Conceptual Limitations of the Probability Density Function Method for Modeling Turbulent Premixed Combustion and Closed-Form Description of Chemical Reactions' Effects

In this paper, we critically analyzed possibilities of probability density function (PDF) methods for the closed-form description of combustion chemical effects in turbulent premixed flames. We came to the conclusion that the concept of a closed-form description of chemical effects in the classical modeling strategy in the PDF method based on the use of reaction-independent mixing models is not applicable to turbulent flames. The reason for this is the strong dependence of mixing on the combustion reactions due to the thin-reaction-zone nature of turbulent combustion confirmed in recent optical studies and direct numerical simulations. In this case, the chemical effect is caused by coupled reaction–diffusion processes that take place in thin zones of instantaneous combustion. We considered possible alternative modeling strategies in the PDF method that would allow the chemical effects to be described in a closed form and came to the conclusion that this is possible only in a hypothetical case where instantaneous combustion occurs in reaction zones identical to the reaction zone of the undisturbed laminar flame. For turbulent combustion in the laminar flamelet regime, we use an inverse modeling strategy where the model PDF directly contains the characteristics of the laminar flame. For turbulent combustion in the distributed preheat zone regime, we offer an original joint direct/inverse modeling strategy. For turbulent combustion in the thickened flamelet regime, we combine the joint direct/inverse and inverse modeling strategies correspondingly for simulation of the thickened flamelet structure and for the determination of the global characteristics of the turbulent flame

Gas premixed combustion at high turbulence. Turbulent flame closure combustion model

This paper is devoted to analyze the special class of turbulent premixed flames that we call intermediate steady propagation (ISP) flames. These flames are common to industrial premixed combustion chambers which operate at intensive turbulence when velocity pulsations are significantly higher than the flamelet combustion velocity. They are characterized by a practically constant turbulent combustion velocity, controlled by turbulence, chemistry and molecular processes, and by an increasing flame width, controlled mainly by turbulent diffusion. The main content of this work is a description of physical backgrounds and outcome of the original asymptotical (i.e., valid at high Re and Da numbers) premixed combustion model, that, from a methodological point of view, is close to Kolmogorov analysis of developed turbulence at high Re numbers. Our analysis starts from the thickened and strongly wrinkled flamelets combustion mechanism. Quantitative results for this model are based on the Kolmogorov assumption of the equilibrium fine-scale turbulence and on additional assumption of the universal small-scale structure of the wrinkled flamelet sheet. From this background it is possible to deduce formulas for the thickened flamelets parameters and the flamelet sheet area and hence the turbulent combustion velocity of the premixed flame. These formulas are used for the closure of the combustion equation written in terms of a progress variable leading to the so called turbulent flame closure (TFC) model for the numerical simulation of ISP flames. Consistent to the ISP flames, in this work the concept of countergradient transport phenomenon in premixed combustion is analyzed

Kolmogorov methodology as a practical way to answer to the challenge of turbulent combustion

This paper analyses possible practical answer to so-called challenge of turbulent combustion (i. e. inability of combustion models predict accurately at real Reynolds and Damkohler numbers combustion rates) using Kolmogorov idea of equilibrium small-scale states. As this challenge is connected with inability to resolve at combustion modeling small space and time scales where takes place coupling between chemistry and turbulence, controlling the rates, our propose is based on assumption some equilibrium small-scale structures of reaction zones at flamelet combustion mechanism, whose properties could be expressed in terms of large-scale parameters. In other words the combustion rates enter in the combustion equation through a physical model similar to the molecular dissipation in the Kolmogorov "k - ε" turbulence model. The concrete analyzed premixed combustion problem refers to the case of strong turbulence and flames with increasing brush width (this combustion regime is preceded to the traditional stationary flames). Two main equilibrium states are assumed for quantitative description of this coupling: equilibrium fine-scale turbulence, which controls thickened flamelet parameters and equilibrium small-scale structure of strongly wrinkled amelet sheet that controls the flamelet area. We examined integral turbulent ame speed Ut and the local combustion rates across the flame ρW. It has been shown that at the same Ut, the possibility of accurate prediction of the ρW distribution is closely connected with the possibility to describe the counter-gradient transport phenomenon. Finally we generalize the premixed combustion model equation in terms of the progress variable to the general case of partially premixed combustion. These more general equations are in terms of PDF of a passive concentration and a conditional progress variable, the transport terms are controlled only by physical gradient diffusion, equations contain only the dissipation of the passive concentration. At equilibrium products (fast chemistry) the coupling between chemistry and turbulence is described similar to the premixed case by a model source term. All coupling effects contains only in the equation in the terms of the conditional progress variable and enter in the source term through the physical model

Development of the TFC turbulent premixed combustion model: the combustion rates and the counter-gradient transport phenomenon

We analyze to “bottlenecks” of turbulent premixed combustion modeling at developed turbulence corresponding to modern lean-premixed large-scale industrial gas-turbine combusters when instantaneous combustion (heat release) takes place in thin strongly wrinkled surface (flamelet sheets)

An optimization problem of combustion in open flow

Description of a method for optimization of external combustion in linear formulation. This method can be used for different optimization problems related to combustion

On the limits of industrial premixed combustion simulation

This work analyses the simulation potential of two premixed turbulent combustion models based on different combustion mechanism concepts: the Eddy Dissipation Concept based on the volume combustion mechanism, and the Turbulent Flame-speed Closure based on the thickened-wrinkled amelets combustion mechanism. Ability of simulating numerically a standard experimental test case (premixed methane-air combustion in a plane channel at high flow velocity) and the influence of flow parameters variation on the combustion process have been tested. The paper shows that the flamelets model describes the standard experimental data more accurately. Furthermore, comparisons of the two models results obtained varying combustion flow parameters show the presence of quantitatively, and in one case even qualitatively different trends. These results are explained, and potentialities and limits of these models are discussed from an industrial premixed burner applications standpoint

Modelling turbulent premixed combustion in the intermediate steady propagation regime

Numerical simulation and comparison with standard experimental data of turbulent premixed combustion occurring at large Reynolds and moderately large Damkohler numbers (a situation which is typical in industrial burners) have been presented. The simulation has been performed in the framework of the Turbulent Flame-speed Closure (TFC) combustion model, developed in [1]-[4], which makes use of a theoretical expression for the turbulent combustion velocity for the closure of the progress variable transport equation. This model is based on the concept of Intermediate Steady Propagatioin (ISP) regime of combustion in real combustors, i.e. when the turbulent flame propagates with equilibrium turbulent flame speed but has flame brush thickness growing according to the turbulent dispersion law. These ISP flames precede usually analysed 1-D stationary flames and from the theoretical point of view they are in fact intermediate asymptotic of the combustion process between the period of formation of developed turbulent flames and 1-D stationary flames. Numerical results of turbulent premixed combustion in a two dimensional planar channel at parameters that correspond to real industrial combustors have been compared with corresponding standard experimental data on a high speed turbulent premixed flame [9]. Finally, it has been explained in the framework of the TFC combustion model that "countergradient diffusion", i.e. the necessity to use a negative effective diffusion coeficient to describe experimental heat and progress variable fluxes inside the flame, is an inherent feature of turbulent premixed flames and is connected with direct dependence of the second order velocity-scalars correlation on combustion. It has been shown that the existence of the countergradient diffusion phenomenon is not in contradiction with the actual increasing of the flame brush width

Gradient, counter-gradient transport and their transition in turbulent premixed flames

We theoretically and numerically analyze the phenomena of counter-gradient transport in open premixed turbulent flames. The focus is on the transition from counter-gradient to gradient transport obtained when reducing the turbulence intensity/laminar flame speed ratio, a phenomenon recently found in open laboratory flames experiments by Frank at el. The analysis is based on the TFC combustion model for the simulation of turbulent premixed flames at strong turbulence (u`>>sι). In this case earlier work suggests that turbulent premixed flames have increasing flame brush with controlled in the model only by turbulence and independent from the counter-gradient transport phenomenon which has gasdynamics nature, and a turbulent flame speed which quickly adapts to a local equilibrium value, i. e. Intermediate Steady Propagation (ISP) flames. According to the present analysis transport in turbulent premixed flames is in fact composed by two contributions: real physical gradient turbulent diffusion, which is responsible for the growth of flame brush thickness, and counter-gradient pressure-driven convective transport related to the differential acceleration of burnt and unburnt gases subject to the average pressure variation across the turbulent flame. The novel gas dynamics model for the pressure-driven transport which is developed here, shows that in open turbulent premixed flames the overall transport may be of gradient or counter-gradient nature according to which of these contributions is dominant and that along the flame a transformation from gradient to counter-gradient transport takes place. Reasonable agreement with the mentioned laboratory experimental data, strongly support the validity of the present modeling ideas. Finally, the model predicts existence of this phenomenon also in large-scale industrial burners at much higher Reynolds number

Numerical simulation of premixed combustion flows: a comparative study

In this work four different commercial and research CFD codes have been compared for the simulation of two combustion test cases. The aim was to get an overview of the capabilities of these different tools to simulate combustion flows in premixed regimes. Codes tested were Fluent, CFX, StarCD and Tanit. Three combustion models have been applied, namely the Eddy Break Up, the Eddy Dissipation Model and the Turbulent Flame Closure, the turbulence model used being the standard k-epsilon. Numerical results have been found to fairly fit experiments and helped to show some drawbacks of combustion models. In its theoretically correct range of applicability the TFC model has been found to give the better agreement with experiments

Combustion model for industrial numerical simulations

An original model for numerical simulation of turbulent premixed and partially premixed combustion at large Re and Da numbers is described. A quantitative description of the coupling between turbulence and chemistry by the flamelet mechanism is proposed, based on the generalized Kolmogorov concept of small scale equilibrium structures in developed turbulence. A model equation for premixed combustion is described in the terms of a reaction progress variable. This model has been implemented in the commercial code FLUENT5, and is validated against the experients by V. Karpov (spherical flames in a well stirred reactor) and P.Moreau (high velocity combustion in a channel). Partially premixed combustion is modeled by transport equations for the PDF of passive concentration and the conditional progress variable. Results of numerical simulations with turbulence-chemistry coupling by equilibrium and laminar flamelet chemistry are compared with experimental data by Barlow and Frank