Flame Heat Flux Research Articles

Experimental study and physical modeling of ceiling temperature and heat flux profiles by wall-attached fires in inclined tunnels

In this work, the longitudinal heat flux, temperature distribution and flame spread length, beneath a sloping tunnel ceiling caused by fire sources attached to the sidewall were experimentally investigated. The effect of heat release rate (HRR) and tunnel slope on the flame spread length, temperature and heat flux profile were comprehensively considered. The present results show that, in the longitudinal direction, the temperature and heat fluxes under ceiling decrease with increasing distance in the downstream and upstream directions from the flame stagnation point. Thermal and flame buoyancy will change the forces on the ceiling jet caused by a wall-attached fire, resulting in differences in the mass flow rate of fire plumes in upstream and downstream directions. A correlation is developed for the flame extent in the longitudinal upward and downward directions. The temperature and heat flux under ceiling increase in the upstream direction for a given distance in the longitudinal direction compared with the downstream direction and with increasing slopes of the tunnel inclination. This is due to the fact that the upstream thermal flow increases, and the flame extension length becomes larger, while the downstream thermal flow decreases exacerbating the difference of heat flux between upstream and downstream. In addition, the correlation between the dimensionless heat flux and the temperature profile under inclined ceiling in the upstream and downstream directions was further analyzed as a function of the flame length variation. These correlations are well described by physically based models for all the experimental results, including the heat flux under the tunnel ceiling at stagnation point and along the longitudinal flame extension.

Predicting the pyrolysis temperature for thermally thin fuels in opposed-flow flame spread in the thermal regime

The thermal theory of opposed-flow flame spread assumes that the fuel pyrolyzes at a constant pyrolysis temperature. However, the pyrolysis temperature cannot be thermodynamically determined, and its value is usually assigned from limited amount of experimental data that are available for different fuels. Detailed numerical modeling which employs finite-rate pyrolysis kinetics indicate that the pyrolysis temperature is not a constant across the pyrolysis zone and its value can also depend on several parameters such as the opposed-flow velocity, fuel thickness, etc. This situation is more pronounced for thermally thin solids where steady state conditions at a constant pyrolysis temperature are not achieved. In this work, a simplified scale analysis is performed to understand the behavior and dependence of the pyrolysis temperature and pyrolysis length on the fuel and environmental conditions. Two non-dimensional numbers - a pyrolysis number and a radiation number – are identified in the energy balance relation that control a competing behavior on the pyrolysis temperature. A closed-form formula for the pyrolysis temperature is developed through this analysis in the thermal regime that explains and qualitatively predicts the parametric behavior of the pyrolysis temperature when compared to a comprehensive numerical model and available experimental results. The agreement of the simplified model with the numerical solution can be improved by more properly quantifying the magnitude of the flame heat flux in the pyrolysing region.

The Flame Characteristics of a Tyre Fire on a Mining Vehicle

With vehicles frequently found in underground mines and tyres being a major fuel item, the risk of tyre fires will be severe underground. This study presents an in-depth analysis of tyre fires on mining vehicles to increase the knowledge of the risk, applying data from full-scale fire experiments and CFD simulations. It was found that the wheelhouse of the loader caused an increase in the flame tilt angle of approximately 10%, decreasing the flame impingement and heat flux downstream. The flame temperature of the drilling rig tyre was found to be approximately 7% higher than the loader tyre, increasing the risk of igniting adjacent fuel items. The construction of the wheelhouse/mudguard will contribute to a longer flame length by creating a fuel-rich environment. The CFD simulations predicted higher flame tilt angles for the drilling rig case for higher flow velocities, indicating the influence of a varying wheelhouse/mudguard construction and tyre geometry on the flame tilt angle. The construction of the loader resulted in a flow behaviour, where the short distance to the front mudguard/tyre and the separation of flow directly downstream of the protruding construction led to fire gases being steered past the front mudguard/tyre. In the drilling rig case, the longer distance to the front mudguard/tyre led to fire gases being directed towards the body of the vehicle after passing the area with flow separation. An increased knowledge of the tyre fire risk on mining vehicles and mitigating measures would improve the fire safety in underground mines.

Experimental investigation of heat transfer characteristics of an inverse diffusion flame in a coaxial tube burner for with and without swirl

Heat transfer by flame jet impingement is widely used in many of the industrial and domestic applications like heating metal bars, scrap melting, shaping the glass, metal slab cutting, domestic cooking and others. Aim of the present experimental work is to study an effect of swirl on a local heat flux distribution of an inverse diffusion flame (IDF) jet impinging on a flat target surface in a coaxial tube burner. The twisted tape of twist ratio 3 (corresponding to the swirl number, S = 0.52) is used to create a swirl in the central air jet of the burner. The flame shapes and heat flux distributions are compared for the with and without swirling IDF under the different air jet Reynolds number (Rea) of 1000 to 2500, equivalence ratio (ϕ) of 0.4 to 1.3 and a burner-to-impingement plate distance (H) of 10 to 100mm. The distributions of heat fluxes are studied within a radius of 75 mm from the point of stagnation on an impingement plate. Results show that the swirling IDF helps in clean combustion of the fuel with much shorter flame height. Swirling in the flame jet enhances the peak heat flux for the higher air jet Reynolds number for slightly fuel rich conditions of ϕ = 1.1 at the optimal burner-to-target plate distance of 40 mm.

The Effect of Inert Fuel Compounds on Flame Characteristics

To describe the effects of inert compounds in gaseous fuel, experiments on three different process burners (staged fuel burner, staged air burner, and low-calorific burner) were carried out. The tested burners are commercially available, but they were specially designed for experimental usage. Tests were carried out in the semi-industrial burner testing facility to investigate the influence of inert gases on the flame characteristics, emissions, and heat flux to the combustion chamber wall. Natural gas was used as a reference fuel, and, during all tests, thermal power of 500 kW was maintained. To simulate the combustion of alternative fuels with lower LHV, N2 and CO2 were used as diluents. The inert gas in the hydrocarbon fuel at certain conditions can lower NOx emissions (up to 80%) and increase heat flux (up to 5%). Once incombustible compounds are present in the fuel, the higher amount of fuel flowing through nozzles affects the flow in the combustion chamber by increasing the Reynolds number. This can change the flame pattern and temperature field, and it can be both positive and negative, depending on actual conditions.

Experimental and numerical study of upward flame spread and heat transfer over expanded polystyrene at different altitudes

Experimental and numerical study on upward, vertical flame spread was carried out on expanded polystyrene (EPS) at two different altitudes of 50 m and 3658 m to understand the effect that altitude has on flame spread of melted material. The experiments show that, with the altitude increase, the flame spread rate would decrease. At low altitude, the flame spread rate accelerated at later time, while at high altitude, the stagnant stage of pyrolysis front was formed. The numerical simulation could well give the trend of pyrolysis front evolution and the different flame spread behaviors with altitudes. It was found that, at low altitude, Raxincreased slowly in the turbulent period with relatively large entrainment air flow rate, mainly due to the increased and then decreased mass loss rate in the wall fire zone. While, at high altitude, the simulated increasing entrainment air flow rate, combined with the larger preheating length δf and the smaller flame heat flux qf", resulted in the stagnancy of pyrolysis front easily. It was hypothesized that extinction occurred eventually at high altitude due to competition between flame spread rate νf and preheating length δf.

Development of a pyrolysis model for poly(vinylidene fluoride-co-hexafluoropropylene) and its application in predicting combustion behaviors

Pyrolysis and combustion behaviors of poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP), a promising polymer matrix in lithium-ion polymer battery, are experimentally and numerically investigated. A pyrolysis reaction scheme consisting of three high order consecutive reactions was established based on the thermogravimetric analysis (TGA) measurements and parameterized combining a modified numerical model and Genetic Algorithm (GA). The results show that in the heating rate range of 5–20 K min−1 the peak temperature of pyrolysis increases from 739 to 770 K. After deriving the pyrolysis kinetics, the thermodynamics was further determined by inversely modeling the measured mass loss rate in cone calorimeter tests. By fitting the measured heat release rate, the effective heat of combustion of each gaseous component, the global effective heat of combustion (9.56 MJ kg−1) and the flame heat flux (15 kW m−2) were quantitatively estimated. Reliability of the fully developed model was validated by alternative experimental results which were not utilized in parameterization, and good agreement was found. The collected ignition times in cone calorimeter tests were well predicted by the numerical model employing the measured critical mass flux, 2.87±0.32 g m−2 s−1. By invoking the ignition theory proposed for thermally intermediate solid and the measured ignition data, thermal diffusivity of PVDF-HFP, critical heat flux and critical temperature were assessed to be 3.00 × 10−7 m−2 s−1, 17.13–24.34 kW m−2 and 763.34–794.13 K, respectively.

Cracking in the translucent alumina ceramic during flame thermal shock

Crack measurement after thermal shock is usually considered as a replacement because real-time observation of thermal shock experiments is difficult to achieve. This paper presents an experimental approach for real-time displaying thermal shock cracking using oxygen-acetylene flame and high-speed imaging of translucent ceramic. We capture the crack propagation process, calculate the crack propagation speed, discuss the effect of sample size and flame heat flux on the crack propagation, and analyze the difference between the crack propagation under cold shock and hot shock. This paper further improves the mechanism of thermal shock damage of ceramic materials.

Chemistry effects in the wall quenching of laminar premixed DME flames

Fundamental studies on Flame-Wall Interaction (FWI) are of the utmost importance to unravel the intricate coupling between chemistry and transport in the near-wall region, and to characterize the quenching dynamics. For this purpose, an accurate description of reaction kinetics is especially needed. In this work, the role of chemistry during the wall quenching of premixed dimethyl ether (DME) flames is numerically investigated, leveraging recently-obtained experimental data in a Side-Wall Quenching configuration (SWQ) in a variety of conditions. A detailed kinetic model describing the low-to-high temperature oxidation of DME is used as starting point. In order to accommodate it into 2D simulations, it is first reduced to a skeletal level, both accounting for (31 species and 140 reactions) and neglecting (20 species and 93 reactions) low-temperature chemistry, and successfully validated against the original model in predicting flame propagation and Head-On Quenching (HOQ). Using an established CFD framework, the SWQ features of DME are investigated in terms of flame structure, heat fluxes and thermochemical CO-T states. A good agreement with the available experimental data is observed in the operating space. In the near-wall region, the prediction of the thermochemical state is most critical, and it is found that diffusion is here the prevailing contribution in defining such state. In the same region, kinetic analysis shows that low-temperature chemistry affects the speciation of the quenching region to a good extent, which is modified with respect to a freely-propagating flame. Yet, due to the lower reactivity, SWQ thermal features are not significantly influenced. As a result, for the purposes of the wall quenching analysis, only high-temperature chemistry needs to be accounted for, and the 20-species mechanism can be safely considered as a consolidated milestone for future studies.

Cellular flame structures and thermal characteristics of axi-symmetric ceiling fires: An experimental study and scaling analysis

The present study provides an experimental characterization of cellular flame structures and thermal characteristics of axi-symmetric ceiling fires. Experiments were carried out employing circular gaseous burners of various diameters at the ceiling facing downward using methane and propane as fuel. For this configuration, a hot buoyant diffusion flame burning beneath the cold fuel gas issuing from the ceiling above was naturally resulted in. A cellular flame structure, due to the inherent “Rayleigh-Taylor’’ instability of this buoyant flow configuration, was formed beneath the ceiling. The flame length (radius), temperature and heat flux distribution along the ceiling as well as characteristic inner cell size evolution of this special cellular flame were quantified experimentally for such ceiling fire of various conditions. Scaling analysis was performed to analyze the obtained parameters of the cellular flame structure and thermal characteristics of the ceiling fire. Results showed that the overall length (radius) of the cellular flame has a 2/5 power dependence on heat release rate and is independent of burner sizes and fuel types. Temperature profile and heat flux distribution for various conditions can be universally expressed as a function of L/Rf, the distance from the burner center normalized by the flame length. The characteristic cell size of the cellular flame was related to temperature, which can be well represented by a 2.33 power function based on the “Rayleigh-Taylor’’ instability scaling analysis. The cell size spatial evolution inside the cellular flame was self-similar corresponding to the dependence of temperature on relative position, and a non-dimensional function was obtained. This study provides fundamental data and a scaling analysis into the basic physics of the cellular flame behavior and thermal characteristics of ceiling fires.

Burning in microgravity: Experimental results and analysis

Burning experiments are analyzed for 59 successfully ignited tests using a gas burner (BRE) to emulate the steady burning of 25 mm diameter flat surface materials. More than half of the tests resulted in long burns of at least 2 and as long as 5 min. Mixtures of ethylene and nitrogen allow for 23.6 and 47.2 kJ/g heats of combustion (LHV). Nominal ambient conditions range from 40% to 21% oxygen and pressures of 1 to about 0.56 bar. NASA human habitat atmospheres have been used. Generally, it has been found that nominal oxygen mole fractions of 26% and above can allow steady flames. The flames are thin blue in color and grow slowly over time for minutes. Some self-extinguish, some had periodic oscillations, and others appear to have become steady and were shut down. Theoretical analyses show the shutdown flames were steady in growth, and all of the test endpoints were more than 94% of steady state in flame heat flux. Flame heat flux for set mass flux allowed the estimation of heats of gasification to relate to steady solid materials that might burn in microgravity. Radiometers allowed the computation of flame radiative fraction that appeared to correlate well with the measured flame height. Results are shown for heat flux, flame height and base radius, radiative fraction as a function of fuel mixture mass flux, and various oxygen and pressure atmospheres.

Concurrent flame spread over vertically oriented paper sheet: The effect of sample thickness

SummaryPacking or printing paper made out of cellulose is widely produced and used in daily life. The thickness of thin material affects the burning process significantly. Concurrent flame spread is an effective approach when analyzing and evaluating the fire hazard for combustible materials. Conducting this work will provide further understanding of the flame spread mechanism and reduce fire hazard. It will also enable investigation of the effect of sample thickness on concurrent flame spreading over the thin paper sheets experimentally. Numerically examining concurrent flame spread over thin paper sheet with varied thicknesses is also performed using Direct Numerical Simulation, which can provide more details on flame spread process. Qualitatively, the model predictions agree reasonably with the experiment in terms of the flame contour, burn duration, and flame spread rate. The moving rates of the flame base and pyrolysis front decrease with sample thickness both experimentally and numerically. The relationship between net heat flux, flame standoff distance, and solid burning rate is analyzed, with the burning rate exhibiting a similar trend to that of the net heat flux. A correlation of the flame net heat flux with the normalized distance in the pyrolysis region is also established where the flame heat flux displays a decay trend with the normalized space.

Quantitative infrared image analysis of simultaneous upstream and downstream microgravity flame spread over thermally thin cellulose fuel in low speed forced flow

Quantitative image analysis of infrared (IR) measurements are compared to visible color images for simultaneous upstream and downstream flame spread over thermally thin cellulose samples in low speed forced flow in microgravity. These results are a unique set of data that provide a wealth of information to guide future modeling efforts. Test conditions at ambient pressure were conducted in 21–50% O2 by volume (N2 balance) and forced flow velocities from 2 cm/s to 20 cm/s. The tests conditions encompass strictly upstream flame spread to simultaneous upstream and downstream flame spread. Steady upstream flame spread is observed while the downstream flame only begins to spread at the highest flow velocities due to the oxygen shadow cast by the upstream flame (oxygen depleted region downstream of the flame). Blackbody surface temperature gradients for the upstream flame are an order of magnitude larger than the downstream gradients. Upstream preheat lengths decrease with flow while downstream preheat lengths increase. Downstream pyrolysis lengths reach steady state for most cases and increase with convective heating while upstream pyrolysis lengths increase with time. Surface thermocouple (TC) histories were non-dimensionalized to obtain a characteristic surface temperature profile using new scaling analyses. Applying the ellipticity of the leading edge to the scaling reveals the local flow velocity at the leading edge is on the order of diffusive velocities and the flame thermal expansion acts as a significant barrier to divert the flow. A surface energy balance reveals that the peak heat flux for both upstream and downstream flames increases with oxygen concentration and forced flow velocity. The upstream flame heat flux is equally divided between fuel heat up and surface radiation. The downstream heat flux goes almost exclusively to surface radiation. Comparisons of these results to previous applicable research are provided throughout the text and generally agree well.

Experimental determination of the evolution of the incident heat flux received by a combustible during a cone calorimeter test: Influence of the flame irradiance

The decomposition kinetic of polymeric materials in a cone calorimeter strongly depends on the irradiance level imposed at the sample’s surface. Indeed, even if the irradiance level is supposed to be kept constant during cone calorimeter test, the amount of heat flux which is emitted by the flame can greatly increase the total heat flux received by the material. Analytical treatment on recently obtained results of an acrylonitrile-butadiene-styrene’s mass loss rate with controlled atmosphere cone calorimeter has shown that the differences observed between well-ventilated and inert environments can be attributed to the impact of the flame. This observation has brought the necessity to determine the impact of the flaming process on the material thermal decomposition. To do so, series of experiments have been devised, based on the insertion of a heat fluxmeter within the matrix of an acrylonitrile butadiene styrene material, during cone calorimeter tests in order to measure the flame heat flux as a function of the decomposition and the combustion processes.

Experimental analysis and modeling of Buoyancy-driven flame spread on cast poly(methyl methacrylate) in corner configuration

A new experimental setup was developed to study turbulent, buoyancy-driven flame spread on a corner wall. Two 146 × 50 × 0.58 cm panels of cast black poly(methyl methacrylate) (PMMA), whose pyrolysis properties were fully characterized in a separate study, were ignited using a triangular propane burner. The corner wall assembly was placed into a well-ventilated enclosure and heat release rate (HRR) and flame heat flux to the corner wall were measured in 7 repeated experiments. The HRR measurement was designed to achieve a fast response time (13 s) and was correlated with the flame heat flux, which was obtained using water-cooled heat flux gauges positioned in 28 locations distributed over the PMMA surface. Simultaneously, a monochromatic, 900 nm, video of the spreading flame was recorded and analyzed to determine the evolution of soot radiation intensity and flame geometry. Using collected data, an empirical model relating spatially resolved heat feedback from the flame to the solid fuel surface and HRR was developed and integrated with a detailed pyrolysis model. Simulations were conducted in an uncoupled and coupled mode. The uncoupled simulations, where the flame heat feedback was effectively prescribed to match the experimental measurements, revealed the importance of the knowledge of the split between the convective and radiative portions of the flame heat flux. The coupled simulations, where the flame heat feedback was computed from the simulated HRR, revealed that the coupling amplifies even relatively small uncertainties in the model parameters to produce large errors in the HRR predictions.

Experimental characterization and modeling of boundary conditions and flame spread dynamics observed in the UL-94V test

Abstract To characterize the UL-94 vertical burning test (UL-94 V), temperature, oxygen content, and heat flux of the burner flame were measured using an R-type thermocouple, oxygen analyzer, and water-cooled Schmidt–Boelter gage, respectively. To account for sample geometry, mock samples from Kaowool PM insulation board were used during the burner measurements. Temperature and heat flux measurements were used to express the heat flux of the burner as a linear, piecewise function of burner flame temperature and a constant convective heat transfer coefficient. UL-94 V tests were conducted using 0.27 cm thick poly(methyl methacrylate) (PMMA) samples with and without insulated sides to investigate edge effects. All UL-94 V tests were recorded on video using a 900-nm narrow-band filter to focus on emissions from soot for tracking flame length over time. In some of these tests, a heat flux gage was embedded into the sample to measure PMMA flame heat flux to verify a previously developed laminar wall flame heat feedback submodel. PMMA flame heat fluxes of insulated samples confirmed the wall flame submodel, while non-insulated samples had significantly greater heat fluxes; the flame submodel was scaled accordingly. The burner and wall flame heat flux submodels were combined with an independently developed pyrolysis model of PMMA to conduct two-dimensional, time-resolved simulations of the UL-94 V test. Burner flame oxygen content was measured to be about 5 vol% and was found to enhance PMMA decomposition. Inclusion of the oxygen effect was essential to predict ignition. The simulation predicted flame length and spread on insulated UL-94 V samples reasonably well, validating the submodels. However, the simulation underpredicted flame length on the non-insulated samples; discrepancies were attributed to burning and spread on the edges which were not modeled explicitly. The developed model can be applied to non-charring polymeric solids with no to moderate amount of dripping. Its applicability for charring and intumescent materials will be explored in the future.

Mechanisms of flame spread and burnout in large enclosure fires

Knowledge of the first principles defining fire behaviour in large enclosures remains limited despite their common use in modern tall buildings. The evolution of a fire in large enclosures can be defined by the relationship between the flame front and burnout velocities (VS/VBO). This relationship can be classified into three distinct fire spread modes being Mode 1 (VS/VBO → ∞), Mode 2 (VS/VBO > 1), and Mode 3 (VS/VBO ≈ 1). The mechanisms governing flame spread and burnout are investigated using four full-scale enclosure fire experiments with high porosity wood cribs with similar enclosure geometries. Flame and burnout front positions and velocities are estimated using video data. Velocities are affected by the heat feedback from the enclosure and smoke layer to the fuel. The spread velocity shows two regimes, a minimum external heat flux above which there is surface spread (q˙s,min″) and a heat flux that defines the onset of very rapid flame spread (q˙rs,crit″). A phenomenological model is developed to help identify the underlying mechanisms controlling the transition between the different spread modes. Both the model and data show that for wood cribs, the dependence of the burnout front velocity to the external radiation is weak, whereas the dependence of the flame spread velocity to the external and flame heat flux is strong. A transition from Mode 3 (VS/VBO ≈ 1) to Mode 2 (VS/VBO > 1) occurs with increasing external heat fluxes above q˙s,min″. The transition to Mode 1 (VS/VBO → ∞) is further defined once q˙rs,crit″ is attained due to a sudden increase in the flame heat flux by changing the ventilation condition, or by significant increases in the external heat flux from the enclosure.

Characteristic of cryogenic hydrogen flames from high-aspect ratio nozzles

Unintentional leaks at hydrogen fueling stations have the potential to form hydrogen jet flames, which pose a risk to people and infrastructure. The heat flux from these jet flames are often used to develop separation distances between hydrogen components and buildings, lot-lines, etc. The heat flux and visible flame length is well understood for releases from round nozzles, but real unintended leaks would be expected to be from higher aspect-ratio cracks. In this work, we measured the visible flame length and heat-flux characteristics of cryogenic hydrogen flames from high-aspect ratio nozzles. Heat flux measurements from 5 radiometers were used to assess the single-point vs the multi-point methods for interpretation of heat flux sensor data, finding the axial distance of the sensor for a single-point heat flux measurement to be important. We compare the flame length and heat flux data to flames of both cryogenic and compressed hydrogen from round nozzles. The aspect ratio of the release does not affect the flame length or heat flux significantly, for a given mass flow under the range of conditions studied. The engineering correlations presented in this work enable the prediction of flame length and heat flux which can be used to assess risk at hydrogen fueling stations with liquid hydrogen and develop science-based separation distances for these stations.

Flame spread over polyethylene-insulated copper and stainless-steel wires at high pressure

This work studied flame spread over polyethylene (PE)-insulated wires at high pressure with an emphasis on the effect of ambient pressure. Laboratory simulated wires were used as a tested wire, which consisted of semi-transparent low-density PE (LDPE) tube as an insulation and copper (Cu) rod or stainless-steel (SS) tube as a core. Increasing ambient pressure produced much soot, leading to an intensively yellow luminous flame. Flame spread rate for Cu rod increased with ambient pressure, whereas that for SS tube decreased. A qualitative analysis via a simplified flame spread model shows that the flame heat flux increases with ambient pressure, but consequently the flame heating decreases due to the decreased flame heating length. Therefore, the flame spread rate for SS tube decreased with increasing ambient pressure. For Cu rod, however, the core heating is dominant enough to compensate the decreased flame heating, and thus the ambient pressure positively affected the flame spread. During the flame spread, melted insulations were often dripped down, but it reduced with increasing ambient pressure. For Cu rod, no dripping occurred when further increasing ambient pressure, which indicates that there is the dripping limit at a high-pressure region. These findings should contribute to electrical fire safety in elevated pressure environments.

Flame shapes and thermal flux of vertical hydrocarbon flames

Hydrocarbon fuels are involved in most fire accidents occurring in industrial facilities, which may lead to catastrophic consequences in terms of life and property losses. The prediction of the related-fire effects can contribute to provide effective protection measures, hence mitigating the consequences of hydrocarbon flames in processing environments. In this regard, there is an essential need for developing state-of-the-art correlations able to accurately estimate the flame shapes and heat fluxes for a wide range of possible hydrocarbon fires. The present paper collects a vast data bank of vertical hydrocarbon fire experiments involving multiple fuels, burner diameters, mass flow rates and wind speeds. Correlations are developed, based on the data collected, to describe the flame-geometry descriptors and the heat fluxes of vertical hydrocarbon flames under different flow regimes.