Combustion Science and Technology

Goddard, J. D.

doi: 10.1080/00102202.2022.2041610pmid: N/A

This brief paper is a continuation of previous work (J.D. Goddard, “Dissipation potentials for reaction-diffusion systems.” I&EC Res.,54.16,4078–4083, 2015) dealing with the application of Edelen’s dissipation potentials to the irreversible thermodynamics of chemical-reaction networks. It is shown that one can achieve non-linear Onsager symmetry by means of constraints on a certain combination of Gibbs free energies dubbed reactivity, from which it follows that reaction rates are given simply as gradients of a dissipation potential. This may open the door to the application of thermodynamics and variational methods to combustion and biochemical reaction networks, including the possibility of enhanced derivation of reduced kinetic mechanisms. A graph-theoretical description of reaction networks is presented, which is based on stoichiometric hypergraphs and encompasses several past treatments in a more economical fashion. It may also suggest hypergraph optimization techniques to enhance the selection of reduced mechanisms.

Lee, Su Ryong; Kim, Jong Soo

doi: 10.1080/00102202.2022.2041611pmid: N/A

The asymptotic structure of stretched chain-branching premixed flames with unity Lewis numbers is analyzed with the Zel’dovich-Liñán two-step mechanism, including (I) temperature-sensitive autocatalytic chain-branching step and (II) first-order chain-recombination step with combustion heat release. Depending on the order-of-magnitude of the Damköhler number ratio between the branching and recombination reactions, three distinct asymptotic limits, namely the fast, intermediate and slow recombination regimes, emerge with their own distinct multi-layer asymptotic structures. Our attention is focused on the asymptotic chain-branching flame-structure analysis within the framework of the intermediate recombination regime, in which the recombination layer is asymptotically thicker than the branching layer, but thinner than the outer convective-diffusive layer. The multi-layer asymptotics, involving the Damköhler number asymptotics for the recombination layer and the activation-energy asymptotics for the branching layer, yields the chain-branching flame-structure solution. The calculation results reveal the unique characteristics of strained chain-branching flames. First, the chain-carrier concentration and temperature at the branching reaction sheet are found to be constant irrespective of the strain rate. The chain-carrier concentration increases as the recombination reaction becomes slower. Moreover, the chain-carrier concentration at the branching reaction sheet is found to be proportional to the laminar flame speed. However, no quasisteady extinction was observed in any calculation results because the branching-reaction rate manages to maintain its strength thanks to the invariant branching-layer temperature. It is worthwhile to note that the present two-step model for chain-branching flames is perhaps the simplest asymptotic model, involving the minimum number of kinetic parameters to properly describe the asymptotic structure without losing any physical essence.

Clavin, P.; Champion, M.

doi: 10.1080/00102202.2022.2041612pmid: N/A

Two recent analytical results concerning i) the direct initiation of gaseous detonations in free space and ii) the deflagration to detonation transition in tubes are revisited in this article. The first problem is treated by an asymptotic analysis in the limit of small heat release, enlightening the mechanisms controlling the direct initiation process of real detonations. The second one is limited to a one-dimensional mechanism of transition at work on the tip of elongated flames in tubes. Particular attention is paid to the physical mechanisms more than to the technical details of the analyses. However, the mathematical formulation as well as the different steps of the analysis are clearly presented in a synthetic manner.*

Li, Brandon; Graña-Otero, José; Sánchez, Antonio L.; Williams, Forman A.

doi: 10.1080/00102202.2022.2041613pmid: N/A

Tsuji burners, in which flames may be anchored in the forward stagnation region of a cylindrical porous fuel injector placed in a uniform air stream, are addressed here for moderately large Reynolds numbers. Attention is focused on conditions under which the fuel-injection velocity is not sufficiently small compared with the outer air velocity for the boundary layer to remain attached to the forward part of the cylinder surface. In the resulting flow, the flame is embedded in the thin mixing layer that forms at the surface separating the outer air stream from the fuel stream, both having, in general, different densities. The flow on the air side of the mixing layer is potential, while that on the fuel side usually is rotational because exit conditions for the fuel injection generate vorticity, for example, by imposing a requirement that the fuel must emerge normal to the cylinder surface, which is the condition analyzed herein. It is shown that introduction of a suitably density-weighted stream function reduces the problem to that of constant-density flow, with the density-square-root-weighted ratio of injection velocity to free-stream velocity emerging as the only controlling parameter. The numerical solution, involving determination of the vorticity distribution in the inviscid fuel flow through an iterative scheme, provides the structure of the flow, including the mixing-layer location and the inviscid-flow strain rate there. Numerical results are presented for values of ranging from small ( ) to large ( ) injection velocities. The inviscid results in the limit of vanishingly small injection velocities ( approaching zero) demonstrate that, unlike the prediction of the potential-flow solution, when the fuel-side flow is rotational the outer air velocity never approaches the classical solution corresponding to potential flow around a solid cylinder ( ), a result affecting the interpretation of analyses of experiments involving flames stabilized on Tsuji burners as the boundary layer is blown off. In particular, with rotational fuel-side flow, the streamline separating the fuel and oxidizer regions lies farther from the cylinder surface, resulting in a larger near-quiescent wake and a lower strain rate along the separating streamline.

Vera, Marcos; Liñán, Amable

doi: 10.1080/00102202.2022.2041614pmid: N/A

We present an asymptotic analysis of a strained premixed flame in the mixing layer between two counterflowing streams: one with fresh reactants at a temperature and other with the burned gases at temperature , which may be different from the adiabatic combustion temperature of the fresh gases. A one-step irreversible Arrhenius reaction model, of high activation energy, is used for the asymptotic analysis, together with the thermal-diffusive approximation of constant density and transport properties – easily generalized to variable density and transport properties with the use of a heat-conduction-weighted coordinate. The analysis for near unity Lewis numbers of the fuel by Libby, Liñán and Williams (1983) is extended here to arbitrary nonunity Lewis numbers, of relevance to a wide variety of applications, ranging from hydrogen-fueled combustors to heavy fuel systems. In analogy with Liñán’s analysis of counterflow diffusion flames, three asymptotic distinguished regimes are identified for premixed flames for large activation energies and the appropriate Damköhler numbers – the ratio of the characteristic diffusion and reaction times. These regimes are the premixed flame regime, the partial burning regime and the nearly frozen ignition regime. The analytical expressions obtained for these regimes, of the dimensionless reaction rate as a function of the Damköhler number, are seen to describe with good accuracy the results obtained from the numerical integration of the full problem.

Mura, Arnaud; Robin, Vincent; Kha, Kim Q.N.; Champion, Michel

doi: 10.1080/00102202.2022.2041615pmid: N/A

The thermal expansion induced by the exothermicity of chemical reactions taking place in a turbulent flame affects the flow dynamics so deeply that the velocity field can be imposed by chemistry rather than turbulence. Moreover, thermal expansion is known to be responsible for flame-generated turbulence (FGT) as well as non-gradient or counter-gradient diffusion (CGD) phenomena. In the present study, a specific description of the joint probability-density function (PDF) of the progress variable and velocity is introduced. The corresponding PDF accounts for the finite thickness of the local flame. On the basis of this theoretical framework, the evolution of the scalar fluxes is analyzed across a planar premixed turbulent flame brush described as a boundary layer. The corresponding analysis recovers a CGD region in the planar flame brush as well as a region controlled by gradient diffusion (GD) transport at its leading edge. This region, which corresponds to small values of the mean progress variable, is dominated by finite Damköhler number effects. Finally, the dependency of the normalized turbulent scalar flux to classical nondimensional numbers – i.e., the Bray, Karlovitz and Reynolds numbers – is put into evidence. The obtained results provide a relatively simple basis for the development of closure models for the turbulent flux of the progress variable.

Kallifronas, D. P.; Ahmed, P.; Massey, J. C.; Talibi, M.; Ducci, A.; Balachandran, R.; Swaminathan, N.; Bray, K. N. C.

doi: 10.1080/00102202.2022.2041616pmid: N/A

The recirculation zone created through vortex breakdown mechanisms in swirling flows plays a vital role for aerodynamic stabilization of turbulent flames in practical combustion systems. This zone interacts with the central recirculation zone (CRZ) of an upstream bluff body and this leads to a complex flow behavior that depends on the blockage ratio and swirl number. It has been previously observed that the vortex breakdown bubble (VBB) merges with the CRZ at large swirl number or blockage ratio. In this study, the influences of heat release on this flow structure and their physical mechanisms are explored through a series of large eddy simulations and experiments of bluff body stabilized premixed flames with swirling flows. Comparisons of simulation results with measurements are good. It is observed that in isothermal flows, as the swirl number or blockage ratio is increased, the vortex breakdown bubble moves upstream and its mean structure changes. The effect of heat release leads to considerable differences in the flow characteristics as the vortex breakdown bubble is pushed downstream due to dilatation. The critical swirl number, at which the VBB and CRZ merge, is observed to be higher in reacting flows for the same blockage ratio.

Ji, Liang; Bai, Xue-Song; Seshadri, Kalyanasundaram

doi: 10.1080/00102202.2022.2041617pmid: N/A

Motivated by the pioneering activation-energy asymptotic analysis of strained laminar premixed flames in counterflow by Libby and his coworkers, a rate-ratio asymptotic analysis is carried out to elucidate the structure and predict the critical conditions of extinction of strained premixed methane flames. Steady, axisymmetric, laminar flow of two counterflowing streams: a reactive mixture stream and a product stream toward a stagnation plane is considered. The temperature of the reactive mixture stream is and it is made up of methane (CH4), oxygen (O2) and nitrogen (N2), while the temperature of the product stream is , and it is made up of O2, carbon dioxide, water vapor and N2. The asymptotic flame structure is presumed to be made up of a thin reaction zone where all chemical reactions take place. On one side of the reaction-zone is an inert, preheat zone containing the reactants and on the other side a post-flame zone made up of products. Analysis of the preheat zone gives matching conditions that is required to analyze the structure of the reaction zone. A four-step, reduced mechanism is used to describe the chemical reactions. The reaction zone is presumed to be made up of an inner layer, where CH4 is consumed. The hydrogen (H2) and carbon monoxide that are formed in this layer are consumed in an oxidation layer that is made up of two layers: an H2-oxidation layer and a CO-oxidation layer. The results of the analysis are used to predict the flame location, , flame temperature, , and the speed of the convective flow, , in the reaction zone as a function of the strain-rate, . Classical C-shaped curves were obtained when , and are plotted as a function of and they were used to predict extinction. A key finding of this work is that is proportional to , where is the crossover temperature predicted by the rate-ratio asymptotic analysis. Whether abrupt extinction will take place or not was found to depend on the value of relative to , which is different from the predictions of activation-energy asymptotic analysis where must be compared with the value of the adiabatic temperature. Similar to the analysis of Libby and his coworkers, the rate-ratio asymptotic analysis predicts the existence of “negative flame speeds,” where the convective flow and the diffusive flow of reactants in the reaction zone, are in opposite directions. The predictions of the rate-ratio asymptotic analysis were found to agree with the results of computations with detailed chemistry and previous experimental data.