Burning rate of homogeneous energetic materials with thermal expansion and varying thermal properties in the condensed phase

We present a study of the one-dimensional flame structure of combusting solid propellants that focuses on the effects of thermal expansion and variable thermal properties in the condensed phase. A nonlinear heat equation is derived for a burning thermo-elastic solid with temperature-dependent specific heat, thermal expansion, and thermal conductivity coefficients. It is solved for different modelling approximations both analytically and numerically. Explicit expressions are derived for the regression rate of the propellant surface as functions of surface temperature and thermal expansion parameters. A simple one-step reaction model of the gas phase is used to study the full structure of propellent flame and illuminate the influence of temperature-dependent material properties on the regression rate, surface temperature, and flame stand-off distance. Results are displayed for HMX and compared with experimental data and numerical simulation with fair success.     

Effects of radiation heat loss on laminar premixed ammonia/air flames

Ammonia (NH₃) direct combustion is attracting attention for energy utilization without CO₂ emissions, but fundamental knowledge related to ammonia combustion is still insufficient. This study was designed to examine effects of radiation heat loss on laminar ammonia/air premixed flames because of their very low flame speeds. After numerical simulations for 1-D planar flames with and without radiation heat loss modeled by the optically thin model were conducted, effects of radiation heat loss on flame speeds, flame structure and emissions were investigated. Simulations were also conducted for methane/air mixtures as a reference. Effects of radiation heat loss on flame speeds were strong only near the flammability limits for methane, but were strong over widely diverse equivalence ratios for ammonia. The lower radiative flame temperature suppressed the thermal decomposition of unburned ammonia to hydrogen (H₂) at rich conditions. The equivalence ratio for a low emission window of ammonia and nitric oxide (NO) in the radiative condition shifted to a lower value than that in the adiabatic condition.     

Theoretical analysis of the evolution from ignition kernel to flame ball and planar flame

Dynamics of flame kernel evolution with and without external energy addition has been investigated analytically and numerically. Emphasis is placed on the effects of radiation heat loss, ignition power and Lewis number on the correlation and transition between the initial flame kernel, the self-extinguishing flame, the flame ball, the outwardly propagating spherical flame and the propagating planar flame. The present study extends previous results by bridging the theories of the non-adiabatic stationary flame balls and travelling flames and allowing rigorous consideration of radiation heat losses. The results show that the effects of radiation heat loss play an important role in flame regimes and flame transition and result in a new isolated self-extinguishing flame. Furthermore, it is found that radiation heat losses significantly increase the critical ignition radius and result in three different dependences of the minimum ignition power on the Lewis number. Comparisons between the results from the transient numerical simulation and those from the quasi-steady state analysis show a good agreement. The results suggest that prediction of flame initiation without appropriate consideration of radiation is not acceptable.     

The importance of thermal radiation transfer in laminar diffusion flames at normal and microgravity

The importance of radiation heat loss in laminar and turbulent diffusion flames at normal gravity has been relatively well recognized in recent years. There is currently lack of quantitative understanding on the importance of radiation heat loss in relatively small scale laminar diffusion flames at microgravity. The effects of radiation heat transfer and radiation absorption on the structure and soot formation characteristics of a coflow laminar ethylene/air diffusion flame at normal- and microgravity were numerically investigated. Numerical calculations were conducted using GRI-Mech 3.0 combustion chemistry without the NO_x mechanism and complex thermal and transport properties, an acetylene based soot formation model, and a statistical narrow-band correlated-k non-grey gas radiation model. Radiation heat transfer and radiation absorption in the microgravity flame were found to be much more important than their counterparts at normal gravity. It is important to calculate thermal radiation transfer accurately in diffusion flame modelling under microgravity conditions.     

Theoretical and experimental studies on mesoscale flame propagation and extinction

Mesoscale flame propagation and extinction of premixed flames in channels are investigated theoretically and experimentally. Emphasis is placed on the effect of wall heat loss and the wall–flame interaction via heat recirculation. At first, an analytical solution of flame speed in mesoscale channels is obtained. The results showed that channel width, flow velocity, and wall thermal properties have dramatic effects on the flame propagation and lead to multiple flame regimes and extinction limits. With the decrease in channel width, there exist two distinct flame regimes, a fast burning regime and a slow burning regime. The existence of the new flame regime and its extended flammability limit render the classical quenching diameter inapplicable. Furthermore, the results showed that at optimum conditions of flow velocity and wall thermal properties, mesoscale flames can propagate faster than the adiabatic flame. Second, numerical simulation with detailed chemistry demonstrated the existence of multiple flame regimes. The results also showed that there is a non-linear dependence of the flame speed on equivalence ratio. Moreover, it is shown that the Nusselt number has a significant impact on this non-linear dependence. Finally, the non-linear dependence of flame speed on equivalence ratio for both flame regimes is measured using a C₃H₈–air mixture. The results are in good agreement with the theory and numerical simulation.     

Instability of a flame front propagating through a fuel-rich droplet–vapour–air cloud

A simple model of a flame front propagating through a fuel-rich droplet–vapour–air mixture is presented in which the fuel droplets are assumed to evaporate in a sharp front ahead of the reaction front. By performing a linear stability analysis neutral stability boundaries are determined. It is shown that the presence of the spray of droplets in the fresh mixture can have a profound effect by causing cellularization of the flame front. Specifically, we demonstrate that under certain circumstances a spray flame can be cellular when its equivalent non-spray flame is completely stable. Furthermore, it is shown that even when the non-spray flame is itself cellular the equivalent spray flame will have a finer cellular structure. These theoretical predictions verify qualitatively for the first time independent experimental observations from the literature. It is thus shown that the primary effect of the spray on the stability of these flames is due to heat loss from the absorption of heat by the droplets for vaporization. The influence of the initial liquid fuel loading and the latent heat of vaporization on the critical wavenumber associated with cellularity provide further evidence of the responsibility of the heat loss mechanism for these spray-related phenomena. Finally, the cellularity of the spray flames with their attendant increase in flame front area suggest a plausible rationale for the experimentally observed burning velocity enhancement induced by the use of a spray of fuel droplets.     

The entropy of a single large finite system undergoing both heat and work transfer

Computing the entropy of a system from a single trajectory is discussed when the energy exchange with the environment includes both mechanical and thermal terms. The physical example chosen as an illustration is a cluster of atoms impacting a hard surface. Each atom of the cluster interacts with the smooth surface by a momentum transfer using the hard cube model [E. K. Grimmelmann, J. C. Tully and M. J. Cardillo, J. Chem. Phys. 72, 1039 (1980)]. Because of the thermal motion of the surface atoms the atoms of the cluster rebound from the surface with a (random) thermal component to their momentum. The change in the internal energy of the cluster has therefore both a mechanical, work, term and a heat transfer and the heat term contributes to the change in entropy of the cluster but the major contribution is the loss of potentially available work.     

Effects of heat loss and viscosity friction at walls on flame acceleration and deflagration to detonation transition

The coupled effect of wall heat loss and viscosity friction on flame propagation and deflagration to detonation transition(DDT) in micro-scale channel is investigated by high-resolution numerical simulations.The results show that when the heat loss at walls is considered, the oscillating flame presents a reciprocating motion of the flame front.The channel width and Boit number are varied to understand the effect of heat loss on the oscillating flame and DDT.It is found that the oscillating propagation is determined by the competition between wall heat loss and viscous friction.The flame retreat is led by the adverse pressure gradient caused by thermal contraction, while it is inhibited by the viscous effects of wall friction and flame boundary layer.The adverse pressure gradient formed in front of a flame, caused by the heat loss and thermal contraction, is the main reason for the flame retreat.Furthermore, the oscillating flame can develop to a detonation due to the pressure rise by thermal expansion and wall friction.The transition to detonation depends non-monotonically on the channel width.     

Flamelet structure in turbulent premixed swirling oxy-combustion of methane

Two key flame macrostructures in swirling flows have been observed in experiments of oxy-combustion (as well as air-combustion); as the equivalence ratio is raised, the flame moves from being stabilized on just the inner shear layer (Flame III) to getting stabilized on both the inner and outer shear layers (Flame IV). We report results of an LES investigation of two different inlet oxy-fuel mixtures, in a turbulent swirling flow at $\text{Re}=20,000,$ that capture these two macrostructures. Previous work on the effects of heat loss have mostly focused on its impact on macro-scale observations. In this paper, we examine how heat loss impacts the flame microstructures as well for these two macrostructures. For both flames, the flamelet structure, as represented by a scatter plot of the normalized fuel concentration against the normalized temperature, depends on whether the combustor walls are adiabatic or non-adiabatic. For the adiabatic case, the flamelets of both macrostructures behave like strained flames. When wall heat transfer is included, Flame III microstructure is more bimodal. Since this flame extends farther downstream and part of it propagates along the walls, heat transfer has a greater impact on it’s microstructure. These results show that heat loss impacts not just the macro properties of the flame such as its shape or interactions with the wall, but also fundamentally changes its internal structure. Scatter plots of the turbulent flames are constructed and compared to different 1D laminar flame profiles (e.g., strained or with heat loss), and comparisons suggest the important role of the wall thermal boundary conditions in the accurate simulations of combustion dynamics and interpretations of experimental data, including data reduction and scaling.     

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.     

A three-dimensional model of steady flame spread over a thin solid in low-speed concurrent flows

Athree-dimensional model of a steady concurrent flame spread over a thin solid in a low-speed flowtunnel in microgravity has been formulated and numerically solved. The gas-phase combustion model includes the full Navier-Stokes equations for the conservation of mass, momentum, energy and species. The solid is assumed to be a thermally thin, non-charring cellulosic sheet and the solid model consists of continuity and energy equations whose solution provides boundary conditions for the gas phase. The gas-phase reaction is represented by a one-step, second-order, finite-rate Arrhenius kinetics and the solid pyrolysis is approximated by a one-step, zeroth-order decomposition obeying an Arrhenius law. Gas-phase radiation is neglected but solid radiative loss is included in the model. Selected results are presented showing detailed three-dimensional flame structures and flame spread characteristics.

In a parametric study, varying the tunnel (solid) widths and the flow velocity, two important three-dimensional effects have been investigated, namely wall heat loss and oxygen side diffusion. The lateral heat loss shortens the flame and retards flame spread. On the other hand, oxygen side diffusion enhances the combustion reaction at the base region and pushes the flame base closer to the solid surface. This closer flame base increases the solid burnout rate and enhances the steady flame spread rate. In higher speed flows, three-dimensional effects are dominated by heat loss to the side-walls in the downstream portion of the flame and the flame spread rate increases with fuel width. In low-speed flows, the flames are short and close to the quenching limit. Oxygen side diffusion then becomes a dominant mechanism in the narrow three-dimensional flames. The flame spreads faster as the solid width is made narrower in this regime. Additional parametric studies include the effect of tunnelwall thermal condition and the effect of adding solid fuel sample holders.     

Stability of a spherical flame ball in a porous medium

Gaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.

Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero.     

Computational Modeling of Boundary Layer Flashback in a Swirling Stratified Flame Using a LES-Based Non-Adiabatic Tabulated Chemistry Approach

When operating under lean fuel–air conditions, flame flashback is an operational safety issue in stationary gas turbines. In particular, with the increased use of hydrogen, the propagation of the flame through the boundary layers into the mixing section becomes feasible. Typically, these mixing regions are not designed to hold a high-temperature flame and can lead to catastrophic failure of the gas turbine. Flame flashback along the boundary layers is a competition between chemical reactions in a turbulent flow, where fuel and air are incompletely mixed, and heat loss to the wall that promotes flame quenching. The focus of this work is to develop a comprehensive simulation approach to model boundary layer flashback, accounting for fuel–air stratification and wall heat loss. A large eddy simulation (LES) based framework is used, along with a tabulation-based combustion model. Different approaches to tabulation and the effect of wall heat loss are studied. An experimental flashback configuration is used to understand the predictive accuracy of the models. It is shown that diffusion-flame-based tabulation methods are better suited due to the flashback occurring in relatively low-strain and lean fuel–air mixtures. Further, the flashback is promoted by the formation of features such as flame tongues, which induce negative velocity separated boundary layer flow that promotes upstream flame motion. The wall heat loss alters the strength of these separated flows, which in turn affects the flashback propensity. Comparisons with experimental data for both non-reacting cases that quantify fuel–air mixing and reacting flashback cases are used to demonstrate predictive accuracy.     

New Experimental Data for the Validation of Radiative Heat Transfer

The numerical simulation of radiative heat transfer is now well established. Key ingredients in such a simulation model are calculated view factors that are used to describe the exchange of radiated energy between different surfaces. Several methods for the calculation of these geometrical factors are available, including Integration, Monte Carlo, and the Hemi-cube methods. Several analytical test cases are also available, such as the well-known “parallel plates” case, which allow modelers to validate their view factor routines. However, there is much less information available that combines both view factor information and heat transfer effects simultaneously.

This article describes the construction of a simple testing rig that allows experiments to be performed that combine view factor effects with measured heat transfer exchanged between surfaces only. The equipment has been used to consider simple cases, such as the parallel plates test case, and also cases where shadowing is important. The results of these experiments are presented as experimental benchmarking data for model users and developers.     

ERP study of the RKKY interaction in metallic EuxGd1−xB6

The RKKY interaction in metallic Eu_xGd_1?xB₆ compounds has been studied by EPR technique for x = 0.00, 0.20, 0.40 and 0.50. In the region of the absorption maximum the experimental spectra can be fitted to a lineshape function consisting of both Lorentzian absorption and dispersion components. Weiss constants, exchange fields, unbottlenecked g-shifts, and thermal broadening are calculated on the basis of the RKKY model and compared to the experimental results. The predicted Weiss constants and exchange fields are in good agreement with experiment, indicating the validity of the RKKY model. However, the predicted g-shifts and thermal broadening are much greater than those measured experimentally. The reduced g-shifts and thermal broadening are interpreted in terms of a magnetic resonance bottleneck, and the relaxation rates due to the interaction of the conduction electrons with the localized moments and lattice are evaluated.     

Effect of flame retardants on side-wall quenching of partially premixed laminar flames

A combined experimental and numerical investigation of partially premixed laminar methane-air flames undergoing side-wall quenching (SWQ) is performed. A well-established SWQ burner is adapted to allow the seeding of the main flow with additional gaseous products issued from a (secondary) wall inlet close to the flame’s quenching point. First, the characteristics of the partially premixed flame that quenches at the wall are assessed using planar laser-induced fluorescence measurements of the OH radical, and a corresponding numerical simulation with fully-resolved transport and chemistry is conducted. A boundary layer of enriched mixture is formed at the wall, leading to a reaction zone parallel to the wall for high injection rates from the wall inlet. Subsequently, in a numerical study, the wall inflow is mixed with dimethylmethylphosphonat (DMMP), a phosphor-based flame retardant. The DMMP addition allows the assessment of the combined effects of heat loss and flame retardants on the flame structure during flame-wall interaction. With an increasing amount of DMMP in the injected mixture, the flame stabilizes further away from the wall and shows a decrease in the local heat-release rate. Thereby, the maximum wall heat flux is significantly reduced. That results in a lower thermal load on the quenching wall. The flame structure analysis shows an accumulation of the intermediate species HOPO at the wall similar to the CO accumulation during the quenching of premixed flames without flame retardant addition. The study shows how the structure of a partially premixed flame is influenced by a wall that releases either additional fuel or a mixture of fuel and flame retardant. The insights gained from the canonical configuration can lead to a better understanding of the combined effects of flame retardants and heat losses in near-wall flames.     

Comparative analysis of methods for heat losses in turbulent premixed flames using physically-derived reduced-order manifolds

Heat losses have the potential to substantially modify turbulent combustion processes, especially the formation of pollutants such as nitrogen oxides. The chemistry governing these species is strongly temperature sensitive, making heat losses critical for an accurate prediction. To account for the effects of heat loss in large eddy simulation (LES) using a precomputed reduced-order manifold approach, thermochemical states must be precomputed not only for adiabatic conditions but also over a range of reduced enthalpy states. However, there are a number of methods for producing reduced enthalpy states, which invoke different implicit assumptions. In this work, a set of a priori and a posteriori LES studies have been performed for turbulent premixed flames considering heat losses within a precomputed reduced-order manifold approach to determine the sensitivity to the method by which reduced enthalpy states are generated. Two general approaches are explored for generating these reduced enthalpy states and are compared in detail to assess any effects on turbulent flame structure and emissions. In the first approach, the enthalpy is reduced at the boundary of the one-dimensional (1D) premixed flame solution, resulting in a single enthalpy deficit for a single premixed flame solution. In the second approach, a variable heat loss source term is introduced into the 1D flame solutions by mimicking a real heat loss to reduce the post-flame enthalpy. The two approaches are compared in methane–air piloted turbulent premixed planar jet flames with different diluents that maintain a constant adiabatic flame temperature but experience different radiation heat losses. Both a priori and a posteriori results, as well as a chemical pathway analysis, indicate that the manner by which the heat loss is accounted for in the manifold is of secondary importance compared to other model uncertainties such as the chemical mechanism, except in situations where heat loss is unphysically fast compared to the flame time scale. A new theoretical framework to explain this insensitivity is also proposed, and its validity is briefly assessed.     

Flame–wall interaction effects on the flame root stabilization mechanisms of a doubly-transcritical LO2/LCH4 cryogenic flame

High-fidelity numerical simulations are used to study flame root stabilization mechanisms of cryogenic flames, where both reactants (O₂ and CH₄) are injected in transcritical conditions in the geometry of the laboratory scale test rig Mascotte operated by ONERA (France). Simulations provide a detailed insight into flame root stabilization mechanisms for these diffusion flames: they show that the large wall heat losses at the lips of the coaxial injector are of primary importance, and require to solve for the fully coupled conjugate heat transfer problem. In order to account for flame–wall interaction (FWI) at the injector lip, detailed chemistry effects are also prevalent and a detailed kinetic mechanism for CH₄ oxycombustion at high pressure is derived and validated. This kinetic scheme is used in a real-gas fluid solver, coupled with a solid thermal solver in the splitter plate to calculate the unsteady temperature field in the lip. A simulation with adiabatic boundary conditions, an hypothesis that is often used in real-gas combustion, is also performed for comparison. It is found that adiabatic walls simulations lead to enhanced cryogenic reactants vaporization and mixing, and to a quasi-steady flame, which anchors within the oxidizer stream. On the other hand, FWI simulations produce self-sustained oscillations of both lip temperature and flame root location at similar frequencies: the flame root moves from the CH₄ to the O₂ streams at approximately 450 Hz, affecting the whole flame structure.     

Numerical study of the effects of gravity on soot formation in laminar coflow methane/air diffusion flames under different air stream velocities

Numerical simulations of laminar coflow methane/air diffusion flames at atmospheric pressure and different gravity levels were conducted to gain a better understanding of the effects of gravity on soot formation by using relatively detailed gas-phase chemistry and complex thermal and transport properties coupled with a semi-empirical two-equation soot model. Thermal radiation was calculated using the discrete-ordinates method coupled with a non-grey model for the radiative properties of CO, CO₂, H₂O, and soot. Calculations were conducted for three coflow air velocities of 77.6, 30, and 5 cm/s to investigate how the coflowing air velocity affects the flame structure and soot formation at different levels of gravity. The coflow air velocity has a rather significant effect on the streamwise velocity and the fluid parcel residence time, especially at reduced gravity levels. The flame height and the visible flame height in general increase with decreasing the gravity level. The peak flame temperature decreases with decreasing either the coflow air stream velocity or the gravity level. The peak soot volume fraction of the flame at microgravity can either be greater or less than that of its normal gravity counterpart, depending on the coflow air velocity. At sufficiently high coflow air velocity, the peak soot volume fraction increases with decreasing the gravity level. When the coflow air velocity is low enough, soot formation is greatly suppressed at microgravity and extinguishment occurs in the upper portion of the flame with soot emission from the tip of the flame owing to incomplete oxidation. The numerical results provide further insights into the intimate coupling between flame size, residence time, thermal radiation, and soot formation at reduced gravity level. The importance of thermal radiation heat transfer and coflow air velocity to the flame structure and soot formation at microgravity is demonstrated for the first time.     

Modelling of lifted turbulent diffusion flames in a channel mixing layer by the flame hole dynamics

The partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics as an effort to develop a prediction model for the turbulent flame lift off. The essence of the flame hole dynamics is derivation of the random walk mapping, from the flame-edge theory, which governs expansion or contraction of the quenching holes initially created by the local quenching events. The numerical simulation for the flame hole dynamics is carried out in two stages. First, a direct numerical simulation is performed for a constant-density fuel–air channel mixing layer to obtain the background turbulent flow and mixing fields, from which a time series of two-dimensional scalar-dissipation-rate array is extracted. Subsequently, a Lagrangian simulation of the flame hole random walk mapping, projected to the scalar dissipation rate array, yields a temporally evolving turbulent extinction process and its statistics on partial quenching characteristics. In particular, the probability of encountering the reacting state, while conditioned with the instantaneous scalar dissipation rate, is examined to reveal that the conditional probability has a sharp transition across the crossover scalar dissipation rate, at which the flame edge changes its direction of propagation. This statistical characteristic implies that the flame edge propagation instead of the local quenching event is the main mechanism controlling the partial quenching events in turbulent flames. In addition, the conditional probability can be approximated by a heavyside function across the crossover scalar dissipation rate.