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.

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 Burning Rate in Impinging Jet Flames

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
A. N. Lipatnikov
Keyword(s):  
Turbulent Combustion ◽  
Burning Velocity ◽  
Impinging Jet ◽  
Turbulent Flames ◽  
Research Groups ◽  
Scalar Flux ◽  
Premixed Turbulent Combustion ◽  
Progress Variable ◽  
Premixed Turbulent Flames ◽  
The Mean

A method for evaluating burning velocity in premixed turbulent flames stabilized in divergent mean flows is quantitatively validated using numerical approximations of measured axial profiles of the mean combustion progress variable, mean and conditioned axial velocities, and axial turbulent scalar flux, obtained by four research groups from seven different flames each stabilized in an impinging jet. The method is further substantiated by analyzing the combustion progress variable balance equation that is yielded by the extended Zimont model of premixed turbulent combustion. The consistency of the model with the aforementioned experimental data is also demonstrated.

A Scale Separation Method for Pollutant Prediction in Turbulent Flames Using Transported Scalars With Flamelet Generated Manifold (FGM) Method

2018 ◽  
Author(s):  
Rakesh Yadav ◽  
Shaoping Li ◽  
Ellen Meeks
Keyword(s):  
Experimental Data ◽  
Mixture Fraction ◽  
Reaction Rates ◽  
Turbulent Flames ◽  
Separation Method ◽  
Scale Separation ◽  
Reduced Order ◽  
Progress Variable ◽  
Flamelet Generated Manifold ◽  
Key Species

In this work, a scale separation method has been proposed and implemented in the framework of Flamelet Generated Manifold (FGM) model. In this approach, first a list of slow evolving species like NO, N2O etc., are identified. Then, a separate transport equation for each of these species (called FGM scalars) is solved in addition to the mixture fraction and progress variable equations. The forward and reverse reaction rates of these slow forming species are computed in two-dimensional FGM flamelets and pre-tabulated as a function of progress variable, mixture fraction and their respective variances. At run time, the pre-tabulated probability density function (PDF) averaged production rates of these FGM scalars are used, while their tabulated reverse rates are modified with a linear scaling based on the ratio of tabulated values of the FGM scalar and the prevailing values of the FGM scalars from three dimensional CFD solution. This mechanism allows the reverse rates to provide continuous feedback and respond to the slow evolution of scalar. Other than the list of selected scalars, all other species and temperature are still computed as a function of the main progress variable and mixture fraction. Since, a small set of scalars can be used to track key species, this methodology remains computationally efficient. The current approach has been implemented into commercial CFD solver, ANSYS Fluent, and has been validated for two lab scale turbulent flames, the first one is Sandia Flame D, while the second one is a lifted turbulent methane flame in vitiated co-flow. In the current work, two additional FGM scalar transport equations are solved for CO and NO and comparisons have been made against the tabulated values as well as the experimental data. It has been seen that the scale separation methodology of these scalars leads ∼10–15% improvements in the CO mass fraction, while it reduces the peak NO formation up to 4 times leading to better agreement with experimental data compared to tabulated values. The quality of predictions from the current method is also evaluated against finite rate chemistry-based model as well as reduced order NO model. It is found that the current model has consistent results, and is an improvement over current reduced order modeling approach.

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.

A spectral closure for premixed turbulent combustion in the flamelet regime

1992 ◽  
Vol 242 ◽  
pp. 611-629 ◽  
Author(s):  
N. Peters
Keyword(s):  
Field Equation ◽  
Scalar Field ◽  
Dimensional Analysis ◽  
Turbulent Combustion ◽  
Burning Velocity ◽  
Turbulent Flames ◽  
Scalar Dissipation ◽  
Premixed Turbulent Combustion ◽  
Flame Stretch ◽  
The Mean

Premixed turbulent combustion in the flamelet regime is analysed on the basis of a field equation. This equation describes the instantaneous flame contour as an isoscalar surface of the scalar field G(x,t). The field equation contains the laminar burning velocity sL as velocity scale and its extension includes the effect of flame stretch involving the Markstein length [Lscr ] as a characteristic lengthscale of the order of the flame thickness. The scalar G(x,t) plays a similar role for premixed flamelet combustion as the mixture fraction Z(x,t) in the theory of non-premixed flamelet combustion.Equations for the mean $\overline{G}$ and variance $\overline{G^{\prime 2}}$ are derived. Additional closure problems arise for the mean source terms in these equations. In order to understand the nature of these terms an ensemble of premixed flamelets with arbitrary initial conditions in constant-density homogeneous isotropic turbulence is considered. An equation for the two-point correlation $\overline{G^{\prime}({\boldmath x},t)G^{\prime}({\boldmath x}+{\boldmath r},t)}$ is derived. When this equation is transformed into spectral space, closure approximations based on the assumption of locality and on dimensional analysis are introduced. This leads to a linear equation for the scalar spectrum function Γ(k,t), which can be solved analytically. The solution Γ(k,t) is analysed by assuming a small-wavenumber cutoff at k0 = lT−1, where lT is the integral lengthscale of turbulence. There exists a $k^{-\frac{5}{3}}$ spectrum between lT and LG, where LG is the Gibson scale. At this scale turbulent fluctuations of the scalar field G(x,t) are kinematically restored by the smoothing effect of laminar flame propagation. A quantity called kinematic restoration ω is introduced, which plays a role similar to the scalar dissipation χ for diffusive scalars.By calculating the appropriate moments of Γ(k,t), an algebraic relation between ω, $\omega,\overline{G^{\prime}({\boldmath x},t)^2}$, the integral lengthscale lT and the viscous dissipation ε is derived. Furthermore, the scalar dissipation χ[Lscr ], based on the Markstein diffusivity [Dscr ][Lscr ] = sL [Lscr ], and the scalar-strain co-variance Σ[Lscr ] are related to ω. Dimensional analysis, again, leads to a closure of the main source term in the equation for the mean scalar $\overline{G}$. For the case of plane normal and oblique turbulent flames the turbulent burning velocity sT and the flame shape is calculated. In the absence of flame stretch the linear relation sT ∼ u′ is recovered. The flame brush thickness is of the order of the integral lengthscale. In the case of a V-shaped flame its increase with downstream position is calculated.

Study of Thermo-Diffusive Effects on Iso-Octane/Air Flames at Fixed Turbulence Karlovitz Number

2011 ◽  
Author(s):  
Akihiro Hayakawa ◽  
Tomohiro Takeo ◽  
Yukito Miki ◽  
Yukihide Nagano ◽  
Toshiaki Kitagawa
Keyword(s):  
Equivalence Ratio ◽  
Burning Velocity ◽  
Turbulent Flame ◽  
Turbulent Flames ◽  
Laminar Burning Velocity ◽  
Markstein Number ◽  
Flame Stretch ◽  
The Mean ◽  
Diffusive Effects ◽  
Turbulent Burning Velocity

Spherically propagating laminar and turbulent flames were studied using iso-octane / air mixtures with and without dilution. The main purpose of this study is to clarify the influence of thermo-diffusive effects on the turbulent flames. In order to examine the thermo-diffusive effects solely by separating them from the effects of flame stretch, turbulent burning velocities were compared at constant flame stretch factors. The mean flame stretch factor acting on turbulent flame front may be represented by the turbulence Karlovitz number. Thus, turbulent explosions were carried out at fixed turbulence Karlovitz numbers. The ratio of turbulent burning velocity to unstretched laminar burning velocity increased with the equivalence ratio for non-diluted mixtures at fixed turbulence Karlovitz numbers. And this ratio for CO2 diluted mixtures was larger than N2 diluted mixtures. The Markstein number that denotes the sensitivity of the flame to thermo-diffusive effects depends on the equivalence ratio and diluents of the mixture. The ratio of turbulent burning velocity to unstretched laminar one increased with decreasing Markstein number. Especially, it changed stepwise around Markstein number of zero. However, the burning velocity ratios did not increase with increasing mixture pressure although the Markstein number decreased with pressure.

scholarly journals Pseudosparse neural coding in the visual system of primates

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Sidney R. Lehky ◽  
Keiji Tanaka ◽  
Anne B. Sereno
Keyword(s):  
Neural Coding ◽  
Macaque Monkey ◽  
Implicit Assumption ◽  
Data Set ◽  
Efficient Coding ◽  
Population Responses ◽  
Lateral Intraparietal Cortex ◽  
Neural Populations ◽  
Neurophysiological Data ◽  
The Mean

AbstractWhen measuring sparseness in neural populations as an indicator of efficient coding, an implicit assumption is that each stimulus activates a different random set of neurons. In other words, population responses to different stimuli are, on average, uncorrelated. Here we examine neurophysiological data from four lobes of macaque monkey cortex, including V1, V2, MT, anterior inferotemporal cortex, lateral intraparietal cortex, the frontal eye fields, and perirhinal cortex, to determine how correlated population responses are. We call the mean correlation the pseudosparseness index, because high pseudosparseness can mimic statistical properties of sparseness without being authentically sparse. In every data set we find high levels of pseudosparseness ranging from 0.59–0.98, substantially greater than the value of 0.00 for authentic sparseness. This was true for synthetic and natural stimuli, as well as for single-electrode and multielectrode data. A model indicates that a key variable producing high pseudosparseness is the standard deviation of spontaneous activity across the population. Consistently high values of pseudosparseness in the data demand reconsideration of the sparse coding literature as well as consideration of the degree to which authentic sparseness provides a useful framework for understanding neural coding in the cortex.

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