Turbulent mean reaction rates in the limit of large activation energies

1981 ◽  
Vol 110 ◽  
pp. 411-432 ◽  
Author(s):  
N. Peters ◽  
W. Hocks ◽  
G. Mohiuddin
Keyword(s):  
Reaction Rate ◽  
Laminar Flame ◽  
Mixture Fraction ◽  
Beta Function ◽  
Reaction Rates ◽  
Activation Energies ◽  
Premixed Combustion ◽  
Flame Velocity ◽  
Progress Variable ◽  
The Mean

Closed-form expressions for the turbulent mean reaction rate and its covariance with the temperature are derived for premixed and non-premixed combustion. The limit of large activation energies is exploited for a chemical reaction rate that, by virtue of coupling functions, depends on the mixture fraction and a non-equilibrium progress variable only. The probability density function (p.d.f.) formulation with an assumed shape of the p.d.f. is used; a beta-function distribution is assumed for the progress variable. The mean reaction rate is expressed in terms of the mean and the variance of the temperature and, for non-premixed combustion, of the mixture fraction. The reaction kinetics are represented by the non-dimensional activation energy and the laminar flame velocity. For non-premixed systems the possibility of local extinction by flame stretch is considered.

scholarly journals Comparison of Presumed PDF Models of Turbulent Flames

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Chen Huang ◽  
Andrei N. Lipatnikov
Keyword(s):  
Heat Release ◽  
Burning Velocity ◽  
Mixture Fraction ◽  
Beta Function ◽  
Reaction Rates ◽  
Turbulent Flames ◽  
Implicit Assumption ◽  
Dirac Delta ◽  
Progress Variable ◽  
The Mean

Over the past years, the use of a presumed probability density function (PDF) for combustion progress variable or/and mixture fraction has been becoming more and more popular approach to average reaction rates in premixed and partially premixed turbulent flames. Commonly invoked for this purpose is a beta-function PDF or a combination of Dirac delta functions, with the parameters of the two PDFs being determined based on the values of their first and second moments computed by integrating proper balance equations. Because the choice of any of the above PDFs appears to be totally arbitrary as far as underlying physics of turbulent combustion is concerned, the use of such PDFs implies weak sensitivity of the key averaged quantities to the PDF shape. The present work is aimed at testing this implicit assumption by comparing mean heat release rates, burning velocities, and so forth, averaged by invoking the aforementioned PDFs, with all other things being equal. Results calculated in the premixed case show substantial sensitivity of the mean heat release rate to the shape of presumed combustion-progress-variable PDF, thus, putting the approach into question. To the contrary, the use of a presumed mixture-fraction PDF appears to be a sufficiently reasonable simplification for modeling the influence of fluctuations in the mixture fraction on the mean burning velocity provided that the mixture composition varies within flammability limits.

scholarly journals Large Eddy Simulation of Premixed Combustion With a Thickened-Flame Approach

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Ashoke De ◽  
Sumanta Acharya
Keyword(s):  
Large Eddy Simulation ◽  
Laminar Flame ◽  
Flame Structure ◽  
Reaction Rates ◽  
Premixed Combustion ◽  
Efficiency Function ◽  
Modeling Approach ◽  
Eddy Simulation ◽  
Reduced Chemistry ◽  
Large Eddy

A thickened-flame (TF) modeling approach is combined with a large eddy simulation (LES) methodology to model premixed combustion, and the accuracy of these model predictions is evaluated by comparing with the piloted premixed stoichiometric methane-air flame data of Chen et al. (1996, “The Detailed Flame Structure of Highly Stretched Turbulent Premixed Methane-Air Flames,” Combust. Flame, 107, pp. 233–244) at a Reynolds number Re=24,000. In the TF model, the flame front is artificially thickened to resolve it on the computational LES grid and the reaction rates are specified using reduced chemistry. The response of the thickened-flame to turbulence is taken care of by incorporating an efficiency function in the governing equations. The efficiency function depends on the characteristics of the local turbulence and on the characteristics of the premixed flame such as laminar flame speed and thickness. Three variants of the TF model are examined: the original thickened-flame model, the power-law flame-wrinkling model, and the dynamically modified TF model. Reasonable agreement is found when comparing predictions with the experimental data and with computations reported using a probability distribution function modeling approach. The results of the TF model are in better agreement with data when compared with the predictions of the G-equation approach.

Modeling of Inhomogeneously Premixed Combustion With an Extended TFC Model

2000 ◽  
Vol 124 (1) ◽  
pp. 58-65 ◽  
Author(s):  
W. Polifke ◽  
P. Flohr ◽  
M. Brandt
Keyword(s):  
Laminar Flame ◽  
Mixture Fraction ◽  
Turbulent Flame ◽  
Flame Temperature ◽  
Flame Speed ◽  
Premixed Combustion ◽  
Combustion Stability ◽  
Model Parameters ◽  
Turbulent Flame Speed ◽  
Functional Relationships

In many practical applications, so-called premixed burners do not achieve perfect premixing of fuel and air. Instead, fuel injection pressure is limited, the permissible burner pressure drop is small and mixing lengths are curtailed to reduce the danger of flashback. Furthermore, internal or external piloting is frequently employed to improve combustion stability, while part-load operation often requires burner staging, where neighboring burners operate with unequal fuel/air equivalence ratios. In this report, an extension of the turbulent flame speed closure (TFC) model for highly turbulent premixed combustion is presented, which allows application of the model to the case of inhomogeneously premixed combustion. The extension is quite straightforward, i.e., the dependence of model parameters on mixture fraction is accounted for by providing appropriate lookup tables or functional relationships to the model. The model parameters determined in this way are adiabatic flame temperature, laminar flame speed and critical gradient. The model has been validated against a test case from the open literature and applied to an externally piloted industrial gas turbine burner with good success.

scholarly journals Simulation of CO-H2-Air Turbulent Nonpremixed Flame Using the Eddy Dissipation Concept Model with Lookup Table Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Kazui Fukumoto ◽  
Yoshifumi Ogami
Keyword(s):  
Mixture Fraction ◽  
Chemical Species ◽  
Reaction Rates ◽  
Lookup Table ◽  
Direct Integration ◽  
Progress Variable ◽  
Look Up Table ◽  
Nonpremixed Flame ◽  
Combustion Simulation ◽  
The Look

We present a new combustion simulation technique based on a lookup table approach. In the proposed technique, a flow solver extracts the reaction rates from the look-up table using the mixture fraction, progress variable, and reaction time. Look-up table building and combustion simulation are carried out simultaneously. The reaction rates of the chemical species are recorded in the look-up table according to the mixture fraction, progress variable, and time scale of the reaction. Once the reaction rates are recorded, a direct integration to solve the chemical equations becomes unnecessary; thus, the time for computing the reaction rates is shortened. The proposed technique is applied to an eddy dissipation concept (EDC) model and it is validated through a simulation of a CO-H2-air nonpremixed flame. The results obtained by using the proposed technique are compared with experimental and computational data obtained by using the EDC model with direct integration. Good agreement between our method and the EDC model and the experimental data was found. Moreover, the computation time for the proposed technique is approximately 99.2% lower than that of the EDC model with direct integration.

A Skewed PDF Combustion Model for Jet Diffusion Flames

1990 ◽  
Vol 112 (4) ◽  
pp. 1002-1007 ◽  
Author(s):  
M. M. M. Abou-Ellail ◽  
H. Salem
Keyword(s):  
Diffusion Flames ◽  
Mixture Fraction ◽  
Beta Function ◽  
Delta Function ◽  
Turbulent Jet ◽  
Combustion Model ◽  
Jet Diffusion Flames ◽  
Numerical Predictions ◽  
Methane Flame ◽  
The Mean

A combustion model based on restricted chemical equilibrium is described. A transport equation for the skewness of the mixture fraction is derived. It contains two adjustable constants. The computed values of the mean mixture fraction (f) and its variance and skewness (g and s) for a jet diffusion methane flame are used to obtain the shape of a skewed pdf. The skewed pdf is split into a turbulent part (beta function) and a nonturbulent part (delta function) at f = 0. The contribution of each part is directly related to the values of f, g, and s. The inclusion of intermittency in the skewed pdf appreciably improves the numerical predictions obtained for a turbulent jet diffusion methane flame for which experimental data are available.

scholarly journals Premixed Combustion of Coconut Oil on Perforated Burner

2013 ◽  
Vol 2 (3) ◽  
pp. 133-139
Author(s):  
I.K.G. Wirawan ◽  
I.N.G. Wardana ◽  
Rudy Soenoko ◽  
Slamet Wahyudi
Keyword(s):  
Equivalence Ratio ◽  
Laminar Flame ◽  
Burning Velocity ◽  
Perforated Plate ◽  
Coconut Oil ◽  
Ambient Air ◽  
Premixed Combustion ◽  
Flame Velocity ◽  
Bunsen Flame ◽  
Rich Mixture

Coconut oil premixed combustion behavior has been studied experimentally on perforated burner with equivalence ratio (φ) varied from very lean until very rich. The results showed that burning of glycerol needs large number of air so that the laminar burning velocity (SL) is the highest at very lean mixture and the flame is in the form of individual Bunsen flame on each of the perforated plate hole. As φ is increased the  SL decreases and the secondary Bunsen flame with open tip occurs from φ =0.54 at the downstream of perforated flame. The perforated flame disappears at φ = 0.66 while the secondary Bunsen flame still exist with SL increases following that of hexadecane flame trend and then extinct when the equivalence ratio reaches one or more. Surrounding ambient air intervention makes SL decreases, shifts lower flammability limit into richer mixture, and performs triple and cellular flames. The glycerol diffusion flame radiation burned fatty acids that perform cellular islands on perforated hole.  Without glycerol, laminar flame velocity becomes higher and more stable as perforated flame at higher φ. At rich mixture the Bunsen flame becomes unstable and performs petal cellular around the cone flame front. Keywords: cellular flame; glycerol; perforated flame;secondary Bunsen flame with open tip; triple flame

Flame Extinction Limits of H2‐CO Fuel Blends

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Ahsan R. Choudhuri ◽  
Mahesh Subramanya ◽  
Subramanyam R. Gollahalli
Keyword(s):  
Laminar Flame ◽  
Critical Value ◽  
Mean Value ◽  
Flame Velocity ◽  
Flame Extinction ◽  
Hydrogen Fuel ◽  
Fuel Blend ◽  
Fuel Blends ◽  
Extinction Limit ◽  
The Mean

The flame extinction limits of syngas (H2‐CO) flames were measured using a twin-flame counterflow burner. Plots of extinction limits (%f: volumetric percent of fuel in air) versus global stretch rates were generated at different fuel blend compositions and were extrapolated to determine the flame extinction limit corresponding to an experimentally unattainable zero-stretch condition. The zero-stretch extinction limit of H2‐CO mixtures decreases with the increase in H2 concentration in the mixture. The average difference between the measured flame extinction limit and the Le Chatelier’s calculation is around 7% of the mean value. The measured OH chemiluminescence data indicates that regardless of blend composition the OH radical concentration reduces to a critical value prior to the flame extinction. The measured laminar flame velocity close to the extinction indicates that regardless of fuel composition, the premixed flame of hydrogen fuel blends extinguishes when the mixture laminar flame velocity falls below a critical value.

Modeling of Inhomogeneously Premixed Combustion With an Extended TFC Model

2000 ◽  
Author(s):  
Wolfgang Polifke ◽  
Peter Flohr ◽  
Martin Brandt
Keyword(s):  
Laminar Flame ◽  
Mixture Fraction ◽  
Turbulent Flame ◽  
Flame Temperature ◽  
Flame Speed ◽  
Premixed Combustion ◽  
Combustion Stability ◽  
Model Parameters ◽  
Turbulent Flame Speed ◽  
Functional Relationships

In many practical applications, so-called premixed burners do not achieve perfect premixing of fuel and air. Instead, fuel injection pressure is limited, the permissible burner pressure drop is small and mixing lengths are curtailed to reduce the danger of flashback. Furthermore, internal or external piloting is frequently employed to improve combustion stability, while part-load operation often requires burner staging, where neighboring burners operate with unequal fuel/air equivalence ratios. In this report, an extension of the Turbulent Flame speed Closure (TFC) model for highly turbulent premixed combustion is presented, which allows application of the model to the case of inhomogeneously premixed combustion. The extension is quite straightforward, i.e. the dependence of model parameters on mixture fraction is accounted for by providing appropriate lookup tables or functional relationships to the model. The model parameters determined in this way are adiabatic flame temperature, laminar flame speed and critical gradient. The model has been validated against a test case from the open literature and applied to an externally piloted industrial gas turbine burner with good success.

Proposal of United Combustion Model for Premixed and Diffusion Flames and Its Evaluation

2008 ◽  
Author(s):  
Shin-Ichi Inage
Keyword(s):  
Diffusion Flame ◽  
Diffusion Flames ◽  
Laminar Flame ◽  
Mixture Fraction ◽  
Turbulence Models ◽  
Premixed Combustion ◽  
Combustion Model ◽  
Laminar Flame Speed ◽  
Turbulent Diffusion Flame ◽  
And Diffusion

A premixed flame assisted by the burning of a diffusion flame is used in gas-turbine combustors to reduce NOx emissions. A united model that can be applied to the premixed and diffusion flames is therefore required to simulate the combustion phenomena. This paper proposes such a united model based on the author’s premixed combustion model for reactive progress variable equation. The proposed model has the following features. 1) It includes the laminar flame speed and the gradient of the mixture fraction as parameters. When the gradient of the mixture fraction is close to zero, the model is also close to the previous premixed combustion model as an asymptotic form. 2) It considers the effects of pressure in the combustor, unburned gas temperature, and flame stretch on combustion based on the laminar flame speed. 3) It can be applied to all types of turbulence models like the k-ε model, large eddy simulations, and direct simulations in the case of wrinkled laminar flames. The effect of turbulence is considered through the turbulent eddy viscosity of all turbulence models. To verify the accuracy of the model, the opposed diffusion flame presented by Tsuji and Yamaoka was numerically simulated, as an example of a laminar diffusion flame. Further, a turbulent diffusion flame, which was assisted by the burning of a pilot jet, was demonstrated using the united combustion model as an example of the turbulent diffusion flame discussed by Barlow and Frank. The flame was known as Sandia Flame D. Model results were in good agreement with the experimental data and this agreement confirmed the proposed united model was able to accurately simulate both diffusion flames.

scholarly journals LES study of the impact of moist thermals on the oxidative capacity of the atmosphere in southern West Africa

2017 ◽  
Author(s):  
Fabien Brosse ◽  
Maud Leriche ◽  
Céline Mari ◽  
Fleur Couvreux
Keyword(s):  
Turbulent Mixing ◽  
Reaction Rate ◽  
Reaction Rates ◽  
Oxidative Capacity ◽  
Detailed Chemistry ◽  
Substantial Modification ◽  
Large Eddy ◽  
On Line ◽  
The Mean ◽  
The Impact

Abstract. The hydroxyl radical (OH) is a highly reactive specie and plays a key role in the oxidative capacity of the atmosphere. The total OH reactivity, corresponding to the inverse of OH lifetime, may have a significant fraction non-attributable to commonly measured compounds. The turbulence-driven segregation of OH and its reactants can cause substantial modification of averaged reaction rates, and thus of the total OH reactivity, when compared to a perfectly mixed assumption. We study the impact of turbulent mixing on the OH reactivity with Large-Eddy Simulations from the Meso-NH model coupled on-line with a detailed chemistry mechanism in two contrasted regimes. Our findings show that the non-mixing of isoprene (resp. aldehydes) and OH leads to 30 % decrease (resp. 16 % increase) of the mean reaction rate at the top of the boundary layer and consequently to 9 % decrease (resp. 5 % increase) of the OH total reactivity in a biogenic (resp. anthropogenic) environment. Moreover, the total OH reactivity is highest inside thermals in both cases.

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