- Email: [email protected]
Flame instability of lean hydrogen–air mixtures in a smooth open-ended vertical channel
Combustion and Flame 162 (2015) 2830–2839
Contents lists available at ScienceDirect
Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Flame instability of lean hydrogen–air mixtures in a smooth open-ended vertical channel Jorge Yanez a,⇑, Mike Kuznetsov a, Joachim Grune b a b
Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany Pro-Science GmbH, Parkstrasse 9, 76275 Ettlingen, Germany
a r t i c l e
i n f o
Article history: Received 19 September 2014 Received in revised form 7 April 2015 Accepted 8 April 2015 Available online 12 May 2015 Keywords: Flame propagation Flame instability Laminar burning velocity Premixed hydrogen–air
a b s t r a c t This work addresses the experimental investigation and analytical interpretation of a flame subject to acoustic–parametric instability exited by self-generated pressure pulses. The research presented herein was carried out with lean hydrogen–air mixtures during flame propagation in a smooth channel with an open end. It was found that very lean mixtures with hydrogen concentrations in air of less than 14% vol. H2 generate acoustic oscillations due to flame instabilities, which, in turn, significantly influence the propagation of the flame. Above a 14% vol. H2 concentration in the air, the flame becomes relatively stable with respect to self-generated acoustic perturbations. It was also found that an external polychromatic sound with a dominant frequency of 1000 Hz inhibits the instabilities and results in a reduced flame propagation velocity. Numerical solutions of the Searby and Rochwerger analytical formulation for the acoustic–parametric instability were utilized in order to analyze the experiments and study the influence of different parameters on the existence of a spontaneous transition from the acoustic to the parametric instability. Ó 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction The interaction between pressure waves and a flame surface is a complex feed-back process in which the wave intensity and the heat released by the flame influence each other. It was firstly concluded by Markstein [1] that the coupling between both phenomena was established through the variation of the total flame surface caused by the pressure changes. The recurrent motion created by the pressure waves interacts with the flame and produces oscillations of amplitude equal to the cellular structures of the flames. This variation of the flame surface alters, in turn, the total amount of fuel consumed and the heat released by the flame which is proportional to the surface. The concept of flame stability represents the capability of the flame front to recover its initial shape after it suffers a perturbation. In this sense, due to the interaction between flames and pressure waves two different instabilities have been identified [2], namely the acoustic and parametric instabilities. In the acoustic instability [3] the cellular structures of the flame front oscillate at the frequency of the acoustic field where two effects tend to
⇑ Corresponding author.
attenuate it. For large wavenumbers, the instability is damped by diffusive processes. For small wavenumbers, it is absorbed by the effect of gravity. For zero amplitude of the excitation velocity, the acoustic instability corresponds to the Darrieus–Landau planar instability. Most notably, for increased values of the cyclic velocity [3], the acoustic instability has the remarkable capability to stabilize the Darrieus–Landau instability. The acoustic instability may evolve, for an enhanced acoustic perturbation, into the parametric one. In this case, the growth rate of the instability is generally superior to that of the acoustic case. Significantly, the cellular structures of the flame oscillate with a frequency which is half that of the acoustic one. This fact was recognized by Markstein as the typical signal of the Kapitsa parametrically damped pendulum, and consequently, decided to name this kind of instability as parametric. Reactive gaseous mixtures can be classified in two groups [4] considering whether transition between the acoustic and the parametric instability is possible. If for some ranges of the amplitude of the acoustic perturbation (see later stability graphs), the flame results to be instable for the both instabilities, transition of regimes may happen meaning that the acoustic instability may transform spontaneously into the parametric one. If the flame is unstable when suffering an acoustic perturbation but the domains of
E-mail address: [email protected] (J. Yanez). http://dx.doi.org/10.1016/j.combustflame.2015.04.004 0010-2180/Ó 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
instability of the acoustic and the parametric instability do not superimpose, the acoustic instability tends to suppress the Darrieus–Landau instability, the parametric instability regime is never reached spontaneously and consequently, planar flame fronts are surprisingly stable as long as the periodic oscillating velocity source exists. These two different propagation regimes have been confirmed by the observations of Searby [2] and Aldredge and Killingsworth [5] who performed experiments with downwards propagating flames inside a cylindrical and annular burner respectively. In those devices, it was found that the flame propagation could be classified in four consecutive stages. Promptly after ignition, the surface of the flame wrinkles due to the Darrieus–Landau and the thermo-diffusive instability. As the flame propagates further, sound starts to be generated. Due to the acoustic instability, these acoustic waves cause an attenuation of flame wrinkles. This attenuation may develop further, even as far as to cause the suppression of the Darrieus–Landau instability. In this stage, the flame becomes planar although its position is oscillating in space with the frequency of the acoustic perturbation. Depending on whether the parametric and the acoustic instability coexist or not, the parametric instability may now develop. This will produce a significant flame acceleration and the appearance of large organized pulsating cellular structures. If they do, the final stage of development is characterized by the transformation of those coherent cellular structures into incoherent flame surface fluctuations. Therefore, gaseous mixtures prone to the parametric instability may suffer, in closed chambers, a very significant acceleration of the flame propagation velocity. Especially in the case of lean mixtures, this increase of the combustion rate can be very considerable. The objective of the present work is to describe the data experimentally obtained by the authors on acoustic parametric instabilities for hydrogen–air mixtures, in a similar way as was done in [2,5] for hydrocarbons. Our study is focused on very lean mixtures that most notably have Lewis numbers smaller than one and negative Markstein numbers. Also, the interpretation of these data utilizing the theoretical findings presented in [6,7] will be presented. An evaluation of the critical conditions for flame instability and the subsequent flame acceleration will also be performed. Additionally, an experimental investigation will be performed on the effect of an external acoustic generator on the flame behavior with a comparison against the theory. To do so this paper is organized as follows. In Section 2 we present the experimental facility, the conditions in which the test were carried out and the results of the experiments performed. In Section 3 we perform the theoretical analysis of the stability of the flame in the same conditions in which the experiments were performed and we subsequently reinterpret the experimental results.
2. Experiments 2.1. Experimental setup A series of combustion experiments with hydrogen–air mixtures was performed in order to study the flame behavior and evaluate critical conditions for the onset of the acoustic-parametric instability. The experiments were carried out in a vertical square channel with a cross-section of 100 100 mm, see Fig. 1. The height of the channel was 1.2 m. The ignition end of the duct was kept open while the opposite end was closed. The channel was constructed by mounting glass windows on two opposing sides of the tube, allowing a visualization of the flame over the whole length of the channel. The conduit was kept entirely clear of any kind of roughness or obstacles, susceptible to alter the propagation of the flame.
2831
Fig. 1. Side view of the conduit utilized to perform the flame instability experiments: (1) open end; (2) metal cover; (3) ignition device; (4) glass window; (5) metal side wall; (6) flanges; (8) pressure sensor; (2) massive base plate.
Premixed lean hydrogen–air mixtures with hydrogen concentration in the range of 8–15 vol.% H2 with a negative Markstein number were used as test mixtures. The initial temperature and pressure conditions correspond to ambient conditions. The main thermodynamic properties of the test mixtures were calculated using the CANTERA code [8] and are summarized in Table 1. The mixtures were prepared using mass flow controllers with an accuracy of ±0.1%H2 (abs.). The ignition of the gaseous mixtures was carried out by utilizing a glow plug device (hot wire). The ignition location was placed on the centerline at the upper or bottom end of the channel, so that the propagation of the flame proceeded in downward or upward direction. Ignition in the upper position aims at the mitigating the effects of the Rayleigh–Taylor instability, which may introduce additional undesired oscillations and perturbations in the system. A high speed camera combined with a Schlieren system was used for the visualization of the flame front. A standard Z-shape Schlieren system consisting of a light source, two mirrors and a camera (Photron type, up to 200,000 fps) was utilized. This technique allows for the capturing of density changes along the full width of the channel over a length of 30 cm and thus enabled the propagation of the flame with an enhanced accuracy to be resolved. As a general remark for this technique, it is noteworthy that the areas in which a positive density gradient exists, will appear brightened. Consequently, areas appearing as darkened will represent negative gradients of density. Acoustic and pressure oscillations of the flame will be registered by a fast pressure transducer of the 103a series produced by the PCB Piezotronics
2832
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Table 1 Main thermodynamic properties of test mixtures. Hydrogen concentration %H2
Sound speed in reactants cr (m/s)
Adiabatic combustion temperature Tc (K)
Sound speed in products cp (m/s)
Expansion ratio H
Laminar velocity UL (m/s)
8 9 10 10.5 11 12 13 14 15
347 359 361 362 363 365 367 368 370
939 1016 1093 1131 1169 1244 1319 1393 1466
612 636 659 670 682 703 724 745 765
3.08 3.31 3.54 3.66 3.77 3.99 4.21 4.42 4.63
0.07 0.09 0.11 0.13 0.15 0.19 0.23 0.28 0.35
company with a resonant frequency of above 500 kHz. Additionally, and in order to disturb the flame propagation, a poly-chromatic sound generator, similar to a ‘‘horn’’, with a dominant frequency of about 1 kHz was utilized in the tests.
the length of the channel, c being the speed of sound in reactants, and n = 1, 2, 3, ... being the resonance nodes. Similarly, the
2.2. Experimental results A sequence of shadow flame images is shown in Fig. 2. After the mixture was ignited at the top axial position, the flame developed initially as a typical tubular flame propagating preferentially along the channel walls, with a Lewis number Le 0.35. The flame propagated with a distinctive cellularity with a characteristic cell size of about 1–2 cm due to the thermo-diffusive instability. After this initial stage, the tongue of the flame started to propagate along a lateral wall with a significant increase of the total surface of the flame. This leads to the augmentation of the transversal flame velocity with the formation of a planar flame structure across the channel. This phenomenon appeared customarily in the second part of the tube, as happened in [2,5], with the difference that, in these papers, oscillations of the flame were mainly governed by Darrieus–Landau instability without an effect of thermo-diffusion instability. Subsequently, the flame started to generate noise and the flame surface started to oscillate. The oscillations were noticeable in the transversal direction but much more significant in the longitudinal direction. The amplitude of oscillations reached several centimeters. The very wrinkled flame structure due to the thermo-diffusion instability transforms from a wedge to almost a planar oscillating flame front after traveling a half of the channel. The characteristic cell size decreases several times during this process. A typical sequence of shadow images of the flame shape is shown in Fig. 2. Independently from the optical thickness of the object, the Schlieren images (Fig. 2) allow to resolve the cellular flame structure and general flame behavior, such as the oscillating flame movement. The flow ahead of the flame appears completely laminar except for the area in vicinity of the flame surface and within the amplitude of the flame oscillations (up to 3 cm). Since the boundary layer is not yet developed after ignition in such a smooth channel, the turbulence cannot appear within the kernel of the channel. The effective Reynolds number is Re = ul/m = 600–2000, corresponding to a laminar flow. For an unsteady flow, such as the one studied herein, the Reynolds number is governed by the flow velocity u 1 m/s, the amplitude of acoustic perturbations l = 1–3 cm and the viscosity m 2 105 m2/s, meaning that the flame structure and flame oscillations are only controlled by self flame instability. For hydrogen concentrations of 10–14 vol.%, the pressure registered simultaneously by the transducers installed at the bottom of the channel is shown in Fig. 3. The maximum amplitude of acoustic oscillations lies in the range of 2–3 kPa with a frequency in the range of f = 100–150 Hz. Such values correspond to the resonance frequency derived for semi-open channel f ¼ nc=ð2LÞ, with L being
Fig. 2. Sequence of Schlieren photographs (4000 fps, every 10th frame is shown). The cuts are taken in the middle part of the channel (30–60 cm from the ignition point). The frame used to capture the leading front trajectory is shown in red. The width of the channel is 10 cm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
2833
Fig. 3. Measured pressure signals for different hydrogen–air mixtures: (a) 10% vol. H2, (b) 10.5% vol. H2, (c) 11% vol. H2, (d) 12% vol. H2, (e) 13% vol. H2, (f) 14% vol. H2.
maximum amplitude of the acoustic oscillations corresponding to a 9% hydrogen concentration in air was about 0.5 kPa with a frequency of about 100 Hz: The spectral analysis of the pressure signals yielded the results shown in Fig. 4. A very clear resonance appears in the range of 100–150 Hz for concentrations of 10–13% vol H2. The spectral analysis of the initial part of the signal, prior to the starting of the oscillations, shows a flat spectrum with no significant peaks around 10 kPa. The only mixture which resulted in a stable flame propagation, 14% vol. H2, has a much less pronounced peak in the range of 170 Hz and exhibited a much different nature than the other tested mixtures. To obtain a time–distance diagram, the video frames containing the propagation of the flame were post-processed. Certainly, in order to receive a high quality representation, a high speed Schlieren video technique (4000 frames per second) was utilized. A 2–3 pixels narrow stripe of each video frame with the flame position in the center (shown in red in Fig. 2) was placed one by one in the horizontal direction (see Fig. 5). In this figure, the horizontal direction is the time scale and the vertical direction corresponds to the flame position along the vertical axis of the channel. Such
a procedure represents the flame dynamics in a longitudinal direction in the center of the channel captured by the red stripe. The position of the stripe is not of great importance since longitudinal oscillations occur for the flame surface within a whole cross-section of the channel. All parts of the flame surface axially oscillate with the same amplitude and frequency. As an example, the evolution of the flame position in 12% H2–air mixture has been evaluated and is plotted in Fig. 5. The flame propagates downwards in the direction of increasing S (see the picture). The longitudinal oscillations appear around 1–2.5 s after ignition. It corresponds to the distance 70 cm from ignition point. A detailed plot of the flame propagation in 12% vol. H2 is depicted in Fig. 6. For clarity the zero point for time and position was set to the instant in which oscillations started to appear. The analysis of the signal reveals that the oscillations appearing in the readings have a frequency of 65.2 Hz, that is, half of the frequency of the perturbation which is a clear indication that the oscillations are due to the parametric instability. The maximum amplitude of the longitudinal oscillations was measured to be in the range of ±(1–3.5) cm, relative to the mean flame position, resulting in a total amplitude up to 7 cm. Subsequent to the
2834
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Fig. 4. Spectrum of the measured pressure signals: (a) 10% vol. H2, (b) 10.5% vol. H2, (c) 11% vol. H2, (d) 12% vol. H2, (e) 13% vol. H2, (f) 14% vol. H2.
Fig. 5. Position of the flame along a vertical axis for the mixture of 12% vol H2. Ignition at the top. Time and distance along horizontal and vertical directions respectively.
appearance of acoustic oscillations, the average flame velocity significantly increases from 0.4 to 1.6 m/s, with a velocity of the longitudinal perturbations ua changing from 1.3 to 4.9 m/s or in terms of laminar flame speed Ua/SL 6–23. This corresponds to an acoustic intensity of 170 dB. In papers [6,7], the ‘‘stability’’ domain for lean hydrogen–air mixtures with negative Markstein number (Ma < 0) was
quantitatively evaluated. It was found to be a frequency of above 400 Hz which governed the stable flame propagation regime. It is supposed that the use of an external source of acoustic oscillations, such as a ‘‘horn’’, with a dominant frequency of about 1000 Hz may significantly change the flame structure and its behavior. The suppression of longitudinal flame oscillations due to the external noise produced by a ‘‘horn’’ with a frequency f 1000 Hz can be seen to
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
2835
Fig. 6. Positions and average velocity of the flame for 12% vol. H2 experiment. For clarity, the origin of coordinates for time and space was selected as the instant in which oscillations appear for the first time.
happen around 1.7 s after the ignition (see Fig. 7), which corresponds to the moment when the ‘‘horn’’ starts to operate. The external noise leads to the attenuation of the amplitude of the flame oscillations in 4–6 times. The average flame velocity also decreases by a factor of 4. Consequently, the cellular structure of the flame changes dramatically. The flame is visually stabilized. From a highly wrinkled surface it is transformed until it reaches a virtually smooth planar structure (see Fig. 8). Figure 9 demonstrates that continuous external acoustic perturbations of 1000 Hz fully suppress own acoustic oscillations of the flame and lead to very smooth and slower flame propagation. The experiment confirmed that an oscillating flame with a reduced flame propagation velocity could be stabilized by an external acoustic generator with a frequency above the stability limit. 3. Analysis 3.1. Analytical considerations The mathematical treatment of acoustic and parametric instabilities is based on the work of Pelce and Clavin [9]. These authors obtained an equation for a perturbed flame front in a gravitational field under the assumptions of high activation energy and large scale wrinkling. Based on these results, Searby and Rochwerger [4] derived an expression for the growth rate of the acoustic and the parametric instability and were able to calculate the stability limits for both cases numerically. This problem with respect to H2–air systems was also analyzed in [7]. For the sake of completeness and understandability, we will include here the Eqs. 1–7 (already appearing in [7], see this reference for details) that will be applied later for the particular conditions of this study and to compare with previous analysis [7]. Suppose the flame front is represented by the function F(x, t) = 0 in a reference frame moving with the flame front. Then, this surface
Fig. 8. Flame structure before (left) and after (right) the application of the external noise (9% H2–air).
divides the calculation domain in two regions: F(x, t) < 0 for the reactants, and F(x, t) > 0 for the products. Small perturbations can be considered in the form F(x, t) = F(t)exp(ikx). Considering the linear stability problem, the second order differential Eq. (1) describes the evolution of the flame surface perturbations of small amplitude, considering periodic monochromatic velocity fluctuations normal to the flame front 2
A
d F dt
2
þ U L kB
dF 2 þ kg a C 1 F kxU a cosðxtÞC 1 F þ U 2L k C 2 F ¼ 0: dt
ð1Þ
Fig. 7. Longitudinal flame oscillations for the 10% H2 experiment. Time and distance along horizontal and vertical directions respectively. The white arrow indicates the moment when the strong external noise was turned on and subsequently started affecting the flame propagation.
2836
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Fig. 9. Flame propagation without (a) and with (b) the application of the external noise (9% H2–air). The interface between dark and light parts corresponds to flame position.
In this equation, A, B, C1, C2, are dimensionless coefficients which take the form,
h1 h 2h A¼ 1þ kL Ma J ; B¼ ð1 þ hkLðMa JÞÞ ; hþ1 h1 hþ1 ð2Þ C1 ¼
h1 Jh ; 1 kL Ma hþ1 h1
ð3Þ
h1 kL C2 ¼ h 1 þ ðð3h 1ÞMa 2Jh þ 2Prhb ðh 1Þ Ið2Pr 1ÞÞ : hþ1 h1 ð4Þ
where Ul is the laminar burning velocity, k is the wavenumber, ga is the constant part of the acceleration, x is the circular frequency, Ua the amplitude of the acoustic perturbation, L is the thickness of the flame and h the expansion ratio. Those coefficients depend on the simple one-step Arrhenius reaction parameters of the flame,
c ¼ ðqu qb Þ=qu ; hð#Þ ¼
# ¼ ðT T u Þ=ðT b T u Þ; ¼
kð#ÞC Pu ku Cð#Þ
qð#Þvð#Þ ; q u vu
ð5Þ
where the u and b subscripts refer to unburned and burned gas respectively, k is the thermal conductivity and v the thermal diffusivity. The Markstein number Ma considered is derived from the definition of Pelce and Clavin [9],
Ma ¼
J
1 ZeðLe 1Þ c 2
Z
1
0
hð#Þlnð#Þ d#; 1 þ #c=ð1 cÞ
ð6Þ
where Ze is the Zeldovich number and Le the Lewis number. The integrals are defined as H¼
Z
1
ðhb hð#ÞÞd#; J ¼ 0
c 1c
Z 0
1
hð#Þ d#; I ¼ ðh 1Þ 1 þ #c=ð1 cÞ
Z
In this paper, the solutions of Eq. (1) will not be treated here since this has been the purpose of paper [7]. The results given there will be used to obtain the stability graphs and analyze current experiments. Nevertheless, it is pertinent to recall that the solution of (1) involves, after some algebra, the resolution of the Mathieu differential equation [11–14] which is responsible for the intricate pattern that the domain of stability displays in the graphs presented hereafter. Eqs. 1–7 must be particularized for the H2–air mixtures and the conditions utilized in the experiments. This requires the finding of molecular transport coefficients, thermodynamic data, activation energy, etc. for every fuel concentration. In this respect, the molecular transport coefficients were obtained utilizing the kinetic theory of gases [15], the thermodynamic data were acquired using the JANAF tables [16] and the Lewis number of the mixture was calculated by means of the formulation proposed by Sun and coworkers [10]. Special care was taken when calculating the overall activation energy. The detailed chemistry scheme of Lutz [17] was coupled with the computer program Cantera [8], thus obtaining the induction time of the analyzed mixtures. This magnitude was then utilized to derive the overall activation energy. The circular frequency of the acoustic perturbation x was found from the analysis of the results obtained in the experiments, see Table 2. Indeed, the interaction of a flame with reflected waves inside a closed volume will depend on the dimensions of the vessel considered. For an open tube, the acoustic resonance frequency can be described approximately by the equation f ¼ nc=ð2LÞ in which c is the speed of sound in the media and n and L are the mode number and the length of the tube. For the channel considered herein, the previous equation particularized for n = 1 yields a resonance frequency of f 150 Hz, which is very close to the registered value. As a result, this value can be considered as the first longitudinal harmonic. 3.2. Results of the analysis
1
hð#Þd#;
0
ð7Þ
A simplification in Eq. (7) may help to understand the meaning of the concept of stability. In the case ga = 0 and Ua = 0, the temporal part of the solution of Eq. (1) has the form F(t) = Y exp(rt) being Y constant. As a result, the planar flame front will be stable with respect to perturbations for all growth rates fulfilling Re(r) < 0 and will be unstable otherwise. In the more complex case under study, the solution is more complicated, see [10,4], nonetheless the concept remains.
Figure 10 contains the results of the application of the method considering a sound excitation with the same frequency that was measured (see Table 2) for the fuel concentrations of 10, 10.5, 11, 12, 13 and 14% vol. H2 at normal conditions. The diagrams represent the growth rate of the instabilities for different combinations of flame surface wavenumbers k (abscissa) and reduced velocities of the excitation Ua/Sl (ordinate). The stable regions, pairs (k, Ua/Sl) for which the growth rate r is less than or equal to 0, are plotted in violet. For clarity, black lines separate the violet stable regions from the unstable ones.
2837
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839 Table 2 Main properties of test mixtures and parameters of the acoustic perturbation measured in the experiments.
a
%H2
Ma (Ze)
Le
Ze
UL (m/s)
Measured frequency, fm (Hz)
Measured max. pressure oscillations (kPa)
9 10 10.5 11 12 13 14 15 20a 21a
2.0 1.8 1.7 1.6 1.39 1.17 0.97 0.8 0.1 0.02
0.34 0.34 0.34 0.34 0.35 0.35 0.36 0.36 0.39 0.39
5.15 4.99 4.89 4.78 4.59 4.41 4.25 4.09 3.46 3.35
0.09 0.11 0.13 0.15 0.19 0.23 0.28 0.35 0.9 1.04
100 110 122 121 130 145 170 – – –
0.5 2.0 2.2 3.1 3.1 1.9 0.4 0.4 – –
Not tested.
Fig. 10. Stability graphs for H2–air mixtures at normal conditions. From left to right and from top to bottom: (a) 10, (b) 10.5, (c) 11, (d) 12, (e) 13 and (f) 14 vol.% H2. Excitation frequencies are 110, 122, 121, 130, 145 and 170 Hz respectively.
In the derivation of the Eqs. 1–7 [9], it was supposed that the flame front was thin compared to the wavelength of the perturbed surface. Therefore, for the representation of the diagrams, the maximum of the abscissa was adjusted to consider a maximum cutoff wavenumber equivalent to one tenth of the wavenumber formed with the flame thickness, 2p/d. It is to be noted that each diagram has a different range for the abscissa.
In the plots of Fig. 10, the acoustic instability region is clearly identifiable in the bottom left corner of each diagram. The parametric instability region is visible in the upper and left areas of the plots. In comparison with the parametric instability, the acoustic instability shows a moderate growth rate that remains below 100 Hz. In contrast, in all diagrams, the first lobe of the parametric instability exhibits a much larger growth rate, close to 400 Hz.
2838
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Fig. 11. Longitudinal flame oscillations for a 10 vol.% H2 experiment, re-interpreted with the theoretical considerations given in previous sections. The white arrow indicates the moment when strong external noise affects the flame.
Fig. 12. Stability graphs for a 10 vol.% H2–air mixture at normal conditions and an excitation frequency of 110 Hz corresponding to the auto excitation of the flame (left) and 1000 Hz corresponding to the major frequency of the horn (right).
All mixtures analyzed show a clear overlap in the acoustic excitation amplitudes between the acoustic and the parametric instability regions. This overlaps demonstrates that the spontaneous transition from the acoustic to the parametric region is possible. The tendency depicted in the diagrams shows a reduction of the overlap with increasing hydrogen concentration. The parametric instability appears to exist for all intensities of acoustic perturbation (full range of Ua/SL) for large wavenumbers. The possibility of the existence of such regions was already investigated in [6,7], identifying the range of wavenumbers in which these phenomena could occur. Due to the limits of this range, and due to the reasons previously mentioned, only the lower wavenumber border is visible in the diagrams. The wavenumbers limiting that range, klim = min(k0A, k0B), are (see Ref. [7])
k0 A ¼
k0 B ¼
h1 L 12 ZeðLe hþ1
R 1 hL 0
1 R 1 1Þ 0
;
1 hð#Þ 1þ#ðh1Þ
d# þ
ð8Þ
hð#Þlnð#Þ d# 1þ#ðh1Þ
1 ZeðLe 2
R 1 1Þ 0
:
hð#Þlnð#Þ d# 1þ#ðh1Þ
ð9Þ
The existence of such domains implies that the response of the flame to an acoustic excitation generated by the flame itself can trigger directly the parametric instability, without requiring any initial stage in which the acoustic instability occurs. 3.3. Re-interpretation of the experimental results The previous analysis allows for the re-interpretation of the spectra and positions of the registered signals shown in Figs. 4 and 6. In the analysis of Fig. 6 it was ascertained that the oscillatory component of the propagation only shows a 65 Hz component. In
the plots contained in Fig. 4, a clear resonance is shown around 120 Hz. The growth rate of the high wavenumber modes (2000 m1), represented in Fig. 10 (upper left plot) may have caused this behavior, in which the parametric instability was triggered directly without any intermediate acoustic phase. The difference of growth rates, significantly less than 100 Hz for the acoustic instability (range 0–700 m1), and 300–400 Hz for the parametric instability in the range above 2000 m1, suggest that even if the simultaneous excitation of the parametric and the acoustic instability is possible, only the parametric one may be detected in experiments. The effect of an external source of noise can be analyzed with regards to the theoretical stability diagrams and the experimental findings, observing Fig. 11. After the sound is applied, the propagation of the flame changes from a regime which is dominated by the parametric instability (65.2 Hz) to an area dominated by the acoustic instability (120 Hz). In the final stage, the instabilities are completely attenuated by the effect of the external noise, obtaining a flame which is not oscillating. The burning velocity of the propagating flame is consistently reduced in a very significant manner. This can be visually ascertained by comparing the propagation slopes in Fig. 11 for the areas dominated by the parametric instability, the acoustic or even the stable region. The significance of the noise generated by the ‘‘horn’’ for the stability of the flame can be more precisely evaluated by comparing the stability graphs corresponding to the same H2–air mixture before and after the application of the sound, Fig. 12. The noise neither alters the domain in which the acoustic instability is existing (bottom left) nor its growth rate. Nevertheless, it strongly decouples the parametric instability from the acoustic one. It shifts the domain of high growth rates corresponding to the parametric instability to the higher frequencies. Specifically, the lobe closer to the acoustic area completely disappears in the stability diagram
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
corresponding to the ‘‘horn’’ perturbation (Fig. 12, right). Therefore, our experiments may be considered as a validation of the theoretical model presented in [6,7].
2839
will suffer the acoustic instability. The experiments show good consistency with the theoretical model. Appendix A. Supplementary material
4. Summary In this paper, the experimental investigation of the influence of noise on the propagation of hydrogen–air flames in the range of 9– 14 vol.% H2 has been presented. The analysis of the influence of the noise spontaneously generated by the flame itself due to its own propagation shows that very significant resonance exists for mixtures between 9–13 vol.% H2 in the range 100–150 Hz. It appears nevertheless that the mixtures with 14 vol.% H2 or higher H2 concentrations seem to have a stable behavior and do not significantly react to the pulses generated by themselves. It was found that the measurements of the propagation of the flame contain an oscillatory component whose frequency is half that of the perturbation frequency. This constitutes an indication for the existence of the parametric instability. It was further observed that an external polychromatic sound generator with a dominant frequency of 1000 Hz suppressed the instabilities for all the tested mixtures, making the flame surface very smooth. Consistently, the external noise significantly reduces the amplitude of flame oscillations and leads to a reduction in the average flame propagation velocity. The theoretical analysis due to Searby and Rochwerger [4] was utilized to obtain the stability maps for the mixtures involved in the experiments. The diagrams of stability obtained, as well as the analysis of the experimental data, suggest that a direct excitation of the parametric instability is possible for a set of wavenumbers and any amplitude of the perturbation. This modus of instability growth may exclude an initial stage in which the flame
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.combustflame. 2015.04.004. References [1] G.H. Markstein, Non-steady Flame Propagation, Pergamon Press, New York, 1964. [2] G. Searby, Combust. Sci. Technol. 81 (1992) 221–231. [3] P. Pelce, D. Rochwerger, J. Fluid Mech. 239 (1999) 293–307. [4] G. Searby, D. Rochwerger, J. Fluid Mech. 231 (1991) 529–543. [5] R.C. Aldredge, N.J. Killingsworth, Combust. Flame 137 (2004) 178–197. [6] J. Yanez, M. Kuznetsov, R. Redlinger, A. Kotchourko, A. Lelyakin, In: Proc. of the 4th International Conference on Hydrogen Safety (ICHS2011), September 12– 14, 2011, San Francisco, USA, paper 127, pp. 1–12. [7] J. Yanez, M. Kuznetsov, R. Redlinger, Combust. Flame 160 (2013) 2009–2016. [8] D.G. Goodwin, Cantera User’s Guide, California Institute of Technology, 2001. [9] P. Pelce, P. Clavin, J. Fluid Mech. 124 (1982) 219–237. [10] C.J. Sun, C.J. Sung, L. He, C.W. Law, Combust. Flame 118 (1999) 108–128. [11] M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Government Printing Office, Washington, D.C., 1972. [12] T. Jones, Mathieu’s equation solution and stability.. [13] E. Sträng, Académie Royale Belgique, Bulletin de la Classe des Sciences, series 6th XVI, fascicule 7/12, 2005, pp. 269–287. [14] E.T. Whittaker, G.N. Watson, A Course of Modern Analysis, Cambridge University Press, 1962. [15] J.O. Hirschfelder, C.F. Curtiss, R.B. Bird, Molecular Theory of Gases and Liquids, John Wiley and Sons, New York, 1954. [16] W. Malcolm, Jr. Chase, NIST-JANAF Thermo-chemical Tables Set, Amer. Inst. of Physics, 1998. [17] A.E. Lutz, Numerical Study of Thermal Ignition, Sandia Report SAND88-8228, 1988.
Contents lists available at ScienceDirect
Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e
Flame instability of lean hydrogen–air mixtures in a smooth open-ended vertical channel Jorge Yanez a,⇑, Mike Kuznetsov a, Joachim Grune b a b
Institute for Nuclear and Energy Technologies, Karlsruhe Institute of Technology, Hermann-von-Helmholtz Platz 1, 76344 Eggenstein-Leopoldshafen, Germany Pro-Science GmbH, Parkstrasse 9, 76275 Ettlingen, Germany
a r t i c l e
i n f o
Article history: Received 19 September 2014 Received in revised form 7 April 2015 Accepted 8 April 2015 Available online 12 May 2015 Keywords: Flame propagation Flame instability Laminar burning velocity Premixed hydrogen–air
a b s t r a c t This work addresses the experimental investigation and analytical interpretation of a flame subject to acoustic–parametric instability exited by self-generated pressure pulses. The research presented herein was carried out with lean hydrogen–air mixtures during flame propagation in a smooth channel with an open end. It was found that very lean mixtures with hydrogen concentrations in air of less than 14% vol. H2 generate acoustic oscillations due to flame instabilities, which, in turn, significantly influence the propagation of the flame. Above a 14% vol. H2 concentration in the air, the flame becomes relatively stable with respect to self-generated acoustic perturbations. It was also found that an external polychromatic sound with a dominant frequency of 1000 Hz inhibits the instabilities and results in a reduced flame propagation velocity. Numerical solutions of the Searby and Rochwerger analytical formulation for the acoustic–parametric instability were utilized in order to analyze the experiments and study the influence of different parameters on the existence of a spontaneous transition from the acoustic to the parametric instability. Ó 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction The interaction between pressure waves and a flame surface is a complex feed-back process in which the wave intensity and the heat released by the flame influence each other. It was firstly concluded by Markstein [1] that the coupling between both phenomena was established through the variation of the total flame surface caused by the pressure changes. The recurrent motion created by the pressure waves interacts with the flame and produces oscillations of amplitude equal to the cellular structures of the flames. This variation of the flame surface alters, in turn, the total amount of fuel consumed and the heat released by the flame which is proportional to the surface. The concept of flame stability represents the capability of the flame front to recover its initial shape after it suffers a perturbation. In this sense, due to the interaction between flames and pressure waves two different instabilities have been identified [2], namely the acoustic and parametric instabilities. In the acoustic instability [3] the cellular structures of the flame front oscillate at the frequency of the acoustic field where two effects tend to
⇑ Corresponding author.
attenuate it. For large wavenumbers, the instability is damped by diffusive processes. For small wavenumbers, it is absorbed by the effect of gravity. For zero amplitude of the excitation velocity, the acoustic instability corresponds to the Darrieus–Landau planar instability. Most notably, for increased values of the cyclic velocity [3], the acoustic instability has the remarkable capability to stabilize the Darrieus–Landau instability. The acoustic instability may evolve, for an enhanced acoustic perturbation, into the parametric one. In this case, the growth rate of the instability is generally superior to that of the acoustic case. Significantly, the cellular structures of the flame oscillate with a frequency which is half that of the acoustic one. This fact was recognized by Markstein as the typical signal of the Kapitsa parametrically damped pendulum, and consequently, decided to name this kind of instability as parametric. Reactive gaseous mixtures can be classified in two groups [4] considering whether transition between the acoustic and the parametric instability is possible. If for some ranges of the amplitude of the acoustic perturbation (see later stability graphs), the flame results to be instable for the both instabilities, transition of regimes may happen meaning that the acoustic instability may transform spontaneously into the parametric one. If the flame is unstable when suffering an acoustic perturbation but the domains of
E-mail address: [email protected] (J. Yanez). http://dx.doi.org/10.1016/j.combustflame.2015.04.004 0010-2180/Ó 2015 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
instability of the acoustic and the parametric instability do not superimpose, the acoustic instability tends to suppress the Darrieus–Landau instability, the parametric instability regime is never reached spontaneously and consequently, planar flame fronts are surprisingly stable as long as the periodic oscillating velocity source exists. These two different propagation regimes have been confirmed by the observations of Searby [2] and Aldredge and Killingsworth [5] who performed experiments with downwards propagating flames inside a cylindrical and annular burner respectively. In those devices, it was found that the flame propagation could be classified in four consecutive stages. Promptly after ignition, the surface of the flame wrinkles due to the Darrieus–Landau and the thermo-diffusive instability. As the flame propagates further, sound starts to be generated. Due to the acoustic instability, these acoustic waves cause an attenuation of flame wrinkles. This attenuation may develop further, even as far as to cause the suppression of the Darrieus–Landau instability. In this stage, the flame becomes planar although its position is oscillating in space with the frequency of the acoustic perturbation. Depending on whether the parametric and the acoustic instability coexist or not, the parametric instability may now develop. This will produce a significant flame acceleration and the appearance of large organized pulsating cellular structures. If they do, the final stage of development is characterized by the transformation of those coherent cellular structures into incoherent flame surface fluctuations. Therefore, gaseous mixtures prone to the parametric instability may suffer, in closed chambers, a very significant acceleration of the flame propagation velocity. Especially in the case of lean mixtures, this increase of the combustion rate can be very considerable. The objective of the present work is to describe the data experimentally obtained by the authors on acoustic parametric instabilities for hydrogen–air mixtures, in a similar way as was done in [2,5] for hydrocarbons. Our study is focused on very lean mixtures that most notably have Lewis numbers smaller than one and negative Markstein numbers. Also, the interpretation of these data utilizing the theoretical findings presented in [6,7] will be presented. An evaluation of the critical conditions for flame instability and the subsequent flame acceleration will also be performed. Additionally, an experimental investigation will be performed on the effect of an external acoustic generator on the flame behavior with a comparison against the theory. To do so this paper is organized as follows. In Section 2 we present the experimental facility, the conditions in which the test were carried out and the results of the experiments performed. In Section 3 we perform the theoretical analysis of the stability of the flame in the same conditions in which the experiments were performed and we subsequently reinterpret the experimental results.
2. Experiments 2.1. Experimental setup A series of combustion experiments with hydrogen–air mixtures was performed in order to study the flame behavior and evaluate critical conditions for the onset of the acoustic-parametric instability. The experiments were carried out in a vertical square channel with a cross-section of 100 100 mm, see Fig. 1. The height of the channel was 1.2 m. The ignition end of the duct was kept open while the opposite end was closed. The channel was constructed by mounting glass windows on two opposing sides of the tube, allowing a visualization of the flame over the whole length of the channel. The conduit was kept entirely clear of any kind of roughness or obstacles, susceptible to alter the propagation of the flame.
2831
Fig. 1. Side view of the conduit utilized to perform the flame instability experiments: (1) open end; (2) metal cover; (3) ignition device; (4) glass window; (5) metal side wall; (6) flanges; (8) pressure sensor; (2) massive base plate.
Premixed lean hydrogen–air mixtures with hydrogen concentration in the range of 8–15 vol.% H2 with a negative Markstein number were used as test mixtures. The initial temperature and pressure conditions correspond to ambient conditions. The main thermodynamic properties of the test mixtures were calculated using the CANTERA code [8] and are summarized in Table 1. The mixtures were prepared using mass flow controllers with an accuracy of ±0.1%H2 (abs.). The ignition of the gaseous mixtures was carried out by utilizing a glow plug device (hot wire). The ignition location was placed on the centerline at the upper or bottom end of the channel, so that the propagation of the flame proceeded in downward or upward direction. Ignition in the upper position aims at the mitigating the effects of the Rayleigh–Taylor instability, which may introduce additional undesired oscillations and perturbations in the system. A high speed camera combined with a Schlieren system was used for the visualization of the flame front. A standard Z-shape Schlieren system consisting of a light source, two mirrors and a camera (Photron type, up to 200,000 fps) was utilized. This technique allows for the capturing of density changes along the full width of the channel over a length of 30 cm and thus enabled the propagation of the flame with an enhanced accuracy to be resolved. As a general remark for this technique, it is noteworthy that the areas in which a positive density gradient exists, will appear brightened. Consequently, areas appearing as darkened will represent negative gradients of density. Acoustic and pressure oscillations of the flame will be registered by a fast pressure transducer of the 103a series produced by the PCB Piezotronics
2832
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Table 1 Main thermodynamic properties of test mixtures. Hydrogen concentration %H2
Sound speed in reactants cr (m/s)
Adiabatic combustion temperature Tc (K)
Sound speed in products cp (m/s)
Expansion ratio H
Laminar velocity UL (m/s)
8 9 10 10.5 11 12 13 14 15
347 359 361 362 363 365 367 368 370
939 1016 1093 1131 1169 1244 1319 1393 1466
612 636 659 670 682 703 724 745 765
3.08 3.31 3.54 3.66 3.77 3.99 4.21 4.42 4.63
0.07 0.09 0.11 0.13 0.15 0.19 0.23 0.28 0.35
company with a resonant frequency of above 500 kHz. Additionally, and in order to disturb the flame propagation, a poly-chromatic sound generator, similar to a ‘‘horn’’, with a dominant frequency of about 1 kHz was utilized in the tests.
the length of the channel, c being the speed of sound in reactants, and n = 1, 2, 3, ... being the resonance nodes. Similarly, the
2.2. Experimental results A sequence of shadow flame images is shown in Fig. 2. After the mixture was ignited at the top axial position, the flame developed initially as a typical tubular flame propagating preferentially along the channel walls, with a Lewis number Le 0.35. The flame propagated with a distinctive cellularity with a characteristic cell size of about 1–2 cm due to the thermo-diffusive instability. After this initial stage, the tongue of the flame started to propagate along a lateral wall with a significant increase of the total surface of the flame. This leads to the augmentation of the transversal flame velocity with the formation of a planar flame structure across the channel. This phenomenon appeared customarily in the second part of the tube, as happened in [2,5], with the difference that, in these papers, oscillations of the flame were mainly governed by Darrieus–Landau instability without an effect of thermo-diffusion instability. Subsequently, the flame started to generate noise and the flame surface started to oscillate. The oscillations were noticeable in the transversal direction but much more significant in the longitudinal direction. The amplitude of oscillations reached several centimeters. The very wrinkled flame structure due to the thermo-diffusion instability transforms from a wedge to almost a planar oscillating flame front after traveling a half of the channel. The characteristic cell size decreases several times during this process. A typical sequence of shadow images of the flame shape is shown in Fig. 2. Independently from the optical thickness of the object, the Schlieren images (Fig. 2) allow to resolve the cellular flame structure and general flame behavior, such as the oscillating flame movement. The flow ahead of the flame appears completely laminar except for the area in vicinity of the flame surface and within the amplitude of the flame oscillations (up to 3 cm). Since the boundary layer is not yet developed after ignition in such a smooth channel, the turbulence cannot appear within the kernel of the channel. The effective Reynolds number is Re = ul/m = 600–2000, corresponding to a laminar flow. For an unsteady flow, such as the one studied herein, the Reynolds number is governed by the flow velocity u 1 m/s, the amplitude of acoustic perturbations l = 1–3 cm and the viscosity m 2 105 m2/s, meaning that the flame structure and flame oscillations are only controlled by self flame instability. For hydrogen concentrations of 10–14 vol.%, the pressure registered simultaneously by the transducers installed at the bottom of the channel is shown in Fig. 3. The maximum amplitude of acoustic oscillations lies in the range of 2–3 kPa with a frequency in the range of f = 100–150 Hz. Such values correspond to the resonance frequency derived for semi-open channel f ¼ nc=ð2LÞ, with L being
Fig. 2. Sequence of Schlieren photographs (4000 fps, every 10th frame is shown). The cuts are taken in the middle part of the channel (30–60 cm from the ignition point). The frame used to capture the leading front trajectory is shown in red. The width of the channel is 10 cm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
2833
Fig. 3. Measured pressure signals for different hydrogen–air mixtures: (a) 10% vol. H2, (b) 10.5% vol. H2, (c) 11% vol. H2, (d) 12% vol. H2, (e) 13% vol. H2, (f) 14% vol. H2.
maximum amplitude of the acoustic oscillations corresponding to a 9% hydrogen concentration in air was about 0.5 kPa with a frequency of about 100 Hz: The spectral analysis of the pressure signals yielded the results shown in Fig. 4. A very clear resonance appears in the range of 100–150 Hz for concentrations of 10–13% vol H2. The spectral analysis of the initial part of the signal, prior to the starting of the oscillations, shows a flat spectrum with no significant peaks around 10 kPa. The only mixture which resulted in a stable flame propagation, 14% vol. H2, has a much less pronounced peak in the range of 170 Hz and exhibited a much different nature than the other tested mixtures. To obtain a time–distance diagram, the video frames containing the propagation of the flame were post-processed. Certainly, in order to receive a high quality representation, a high speed Schlieren video technique (4000 frames per second) was utilized. A 2–3 pixels narrow stripe of each video frame with the flame position in the center (shown in red in Fig. 2) was placed one by one in the horizontal direction (see Fig. 5). In this figure, the horizontal direction is the time scale and the vertical direction corresponds to the flame position along the vertical axis of the channel. Such
a procedure represents the flame dynamics in a longitudinal direction in the center of the channel captured by the red stripe. The position of the stripe is not of great importance since longitudinal oscillations occur for the flame surface within a whole cross-section of the channel. All parts of the flame surface axially oscillate with the same amplitude and frequency. As an example, the evolution of the flame position in 12% H2–air mixture has been evaluated and is plotted in Fig. 5. The flame propagates downwards in the direction of increasing S (see the picture). The longitudinal oscillations appear around 1–2.5 s after ignition. It corresponds to the distance 70 cm from ignition point. A detailed plot of the flame propagation in 12% vol. H2 is depicted in Fig. 6. For clarity the zero point for time and position was set to the instant in which oscillations started to appear. The analysis of the signal reveals that the oscillations appearing in the readings have a frequency of 65.2 Hz, that is, half of the frequency of the perturbation which is a clear indication that the oscillations are due to the parametric instability. The maximum amplitude of the longitudinal oscillations was measured to be in the range of ±(1–3.5) cm, relative to the mean flame position, resulting in a total amplitude up to 7 cm. Subsequent to the
2834
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Fig. 4. Spectrum of the measured pressure signals: (a) 10% vol. H2, (b) 10.5% vol. H2, (c) 11% vol. H2, (d) 12% vol. H2, (e) 13% vol. H2, (f) 14% vol. H2.
Fig. 5. Position of the flame along a vertical axis for the mixture of 12% vol H2. Ignition at the top. Time and distance along horizontal and vertical directions respectively.
appearance of acoustic oscillations, the average flame velocity significantly increases from 0.4 to 1.6 m/s, with a velocity of the longitudinal perturbations ua changing from 1.3 to 4.9 m/s or in terms of laminar flame speed Ua/SL 6–23. This corresponds to an acoustic intensity of 170 dB. In papers [6,7], the ‘‘stability’’ domain for lean hydrogen–air mixtures with negative Markstein number (Ma < 0) was
quantitatively evaluated. It was found to be a frequency of above 400 Hz which governed the stable flame propagation regime. It is supposed that the use of an external source of acoustic oscillations, such as a ‘‘horn’’, with a dominant frequency of about 1000 Hz may significantly change the flame structure and its behavior. The suppression of longitudinal flame oscillations due to the external noise produced by a ‘‘horn’’ with a frequency f 1000 Hz can be seen to
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
2835
Fig. 6. Positions and average velocity of the flame for 12% vol. H2 experiment. For clarity, the origin of coordinates for time and space was selected as the instant in which oscillations appear for the first time.
happen around 1.7 s after the ignition (see Fig. 7), which corresponds to the moment when the ‘‘horn’’ starts to operate. The external noise leads to the attenuation of the amplitude of the flame oscillations in 4–6 times. The average flame velocity also decreases by a factor of 4. Consequently, the cellular structure of the flame changes dramatically. The flame is visually stabilized. From a highly wrinkled surface it is transformed until it reaches a virtually smooth planar structure (see Fig. 8). Figure 9 demonstrates that continuous external acoustic perturbations of 1000 Hz fully suppress own acoustic oscillations of the flame and lead to very smooth and slower flame propagation. The experiment confirmed that an oscillating flame with a reduced flame propagation velocity could be stabilized by an external acoustic generator with a frequency above the stability limit. 3. Analysis 3.1. Analytical considerations The mathematical treatment of acoustic and parametric instabilities is based on the work of Pelce and Clavin [9]. These authors obtained an equation for a perturbed flame front in a gravitational field under the assumptions of high activation energy and large scale wrinkling. Based on these results, Searby and Rochwerger [4] derived an expression for the growth rate of the acoustic and the parametric instability and were able to calculate the stability limits for both cases numerically. This problem with respect to H2–air systems was also analyzed in [7]. For the sake of completeness and understandability, we will include here the Eqs. 1–7 (already appearing in [7], see this reference for details) that will be applied later for the particular conditions of this study and to compare with previous analysis [7]. Suppose the flame front is represented by the function F(x, t) = 0 in a reference frame moving with the flame front. Then, this surface
Fig. 8. Flame structure before (left) and after (right) the application of the external noise (9% H2–air).
divides the calculation domain in two regions: F(x, t) < 0 for the reactants, and F(x, t) > 0 for the products. Small perturbations can be considered in the form F(x, t) = F(t)exp(ikx). Considering the linear stability problem, the second order differential Eq. (1) describes the evolution of the flame surface perturbations of small amplitude, considering periodic monochromatic velocity fluctuations normal to the flame front 2
A
d F dt
2
þ U L kB
dF 2 þ kg a C 1 F kxU a cosðxtÞC 1 F þ U 2L k C 2 F ¼ 0: dt
ð1Þ
Fig. 7. Longitudinal flame oscillations for the 10% H2 experiment. Time and distance along horizontal and vertical directions respectively. The white arrow indicates the moment when the strong external noise was turned on and subsequently started affecting the flame propagation.
2836
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Fig. 9. Flame propagation without (a) and with (b) the application of the external noise (9% H2–air). The interface between dark and light parts corresponds to flame position.
In this equation, A, B, C1, C2, are dimensionless coefficients which take the form,
h1 h 2h A¼ 1þ kL Ma J ; B¼ ð1 þ hkLðMa JÞÞ ; hþ1 h1 hþ1 ð2Þ C1 ¼
h1 Jh ; 1 kL Ma hþ1 h1
ð3Þ
h1 kL C2 ¼ h 1 þ ðð3h 1ÞMa 2Jh þ 2Prhb ðh 1Þ Ið2Pr 1ÞÞ : hþ1 h1 ð4Þ
where Ul is the laminar burning velocity, k is the wavenumber, ga is the constant part of the acceleration, x is the circular frequency, Ua the amplitude of the acoustic perturbation, L is the thickness of the flame and h the expansion ratio. Those coefficients depend on the simple one-step Arrhenius reaction parameters of the flame,
c ¼ ðqu qb Þ=qu ; hð#Þ ¼
# ¼ ðT T u Þ=ðT b T u Þ; ¼
kð#ÞC Pu ku Cð#Þ
qð#Þvð#Þ ; q u vu
ð5Þ
where the u and b subscripts refer to unburned and burned gas respectively, k is the thermal conductivity and v the thermal diffusivity. The Markstein number Ma considered is derived from the definition of Pelce and Clavin [9],
Ma ¼
J
1 ZeðLe 1Þ c 2
Z
1
0
hð#Þlnð#Þ d#; 1 þ #c=ð1 cÞ
ð6Þ
where Ze is the Zeldovich number and Le the Lewis number. The integrals are defined as H¼
Z
1
ðhb hð#ÞÞd#; J ¼ 0
c 1c
Z 0
1
hð#Þ d#; I ¼ ðh 1Þ 1 þ #c=ð1 cÞ
Z
In this paper, the solutions of Eq. (1) will not be treated here since this has been the purpose of paper [7]. The results given there will be used to obtain the stability graphs and analyze current experiments. Nevertheless, it is pertinent to recall that the solution of (1) involves, after some algebra, the resolution of the Mathieu differential equation [11–14] which is responsible for the intricate pattern that the domain of stability displays in the graphs presented hereafter. Eqs. 1–7 must be particularized for the H2–air mixtures and the conditions utilized in the experiments. This requires the finding of molecular transport coefficients, thermodynamic data, activation energy, etc. for every fuel concentration. In this respect, the molecular transport coefficients were obtained utilizing the kinetic theory of gases [15], the thermodynamic data were acquired using the JANAF tables [16] and the Lewis number of the mixture was calculated by means of the formulation proposed by Sun and coworkers [10]. Special care was taken when calculating the overall activation energy. The detailed chemistry scheme of Lutz [17] was coupled with the computer program Cantera [8], thus obtaining the induction time of the analyzed mixtures. This magnitude was then utilized to derive the overall activation energy. The circular frequency of the acoustic perturbation x was found from the analysis of the results obtained in the experiments, see Table 2. Indeed, the interaction of a flame with reflected waves inside a closed volume will depend on the dimensions of the vessel considered. For an open tube, the acoustic resonance frequency can be described approximately by the equation f ¼ nc=ð2LÞ in which c is the speed of sound in the media and n and L are the mode number and the length of the tube. For the channel considered herein, the previous equation particularized for n = 1 yields a resonance frequency of f 150 Hz, which is very close to the registered value. As a result, this value can be considered as the first longitudinal harmonic. 3.2. Results of the analysis
1
hð#Þd#;
0
ð7Þ
A simplification in Eq. (7) may help to understand the meaning of the concept of stability. In the case ga = 0 and Ua = 0, the temporal part of the solution of Eq. (1) has the form F(t) = Y exp(rt) being Y constant. As a result, the planar flame front will be stable with respect to perturbations for all growth rates fulfilling Re(r) < 0 and will be unstable otherwise. In the more complex case under study, the solution is more complicated, see [10,4], nonetheless the concept remains.
Figure 10 contains the results of the application of the method considering a sound excitation with the same frequency that was measured (see Table 2) for the fuel concentrations of 10, 10.5, 11, 12, 13 and 14% vol. H2 at normal conditions. The diagrams represent the growth rate of the instabilities for different combinations of flame surface wavenumbers k (abscissa) and reduced velocities of the excitation Ua/Sl (ordinate). The stable regions, pairs (k, Ua/Sl) for which the growth rate r is less than or equal to 0, are plotted in violet. For clarity, black lines separate the violet stable regions from the unstable ones.
2837
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839 Table 2 Main properties of test mixtures and parameters of the acoustic perturbation measured in the experiments.
a
%H2
Ma (Ze)
Le
Ze
UL (m/s)
Measured frequency, fm (Hz)
Measured max. pressure oscillations (kPa)
9 10 10.5 11 12 13 14 15 20a 21a
2.0 1.8 1.7 1.6 1.39 1.17 0.97 0.8 0.1 0.02
0.34 0.34 0.34 0.34 0.35 0.35 0.36 0.36 0.39 0.39
5.15 4.99 4.89 4.78 4.59 4.41 4.25 4.09 3.46 3.35
0.09 0.11 0.13 0.15 0.19 0.23 0.28 0.35 0.9 1.04
100 110 122 121 130 145 170 – – –
0.5 2.0 2.2 3.1 3.1 1.9 0.4 0.4 – –
Not tested.
Fig. 10. Stability graphs for H2–air mixtures at normal conditions. From left to right and from top to bottom: (a) 10, (b) 10.5, (c) 11, (d) 12, (e) 13 and (f) 14 vol.% H2. Excitation frequencies are 110, 122, 121, 130, 145 and 170 Hz respectively.
In the derivation of the Eqs. 1–7 [9], it was supposed that the flame front was thin compared to the wavelength of the perturbed surface. Therefore, for the representation of the diagrams, the maximum of the abscissa was adjusted to consider a maximum cutoff wavenumber equivalent to one tenth of the wavenumber formed with the flame thickness, 2p/d. It is to be noted that each diagram has a different range for the abscissa.
In the plots of Fig. 10, the acoustic instability region is clearly identifiable in the bottom left corner of each diagram. The parametric instability region is visible in the upper and left areas of the plots. In comparison with the parametric instability, the acoustic instability shows a moderate growth rate that remains below 100 Hz. In contrast, in all diagrams, the first lobe of the parametric instability exhibits a much larger growth rate, close to 400 Hz.
2838
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
Fig. 11. Longitudinal flame oscillations for a 10 vol.% H2 experiment, re-interpreted with the theoretical considerations given in previous sections. The white arrow indicates the moment when strong external noise affects the flame.
Fig. 12. Stability graphs for a 10 vol.% H2–air mixture at normal conditions and an excitation frequency of 110 Hz corresponding to the auto excitation of the flame (left) and 1000 Hz corresponding to the major frequency of the horn (right).
All mixtures analyzed show a clear overlap in the acoustic excitation amplitudes between the acoustic and the parametric instability regions. This overlaps demonstrates that the spontaneous transition from the acoustic to the parametric region is possible. The tendency depicted in the diagrams shows a reduction of the overlap with increasing hydrogen concentration. The parametric instability appears to exist for all intensities of acoustic perturbation (full range of Ua/SL) for large wavenumbers. The possibility of the existence of such regions was already investigated in [6,7], identifying the range of wavenumbers in which these phenomena could occur. Due to the limits of this range, and due to the reasons previously mentioned, only the lower wavenumber border is visible in the diagrams. The wavenumbers limiting that range, klim = min(k0A, k0B), are (see Ref. [7])
k0 A ¼
k0 B ¼
h1 L 12 ZeðLe hþ1
R 1 hL 0
1 R 1 1Þ 0
;
1 hð#Þ 1þ#ðh1Þ
d# þ
ð8Þ
hð#Þlnð#Þ d# 1þ#ðh1Þ
1 ZeðLe 2
R 1 1Þ 0
:
hð#Þlnð#Þ d# 1þ#ðh1Þ
ð9Þ
The existence of such domains implies that the response of the flame to an acoustic excitation generated by the flame itself can trigger directly the parametric instability, without requiring any initial stage in which the acoustic instability occurs. 3.3. Re-interpretation of the experimental results The previous analysis allows for the re-interpretation of the spectra and positions of the registered signals shown in Figs. 4 and 6. In the analysis of Fig. 6 it was ascertained that the oscillatory component of the propagation only shows a 65 Hz component. In
the plots contained in Fig. 4, a clear resonance is shown around 120 Hz. The growth rate of the high wavenumber modes (2000 m1), represented in Fig. 10 (upper left plot) may have caused this behavior, in which the parametric instability was triggered directly without any intermediate acoustic phase. The difference of growth rates, significantly less than 100 Hz for the acoustic instability (range 0–700 m1), and 300–400 Hz for the parametric instability in the range above 2000 m1, suggest that even if the simultaneous excitation of the parametric and the acoustic instability is possible, only the parametric one may be detected in experiments. The effect of an external source of noise can be analyzed with regards to the theoretical stability diagrams and the experimental findings, observing Fig. 11. After the sound is applied, the propagation of the flame changes from a regime which is dominated by the parametric instability (65.2 Hz) to an area dominated by the acoustic instability (120 Hz). In the final stage, the instabilities are completely attenuated by the effect of the external noise, obtaining a flame which is not oscillating. The burning velocity of the propagating flame is consistently reduced in a very significant manner. This can be visually ascertained by comparing the propagation slopes in Fig. 11 for the areas dominated by the parametric instability, the acoustic or even the stable region. The significance of the noise generated by the ‘‘horn’’ for the stability of the flame can be more precisely evaluated by comparing the stability graphs corresponding to the same H2–air mixture before and after the application of the sound, Fig. 12. The noise neither alters the domain in which the acoustic instability is existing (bottom left) nor its growth rate. Nevertheless, it strongly decouples the parametric instability from the acoustic one. It shifts the domain of high growth rates corresponding to the parametric instability to the higher frequencies. Specifically, the lobe closer to the acoustic area completely disappears in the stability diagram
J. Yanez et al. / Combustion and Flame 162 (2015) 2830–2839
corresponding to the ‘‘horn’’ perturbation (Fig. 12, right). Therefore, our experiments may be considered as a validation of the theoretical model presented in [6,7].
2839
will suffer the acoustic instability. The experiments show good consistency with the theoretical model. Appendix A. Supplementary material
4. Summary In this paper, the experimental investigation of the influence of noise on the propagation of hydrogen–air flames in the range of 9– 14 vol.% H2 has been presented. The analysis of the influence of the noise spontaneously generated by the flame itself due to its own propagation shows that very significant resonance exists for mixtures between 9–13 vol.% H2 in the range 100–150 Hz. It appears nevertheless that the mixtures with 14 vol.% H2 or higher H2 concentrations seem to have a stable behavior and do not significantly react to the pulses generated by themselves. It was found that the measurements of the propagation of the flame contain an oscillatory component whose frequency is half that of the perturbation frequency. This constitutes an indication for the existence of the parametric instability. It was further observed that an external polychromatic sound generator with a dominant frequency of 1000 Hz suppressed the instabilities for all the tested mixtures, making the flame surface very smooth. Consistently, the external noise significantly reduces the amplitude of flame oscillations and leads to a reduction in the average flame propagation velocity. The theoretical analysis due to Searby and Rochwerger [4] was utilized to obtain the stability maps for the mixtures involved in the experiments. The diagrams of stability obtained, as well as the analysis of the experimental data, suggest that a direct excitation of the parametric instability is possible for a set of wavenumbers and any amplitude of the perturbation. This modus of instability growth may exclude an initial stage in which the flame
Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.combustflame. 2015.04.004. References [1] G.H. Markstein, Non-steady Flame Propagation, Pergamon Press, New York, 1964. [2] G. Searby, Combust. Sci. Technol. 81 (1992) 221–231. [3] P. Pelce, D. Rochwerger, J. Fluid Mech. 239 (1999) 293–307. [4] G. Searby, D. Rochwerger, J. Fluid Mech. 231 (1991) 529–543. [5] R.C. Aldredge, N.J. Killingsworth, Combust. Flame 137 (2004) 178–197. [6] J. Yanez, M. Kuznetsov, R. Redlinger, A. Kotchourko, A. Lelyakin, In: Proc. of the 4th International Conference on Hydrogen Safety (ICHS2011), September 12– 14, 2011, San Francisco, USA, paper 127, pp. 1–12. [7] J. Yanez, M. Kuznetsov, R. Redlinger, Combust. Flame 160 (2013) 2009–2016. [8] D.G. Goodwin, Cantera User’s Guide, California Institute of Technology, 2001. [9] P. Pelce, P. Clavin, J. Fluid Mech. 124 (1982) 219–237. [10] C.J. Sun, C.J. Sung, L. He, C.W. Law, Combust. Flame 118 (1999) 108–128. [11] M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Government Printing Office, Washington, D.C., 1972. [12] T. Jones, Mathieu’s equation solution and stability.