Analysis of chemiluminescence, density and heat release rate fluctuations in acoustically perturbed laminar premixed flames

Combustion and Flame 162 (2015) 3934–3945

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Analysis of chemiluminescence, density and heat release rate fluctuations in acoustically perturbed laminar premixed flames J. Li a,b, D. Durox a,b, F. Richecoeur a,b, T. Schuller a,b,∗ a b

CNRS, UPR 288 Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion (EM2C), Grande Voie des Vignes, Châtenay-Malabry 92295, France Centrale-Supélec, Grande Voie des Vignes, Châtenay-Malabry 92295, France

a r t i c l e

i n f o

Article history: Received 4 April 2014 Revised 21 July 2015 Accepted 24 July 2015 Available online 19 August 2015 Keywords: Laser interferometric vibrometry Heat release rate disturbances Density fluctuations Chemiluminescence Flame dynamics

a b s t r a c t Laser interferometric vibrometry (LIV) has recently been proposed as an alternative mean to obtain timeresolved density and heat release rate measurements at relatively low cost and experimental effort. This technique is sensitive to fluctuations of the refractive index of gases resulting from density and composition changes along the laser beam intersecting the reacting flow. It yields a line-of-sight integrated signal of the probed flow from which density and heat release rate disturbances may be inferred. The link between these signals with chemiluminescence is examined in the present study by first considering a theoretical analysis to determine the relationships between the LIV, density and heat release rate perturbation signals in a multi-species reactive mixture of gases. For air combustion systems interacting with sound waves, low frequency density perturbations in the flame zone, result mainly from heat release rate fluctuations below a certain frequency threshold. An experimental analysis is then conducted with confined conical laminar premixed flames submitted to harmonic flow modulations. Measurements are presented for methane–air mixtures at different equivalence ratios 0.8 ≤ φ ≤ 1.2 and thermal powers. It is shown that fluctuations of the chemiluminescence signal examined in different wavelength bands, including the OH∗ , CH∗ or the entire visible emission bands, always capture the same dynamics. This indicates that heat release rate fluctuations can be deduced without specific filters for the laminar premixed methane–air flames investigated. It is then shown that heat release rate measurements deduced from LIV and chemiluminescence data match well. A proportional relation is found that does not depend on the measurement position, modulation frequency and modulation level for fixed injection conditions. This linear relation slightly depends on the mean flow operating conditions partly due to the difficulty to interpret chemiluminescence emission for rich flames. © 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Monitoring and controlling density and heat release rate disturbances is an important issue in practical combustion chambers because these perturbations generate direct and indirect combustion noise [1]. They may also trigger self-sustained thermoacoustic instabilities causing potential severe damages and early aging of components of the combustor. It is therefore important to control these disturbances and have reliable time-resolved diagnostics to measure these quantities. There are different possibilities to determine heat release rate perturbations that were recently reviewed in [2,3]. The main ones are briefly described. Recording the natural emission from the flame ∗ Corresponding author at: CNRS, UPR 288 Laboratoire d’Energétique Moléculaire et Macroscopique, Combustion (EM2C), Grande Voie des Vignes, 92295 ChâtenayMalabry, France. E-mail address: [email protected] (T. Schuller).

http://dx.doi.org/10.1016/j.combustflame.2015.07.031 0010-2180/© 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

is the simplest diagnostic yielding time-resolved estimates of heat release rate fluctuations [4,5]. Effects of the turbulence intensity, strain rate, flame front curvature, mixture composition, temperature and pressure need however to be included to obtain quantitative heat release rate data [6–14]. These studies stress out the need of alternative techniques to measure heat release rate disturbances. Measurements are then often limited to flame images for qualitative analysis except in a few studies where the signal is calibrated using specific post-processing procedures to map the heat release rate on two-dimensional images [15,16]. Another limitation is that the chemiluminescence emission yields a signal integrated in the line-of-sight and it is difficult to obtain spatially resolved data without additional hypothesis on the system symmetry. One possibility to improve spatial resolution is to use Laser Induced Fluorescence (LIF) by stimulating certain electronic transitions of specific species present within a laser sheet intersecting the flow. Time resolved data are more difficult to obtain due to the limited repetition rates and limited energies delivered per pulse from the lasers,

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although OH and CH concentration measurements at a few kHz were recently reported in flames to characterize transient phenomena in turbulent reacting flows (see for example [17–19]). Quantitative spatially resolved heat release rate measurements deduced from LIF signals are still challenging [20]. This has motivated a series of studies based on LIF measurements of different species concentrations to estimate the local distribution of heat release rate in flow configurations of increasing complexity [10,21–24]. Simultaneous measurements in unsteady flows remain however difficult and require high power well-tuned laser beams at different wavelengths and specific optics. A novel approach yielding line-of-sight integrated data was recently examined by exploiting the link between heat release rate fluctuations and density disturbances in acoustically perturbed laminar premixed flames [3] and turbulent swirling flames [25,26]. The following relation is exploited:

detailed analysis of the chemiluminescence signal. The laser interferometric technique used to detect density fluctuations is presented in Section 3. The experimental setup is described in Section 4 together with the different diagnostics. An analysis of the flame chemiluminescence signal with different interference filters is conducted in Section 5. It is shown that in the configurations investigated the signal collected by a camera with a glass lens is a good tracer of heat release rate fluctuations without interference filter when the equivalence ratio is lower than φ ≤ 1.2. Measurements of density fluctuations integrated along the line-of-sight determined with the laser interferometric technique are presented in section 6. Heat release rate fluctuations determined with the different techniques are then compared for the different flow operating and perturbation conditions explored. Conclusions regarding the validation of the proposed technique for measuring time-resolved heat release rate disturbances are finally presented.

∂ρ  γ −1  − 2 q˙  ∂t c

2. Theoretical analysis

(1)

where ρ  and q˙  denote density and heat release rate (per unit volume) perturbations, respectively, c corresponds to the speed of sound and γ indicates the specific heat capacity ratio of gases. Similar expressions were already used in simulations of combustion noise radiated by turbulent diffusion flames [27–29]. It constitutes an interesting alternative to measure heat release rate fluctuations because different techniques may be envisaged to detect density fluctuations. Eq. (1) provides then a simple way to reconstruct heat release rate disturbances provided that the speed of sound and the heat capacity ratio are known with sufficient accuracy if quantitative data are needed. One of the main advantage of this reconstruction is that Eq. (1) does not depend on the combustion mode. It is well known that the current diagnostics based on the interpretation of the LIF or chemiluminescence signals to infer heat release rate are often limited to perfectly premixed systems. Heat release rate disturbances in nonperfectly premixed systems when mixture inhomogeneities have to be taken into account are more difficult to measure. Several approximations were made in [3] to derive Eq. (1) that was obtained in a single species flow context. Measurements in [3] were also carried out for a rich unconfined M-flame, at a fixed flowrate and at a fixed equivalence ratio φ = 1.19. The flame was submitted to harmonic flow disturbances at two forcing frequencies f = 51 Hz and f = 102 Hz and at a single forcing level. The motion of the unsteady plume of burnt gases surrounding the unconfined perturbed flame precluded a clear identification of the density perturbations detected, because this motion has to be taken into account in the signal processing. This problem has recently been modeled by Li et al. [30] for perturbed unconfined conical flames, but in general the link between the flame motion and the motion of the interface between the burnt gases and ambient air is not known. Only a qualitative agreement between low frequency heat release rate and density fluctuation signals was obtained, but it was not possible to reproduce the correct heat release rate oscillation level. Differences between the rate of change of density fluctuations and heat release rate perturbations were also observed at high frequencies. In a recent analysis of the response of turbulent premixed swirling flames to acoustic forcing [25,26], differences between heat release rate disturbances deduced from chemiluminescence emission measurements and exploitation of Eq. (1) were also found due to a series of contributions to density fluctuations which were not linked to heat release rate perturbations. To avoid the complexity inherent to turbulent flows, acoustically perturbed laminar premixed flames are considered in this study. The difficulties identified in [3] are reconsidered here first theoretically to determine the validity limits of Eq. (1) in Section 2 for a reactive mixture of gases, and then secondly experimentally with an improved experimental setup allowing quantitative measurements of density fluctuations and

2.1. Density disturbances in a reacting flow Considering a single species flow of a perfect gas, the link between density ρ and pressure p is given by [31]:

1 dp dρ ρ ds = 2 − dt c p dt c dt

(2)

where c denotes the speed of sound, cp is the heat capacity at constant pressure and s stands for entropy that contributes to density changes which are not linked with the sound wave. For a reactive mixture of gases obeying to the perfect gas law p = ρ rT, a transport equation linking density ρ , pressure p and the volumetric rate of heat released by combustion q˙ may be derived as shown in Appendix:

1 dp ρ dr dρ = 2 − − dt r dt c dt

γ −1 c2

˙ [∇ · (λ∇ T ) + τ : ∇ v + q]

(3)

where γ denotes the ratio of the specific heats of the gaseous mixture and r = R/W is the coefficient appearing in the mixture perfect gas law, R being the universal gas constant and W is the mixture molar mass. The terms in the brackets correspond to the thermal conductivity λ, the viscous stress tensor τ and the flow velocity v. This transport equation may be found in slightly different forms in [28,31,32] with other approximations. Body forces, such as gravity forces, can be neglected in most practical combustion chambers because the flames are submitted to large pressure gradients. Radiative heat fluxes are also often neglected [33]. Changes of density due to interactions with body forces, radiative heat transfer, Soret and Dufour effects were thus neglected in Eq. (3). Combustion is generally a non iso-molar transformation, but except in oxy-combustion systems [34], changes of the mixture molar  mass W = k YkWk , where Yk denotes the mass fraction of species k and Wk its molar mass, remain weak during the transformation in air combustion systems because of the strong dilution of the reactants and products by nitrogen. One may then neglect changes of r in Eq. (3) when the oxidant is air. It is difficult to further simplify Eq. (3) for instantaneous flow quantities transported by the mean flow. Considering now perturbations (a ) of the flow variables (a) around a steady state (a) in a combustor operating in a continuous mode, one finds to the leading order:

1 ∂ p ∂ρ  γ −1 = 2 − [∇ · (λ∇ T  ) + q˙  ] ∂t c ∂t c2

(4)

if the flow Mach number remains small. This expression shows that in multi-species reacting flows, density disturbances ρ  result mainly from pressure perturbations p , density changes associated to temperature fluctuations T and perturbations of the rate of heat released by combustion q˙  . The first term in the brackets in Eq. (4) corresponds

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to volumetric heat losses by diffusion of temperature fluctuations to the surrounding flow and may be discarded with respect to heat release rate disturbances except close to blow off limits or if combustion takes place near solid boundaries. Under these particular conditions, unsteady heat conduction to the wall may compete with heat release rate disturbances. Away from these limits, one is finally left with:

1 ∂ p ∂ρ  γ −1  = 2 − q˙ ∂t c ∂t c2

(5)

It is shown in the next section that these contributions to density changes have different orders of magnitudes in acoustically perturbed flows. 2.2. Density disturbances in low frequency perturbed flows In an acoustically perturbed reacting flow, acoustic pressure, acoustic velocity and heat release rate disturbances are related. For a traveling plane wave, the sound pressure level is given by prms  ρ cvrms , where vrms denotes the root-mean-square (rms) value of the acoustic velocity. The flame response is barely sensitive to low frequency pressure disturbances and heat release rate fluctuations q˙  may be deduced from the flame transfer function F(ω) to acoustic velocity disturbances [35]:

q˜˙ q˙

= F (ω)

v˜ v

(6)

where v˜ and q˜˙ denote the Fourier components of velocity v and heat release rate q˙  disturbances respectively taken at the angular frequency ω, q˙ denotes the heat release rate value in the steady configuration, v represents the bulk flow velocity at the injection outlet of the burner, and F(ω) is a low-pass filter which is a function of angular frequency ω for a fixed oscillation level [36]. For weak perturbations, the higher order terms of heat release rate fluctuations can be neglected and Eq. (6) can be changed to rms form:

q˙ rms q˙

= |F (ω)|

vrms v

(7)

For a fixed acoustic velocity fluctuation vrms at the perturbation frequency f = ω/(2π ), pressure and heat release rate contributions to density changes in Eq. (5) are of the same order of magnitude when:

ω prms  (γ − 1)q˙ rms

(8)

One may then neglect density disturbances associated to sound waves in Eq. (5) when the following criterion for the forcing frequency f  f0 is satisfied, where

f0 

γ − 1 q˙ |F (ω)| 2π ρ c v

(9)

which can be obtained by substituting Eq. (7) and prms  ρ cvrms into Eq. (8). It is worth noting that f0 is proportional to q.˙ The mean volumetric heat release rate ranges typically within 107 ≤ q˙ ≤ 1012 W m−3 in combustors operating in a continuous mode. The lower limit is reached for combustion of low heat value fuels with air in a laminar mode under atmospheric conditions and the upper one is reached under extreme conditions in high-pressure oxygenhydrogen rocket engines. In these systems, the injection velocity typically varies between v  1 and 100 m s−1 and the speed of sound is comprised between c ࣃ 300 and 1000 m s−1 . Eq. (9) slightly depends also on the gain |F(ω)| of the flame transfer function. Flames being sensitive to low frequency disturbances, act as low-pass filters [36,37]. A cut-off frequency fc = ωc /(2π ) may then be defined for the flame transfer function by |F(ωc )| ≤ 1/2 when ω ≥ ωc . One may then safely replace |F(ω)| by 1/2 in Eq. (9) to estimate f0 and then check that the value found for f0 is higher than fc .

It is interesting to estimate f0 in a typical configuration. Palies et al. [15] studied the response of a turbulent lean methane–air swirling flame, with an injection velocity v = 4.13 m s−1 and an equivalence ratio φ = 0.7, that is submitted to harmonic flow disturbances in a setup operating under atmospheric conditions. The Reynolds number ReD = 6131 based on the injection tube diameter D = 0.022 m is relatively moderate, but the flow is turbulent due to the swirl imparted to the flow. The swirl number is S = 0.55. Using data presented in [15] for the flame transfer function, one finds a value for the flame response cut-off frequency equal to fc = 300 Hz. Values taken by the heat release rate were also determined in this study in the symmetry plane of the burner. In the reaction layers, these values are higher than q˙ ≥ 108 W m−3 (see Fig. 4 in Ref. [15]). Assuming c = 340 m s−1 and ρ = 1.2 kg m−3 , Eq. (9) yields the critical forcing frequency f0 ࣃ 1890 Hz below which density disturbances due to acoustic forcing may be neglected. The value found for f0 is also well above the flame transfer function cut-off frequency fc = 300 Hz indicating that density changes within the reaction layers may safely be calculated by neglecting the acoustic contribution in Eq. (5) for forcing frequencies lower than f < f0 . This example shows that as long as the mean heat release rate takes large values, the influence of the acoustic field on low frequency density changes within unsteady reacting flows may be discarded. This will be further confirmed experimentally for laminar flames submitted to acoustic forcing of increasing amplitudes in the next sections. 3. Density fluctuation measurements Reconstruction of heat release rate disturbances with Eq. (5) requires measurements of density perturbations. Different spectroscopic techniques can be envisaged to this purpose [38–41]. These perturbations are inferred here with a Laser interferometric vibrometer (LIV). This technique was already successfully used to determine density fluctuations in turbulent non reacting flows [42,43] as well as in perturbed reacting flows [25,26,44]. It was more recently used to examine heat release rate perturbations in an unconfined M-shaped laminar premixed flame submitted to harmonic flow modulations [3]. Post-processing of LIV measurements showed a qualitatively reasonable agreement with data obtained by recording the flame chimiluminescence emission with a CCD camera, but it was not possible to fully reproduce the heat release rate fluctuating signal. As no calibration of the chimiluminescence signal was conducted, heat release rate measurements were presented with arbitrary units and the LIV and chimiluminescence signals were arbitrarily rescaled. The origin of differences observed between the post-processed LIV and chemiluminescence signals were mainly attributed to the configuration treated. In the unconfined configuration studied in [3], it was difficult to circumscribe the flow region where density fluctuations are taking place because the burnt gases plume width was perturbed by natural convection [2] and by the acoustically disturbed flow [30]. These additional perturbations modified in turn the optical path of the laser beam that was used to probe the flow and detect density fluctuations. The LIV technique used to measure density fluctuations was already presented in [3], only the principle is briefly described herein. A laser is coupled to an interferometer. Along one arm of the interferometer, the laser beam crosses a flow, is reflected back by a fixed mirror before being combined with a reference beam in the laser head (Fig. 1). The resulting interferences are detected by a photomultiplier located in the laser head. The signal intensity recorded by the photomultiplier depends on the optical path difference L between the two beams along their respective trajectories. If n(z, t) denotes the refractive index of gases along the laser trajectory z at a certain time t, the optical path difference between the beam probing the flow, designated with the subscript 1, and the reference beam, designated with

J. Li et al. / Combustion and Flame 162 (2015) 3934–3945

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Fig. 1. Schematic of experimental setup.

the subscript 0, is a function of time given by:

L(t ) =



L1

n1 (z, t )dz −



L0

n0 (z, t )dz

(10)

For a perfect gas, the refractive index is linked to density through the Gladstone–Dale relation:

n − 1 = Gρ

(11)

N

where G = k=1 Yk Gk denotes the Glastone–Dale coefficient of the mixture and Gk corresponds to the value of this coefficient for each species k. Values of Gk depend on the light wavelength considered, but they only weakly depend on temperature [45]. Table 1 provides values of indices for the main species in a methane–air flame for an orange light. For air diluted combustion, changes of G between the reactants and products may be neglected. For example, the Glastone–Dale coefficient G of the mixture equals to GCH + (Gair − GCH )/(1 − 0.058φ) 4 4 for methane–air premixed combustion and only weakly depends on the equivalence ratio. The same constant Glastone–Dale coefficient may be used for the reference beam L0 crossing air and the beam probing the reacting flow L1 as shown in [3,44]. In the absence of moving elements along the laser optical path within the interferometer, the system is first aligned in a situation where the refractive index without along beams L1 and L0 are equal. This situation is obtained  flow through the burner. A phase lag ϕ(t ) = 2π L(t ) λ0 , where λ0 denotes the laser wavelength, is then defined to link the light intensity I recorded by the photomultiplier:

I(t ) =

I0 [1 + cos (ϕ(t ))] 2

(12)

where I0 denotes the laser intensity which is equally split between beams L0 and L1 . A phase ϕ = 2Nπ corresponds then to a maximum of intensity measured by the photomultiplier, where N is an integer.

Assuming the geometrical path within the interferometer is kept constant, and the optical index n0 along the reference beam L0 remains unmodified, fluctuations of the phase lag ϕ  are then directly linked to density changes integrated along the beam L1 probing the flow [43,44]:

ϕ  (t ) =

4π G

λ0



L1

ρ  (z, t )dz

(13)

This technique provides then density fluctuations integrated along the line-of-sight of laser beam L1 crossing the perturbed reacting flow. It is used with the setup described in the next section to probe density disturbances in acoustically perturbed flames. 4. Experimental configuration 4.1. Burner Measurements are conducted on a burner with a d = 20 mm outlet nozzle diameter represented in Fig. 1. The configuration is similar to that used in [30,47]. Laminar conical premixed methane–air flames are stabilized on the rim of the burner and are submitted to velocity modulations by a loudspeaker fixed at the base of the burner. A two axis micrometric displacement table is used to move the setup in the vertical and horizontal directions by increments of 1 μm. The mean axial velocity vu and its rms fluctuation vu, rms are determined with a hot-wire probe placed at the burner outlet when the flow is perturbed harmonically in the absence of combustion. A quartz tube with a D = 27 mm inner diameter and a 150 mm length is placed at the top of the burner to confine the flame and avoid interactions of the hot flow with the surrounding ambient air. Experiments are conducted for flames with different equivalence ratios at a fixed flame height and with different flowrates to modify the flame height. The conditions explored are synthesized in Table 2.

Table 2 Flame operating conditions. Table 1 Refractive indices n of the main species for methane–air combustion. Indices are given for λ = 589.3 nm at p = 101, 325 Pa and T = 273 K. Reproduced from [46]. Gas

n

Gas

n

Air Carbon dioxide Methane

1.000 292 1.000 449 1.000 444

Nitrogen Oxygen Water vapor

1.000 298 1.000 271 1.000 256

Flame

Equivalence ratio,

φ

Flow velocity, v [m s−1 ]

Flame height, H [mm]

Flame-1 Flame-2-1 Flame-3 Flame-2-2 Flame-2-3

1.00 1.00 1.00 0.85 1.20

1.06 1.50 1.91 1.06 1.35

30 42 54 42 42

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60

50

50

50

40

40

40

30

y [mm]

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y [mm]

y [mm]

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30

30

20

20

20

10

10

10

0

−10

0 10 x [mm]

0

−10

0

0 10 x [mm]

−10

0 10 x [mm]

Fig. 2. Steady stoichiometric flame-2-1 (left), lean flame-2-2 (center) and rich flame-2-3 (right) with three interrogation regions indicated by red disks of diameter d = 2 mm. These regions are used to compare the chemiluminescence signals at different wavelengths. Images were taken here with an ICCD camera without interference filter in front of the UV-Nikkor lens. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

The shape taken by these flames is shown in Fig. 2. The burnt gases around the flame cannot fully expand and are directly in contact with the quartz tube confining the flow. The conical shape of the flame is then slightly bent towards the fresh gases due to the over pressure in the burnt gases, which causes as a feedback a vertical acceleration of the fresh gases in the centerline [47]. For all flow conditions and all excitations explored, the flame shape remains perfectly axisymmetric over time. 4.2. Laser interferometric vibrometer A slightly different interferometer, LIV model LS-V 2500 from SIOS Meβ technik GmbH is used in these experiments compared to that used in [3]. The system comprises a He–Ne laser (λ0 = 632.8 nm) combined with a Michelson interferometer. One branch of the interferometer is equipped with a compact lens to transmit and receive the light probing the flow. The beam passes through the reacting flow in the forward direction. It is then reflected by a fixed flat aluminum mirror and passes again through the reacting flow in the reverse direction (see Fig. 1). This signal is then combined to the reference beam L0 within the interferometer located in the laser head. The resulting combined light beam is finally split in two beams by a birefringent crystal. The intensity of these light beams is recorded by two photomultipliers, one beam crosses first a quarter-wave plate to obtain a signal in quadrature with the first beam. The phase lag ϕ in Eq. (12) may then easily be deduced. In these experiments, the distance between the sensor head and burner axis was fixed to Lbl = 500 mm, and the distance between the mirror and burner axis is fixed to Lbm = 200 mm. The laser beam is focused on the mirror and the laser beam size has a radius of about rd = 1 mm in the flame zone. Measurements are made at five different heights above the burner outlet from y = 5 mm to 25 mm separated by 5 mm increments along the burner axis. These regions are indicated in Fig. 3 by five yellow disks. 4.3. Flame imaging Flame images were recorded with two different cameras. The first one, designated by ICCD, is an 512 × 512 pixels intensified CCD camera (PIMAX2, Princeton Instruments) equipped with an UV-Nikkor lens (focal length 105 mm/aperture 4.5) and different interference filters in front of the lens. Figure 2 shows images of steady flames taken with this camera. The camera was triggered by a TTL signal synchronized with the acoustic forcing and 50 phase-locked images with an exposure time of 20 μ s were accumulated to increase the contrast. This camera was used to record the light emitted by the

Table 3 Interference filter transmission characteristics. λm indicates the peak transmission wave length and λm the wave length bandwidth around this peak at half the peak transmission. Filter ∗

OH CH∗

λm [nm]

λm [nm]

310 430

±15 ±15

flame and examine its response to acoustic forcing in different UV– visible wavelength bands. Experiments conducted without interference filter were repeated with interference filters to detect CH∗ and OH∗ emissions. Table 3 gives the transmission characteristics of the OH∗ and CH∗ filters. To reproduce these experiments with different filters, the flow conditions were unchanged except the gain of the light intensification of the ICCD camera. This gain was set to a value so that the maximum pixel value recorded in each set of experiments was kept roughly constant when the filters were changed. The highest gain value was fixed to detect OH∗ emission because the corresponding filter features the lowest transmission coefficient. It was slightly reduced for the CH∗ experiments and had to be reduced to a significantly lower value for experiments without interference filter. These experiments presented in Section 5 are used to demonstrate that it is not necessary to operate with an interference filter in front of the camera to examine heat release rate fluctuations of laminar premixed flames from hydrocarbon combustibles submitted to flowrate disturbances when the equivalence ratio is lower than φ < 1.2. Images of the perturbed flames were also recorded with a color CCD camera (Pulnix TMC-6), equipped with a glass lens (focal length 25 mm/ aperture 1.4) operating at a fixed frame rate of 50 Hz with an exposure time equal to 1/4000 s. No filter is put in front of the lens. When the acoustic modulation frequency is tuned close but not exactly to a multiple of 50 Hz, a stroboscopic effect is obtained. This method allows for example to record 20 phases per period for a flame modulated with a frequency of 100.05 Hz. The focus of the camera is well adjusted to the size of the flame to maximize resolution on the CCD pixel array. Images are digitized with a matrix of 752 × 582 pixels. The optical magnification of the images gathered corresponds to 1 mm for 9.6 pixels in both directions. More than 400 images are recorded for each operating condition enabling to sort the images and reconstruct the evolution of the flame motion at 20 regularly distributed phases in the modulation cycle. The signal-to-noise ratio in the snapshots is improved by accumulating 4 images at the same phase to increase the contrast. Examples of images with this camera are shown in Fig. 3(b)–(d) for flame-2-1 (Table 2) under different forcing conditions.

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(a)

(b)

(c)

3939

(d)

50

y [mm]

40 30 20 10 0

−10

0 10 −10 0 10 −10 0 10 −10 0 10 x [mm] x [mm] x [mm] x [mm]

Fig. 3. Images of flame-2-1 taken with the CCD color camera. (a) Steady flame. (b) Modulation at frequency f = 100.05 Hz and amplitude vu,rms /v¯ u = 0.07. (c) Modulation at frequency f = 100.05 Hz and amplitude vu,rms /vu = 0.21. (d) Modulation at frequency f = 250.05 Hz and amplitude vu,rms /vu = 0.21. The five yellow disks in these images indicate the regions where the chemiluminescence signal is compared to the LIV signal. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

4.4. Photomultiplier A photomultiplier PM (Hamamatsu H5783) is also used to record the chemiluminescence from the flame in the 300–650 nm UV– visible band. The PM featuring a large solid view angle yields a signal integrated over the entire field of view, while the camera gives a lineof-sight integrated information. No optical filter was used in front of the PM in these experiments. 5. Analysis of the chemiluminescence signal Figure 2 shows images taken with the ICCD camera without interference filter of the steady flames under stoichiometric (flame-2-1), lean (flame-2-2) and rich (flame-2-3) conditions. The light collected by the camera is only filtered by the transmission bands of the UVNikkor lens and the ICCD camera sensor. These flames have the same height H = 42 mm (Table 2). A sequence of phase conditioned images of flame-2-1 motion during an oscillation cycle is presented in Fig. 4 for a forcing frequency f = 125 Hz and a forcing amplitude vu,rms /vu = 0.07 when the ICCD camera is equipped with different interference filters. Qualitatively, there are no obvious differences between these images gathered with the CH∗ , OH∗ filters or without filter. The brightest zones are located in the same regions of the flame front in these images. It is worth analyzing these data on a quantitative basis using different interrogation regions distributed along the burner axis. These regions are represented by red disks in Fig. 2 centered at y = 6, 16 and 26 mm above the burner outlet. The signals recorded by the ICCD camera with different filters are averaged over these circular regions of radius rd = 1 mm. The surface area covered by these regions corresponds approximatively to the size of the laser beam from the LIV crossing the flame. By noting I(i, j) the (i, j) pixel value in the image, an average value over the interrogation region is first determined for each phase tk /T, k = 1, . . . , M explored in the oscillation cycle of period T:

Ik =

N 1 I(i, j) N

(14)

(i, j)

Fig. 4. From top to bottom : phase conditioned average images of flame-2-1 at different phases t/T = 0, 1/4, 1/2 and 3/4 in the oscillation cycle for a modulation at f = 125 Hz and a forcing level vu,rms /vu = 0.07. Images are recorded with the ICCD camera equipped with a CH∗ filter (left), OH∗ filter (middle) or without filter (right) in front of the UV-Nikkor lens.

where N indicates the number of couples (i, j) to fully cover the surface area of the interrogation region. The M phases explored are regularly distributed over the oscillation cycle and tM /T = 1 corresponds to tM = t1 + T . This signal is then divided by the mean value of the intensity over the oscillation cycle:

< I >=

M−1 1  Ik M k=1

(15)

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1.2

1.2

Ik/

1.2

(a)

z = 6 mm

1.2

(b)

(c)

(d)

1.1

1.1

1.1

1.1

1.0

1.0

1.0

1.0

0.9

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0.8 0 1.2

0.2

0.4

0.6

0.8

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Ik/

z = 16 mm 1.1

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Fig. 5. Relative CH∗ (blue symbols), OH∗ (red symbols) and global emission (green symbols) intensities Ik /< I > as a function of the phase tk /T in the modulation cycle, k = 0, . . . , 20, t20 = t0 + T . Signals are collected by the ICCD camera in the interrogation zones at y = 6 mm (top), y = 16 mm (middle) and y = 26 mm (bottom) for different flow and forcing conditions. (a) Stoichiometric flame-2-1, f = 125 Hz, vu,rms /vu = 0.07. (b) Stoichiometric flame-2-1, f = 200 Hz, vu,rms /vu = 0.21. (c) Lean flame-2-2, f = 125 Hz, vu,rms /vu = 0.21. (d) Rich flame-2-3, f = 125 Hz, vu,rms /vu = 0.07. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The resulting signals Ik /< I > obtained with the different filters are plotted in Fig. 5(a) for the stoichiometric flame-2-1 submitted to harmonic flow oscillations at a forcing frequency f = 125 Hz and for a perturbation level vu,rms /vu = 0.07. The CH∗ , OH∗ and unfiltered chemiluminescence signals collapse on the same curves with less than 2% relative difference for the three different interrogation zones distributed along the burner axis. The same type of results are obtained in Fig. 5(b) when flame-2-1 is perturbed with a higher forcing frequency f = 200 Hz at a higher forcing level vu,rms /vu = 0.21. These experiments are repeated with the lean φ = 0.85 (flame2-2) and rich φ = 1.20 (flame-2-3) flames. Results for flame-2-2 are plotted in Fig. 5(c) for a modulation at f = 125 Hz and vu,rms /vu = 0.21. Results for flame-2-3 are plotted in Fig. 5(d) for the same forcing frequency f = 125 Hz, but at a lower modulation level vu,rms /vu = 0.07. These data confirm the previous observations, and one may safely conclude that relative fluctuations of the chemiluminescence signal examined with an OH∗ , CH∗ or in the absence of filter in front of the camera yield the same signal Ik / < I > for these acoustically perturbed premixed flames. The same type of results were found for the different conditions explored by varying the flowrate or the mixture equivalence ratio for a wide set of forcing frequencies and forcing levels covering all conditions of interest for the present analysis of flame dynamics. Experiments are now conducted by replacing the ICCD camera with the UV-Nikkor lens by the color CCD camera with the glass lens. Measurements of flame chemiluminescence integrated over the flame volume recorded with this camera setup are first compared to the signal detected by the PM. Each RGB pixel values from the CCD array is converted to a double precision number corresponding to the total light intensity obtained by a summation of the red (R), green (G) and blue (B) values of this pixel. A summation of this intensity over the entire CCD array yields the global light intensity ICCD mea-

sured by the camera. Methane–air premixed flames appear with a blue to blueish-green color. The light emission in the visible spectrum is mainly due to the chemiluminescence of CH∗ and C∗2 radicals. Up to φ = 1.2, the CH∗ emission in the blue spectrum is much more important than the peak emissions of other radicals in the visible band. The light intensity collected by the RGB sensors is summed over the three colors, but the green and red component contributions were found much lower than the blue value. This quantity can be compared to the light intensity IPM recorded by the PM . Measurements are first presented for steady flames at different equivalence ratios when the flowrate is varied. Results for IPM and ICCD are presented in Fig. 6 as a function of the bulk flow velocity v at the burner outlet. The heat release rate is also indicated in these figures and is calculated as Q˙ = ρu vA q, where ρ u denotes the density of the fresh combustible mixture, A = π d2 /4 is the surface area of the burner nozzle outlet and q represents the heat released per unit mass of mixture. For lean and stoichiometric flames, this last quantity is given by q = Y f ( − hof ), where Yf is the fuel mass fraction in the mixture and − h0f is the heat value per unit mass of fuel. For

rich flames, the heat released is deduced from q = αsYo( − hof ), where Yo denotes the oxidant mass fraction in the mixture and α s is the mass of fuel per unit mass of air under stoichiometric conditions. This approximation holds when endothermic reactions taking place in the combustion products with the fuel in excess can be neglected with respect to the heat released by the premixed rich flame. This is a reasonable approximation for methane–air flames when φ ≤ 1.2. Figure 6 clearly shows that IPM and ICCD are proportional to the heat  ˙ where V is the flame volume. For all condirelease rate Q˙ = qdV, V

tions explored one finds:

Q˙ = k1 I + k0

(16)

J. Li et al. / Combustion and Flame 162 (2015) 3934–3945

(a)

(b)

3941

(c)

Fig. 6. Evolutions of light intensities ICCD and IPM recorded by the color CCD camera (marker ) and by the PM (marker ∗) as a function of the bulk flow velocity v¯ at the burner outlet for three flames. The corresponding heat release rate Q˙ is also indicated. See Table 2 for the operating conditions.

The coefficient k1 is further designated by kPM for experiments conducted with the PM and by kCCD for those carried out with the CCD camera. The coefficient k0 varies with the photomultiplier and CCD camera gains that were not kept constant in these experiments carried out at different equivalence ratios. Values of k0 differ from zero because of the background noise light and of the light radiated by the burnt gases at elevated temperature. The intensity of these emission sources is not proportional to the flow velocity. It is also worth noting that for the rich flame case, a diffusion flame burns on the top of the flame tube when the fuel in excess in the combustion products and ambient air mix. This diffusion flame is out of the field of view of the photomultiplier and the CCD camera, so that these sensors only collect the light originating from the rich premixed flame stabilized on the burner rim. These series of experiments revealed that the flame chemiluminescence emission can be exploited without specific UV or visible interference filter to determine the mean heat release rate and fluctuations of this signal when the equivalence ratio is lower than φ = 1.2. These results are used in the next section to explore the link between heat release rate and density disturbances in these acoustically perturbed flames. 6. Analysis of density and heat release rate disturbances The LIV signal ϕ  (t) is now used to infer density disturbances along the burner axis when flames are submitted to low frequency flow modulations produced by the loudspeaker. Density fluctuations integrated along the line of sight of the laser beam crossing the perturbed flow may be deduced from Eq. (13):

λ0  ϕ (t ) = 4π G



L1

ρ  (z, t )dz =< ρ  (t ) > L

(17)

where the distance L corresponds to the flame tube internal diameter L = D = 27 mm crossed by the laser beam if density fluctuations can be neglected elsewhere along the optical path of the interferometer. This was for example not the case in [3] where the flame was unconfined. The quartz tube allows here to delineate without ambiguity regions where large density fluctuations take place. For low frequency disturbances satisfying Eq. (9), line-of-sight integrated heat release rate perturbations may be deduced from Eq. (5):

d < ρ  (t ) > L γ −1 = − 2 < q˙  > L dt c

(18)

because L = D is a fixed distance. It is assumed here that (γ − 1)/c2 represents a fixed quantity corresponding to the mean value of this quantity along the distance D. This hypothesis will be later checked.

Eq. (18) shows that < q˙  > L may be deduced by taking the time derivative of the LIV signal ϕ  (t):

< q˙  > L = −

c2 λ0 dϕ  γ − 1 4π G dt

(19)

 The heat release rate fluctuation Q˙  = V q˙  dV integrated over the   and IPM flame volume is deduced from the intensity fluctuations ICCD of the chemiluminescence emission collected with the CCD camera and with the PM during the excitation using the calibration procedure presented in Section 5:  Q˙  = kCCD ICCD

 or Q˙  = kPM IPM

(20)

These signals are also used to synchronize the different diagnostics as will be later described. The fluctuation intensity Ir of the signal recorded by the CCD d

camera limited to the cross section area Ad = π rd2 swept by the LIV laser beam intersecting the flame tube is also determined. This provides a second mean to infer the heat release rate fluctuation integrated in the line-of-sight < q˙  > L over the volume probed by the interferometer:

< q˙  > L =

kCCD  I A d rd

(21)

This signal is determined for the five regions represented in Fig. 3. Measurements not presented here show that the phase of this signal is weakly sensitive to modifications of the radius rd of the integration region. The phase changes within ± π /10 when the integration radius is varied from rd = 0.5 to 2.5 mm, but the modulus of the signal increases roughly with rd2 as expected theoretically. In the remaining part of this study, the integration radius rd was fixed to fit the finite width of the laser beam rd = 1 mm. The LIV signal ϕ  (t) is contaminated by low frequency noise due to the internal electronic of the device. A high-pass zero-phase shift filter with a cut-off frequency equal to f/2, where f is the acoustic forcing frequency, is then used to filter the data. In these experiments, the LIV and PM signals are simultaneously recorded and sampled at a frequency of 8192 Hz during 10 s. Flame images recorded with the color CCD camera are obtained in a separate set of experiments. For each set of measurements, the global heat release rate fluctuations determined from the PM and CCD signals are first cross-correlated to find the phase difference between these measurements and synchronize the different diagnostics. One example of results is shown at the top in Fig. 7 for flame2-1 submitted to different flow modulations. Symbols indicate the heat release rate fluctuation determined by integration of the CCD pixel values at regularly distributed phases in the modulation cycle. The continuous lines denote measurements made with the PM. This

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J. Li et al. / Combustion and Flame 162 (2015) 3934–3945

Fig. 7. Heat release rate and density measurements for the stoichiometric flame-2-1 under different forcing conditions. Top graphs: comparison between heat release rate perturbations Q˙  determined with the PM (continuous line) and with the CCD camera (symbols) over the entire flame region. Middle graphs: comparison at y = 15 mm on the axis between < ρ  > L (continuous line) and < q˙  > L (symbols). Bottom graphs: comparison at y = 15 mm on the axis between d( < ρ  > L)/dt (continuous line) and < q˙  > L (symbols). Time t is made dimensionless by the forcing period T = 1/ f . (a) f = 100.05 Hz, vu,rms /vu = 0.07; (b) f = 100.05 Hz, vu,rms /vu = 0.21; and (c) f = 250.05 Hz, vu,rms /vu = 0.21.

Fig. 8. Spectra of the signals d( < ρ  > L)/dt (solid line) and < q˙  > L (dashed lines) recorded at y = 15 mm. Stoichiometric flame-2-1, f = 100.05 Hz and vu rms /vu = 0.07.

figure also shows that the two signals match well in phase and amplitude for all cases explored. The line-of-sight integrated heat release rate fluctuation < q˙  > L deduced from CCD images (symbols) and the line-of-sight integrated density signal < ρ  > L determined with LIV (continuous line) are plotted in the middle graphs in Fig. 7 for a height y = 15 mm above the burner outlet. Both signals feature a periodic motion with the same period, but it is more interesting to compare the rate of change d( < ρ  > L)/dt and the signal < q˙  > L represented at the bottom of the same figures. Signals are rescaled here to obtain comparable oscillation levels. The scaling factor is a measure of (γ − 1)/c2 appearing in Eq. (18) averaged over the integration distance L = D. These two signals collapse in Fig. 7(a)–(c) for the different forcing conditions explored. The same signals d( < ρ  > L)/dt and < q˙  > L examined at different positions along the burner axis always match well for these flow operating conditions. When the modulation amplitude is increased, the shapes of the four signals Q˙  , < q˙  > L, < ρ  > L and d( < ρ  > L)/dt feature larger differences with pure harmonic responses. A spectral analysis shows however that the main oscillation peak is still clearly associated to the forcing frequency for all cases investigated. An example is given in Fig. 8 for a small perturbation level. When the forcing level reaches higher values, Fig. 7(b) indicates small differences between < q˙  > L and d( < ρ  > L)/dt at y = 15 mm for vurms /vu = 0.21. This is caused by the intermittent presence of un-

burnt and burnt gases at this location during the modulation cycle. The tip of the flame lies periodically below and above y = 15 mm for these forcing conditions. In Fig. 3(c), the tip lies above y = 15 mm at the specific phase presented. The motion near the flame tip is more difficult to freeze in the images collected with the CCD camera due to the relatively large exposure time with respect to the flame tip dynamics. Heat release rate perturbations < q˙  > L deduced from integration of the chemiluminescence signal in the CCD images over a radius rd show thus small variations of their phase when rd increases. This phenomenon which is not observed in regions where the laser beam always intersects the flame causes the differences observed between heat release rate measurements deduced from LIV and from CCD images in Fig. 7(b). The link between the signals d( < ρ  > L)/dt deduced from LIV and < q˙  > L deduced from post-processing of CCD images is now examined using Fourier analysis. It is justified to use the cycle reconstructed from the series of images, because the flame movements are perfectly cyclic and there is no parasitic effects due to buoyancy, as a confinement tube was placed around the flames to avoid flickering [2,30]. Figure 8 shows the modulus of the Fast Fourier Transform (FFT) of these signals for flame-2-1 modulated at f = 100.05 Hz at a small perturbation level vurms /vu =0.07. The spectral resolution of the LIV signal is limited here by the chosen sampling rate of 8192 Hz to record the data. The signal d( < ρ  > L)/dt features two sharp peaks at the forcing frequency f = 100.05 Hz and at the first harmonics f = 200.1 Hz well above the background noise. One also identifies a low frequency broad band content, with a relatively broad peak around 25 Hz, one harmonics of this peak near 50 Hz and sub-harmonics of this signal. These low frequencies are not correlated to the acoustic excitation. Low frequency broad peaks also emerge for all other forcing conditions tested, even in the absence of flame and flow. It was not possible to eliminate these contributions with our experimental setup and they are believed to be one limitation of our LIV system. These disturbances remain however one order of magnitude lower than the peak detected at the forcing frequency even for the smallest perturbation level vurms /vu =0.04 investigated. Their contribution may also be separated as they are not correlated to the forcing signal.

J. Li et al. / Combustion and Flame 162 (2015) 3934–3945

3943

Fig. 9. FFT modulus values of < q˙  > L as a function of d( < ρ  > L)/dt examined at different forcing frequencies f when the forcing level vu,rms /vu is increased. Measurements correspond to the vertical position y = 15 mm for the stoichiometric flame-2-1.

Fig. 10. FFT modulus values of < q˙  > L as a function of d( < ρ  > L)/dt examined at the forcing frequency f = 100.05 Hz when the forcing level is increased from vu,rms /vu = 0.04 to 0.21 for different positions y = 5–25 mm above the burner. Stoichiometric flame-2-1.

The 20 phase conditioned images collected by the CCD camera in the modulation cycle lead to a much lower spectral resolution for the FFT of < q˙  > L in Fig. 8. One however clearly identifies the same peaks at 100 Hz and 200 Hz as in the spectrum of d( < ρ  > L)/dt. It is difficult in this figure to compare their respective contributions to the global signal due to the different scales used to plot the d( < ρ  > L)/dt and < q˙  > L spectra. The analysis is now carried out by considering only the principal component of the signals d( < ρ  > L)/dt and < q˙  > L at the forcing frequency f when the forcing level is modified. A proportional relation is demonstrated for flame-2-1 in Fig. 9 for the data collected at the position y = 15 mm. The proportionality coefficient is independent of the forcing frequency and modulation level. Data collapse on the same line except for the forcing frequency f = 60.05 Hz. Measurements in this case have a larger dispersion. The LIV signal features a poor signal-to-noise ratio at this forcing frequency due to a low frequency background noise from the LIV electronics. For a forcing frequency f = 150.05 Hz, linearity is verified up to a modulation level vu,rms /vu = 0.50 even though a larger spread of data is observed at high forcing amplitudes. Flames submitted to higher modulation levels could not be stabilized on the burner rim. The highest forcing frequency investigated in this study is f = 250.05 Hz because higher frequencies are filtered by the flame without changes of the flame shape and chemiluminescence emission. The two signals < q˙  > L and d( < ρ  > L)/dt still match well as shown in Fig. 7(c) when f = 250.05 Hz and vu,rms /vu = 0.21. The same linear link is found in Fig. 10 between < q˙  > L and d( < ρ  > L)/dt for the other positions y explored above the burner outlet when the forcing frequency is fixed to f = 100.05 Hz. As the distance y increases from y = 5 mm to 25 mm, the optical path of the laser beam intersecting the flow within the burnt gases increases due to the conical shape of the flame. Figure 3(a) shows that the laser beam mainly intersects fresh reactants at y = 5 mm and hot burnt gases at y = 25 mm, but the data still collapse on the same line in Fig. 10 when the distance y increases. This observation confirms that the mean

Fig. 11. FFT modulus values of < q˙  > L as a function of d( < ρ  > L)/dt examined at the forcing frequency f = 100.05 Hz when the forcing level vu,rms /v¯ u is increased. Each symbol corresponds to a mean value averaged over three different measurement heights y = 10, 15 and 20 mm. See Table 2 for the operating conditions.

value of (γ − 1)/c2 in Eq. (18) could effectively be considered constant in these experiments, despite the regions of different temperatures and species concentrations crossed by the laser beam. A linear regression of the data yields c2 /(γ − 1) = 1.22 × 106 m2 s−2 . Assuming that γ = 1.4, this leads to a reasonable estimate of the mean value of the speed of sound within the flame tube c = 698 m s−1 . As demonstrated in Section 2.1, changes of the mixture molar mass W remain weak within the flame tube due to the strong dilution of the reactants and combustion products by nitrogen naturally present in air. One thus assumes W  = Wair and the mean temperature can be deduced from c2 = γ RT W, which yields T = 1212 K. It is now worth examining the response of flames operated under different injection conditions. Stoichiometric flames featuring increasing heights obtained by increasing the mass flowrate of reactants are first considered. This comprises flame-1, flame-2-1 and flame-3 (Table 2). The thermal power of flame-3 is roughly the double of that of flame-1 (Table 2). Flames featuring the same height but different equivalence ratios are then examined. This includes a stoichiometric (flame-2-1), lean (flame-2-2) and rich (flame-2-3) configurations. Experiments are conducted for different forcing conditions. Records not presented here show that the two signals < q˙  > L and d( < ρ  > L)/dt still match well for the forcing frequencies lower than 250 Hz investigated. Evolutions of the FFT modulus of < q˙  > L and d( < ρ  > L)/dt examined at the forcing frequency f = 100.05 Hz are presented in Figs. 11(a) and (b) when the forcing level is increased. Each symbol in these figures corresponds to a mean value of measurements averaged over three different heights y = 10, 15 and 20 mm for fixed injection and forcing conditions. This averaging operation is possible because it has been shown in Fig. 10 that for

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J. Li et al. / Combustion and Flame 162 (2015) 3934–3945

fixed injection conditions, the relationship between the two signals does not depend on the measurement height above the burner. Figure 11(a) shows that measurements collapse roughly on the same line intersecting the origin of the plot for the stoichiometric flames investigated when the thermal power is increased. A linear regression of the data indicates a good correlation for each data set, but the slope of this regression slightly changes with the flowrate. When the flowrate increases, the flame height increases, and the slope of the linear regression decreases in Fig. 11(a). A larger dispersion of the data may also be noted for the highest perturbation levels explored. Heat release rate disturbances deduced from chemiluminescence emission fluctuations need however to be treated with caution at high forcing amplitudes because of the intermittent presence of a flame front at the highest measurement locations during the forcing cycle. It was difficult to freeze the flame motion with the CCD camera in these regions. Results in Fig. 11(b) are now examined when the equivalence ratio is varied and the flame height is kept constant. These data show that < q˙  > L and d( < ρ  > L)/dt are still proportional, but the proportionality coefficient slightly differs for the rich flame case (flame-2-3) compared to the lean (flame-2-2) and stoichiometric (flame-2-1) flames investigated. A linear regression of the data also indicates a small offset with respect to the origin of the plot for the rich flame case. This offset disappears for the lean and stoichiometric flames. This is again due to the difficult interpretation of the mean value of the chemiluminescence signal for rich conditions. These experiments reveal that heat release rate fluctuations deduced from LIV and from chemiluminescence emission fluctuations are always proportional for the lean, stoichiometric and rich conditions explored or when the flowrate is varied. For fixed injection conditions, this proportional link does not depend on the measurement location and forcing conditions except at very high forcing levels. The proportionality coefficient however changes slightly with the mean flow operating conditions. Deviations with respect to the model Eq. (18) were shown to be mainly linked to the difficulty to safely interpret the chemiluminescence signal in regions where the flame is intermittently present at high forcing amplitudes and for rich conditions. As the LIV technique is not sensitive to the combustion mode, it is believed that this diagnostic is a good candidate to probe heat release rate fluctuations in non-perfectly premixed systems, where chemiluminescence emission is difficult to interpret. One limitation that needs to be further investigated is the small dependence of measurements on the mean flow operating conditions if quantitative measurements of heat release rate fluctuations are needed. 7. Conclusion Line-of-sight measurements of density fluctuations were used to reconstruct heat release rate fluctuations from confined premixed conical flames submitted to harmonic velocity disturbances of increasing amplitudes at different forcing frequencies. Heat release rate fluctuations deduced from LIV were compared to data obtained by analyzing the chemiluminescence emission of the flame. It was first shown that the chemiluminescence signal filtered in different UV and visible wavelength bands may be used equivalently to infer heat release rate fluctuations from confined laminar methane–air flames with an equivalence ratio ranging from 0.8 ≤ φ ≤ 1.2. Heat release rate fluctuations deduced from the two techniques showed a good agreement at the different forcing frequencies explored for small to moderate perturbation levels. A proportional relation between the two signals was found that does not depend on the measurement position and modulation frequency, but that slightly depends on the mean flow operating conditions. Results for rich flames featured the largest deviations with respect to measurements gathered under lean and stoichiometric conditions. This is mainly due to the difficulty to interpret the chemiluminescence signal in these conditions.

One advantage of the LIV technique is that it does not require a heavy hardware setup compared to other laser diagnostics. Provided that a mean value for the speed of sound along the laser beam probing the flow may be measured or inferred, LIV yields time-resolved quantitative data for heat release rate fluctuations, which are in principle not limited to perfectly premixed combustion modes. The link between density and heat release rate perturbations was established without any assumption on the type of combustion mode, although the technique was only validated yet for acoustically perturbed laminar premixed flames. Validations for unsteady partially premixed and diffusion flames need to be considered, but they are more difficult to handle since there is no reference technique to easily determine heat release rate fluctuations in these combustion modes. Acknowledgment Jingxuan Li was supported by a doctoral fellowship from China Scholarship Council, Project 111, Grant no. B08009. Appendix The transport equation for density Eq. (3) presented in Section 2 is derived here for a reacting mixture of perfect gases. This expression can be found in other references, as for examples in [28,31,32], using different approximations. The objective is to clarify the hypotheses made in this study to obtain Eq. (3). One considers a perfect gas made up of N species, each characterized by a mass fraction Yk , enthalpy hk and molar mass Wk , where k = 1, . . . , N. This mixture obeys to the perfect gas law p = ρ rT, where  r = k Yk rk , rk = R/Wk and R being the universal gas constant. Neglecting body forces interactions, one may start with Williams’ equation for density (Chapter 4, Eq. (50) in [32]) extended to include transport effects [31]:

1 dp dρ = 2 dt c dt



1 − cpT

N 



k=1

∂h ∂ Yk



p,ρ ,Yl

dY ρ k − ∇ · Q − τ : ∇v dt

(22)

 where c denotes the speed of sound and h = k Yk hk is the mixture enthalpy. In this expression Q denotes the heat flux vector, τ is the viscous stress tensor and v is the velocity vector. Change of the mixture enthalpy with respect to Yk , ∂ hk /∂ Yk , at constant pressure, constant density and when all other species Yl , l = k, are frozen may be deduced from the enthalpy differential:

dh = c p dT +

N 

hk dYk

k=1





 r T T = c p dp − c p dρ + hk − c p T k dYk p ρ r N

(23)

k=1

where cp is the mixture specific heat capacity at constant pressure and where use has been made of the perfect gas law to eliminate the temperature differential dT. By substituting the expression for ∂ hk /∂ Yk deduced from Eq. (23), one is left with:

1 dp ρ dr 1 dρ = 2 − + dt r dt cpT c dt



N  k=1



dY hk ρ k − ∇ · Q − τ : ∇ v dt

(24)

Using the transport equation for the mass fraction Yk of each species k:

ρ

dYk = ω˙ k − ∇ · jk dt

(25)

J. Li et al. / Combustion and Flame 162 (2015) 3934–3945

where ω˙ k denotes the volumetric production rate and jk the diffusion flux of species k, one finally obtains:

1 dp ρ dr dρ = 2 − dt r dt c dt +

γ −1 c2



∇ · Q−

N 

 hk jk

− τ : ∇ v − q˙

(26)

k=1

 where q˙ = − k ω˙ k hk denotes the volumetric rate of heat released by combustion. The relations c p = rγ /(γ − 1) and c2 = γ rT valid for perfect gases have been used to eliminate cp in Eq. (26). The definition retained here for the heat release rate q˙ includes changes in the formation and sensible enthalpies of the species. This expression q˙ appears in the transport equation for the temperature (see for example [33] for a discussion on this aspect). In air combustion systems, one may further simplify Eq. (26) by neglecting the radiative contribution, Soret and Dufour effects to the  heat flux Q ([32, Chapter 4]). The difference Q − k hk jk may then be replaced by the Fourier law −λ∇ T in Eq. (26), where λ is the mixture thermal conductivity. This yields the expression given by Eq. (3). References [1] S. Candel, D. Durox, S. Ducruix, A.-L. Birbaud, N. Noiray, T. Schuller, Int. J. Aeroacoust. 8 (1) (2009) 1–56, doi:10.1260/147547209786234984. [2] J. Li, F. Richecoeur, T. Schuller, Combust. Sci. Technol. 184 (2012) 533–555, doi:10.1080/00102202.2011.649323. [3] T. Leitgeb, T. Schuller, D. Durox, F. Giuliani, S. Köberl, J. Woisetschläger, Combust. Flame 160 (2013) 589–600, doi:10.1016/j.combustflame.2012.11.001. [4] I.R. Hurle, R.B. Price, T.M. Sugden, A. Thomas, Proc. Roy. Soc. Lond. Ser. A 303 (1968) 409–427, doi:10.1098/rspa.1968.0058. [5] R. Price, I. Hurle, T. Sugden, Proc. Combust. Inst. 12 (1) (1969) 1093–1102, doi:10.1016/S0082-0784(69)80487-X. [6] Y. Hardalupas, M. Orain, Combust. Flame 139 (3) (2004) 188–207, doi:10.1016/j.combustflame.2004.08.003. [7] N. Docquier, S. Belhalfaoui, F. Lacas, N. Darabiha, C. Rolon, Proc. Combust. Inst. 28 (2) (2000) 1765–1774, doi:10.1016/S0082-0784(00)80578-0. [8] B. Higgins, M.Q. McQuay, F. Lacas, S. Candel, Fuel 80 (11) (2001) 1583–1591, doi:10.1016/S0016-2361(01)00040-0. [9] Y. Ikeda, J. Kojima, H. Hashimoto, Proc. Combust. Inst. 29 (2) (2002) 1495–1501, doi:10.1016/S1540-7489(02)80183-3. [10] B. Ayoola, R. Balachandran, J. Frank, E. Mastorakos, C. Kaminski, Combust. Flame 144 (1–2) (2006) 1–16, doi:10.1016/j.combustflame.2005.06.005. [11] V.N. Nori, J.M. Seitzman, Proc. Combust. Inst. 32 (1) (2009) 895–903, doi:10.1016/j.proci.2008.05.050. [12] M. Lauer, T. Sattelmayer, J. Eng. Gas Turb. Power 132 (2010) 061502, doi:10.1115/1.4000126. [13] F. Guethe, D. Guyot, G. Singla, N. Noiray, B. Schuermans, Appl. Phys. B: Lasers Opt.. 107 (2012) 619–636, doi:10.1007/s00340-012-4984-y. [14] T. García-Armingol, Y. Hardalupas, A. Taylor, J. Ballester, Exp. Therm. Fluid Sci. 53 (2014) 93–103, doi:10.1016/j.expthermflusci.2013.11.009. [15] P. Palies, D. Durox, T. Schuller, S. Candel, Combust. Flame 157 (9) (2010) 1698–1717, doi:10.1016/j.combustflame.2010.02.011. [16] M. Lauer, M. Zellhuber, T. Sattelmayer, C. Aul, J. Eng. Gas Turb. Power 133 (2011) 121501, doi:10.1115/1.4004124.

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