Coupling of simplified chemistry with mixing processes in PDF simulations of turbulent flames

doi:10.1016/j.proci.2018.05.126

Proceedings of the Combustion Institute

Volume 37, Issue 2, 2019, Pages 2183-2190

https://doi.org/10.1016/j.proci.2018.05.126 Get rights and content

Abstract

Numerical simulation of turbulent reacting flow is still a challenging task. For the efficient computational simulation and applicability for technical systems, simplifications for both chemistry and turbulence are needed. However, both simplifications are typically treated separately, without considering the coupling between them. In manifold based simplified chemical models, it is assumed that the full thermokinetic state is restricted to slow manifolds, while the turbulent mixing processes pull the states off the manifold. We derive a strategy based on the Global Quasi-linearization (GQL) that allows an efficient coupling of manifold based reduction methods with mixing models in transported Probability Density Function (PDF) models for turbulent reacting flows.

The GQL approach identifies a suitable choice of the reaction progress variables which allows a direct application of the mixing models on the reduced variables without having to perform mixing in the full state space and back relaxation to the manifold. To test the validity of the reduced variable, it has been applied for PDF-modeling of a turbulent flame. For the turbulent flame with strong turbulence-reaction interaction, the local-extinction and re-ignition can be captured very well.

Introduction

The numerical simulation of turbulent reacting flow is still a challenging problem. One of the challenges is the modeling of the averaged chemical source term [1], [2]. The transport equation for the joint probability density function (PDF) method [3] is one solution to this problem. In the transported-PDF model the chemical source term appears in a closed form and can be solved exactly [4]. To increase the efficiency of computational calculation Monte-Carlo particle method is used to solve the transported-PDF equation [4], [5]. However, in the transported-PDF equation the effect of molecular transport must be modeled and, therefore, a mixing model is needed [3], [4].

Another problem is the simulation based on detailed chemistry, because it always causes an enormous computational effort. Thus, a simplified chemistry is desired and can be used in the Monte-Carlo particle method. One group of simplification methods is manifold based method, assuming that the thermokinetic states at any time and at any point in the flow are restricted on an attracting low-dimensional slow manifold [6]. However, the physical transport such as molecular transport can cause system states moving off this slow manifold. In this case, a projection back onto the slow manifold is needed [6], [7], which couples the processes between mixing and manifold based simplified chemistry.

One simple way to deal with this projection process is to find out the reduced variables so that during the fast relaxation process (back onto the slow manifold) the chosen reduced variables have only small marginal changes [7]. In this case, the choice of reduced variables is compatible with fast relaxation. However, such reduced variables are difficult to find. In practical applications, typically a linear combination is used [8], although finding out such combination with appropriate weights of each element to obtain a suitable linear combination is not a trivial task. In the present work, we use the Global Quasi-Linearization (GQL) approach [9], [10] to find out an adequate reduced variable sufficiently.

In the current study, the GQL method is applied to find a suitable reduced variable for combustion in the CH₄ single bond O₂N₂ system, which can be further used for the application of manifold based simplified chemistry in the PDF calculation. Then the simplified chemistry is parametrized by the found reduced variable, which is applied in the simulation of a turbulent jet-piloted flame: Sandia Flame E [11]. In the simulation of this turbulent flame, the EMST [12] is selected as mixing model in the PDF-method and Reaction–Diffusion-Manifolds (REDIM) [13] are used for simplified chemistry. The results show that based on GQL approach, the found reduced variable can indeed describe better the coupling between mixing process and manifold based simplified chemistry.

Section snippets

Coupling of mixing with simplified chemistry

In a general reacting flow, the thermokinetic state ψ can be given as $ψ = {(h, p, w_{1} / M_{1}, w_{2} / M_{2}, \dots, w_{n_{s}} / M_{n_{s}})}^{T}$ , where h is the enthalpy, p the pressure, n_s the number of species and w_i and M_i the mass fraction and the molar mass of species i. For simplicity, the specific mole number is introduced as $ϕ_{i} = w_{i} / M_{i}$ . Therefore, the actual thermokinetic space has a dimension $n = n_{s} + 2$ . In the application of manifold based simplified chemistry, the original thermokinetic states ψ are restricted on a n_r-dimensional

Choice of a suitable parametrization for the CH₄O₂N₂ reaction system

In principle, there are many different ways to parametrize reduced schemes, and from a mathematical (or numerical) point of view a non-linear parametrization has several advantages such as a local parametrization or a unique mapping etc. (see e.g., [23]). For practical applications, however, a constant parametrization has the advantage of being simple to implement and interpret the results. In this case the θ can be recovered via $θ = C \cdot ψ$ , where C is a constant (n_r by n)-dimensional

Hybrid finite-volume/Transported-PDF method for turbulent reacting flow

In the current work a hybrid finite-volume/Transported-PDF method is used (details can be found in [26]). This hybrid method consists of two parts: one is the finite-volume solver (FV part) providing the mean fields of hydro-dynamic quantities such as velocities; the other is the transported-PDF equation providing the velocity fluctuation and thermos-kinetic state of the flow such as temperatures. More details about coupling of RANS and transported-PDF can be found in [26].

In the PDF model, a

Simplified chemistry: Reaction–Diffusion Manifolds (REDIM)

Usually reaction mechanism always consists of a large number of chemical species and reaction steps, which is difficult to solve a complete solution of the governing conservation equations including detailed chemistry [24]. In this work, the simplified chemistry, Reaction–Diffusion Manifolds (REDIM) [13], is applied to reduce both the dimensionality and stiffness of the partial differential equation (PDE) systems to be integrated in the numerical simulation. The REDIM technique decouples the

Results and discussion for the Sandia Flame

To study the influence of parametrization strategy in the coupling of mixing process and simplified chemistry for a realistic case, one of the non-premixed piloted CH₄/Air jet flames investigated in [11], Flame E, is considered. Due to its relative high Reynold number (33,600), a moderate degree of local extinction and re-ignition can be observed and the parametrization (choice of reduced variable θ) can largely effect the accurate prediction of extinction and re-ignition phenomenon.

For the

Conclusions

In this work, we investigated the coupling of turbulent mixing processes with simplified chemistry. By using the Global Quasi-Linearization (GQL) method, we find out a suitable parametrization matrix based on the slow invariant subspaces. For practical application, this parametrization matrix is further simplified without loss of accuracy. This parametrization is tested for a homogeneous reacting system, and then the found reduced variable is applied in the simulation of turbulent flame. It

Acknowledgments

Financial support of this work by the German Research Foundation within the framework of the DFG research unit SFB TR150 is gratefully acknowledged.

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The Monte Carlo method is the conventional way to generate the PDF over n stochastic samples and the transport equation is often solved using a Lagrangian stochastic particle method for RANS [2,3]. The method can be also coupled with reduced chemistry models, such as the Reaction Diffusion Manifold (REDIM) [4], or with the In-Situ Adaptive Tabulation algorithm (ISAT) [5], where an unstructured table is built directly at run-time for the accessed composition space via direct chemistry integration. The computational cost required by Lagrangian particle methods applied to LES could be significantly reduced by using the Multiple Mapping Conditioning (MMC) method in its ‘sparse’ formulation [6].
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Coupling of simplified chemistry with mixing processes in PDF simulations of turbulent flames

Abstract

Introduction

Section snippets

Coupling of mixing with simplified chemistry

Choice of a suitable parametrization for the CH4O2N2 reaction system

Hybrid finite-volume/Transported-PDF method for turbulent reacting flow

Simplified chemistry: Reaction–Diffusion Manifolds (REDIM)

Results and discussion for the Sandia Flame

Conclusions

Acknowledgments

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Prog. Energy Combust. Sci.

Symp. (Int.) Combust.

Combust. Flame

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Combust. Flame

Symp. (Int.) Combust.

Chem. Eng. Sci.

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Proc. Combust. Inst.

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Acta Astronautica

Proc. Combust. Inst.

Proc. Combust. Inst.

Choice of a suitable parametrization for the CH₄O₂N₂ reaction system