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Short title : LES, acoustics, experiments in gas turbines. AbstractThe turbulent flow within a complex swirled combustor is studied with compressible LES (Large Eddy Simulation), acoustic analysis and experiments for both cold and reacting flows. Detailed fields of axial, tangential and radial velocities (average and RMS) given by LES are compared to experimental values measured by LDV. The unsteady activity is identified using LES and acoustic tools for the whole geometry from inlet (far upstream of the swirler) to the atmosphere (far downstream of the chamber exhaust). Concerning comparisons between experiments and LES, this nose-to-tail procedure removes all ambiguities related to the effects of boundary conditions. Results for the cold flow show that the second acoustic mode at 360 Hz dominates in the plenum while a hydrodynamic mode at 540 Hz due to a Precessing Vortex Core (PVC) is found in the combustion chamber. With combustion, the PVC mode is damped and the main mode frequency dominating all unsteady activity is 500 Hz. Acoustic analysis shows that this mode is still the second acoustic mode observed in the cold flow: its frequency shifts from 360 Hz to 500 Hz when combustion is activated. More generally, these results illustrate the power of combined numerical tools (LES and acoustic analysis) to predict mean flow as well as instabilities in combustors.

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Fisher's least significant difference (LSD) procedure is a two-step testing procedure for pairwise comparisons of several treatment groups. In the first step of the procedure, a global test is performed for the null hypothesis that the expected means of all treatment groups under study are equal. If this global null hypothesis can be rejected at the pre-specified level of significance, then in the second step of the procedure, one is permitted in principle to perform all pairwise comparisons at the same level of significance (although in practice, not all of them may be of primary interest). Fisher's LSD procedure is known to preserve the experimentwise type I error rate at the nominal level of significance, if (and only if) the number of treatment groups is three. The procedure may therefore be applied to phase III clinical trials comparing two doses of an active treatment against placebo in the confirmatory sense (while in this case, no confirmatory comparison has to be performed between the two active treatment groups). The power properties of this approach are examined in the present paper. It is shown that the power of the first step global test--and therefore the power of the overall procedure--may be relevantly lower than the power of the pairwise comparison between the more-favourable active dose group and placebo. Achieving a certain overall power for this comparison with Fisher's LSD procedure--irrespective of the effect size at the less-favourable dose group--may require slightly larger treatment groups than sizing the study with respect to the simple Bonferroni alpha adjustment. Therefore if Fisher's LSD procedure is used to avoid an alpha adjustment for phase III clinical trials, the potential loss of power due to the first-step global test should be considered at the planning stage.

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