The thermoacoustic state of the test rig developed in this work has been ana-lyzed when the combustion exhaust length is modied and some components of the injector are replaced. Experiments have been conducted at xed equiv-alence ratioφ= 0.82and bulk ow velocity Ub = 5.44m/s.
It has rst been shown that the thermal state of the combustor strongly al-ters the thermoacoustic state of the system. This has been checked for one conguration of the injector. It is found that the sound power level (SPL) inside the combustion chamber strongly builds up in the rst minutes after ignition and then reaches a plateau at about t' 20 min. The instability fre-quency constantly increases in the rst minutes and then reaches a limit cycle fort≥20min. It is then necessary to wait for the system to reach its thermal-ization before one can conclude about its thermoacoustic state.
It has been shown that increasing the combustor exhaust length can lead to increasingly higher oscillation levels or lower oscillation levels depending on the distance between the swirler and injector outlet, if all other parameters are kept xed. This has been shown for two dierent values of the distanceδ between the swirler exit and the combustion chamber backplane. For a swirler mounted at a distance δ = 35 mm, we observed a reduction of the SPL inside the combustion chamber for increasing length of the combustor exhaust, while the opposite was observed for a distanceδ = 50 mm. It has also been shown that modifying the swirling vane does not necessarily help to control the oscillation level in the combustion chamber. This was checked for two dierent designs of the radial swirling vane. Despite the fact that the shape of the ame stabilized with these dierent swirling vanes in the absence of acoustic forcing diers, the SPL measured in the combustion chamber for the two congurations is close.
These two observations are discussed in more detail in chapter6with the help of FTF measurements.
Chapter 6
Eects of injector design and injection conditions on Flame Transfer Functions
The eects of dierent injector geometries and injection conditions on the ame transfer function are examined in this chapter. The objective here is to describe the shape taken by the FTF and assess the main pa-rameters altering the ame response. The next chapter is dedicated to the analysis of the mechanisms controlling this response. The chapter is organized in the following way. After a brief introduction, a typical ame describing function determined for a given injector conguration is illustrated. It is shown that the shape of this response features the same characteristics for all forcing levels. In the second part of the chapter, results are reported at a xed forcing level but for dierent ge-ometrical congurations. The eects of modications of the distance between the swirler exit and the combustion chamber backplane are con-sidered rst, followed by the eects of a change of the bulk ow velocity.
In the last part of the chapter, results obtained while changing the injec-tor exit diameter, the blu-body end piece diameter or the swirler design are considered.
6.1 Introduction
In fully premixed systems and in absence of mixture composition disturbances, the ame transfer function (FTF) between heat release rate uctuationsQ˙0and harmonic velocity disturbances u0 that produce them is dened as (Ducruix et al., 2003):
F(f) = Q˙0/Q˙
u0/u =G(f) exp(iϕ(f)) (6.1)
96 Chapter 6 - Effects of injector design and injection conditions on Flame Transfer Functions
whereGdenotes the gain andϕstands for the phase lag of the FTF, both de-pending on the forcing frequencyf. In recent developments, this linear concept has been extended to the Flame Describing Function (FDF) when eects of the perturbation level|u0|/u¯are explicitly considered (Noiray et al., 2008;Hosseini et al., 2012;Palies et al., 2011b;osi¢ et al., 2015):
F(f,|u0|/u) = Q˙0/Q˙
u0/u =G(f,|u0|/u) exp(iϕ(f,|u0|/u)). (6.2)
The objective of this chapter is to characterize the dierences between the FTF of swirled ames stabilized on various injection system designs. Only fully pre-mixed ames at xed equivalence ratio φ = 0.82 stabilized on radial swirling injectors are considered. Their FTF is determined and the main elements lead-ing to the largest drop of the FTF gain are analyzed with a set of experiments.
The design modications comprise changes of (1) the distance between the swirler exit and the combustion chamber backplate, (2) the main dimensions of the radial swirler, (3) the diameter of the injection nozzle and (4) the design of the top cone of variable diameter of the central blu body. Experiments start by examining eect of the forcing level. All experiments are conducted for xed ow injection conditions with a bulk ow velocity Ub = 5.44 m/s at the outlet of the convergent nozzle, except in a specic set of experiments conducted to analyze the eects of a change of this velocity.
The experimental setup used to determine the FTF/FDF is shown in Fig. 6.1 and was described in detail in Chapter 1. The FTFs are determined from Eq. (6.1) by submitting the ame to harmonic modulations of the owrate.
The velocity uctuationu0 is controlled by the hot wire anemometer HW. This probe is located in the nozzle of the convergent unit in Fig. 6.1 at a distance of 40 mm upstream the swirling vane. It has been checked that the velocity has a top hat prole and is laminar at this location. The photomultiplier equipped with an OH* lter is used to determine the mean I¯and uctuating I0 luminosity signals integrated over the ame volume and over the line of sight. These signals are assumed to be a good tracer of the heat release rate for the lean premixed ames investigated here (Hurle et al., 1968). The transfer function is then deduced from the cross and power-spectral densities between the photomultiplier and hot wire signals examined at the forcing frequency f. These signals are recorded at a sampling rate of fs = 8192 Hz over 4 seconds and Welch periodograms are used to obtain statistically converged results. More details were given in chapter2.
CONTENTS 97
All dimensions
in mm Loudspeaker
CH4 + air
⌀ 22 Hot Wire
Swirler
40150104
70
82
⌀65 8
Perforated grid Honeycomb Water cooling Quartz window
2018568
Pressure tap
Upstream plenum Convergent exhausts
40
PM + OH*
filter
Figure 6.1: Experimental setup used to determine the FTF/FDF.
98 Chapter 6 - Effects of injector design and injection conditions on Flame Transfer Functions