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Title: Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity

Abstract

A flamelet approach is adopted in a study of the factors affecting the volumetric heat release source term in turbulent combustion. This term is expressed as the product of an instability enhanced burning rate factor, P{sub bi}, and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression for P{sub bi} are a pdf of the flame stretch rate and a flame stretch factor. Fractal considerations link the turbulent burning velocity normalised by the effective rms turbulent velocity to P{sub bi}. Evaluation of this last parameter focuses on problems of (i) the pdfs of the flame stretch rate, (ii) the effects of flame stretch rate on the burning rate, (iii) the effects of any flamelet instability on the burning rate, (iv) flamelet extinctions under positive and negative flame stretch rates, and (v) the effects of the unsteadiness of flame stretch rates. The Markstein number influences both the rate of burning and the possibility of flamelet instabilities developing which, through their ensuing wrinkling, increase the burning rate. The flame stretch factor is extended to embrace potential Darrieus-Landau thermo-diffusive flamelet instabilities. A major limitation is the insufficient understanding of the effects of negative stretchmore » rates that might cause flame extinction. The influences of positive and negative Markstein numbers are considered separately. For the former, a computed theoretical relationship for turbulent burning velocity, normalised by the effective rms velocity, is developed which, although close to that measured experimentally, tends to be somewhat lower at the higher values of the Karlovitz stretch factor. This might be attributed to reduced flame extinction and reduced effective Markstein numbers when the increasingly nonsteady conditions reduce the ability of the flame to respond to changes in flame stretch rates. As the pressure increases, Markstein numbers decrease. For negative Markstein numbers the predicted values of P{sub bi} and turbulent burning velocity are significantly increased above the values for positive Markstein numbers. This is confirmed experimentally, and these values are close to those predicted theoretically. The increased values are due to the greater stretch rate required for flame extinction, the increased burning rate at positive values of flame stretch rate, and, in some instances, the development of flame instabilities. At lower values of turbulence than those covered by these computations, burning velocities can be enhanced by flame instabilities, as they are with laminar flames, particularly at negative Markstein numbers.« less

Authors:
; ;  [1];  [2]
  1. School of Mechanical Engineering, University of Leeds, Leeds LS2 9JT (United Kingdom)
  2. Department of Computational Science and Engineering, CLRC Daresbury Laboratory, Warrington WA4 4AD (United Kingdom)
Publication Date:
OSTI Identifier:
20677731
Resource Type:
Journal Article
Resource Relation:
Journal Name: Combustion and Flame; Journal Volume: 143; Journal Issue: 3; Other Information: Elsevier Ltd. All rights reserved
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMBUSTION KINETICS; MATHEMATICAL MODELS; TURBULENCE; FLAMES; VELOCITY; COMBUSTION INSTABILITY; PRESSURE DEPENDENCE

Citation Formats

Bradley, D., Gaskell, P.H., Sedaghat, A., and Gu, X.J.. Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity. United States: N. p., 2005. Web. doi:10.1016/j.combustflame.2005.05.014.
Bradley, D., Gaskell, P.H., Sedaghat, A., & Gu, X.J.. Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity. United States. doi:10.1016/j.combustflame.2005.05.014.
Bradley, D., Gaskell, P.H., Sedaghat, A., and Gu, X.J.. Tue . "Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity". United States. doi:10.1016/j.combustflame.2005.05.014.
@article{osti_20677731,
title = {Premixed flamelet modelling: Factors influencing the turbulent heat release rate source term and the turbulent burning velocity},
author = {Bradley, D. and Gaskell, P.H. and Sedaghat, A. and Gu, X.J.},
abstractNote = {A flamelet approach is adopted in a study of the factors affecting the volumetric heat release source term in turbulent combustion. This term is expressed as the product of an instability enhanced burning rate factor, P{sub bi}, and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression for P{sub bi} are a pdf of the flame stretch rate and a flame stretch factor. Fractal considerations link the turbulent burning velocity normalised by the effective rms turbulent velocity to P{sub bi}. Evaluation of this last parameter focuses on problems of (i) the pdfs of the flame stretch rate, (ii) the effects of flame stretch rate on the burning rate, (iii) the effects of any flamelet instability on the burning rate, (iv) flamelet extinctions under positive and negative flame stretch rates, and (v) the effects of the unsteadiness of flame stretch rates. The Markstein number influences both the rate of burning and the possibility of flamelet instabilities developing which, through their ensuing wrinkling, increase the burning rate. The flame stretch factor is extended to embrace potential Darrieus-Landau thermo-diffusive flamelet instabilities. A major limitation is the insufficient understanding of the effects of negative stretch rates that might cause flame extinction. The influences of positive and negative Markstein numbers are considered separately. For the former, a computed theoretical relationship for turbulent burning velocity, normalised by the effective rms velocity, is developed which, although close to that measured experimentally, tends to be somewhat lower at the higher values of the Karlovitz stretch factor. This might be attributed to reduced flame extinction and reduced effective Markstein numbers when the increasingly nonsteady conditions reduce the ability of the flame to respond to changes in flame stretch rates. As the pressure increases, Markstein numbers decrease. For negative Markstein numbers the predicted values of P{sub bi} and turbulent burning velocity are significantly increased above the values for positive Markstein numbers. This is confirmed experimentally, and these values are close to those predicted theoretically. The increased values are due to the greater stretch rate required for flame extinction, the increased burning rate at positive values of flame stretch rate, and, in some instances, the development of flame instabilities. At lower values of turbulence than those covered by these computations, burning velocities can be enhanced by flame instabilities, as they are with laminar flames, particularly at negative Markstein numbers.},
doi = {10.1016/j.combustflame.2005.05.014},
journal = {Combustion and Flame},
number = 3,
volume = 143,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}
  • This short paper describes the application of the flamelet modelling approach to the prediction of the species concentration field in a turbulent propane-air flame. The structure of the laminar flamelet, the microscopic element in the model, is computed using a semi-global expression for fuel disappearance in conjunction with an established reaction scheme for the oxidation of CO and H/sub 2/. Detailed predictions for a turbulent jet-flame are compared with available experimental data. The significant measure of non-equilibrium which the flamelet introduces leads to substantial improvements in the prediction of CO, H/sub 2/, and C/sub 3/H/sub 8/ mass fractions in comparisonmore » with the simplest alternative model, that of full chemical equilibrium.« less
  • Effects of turbulent flame stretch on mean local laminar burning velocity of flamelets, u{sub n}, were investigated experimentally in an explosion vessel at normal temperature and pressure. In this context, the wrinkling, A{sub t}/A{sub l}, and the burning velocity, u{sub t}, of turbulent flames were measured simultaneously. With the flamelet assumption the mean local laminar burning velocity of flamelets, u{sub n}=u{sub t} x (A{sub t}/A{sub l}){sup -1}, was calculated for different turbulence intensities. The results were compared to the influence of stretch on spherically expanding laminar flames. For spherically expanding laminar flames the stretched laminar burning velocity, u{sub n}, variedmore » linearly with the Karlovitz stretch factor, yielding Markstein numbers that depend on the mixture composition. Six different mixtures with positive and negative Markstein numbers were investigated. The measurements of the mean local laminar burning velocity of turbulent flamelets were used to derive an efficiency parameter, I, which reflects the impact of the Markstein number and turbulent flame stretch - expressed by the turbulent Karlovitz stretch factor - on the local laminar burning velocity of flamelets. The results showed that the efficiency is reduced with increasing turbulence intensity and the reduction can be correlated to unsteady effects. (author)« less
  • Heat release rate is a fundamental property of great importance for the theoretical and experimental elucidation of unsteady flame behaviors such as combustion noise, combustion instabilities, and pulsed combustion. Investigations of such thermoacoustic interactions require a reliable indicator of heat release rate capable of resolving spatial structures in turbulent flames. Traditionally, heat release rate has been estimated via OH or CH radical chemiluminescence; however, chemiluminescence suffers from being a line-of-sight technique with limited capability for resolving small-scale structures. In this paper, we report spatially resolved two-dimensional measurements of a quantity closely related to heat release rate. The diagnostic technique usesmore » simultaneous OH and CH{sub 2}O planar laser-induced fluorescence (PLIF), and the pixel-by-pixel product of the OH and CH{sub 2}O PLIF signals has previously been shown to correlate well with local heat release rates. Results from this diagnostic technique, which we refer to as heat release rate imaging (HR imaging), are compared with traditional OH chemiluminescence measurements in several flames. Studies were performed in lean premixed ethylene flames stabilized between opposed jets and with a bluff body. Correlations between bulk strain rates and local heat release rates were obtained and the effects of curvature on heat release rate were investigated. The results show that the heat release rate tends to increase with increasing negative curvature for the flames investigated for which Lewis numbers are greater than unity. This correlation becomes more pronounced as the flame gets closer to global extinction.« less
  • A new definition of turbulent consumption speed is proposed in this work that is based on the heat release rate integral, rather than the mass burning rate integral. Its detailed derivation and the assumptions involved are discussed in a general context that applies to all properly defined reaction progress variables. The major advantage of the proposed definition is that it does not require the thin-flame assumption, in contrast to previous definitions. Experimental determination of the local turbulent displacement speed, S{sub D}, and the local turbulent consumption speed, S{sub C}, is also demonstrated with the particle image velocimetry technique in threemore » turbulent premixed stagnation flames. The turbulence intensity of these flames is of the same order of the laminar burning velocity. Based on the current data, a model equation for the local mean heat release rate is proposed. The relationship between S{sub D} and S{sub C} is discussed along with a possible modeling approach for the turbulent displacement speed. (author)« less
  • The effects of combustion on the strain rate field are investigated in turbulent premixed CH 4/air Bunsen flames using simultaneous tomographic PIV and OH LIF measurements. Tomographic PIV provides three-dimensional velocity measurements, from which the complete strain rate tensor is determined. The OH LIF measurements are used to determine the position of the flame surface and the flame-normal orientation within the imaging plane. This combination of diagnostic techniques enables quantification of divergence as well as flame-normal and tangential strain rates, which are otherwise biased using only planar measurements. Measurements are compared in three lean-to-stoichiometric flames that have different amounts ofmore » heat release and Damköhler numbers greater than unity. The effects of heat release on the principal strain rates and their alignment relative to the local flame normal are analyzed. The extensive strain rate preferentially aligns with the flame normal in the reaction zone, which has been indicated by previous studies. The strength of this alignment increases with increasing heat release and, as a result, the flame-normal strain rate becomes highly extensive. These effects are associated with the gas expansion normal to the flame surface, which is largest for the stoichiometric flame. In the preheat zone, the compressive strain rate has a tendency to align with the flame normal. Away from the flame front, the flame – strain rate alignment is arbitrary in both the reactants and products. The flame-tangential strain rate is on average positive across the flame front, and therefore the turbulent strain rate field contributes to the enhancement of scalar gradients as in passive scalar turbulence. As a result, increases in heat release result in larger positive values of the divergence as well as flame-normal and tangential strain rates, the tangential strain rate has a weaker dependence on heat release than the flame-normal strain rate and the divergence.« less