, namely, 60 vol% and 85 vol% were investigated. The addition of ethanol to FACE-C and its surrogate TRF-1 (17.60% n-heptane + 77.40% iso-octane + 5% toluene) resulted in a relatively similar increase in the laminar burning velocities. The high-pressure measured values of Markstein length for the studied fuels blended with ethanol showed minimal influence of ethanol addition on the flame’s response to stretch rate and thermo-diffusive instability.

Combustion promotion and extinction of premixed counterflow methane/air flames by C6F12O fire suppressant

Along with the phase-out of CF3Br (Halon 1301), several agents have been proposed as halon replacements for use in suppressing fires in aircraft cargo bays. However, these potential drop-in replacements were found to have a promotion effect on the explosion of an aerosol can, which tested by the US Federal Aviation Administration. Motivated by this problem, we measured the laminar burning velocity of premixed methane/air flames with added one of these agents, C6F12O (Novec 1230), in the counterflow configuration, for fuel/air equivalence ratios of 0.63, 0.68, 0.74, and 0.82. C6F12O was added at levels up to 3.5% by volume fraction to each mixture. Numerical simulations were performed using the detailed kinetic mechanism. The predicted results were in good agreement with the experimental measurements. The burning velocity for the very lean flames ( Φ = 0.63) was increased with C6F12O added at low concentrations due to the additional heat release from C6F12O reaction, whereas for higher equivalence ratios ( Φ = 0.68–0.82), it always decreased with all added agent concentrations. The extinction stretch rates have also been measured using the counterflow technique to gain further insight into the promotion/inhibition behavior of C6F12O in ultra-lean ( Φ < 0.63) flames. The results showed that C6F12O has larger promotion effect for the ultra-lean conditions. Sensitivity analyses showed that lean flames are more sensitive to the fluorinated reactions compared to the rich. In addition, direct images of hydrocarbon flame inhibition by fluorinated ketone were provided for the first time to help interpret the experiments.

Flame Structure and Propagation in Turbulent Flame-Droplet Interaction: A Direct Numerical Simulation Analysis

Three-dimensional Direct Numerical Simulations (DNS) in canonical configuration have been employed to study the combustion of mono-disperse droplet-mist under turbulent flow conditions. A parametric study has been performed for a range of values of droplet equivalence ratio ϕd, droplet diameter ad and root-mean-square value of turbulent velocity u′. The fuel is supplied entirely in liquid phase such that the evaporation of the droplets gives rise to gaseous fuel which then facilitates flame propagation into the droplet-mist. The combustion process in gaseous phase takes place predominantly in fuel-lean mode even for ϕd>1. The probability of finding fuel-lean mixture increases with increasing initial droplet diameter because of slower evaporation of larger droplets. The chemical reaction is found to take place under both premixed and non-premixed modes of combustion: the premixed mode ocurring mainly under fuel-lean conditions and the non-premixed mode under stoichiometric or fuel-rich conditions. The prevalence of premixed combustion was seen to decrease with increasing droplet size. Furthermore, droplet-fuelled turbulent flames have been found to be thicker than the corresponding turbulent stoichiometric premixed flames and this thickening increases with increasing droplet diameter. The flame thickening in droplet cases has been explained in terms of normal strain rate induced by fluid motion and due to flame normal propagation arising from different components of displacement speed. The statistical behaviours of the effective normal strain rate and flame stretching have been analysed in detail and detailed physical explanations have been provided for the observed behaviour. It has been found that the droplet cases show higher probability of finding positive effective normal strain rate (i.e. combined contribution of fluid motion and flame propagation), and negative values of stretch rate than in the stoichiometric premixed flame under similar flow conditions, which are responsible for higher flame thickness and smaller flame area generation in droplet cases.

Axisymmetric rotational stagnation point flow impinging on a radially stretching sheet

The normal impingement of the rotational stagnation-point flow of Agrawal (1957) [8] on a sheet radially stretching at non-dimensional stretch rate β is studied. A similarity reduction of the Navier–Stokes equations yields an ordinary differential equation which is solved numerically over a range of β. A unique solution exists at the turning point β=βt and dual solutions are found in the region β>βt where βt=−0.657 is the turning point in the parametric shear stress curve separating upper from lower branch solutions. An analysis of solutions near the Agrawal point β=0 is provided, and the large-β asymptotic behavior of solutions is determined. Sample velocity profiles along both solution branches are presented. A linear temporal stability analysis reveals that solutions along the upper branch are stable while those on the lower branch are unstable.

Jet flame heights, lift-off distances, and mean flame surface density for extensive ranges of fuels and flow rates

An extensive review and re-thinking of jet flame heights and structure, extending into the choked/supersonic regime is presented, with discussion of the limitations of previous flame height correlations. Completely new dimensionless correlations for the plume heights, lift-off distances, and mean flame surface densities of atmospheric jet flames, in the absence of a cross wind, are presented. It was found that the same flow rate parameter could be used to correlate both plume heights and flame lift-off distances. These are related to the flame structure, jet flame instability, and flame extinction stretch rates, as revealed by complementary experiments and computational studies. The correlations are based on a vast experimental data base, covering 880 flame heights. They encompass pool fires and flares, as well as choked and unchoked jet flames of CH4, C2H2, C2H4, C3H8, C4H10 and H2, over a wide range of conditions. Supply pressures range from 0.06 to 90 MPa, discharge diameters from 4 × 10−4 to 1.32 m, and flame heights from 0.08 to 110 m. The computational studies enabled reaction zone volumes to be estimated, as a proportion of the plume volumes, measured from flame photographs, and temperature contours. This enabled mean flame surface densities to be estimated, together with mean volumetric heat releases rates. There is evidence of a “saturation” mean surface density and increases in turbulent burn rates being accomplished by near pro rata increases in the overall volume of reacting mixture.