**Principal Investigator:**

Christian Hasse

**Local Project ID:**

pr74li

**HPC Platform used:**

SuperMUC of LRZ

**Date published:**

**Introduction**

In today’s industrialized world, energy requirements have constantly increased over recent decades, and they will possibly still do so in the foreseeable future. Although the amount of renewable energies will have increased by more than 150% by the year 2050, according to the International Energy Outlook 2017, fossil fuels such as petroleum, coal and natural gas are still market-dominating. Therefore, the importance of combustion is obvious, and will possibly be unchallenged even after the year 2050. However, the conversion of chemical energy to thermal energy by combusting fossil fuels has adverse effects and novel concepts are required for future combustion devices. While admission procedures are often interminable for new devices and are still largely based on laboratory experiments, such developments could be achieved faster and at lower costs if accurate, robust, and truly predictive computational design tools were available. However, reacting flows are one of the most difficult flow scenarios, since many highly complex physical processes are involved which have to be coupled nonlinearly to accurately describe the behavior of the overall system. Furthermore, chemical reacting flows are multi-scale problems, meaning that a fully coupled description involves various time and length scales, which additionally stresses a numerical treatment.

A promising approach for the modeling of turbulent non-premixed combustion are flamelet models. They are based on the assumption that chemical reactions are fast and occur in thin confined layers around the reaction zone. If the characteristic length scale of these layers is smaller than that of the surrounding turbulent eddies, turbulence is unable to penetrate the reaction zone and the flame is assumed to be embedded in a quasi-laminar flow field. This view of turbulent flame structures allows the complex chemical structures of the flame to be decoupled from the flow dynamics. This decoupling of scales constitutes an important advantage of flamelet models compared to other combustion models, as it allows for a pre-tabulation of thermo-chemical states based on a small number of independent parameters.

One of these quantities and at the same time a central quantity in the modeling of non-premixed combustion is the mixture fractionwhich is used to determine the mixedness of the initially unmixed fuel and oxidizer streams.

However, depending on the physics, the choice of these parameters is not obvious and different flamelet modeling strategies have been proposed in the past, e.g. accounting for differential diffusion of the chemical species and curvature effects [1]. Furthermore, the decoupling of scales introduces an additional closure problem for the flamelet equations since effects of the surrounding flow field have to be considered in order to accurately describe the physics.

Parts of this SuperMUC project focused on the analysis of dissipation elements, a recent concept of Wang and Peters [2], which might promote novel insights into flamelet-based modeling strategies.

**Results and Methods**

Within this project all analyses were based on direct numerical simulations (DNS) which were conducted with the DNS code DINO [3]. The solver is designed for the simulation of low-Mach number reactive flows, where spatial derivatives in the governing equations are discretized with 6^{th} order finite differences. The temporal integration is done by a 3^{rd} order semi-implicit Runge-Kutta scheme. Based on the distributed memory architecture of SuperMUC parallelization of the solver is achieved by the message passing interface (MPI), where an excellent scalability up to 65536 cores is achieved, see Figure 1

A working copy of DINOcan be obtained on request by contacting the group of Prof. Thévenin at the Otto von Guericke University Magdeburg.

The setup used for the simulation is based on a temporally evolving jet configuration which was originally proposed by Hawkes et al. [4]. The simulations were carried out on an isotropic mesh with a grid spacing of 14 μm and required nearly 3 billion grid points. A single run consumed 2 MCPUh on 23904 cores and generated roughly 10 TB of raw data. To give an example of the turbulent nature of the jet, figure 2 shows iso-contours of the scalar dissipation rate,

normalized by, *X _{q}* , where

Based on the highly resolved DNS the mixture fraction field is decomposed into small subunits called “dissipation elements”.

The essence of the theory of Wang and Peters [4] is to trace gradient trajectories along the ascending and descending gradient until a local extremal point is reached. The ensemble of all trajectories that end at the same local extremal points form a dissipation element, eventually leading to a geometrical decomposition of the mixture fraction field. A schematic of this procedure is shown in figure 3 and a visual representation of two dissipation elements in three dimensional space is given in figure 4.

Based on this geometrical decomposition, a parametrization solely based on the endpoints was introduced [5]. Apart from this parametrization, a regime classification based on the stoichiometric mixture fraction is proposed which distinguishes between: (i) a fuel rich regime, (ii) a stoichiometric regime and (iii) a fuel lean regime. This classification in conjunction with the twopoint character of dissipation elements allows conclusions to be drawn about the connectivity of different regions of the jet, e.g. the connection between the reaction zone and the turbulent core. Based on these regimes, dissipation elements are classified according to the location of their endpoints and various statistics related to the endpoints are computed.

**On-going Research / Outlook**

The analysis of turbulent reactive flows by means of dissipation elements complements the on-the-fly analysis, conducted in an earlier SuperMUC project (pr83xa), by providing a statistical characterization of flamelet-related parameters. This statistical analysis in turn could be used to develop possible closure strategies for the extended flamelet equations [1] by providing further insights into the topology of the mixture fraction field.

**Research Team**

Felix Dietzsch^{1}, Wang Han^{1}, Christian Hasse^{1} (PI), Michael Gauding^{2}, Sebastian Popp^{1}, Arne Scholtissek^{1}

^{1} Institute for Simulation of reactive Thermo-Fluid Systems, TU Darmstadt (Germany)^{2} CORIA – CNRS UMR 6614, Saint Etienne du Rouvray (France)

**Project Partners**

Dominique Thévenin, ISUT, Otto von Guericke University, Magdeburg (Germany)

**References**

[1] Arne Scholtissek, Felix Dietzsch, Michael Gauding and Christian Hasse. 2017. Combust. Flame 175, 243-258.

[2] L. Wang and N. Peters. 2006. J. Fluid Mech. 554, 457–475.

[3] Abouelmagd Abdelsamie, Gordon Fru, Timo Oster, Felix Dietzsch, Gábor Janiga and Dominique Thevenin. 2016. Comput. Fluids 131, 123-141.

[4] Evatt R. Hawkes, Ramanan Sankaran, James C. Sutherland and Jacqueline H. Chen. 2007. Proc. Combust. Inst. 31, 1633-1640.

[5] Michael Gauding, Felix Dietzsch, Jens Henrik Goebbert, Dominique Thevenin, Abouelmagd

Abdelsamie and Christian Hasse. 2017. Phys. Fluids 29.

**Scientific Contact**

Prof. Dr. Christian Hasse

Technische Universität Darmstadt

Simulation of Reactive Thermo-Fluid Systems

Otto-Berndt-Str. 2, D-64287 Darmstadt (Germany)

e-mail: hasse [@] stfs.tu-darmstadt.de

**NOTE:** This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2018".

*LRZ project ID: pr74li*

*Date published: February 2020*