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EnglerBunteRing 1
76131 Karlsruhe
Building 40.13.II
Phone: +49(0)721 608 7078
Fax: +49(0)721 661501
Email: Sekretariat
... you will find on our event schedule page
I Numerical Method
The direct numerical simulation approach consists of solving the NavierStokes equations in their complete form, without any averaging or filtering accounted for by a model.
The code employed for this task is the code Parcomb, developed by Thévenin and coworkers [6].
Apart from the equations for continuity, momentum and energy, Ns equations are solved for the transport of chemical species, with Ns = 9 in the present cases.
Highorder discretization is used in order to reduce numerical dissipation. In space, this is a sixth order central finitedifference scheme along with a third order differencing at the boundaries. In time, a fourthorder RungeKutta scheme is employed. The NavierStokes characteristic boundary conditions [7, 8] are implemented taking into account detailed chemistry and thermodynamics.
Isotropic turbulence is generated in Fourier space with a von Kàrmàn energy spectrum with Pao correction [9].
In Fourier space, the definition of the kinetic energy E(k) is given by :
where k is the wave number, u' the rms value of velocity fluctuations, ε is the dissipation, while A and α are constants of the model (A = 1.5 and α = 1.5).
Furthermore, k_{e} = 1 / L_{e} where L_{e } is the peak energy wavelength, and k_{d} = 1 / L_{d} where L_{d} is the Kolmogorov wavelength.
After the initialization, no forcing of the turbulent flow field is applied and the fluctuations are allowed to decay. The propagation of the flame is relatively fast, however, so that this decay is not too strong. Examples of calculations with Parcomb and postprocessing intended towards turbulent combustion modeling are available in [10, 11, 12].
II Experiments of Zarzalis in the framework of SFB 606
The experimental setup of Weiss and Zarzalis, investigated in Projekt A9 of SFB 606, is considered as a basis for the present simulations.These experiments investigate isochoric premixed spherical flames, evolving in a cubic box (Fig. 1).The burning velocity and the Markstein number are determined. The Markstein number Ma is a suitable parameter to quantify the influence of flame strech and has to be included in the modeling of turbulent flame velocity [3, 4, 5].

III Results
III.1 Parallelization : PVM versus MPI
Parcomb is a fully parallel program with dynamic load balancing capabilities. The message passing library originally used in Parcomb is PVM. All the validations performed by the authors was
also using PVM. Thus, it was natural to continue using the program with PVM. PVM, however, is now superseeded by MPI and no more maintained on current installations. Hence, in a first phase of the project it was converted to MPI and fully tested and validated on the XC using HPMPI.
An attempt to use MPI instead of PVM in Parcomb had been made previously during the development, using wrappers around the PVM calls. However, this revision was not validated and could not be compiled with the present installation. Most of the parallelizaiton calls were therefore rewritten. Tests with MPICH and HPMPI served to avoid lacks of portability. The communication of the number of processors in each direction to all processes may serve as an example. The sets of original calls
PVMFINITSEND
PVMFPACK
PVMFMCAST
coupled with the receiving instructions:
PVMFRECV
PVMFUNPACK
were replaced by a single MPI_BCAST instruction.
Since these blocking instructions are in the initialization part, they do not reduce the overall performance of the code. The code was then thoroughly tested against the serial version, both in 1D and 2D configurations and using different numbers of processors.
Efficiency of runs
Benchmarking of the code was performed with a 2D reacting configuration. The test case used corresponds to the 2D ignition of a turbulent premixed hydrogenair flame. Timings are presented for a scaled problem, which means that all nodes possess the same number of grid points (201 x 201 points and a 7mm x 7mm domain). When increasing the number of processors, the size of the domain and the total number of grid points are increasded proportionally. The simplest definition of the parallel efficiency is used here, i.e. E(N) = t_{CPU}(1) / t_{CPU} (N), where N is the number of processors. Since dual nodes were employed only even numbers where chosen.
Efficiency results are given in Figure 2 and corresponding CPU times are shown in Figure 3. These data show that the parallelization performs very well, with generally no decrease in the performance when using more processors. Of course, these results should not be used as a direct measurement of the performance of the machine,
but they can give some insights about the practical achievement of Parcomb on the XC.

III.2 Typical flow configurations
The present work is concerned with 2D configurations of premixed flames. The main parameters of the simulations are :
Thermochemistry :
H_{2 }Air mechanism, 9 species / 37 steps (Warnatz scheme) or 38 steps (Miller scheme)
CH_{4 }Air mechanism, 50 species / 300 steps
Initial conditions :
One initial condition consists of a 1D steady state solution that is extended to a 2D laminar plane flame. Spherical flame in 2D can also be computed.
The turbulent flow field is obtained from a 2D turbulent kinetic energy spectrum. Velocity and concentration field are then superimposed.
Figure 4 – Illustrations of available runs, planar and spherical flame.
Domain and grid :
We consider a square computational domain, discretized with an equispaced grid in both directions.
Boundary conditions :
Periodic boundary conditions are used along the planar flame, while nonreflecting boundary conditions are used in the direction normal to the flame on inflow and outflow boundaries. The calculations are initialized with reactants on one side of the computational domain and products on the other; they are separated by a laminar premixed flame.
III.3 Influence of Soret effect – Thermodiffusion
Thermal diffusion also known as Soret effect represents the diffusion of species due to temperature gradients and is often neglected in the simulations
To investigate the validity of this assumption for the H2 flame considered, two simulations were performed,
one with and the other without accounting for the Soret effect, with the following parameters.
H2 /Air 2D premixed planar flame,
Ф = 0.33
Kinetic scheme of Miller.
Mesh : 600 x 600 pts
Domain size 4cm x 4cm
Turbulence field superimposed :
rms value of velocity fluctuations :U´= 1.59 m/s,
turbulent length scale L = 3.10^{3} m.

These results are in good agreements with the literature that indicates that Soret effect inhibits the diffusion of active chemical radicals such as H_{2}O and OH around the flame front, thus making flame propagation slower.
Hence, the Soret effect will be taken into account in all our simulations.
III.4 Turbulence forcing
As calculations have to be compared to experimental results, the same conditions have to be used in both cases. In Parcomb,a turbulence spectrum is generated in Fourier space with a random phase.
That implies a flow in real space without the correct physical structures. As described in the literature, physical structures appear with time, after one or two eddy turnover times. On the other hand, after one or two eddy turnover times, a decrease of the energy spectrum is generated due to dissipation (Fig. 7), the energy spectrum has changed and we do not obtain the turbulence field used during
experiments.
Figure 7 – Evolution of energy spectrum shape in Fourier space
with time
What we did to avoid this problem :
With Parcomb, we create a reference spectrum. This spectrum has the desired amplitude u’, the rms value of turbulent fluctuations, and the desired length scale L, The phase, however is random.
The idea is to continue the run in order to have physically realistic phases but to maintain the energy level This is done by comparing the energy level during the run with the reference energy spectrum. The Fourier coefficients of the solution are then multiplied after each time step such that the initial spectrum is maintained
but allowing the phase to adjust to physically realistic structures. By inverse Fourier transform,the velocity field in physical space is obtained to continue with the next time step This is visualized in Fig. 8..
Figure 8 – Principe of turbulence forcing
At the end, we obtain turbulent fields with u’ and L related to experiments and that possess physical structures.
III.5 Modification of inflow conditions
As we want to reproduce the experimental conditions, modification of inflow conditions were needed. In fact, during all the experiments, the turbulence, created by the eight fans is maintained.
That is to say, we can not consider this turbulence as a decaying turbulence. We choose the following solution to avoid this problem.
During a run, at each time step we modify the inflow conditions (Fig. 9)
Figure 9 – Injection of turbulence at the inlet
From a frozen periodic field of turbulence (velocities fluctuations) previously determined as described above, slices are extracted and fed into the computational domain as inflow conditions.
Example of result :
H2  Air premixed flame, F = 0.33
u’ = 1.6 m/s, L = 3.9 mm, Mesh : 4cm x 4cm, 600 x 600 pts
Velocity fluctuations profile at the inlet + superimposed fluctuations field at the run beginning – Re = 305 u’/ Sl = 12.3
Figure 10  Heat Release field Figure 11 – Vorticity field
IV Cooperations with other projects
Within the framework of the SFB 606, intern cooperations have been realized and are in progress.
A9: The experimental project A9 (Zarzalis, Weiß) provides data on the experimental setup and
results of the measurements. these are discussed extensively and routines for postprocessing are exchanged.
A5: In a cooperation with A5 (Class, Bruzzese) the present project provides the DNS result in order to compute modelling terms in the hierarchical model developed in this project
A6: Together with A6 (Fröhlich, Wang) comparison of DNS data is undertaken.
Example : in A5 Project, the flame is considerated as a gasdynamic discontinuity
Figure 12 – Principe of Class’s model
The flamefront position is determined when the integrals are equal to zero
Compared case : Lean H_{2} / Air, F = 0.5 u´= 1.68 m/s , L= 9.7 10^{4} m, Re = 101
u´/S_{L}=2.5 L / d_{L} = 2.5 Mesh : 1cm x 1cm – 500 x 500 points
Figure 13 – Heat release profile Figure 14 – Representation of the 2 flamefront definitions
With the Class’s model, a small window (in red) is needed to build the flamefront (small contour in black in Fig. 14)
whereas we use an iso contour of YO_{2 }
The value of this iso contour is determined when the laminar heat release is maximal
Correlations flame speed / stretch can be computed and compared (red : Class’s model, blue : our results)
Figure 15 – Total stretch Figure 16 – Flame speed
The shape of the curves are similar even if the values are different, due to the two different definitions of the flamefront
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