Confirmation of paper submission - flame-structure-2014.comflame-structure-2014.com/wp-content/uploads/Seung-Jin-Baik.pdf · Berlin Institute of TechnologyChair of Fluid Dynamics,

www.flame-structure-2014.com Berlin Institute of Technology (TU Berlin) Prof. Dr. Frank Behrendt Fakultät III: Prozesswissenschaften, Institut für Energietechnik Chair Energy Process Engineering and Conversion Technologies for Renewable Energies (EVUR) Fasanenstr. 89 10623 Berlin Contact [email protected] [email protected]

Berlin Institute of Technology • Fasanenstr. 89 • 10623 Berlin

Ruhr-Universität Bochum Seung Jin Baik Universitätsstr. 150 44801 Bochum 27. Mai 14

Confirmation of paper submission Name: Seung Jin Baik Email: [email protected] Co-author: Prof. Dr.-Ing. B. Rogg 2nd co-author: - 3rd co-author: - Title of Paper: Detailed Flame-Structure Predictions with a

Fully Stochastic Particle Method Program: Turbulent flames Name of Institute: Ruhr-Universität Bochum


Detailed Flame-Structure Predictions with a Fully Stochastic Particle Method

S.J. Baik and B. Rogg

Chair of Fluid Dynamics, Faculty of Mechanical Engineering, Ruhr-University Bochum, Germany

Abstract

A fully stochastic approach to the formulation and solution of Lagrangian-type particle equations governing turbulent flame structure is developed. The approach is exemplarily applied to two types of gaseous flames. It is shown that flame structures are very well resolved if detailed chemistry is taken into account. In addition, as part of the numerical solution, the spatially and temporally resolved velocity-temperature-concentrations joint probability density function is obtained.

Introduction

Traditional approaches to the numerical simulation of turbulent reactive flows are based on Reynolds-averaged, Eulerian equations for a gaseous phase combined – depending on the spatial complexity of a problem at hand – over-simplified to acceptably detailed chemistry models. Representatives of the latter category of acceptable chemistry models are, e.g., both flamelet models [1, 2] and models based on conditional moment closure [3, 4]. Stochastic methods, so-called PDF-methods, have mainly been used to model chemistry by Monte-Carlo methods resulting in in a so-called hybrid approach [5, 6, 7], in which the momentum equations are solved using a RANS formulation.

In the present paper, we combine the advantage of a full Monte-Carlo stochastic description for chemistry, which does not require modelling [5], with the advantage of a full Monte-Carlo stochastic description of the flow field. This essentially reduces the task of solving a turbulent combustion problem to solving only a single PDF-transport equation. Not only does such a consequent approach give more flexibility to the modelling of turbulence for complex combustion problems, it also represents a useful prerequisite for tackling two-phase problems where the gas-liquid or gas-solid interaction is treated exclusively stochastically. In the present paper, however, we concentrate exemplarily on two pure-gasphase combustion problems, viz., a 2D turbulent counterflow flame and a 2D turbulent jet flame, both simulated with detailed chemistry.


Approach

Referring, on the l.h.s. of (1), to the term involving the gradient of mean pressure, it is noteworthy that we use a SIMPLE-like numerical algorithm for pressure correction in which we split pressure correction into a deterministic numerical error and a stochastic fluctuation around the mean. At each time step, only the deterministic error can be made arbitrarily small by a suitable number of iterations.

The overall computational domain is split into a certain number of non-overlapping sub- domains and hence is made accessible to parallelization. For the parallel solution of the pressure-correction equation the Schur-complement method is used. The discretization results in an unstructured mesh, in which suitable finite volumes are defined. Typical numbers used in the computations are 8 for the number of processors, 160000 for the number of Monte-Carlo particles, and 8500 for the number of grid points. For a specific computation typically 3000 time steps are taken until, in the statistical mean, a steady state solution is obtained.

Results and Discussion

Exemplarily we here present results for a counterflow ozone-decomposition flame and a jet diffusion flame, respectively. Ozone decomposition proceeds via only three reversible chemical reactions – see, e.g. [10, 11, 12] – and hence provides the ideal testing ground for any computer code employing detailed chemistry. Figure 1 shows the counterflow geometry and two sample results obtained ��in it. Specifically, Fig. 1 (left) illustrates


Figure 1: Selected results for an ozone-decomposition flame in counterflow geometry.

the geometry in terms of stream lines. It is ��seen that the two opposed nozzles are ar- ��ranged vertically atop of each other, and ��that the typical stagnation-point flow re- ��sults. The simulations were done assum- ��ing a planar geometry. The ozone mass ��fraction in the nozzle-exit cross-sections ��was taken as 0.33, and the temperature ��there as 500 K. Neglecting gravity effects, ��a symmetrical configuration with respect ��to y = 0 was considered. Figure 1 (right) ��shows a surface plot of the O-atom mass ��fraction. As expected on physical grounds, ��it is seen that the flame, or flame struc- ��ture, is rather thin. Shown in Fig. 2 is the ��marginal PDF of the O-atoms mass frac- ��tion, YO. It is seen that in the vicinity of the position if either flame that PDF is smooth with a singe maximum offset towards larger values of YO. Off the two flame zones, the PDF shape is close to a delta function at YO = 0, as it is to be expected on physical grounds.

Figure 2: Marginal distributions of the density function for mass fraction of O-atoms.

Shown in Figs. 3 and 4 are selected results from the simulation of a hydrogen-air jet diffusion flame. The detailed mechanism [13] comprises 10 chemical species and 21 chemical reactions. Figure 3a shows, exemplarily, how the overall computational domain

Figure 3: Selected results for a hydrogen-air jet diffusion flame.

is composed of 8 sub-domains, each domain being represented by one processor. The mesh itself is unstructured – see Fig. 3b. The mesh is finest


where the flame structure is located and where the radi- cals reach their peak concentrations. Shown in the right half of Fig. 3 are surface plots of the OH-radical. Specifically. the left picture shows experimental data from [14], the right picture shows the computational result. The lift-off height can be estimated from these pictures.

Shown in Fig. 4 are the experimental [14] radial temperature profiles. Figure 4 (square- solid line and dashed line) is for z/D = 1 and Fig. 4 (triangle- solid line and solid line) for z/D = 14. It is seen that the agreement between experimental and computational results is quite reasonable.

Acknowledgement

This work has been funded by Deutsche Forschungsgemeinschaft (DFG) under grant no RO2249/3-1.

References

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Confirmation of paper submission - flame-structure-2014.comflame-structure-2014.com/wp-content/uploads/Seung-Jin-Baik.pdf · Berlin Institute of TechnologyChair of Fluid Dynamics,