Effect of non-zero relative velocity on the flame speed of two-phase laminar flames

A numerical study of one-dimensional n-heptane/air spray flames is presented. The objective is to evaluate the flame propagation speed in the case where droplets evaporate inside the reaction zone with possibly non-zero relative velocity. A Direct Numerical Simulation approach for the gaseous phase is coupled to a discrete particle Lagrangian formalism for the dispersed phase. A global two-step n-heptane/air chemical mechanism is used. The effects of initial droplet diameter, overall equivalence ratio, liquid loading and relative velocity between gaseous and liquid phases on the laminar spray flame speed and structure are studied. For lean premixed cases, it is found that the laminar flame speed decreases with increasing initial droplet diameter and relative velocity. On the contrary, rich premixed cases show a range of diameters for which the flame speed is enhanced compared to the corresponding purely gaseous flame. Finally, spray flames controlled by evaporation always have lower flame speeds. To highlight the controlling parameters of spray flame speed, approximate analytical expressions are proposed, which give the correct trends of the spray flame propagation speed behavior for both lean and rich mixtures.     

Flame structure and burning velocity of flames propagating in binary iron aerosols

A numerical study was performed for binary dispersed iron aerosols in air using different particle sizes with constant average particle size. The effects of particle size and density of the two aerosols on flame structure and speed are systematically investigated. Varying the amount of small and big particles results in separated and overlapped flame fronts. For higher values of particle size ratio (ratio between the size of big and small particles) and density of small particles, flame fronts are observed to overlap. The flame speed of the binary mixture is compared with the mono-dispersed case and the difference is analyzed for different particle size ratios. The addition of a small fraction of small particles in the binary mixture is found to result in a substantial increase in the flame speed if the particle size ratio is large. Detailed analyses on the variation of the total amount of fuel shows the particle size ratio determines the equivalence ratio at which the maximum flame speed occurs. The maximum flame speed as a function of equivalence ratio was observed to move from the lean to the rich side for particle size ratio sufficiently large enough.     

Pressure gradient tailoring effects on vorticity dynamics in the near-wake of bluff-body premixed flames

We investigate the role of mean streamwise pressure gradients in the development of a bluff-body-stabilized premixed flame in the near-wake of the bluff body. To this end, a triangular prism flame holder is situated in three different channel geometries: a nominal case with straight walls, a nozzle with a stronger mean pressure gradient, and a diffuser with a comparatively weaker mean pressure gradient. All geometries are implemented using embedded boundaries, and adaptive mesh refinement is used to locally resolve all relevant thermal (i.e., flame) and fluid-mechanical (i.e., vorticity) scales. A premixed propane flame, modeled using a 66-step skeletal mechanism, interacts with vorticity in the boundary layer of the triangular bluff body in the presence of each mean pressure gradient. Analysis of flame-related enstrophy budget terms reveals key differences in the behavior of baroclinic torque between cases, the specifics of which are tied to larger variations in the mean flow structure, recirculation zone structure, and confinement effects. Our results show that the baroclinic torque changes significantly among the configurations, with the nozzle exhibiting the largest baroclinic torque production. However, these differences are shown to be only a secondary consequence of the background pressure gradient, with the primary consequence being the change in the recirculation zone length resulting from the different channel configurations. These results are relevant for flame stabilization with bluff bodies, where clear understanding of the sensitivities to global mean pressure gradient is important to engineering design.     

Stability of inclined planar flames as a local approximation of weakly curved flames

To evaluate the effect of vorticity usually generated by curved flames on the flame stability, laminar premixed planar flames inclined in the gravitational field is asymptotically examined. The flame structure is resolved by a large activation energy asymptotics and a long wave approximation. The coupling between hydrodynamics and diffusion processes is included and near-unity Lewis number is assumed. The results show that as the flame is more inclined from the horizontal plane it shows more unstable characteristics due to not only the decrease of the stabilizing effect of gravity but also the increase of the destabilizing effect of rotational flow. Unlike the planar flame propagating downward with the right angle to the upstream flow, the obtained dispersion relation involves the Prandtl number and shows the destabilizing effect of viscosity. The analysis predicts that the phase velocity of unstable wave depends on the Lewis number as well as the flame angle and, especially for unity Lewis number, it is the same with tangential velocity at the reaction zone. For relatively short wave disturbances, still much larger than flame thickness, the most unstable wavelength is nearly independent on the flame angle and the flame can be stabilized by gravity and diffusion mechanism.     

Effect of fuel mixture fraction and velocity perturbations on the flame transfer function of swirl stabilized flames

A novel methodology is developed to decompose the classic Flame Transfer Function (FTF) used in the thermo-acoustic stability analysis of lean premix combustors into contributions of different types. The approach is applied, in the context of Large Eddy Simulation (LES), to partially-premixed and fully-premixed flames, which are stabilized via a central recirculation zone as a result of the vortex breakdown phenomenon. The first type of decomposition is into contributions driven by fuel mixture fraction and dynamic velocity fluctuations. Each of these two contributions is further split into the components of turbulent flame speed and flame surface area. The flame surface area component, driven by the pure dynamic velocity fluctuation, which is shown to be a dominant contribution to the overall FTF, is also additionally decomposed over the coherent flow structures using proper orthogonal decomposition. Using a simplified model for the dynamic response of premixed flames, it is shown that the distribution of the FTF, as obtained from LES, is closely related to the characteristics of the velocity field frequency response to the inlet perturbation. Initially, the proposed method is tested and validated with a well characterized laboratory burner geometry. Subsequently, the method is applied to an industrial gas turbine burner.     

Nonlinear equation for curved nonstationary flames and flame stability

A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.     

Effect of velocity gradient on propagation speed of tribrachial flames in laminar coflow jets

The effect of velocity gradient on the propagation speed of tribrachial flame edge has been investigated experimentally in laminar coflow jets for propane fuel. It was observed that the propagation speed of tribrachial flame showed appreciable deviations at various jet velocities in high mixture fraction gradient regime. From the similarity solutions, it was demonstrated that the velocity gradient varied significantly during the flame propagation. To examine the effect of velocity gradient, detail structures of tribrachial flames were investigated from OH LIF images and Abel transformed images of flame luminosity. It was revealed that the tribrachial point was located on the slanted surface of the premixed wing, and this slanted angle was correlated with the velocity gradient along the stoichiometric contour. The temperature field was visualized qualitatively by the Rayleigh scattering image. The propagation speed of tribrachial flame was corrected by considering the direction of flame propagation with the slanted angle and effective heat conduction to upstream. The corrected propagation speed of tribrachial flame was correlated well. Thus, the mixture fraction gradient together with the velocity gradient affected the propagation speed.     

Numerical studies of flames in wide tubes: stability limits of curved stationary flames

Flame dynamics in wide tubes with ideally adiabatical and slip walls is studied by means of direct numerical simulations of the complete set of hydrodynamical equations including thermal conduction, fuel diffusion, viscosity, and chemical kinetics. Stability limits of curved stationary flames in wide tubes and the hydrodynamic instability of these flames (the secondary Darrieus-Landau instability) are investigated. The stability limits found in the present numerical simulations are in a very good agreement with the previous theoretical predictions. It is obtained that close to the stability limits the secondary Darrieus-Landau instability results in an extra cusp at the flame front. It is shown that the curved flames subject to the secondary Darrieus-Landau instability propagate with velocity considerably larger than the velocity of the stationary flames.     

Effect of pressure on structure and extinction of near-limit hydrogen counterflow diffusion flames

Results of measurements of critical conditions for extinction and of temperature profiles in counterflow diffusion flames are reported. The fuel was a hydrogen–nitrogen mixture with 14 mole percent hydrogen, and the oxidizer was air. Pressures ranged from 0.1 MPa to 1.5 MPa; measurements were made in a facility especially constructed for carrying out counterflow combustion experiments at high pressures. With increasing pressure, the strain rate at extinction first increases and then decreases, in qualitative agreement with predictions, but there are observable quantitative differences. Temperature profiles, obtained employing an R-type thermocouple at a fixed strain rate of 100/s, agree well with predictions, within experimental uncertainty. The results may help to improve knowledge of underlying chemical-kinetic and transport parameters at elevated pressures.     

Numerical studies of curved stationary flames in wide tubes

The nonlinear problem of the propagation of curved stationary flames in tubes of different widths is studied by means of direct numerical simulation of the complete system of hydrodynamic equations including thermal conduction, viscosity, fuel diffusion and chemical kinetics. While only a planar flame can propagate in a narrow tube of width smaller than half of the cut–off wavelength determined by the linear theory of the hydrodynamic instability of a flame front, in wider tubes stationary curved flames propagate with velocities considerably larger than the corresponding velocity of a planar flame. It is shown that only simple ‘single-hump’ slanted stationary flames are possible in wide tubes, and ‘multi–hump’ flames are possible in wide tubes only as a nonstationary mode of flame propagation. The stability limits of curved stationary flames in wider tubes and the secondary Landau–Darrieus instability are investigated. The dependence of the velocity of the stationary flame on the tube width is studied. The analytical theory describes the flame reasonably well when the tube width does not exceed some critical value. The dynamics of the flame in wider tubes is shown to be governed by a large–scale stability mechanism resulting in a highly slanted flame front. In wide tubes, the skirt of the slanted flame remains smooth with the length of the skirt and the flame velocity increasing progressively with the increase of the tube width above the second critical value. Results of the analytical theory and numerical simulations are discussed and compared with the experimental data for laminar flames in wide tubes.     

非饱和土结构对声速的影响

对非饱和土的几种结构模型进行了分析,提出了几种模型非饱和土中声速的计算公式,从中可以看出非他和土的结构对声速的影响,通过声波波速的计算;阐明了含气量对非他和土的声速的影响.对工程勘测上的声速方法有十分重要的指导意义.     

Effects of Rayleigh-Taylor instabilities on turbulent premixed flames in a curved rectangular duct

Large-eddy simulations are used to demonstrate the effects of Rayleigh-Taylor instabilities (RTIs) on constant-pressure, turbulent premixed flames stabilized in a curved rectangular duct. A splitter plate of constant radius separates a reactant and pilot stream such that the flame stabilizes in the mixing layer between the two streams. Centrifugal acceleration due to the duct curvature induces the RTI, increasing the mixing of the higher-density reactant stream with the lower-density pilot stream. In both non-reacting and reacting flows, the resulting mixing layer thickness grows at rates comparable to those in unconfined RTIs until the flame occupies approximately half of the duct, at which point the duct walls limit the growth rate. The conservative equations are modified with artificial body forces to negate the centrifugal effect (and the RTI) to isolate the impact of the curved geometry. A comparison between the flames with and without the RTI shows that the RTI increases the turbulent flame speed primarily through increased flame surface area. The RTI also increases the range of local flame stretches and curvatures. The increased turbulent flame speed and growth rates due to RTI suggest a viable mechanism to increase turbulent flame speed in gas turbine engines though the application of flow path curvature.     

Small-scale vorticity filaments and structure functions of the developed turbulence

We develop a theory of turbulence based on the Navier-Stokes equation, without using dimensional or phenomenological considerations. A small scale vortex filament is the main element of the theory. The theory allows to obtain the scaling law and to calculate the scaling exponents of Lagrangian and Eulerian velocity structure functions in the inertial range. The obtained results are shown to be in very good agreement with numerical simulations and experimental data. The introduction of stochasticity into the equations and derivation of scaling exponents are discussed in details. A weak dependence on statistical propositions is demonstrated. The relation of the theory to the multifractal model is discussed.     

Burning velocity of triple flames with gentle concentration gradient

We investigated the local flame speed of a two-dimensional, methane-air triple flame in a rectangular burner. The velocity fields and the concentration profiles were measured with particle image velocimetry and the Rayleigh scattering method, respectively. There was a requisite combination of initial velocity and initial concentration gradient for consistency of the local concentration gradient at the leading edge of the flame. In these cases, the flame curvatures were also consistent. Accordingly, the burning velocity, defined as local flow velocity at the triple point, was determined by the flame curvature. The burning velocity increased with increasing flame curvature, when the curvature was near zero. After that, the burning velocity decreased with increasing curvature. The peak value thus exceeded the adiabatic one-dimensional laminar burning velocity. Comparing the effects of the measured flame stretch rate on the flow strain κ_s and flame curvature κ_c, κ_s is larger and increases more rapidly than κ_c for flame curvatures satisfying 1/R_f < 250 m⁻¹ and then becomes constant while κ_c still increases for 250 m⁻¹ < 1/R_f, so that κ_c becomes much larger than κ_s. There is also a peak in burning velocity at roughly the transition in flame curvature specified above. Therefore, the burning velocity for a low concentration gradient correlates with the flame stretch rate.     

A flamelet analysis of the burning velocity of premixed turbulent expanding flames

Direct numerical simulation is a very powerful tool to evaluate the validity of new models and theories for turbulent combustion. In this paper, direct numerical simulations of spherically expanding premixed turbulent flames in the corrugated flamelet regime are performed. The flamelet-generated manifold method is used to deal with detailed reaction kinetics. The numerical method is validated for both laminar and turbulent expanding flames. The computational results are analyzed by using an extended flame stretch theory. It is investigated whether this theory is able to describe the influence of flame stretch and curvature on the local burning velocity of the flame. If the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is predicted accurately. The influence of several approximations, which are used in other existing theories, is studied. When flame stretch is assumed to be constant through the flame front or when curvature of the flame front is neglected, the theory fails to predict the local mass burning rate.     

Numerical study of buoyancy effects on the structure and propagation of triple flames

The structure and propagation properties of diffusion neutral triple flames subject to buoyancy effects are studied numerically using a high-accuracy scheme. A wide range of gravity conditions, heat release, and mixing widths for a scalar mixing layer are computed for downward-propagating (in the same direction as the gravity vector) and upward-propagating (in the opposite direction to the gravity vector) triple flames. These results are used to identify non-dimensional quantities, which parametrize the triple flame responses. Results show that buoyancy acts primarily to modify the overall span of the premixed branches in response to gas acceleration across the triple flame. The impact of buoyancy on the structure of triple flame is less pronounced than its impact on the topology of the branches. The trailing diffusion branch is affected by buoyancy primarily as a result of the changes in the overall flame size, which consequently modifies the rates of diffusion of excess fuel and oxidizer from the premixed branches to the diffusion branch. A simple analytical model for the triple flame speed, which accounts for both buoyancy and heat release is developed. Comparisons of the proposed model with the numerical results for a wide range of gravity, heat release and mixing width conditions, yield very good agreement. The analysis shows that under neutral diffusion, downward propagation reduces the triple flame speed, while upward propagation enhances it. For the former condition, a critical Froude number may be evaluated, which corresponds to a vanishing triple flame speed.     

Nonlinear kinematic response of premixed flames to harmonic velocity disturbances

This paper analyzes the nonlinear dynamics of premixed flames responding to harmonic velocity disturbances. These nonlinear dynamics were studied by solving a constant flame speed front tracking equation for the flame’s response to harmonically oscillating velocity disturbances. The solution to these equations is used to quantify the transfer function relating the ratio of the normalized flame area to velocity fluctuations, G = (A′/A_o)/(u′/u_o), upon the amplitude of velocity oscillations, ε = u′/u_o. Due to nonlinearities, the amplitude of this transfer function relative to its linear value decreases with increasing amplitude of velocity oscillation, u′/u_o. In contrast, the transfer function phase exhibits almost no amplitude dependence. The velocity amplitude where transfer function nonlinearities become significant depends strongly upon three parameters: a Strouhal number, St = ωL_f/u_o (where L_f is the flame length), the ratio of the flame length to width, β = L_f/R, and the flame shape in the absence of perturbations (i.e., conical, inverted wedge, etc.). In the linear case, the transfer function, G, depends only upon an algebraic combination of the first two parameters, given by St₂ = St (1 + β²)/β². In general, however, G exhibits a distinct dependence upon both parameters St and β. In particular, we show that the nonlinear response of G is an intrinsically dynamic phenomenon; i.e., its quasi-steady response (St 1) is purely linear. As such, nonlinearity is enhanced with increasing Strouhal numbers. In contrast, nonlinearity is suppressed at large β values; as such, the response of a long flame remains quite similar to its linear value, even at large ε values where the flame front exhibits substantial corrugation and cusping. Finally, we show that the response of conical flames remains much more linear at comparable disturbance amplitudes than for “V” or wedge-shaped flames. These predictions are shown to be consistent with available experimental data.     

A simple property of the Weyl tensor for a shear,vorticity and acceleration-free velocity field

We prove that, in a space-time of dimension \(n>3\) with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant divergence of the Weyl tensor is zero if and only if the contraction of the Weyl tensor with the velocity is zero. This extends a property found in generalised Robertson–Walker spacetimes, where the velocity is also eigenvector of the Ricci tensor. Despite the simplicity of the statement, the proof is involved. As a product of the same calculation, we introduce a curvature tensor with an interesting recurrence property.