CONTENTS 55
Figure 2.10: Grid used to obtain ame dimensions.
the calculated displacement.
Examples of measurements for the mean and root mean square RMS axial component of velocity are reported in Fig. 2.9 in steady cold (left) and hot (right) conditions. These measurements are conducted in the central axial plane. One can clearly observe the recirculation zone with negative velocities in the central region downstream the blu-body, typical of swirling ows. This region is larger and longer in the right of Fig.2.9for reactive conditions. One can also identify the jets of high velocities at the sides of the central recirculation zones and observe that the radial expansion of the jet increases for reactive conditions. The RMS uctuations feature high values in the shear layers of the ow, as reported also in Fig.2.5 showing the LDV measurements.
56 Chapter 2 - Diagnostics
Figure 2.11: OH* chemiluminescence for SW3, Do = 20 mm, C = 10 mm, Ub = 5.44 m/s, φ = 0.82. Top row: without acoustic forcing. Bottom row: f = 185 Hz, u0/¯u= 0.72 RMS. On the right an Abel deconvolution is applied to the line of sight integrated image shown on the left.
The integration time needs to be reduced for phase-conditioned measurements in pulsed conditions with respect to the acoustic forcing signal. In these cases, an exposure time not exceeding T /120was always selected, where T = 1/f is the period of the harmonic forcing signal at the frequency f. In both cases, a hundred snapshot are averaged to obtain the nal result.
The chemiluminescence signal shown in the left of Fig. 2.11is integrated in the line of sight. Assuming that the ame is axisymmetric in average, an Abel de-convolution can be applied to the chemiluminescence images to get an informa-tion on the OH∗ light distribution in an axial slice of the ame in the symmetry axis (Poularikas, 2010). This is useful during images post-processing, for in-stance it allows to better determine the angle of the reaction layer at the base of the ame. An home-made Matlab routine is used to compute Abel transforms.
Results are shown in Fig. 2.11-right. The high level of noise along the central axis is due to the mathematical formalism of the Abel transform that yields a singularity along the symmetry axis (Poularikas, 2010). Figure 2.12 shows 6 phase averaged pictures covering a full cycle of oscillation. The phase angle indicated on each picture in Fig. 2.12is referred to the velocity signal recorded by the hot wire. The phase average imaging procedure is performed as follows.
CONTENTS 57 When the ame is submitted to harmonic acoustic forcing, it oscillates at the forcing frequency. The harmonic forcing signal provided by the loudspeaker, is also used to trigger the ICCD camera. Each image in Fig.2.12 is obtained by adding a constant time oset to the triggering signal. By recording simultane-ously the velocity signal measured by the hot wire, each image is related to an instant in the cycle, as shown at the bottom in Fig.2.12.
Figure 2.12: Abel deconvoluted OH* chemiluminescence for SW3, Do = 20 mm, C= 10 mm,Ub = 5.44 m/s,φ= 0.82. The ame is forced with a harmonic signal at f = 185Hz andu0/¯u= 0.72RMS. The phase angle indicated on the gures is referred to the velocity signal recorded by the hot wire as shown in the bottom gure.
Chapter 3
Numerical setup
This chapter is dedicated to the description of the numerical setup used throughout this work for the comparison between LES and experimental data. The code selected for the numerical simulations is briey de-scribed. Simulations are carried out for one selected geometry of the injector, which is described in the second section of the chapter; to-gether with details on the mesh and the boundary conditions applied.
A comparison between numerical simulations and measurements for the ow in absence of acoustic forcing is presented in the last section of the chapter.
3.1 Large Eddy Simulations with AVBP
Large Eddy Simulations (LES) are dedicated to solve the turbulent compressible Navier-Stokes equations and are an intermediate numerical concept between Di-rect Numerical Simulations (DNS) and the Reynolds Averaged Navier-Stokes (RANS) methodology (Poinsot and Veynante, 2005).
A DNS solves the full instantaneous Navier-Stokes equations explicitly, without any modeling. RANS simulations compute only averaged values, without solv-ing turbulent quantities. LES is an intermediate concept, since it resolves the large turbulent scales and models the small scales by applying a lter (Poinsot and Veynante, 2005). RANS, LES and DNS properties are summarized in terms of energy spectrum in Fig. 3.1. All spatial frequencies in the spectrum are resolved in direct numerical simulations. Only the largest ones, up to a cut-o wave number kc, are computed in LES while the others are modeled.
Turbulence is fully modeled in RANS.
In this thesis, LES are carried out with AVBP, a parallel CFD code devel-oped by Cerfacs in partnership with IFP Energies Nouvelles (Schönfeld and Rudgyard, 1999; Moureau et al., 2005; Sengissen et al., 2007). AVBP solves the three-dimensional laminar and turbulent compressible non-reactive and
re-60 Chapter 3 - Numerical setup
E(k)
kc k
Computed in LES Modeled in LES Modeled in RANS
Computed in DNS
Figure 3.1: Turbulence energy spectrum plotted as a function of wave numbers (pro-portional to the inverse of the length scales). RANS, LES and DNS are summarized in terms of spatial frequency range. kc is the cut-o wave number used in LES (log-log diagram). Reproduced fromPoinsot and Veynante, 2005.
active Navier-Stokes equations, handling unstructured grids of any cell type.
The code is not described here, as no developments have been made in this code during this work. The interested reader is referred to the cited references.
Calculations are performed only for a non-reactive case and the AVBP code was chosen for its ability to retrieve the largest unsteady ow structures and the propagation of acoustic waves, two mandatory characteristics for the study that we wish to conduct.