Structure of locally quenched highly turbulent lean premixed flames

Surface-averaged quantities in turbulent reacting flows and relevant evolution equations

While quantities conditioned to an isosurface of reaction progress variable c, which characterizes fluid state in a turbulent reacting flow, have been attracting rapidly growing interest in the recent literature, a mathematical and physical framework required for research into such quantities has not yet been elaborated properly. This paper aims at filling two fundamental gaps in this area, i.e., (i) ambiguities associated with a definition of a surface-averaged quantity and (ii) the lack of rigorous equations that describe evolutions of such quantities. In the first (theoretical) part of the paper, (a) analytical relations between differently defined (area-weighted and unweighted) surface-averaged quantities are obtained and differences between them (quantities) are discussed, (b) a unified method for deriving an evolution equation for bulk area-weighted surface-averaged value of a local characteristic ϕ of a turbulent reacting flow is developed, and (c) the method is applied for deriving evolution equations for the bulk area-weighted surface-averaged reaction-surface density |∇c|, local reaction-wave thickness 1/|∇c|, and local displacement speed S_{d}, i.e., the speed of an isosurface of the c(x,t) field with respect to the local flow. In the second (numerical) part of the paper, direct numerical simulation data obtained recently from a highly turbulent reaction wave are analyzed in order to (1) highlight substantial differences between area-weighted and unweighted surface-averaged quantities and (2) show that various terms in the derived evolution equations are amenable to accurate numerical evaluation in spite of appearance of the so-called zero-gradient points [C. H. Gibson, Phys. Fluids 11, 2305 (1968)PFLDAS0031-917110.1063/1.1691820] in a highly turbulent medium. Finally, the obtained analytical and numerical results are used to shed light on the paradox of local flame thinning and broadening which is widely discussed in the turbulent combustion literature.

A Two-Fluid Conditional Averaging Paradigm for the Theory and Modeling of Turbulent Premixed Combustion

This paper extends a recent theoretical study that was previously presented in the form of a brief communication (Zimont, C&F, 192, 2018, 221-223), in which we proposed a simple splitting method for the derivation of two-fluid conditionally averaged equations of turbulent premixed combustion in the flamelet regime, formulated more conveniently for applications involving unclosed equations without surface-averaged unknowns. This two-fluid conditional averaging paradigm avoids the challenge in the Favre averaging paradigm of modeling the countergradient scalar transport phenomenon and the unusually large velocity fluctuations in a turbulent premixed flame. It is a more suitable conceptual framework that is likely to be more convenient in the long run than the traditional Favre averaging method. In this article, we further develop this paradigm and pay particular attention to the problem of modeling turbulent premixed combustion in the context of a two-fluid approach. We formulate and analyze the unclosed differential equations in terms of the conditions of the Reynolds stresses τij,u, τij,b and the mean chemical source ρW¯, which are the only modeling unknowns required in our alternative conditionally averaged equations. These equations are necessary for the development of model differential equations for the Reynolds stresses and the chemical source in the advanced modeling and simulation of turbulent premixed combustion. We propose a simpler approach to modeling the conditional Reynolds stresses based on the use of the two-fluid conditional equations of the standard “k-ε” turbulence model, which we formulate using the splitting method. The main problem arising here is the appearance in these equations of unknown terms describing the exchange of the turbulent energy k and dissipation rate ε in the unburned and burned gases. We propose an approximate way to avoid this problem. We formulate a simple algebraic expression for the mean chemical source that follows from our previous theoretical analysis of the transient turbulent premixed flame in the intermediate asymptotic stage, in which small-scale wrinkles in the instantaneous flame surface reach statistical equilibrium, while the large-scale wrinkles remain in statistical nonequilibrium.

Laser Diagnostics for the Model Development in Turbulent Premixed Flames

The interaction of turbulent flow and chemical processes is complex. Due to the strong turbulent fluctuations on very small scales, a direct insight into the processes has not been possible for long time. New laser diagnostics with sufficient spatial and temporal resolution allow now the answer to long discussed questions, for instance concerning the contradictory ideas of thin or thickened flame fronts in turbulent premixed combustion. More and more also numerical models allow the combined calculation of the local processes describing turbulent flow and combustion reaction. However, often unknown terms coming from the averaging procedure of the turbulence models need to have closures. Advanced application of the planar PIV measurement technique allowed the velocity field evaluation conditioned to the either unburnt or burnt gas state in turbulent premixed flames. Herewith, the direct evaluation of unclosed model terms has been possible for both RANS models as well as for models for the large-eddy simulation method. The mutual interaction of advanced laser diagnostics and numerical models is seen as one of the milestones for the development of advanced technical combustion.

Phase-locked two-line OH planar laser-induced fluorescence thermometry in a pulsating gas turbine model combustor at atmospheric pressure

Two-line OH planar laser-induced fluorescence (PLIF) thermometry was applied to a swirling CH4/air flame in a gas turbine (GT) model combustor at atmospheric pressure, which exhibited self-excited combustion instability. The potential and limitations of the method are discussed with respect to applications in GT-like flames. A major drawback of using OH as a temperature indicator is that no temperature information can be obtained from regions where OH radicals are missing or present in insufficient concentration. The resulting bias in the average temperature is addressed and quantified for one operating condition by a comparison with results from laser Raman measurements applied in the same flame. Care was taken to minimize saturation effects by decreasing the spectral laser power density to a minimum while keeping an acceptable spatial resolution and signal-to-noise ratio. In order to correct for the influence of laser light attenuation, absorption measurements were performed on a single-shot basis and a correction procedure was applied. The accuracy was determined to 4%-7% depending on the location within the flame and on the temperature level. A GT model combustor with an optical combustion chamber is described, and phase-locked 2D temperature distributions from a pulsating flame are presented. The temperature variations during an oscillation cycle are specified, and the general flame behavior is described. Our main goals are the evaluation of the OH PLIF thermometry and the characterization of a pulsating GT-like flame.