Strained flamelets for turbulent premixed flames, I: Formulation and planar flame results (original) (raw)
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Modelling of Turbulent Premixed Flames using Strained–Flamelets
A model for the mean reaction rate in turbulent premixed flames, that accounts for effects of strain rate on flame structure is presented. This model is based on the strained asymmetric counterflow unburnt-toburnt laminar flame and its characteristics. The conditional scalar dissipation rate is chosen to parametrise the strained-flamelet structure since it is dictated by the convection-diffusion-reaction balance. RANS calculations of laboratory scale flames using this approach give good comparisons with experimental results and suggest that commonly used unstrained-flamelet formulation overpredicts the mean reaction rate leading to smaller flame brush compared to experiment.
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 bi , and the mean volumetric heat release rate in an unstretched laminar flamelet of the mixture. Included in the expression for P 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 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 thermodiffusive 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 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.
A mixedness-reactedness flamelet model for turbulent diffusion flames
Symposium (International) on Combustion, 1991
A novel, non-equilibrium, combustion model is proposed, to simulate turbulent diffusion flames, based on a laminar flamelet approach that was originally developed for premixed combustion. The model embodies a mixedness factor to describe the mixture strength and a reactedness parameter to describe the degree of completeness of combustion. The effect of straining is accounted for in prior laminar flame computations and the imposition of a known distribution of flame straining on the flamelets. Profiles of laminar, heat release rate against temperature and the assumed independence of fluctuations in mixedness, reactedness and flame straining enable a simple evaluation of turbulent mean heat release rate to be made, This approach is used to predict numerically the field solutions for lifted, turbulent jet, methane-air, diffusion flames, in conjunction with the k-9 turbulence model. The computations predict an approximately linear relationship between lift-off height and fuel jet velocity, in good agreement with available experimental data. Results suggest that the mechanism of flame stabilization is associated with the complex interactions between convection, turbulent mixing, heat release rate under strain and thermal expansion, rather than with a single phenomenological parameter such as, for example, the flame strain extinction limit.
Analysis of the flamelet concept in the numerical simulation of laminar partially premixed flames
Combustion and Flame, 2008
The aim of this work is to analyze the application of flamelet models based on the mixture fraction variable and its dissipation rate to the numerical simulation of partially premixed flames. Although the main application of these models is the computation of turbulent flames, this work focuses on the performance of flamelet concept in laminar flame simulations removing, in this way, turbulence closure interactions. A well-known coflow methane/air laminar flame is selected. Five levels of premixing are taken into account from an equivalence ratio Φ = ∞ (nonpremixed) to Φ = 2.464. Results obtained using the flamelet approaches are compared to data obtained from the detailed solution of the complete transport equations using primitive variables. Numerical simulations of a counterflow flame are also presented to support the discussion of the results. Special emphasis is given to the analysis of the scalar dissipation rate modeling.
Flamelet Analysis of Turbulent Combustion
Lecture Notes in Computer Science, 2005
Three-dimensional direct numerical simulations are performed of turbulent combustion of initially spherical flame kernels. The chemistry is described by a progress variable which is attached to a flamelet library. The influence of flame stretch and curvature on the local mass burning rate is studied and compared to an analytical model. It is found that there is a good agreement between the simulations and the model. Then approximations to the model are evaluated.
Combustion and Flame, 2002
The laminar flamelet approach is frequently applied to model turbulent non-premixed flames based on the assumption of adiabatic combustion. This generally results in the significant overprediction of temperatures for flames where thermal radiation is important. In the present study, an adiabatic, mixedness-reactedness flamelet combustion model has been extended to incorporate the effect of radiation heat transfer using the concept of enthalpy defect. This requires the generation of flamelet data sets using a detailed chemical kinetic mechanism and introduction of enthalpy defect as an additional flamelet parameter. The methodology developed has been applied to simulate lifted, free, turbulent non-premixed natural gas flames for which measurements are reported in the literature. A non-adiabatic flamelet data library for methane-air flames has been generated with the GRI reaction mechanism using the modified CHEMKIN code for the modeling of turbulent radiating flames. The turbulent flame computational results, with and without radiation heat transfer, are compared with experimental data for mean gas temperatures, species concentrations and flame lift-off heights for a number of laboratory-and large-scale lifted turbulent jet flames. Predictions obtained using the non-adiabatic flamelet model are found to be in good agreement with temperature measurements, whereas the original adiabatic model significantly overestimates temperatures in the downstream regions of flames where significant heat loss occurs. Species concentration and lift-off height results show small differences between predictions with and without radiation losses in regions close to the base of the flame, although both methodologies provide satisfactory agreement with the available data.
A balance equation for the mean rate of product creation in premixed turbulent flames
Proceedings of the Combustion Institute, 2017
Transport equations for reaction rate W and its Favre-averaged valueW are derived from first principle in the case of premixed turbulent combustion. The assumptions made for derivation hold for unity Lewis number premixed flames at least in the flamelet regime of turbulent burning. Analysis of the latter equation shows that it involves two dominant terms, but the difference between them vanishes if reaction zones retain the structure of the zone in the unperturbed laminar flame. However, in such a case, turbulent burning velocity cannot grow with time during interaction of an initially laminar flame with a turbulent flow. Therefore, the analysis indicates a vital role played by local perturbations of reaction zone structure in premixed turbulent combustion. The dominance of these two terms and the important role played by the difference between them are confirmed by analyzing three DNS databases associated with both the corrugated flamelets and thin reaction zones regimes of premixed turbulent burning. Moreover, the DNS data show that perturbations of local displacement speed due to perturbations of local flamelet structure are also of paramount importance for modeling transport of flame surface density even in weakly turbulent flows. Finally, by simulating curved and/or strained 1 laminar premixed flames and integrating the transport equation for W across the flames, the integral is shown to depend linearly on the stretch rate even in highly perturbed flames, with results obtained from variously stretched flames being close to each other. Based on this finding, the difference between the two dominant terms in the transport equation for the mean rateW is hypothesized to depend linearly on the stretch rate conditioned to the reaction zone. Application of this hypothesis to the DNS data associated with the corrugated flamelets combustion regime yields encouraging results, thus, confirming a crucial role played by local perturbations of reaction zone structure even in weakly turbulent flames.
Flamelet models for nonisenthalpic turbulent premixed jet flames
34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 1998
A computational study of a nonisenthalpic premixed turbulent jet flame is described. The flame burns a homogeneously premixed stoichiometric methane-air mixture injected into a co-flow of air. The enthalpy (chemical +sensible) varies because of mixing between the jet fluid and the co-flow. The performance of the Bray-Moss (BM) model and three flame surface density (FSD) models is evaluated by comparing the predictions of mean velocity and temperature profiles with recent experimental data. The reaction progress variable approach, which is established for isenthalpic flames, is extended to the present nonisenthalpic flames by including mean and mean square mixture fraction equations. The joint probability density function (PDF) of the reaction progress variable and the mixture fraction is modeled in terms of two statistically independent PDFs. The time averaged reaction rate term is modeled using the BM and the FSD models. All models yielded reasonable predictions of mean velocity. The BM and MB models provided the best agreement with the mean temperature data but the other FSD models with slight tuning of the constants could provide similar agreement as well. The results show that a simple extension of the FSD models is promising for the treatment of nonisenthalpic flames. It appears that the differences in the conceptual framework of the FSD models disappears in their implementation using basically the same turbulence properties of kinetic energy and dissipation rates.
Flow, Turbulence and Combustion, 2005
Direct numerical simulation is a very powerful tool to evaluate the validity of new models and theories for turbulent combustion. In this paper, direct numerical simulations of spherically expanding premixed turbulent flames in the thin reaction zone regime and in the broken reaction zone regime are performed. The flamelet-generated manifold method is used in order to deal with detailed reaction kinetics. The computational results are analyzed by using an extended flame stretch theory. It is investigated whether this theory is able to describe the influence of flame stretch and curvature on the local burning velocity of the flame. It is found that if the full profiles of flame stretch and curvature through the flame front are included in the theory, the local mass burning rate is well predicted. The influence of using a reduced chemistry model is investigated by comparing flamelet simulations with reduced and detailed chemistry. Adding a second dimension to the flamelet-generated manifold increases the accuracy of the reduced model with an order of magnitude.