Effects of molecular diffusion and of thermal expansion on the structure and dynamics of premixed flames in turbulent flows of large scale and low intensity

1982 ◽  
Vol 116 ◽  
pp. 251-282 ◽  
Author(s):  
P. Clavin ◽  
F. A. Williams
Keyword(s):  
Thermal Expansion ◽  
Flame Front ◽  
Turbulent Flows ◽  
Thermal Model ◽  
Laminar Flame ◽  
Premixed Flames ◽  
Turbulent Flames ◽  
Flame Thickness ◽  
The Mean ◽  
Diffusivity Ratio

To study effects of flow inhomogeneities on the dynamics of laminar flamelets in turbulent flames, with account taken of influences of the gas expansion produced by heat release, a previously developed theory of premixed flames in turbulent flows, that was based on a diffusive-thermal model in which thermal expansion was neglected, and that applied to turbulence having scales large compared with the laminar flame-thickness, is extended by eliminating the hypothesis of negligible expansion and by adding the postulate of weak-intensity turbulence. The consideration of thermal expansion motivates the formal introduction of multiple-scale methods, which should be useful in subsequent investigations. Although the hydrodynamic-instability mechanism of Landau is not considered, no restriction is imposed on the density change across the flame front, and the additional transverse convection correspondingly induced by the tilted front is described. By allowing the heat-to-reactant diffusivity ratio to differ slightly from unity, clarification is achieved of effects of phenomena such as flame stretch and the flame-relaxation mechanism traceable to transverse diffusive processes associated with flame-front curvature. By carrying the analysis to second order in the ratio of the laminar flame thickness to the turbulence scale, an equation for evolution of the flame front is derived, containing influences of transverse convection, flame relaxation and stretch. This equation explains anomalies recently observed at low frequencies in experimental data on power spectra of velocity fluctuations in turbulent flames. It also shows that, concerning the diffusive-stability properties of the laminar flame, the density change across the flame thickness produces a shift of the stability limits from those obtained in the purely diffusive-thermal model. At this second order, the turbulent correction to the flame speed involves only the mean area increase produced by wrinkling. The analysis is carried to the fourth order to demonstrate the mean-stretch and mean-curvature effects on the flame speed that occur if the diffusivity ratio differs from unity.

scholarly journals Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates

2021 ◽  
Author(s):  
Meysam Sahafzadeh ◽  
Seth B. Dworkin ◽  
Larry W. Kostiuk
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Time Scale ◽  
Transfer Functions ◽  
Laminar Flame ◽  
Premixed Flames ◽  
Turbulent Flames ◽  
Response Analysis ◽  
Phase Lag

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.

Theory of flame-front stability

1961 ◽  
Vol 10 (1) ◽  
pp. 80-100 ◽  
Author(s):  
Wiktor Eckhaus
Keyword(s):  
Flame Front ◽  
Laminar Flame ◽  
Flame Structure ◽  
Flame Velocity ◽  
Flame Propagation Velocity ◽  
Flame Thickness ◽  
Fluid Velocities ◽  
Laminar Flame Front ◽  
Coefficient Of Heat Conductivity ◽  
The Stability

A study of the stability of a plane laminar flame front is made. The effects of disturbances on the flame structure are investigated by a small perturbations technique, taking into account the mechanism of diffusion, heat conduction and unsteady combustion. By use of a simplified model of the flame structure, and the assumption that the flame thickness is small compared with the wavelength of disturbances, a formula for the perturbation of the flame propagation velocity is derived. The flame velocity is shown to depend on the curvature of the flame, and on the rates of change of fluid velocities at the flame boundary. From stability analysis it then follows that properties of the mixture, as expressed in terms of the coefficient of heat conductivity and various coefficients of diffusion, play an important role in determining the stability picture. For some estimated values of these parameters the theoretical results are shown to agree with the general trend of the experimentally observed behaviour.

Lean Premixed Turbulent Flame Front Structure and Implications for Modeling

2010 ◽  
Author(s):  
Frank T. C. Yuen ◽  
O¨mer L. Gu¨lder
Keyword(s):  
Flame Front ◽  
Turbulent Flame ◽  
Turbulent Flames ◽  
Experimental Conditions ◽  
Flame Thickness ◽  
Premixed Turbulent Combustion ◽  
Wide Range ◽  
Significant Difference ◽  
Lean Premixed ◽  
Front Curvature

Premixed turbulent flames of methane-air and propane-air stabilized on a Bunsen type burner were studied to investigate the structure of the flame front at a wide range of turbulence intensities covering the range of interest in lean premixed combustors. The flame front data were obtained using planar Rayleigh imaging, and particle image velocimetry was used to measure instantaneous velocity field for the experimental conditions studied. The fuel-air equivalence ratio range was from lean 0.6 to stoichiometric for methane flames, and from 0.7 to stoichiometric for propane flames. The non-dimensional turbulent rms velocity, u′/SL, covered a range from 3 to 24. Flame front thickness and flame front curvature statistics were obtained from 2D measurements. Flame front thickness increased slightly with increasing non-dimensional turbulence rms velocity in both methane and propane flames, although the flame thickening was more prominent in propane flames. There was not any significant difference in flame thickening whether the flame thickness is evaluated at progress variable 0.5, corresponding to the reaction zone, or 0.3, corresponding to the preheat zone. Variations of front curvature and flame thickness are presented for different premixed combustion regimes and implications of these findings for modelling premixed turbulent combustion are discussed.

scholarly journals Predicting the consumption speed of a premixed flame subjected to unsteady stretch rates

2021 ◽  
Author(s):  
Meysam Sahafzadeh ◽  
Seth B. Dworkin ◽  
Larry W. Kostiuk
Keyword(s):  
Heat Release ◽  
Heat Release Rate ◽  
Release Rate ◽  
Time Scale ◽  
Transfer Functions ◽  
Laminar Flame ◽  
Premixed Flames ◽  
Turbulent Flames ◽  
Response Analysis ◽  
Phase Lag

The stretched laminar flame model provides a convenient approach to embed realistic chemical kinetics when simulating turbulent premixed flames. When positive-only periodic strain rates are applied to a laminar flame there is a notable phase lag and diminished amplitude in heat release rate. Similar results have being observed with respect to the other component of stretch rate, namely the unsteady motion of a curved flame when the stretch rates are periodic about zero. Both cases showed that the heat release rate or consumption speed of these laminar-premixed flames vary significantly from the quasi-steady flamelet model. Deviation from quasi-steady behaviour increases as the unsteady flow time scale approaches the chemical time scale that is set by the stoichiometry. A challenge remains in how to use such results predictively for local and instantaneous consumption speed for small segments of turbulent flames where their unsteady stretch history is not periodic. This paper uses a frequency response analysis as a characterization tool to simplify the complex non-linear behaviour of premixed methane air flames for equivalence ratios from 1.0 down to 0.7, and frequencies from quasi-steady up to 2000 Hz using flame transfer functions. Various linear and nonlinear models were used to identify appropriate flame transfer functions for low and higher frequency regimes, as well as extend the predictive capabilities of these models. Linear models were only able to accurately predict the flame behaviour below a threshold of when the fluid and chemistry time scales are the same order of magnitude. Other proposed transfer functions were tested against arbitrary multi-frequency stretch inputs and were shown to be effective over the full range of frequencies.

Propagation of wrinkled turbulent flames in the context of hydrodynamic theory

2011 ◽  
Vol 680 ◽  
pp. 225-264 ◽  
Author(s):  
F. CRETA ◽  
M. MATALON
Keyword(s):  
Thermal Expansion ◽  
Turbulence Intensity ◽  
Isotropic Turbulence ◽  
Hydrodynamic Instability ◽  
Normal Component ◽  
Propagation Speed ◽  
Turbulent Flames ◽  
Hydrodynamic Theory ◽  
Integral Scale ◽  
The Mean

We study the propagation of premixed flames in two-dimensional homogeneous isotropic turbulence using a Navier–Stokes/front-capturing methodology within the context of hydrodynamic theory. The flame is treated as a thin layer separating burnt and unburnt gases, of vanishingly small thickness, smaller than the smallest fluid scales. The method is thus suitable to investigate the flame propagation in the wrinkled flamelet regime of turbulent combustion. A flow-control system regulates the mean position of the flame and the incident turbulence intensity. In this context we study the individual effects of turbulence intensity, turbulence scale, thermal expansion, hydrodynamic strain and hydrodynamic instability on the propagation characteristics of the flame. Results are obtained assuming positive Markstein length, corresponding to lean hydrocarbon–air or rich hydrogen–air mixtures. For stable planar flames we find a quadratic dependence of turbulent speed on turbulence intensity. Upon onset of hydrodynamic instability, corrugated structures replace the planar conformation and we observe a greater resilience to turbulence, the quadratic scaling being replaced by scaling exponents less than one. Such resilience is also confirmed by the observation of a threshold turbulence intensity below which the propagation speed of corrugated flames is indistinguishable from the laminar speed. Turbulent speed is found to increase and later plateau with increasing thermal expansion, this affecting the average flame displacement but not the mean flame curvature. In addition, turbulence integral scale is also observed to affect the propagation of the flame with the existence of an intermediate scale maximizing the turbulent speed. This maximizing scale is smaller for corrugated flames than it is for planar flames, implying that small eddies that will be unable to significantly perturb a planar front could be rather effective in perturbing a corrugated flame. Turbulent planar flames, and more so corrugated flames, were observed to experience a positive mean hydrodynamic strain, which was explained in terms of the overwhelming mean contribution of the normal component of strain. The positive straining causes a decrease in the mean laminar propagation speed which in turn can decrease the turbulent speed. The effect of the flame on the incident turbulent field was examined in terms of loss of isotropy and vorticity destruction by thermal expansion. The latter can be mitigated by a baroclinic vorticity generation which is enhanced for corrugated flames.

scholarly journals On velocity and reactive scalar spectra in turbulent premixed flames

2014 ◽  
Vol 754 ◽  
pp. 456-487 ◽  
Author(s):  
H. Kolla ◽  
E. R. Hawkes ◽  
A. R. Kerstein ◽  
N. Swaminathan ◽  
J. H. Chen
Keyword(s):  
Kinetic Energy ◽  
Reaction Rate ◽  
Laminar Flame ◽  
Premixed Flames ◽  
Inertial Range ◽  
Turbulent Premixed Flames ◽  
Flame Thickness ◽  
Kolmogorov Scale ◽  
Reactive Scalar ◽  
Turbulent Premixed

AbstractKinetic energy and reactive scalar spectra in turbulent premixed flames are studied from compressible three-dimensional direct numerical simulations (DNS) of a temporally evolving rectangular slot-jet premixed flame, a statistically one-dimensional configuration. The flames correspond to a lean premixed hydrogen–air mixture at an equivalence ratio of 0.7, preheated to 700 K and at 1 atm, and three DNS are considered with a fixed jet Reynolds number of 10 000 and a jet Damköhler number varying between 0.13 and 0.54. For the study of spectra, motivated by the need to account for density change, which can be locally strong in premixed flames, a new density-weighted definition for two-point velocity/scalar correlations is proposed. The density-weighted two-point correlation tensor retains the essential properties of its constant-density (incompressible) counterpart and recovers the density-weighted Reynolds stress tensor in the limit of zero separation. The density weighting also allows the derivation of balance equations for velocity and scalar spectrum functions in the wavenumber space that illuminate physics unique to combusting flows. Pressure–dilatation correlation is a source of kinetic energy at high wavenumbers and, analogously, reaction rate–scalar fluctuation correlation is a high-wavenumber source of scalar energy. These results are verified by the spectra constructed from the DNS data. The kinetic energy spectra show a distinct inertial range with a $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}-5/3$ scaling followed by a ‘diffusive–reactive’ range at higher wavenumbers. The exponential drop-off in this range shows a distinct inflection in the vicinity of the wavenumber corresponding to a laminar flame thickness, $\delta _L$, and this is attributed to the contribution from the pressure–dilatation term in the energy balance in wavenumber space. Likewise, a clear spike in spectra of major reactant species (hydrogen) arising from the reaction-rate term is observed at wavenumbers close to $\delta _L$. It appears that in the inertial range classical scaling laws for the spectra involving the Kolmogorov scale are applicable, but in the high-wavenumber range where chemical reactions have a strong signature the laminar flame thickness produces a better collapse. It is suggested that a full scaling should perhaps involve the Kolmogorov scale, laminar flame thickness, Damköhler number and Karlovitz number.

scholarly journals A Combustion Regime-Based Model for Large Eddy Simulation

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4934
Author(s):  
Eugenio Giacomazzi ◽  
Donato Cecere
Keyword(s):  
Large Eddy Simulation ◽  
Volume Fraction ◽  
Laminar Flame ◽  
Combustion Regime ◽  
Turbulent Flames ◽  
Scale Model ◽  
Flame Thickness ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Turbulent Premixed

The aim of this work is to propose a unified (generalized) closure of the chemical source term in the context of Large Eddy Simulation able to cover all the regimes of turbulent premixed combustion. Turbulence/combustion scale interaction is firstly analyzed: a new perspective to look at commonly accepted combustion diagrams is provided based on the evidence that actual turbulent flames can experience locally several combustion regimes although global non-dimensional numbers would locate such flames in a single specific operating point of the standard combustion diagram. The deliverable is a LES subgrid scale model for turbulent premixed flames named Localized Turbulent Scales Model (LTSM). This is founded on the estimation of the local reacting volume fraction of a computational cell that is related to the local turbulent and laminar flame speeds and to the local flame thickness.

The Effect of Lewis Number on Instantaneous Flamelet Speed and Position Statistics in Counter-Flow Flames With Increasing Turbulence

2017 ◽  
Author(s):  
Sean D. Salusbury ◽  
Ehsan Abbasi-Atibeh ◽  
Jeffrey M. Bergthorson
Keyword(s):  
Flame Front ◽  
Turbulence Intensity ◽  
High Speed ◽  
Rayleigh Scattering ◽  
Turbulent Flame ◽  
Lewis Number ◽  
Turbulent Flames ◽  
Flame Speed ◽  
Laminar Flames ◽  
Counter Flow

Differential diffusion effects in premixed combustion are studied in a counter-flow flame experiment for fuel-lean flames of three fuels with different Lewis numbers: methane, propane, and hydrogen. Previous studies of stretched laminar flames show that a maximum reference flame speed is observed for mixtures with Le ≳ 1 at lower flame-stretch values than at extinction, while the reference flame speed for Le ≪ 1 increases until extinction occurs when the flame is constrained by the stagnation point. In this work, counter-flow flame experiments are performed for these same mixtures, building upon the laminar results by using variable high-blockage turbulence-generating plates to generate turbulence intensities from the near-laminar u′/SLo=1 to the maximum u′/SLo achievable for each mixture, on the order of u′/SLo=10. Local, instantaneous reference flamelet speeds within the turbulent flame are extracted from high-speed PIV measurements. Instantaneous flame front positions are measured by Rayleigh scattering. The probability-density functions (PDFs) of instantaneous reference flamelet speeds for the Le ≳ 1 mixtures illustrate that the flamelet speeds are increasing with increasing turbulence intensity. However, at the highest turbulence intensities measured in these experiments, the probability seems to drop off at a velocity that matches experimentally-measured maximum reference flame speeds in previous work. In contrast, in the Le ≪ 1 turbulent flames, the most-probable instantaneous reference flamelet speed increases with increasing turbulence intensity and can, significantly, exceed the maximum reference flame speed measured in counter-flow laminar flames at extinction, with the PDF remaining near symmetric for the highest turbulence intensities. These results are reinforced by instantaneous flame position measurements. Flame-front location PDFs show the most probable flame location is linked both to the bulk flow velocity and to the instantaneous velocity PDFs. Furthermore, hydrogen flame-location PDFs are recognizably skewed upstream as u′/SLo increases, indicating a tendency for the Le ≪ 1 flame brush to propagate farther into the unburned reactants against a steepening average velocity gradient.

scholarly journals Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean ◽  
Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

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