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Electrical probe diagnostics for the laminar flame quenching distance
Experimental Thermal and Fluid Science 34 (2010) 131–141
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Electrical probe diagnostics for the laminar flame quenching distance Maxime Karrer b,*, Marc Bellenoue a, Sergei Labuda a, Julien Sotton a, Maxime Makarov b a b
Laboratoire de Combustion et de Détonique, CNRS, 86961 Futuroscope Chasseneuil, France Renault Technocentre, 78288 Guyancourt Cedex, France
a r t i c l e
i n f o
Article history: Received 6 February 2009 Received in revised form 30 September 2009 Accepted 4 October 2009
Keywords: Electrical probe Quenching distance Premixed flame Laminar combustion
a b s t r a c t A simplified theory, previously developed for the general case of weakly ionized gas flow, is used to predict electrical probe response when the flame is quenched on the probe surface. This theory is based on the planar model of space charge sheaths around the measuring electrode. For the flame quenching case, by assuming that the sheath thickness is comparable with the thermal boundary layer thickness, probe current can be related to flame quenching distance. The theoretical assumptions made to obtain the analytical formulation of probe current were experimentally proved by using direct visualization and highfrequency PIV. The direct visualization method was also used to validate the results of flame quenching distance values obtained with electrical probe. The electrical probe diagnostics have been verified for both head-on and sidewall flame quenching regimes and for stoichiometric methane/air and propane/ air mixtures in a pressure range of 0.05–0.6 MPa. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Electrical probes have been used for many years to carry out some measurements on plasmas. Research on the ionization processes in combustion front is motivated by the attractive idea of using an electrical probe as a combustion diagnostic tool. Several studies [1] on the flame chemistry highlighted the production of electrically charged species on the flame front which can be considered as high pressure weakly ionized plasma. Inserting an electrical probe in the combustion zone could, in principle, yield information on the combustion process. Many works have investigated the different applications of an electrical probe as a diagnostic tool. The electrical probe can be used in flame plasma in order to measure ion concentration [2,3], temperature [4], ion mobility [5] and flame velocity [6]. In these studies different electrical and geometrical characteristics for probe were used. In particular the probe signal depends on the bias voltage and on the surface of the probe’s electrodes [7]. The electrode’s polarization can be either positive or negative with a DC or AC voltage [8,9]. Improving probe diagnostics systems requires adapting the probe’s design to the physical phenomenon studied. These different approaches in the use of electrical probes can lead to measure other combustion parameters such as flame–wall interaction characteristics. The
Abbreviations: HOQ, head-on quenching; SWQ, sidewall quenching. * Corresponding author. Address: Maxime Karrer LCD, UPR 9028, BP 40109 téléport 2, 1 avenue clément Ader, 86961 Futuroscope Chasseneuil Cedex, France. Tel.: +33 (0)5 49 49 81 82; fax: +33 (0)5 49 49 82 91. E-mail address: [email protected] (M. Karrer). 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.10.002
study of flame–wall interaction is very important for the understanding of near-wall combustion. As a matter of fact, it is known that in vicinity of the wall, flame quenching occurs because the heat losses become large enough to slow down the chemical reactions. Quenching phenomena implies that the flame slows down and stops propagating towards the wall. The minimal distance between the quenched flame and the wall is called the quenching distance, dq. This parameter, which is related to the wall heat flux [10], is one of the main characteristics of flame quenching. The study of flame quenching is still related to unsolved theoretical problems of ignition, optimization of combustion and reduction of the amount of unburned hydrocarbons. The existing near-wall combustion diagnostics like wall heat flux gauge measurements as well as near-wall optical visualization of flame front, are difficult to be implemented in the industrial scale due to their high cost, the technical complexity, or the limited range of use. Therefore it is relevant to develop new diagnostics based on a low cost electrical sensor such as probes. The aim of this study is to use the electrical probe for flame– wall interaction diagnostics. It is used to detect the ionization current within a thin layer which is located in the vicinity of the wall. In our geometrical configuration flame–probe interaction is very similar to flame–wall interaction. The Current Voltage Characteristic (CVC) of the probe located in the combustion chamber is affected by the phenomenon of flame quenching [11]. For the diagnostics of this phenomenon a low and negative bias voltage is used to collect positive ions in a local area. The advantage of this diagnostic relies on the fact that flame–wall interaction is analyzed through the time-resolved evolution of the probe current recorded.
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Nomenclature Cp e j k L m M N 0 N n P Re t T v V VBohm U UBias
v
specific heat at constant pressure electronic charge current density Boltzmann constant probe length mass relative mass normalized density concentration density pressure electric Reynolds number time temperature normalized velocity velocity Bohm velocity electric potential bias voltage normalized potential
In this work a simplified model of ion current is used, which must agree with the electrical probe’s measurement in order to estimate the quenching distance. Moreover, electrical probe diagnostics require no calibration to perform a quenching distance measurement. 2. Experimental setup and diagnostics Experiments are carried out in a combustion chamber fitted with glass windows which allows a single shot combustion of a quiescent premixed mixture (see Fig. 1). Ignition is performed by spark electrodes situated in a rectangular vessel 70 75 120 mm3. Side wall windows allow the observation of all the
Fig. 1. View of combustion chamber.
thickness free space permittivity scaled normal coordinate Debye length kDe ion mean-free-path ki l mobility r collisional cross section t thermal velocity Subscripts a adiabatic e electron f flame i ion in sheath edge q quenching u unburned mixture w wall 0 reference 1 free stream
d
e0 g
cross-sections in the combustion chamber. The electrical probe used for diagnostics is placed through a side-wall of the combustion chamber. In the present study, both types of single-wall interaction are investigated: head-on and sidewall interactions. The flame quenching geometry depends on the electrostatic probe’s relative position and the spark electrodes. For head-on interaction the ignition point is located at the symmetry axis of the probe at a distance of 2 cm. Due to this geometrical arrangement, the flame front propagates perpendicularly to the ionization probe’s surface, allowing the head-on quenching regime [10,11]. For sidewall interaction the probe is shifted in the spark electrodes’s symmetry plane. Then the flame front propagated tangentially to the probe surface. The ionization probe consists of two electrodes (see Fig. 2). A probe’s central electrode of 3 mm in diameter (cathode) used for the ion current’s measurements is inserted in a steel pipe (external probe electrode – anode) of 10 mm in external diameter. Electrodes are isolated by a 2 mm thick epoxy layer and placed flushing with the probe end surface. The external probe electrode is electrically connected to the combustion chamber body and is used to polarize the flame through antennas system [12]. Polarization antennas provide good electrical contact with the combustion
Fig. 2. Electrical probe (cross-section view).
M. Karrer et al. / Experimental Thermal and Fluid Science 34 (2010) 131–141
plasma and the flame potential, which remains constant in the whole flame, is close to the anode potential [7]. Thus, the voltage applied to the probe electrodes could be considered as Ubias. The geometry of the probe’s antennas was chosen not to affect the flame quenching in the measuring probe electrode zone. Visualization tests showed that the antennas length must be less than one third of the probe radius to avoid flame front disturbances. The antennas used were about 1 mm long and the diameter was less than 0.2 mm. Antennas extend inside the combustion chamber in about 0.5 mm. In our study the central probe electrode was biased negatively. Typically triangular pulses of 12 V in amplitude and with a frequency of 10 kHz were used to polarize the flame relatively to the measuring electrode. For this work, the frequency is sufficiently low for both ions and electrons to respond without an appreciable delay [13] to the bias voltage variations. A previous paper demonstrated [14] that at frequencies below the ion plasma frequency the ion current across the sheath is all the time in equilibrium with the applied voltage. To validate the working frequency of 10 kHz the ion transit times in sheath layer was estimated for moderate potentials. The current density in the sheath layer is supposed constant, and at the sheath edge the current density is given by:
j ¼ nf eV in
ð1Þ
where nf is the ion density in flame front, and Vin is the ion velocity at the sheath edge. By using the Bohm criterion an expression of the ion velocity at the sheath edge is proposed:
V in
sffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi kT f 2 ki and V Bohm ¼ ¼ V Bohm p kDe Mi
ð2Þ
The estimated ion transit time in the sheath layer is calculated by using some experimental results obtained with a stoichiometric methane–air mixture at atmospheric pressure during head-on quenching (see Table 1).The mean-free-path for ion in flames is given by:
8 l ki ¼ pffiffiffiffi 3 p e
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kT f M a 80:5 nm Na 2
ð3Þ
The Debye length is estimated:
kDe
sffiffiffiffiffiffiffiffiffiffiffiffi e0 kT f 27:3 lm ¼ n f e2
ð4Þ
Thus the ion velocity at sheath edge is:
V in
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ki kT f 28:1 m s1 ¼ p kDe Mi
ð5Þ
Ions enter the sheath with a velocity of Vin 28 m s1. The electrical field in the sheath region was calculated with Poisson equation: Table 1 Data for stoichiometric methane–air mixture. Experimental parameters
Range
Dielectric permittivity Boltzmann constant k Avogadro Air mass Electron mass Electron charge Ion a.m.u Ion mass Ion mobility Flame temperature Pressure Quenching distance
8.854 1012 F m1 1.38 1023 J K1 6.0221 1023 mol 0.028 kg mol1 9.109 1031 kg 1.6e19 C 50 a.m.u1.66 1027 kg 3 104 m2 V1s1 2500 K 1 bar 160 lm
133
Fig. 3. Characteristic time of current stabilization.
E¼
sffiffiffiffiffiffiffiffiffi 2jdq
li e0
9:375 104 V m1
ð6Þ
And by using the ion mobility li, the ion velocity under the effect of the electrical field was estimated:
V i ¼ li E 28 m s1
ð7Þ
By making the assumption that at first order the quenching zone corresponds to the electric sheath layer the ion transit characteristic time is about:
t¼
dq ¼ 5:7 ls Vi
ð8Þ
Evaluation shows that processes of current stabilization occur much faster than the characteristic time of CVC measurement. However measuring frequency is limited by the electronic device’s response time, which is used to amplify the ion current, and by the current stabilization’s characteristic time. The existence of parallel resistive and capacitive components of low frequency sheath impedance has been previously predicted and demonstrated [15,16]. Thus some experiments were performed to estimate the characteristic time of current stabilization related in particular to [7]. A square voltage is applied to the electrical probe. the term: @U @t By increasing the bias voltage, the space charges are collected by the electrode and a sheath layer is formed. Recording the current’s time evolution gives an estimation of the current stabilization’s characteristic time. In Fig. 3 the black stars correspond to the experimental evaluation of current stabilization time and the dotted line is the characteristic time of ion transit in the sheath layer estimated from Eq. (8). Actually, the characteristic time of current stabilization, s1, is about 20 ls whereas the characteristic time of flame quenching, s2, is about 100 ls [11]. With a pressure rise, the sheath’s relaxation times increase. Because s1s < s2, where s is the time of CVC recording, the sheath layer geometry and plasma around the probe are supposed to be stationary during the measurements. The CVC was recorded and used for reconstruction of flame position relative to the probe. To study flame–probe interaction, a coupling of experimental diagnostics is performed. The pressure is recorded with a piezoelectric transducer Kistler 601 and the direct photography method is used to detect the flame’s position in vicinity of the wall. Flame front images are recorded by a PHOTRON APX-RS 3000 camera supplied a HAMAMATSU C9548 model high-speed gated image intensifier. The camera has a resolution of 256 384 pixels and 1024 grey levels, which allows registration 20,000 images/s with an exposure time of 30 ls. A spatial resolution range of [5–14] lm/pixel is obtained due to the
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applied optical magnification. The procedure of image treatment to determine the flame position was described in a previous work [17] and we just follow the same treatment: the quenching distance is determined as the ‘‘dead space” between the flame front and the wall, and computed through image processing. The head of the luminous zone is associated with the appearance of excited radicals, mainly CH* and C2 , as a result of elementary reactions in the chemical zone of flame front [11]. The uncertainty of quenching distance measurement through the direct visualization method takes into account the standard deviation of each experimental dataset (statistical uncertainty) and the precision of image processing (physical uncertainty), which is of two pixels i.e. [10–28] lm [17]. The evolution of flow field was investigated during flame quenching by using a high-frequency PIV system. To study flame dynamics within the quenching zone, a high spatial resolution involving high optical magnification is necessary. An appropriate imaging system was used. It relies on a long-distance microscope Questar QM-1 which allows a study with 5 lm/pixel spatial resolution at a minimal working distance from the object of 56 cm. Questar QM-1 was coupled with a high-speed camera (Photron APX RS-3000) synchronized with a double-cavity laser (Pegasus, New wave research). The 5 kHz working frequency of PIV system allows a visualization window of 1023 360 pixels. Two types of seeding, vegetable oil and zirconium oxide particles were used. Vegetable oil seeding was used to achieve velocity measurement in fresh gases located within the quenching zone. For determination of gas velocity in flame front and burnt gases, seeding with zirconium oxide ZrO2 was used. The particles’ size is lower than 5 lm. To realize high spatial resolution measurements in vicinity of the wall the parasitic reflection of the surface was eliminated by orienting the illuminating laser sheet parallel to the wall. Another difficulty was the strong density gradients along the observation optical axis decreasing the quality of PIV results. This parasitic effect was significantly decreased by using a 10 mm thick rectangular obstacle inserted into the combustion chamber. So, the flame quenching and the corresponding velocity field were studied in vicinity of the obstacle’s surface. The velocity field was recorded at minimal distance 100 lm from the wall [18]. 3. Model Some probe theories were previously developed for the flow of a weakly ionized gas over a solid body at pressure of 0.1 MPa. The different papers will be quoted in this part. These works have demonstrated the relation between the electrical response of the probe and the flow characteristics. Thus, in the next part of this paper, we analyze the possibility of using these theories for the flame quenching study. It is relevant to explain that in the flame–wall interaction case, the ‘‘sheath” physics are different due to the presence of the thermal boundary layer between the flame front and the probe’s surface. In this paragraph, the theory for a weakly ionized gas flow is developed in order to simplify the theory’s understanding and to justify all the assumptions which are needed to apply this theory in our case. 3.1. Theory for a weakly ionized gas flow Lam proposed a general theory for the flow of weakly ionized gases about an arbitrary solid body with absorbing surfaces [19]. Lam theoretically proved that for high pressure flowing plasma, the ion current to the probe becomes a function of plasma velocity when the electric Reynolds number exceeds unity. He worked on a general theory for a thin sheath in flowing plasma. For this theory he made the assumption that the diffusion velocities of the ions and electrons due to any electrical field are small in comparison
with their thermal velocities. In this case Lam’s theory involves diffusion rather than convection dominated sheath then the current presents a true saturation with increasing bias voltage if the qffiffiffiffiffiffiffi e0 kT e
¼ parameter Re a2 1. Here Re ¼ lV11kTLe and a ¼ kDe L
ne e2
L
where
e
V 1 is the free stream flow velocity, l1 is the free stream ion mobility, L is the probe length, k is the Boltzmann’s constant, Te is the electron temperature, e is the electronic charge, and ne is the free stream electron density. Clements and Smy [20] have extended Lam’s general theory to cover the case of flowing continuum plasma in which the situation was demonstrated to depend on convection dominated sheath. For this case the conditions become Re a2 v2 1 where v is the normalbias where Ubias is the bias ized potential which is defined as: v ¼ eU kT e
voltage which is applied to the electric probe. In this condition no saturation current is obtained, and with the bias voltage rise the sheath increases in thickness and thus takes more ions. In this work the sheath is thin compared to the probe size but is thick compared to the boundary layer. Thus the theory developed by Clements and Smy for this case relies on Lam’s model derived with the following assumption: (i) The mean-free-path of the charged particles is very small and is much smaller than the thickness of the sheath adjacent to the probe surface. (ii) The characteristic length L of the problem is much larger 1 than kDe, which is the Debye length a ¼ kDe L 1, where U is the electric potential. (iii) v ¼ eU kT e V1L >1 (iv) Re is the electric Reynolds number equals: Re ¼ l =ðkT e =eÞ i
with V 1 V f where Vf is the undisturbed flame velocity (m/s) relative to the probe. The general equation obtained by Lam for ion density is:
Re ðv rNi Þ ¼ r2 Ni r ðNi rvÞ
ð9Þ
where Ni is the normalized ion density at any point (normalized to the undisturbed ion density ne1 ) and v is the local flow velocity at any point (normalized with V 1 ). By introducing a scaled normal coordinate g defined as: g ¼ yR1=2 and by neglecting all small terms, Lam’s obtained: e
@ 2 Ni @N i 1=2 @N i þ ¼ Re a2 Q v v R x y e @ g2 @x @g " # @ @v @2v @3v Q¼ þ @ g @ g @ g2 @ g3
2
ð10Þ
where x and y are boundary coordinates with x parallel to the probe surface and y normal to the probe surface, vx and vy are normalized flow velocity along x and y axes. Eq. (10) shows that the first term is order of oð1=g2 Þ and represents diffusion current, the second terms is order of oð1Þ and represents the convection current, and at last 2 2 the third term is of order o Re ag4v and represents the current of ion driven by the sheath electric fields. For Re a2 v2 1 the first term in Eq. (10) can be neglected and the current will be governed by convection and sheath effects. In addition if Re a2 < 1; Lam shows that all ions convected into the sheath are then driven by the electrical field to the probe, it is the sheath-convection regime. If v is large enough so that Re a2 v2 1 , the Eq. (9) becomes: Re ðv rN i Þ ¼ r ðN i rvÞ with r ðv N i Þ ¼ N i rV þ v rN i ¼ v rN i for incompressible flow. Thus Clements and Smy obtained:
r ðRe v Ni þ N i rvÞ ¼ 0
ð11Þ
M. Karrer et al. / Experimental Thermal and Fluid Science 34 (2010) 131–141
135
And by using this equation to an element of sheath situated at a distance y* from the electrode, they obtained:
dy u ne e ¼ ni eli E ¼ ji dx
ð12Þ
where Ji is the current density to the electrode surface at x and u* is the flow component parallel to the electrode surface at the sheath edge and ni is the ion density in sheath (see Fig. 4). By using Poisson equation: ni ¼ ðe0 =eÞð@E Þ, and the boundary @y condition of E = 0 and V = 0 at the sheath edge, the usual planar, mobility-dominated space charge equation is obtained:
j¼
9 8
li e0 U 2 y3
ð13Þ
These theoretical results are presented for the ion sheath which forms on a flat plate parallel to the stream direction of a slightly ionized gas. The boundary layer is assumed to be thin compared with the sheath and the solution Eq. (13) could be obtained in a simple algebraic form [20]. 3.2. Assumptions for the quenching phenomenon For our work, we study the flame quenching and the plasma– probe interaction. We work in the case of non-continuum flowing plasma and unsteady boundary conditions. In the case of flame– wall interaction the term of ‘‘sheath” is used to describe the area located between the flame and the ionization probe. One of the main objectives of this study is to use a simplified theoretical 1D model in order to obtain an equation relating current density to quenching distance. Thus, a simplified model of flame–wall interaction is used (see Fig. 5). The temperature profile in unburned gases is supposed to be linear, as a combination of flame propagation and heat conduction through a slab. According to previous studies [10], the wall surface temperature Tw is supposed to be constant and equal to the room’s temperature T0. At ignition, the unburned gases’ initial temperature Tu is the room’s temperature T0. During combustion, unburned gases are heated under the effect of compression which is assumed to be isentropic. During flame propagation in a constant volume chamber, flame temperature Tf increases, as shown in [21,22]; because flame quenching occurs much slower than CVC recording, we supposed that in the measurement zone, combustion occurs at almost constant pressure, and Tf is constant during the ionization current measurement. Previous studies have demonstrated that the chemi-ionization process occurs mainly in the flame front. Some of these works also proposed the ion profiles in flame [23]. Positive charges start occurring at the beginning of the reaction zone where temperature rises, then reach a maximum and disappear in the burnt-gas region. For this work the ion profile is simplified as proposed in Fig. 5 [24]. The ion profile is shown in this figure by a double dotted line. In their study Warnatz et al. [25] have shown that the concentration of ions varies dramatically across the flame front. For our
Fig. 5. Schematic view of simplified flame–wall interaction.
study we simplify the ion distribution within the flame front. We suppose a step distribution of charged species across the flame front. According to Bell et al. [26] we also suppose that in this zone ion concentration is relatively low and varies insignificantly. Flame quenching may be due to three phenomenons:
Radical adsorption.
Flame stretch.
Thermal heat losses. Popp and Baum [27] have studied the interaction of a premixed flame (methane–air) with an inert wall by taking into account the effects of thermal diffusion and adsorption of radicals by the wall. They showed that for wall temperature of 300 K, the effects of thermal diffusion and radical recombination near the wall are negligible. In our study the wall’s temperature did not exceed 320 K, so we can also consider the effect of radical recombination in vicinity of wall as a non-significant one. To study the effect of flame stretch on flame quenching we have to analyze the flame front geometry and the flame dynamic by using the PIV system. For the sidewall
Fig. 4. Schematic view of sheaths [19].
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Fig. 6. Picture of sidewall quenching with high optical magnification (5 lm/pixel).
Fig. 7. Velocity flow field for sidewall quenching.
configuration the flame propagates and quenches continuously along the obstacle (see Fig. 6). The post-treatment of direct visualization and ion current measurements shows that the ion current strongly increases when the reactive zone is located in front of the probe and is parallel to the electrode’s surface. An estimated value of near-wall flame front velocity was calculated by using direct visualization. The luminous zone located at 180 lm from the wall propagates at 1 m/s while the part of reactive zone located at 800 lm propagates at 2 m/s. These evaluations were validated by using PIV imaging system. A typical velocity field obtained with PIV system is given on Fig. 7. For these experiments, the pressure of interaction is less than 0.2 MPa and the quenching distance is about 180 lm. By using a specific post-processing method [28] for time-resolved PIV data dedicated to resolve near-wall gradient, the evolution of flow field related to the wall distance was calculated. Velocity fields are studied in the (x, y) plane; x is the spatial coordinate parallel to the probe surface and y is directed from the normal to the wall surface. Near-wall flow fields are characterized by spatial gradients of velocity and the mean flow field should be calculated as the sliding average of velocity over time as shown on Eq. (14):
P hViðx; y; tÞ ¼
t Vðx; y; tÞ
nt
ð14Þ
where nt is the number of velocity fields in the time windows. In our case, the time window is chosen as the characteristic time of flame– wall interaction (1 ms), and the evolution of parallel component Vx related to the wall distance is given in Fig. 8. Flame front velocity located at 180 lm from the wall surface is about 0.8 m/s which corresponds to the evaluation obtained from direct visualization. During sidewall quenching the flame propagates along the obstacle and the normal components of flow velocity are negligible in fresh gases and in flame front. The normal component of mean flow velocity represents the expansion of burned gases (see Fig. 8). The character-
Fig. 8. Mean flow velocity profiles in the area defined on Fig. 7 for sidewall interaction.
istic length of the thermal boundary layer is supposed to be constant during quenching phenomenon and the mean flow field is parallel to the electrode surface with a velocity of 1 m/s. The tangential strain rate defined by the tangential velocity’s gradient of fresh gases was estimated in the quenching zone:
jS ¼ rt ~ Vr ~ n
ð15Þ
~ V r is the fresh gases’ velocity associated to the contour of flame front, t is the tangential vector and n the normal vector of the flame front. In our experiments jS was about 1900 s1. The total flame strain j is defined as:
j ¼ jS þ jC
ð16Þ
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Fig. 9. Schematic view of simplified sidewall flame–probe interaction.
where jC is the stretch due to the curvature of the flame front. In the quenching zone, the flame stretch due to curvature 2Su/R is inferior to 32 s1 [10] which is negligible compared to the tangential strain rate. The total flame strain is about 2000 s1 and thus has an influence on the sidewall flame quenching [29]. In our study the quenching phenomenon is mainly due to thermal heat losses but the flame strain is not negligible for the sidewall interaction. In the case of head-on configuration, the mean flow field is directed towards the wall and the velocity component parallel to the electrode is negligible. There is no flame stretch, thus the head-on flame quenching is mainly due to thermal heat losses. The characteristic time of flame quenching is about 100 ls whereas the characteristic time of CVC recording is 50 ls and during quenching the flame is supposed to be stationary in direction of the electrode. The flame containing charged species is a good conductor and the electrode is another, thus together they act as a parallel plate capacitor with the thermal boundary layer as dielectric [8]. During flame quenching, the distance between the two plates of the capacitor is constant, thus the variation of current density is related to the resistive component of current which corresponds to the sheath-convection regime. An experimental evaluation of the sheath layer formation shows that it occurs much faster than the characteristic time of CVC measurement and flame quenching. In the case of the sidewall quenching, flame–probe interaction is very close to the case which was studied by Clements and Smy or De Boer and Johnson [30]. The simplified sidewall quenching geometry is depicted in Fig. 9. In this figure the flame propagates along the obstacle with a relative velocity of 1 m/s and is quenched at the distance dq from the probe’s surface. In the thermal boundary layer, the mean flow velocity of fresh gases is negligible. By using data from Table 2, a dimensional analysis of different parameters proposed by Lam’s theory is given for sidewall interaction. Under these conditions, the results correspond to the sheath-convection regime and the current depends on the previous formulation Eq. (13). Thus the final formulation is:
j¼
9 8
li e0 U 2 d3q
ð17Þ
By working on the current density’s derivative function, the current’s capacitive component can be neglected and the current’s evolution is directly related to (17). For the head-on quenching, the flame propagates towards the wall, and the flow parallel to the probe is negligible. In Fig. 10 a schematic drawing of the simplified head-on interaction is proposed. The flame stops propagating towards the wall at the minimal distance dq. In this case the negatively biased probe’s current is formed mainly due to the motion of positive ions to the probe’s surface and the electrons near the probe are repelled when the negative probe’s potential magnitude Ubias is sufficiently large: U bias kTe e .
Table 2 Ranges of various experimental and non dimensional parameters for sidewall quenching. Values Experimental parameters Flame velocity Ion density Probe size Mobility Ion temperature Debye length
1 m s1 1.62 1016 m3 2 103 m 1 104 m2 V1 s1 1500–2500 K 2 105 m
Non dimensional parameters
a ¼ hLe
102
Reynolds’s Number Normalized potential RE a2 v2 RE a2
250 40–80 40–160 102
Evaluations show that in our conditions the magnitude of bias voltage is sufficiently large (Ubias > 0.17 V) so that the electron density falls rapidly to zero in the quenching zone. For these conditions the probe’s current density is:
j ¼ ji þ je ji ¼ e ni li E
ð18Þ
The spatial distribution of the electrical field between two plates is given by Poisson’s equation in the following form:
@E e ðni ne Þ e ni j ¼ ¼ @x eo eo li eo E
ð19Þ
With the boundary condition of E = 0 and V = 0 at the sheath edge, we obtained the usual planar, mobility-dominated space charge equation again (cf Eq. (17)). Thus, the evolution of CVC with Ubias allows, in principle, the evaluation of quenching distance using Eq. (17) in both cases of sidewall or head-on quenching. It is worth mentioning that the choice of ion mobility value in Eq. (17) would be difficult. An expression for li proposed by Fialkov [31] is used:
li ¼
1 3 e 1 1 mþM 2 pkT 8rP 2 M m
ð20Þ
In order to calculate ion mobility, it is necessary to take into account compressing and cooling effects in the quenching zone. According to chemical studies of stoichiometric methane/air mixture [1], the dominant positive ions within the flame are H3O+, C2H3O+ and CH3+. These different ion’s mobility values are of the same order of magnitude. Moreover, (Eq. (20)) gives just an average of ion mobility. Thus, we take a mean value of the mobility of these different ions. The gas temperature used for calculation of ion mobility
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Fig. 10. Schematic view of simplified head-on flame–probe interaction.
was chosen to be the mean value between the gas temperature near the wall and the flame temperature [10,11].
Finally the ion mobility in the quenching zone is calculated for a pressure of 10 bars and for a temperature of 550 K:
3.3. Influence of model assumptions on results
l¼
In the following the effects of the different assumptions which have been made to develop the theoretical model are analyzed.
l ¼ 5:2 105 m2 V1 s1
(i) As explained in several studies [1] H3O+ is one of the dominant ions in flame for saturated hydrocarbon. Thus by using an equation proposed by Fialkov, the H3O+ mobility value was calculated. As it was shown in [32] the H3O+ mobility value is about 30% less than the corresponding value for C2H3O+. Our estimations show that for the same value of probe current, the variation of quenching distance by using the C2H3O+ mobility value or the H3O+ mobility value is less than 10%. Such precision is compatible with first-order estimations of quenching distance. (ii) Some experimental works have shown that C2H3O+ has the structure of an oxygen protonated ketene [CH2@C@OH]+. By using this approximation, the ion mobility within the quenching zone is calculated for a pressure of 10 bars and a temperature of 550 K [33]. The size of C2H3O+ is about 427 pm and N2 size about 145 pm. Thus the collisional elastic section is given by:
re p
2 427 þ 145 2:57 1015 cm2 2
ð21Þ
The relative mass is estimated:
M¼
M ion M N2 3:32 1023 g Mion þ M N2
ð22Þ
The polarizability of N2 aN2 is 1:7 1024 cm3 . The relative thermal velocity for a temperature of Tu 550 K in the boundary layer (under the assumption of isentropic compression of unburned gases) is:
t ¼ 1:45 10
4
sffiffiffiffi T
l
7:6 104 cm s1
ð23Þ
The collisionnal cross section is also deduced:
rtr 2:21p
sffiffiffiffiffiffiffiffiffiffiffiffi aN2 e2
lt
2:73 1012 cm2
ð24Þ
Under atmospheric pressure and for a temperature of 273 K the ion concentration is N0 = 5.69 1019 cm3. The calculated ion concentration in the boundary layer for a temperature of 500 K and under a pressure of 10 bars equals: N 0 2:85 1020 cm3 .
e Mt
¼
e MN0 rtr t
0:52 cm2 V1 s1
ð25Þ
By using Fialkov expression, the ion mobility is:
sffiffiffiffiffi
T P l ¼ l0 4:11 105 m2 V1 s1 T 0 P0 The difference is less than 20%. The ion mobility is well approximate with Fialkov’s expression by taking into account the compressing and cooling effects in the boundary layer. (iii) Ion temperature is the mean value between initial gas temperature just before flame–wall interaction and the adiabatic flame temperature. Another approach consists on using non-adiabatic flame temperature during quenching for calculation. This temperature could be estimated by using experimental values of wall heat flux during quenching. An equation relating flame temperature to wall heat flux was proposed in [34]:
T f ¼ T af
qloss
qu ShT f iC p
ð26Þ
where T af is the adiabatic temperature, qloss is the wall heat flux, qu is the unburned gases density, ShT f i is the laminar flame burning velocity, and C p is the heat capacity. The ion mobility calculated for both flame temperatures gives a variation on mobility values of about 7%. Since the effect of the dominant ion on mobility values is about 30%, it can be concluded that the first-order estimation of the quenching distance is not modified by the assumption made on the temperature. 3.4. Analysis of the ionization current during quenching It has been mentioned above that the probe current is a function of the inward or outward movement of the spatial charges at the sheath edge which depends on bias voltage. For small Ubias, the ion sheath’s edge is located in a low ion density region of the flame front. In our theoretical model the ion concentration is supposed to be constant within this area with the ion density defined by the spatial charge moving to the probe electrode in the electrical field created by the applied voltage. Thus, the probe current is related to the ion flux located in the sheath layer which is coincident at first order with the quenching zone. The typical probe CVC obtained during quenching phenomenon for a 0.26 MPa pressure, a 380 K unburned gas temperature and a 10 kHz Ubias frequency is shown
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139
Fig. 11. Relative variation of current density for stoichiometric methane–air mixture.
in Fig. 11. The theoretical model which was previously described allows the determination of the current density’s variation according to the difference of potential between probe and flame, Ubias and quenching distance. By varying the quenching distance’s value, which is a parameter of Eq. (17), the calculated derivative current densities related to the bias voltage are compared with the experimental values. The quenching distance’s value is also estimated by minimizing the gap between experimental CVC variation and theoretical CVC evolution calculated by Eq. (17). Numerical iterative processes is used for this application and for each quenching distance’s value the gap between an experimental and a theoretical curve is thus evaluated (see Fig. 11). 4. Results and discussion In order to validate the electrical probe technique, the results of quenching distance measurement obtained with the electrical probe were compared with those obtained by the direct visualization method. The comparison is carried out for head-on and sidewall flame quenching regimes and for methane/air and propane/ air mixtures. In Fig. 12, the values of quenching distance obtained with two methods for head-on quenching and for stoichiometric methane/ air and propane/air mixtures are shown. In this figure, as in Fig. 14, plotted values are the results of simultaneous measurements of quenching distance by both methods. Quenching distance values measured from probe CVC correlate reasonably to the estimated values of quenching distance obtained by the direct visualization method. It can be noticed that the evolution of the quenching distance related to pressure is the same for both methods, while the ionization probe values’ magnitude differs from the direct visualization method by 25% in worst case and for the same combustion shot. The experimental uncertainties may partially explain these slight differences between the results of the two methods. In fact, the measurement of the quenching distance by the direct visualization method has a number of limitations. For low pressures uncertainties depend on the low resolution of flame front images which are less bright. Whereas for high pressure the quenching distance becomes too small to be estimated optically. This explains the increasing difference between the results for pressures less than 0.1 MPa and higher than 0.3 MPa. In the case of probe measurement additional uncertainties may be introduced by the assumption of the theoretical model as explained in the previous part. The spatial and temporal resolutions of the electrical probe diagnostics depend on the frequency and the amplitude of
Fig. 12. Quenching distance related to pressure for stoichiometric mixtures in head-on configuration.
Fig. 13. Comparison of ionization diagnostic to previous data.
the bias voltage. For this work the choice of the polarization voltage was limited partially by the electronic device used for the probe current amplification. By increasing the spatial and temporal resolution of the electrical probe diagnostics, we can improve the accuracy of the method. In the pressure range of 0.1–0.3 MPa standard derivation of dq measurement is about the same for both methods independent to the mixture used and equaled about 12%. Values of dq calculated from the CVC correlate well with the
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Fig. 15. Comparison of quenching distance values deduced from ion current for both geometries and propane/air mixtures.
Fig. 14. Quenching distance related to pressure for stoichiometric mixtures in sidewall configuration.
results of the snapshot’s treatment within this pressure range. As one can see in Fig. 12, head-on quenching distance decreases monotonically with pressure rise. Within the pressure range of 0.1–0.5 MPa the quenching distance varies a little bit more for propane/air mixture (three times for C3H8/air mixture in contrast to 2.7 times for CH4/air one) that reasonably correlates with results of Vosen et al. [35]. It is worth noting that results of probe measurements give the quenching distance value (0.05 mm) in high pressure range P > 0.5 MPa where visualization methods do not work (see Fig. 12). The pressure evolution of laminar flame quenching distance obtained with the electrical probe technique is also compared with data of Boust et al. [10] obtained for the same experimental condition as ours (Fig. 13). Results presented in Fig. 13 correlate well. It is worth noting that the scatter of experimental results in [10] is about the same as for probe measurements. It allows the suggestion that the scatter of results is related to the flame nature. In Fig. 13 we have compared the results of quenching distance measurements by chemi-luminescence with and without the presence of the probe in the wall. Fig. 13 shows a good correlation of results obtained for flame quenching on the wall containing the ionization probe (points corresponding to ‘‘visualization”) and without the probe (points ‘‘Boust et al.”). It allows the suggestion that the ionization probe’s presence does not significantly change the quenching distance and the wall heat flux; although according to Sotton et al. [36] the quenching distance depends on the wall material.
In particular, it was found that at head-on flame quenching on ceramic the quenching distance value only decreases 20% in contrast to the one on steel wall, although the thermal conductivity of these materials differs about 50 times. The shape of the flame front quenched on the wall consisting of two different materials (for example, a metal and an insulator) and the probe’s minimal size needed to avoid its influence on the quenching distance measurements’ results, are other intrinsic questions. It is evident that the probe and the wall materials must have similar thermophysical characteristics to minimize the probe’s influence on the quenching phenomenon. Sotton et al. [36] have showed that in a case of wall consisting of steel and plastics the shape of flat flame front is affected by the different heat losses to the walls. It was found that for the pressure P = 0.1 MPa, at the flame quenching instant the length of flame front deformation (this length characterizes the size of flame’s zone influenced by the junction of different thermal conductivity materials) decreases to about 2 mm. Because in our tests the materials of probe’s electrode and wall are the same and the epoxy layer is less than 2 mm, the wall heat flux is supposed not to be influenced by the probe’s presence. This assumption was confirmed by our visualization tests. The comparison between the results of dq measurements obtained by the electrical probe and direct visualization in SWQ regime for C3H8/air and CH4/air mixtures is presented in Fig. 14. The difference between HOQ and SWQ regimes is related to the fact that for SWQ the flame moves parallel to the probe surface. Nevertheless, in this regime, similar to HOQ, the electrical sheath layer formation’s characteristic time is shorter than the flame quenching characteristic time, thus the flame is supposed to be stationary during probe measurements. Another difference between both interactions is the flame stretch. The flame stretch tends to zero in head-on configuration [37], whereas it takes finite values in sidewall configuration (2000 s1), due to gas dynamics. In the case of the head-on quenching, the results of PIV study show that flame quenching is driven mainly by thermal losses which prevail over flame stretch effects. However in the sidewall interaction case, the flame stretch has an influence on the flame quenching. As for HOQ, the quenching distance’s values measured by the probe are in good correlation with the direct visualization’s results. The scatter of experimental data of dq obtained with two methods is about the same and reasonably higher than for HOQ regime that is related with possible influence of hydrodynamics and flame stretching effects in the quenching zone on the flame quenching process. The quenching distance probe measurement results for
M. Karrer et al. / Experimental Thermal and Fluid Science 34 (2010) 131–141
propane/air mixture in HOQ and SWQ regimes are summarized in Fig. 15. Values of dq for this mixture are less for both regimes in contrast to methane/air mixture. Similar to results of Sotton et al. [11] quenching distance in HOQ regime is less by a factor 1.3–1.4 than that for SWQ in the pressure range 0.1–0.0.25 MPa and by factor 1.6 for higher pressure. The results obtained show that the quenching distance could be obtained with a probe technique. Moreover, Eq. (17) allows the estimation of ion mobility within the sheath layer. For the pressure range 0.05–0.25 MPa the value of li varies between 5.7 104 and 3.9 104 m2/(s V). The mean value of ion concentration in quenched flame could be obtained from Eq. (17) under the suggestion that E = Ubias/dq. It was found that ni rises from 2.2 1016 m3 to 4.3 1016 m3 when pressure increases from 0.07 to 0.24 MPa. 5. Conclusion A simplified analysis of probe CVC shows that one of the main parameters of flame/wall interaction – flame quenching distance dq – can be evaluated through the time-resolved measurements of probe CVC that is the main result of this work. A diagnostics method was validated in the cases of head-on quenching as well as sidewall quenching and in a pressure range of [0.05–0.6 MPa]. In this study a simplified model of ion current in the quenching zone was used. This model actually gives the relation between ion current density, bias voltage and quenching distance. This formulation depends also on the ion mobility values. Probe current formulation is used to estimate the quenching distance from the probe CVC. The simultaneous measurement of the quenching distance by using electrostatic probe method and the direct visualization were carried out with both methane/air and propane/air mixtures. In each case, this diagnostic method was verified. Due to the fact that optical diagnosis does not allow the determination of the quenching distance for high pressure, the method has been verified for a limited pressure range. Another method must be used to compare with the results of probe diagnosis for higher pressure. In particular a thermal formulation that describes the relation between quenching distance and maximal heat flux was presented in a previous work [10]. This relation takes into account the effects of pressure and mixtures. Simultaneous measurements of ion current and wall heat flux might possibly be used to validate the probe technique for higher pressure. For our work, modeling the ion current measured by electrical probe is crucial in order to identify the physical parameters of combustion process which can be estimated with the probe current–voltage characteristic. Acknowledgements The authors are grateful to A. Ahmed, A. Agneray, A. Claverie and B. Ruttun for their collaboration for this work. References [1] J. Prager, U. Riedel, J. Warnatz, Modelling in chemistry and charged species diffusion in lean methane–oxygen flames, Proc. Combust. Inst. 31 (2007) 1129–1137. [2] J.M. Goodings, J. Guo, A.N. Hayhurst, S.G. Taylor, A simple method for measuring ion concentrations in flames and the calibration of a nebulizer/ atomizer, Combust. Flame 133 (2003) 335–343. [3] R. Carabetta, R.P Porter, Absolute positive-ion concentration measurements in flames with Langmuir probes, in: 12th Symposium of Combustion, 1969.
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[4] C.S. MAcLatchy, J.R. Miner, A Langmuir probe technique for measuring temperatures in a flame plasma, J. Phys. 55 (1977) 27. [5] M.S. Benilov, Can the temperature of electrons in a high-pressure plasma be determined by means of an electrostatic probe, J. Phys. D: Appl. Phys. 33 (2000) 1683–1696. [6] C.S. MacLatchy, R. Didsbury, The Langmuir probe measurement of flow velocity in a flame plasma, J. Phys. 57 (1979) 381. [7] J.M. Rodrigues, A. Agneray, E. Domingues, X. Jaffrezic, P. Vervisch, Ionic current and flame electric potential measurements in a premixed laminar insulated flame, ECM 2005, Paper 45, 2005. [8] P.R. Smy, The alternating-current Langmuir probe in high-pressure flowing plasma, J. Phys. D: Appl. Phys. 7 (1974). [9] B.M. Oliver, R.M. Clements, P.R. Smy, The AC motion of the sheath edge in a flowing high-pressure plasma, J. Phys. D: Appl. Phys. 9 (1976). [10] B. Boust, J. Sotton, S.A. Labuda, M. Bellenoue, A thermal formulation for singlewall quenching of transient flame, Combust. Flame 149 (2007) 286. [11] J. Sotton, B. Boust, S. Labuda, M. Bellenoue, Head-on quenching of transient laminar flame: heat flux and quenching distance measurements, Combust. Sci. Technol. 177 (2005) 1305. [12] M. Bellenoue, J. Sotton, S. Labuda, M. Makarov, Dispositif de mesure du courant d’ionisation dans une chambre de combustion, patent FR 07-56270, 2007. [13] F.W. Crawford, R. Grard, Low frequency impedance characteristics of a Langmuir probe in a plasma, J. Appl. Phys. 37 (1966) 180. [14] R. Rosa, Ion transit time effects in the plasma sheath, J. Phys. A: Gen. Phys. 4 (1971). [15] K. Takayama, H. Ikegami, S. Miyasaki, Phys. Rev. Lett. 5 (1960) 238. [16] R.F. Mlodnosky, O.K. Garriott, in: Proceedings of the International Conference on the Ionosphere, London, 1962. [17] M. Bellenoue, T. Kageyama, S. Labuda, J. Sotton, Direct measurement of laminar flame quenching distance in a closed vessel, Exp. Therm. Fluid Sci. 27 (2003) 323–331. [18] M. Karrer, S. Labuda, J. Sotton, A. Claverie, M. Bellenoue, Système de vélocimétrie par image de particules (PIV) à haute fréquence et très haute résolution optique pour l’étude du phénomène de coincement de flamme, 11th CFTL, Futuroscope, 2008. [19] S.H. Lam, A general theory for the flow of weakly ionized gases, AIAA J. 2 (1964) 256. [20] R.M. Clements, P.R. Smy, Sheath-convection effects with flush-mounted electrostatic probe, Can. J. Phys. 49 (1971) 2540–2546. [21] T. Suzuki, K. Uchida, Y. Oguri, M. Yoshida, SAE Technical Paper 2004-01-1761, 2004. [22] M. Jennings, T. Morel, SAE Technical Paper 910459, 1991, pp. 641–656. [23] J. Prager, U. Riedel, J. Warnatz, On the importance of negative ion, diffusion model, and temperature for charged-species profiles in premixed lean flames, in: Third European Combustion Meeting ECM 2007, 2007. [24] P.R. Smy, The use of Langmuir probes in the study of high pressure plasmas, Adv. Phys. 25 (5) (1976) 517–553. [25] J. Warnatz, J. Prager, U. Riedel, Modeling ion chemistry and charged species diffusion in lean methane–oxygen flames, Proc. Combust. Inst. 31 (2007) 1129–1137. [26] J.C. Bell, D. Bradley, L.F. Jesch, Chemi-ionization, chemiluminescence, and electron energy exchange in hydrocarbon air flames, Proc. Combust. Inst. 13 (1971). [27] P. Popp, M. Baum, SAE Paper, 952387, 1995, Comb. Flame, 108, (1997) 327– 348. [28] B. Boust, PhD Thesis, University of Poitiers, 2006. [29] D. Bradley, P.H. Gaskell, X.J. Gu, Burning velocity, Markstein lengths, and flame quenching for spherical methane–air flames: a computational study, Combust. Flame 104 (1996) 176–198. [30] P.C.T. De Boer, R.A. Johnson, Theory of flat-plate ion density probe, Phys. Fluids 11 (1968) 909–911. [31] A.B. Fialkov, Investigations of ions in flames, Prog. Energy Combust. Sci. 23 (1997) 399. [32] A. Cenian, A. Chernukho, Modelling of Langmuir probe interactions with combustion plasma: dependence on ion composition, in: International Workshop ‘‘Non Equilibrium Processes in Combustion and Plasma Based Technologies”, Minsk, Belarus, 2006. [33] R. Weber, K. Levsen, Gaseous [C2H3O+] ions, Org. Mass Spectrom. 15 (3) (1980) 138–139. [34] M. Enomoto, Head-on quenching of a premixed flame on the single wall surface, JSME Int. J. 44 (4) (2001) 624–633. [35] S.R. Vosen, R. Greif, C.K. Westbrook, Unsteady heat transfer during laminar flame quenching, Proc. Combust. Inst. 20 (1984) 75–83. [36] J. Sotton, M. Bellenoue, S. Labuda, B. Ruttun, in: Seventh Triennal International Symposium on Fluid control, Measurement and Visualization – FLUCOME’03, Sorrento, Italia, 2003. [37] F. Foucher, Flame wall interaction: effect of stretch, Exp. Therm. Fluid Sci. 27 (2003) 431–437.
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Electrical probe diagnostics for the laminar flame quenching distance Maxime Karrer b,*, Marc Bellenoue a, Sergei Labuda a, Julien Sotton a, Maxime Makarov b a b
Laboratoire de Combustion et de Détonique, CNRS, 86961 Futuroscope Chasseneuil, France Renault Technocentre, 78288 Guyancourt Cedex, France
a r t i c l e
i n f o
Article history: Received 6 February 2009 Received in revised form 30 September 2009 Accepted 4 October 2009
Keywords: Electrical probe Quenching distance Premixed flame Laminar combustion
a b s t r a c t A simplified theory, previously developed for the general case of weakly ionized gas flow, is used to predict electrical probe response when the flame is quenched on the probe surface. This theory is based on the planar model of space charge sheaths around the measuring electrode. For the flame quenching case, by assuming that the sheath thickness is comparable with the thermal boundary layer thickness, probe current can be related to flame quenching distance. The theoretical assumptions made to obtain the analytical formulation of probe current were experimentally proved by using direct visualization and highfrequency PIV. The direct visualization method was also used to validate the results of flame quenching distance values obtained with electrical probe. The electrical probe diagnostics have been verified for both head-on and sidewall flame quenching regimes and for stoichiometric methane/air and propane/ air mixtures in a pressure range of 0.05–0.6 MPa. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Electrical probes have been used for many years to carry out some measurements on plasmas. Research on the ionization processes in combustion front is motivated by the attractive idea of using an electrical probe as a combustion diagnostic tool. Several studies [1] on the flame chemistry highlighted the production of electrically charged species on the flame front which can be considered as high pressure weakly ionized plasma. Inserting an electrical probe in the combustion zone could, in principle, yield information on the combustion process. Many works have investigated the different applications of an electrical probe as a diagnostic tool. The electrical probe can be used in flame plasma in order to measure ion concentration [2,3], temperature [4], ion mobility [5] and flame velocity [6]. In these studies different electrical and geometrical characteristics for probe were used. In particular the probe signal depends on the bias voltage and on the surface of the probe’s electrodes [7]. The electrode’s polarization can be either positive or negative with a DC or AC voltage [8,9]. Improving probe diagnostics systems requires adapting the probe’s design to the physical phenomenon studied. These different approaches in the use of electrical probes can lead to measure other combustion parameters such as flame–wall interaction characteristics. The
Abbreviations: HOQ, head-on quenching; SWQ, sidewall quenching. * Corresponding author. Address: Maxime Karrer LCD, UPR 9028, BP 40109 téléport 2, 1 avenue clément Ader, 86961 Futuroscope Chasseneuil Cedex, France. Tel.: +33 (0)5 49 49 81 82; fax: +33 (0)5 49 49 82 91. E-mail address: [email protected] (M. Karrer). 0894-1777/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2009.10.002
study of flame–wall interaction is very important for the understanding of near-wall combustion. As a matter of fact, it is known that in vicinity of the wall, flame quenching occurs because the heat losses become large enough to slow down the chemical reactions. Quenching phenomena implies that the flame slows down and stops propagating towards the wall. The minimal distance between the quenched flame and the wall is called the quenching distance, dq. This parameter, which is related to the wall heat flux [10], is one of the main characteristics of flame quenching. The study of flame quenching is still related to unsolved theoretical problems of ignition, optimization of combustion and reduction of the amount of unburned hydrocarbons. The existing near-wall combustion diagnostics like wall heat flux gauge measurements as well as near-wall optical visualization of flame front, are difficult to be implemented in the industrial scale due to their high cost, the technical complexity, or the limited range of use. Therefore it is relevant to develop new diagnostics based on a low cost electrical sensor such as probes. The aim of this study is to use the electrical probe for flame– wall interaction diagnostics. It is used to detect the ionization current within a thin layer which is located in the vicinity of the wall. In our geometrical configuration flame–probe interaction is very similar to flame–wall interaction. The Current Voltage Characteristic (CVC) of the probe located in the combustion chamber is affected by the phenomenon of flame quenching [11]. For the diagnostics of this phenomenon a low and negative bias voltage is used to collect positive ions in a local area. The advantage of this diagnostic relies on the fact that flame–wall interaction is analyzed through the time-resolved evolution of the probe current recorded.
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Nomenclature Cp e j k L m M N 0 N n P Re t T v V VBohm U UBias
v
specific heat at constant pressure electronic charge current density Boltzmann constant probe length mass relative mass normalized density concentration density pressure electric Reynolds number time temperature normalized velocity velocity Bohm velocity electric potential bias voltage normalized potential
In this work a simplified model of ion current is used, which must agree with the electrical probe’s measurement in order to estimate the quenching distance. Moreover, electrical probe diagnostics require no calibration to perform a quenching distance measurement. 2. Experimental setup and diagnostics Experiments are carried out in a combustion chamber fitted with glass windows which allows a single shot combustion of a quiescent premixed mixture (see Fig. 1). Ignition is performed by spark electrodes situated in a rectangular vessel 70 75 120 mm3. Side wall windows allow the observation of all the
Fig. 1. View of combustion chamber.
thickness free space permittivity scaled normal coordinate Debye length kDe ion mean-free-path ki l mobility r collisional cross section t thermal velocity Subscripts a adiabatic e electron f flame i ion in sheath edge q quenching u unburned mixture w wall 0 reference 1 free stream
d
e0 g
cross-sections in the combustion chamber. The electrical probe used for diagnostics is placed through a side-wall of the combustion chamber. In the present study, both types of single-wall interaction are investigated: head-on and sidewall interactions. The flame quenching geometry depends on the electrostatic probe’s relative position and the spark electrodes. For head-on interaction the ignition point is located at the symmetry axis of the probe at a distance of 2 cm. Due to this geometrical arrangement, the flame front propagates perpendicularly to the ionization probe’s surface, allowing the head-on quenching regime [10,11]. For sidewall interaction the probe is shifted in the spark electrodes’s symmetry plane. Then the flame front propagated tangentially to the probe surface. The ionization probe consists of two electrodes (see Fig. 2). A probe’s central electrode of 3 mm in diameter (cathode) used for the ion current’s measurements is inserted in a steel pipe (external probe electrode – anode) of 10 mm in external diameter. Electrodes are isolated by a 2 mm thick epoxy layer and placed flushing with the probe end surface. The external probe electrode is electrically connected to the combustion chamber body and is used to polarize the flame through antennas system [12]. Polarization antennas provide good electrical contact with the combustion
Fig. 2. Electrical probe (cross-section view).
M. Karrer et al. / Experimental Thermal and Fluid Science 34 (2010) 131–141
plasma and the flame potential, which remains constant in the whole flame, is close to the anode potential [7]. Thus, the voltage applied to the probe electrodes could be considered as Ubias. The geometry of the probe’s antennas was chosen not to affect the flame quenching in the measuring probe electrode zone. Visualization tests showed that the antennas length must be less than one third of the probe radius to avoid flame front disturbances. The antennas used were about 1 mm long and the diameter was less than 0.2 mm. Antennas extend inside the combustion chamber in about 0.5 mm. In our study the central probe electrode was biased negatively. Typically triangular pulses of 12 V in amplitude and with a frequency of 10 kHz were used to polarize the flame relatively to the measuring electrode. For this work, the frequency is sufficiently low for both ions and electrons to respond without an appreciable delay [13] to the bias voltage variations. A previous paper demonstrated [14] that at frequencies below the ion plasma frequency the ion current across the sheath is all the time in equilibrium with the applied voltage. To validate the working frequency of 10 kHz the ion transit times in sheath layer was estimated for moderate potentials. The current density in the sheath layer is supposed constant, and at the sheath edge the current density is given by:
j ¼ nf eV in
ð1Þ
where nf is the ion density in flame front, and Vin is the ion velocity at the sheath edge. By using the Bohm criterion an expression of the ion velocity at the sheath edge is proposed:
V in
sffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffi kT f 2 ki and V Bohm ¼ ¼ V Bohm p kDe Mi
ð2Þ
The estimated ion transit time in the sheath layer is calculated by using some experimental results obtained with a stoichiometric methane–air mixture at atmospheric pressure during head-on quenching (see Table 1).The mean-free-path for ion in flames is given by:
8 l ki ¼ pffiffiffiffi 3 p e
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kT f M a 80:5 nm Na 2
ð3Þ
The Debye length is estimated:
kDe
sffiffiffiffiffiffiffiffiffiffiffiffi e0 kT f 27:3 lm ¼ n f e2
ð4Þ
Thus the ion velocity at sheath edge is:
V in
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ki kT f 28:1 m s1 ¼ p kDe Mi
ð5Þ
Ions enter the sheath with a velocity of Vin 28 m s1. The electrical field in the sheath region was calculated with Poisson equation: Table 1 Data for stoichiometric methane–air mixture. Experimental parameters
Range
Dielectric permittivity Boltzmann constant k Avogadro Air mass Electron mass Electron charge Ion a.m.u Ion mass Ion mobility Flame temperature Pressure Quenching distance
8.854 1012 F m1 1.38 1023 J K1 6.0221 1023 mol 0.028 kg mol1 9.109 1031 kg 1.6e19 C 50 a.m.u1.66 1027 kg 3 104 m2 V1s1 2500 K 1 bar 160 lm
133
Fig. 3. Characteristic time of current stabilization.
E¼
sffiffiffiffiffiffiffiffiffi 2jdq
li e0
9:375 104 V m1
ð6Þ
And by using the ion mobility li, the ion velocity under the effect of the electrical field was estimated:
V i ¼ li E 28 m s1
ð7Þ
By making the assumption that at first order the quenching zone corresponds to the electric sheath layer the ion transit characteristic time is about:
t¼
dq ¼ 5:7 ls Vi
ð8Þ
Evaluation shows that processes of current stabilization occur much faster than the characteristic time of CVC measurement. However measuring frequency is limited by the electronic device’s response time, which is used to amplify the ion current, and by the current stabilization’s characteristic time. The existence of parallel resistive and capacitive components of low frequency sheath impedance has been previously predicted and demonstrated [15,16]. Thus some experiments were performed to estimate the characteristic time of current stabilization related in particular to [7]. A square voltage is applied to the electrical probe. the term: @U @t By increasing the bias voltage, the space charges are collected by the electrode and a sheath layer is formed. Recording the current’s time evolution gives an estimation of the current stabilization’s characteristic time. In Fig. 3 the black stars correspond to the experimental evaluation of current stabilization time and the dotted line is the characteristic time of ion transit in the sheath layer estimated from Eq. (8). Actually, the characteristic time of current stabilization, s1, is about 20 ls whereas the characteristic time of flame quenching, s2, is about 100 ls [11]. With a pressure rise, the sheath’s relaxation times increase. Because s1s < s2, where s is the time of CVC recording, the sheath layer geometry and plasma around the probe are supposed to be stationary during the measurements. The CVC was recorded and used for reconstruction of flame position relative to the probe. To study flame–probe interaction, a coupling of experimental diagnostics is performed. The pressure is recorded with a piezoelectric transducer Kistler 601 and the direct photography method is used to detect the flame’s position in vicinity of the wall. Flame front images are recorded by a PHOTRON APX-RS 3000 camera supplied a HAMAMATSU C9548 model high-speed gated image intensifier. The camera has a resolution of 256 384 pixels and 1024 grey levels, which allows registration 20,000 images/s with an exposure time of 30 ls. A spatial resolution range of [5–14] lm/pixel is obtained due to the
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applied optical magnification. The procedure of image treatment to determine the flame position was described in a previous work [17] and we just follow the same treatment: the quenching distance is determined as the ‘‘dead space” between the flame front and the wall, and computed through image processing. The head of the luminous zone is associated with the appearance of excited radicals, mainly CH* and C2 , as a result of elementary reactions in the chemical zone of flame front [11]. The uncertainty of quenching distance measurement through the direct visualization method takes into account the standard deviation of each experimental dataset (statistical uncertainty) and the precision of image processing (physical uncertainty), which is of two pixels i.e. [10–28] lm [17]. The evolution of flow field was investigated during flame quenching by using a high-frequency PIV system. To study flame dynamics within the quenching zone, a high spatial resolution involving high optical magnification is necessary. An appropriate imaging system was used. It relies on a long-distance microscope Questar QM-1 which allows a study with 5 lm/pixel spatial resolution at a minimal working distance from the object of 56 cm. Questar QM-1 was coupled with a high-speed camera (Photron APX RS-3000) synchronized with a double-cavity laser (Pegasus, New wave research). The 5 kHz working frequency of PIV system allows a visualization window of 1023 360 pixels. Two types of seeding, vegetable oil and zirconium oxide particles were used. Vegetable oil seeding was used to achieve velocity measurement in fresh gases located within the quenching zone. For determination of gas velocity in flame front and burnt gases, seeding with zirconium oxide ZrO2 was used. The particles’ size is lower than 5 lm. To realize high spatial resolution measurements in vicinity of the wall the parasitic reflection of the surface was eliminated by orienting the illuminating laser sheet parallel to the wall. Another difficulty was the strong density gradients along the observation optical axis decreasing the quality of PIV results. This parasitic effect was significantly decreased by using a 10 mm thick rectangular obstacle inserted into the combustion chamber. So, the flame quenching and the corresponding velocity field were studied in vicinity of the obstacle’s surface. The velocity field was recorded at minimal distance 100 lm from the wall [18]. 3. Model Some probe theories were previously developed for the flow of a weakly ionized gas over a solid body at pressure of 0.1 MPa. The different papers will be quoted in this part. These works have demonstrated the relation between the electrical response of the probe and the flow characteristics. Thus, in the next part of this paper, we analyze the possibility of using these theories for the flame quenching study. It is relevant to explain that in the flame–wall interaction case, the ‘‘sheath” physics are different due to the presence of the thermal boundary layer between the flame front and the probe’s surface. In this paragraph, the theory for a weakly ionized gas flow is developed in order to simplify the theory’s understanding and to justify all the assumptions which are needed to apply this theory in our case. 3.1. Theory for a weakly ionized gas flow Lam proposed a general theory for the flow of weakly ionized gases about an arbitrary solid body with absorbing surfaces [19]. Lam theoretically proved that for high pressure flowing plasma, the ion current to the probe becomes a function of plasma velocity when the electric Reynolds number exceeds unity. He worked on a general theory for a thin sheath in flowing plasma. For this theory he made the assumption that the diffusion velocities of the ions and electrons due to any electrical field are small in comparison
with their thermal velocities. In this case Lam’s theory involves diffusion rather than convection dominated sheath then the current presents a true saturation with increasing bias voltage if the qffiffiffiffiffiffiffi e0 kT e
¼ parameter Re a2 1. Here Re ¼ lV11kTLe and a ¼ kDe L
ne e2
L
where
e
V 1 is the free stream flow velocity, l1 is the free stream ion mobility, L is the probe length, k is the Boltzmann’s constant, Te is the electron temperature, e is the electronic charge, and ne is the free stream electron density. Clements and Smy [20] have extended Lam’s general theory to cover the case of flowing continuum plasma in which the situation was demonstrated to depend on convection dominated sheath. For this case the conditions become Re a2 v2 1 where v is the normalbias where Ubias is the bias ized potential which is defined as: v ¼ eU kT e
voltage which is applied to the electric probe. In this condition no saturation current is obtained, and with the bias voltage rise the sheath increases in thickness and thus takes more ions. In this work the sheath is thin compared to the probe size but is thick compared to the boundary layer. Thus the theory developed by Clements and Smy for this case relies on Lam’s model derived with the following assumption: (i) The mean-free-path of the charged particles is very small and is much smaller than the thickness of the sheath adjacent to the probe surface. (ii) The characteristic length L of the problem is much larger 1 than kDe, which is the Debye length a ¼ kDe L 1, where U is the electric potential. (iii) v ¼ eU kT e V1L >1 (iv) Re is the electric Reynolds number equals: Re ¼ l =ðkT e =eÞ i
with V 1 V f where Vf is the undisturbed flame velocity (m/s) relative to the probe. The general equation obtained by Lam for ion density is:
Re ðv rNi Þ ¼ r2 Ni r ðNi rvÞ
ð9Þ
where Ni is the normalized ion density at any point (normalized to the undisturbed ion density ne1 ) and v is the local flow velocity at any point (normalized with V 1 ). By introducing a scaled normal coordinate g defined as: g ¼ yR1=2 and by neglecting all small terms, Lam’s obtained: e
@ 2 Ni @N i 1=2 @N i þ ¼ Re a2 Q v v R x y e @ g2 @x @g " # @ @v @2v @3v Q¼ þ @ g @ g @ g2 @ g3
2
ð10Þ
where x and y are boundary coordinates with x parallel to the probe surface and y normal to the probe surface, vx and vy are normalized flow velocity along x and y axes. Eq. (10) shows that the first term is order of oð1=g2 Þ and represents diffusion current, the second terms is order of oð1Þ and represents the convection current, and at last 2 2 the third term is of order o Re ag4v and represents the current of ion driven by the sheath electric fields. For Re a2 v2 1 the first term in Eq. (10) can be neglected and the current will be governed by convection and sheath effects. In addition if Re a2 < 1; Lam shows that all ions convected into the sheath are then driven by the electrical field to the probe, it is the sheath-convection regime. If v is large enough so that Re a2 v2 1 , the Eq. (9) becomes: Re ðv rN i Þ ¼ r ðN i rvÞ with r ðv N i Þ ¼ N i rV þ v rN i ¼ v rN i for incompressible flow. Thus Clements and Smy obtained:
r ðRe v Ni þ N i rvÞ ¼ 0
ð11Þ
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135
And by using this equation to an element of sheath situated at a distance y* from the electrode, they obtained:
dy u ne e ¼ ni eli E ¼ ji dx
ð12Þ
where Ji is the current density to the electrode surface at x and u* is the flow component parallel to the electrode surface at the sheath edge and ni is the ion density in sheath (see Fig. 4). By using Poisson equation: ni ¼ ðe0 =eÞð@E Þ, and the boundary @y condition of E = 0 and V = 0 at the sheath edge, the usual planar, mobility-dominated space charge equation is obtained:
j¼
9 8
li e0 U 2 y3
ð13Þ
These theoretical results are presented for the ion sheath which forms on a flat plate parallel to the stream direction of a slightly ionized gas. The boundary layer is assumed to be thin compared with the sheath and the solution Eq. (13) could be obtained in a simple algebraic form [20]. 3.2. Assumptions for the quenching phenomenon For our work, we study the flame quenching and the plasma– probe interaction. We work in the case of non-continuum flowing plasma and unsteady boundary conditions. In the case of flame– wall interaction the term of ‘‘sheath” is used to describe the area located between the flame and the ionization probe. One of the main objectives of this study is to use a simplified theoretical 1D model in order to obtain an equation relating current density to quenching distance. Thus, a simplified model of flame–wall interaction is used (see Fig. 5). The temperature profile in unburned gases is supposed to be linear, as a combination of flame propagation and heat conduction through a slab. According to previous studies [10], the wall surface temperature Tw is supposed to be constant and equal to the room’s temperature T0. At ignition, the unburned gases’ initial temperature Tu is the room’s temperature T0. During combustion, unburned gases are heated under the effect of compression which is assumed to be isentropic. During flame propagation in a constant volume chamber, flame temperature Tf increases, as shown in [21,22]; because flame quenching occurs much slower than CVC recording, we supposed that in the measurement zone, combustion occurs at almost constant pressure, and Tf is constant during the ionization current measurement. Previous studies have demonstrated that the chemi-ionization process occurs mainly in the flame front. Some of these works also proposed the ion profiles in flame [23]. Positive charges start occurring at the beginning of the reaction zone where temperature rises, then reach a maximum and disappear in the burnt-gas region. For this work the ion profile is simplified as proposed in Fig. 5 [24]. The ion profile is shown in this figure by a double dotted line. In their study Warnatz et al. [25] have shown that the concentration of ions varies dramatically across the flame front. For our
Fig. 5. Schematic view of simplified flame–wall interaction.
study we simplify the ion distribution within the flame front. We suppose a step distribution of charged species across the flame front. According to Bell et al. [26] we also suppose that in this zone ion concentration is relatively low and varies insignificantly. Flame quenching may be due to three phenomenons:
Radical adsorption.
Flame stretch.
Thermal heat losses. Popp and Baum [27] have studied the interaction of a premixed flame (methane–air) with an inert wall by taking into account the effects of thermal diffusion and adsorption of radicals by the wall. They showed that for wall temperature of 300 K, the effects of thermal diffusion and radical recombination near the wall are negligible. In our study the wall’s temperature did not exceed 320 K, so we can also consider the effect of radical recombination in vicinity of wall as a non-significant one. To study the effect of flame stretch on flame quenching we have to analyze the flame front geometry and the flame dynamic by using the PIV system. For the sidewall
Fig. 4. Schematic view of sheaths [19].
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Fig. 6. Picture of sidewall quenching with high optical magnification (5 lm/pixel).
Fig. 7. Velocity flow field for sidewall quenching.
configuration the flame propagates and quenches continuously along the obstacle (see Fig. 6). The post-treatment of direct visualization and ion current measurements shows that the ion current strongly increases when the reactive zone is located in front of the probe and is parallel to the electrode’s surface. An estimated value of near-wall flame front velocity was calculated by using direct visualization. The luminous zone located at 180 lm from the wall propagates at 1 m/s while the part of reactive zone located at 800 lm propagates at 2 m/s. These evaluations were validated by using PIV imaging system. A typical velocity field obtained with PIV system is given on Fig. 7. For these experiments, the pressure of interaction is less than 0.2 MPa and the quenching distance is about 180 lm. By using a specific post-processing method [28] for time-resolved PIV data dedicated to resolve near-wall gradient, the evolution of flow field related to the wall distance was calculated. Velocity fields are studied in the (x, y) plane; x is the spatial coordinate parallel to the probe surface and y is directed from the normal to the wall surface. Near-wall flow fields are characterized by spatial gradients of velocity and the mean flow field should be calculated as the sliding average of velocity over time as shown on Eq. (14):
P hViðx; y; tÞ ¼
t Vðx; y; tÞ
nt
ð14Þ
where nt is the number of velocity fields in the time windows. In our case, the time window is chosen as the characteristic time of flame– wall interaction (1 ms), and the evolution of parallel component Vx related to the wall distance is given in Fig. 8. Flame front velocity located at 180 lm from the wall surface is about 0.8 m/s which corresponds to the evaluation obtained from direct visualization. During sidewall quenching the flame propagates along the obstacle and the normal components of flow velocity are negligible in fresh gases and in flame front. The normal component of mean flow velocity represents the expansion of burned gases (see Fig. 8). The character-
Fig. 8. Mean flow velocity profiles in the area defined on Fig. 7 for sidewall interaction.
istic length of the thermal boundary layer is supposed to be constant during quenching phenomenon and the mean flow field is parallel to the electrode surface with a velocity of 1 m/s. The tangential strain rate defined by the tangential velocity’s gradient of fresh gases was estimated in the quenching zone:
jS ¼ rt ~ Vr ~ n
ð15Þ
~ V r is the fresh gases’ velocity associated to the contour of flame front, t is the tangential vector and n the normal vector of the flame front. In our experiments jS was about 1900 s1. The total flame strain j is defined as:
j ¼ jS þ jC
ð16Þ
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Fig. 9. Schematic view of simplified sidewall flame–probe interaction.
where jC is the stretch due to the curvature of the flame front. In the quenching zone, the flame stretch due to curvature 2Su/R is inferior to 32 s1 [10] which is negligible compared to the tangential strain rate. The total flame strain is about 2000 s1 and thus has an influence on the sidewall flame quenching [29]. In our study the quenching phenomenon is mainly due to thermal heat losses but the flame strain is not negligible for the sidewall interaction. In the case of head-on configuration, the mean flow field is directed towards the wall and the velocity component parallel to the electrode is negligible. There is no flame stretch, thus the head-on flame quenching is mainly due to thermal heat losses. The characteristic time of flame quenching is about 100 ls whereas the characteristic time of CVC recording is 50 ls and during quenching the flame is supposed to be stationary in direction of the electrode. The flame containing charged species is a good conductor and the electrode is another, thus together they act as a parallel plate capacitor with the thermal boundary layer as dielectric [8]. During flame quenching, the distance between the two plates of the capacitor is constant, thus the variation of current density is related to the resistive component of current which corresponds to the sheath-convection regime. An experimental evaluation of the sheath layer formation shows that it occurs much faster than the characteristic time of CVC measurement and flame quenching. In the case of the sidewall quenching, flame–probe interaction is very close to the case which was studied by Clements and Smy or De Boer and Johnson [30]. The simplified sidewall quenching geometry is depicted in Fig. 9. In this figure the flame propagates along the obstacle with a relative velocity of 1 m/s and is quenched at the distance dq from the probe’s surface. In the thermal boundary layer, the mean flow velocity of fresh gases is negligible. By using data from Table 2, a dimensional analysis of different parameters proposed by Lam’s theory is given for sidewall interaction. Under these conditions, the results correspond to the sheath-convection regime and the current depends on the previous formulation Eq. (13). Thus the final formulation is:
j¼
9 8
li e0 U 2 d3q
ð17Þ
By working on the current density’s derivative function, the current’s capacitive component can be neglected and the current’s evolution is directly related to (17). For the head-on quenching, the flame propagates towards the wall, and the flow parallel to the probe is negligible. In Fig. 10 a schematic drawing of the simplified head-on interaction is proposed. The flame stops propagating towards the wall at the minimal distance dq. In this case the negatively biased probe’s current is formed mainly due to the motion of positive ions to the probe’s surface and the electrons near the probe are repelled when the negative probe’s potential magnitude Ubias is sufficiently large: U bias kTe e .
Table 2 Ranges of various experimental and non dimensional parameters for sidewall quenching. Values Experimental parameters Flame velocity Ion density Probe size Mobility Ion temperature Debye length
1 m s1 1.62 1016 m3 2 103 m 1 104 m2 V1 s1 1500–2500 K 2 105 m
Non dimensional parameters
a ¼ hLe
102
Reynolds’s Number Normalized potential RE a2 v2 RE a2
250 40–80 40–160 102
Evaluations show that in our conditions the magnitude of bias voltage is sufficiently large (Ubias > 0.17 V) so that the electron density falls rapidly to zero in the quenching zone. For these conditions the probe’s current density is:
j ¼ ji þ je ji ¼ e ni li E
ð18Þ
The spatial distribution of the electrical field between two plates is given by Poisson’s equation in the following form:
@E e ðni ne Þ e ni j ¼ ¼ @x eo eo li eo E
ð19Þ
With the boundary condition of E = 0 and V = 0 at the sheath edge, we obtained the usual planar, mobility-dominated space charge equation again (cf Eq. (17)). Thus, the evolution of CVC with Ubias allows, in principle, the evaluation of quenching distance using Eq. (17) in both cases of sidewall or head-on quenching. It is worth mentioning that the choice of ion mobility value in Eq. (17) would be difficult. An expression for li proposed by Fialkov [31] is used:
li ¼
1 3 e 1 1 mþM 2 pkT 8rP 2 M m
ð20Þ
In order to calculate ion mobility, it is necessary to take into account compressing and cooling effects in the quenching zone. According to chemical studies of stoichiometric methane/air mixture [1], the dominant positive ions within the flame are H3O+, C2H3O+ and CH3+. These different ion’s mobility values are of the same order of magnitude. Moreover, (Eq. (20)) gives just an average of ion mobility. Thus, we take a mean value of the mobility of these different ions. The gas temperature used for calculation of ion mobility
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Fig. 10. Schematic view of simplified head-on flame–probe interaction.
was chosen to be the mean value between the gas temperature near the wall and the flame temperature [10,11].
Finally the ion mobility in the quenching zone is calculated for a pressure of 10 bars and for a temperature of 550 K:
3.3. Influence of model assumptions on results
l¼
In the following the effects of the different assumptions which have been made to develop the theoretical model are analyzed.
l ¼ 5:2 105 m2 V1 s1
(i) As explained in several studies [1] H3O+ is one of the dominant ions in flame for saturated hydrocarbon. Thus by using an equation proposed by Fialkov, the H3O+ mobility value was calculated. As it was shown in [32] the H3O+ mobility value is about 30% less than the corresponding value for C2H3O+. Our estimations show that for the same value of probe current, the variation of quenching distance by using the C2H3O+ mobility value or the H3O+ mobility value is less than 10%. Such precision is compatible with first-order estimations of quenching distance. (ii) Some experimental works have shown that C2H3O+ has the structure of an oxygen protonated ketene [CH2@C@OH]+. By using this approximation, the ion mobility within the quenching zone is calculated for a pressure of 10 bars and a temperature of 550 K [33]. The size of C2H3O+ is about 427 pm and N2 size about 145 pm. Thus the collisional elastic section is given by:
re p
2 427 þ 145 2:57 1015 cm2 2
ð21Þ
The relative mass is estimated:
M¼
M ion M N2 3:32 1023 g Mion þ M N2
ð22Þ
The polarizability of N2 aN2 is 1:7 1024 cm3 . The relative thermal velocity for a temperature of Tu 550 K in the boundary layer (under the assumption of isentropic compression of unburned gases) is:
t ¼ 1:45 10
4
sffiffiffiffi T
l
7:6 104 cm s1
ð23Þ
The collisionnal cross section is also deduced:
rtr 2:21p
sffiffiffiffiffiffiffiffiffiffiffiffi aN2 e2
lt
2:73 1012 cm2
ð24Þ
Under atmospheric pressure and for a temperature of 273 K the ion concentration is N0 = 5.69 1019 cm3. The calculated ion concentration in the boundary layer for a temperature of 500 K and under a pressure of 10 bars equals: N 0 2:85 1020 cm3 .
e Mt
¼
e MN0 rtr t
0:52 cm2 V1 s1
ð25Þ
By using Fialkov expression, the ion mobility is:
sffiffiffiffiffi
T P l ¼ l0 4:11 105 m2 V1 s1 T 0 P0 The difference is less than 20%. The ion mobility is well approximate with Fialkov’s expression by taking into account the compressing and cooling effects in the boundary layer. (iii) Ion temperature is the mean value between initial gas temperature just before flame–wall interaction and the adiabatic flame temperature. Another approach consists on using non-adiabatic flame temperature during quenching for calculation. This temperature could be estimated by using experimental values of wall heat flux during quenching. An equation relating flame temperature to wall heat flux was proposed in [34]:
T f ¼ T af
qloss
qu ShT f iC p
ð26Þ
where T af is the adiabatic temperature, qloss is the wall heat flux, qu is the unburned gases density, ShT f i is the laminar flame burning velocity, and C p is the heat capacity. The ion mobility calculated for both flame temperatures gives a variation on mobility values of about 7%. Since the effect of the dominant ion on mobility values is about 30%, it can be concluded that the first-order estimation of the quenching distance is not modified by the assumption made on the temperature. 3.4. Analysis of the ionization current during quenching It has been mentioned above that the probe current is a function of the inward or outward movement of the spatial charges at the sheath edge which depends on bias voltage. For small Ubias, the ion sheath’s edge is located in a low ion density region of the flame front. In our theoretical model the ion concentration is supposed to be constant within this area with the ion density defined by the spatial charge moving to the probe electrode in the electrical field created by the applied voltage. Thus, the probe current is related to the ion flux located in the sheath layer which is coincident at first order with the quenching zone. The typical probe CVC obtained during quenching phenomenon for a 0.26 MPa pressure, a 380 K unburned gas temperature and a 10 kHz Ubias frequency is shown
M. Karrer et al. / Experimental Thermal and Fluid Science 34 (2010) 131–141
139
Fig. 11. Relative variation of current density for stoichiometric methane–air mixture.
in Fig. 11. The theoretical model which was previously described allows the determination of the current density’s variation according to the difference of potential between probe and flame, Ubias and quenching distance. By varying the quenching distance’s value, which is a parameter of Eq. (17), the calculated derivative current densities related to the bias voltage are compared with the experimental values. The quenching distance’s value is also estimated by minimizing the gap between experimental CVC variation and theoretical CVC evolution calculated by Eq. (17). Numerical iterative processes is used for this application and for each quenching distance’s value the gap between an experimental and a theoretical curve is thus evaluated (see Fig. 11). 4. Results and discussion In order to validate the electrical probe technique, the results of quenching distance measurement obtained with the electrical probe were compared with those obtained by the direct visualization method. The comparison is carried out for head-on and sidewall flame quenching regimes and for methane/air and propane/ air mixtures. In Fig. 12, the values of quenching distance obtained with two methods for head-on quenching and for stoichiometric methane/ air and propane/air mixtures are shown. In this figure, as in Fig. 14, plotted values are the results of simultaneous measurements of quenching distance by both methods. Quenching distance values measured from probe CVC correlate reasonably to the estimated values of quenching distance obtained by the direct visualization method. It can be noticed that the evolution of the quenching distance related to pressure is the same for both methods, while the ionization probe values’ magnitude differs from the direct visualization method by 25% in worst case and for the same combustion shot. The experimental uncertainties may partially explain these slight differences between the results of the two methods. In fact, the measurement of the quenching distance by the direct visualization method has a number of limitations. For low pressures uncertainties depend on the low resolution of flame front images which are less bright. Whereas for high pressure the quenching distance becomes too small to be estimated optically. This explains the increasing difference between the results for pressures less than 0.1 MPa and higher than 0.3 MPa. In the case of probe measurement additional uncertainties may be introduced by the assumption of the theoretical model as explained in the previous part. The spatial and temporal resolutions of the electrical probe diagnostics depend on the frequency and the amplitude of
Fig. 12. Quenching distance related to pressure for stoichiometric mixtures in head-on configuration.
Fig. 13. Comparison of ionization diagnostic to previous data.
the bias voltage. For this work the choice of the polarization voltage was limited partially by the electronic device used for the probe current amplification. By increasing the spatial and temporal resolution of the electrical probe diagnostics, we can improve the accuracy of the method. In the pressure range of 0.1–0.3 MPa standard derivation of dq measurement is about the same for both methods independent to the mixture used and equaled about 12%. Values of dq calculated from the CVC correlate well with the
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Fig. 15. Comparison of quenching distance values deduced from ion current for both geometries and propane/air mixtures.
Fig. 14. Quenching distance related to pressure for stoichiometric mixtures in sidewall configuration.
results of the snapshot’s treatment within this pressure range. As one can see in Fig. 12, head-on quenching distance decreases monotonically with pressure rise. Within the pressure range of 0.1–0.5 MPa the quenching distance varies a little bit more for propane/air mixture (three times for C3H8/air mixture in contrast to 2.7 times for CH4/air one) that reasonably correlates with results of Vosen et al. [35]. It is worth noting that results of probe measurements give the quenching distance value (0.05 mm) in high pressure range P > 0.5 MPa where visualization methods do not work (see Fig. 12). The pressure evolution of laminar flame quenching distance obtained with the electrical probe technique is also compared with data of Boust et al. [10] obtained for the same experimental condition as ours (Fig. 13). Results presented in Fig. 13 correlate well. It is worth noting that the scatter of experimental results in [10] is about the same as for probe measurements. It allows the suggestion that the scatter of results is related to the flame nature. In Fig. 13 we have compared the results of quenching distance measurements by chemi-luminescence with and without the presence of the probe in the wall. Fig. 13 shows a good correlation of results obtained for flame quenching on the wall containing the ionization probe (points corresponding to ‘‘visualization”) and without the probe (points ‘‘Boust et al.”). It allows the suggestion that the ionization probe’s presence does not significantly change the quenching distance and the wall heat flux; although according to Sotton et al. [36] the quenching distance depends on the wall material.
In particular, it was found that at head-on flame quenching on ceramic the quenching distance value only decreases 20% in contrast to the one on steel wall, although the thermal conductivity of these materials differs about 50 times. The shape of the flame front quenched on the wall consisting of two different materials (for example, a metal and an insulator) and the probe’s minimal size needed to avoid its influence on the quenching distance measurements’ results, are other intrinsic questions. It is evident that the probe and the wall materials must have similar thermophysical characteristics to minimize the probe’s influence on the quenching phenomenon. Sotton et al. [36] have showed that in a case of wall consisting of steel and plastics the shape of flat flame front is affected by the different heat losses to the walls. It was found that for the pressure P = 0.1 MPa, at the flame quenching instant the length of flame front deformation (this length characterizes the size of flame’s zone influenced by the junction of different thermal conductivity materials) decreases to about 2 mm. Because in our tests the materials of probe’s electrode and wall are the same and the epoxy layer is less than 2 mm, the wall heat flux is supposed not to be influenced by the probe’s presence. This assumption was confirmed by our visualization tests. The comparison between the results of dq measurements obtained by the electrical probe and direct visualization in SWQ regime for C3H8/air and CH4/air mixtures is presented in Fig. 14. The difference between HOQ and SWQ regimes is related to the fact that for SWQ the flame moves parallel to the probe surface. Nevertheless, in this regime, similar to HOQ, the electrical sheath layer formation’s characteristic time is shorter than the flame quenching characteristic time, thus the flame is supposed to be stationary during probe measurements. Another difference between both interactions is the flame stretch. The flame stretch tends to zero in head-on configuration [37], whereas it takes finite values in sidewall configuration (2000 s1), due to gas dynamics. In the case of the head-on quenching, the results of PIV study show that flame quenching is driven mainly by thermal losses which prevail over flame stretch effects. However in the sidewall interaction case, the flame stretch has an influence on the flame quenching. As for HOQ, the quenching distance’s values measured by the probe are in good correlation with the direct visualization’s results. The scatter of experimental data of dq obtained with two methods is about the same and reasonably higher than for HOQ regime that is related with possible influence of hydrodynamics and flame stretching effects in the quenching zone on the flame quenching process. The quenching distance probe measurement results for
M. Karrer et al. / Experimental Thermal and Fluid Science 34 (2010) 131–141
propane/air mixture in HOQ and SWQ regimes are summarized in Fig. 15. Values of dq for this mixture are less for both regimes in contrast to methane/air mixture. Similar to results of Sotton et al. [11] quenching distance in HOQ regime is less by a factor 1.3–1.4 than that for SWQ in the pressure range 0.1–0.0.25 MPa and by factor 1.6 for higher pressure. The results obtained show that the quenching distance could be obtained with a probe technique. Moreover, Eq. (17) allows the estimation of ion mobility within the sheath layer. For the pressure range 0.05–0.25 MPa the value of li varies between 5.7 104 and 3.9 104 m2/(s V). The mean value of ion concentration in quenched flame could be obtained from Eq. (17) under the suggestion that E = Ubias/dq. It was found that ni rises from 2.2 1016 m3 to 4.3 1016 m3 when pressure increases from 0.07 to 0.24 MPa. 5. Conclusion A simplified analysis of probe CVC shows that one of the main parameters of flame/wall interaction – flame quenching distance dq – can be evaluated through the time-resolved measurements of probe CVC that is the main result of this work. A diagnostics method was validated in the cases of head-on quenching as well as sidewall quenching and in a pressure range of [0.05–0.6 MPa]. In this study a simplified model of ion current in the quenching zone was used. This model actually gives the relation between ion current density, bias voltage and quenching distance. This formulation depends also on the ion mobility values. Probe current formulation is used to estimate the quenching distance from the probe CVC. The simultaneous measurement of the quenching distance by using electrostatic probe method and the direct visualization were carried out with both methane/air and propane/air mixtures. In each case, this diagnostic method was verified. Due to the fact that optical diagnosis does not allow the determination of the quenching distance for high pressure, the method has been verified for a limited pressure range. Another method must be used to compare with the results of probe diagnosis for higher pressure. In particular a thermal formulation that describes the relation between quenching distance and maximal heat flux was presented in a previous work [10]. This relation takes into account the effects of pressure and mixtures. Simultaneous measurements of ion current and wall heat flux might possibly be used to validate the probe technique for higher pressure. For our work, modeling the ion current measured by electrical probe is crucial in order to identify the physical parameters of combustion process which can be estimated with the probe current–voltage characteristic. Acknowledgements The authors are grateful to A. Ahmed, A. Agneray, A. Claverie and B. Ruttun for their collaboration for this work. References [1] J. Prager, U. Riedel, J. Warnatz, Modelling in chemistry and charged species diffusion in lean methane–oxygen flames, Proc. Combust. Inst. 31 (2007) 1129–1137. [2] J.M. Goodings, J. Guo, A.N. Hayhurst, S.G. Taylor, A simple method for measuring ion concentrations in flames and the calibration of a nebulizer/ atomizer, Combust. Flame 133 (2003) 335–343. [3] R. Carabetta, R.P Porter, Absolute positive-ion concentration measurements in flames with Langmuir probes, in: 12th Symposium of Combustion, 1969.
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