Does Density Ratio Significantly Affect Turbulent Flame Speed?

In order to experimentally study whether or not the density ratio σ substantially affects flame displacement speed at low and moderate turbulent intensities, two stoichiometric methane/oxygen/nitrogen mixtures characterized by the same laminar flame speed S _L = 0.36 m/s, but substantially different σ were designed using (i) preheating from T _u = 298 to 423 K in order to increase S _L , but to decrease σ, and (ii) dilution with nitrogen in order to further decrease σ and to reduce S _L back to the initial value. As a result, the density ratio was reduced from 7.52 to 4.95. In both reference and preheated/diluted cases, direct images of statistically spherical laminar and turbulent flames that expanded after spark ignition in the center of a large 3D cruciform burner were recorded and processed in order to evaluate the mean flame radius \(\bar {R}_{f}\left (t \right )\) and flame displacement speed \(S_{t}=\sigma ^{-1}{d\bar {R}_{f}} \left / \right . {dt}\) with respect to unburned gas. The use of two counter-rotating fans and perforated plates for near-isotropic turbulence generation allowed us to vary the rms turbulent velocity \(u^{\prime }\) by changing the fan frequency. In this study, \(u^{\prime }\) was varied from 0.14 to 1.39 m/s. For each set of initial conditions (two different mixture compositions, two different temperatures T _u , and six different \(u^{\prime })\), five (respectively, three) statistically equivalent runs were performed in turbulent (respectively, laminar) environment. The obtained experimental data do not show any significant effect of the density ratio on S _t . Moreover, the flame displacement speeds measured at u′/S _L = 0.4 are close to the laminar flame speeds in all investigated cases. These results imply, in particular, a minor effect of the density ratio on flame displacement speed in spark ignition engines and support simulations of the engine combustion using models that (i) do not allow for effects of the density ratio on S _t and (ii) have been validated against experimental data obtained under the room conditions, i.e. at higher σ.     

Large Eddy Simulation of a Methane–Air Diffusion Flame

Large Eddy Simulation has been applied to a piloted methane/air diffusion flame—the Sandia D flame—for which detailed experimental data are available. To evaluate the reacting density, temperature and species mass fractions a conserved scalar laminar flamelet formulation is employed, utilising a single virtually unstrained flamelet. The results of two simulations are discussed, comparing the use of the standard Smagorinsky model and a dynamic variant for closure of the unknown sub-grid stress. The chosen sub-grid scale model is shown to be extremely influential on the final solution. Whilst the use of the standard model results in a relatively poor simulation the dynamic closure offers an excellent velocity field prediction throughout the flame. Although the flame does show some strain rate influence on burning, particularly close to the inlet nozzle, the relatively simple ‘unstrained’ flamelet model applied is shown to provide an accurate representation of temperature and major species distribution.     

Damköhler-Shelkin Paradox in the Theory of Turbulent Flame Propagation,and a Concept of the Premixed Flame at the Intermediate Asymptotic Stage

We formulated a paradox in the theory of turbulent premixed flame in the flamelet regime: discrepancy between the Damköhler (1940) and Shelkin (1943) estimate of the turbulence flame speed \(U_{t} \sim {u}^{\prime }\) in the case of strong turbulence (\({u}^{\prime }>>S_{L} \)) and numerous experiments that show a strong dependence of U_t on the speed of the instantaneous flame S_L. We name this discrepancy the Damköhler-Shelkin paradox. The first aim of the research is to validate and clarify this estimate, which is based on intuitive considerations, as the paradox must be a statement that seems contradictory to observations but is actually true. We analysed the turbulent flame in the context of the original hyperbolic combustion equation that directly describes the leading edge of the flame, which is a locus of the Zel’dovich “leading points” controlling the speed of the turbulent flame. Analysis of the corresponding characteristic equations results in the expression for speed on the steady-state turbulent flame \(U_{t} ={u}^{\prime }\sqrt {1+(S_{L} /{u}^{\prime })^{2}} \), which is the case when \({u}^{\prime }>>S_{L} \) becomes \(U_{t} \cong {u}^{\prime }\). This result confirms and improves the Damköhler-Shelkin estimate \(U_{t} \sim {u}^{\prime }\). The second aim is to resolve the Damköhler-Shelkin paradox. We explain the discrepancy with observations by the fact that turbulent flames are transient due to insufficient residence time in the real burners to reach statistical equilibrium of wrinkle structures of the random flame surface. We consider the transient flame in the intermediate asymptotic stage when the small-scales wrinkles are in statistical equilibrium, while at the same time the large-scale wrinkles are far from equilibrium. The expressions for the flame speed and width, which we deduce using the dimensional analysis and general properties of the ransom surface, \(U_{t} \sim ({u}^{\prime }S_{L})^{1/2}\) and \(\delta _{t} \sim ({u}^{\prime }Lt)^{1/2}\), show that this transient flame is in fact a turbulent mixing layer travelling with constant speed U_t depending on S_L, the intermediate steady propagation (ISP) flame. Qualitative estimations of the times required for the small-scale and large-scale wrinkles to reach statistical equilibrium show that the turbulent Bunsen- and V-flames correspond to the intermediated asymptotic stage, and the turbulent flames with a complete equilibrium structure of the wrinkled flamelet surface are not attainable under laboratory conditions. We present the results of numerical simulations of the impingent flames, which count in favour of the belief that these flames are also transient.     

Large Eddy Simulation of Premixed Turbulent Combustion Using Ξ Flame Surface Wrinkling Model

One commonly-used method for deriving the RANS equations for multicomponent flow is the technique of conditional averaging. In this paper the concept is extended to LES, by introducing the operations of conditional filtering and surface filtering. Properties of the filtered indicator function are investigated mathematically and computationally. These techniques are then used to derive conditionally filtered versions of the Navier–Stokes equations which are appropriate for simulating multicomponent flow in LES. Transport equations for the favre-averaged indicator function and the unresolved interface properties (the wrinkling and the surface area per unit volume) are also derived. Since the paper is directed towards modelling premixed combustion in the flamelet regime, closure of the equations is achieved by introducing physical models based on the picture of the flame as a wrinkled surface separating burnt and unburnt components of the fluid. This leads to a set of models for premixed turbulent combustion of varying complexity. The results of applying one of this set of models to propagation of a spherical flame in isotropic homogeneous turbulence are analysed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Forced convective heat transfer from premixed flames: —Part 1: Flame structure

In this, the first part of a two-part study of convective heat transfer from impinging flames, the aerodynamic structure of four flames was studied. The flames examined were of stoichiometric mixtures of methane and air with a Reynolds number range extending from the laminar to fully turbulent flow regimes. Instantaneous Schlieren photographs revealed that with increasing Reynolds number the flame reaction zone extended further downstream and became thicker and more diffuse. Associated with this, measurements of mean and rms velocities and mean temperatures showed that the properties of the flames became drawn out in the downstream direction as Reynolds number increased. Schlierenstroboscopic techniques also revealed the existence of large scale vortex rings which originated in the shear layer of the flames, and which were found to cause low frequency oscillations in measured instantaneous velocities. These oscillations lead to misleadingly high levels of rms velocities downstream of the flame reaction zone which should not be interpreted as representing turbulence within the flame.     

Numerical Simulation of Diesel Spray Evaporation in a “Stabilized Cool Flame” Reactor: A Comparative Study

The major objective of this work is to numerically investigate the interacting physical and chemical phenomena that characterize the flow in a stabilized cool flame diesel fuel spray evaporation system. A two-phase RANS computational fluid dynamics code has been developed and used to predict the characteristics of the developing turbulent, multiphase, multi-component, reactive flow-field. The code employs a Eulerian–Lagrangian approach, taking into account the mass, momentum, thermal and turbulent energy exchange between the phases. A variety of physical phenomena, such as turbulent dispersion, droplet evaporation, droplet-wall collision, conjugate heat transfer, drift correction, two-way coupling are taken into account by implementing respective sub-models. Two alternative modelling approaches for the simulation of cool flame reactions have been validated and evaluated by comparing numerical predictions with experimental data from two atmospheric pressure, evaporating Diesel spray, Stabilized Cool Flame reactors. Both models have achieved good quantitative agreement in the majority of the considered test cases. The results have been used to estimate the local physical and chemical characteristic time scales of the occurring phenomena, thus allowing, for the first time, the classification of stabilized cool flames.