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I         Numerical Method

 

 

The direct numerical simulation approach consists of solving the Navier-Stokes 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 co-workers [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.

High-order discretization is used in order to reduce numerical dissipation. In space, this is a sixth order central finite-difference scheme along with a third order differencing at the boundaries. In time, a fourth-order Runge-Kutta scheme is employed. The Navier-Stokes 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, ke = 1 / Le where Le  is the peak energy wavelength, and kd = 1 / Ld where Ld  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].

 

 

                                                     Figure 1 – Weiss / Zarzalis experimental setup

 
 

 

 

 

 

 


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 HP-MPI.

 

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 HP-MPI 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 1-D and 2-D configurations and using different numbers of processors.

 

Efficiency of runs

 

Benchmarking of the code was performed with a 2-D reacting configuration. The test case used corresponds to the 2-D ignition of a turbulent premixed hydrogen-air 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) = tCPU(1) / tCPU (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.

 

 

 

                                            

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2 – Evolution of CPU Time versus processors              Figure 3 – Evolution of Efficiency versus processors number                                                                                         number

 

 
 

 

 

 

 


III.2     Typical flow configurations

 

 

The present work is concerned with 2-D configurations of premixed flames. The main parameters of the simulations are :

 

Thermochemistry :

 

H2 -Air mechanism, 9 species / 37 steps (Warnatz scheme) or 38 steps (Miller scheme)

CH4 -Air mechanism, 50 species / 300 steps

 

 

Initial conditions :

 

One initial condition consists of a 1-D steady state solution that is extended to a 2-D laminar plane flame. Spherical flame in 2-D can also be computed.

The turbulent flow field is obtained from a 2-D 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 non-reflecting 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.

 

 

 

                                                                                                                    

 

                                                          

 

 

 

 

 

 

 

 

 

 

 

 

    Figure 5 – Heat release field.Thermal diffusion not taken          Figure 6 – Heat release field.Thermal diffusion taken into

    into account in the simulation                                                        account in the simulation

 

 
 

 

 

 

 


These results are in good agreements with the literature that indicates that Soret effect inhibits the diffusion of active chemical radicals such as H2O 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      Co-operations 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 post-processing 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 H2 / Air, F = 0.5  u´= 1.68 m/s , L= 9.7 10-4 m,  Re = 101

u´/SL=2.5    L / dL = 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 YO2  

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

 

 

 

Bibliography

 

[1]       R.G. Abdel-Gayed and D. Bradley. Lewis number effects on turbulent burning velocity. Proceedings of the Combustion Institute, 20:505-512,1984.

 

[2]      H.-P Schmid, P. Habisreuther, and W.Leukel. A model for calculating heat release in premix turbulent flames. Combustion and Flame,13:79-91,1998.

 

[3]      D. Bradley P.-H. Gaskel, and X.-J. Gu. Burning velocities, Markstein lengths and flame quenching for spherical methane-air flames. Combustion and

Flame,104:176-198,1996.

 

[4]      T. Brutsher, N. Zarzalis, and H.Bockhorn. An experimentally based approach for the space-averaged burning velocity used for modelling premixed turbulent combustion. Proceedings of the Combustion Institute,29:1825-1832,2002.

 

[5]       D.Bradley P.-H Gaskel X-JGu, and A.Sedaghat. Premixed flamelet modelling : factors influencing the turbulent heat release rate source and the turbulent burning velocity. Combustion and Flame,143:227-245,2005.

 

[6]       D.Thévenin, F Behrendt, U.Maas, B.Przywara,and J.Warnatz. Development of a parallel direct simulation code to investigate reactive flows. Computers and Fluids,25:485-496,1996.

 

[7]       T.Poinsot and S. Lele. Boundary conditions for direct simulations of compressible viscous flows. Journal of Computational Physics,101:104-129,1992.

 

[8]       M.Baum T Poinsot, and D.Thévenin .Accurate boundary conditions for multicomponent reactive flows. Journal of Computational Physics,116:247-261,1994.

 

[9]       J.O Hinze.Turbulence. MGraw-Hill,2nd editon,1975.

 

[10]     De Charentenay, D.Thévenin ,and B.Zamuner. Comparison of direct numerical simulations of turbulent flames using compressible or low-Mach number formulations. International Journal For Numerical Methods In Fluids,39:497-551,2002.

 

[11]     R. Hilbert and D. Thévenin. Influence of differential diffusion on maximum flame temperature in turbulent non-premixed hydrogen / air flames. Combustion and flames, 138:175-187, 2004.

 

[12]     D. Thévenin, P.-H. Renard, J.-C. Rolon, and S. Candel. Extinction processes during a non-premixed flame / vortex interaction. Proceedings of the Combustion Institute, 27:719-726,1998.

 

[13]     J.H. Chen and H.G. Im. Correlation of flame speed with stretch in turbulent premixed methane / air flames. Proceedings of the Combustion Institute,27:819-826,1998.

 

[14]     J.H. Chen and H.G. Im. Stretch effects on the burning velocity of turbulent premixed hydrogen / air flames. Proceedings of the Combustion Institute,28:211-218,2000.