Post discharge evolution of a spark igniter kernel

Combustion and Flame 162 (2015) 181–190

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Combustion and Flame j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m b u s t fl a m e

Post discharge evolution of a spark igniter kernel Brandon Sforzo ⇑, Alexander Lambert, Jaecheol Kim, Jeff Jagoda, Suresh Menon, Jerry Seitzman Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, United States

a r t i c l e

i n f o

Article history: Received 22 April 2014 Received in revised form 8 July 2014 Accepted 24 July 2014 Available online 14 August 2014 Keywords: Ignition Spark kernel High energy Simulation Experiments

a b s t r a c t In many practical combustion devices, short duration, high-energy spark kernels are used to ignite combustible gases in turbulent flows. Here we examine the development of a high energy (0.25 J) spark kernel created by a short duration (<1 ls) breakdown discharge across two opposed electrodes situated in a uniform air flow. Measurements of electrical energy supplied to the electrodes compare well to thermal energy deposited in the flow with deposition efficiencies exceeding 90%. These spark energies are used as inputs to a numerical model that simplifies the computations by replacing the complex, finite duration, energy deposition process with an instantaneously created, uniform kernel. The evolution of the kernel shape and size predicted by the computational model agrees well with experimental data obtained from high-speed schlieren images, including development of an asymmetry of the kernel between its upstream and downstream regions at later times. The predicted kernel evolution is shown to be essentially independent of the initial size and the composition of the kernel for a fixed deposition energy. The numerical results also reveal the importance of rapid entrainment of ambient air into the central region of the kernel, which quickly reduces the maximum temperatures in the kernel. In addition, the predicted O atom concentrations are well above equilibrium values, especially in the lower temperature regions of the kernel. The higher temperatures and O mole fractions found in the leading portion of the kernel are expected to be an important contributor to ignition in non-premixed combustion flows. Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Most practical combustion devices rely on some form of forced ignition to initiate the combustion process. The most common approach to forced ignition is an electric discharge [1], which typically results in the creation of a high energy spark kernel. Challenges associated with spark ignition are mainly due to operational constraints. For example, regulations limiting emissions and industrial standards requiring high efficiencies have driven a trend toward lean combustion, resulting in less reactive mixtures that are, therefore, more difficult to ignite [2,3]. Other challenging constraints on ignition include high altitude relight [4], high performance operation [5], and safety concerns [6]. Meeting these challenges necessitates improvements in our fundamental understanding of the spark ignition process [7]. Key developmental properties of the spark kernel depend on the energy and the duration over which energy deposition occurs. Much of the experimental work on spark ignition has been for low energy discharges [2,8] or long energy discharge durations [7,9], motivated by automotive applications. On the other hand, ⇑ Corresponding author. E-mail address: [email protected] (B. Sforzo).

gas turbine combustors use a high energy (1 J/pulse) igniter with capacitively coupled charge storage [10]. These systems discharge quickly (ns to ls), resulting in reduced thermal losses to the electrodes [8,11]. Similarly, high speed and high performance reciprocating engines have increasingly shifted to use short duration, high efficiency capacitive discharge ignition systems [12], to increase deposition efficiency and expand engine operating ranges. Additionally, much of the previous experimental work has been performed under quiescent conditions [2,6,13,14]. However, the evolution of a spark kernel in many devices, including ground power gas turbines, aircraft engines, process air heaters and, to a lesser extent, automotive engines, occurs in a flowing environment. Likewise in many combustor environments where fuel and oxidizer are not premixed, or where there is significant non-uniformity in the local fuel–air ratio, the igniter location may experience nonflammable conditions [15]. Therefore, it is important to understand the evolution of a spark kernel created in a non-flammable region that must transit to a flammable region. Additionally, studying the development of a spark kernel in an air flow can also improve the understanding of ignition in premixed flows. Computational models that can accurately predict the development of a spark kernel can provide information that is difficult to measure experimentally. For example, simulations can capture

http://dx.doi.org/10.1016/j.combustflame.2014.07.024 0010-2180/Ó 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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the non-equilibrium composition during the kernel evolution, including persistence of ionized species and radicals, which can greatly influence the ignition process [16–20]. Specifically, Kosarev et al. [21] highlighted the importance of O and H radicals on the chain reactions during ignition, and Takita et al. [22] investigated the effect of O, H, and N atoms on flame speed. A number of efforts have focused on understanding the plasma physics associated with gas discharges [23]. These numerical approaches usually include the solution of the complex magnetohydrodynamic equations governing the plasma development. Simplifications to spark kernel simulations have been performed that replace the complicated plasma modeling with a temporally distributed energy deposition process. For example, a number of premixed ignition studies exploring quiescent background conditions have employed numerical models where the deposited electrical energy was distributed within either a cylindrical or spherical volume in space [14,24–27], while the temporal energy deposition profile was specified or matched to experimental data. Since the temporal energy deposition profile is not easy to measure for short duration discharges, it is desirable to employ a simpler initialization method for numerical simulations that requires only knowledge of the deposited spark energy. The deposited energy has been shown to be influential in the development of the kernel [28,29], and to the overall ignition probability [7]. Previous studies have employed various means to determine deposited spark energies, in both flowing systems [15,30,8] and bomb calorimeters [13,31,32]. For capacitive discharges, electrical energies can be calculated from 1/2CV2, which is typically greater than the deposited energy due to thermal energy losses in lines and electrodes. Here, C and V are capacitance and voltage, respectively. More accurate electrical energy measurements can be obtained by measurements of the current through and voltage across the electrodes. In bomb calorimeters, deposited energies have also been determined using pressure rise in a fixed volume. It has been suggested that deposition efficiencies, i.e., deposited thermal energy as a fraction of supplied electrical energy, should range from 30% for glow discharge, 50% for arc discharges, and up to 94% for breakdown discharge modes [11]. Most of the previous numerical studies of spark evolution in quiescent environments employed one- or two-dimensional simulations that assumed rotational symmetry. However, for spark kernel development in a flowing system, it is necessary to account for non-uniform mixing and convection that may be important to the ignition process. For example, the orientation of the electrodes with respect to the flow direction has been shown to effect the spark kernel [8]. This coupling with a flow has not been investigated and requires the inclusion of a 3D computational domain. In studies where the spark development has been validated against experimental measurements, a common measure of comparison has been growth in kernel size [26,33]. In order to address some of the deficiencies identified above, this paper focuses on characterizing the development of a spark kernel initiated in a crossflow of air. A computational model with a simplified initiation that represents short duration electrical discharges and accounts for ionized species is presented. Experimental measurements of kernel growth are used as a model validation database. The experimental data include precise energy measurements of the deposited spark energy.

which is a common choice for ignition experiments [8,34]. The discharge was characterized by a combination of electrical measurements and a flow calorimeter to obtain the energy deposited into the gas. The subsequent evolution of the spark kernel was obtained from high speed schlieren and emission imaging. The details of the experiment are described below. 2.1.1. Spark discharge system and electrical measurements The spark is generated in a gap between the ends of two co-linear cylindrical copper electrodes. The diameter of the copper electrodes, chosen to produce low impedance, is 3.18 mm, and the gap spacing is 6.4 mm to ensure a high breakdown voltage. The high energy, short duration discharge is created by a modified copper vapor laser (Metalaser 2051) capacitive power supply (see schematic in Fig. 1). The pulse rate of the supply is variable, and was set between 10 and 300 Hz in the current measurements. The voltage across the electrodes was measured close (2 cm) to the gap using a high voltage probe (Tektronix P6015A). Current through the electrodes was measured 10 cm from the gap on the cathode side using a current monitor with a 5 ns response (Pearson model 6600). Examples of measured current (I) and voltage (V) time traces are shown in Fig. 2. The results shown were obtained for the electrodes placed in a uniform, 8 m/s flow moving parallel to the electrode faces. From these measurements, the discharge lasts between 300 and 500 ns, depending on the metric used to define the duration. Also included in the figure is the evolution of the supplied electrical energy, as calculated from Eq. (1). Within 500 ns, essentially all of the approximately 0.25 J is supplied to the electrodes.

Esupplied ¼

Z

VðtÞIðtÞdt

ð1Þ

2.1.2. Flow calorimeter and deposited energy measurements In order to measure the fraction of supplied electrical energy deposited into the flow, a special calorimeter was developed. The

Fig. 1. Circuit diagram for electrode power supply.

25

0.5

20

Voltage

0.4

15

0.3

Energy

0.2

10 Current 5

0.1

0

0

2. Methods −5

2.1. Experimental setup Measurements were acquired from a short duration, high energy spark discharge in an opposed electrode configuration,

0

0.2

0.4

0.6

0.8

1

−0.1

Fig. 2. Measured voltage (V) and current (I) time traces as well as integrated energy supplied (E).

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183

Fig. 3. Schematic of flow facility with calorimeter insulation.

Fig. 4. Schematic of calorimeter measurements with respect to electrodes.

Fig. 5. Schematic of the Schlieren imaging system: LS–light source, PM–parabolic mirror, M–mirror, S–Schlieren stop, C–high speed camera.

electrodes are placed in a rectangular channel (19 mm wide  31.8 mm tall cross section) shown schematically in Fig. 3. The supplied air flow first passes through a perforated plate and development section to produce a nearly uniform flow. Located just before the test section, wire screens control the turbulence level at the electrodes. High turbulence conditions are produced by placing a small bluff body upstream of the electrodes, but downstream from the wire screens. The electrodes are introduced through the top and bottom walls of the test section, 25 mm downstream of the turbulence screens. The test section has full-view quartz windows on opposite sides. To reduce heat losses, the 12.7 cm long channel downstream of the electrodes was wrapped in fiber glass insulation, and the steady-state heat loss was calculated to be 0.5% of the supplied electrical power. The flow temperatures were measured upstream and downstream of the electrodes, as depicted in Fig. 4, with thermistors. The length of the plasma evolution section was chosen such that the heated kernel in the flow grew, on average, to be nearly the width of the channel, reducing sharp spatial thermal gradients, while restricting the overall contact with the walls minimizing heat losses. With the spark kernel having mixed with a significant amount of the surrounding air, the maximum temperatures experienced by the thermistors was significantly reduced. In addition to the flow temperatures, the velocity at the downstream location was obtained with a pitot probe. Temperatures and velocities at the downstream station were measured at a number of points to characterize the nonuniform flow produced by the discharge. The thermistor time response was not sufficiently fast enough to capture the time-varying temperatures produced by the pulsed discharge. Instead, measurements were acquired only after the calorimeter had achieved quasi-steady operation, and the timevarying temperature from the thermistor was time-averaged to obtain the thermal energy of the flow. Additionally, the calorimeter data was obtained with the discharge firing at a high repetition rate (100–300 Hz) to ensure that the thermistor temperature rise was sufficient to produce accurate energy measurements. The velocity and temperature data were converted to the deposited thermal energy with the energy balance described by Eq. (2). This expression is based on a calorically perfect assumption, which requires that the gas entering and leaving the calorimeter are sufficiently close in temperature (within a few hundred K) and composition. This is a reasonable assumption, because by the time the kernel reaches the downstream measurement location, after

having mixed with the surrounding air, the temperature is low again (within 20 K of the initial temperature) and there has been significant time (5–15 ms, depending on velocity) for recombination to occur. Combining the uncertainties in the temperature, velocity and electrical measurements, the propagated uncertainty in the energy deposition efficiency (energy deposited/energy supplied) was calculated to be less than 5%.

Edeposited ¼

1 frep

cp

Z exit

p u2 ðT 2  T 1 ÞdA RT 2

ð2Þ

2.1.3. High speed schlieren and emission imaging The evolution of the spark kernel was characterized with a combination of high-speed schlieren and emission imaging. The kernel was viewed through quartz windows on the sides of the test section. The single pass collimated schlieren system (Fig. 5) uses a 50 W halogen light source. The light passes through a 0.4 mm diameter pin hole and is then collimated by a 0.2 m diameter, 1 m focal length off-axis parabolic mirror. The reflected collimated light is directed to a flat mirror, which redirects the light at right angles through the test section. The rays are redirected once again toward a second (identical) parabolic mirror. This mirror refocuses the light onto a schlieren stop, produced by printing an opaque spot on a glass slide. The spot size was chosen to be roughly the size of the light beam focus with the flow facility not running. A high speed CMOS camera (Photron Fastcam SA3) recorded the schlieren images of the test section. An 80 mm telephoto photographic lens with a 2 teleconverter was mounted on the camera, and a 200 mm plano-concave diverging lens was placed in front to compensate for refraction from the focusing mirrors. A digital delay and pulse generator (SRS DG535) triggers the discharge and the camera, with a delay between the two triggers (Fig. 6). This allows the spark to fire just before the camera exposure begins. The framing rate of the camera was set to 250 Hz. Combined schlieren and spark emission images are obtained with the halogen light source operating. With the light source off, the images contain only the kernel emission. 2.2. Numerical approach A numerical study was performed for the same opposed electrode geometry used in the experiments. After some initial grid

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(a)

(b) Fig. 6. (a) Schematic of signal transfer between components of the image capturing system; (b) timing diagram of the camera output signal, C, and the resulting spark emission, S, with delay Dt.

studies, a grid containing 5.6 million points in a multi-block geometry was employed. The electrodes were modeled as circular cylinders, which necessitated the use of a cylindrical coordinate system in the vicinity of the electrodes, smoothly merging with a Cartesian system throughout the rest of the channel (Fig. 7). As in previous work on spark modeling [24,25], the cylindrical portion of the grid allowed proper resolution of the initial radial expansion of the kernel. The finest grid spacing (30 lm between nodes) was located between the electrodes in order to resolve the large temperature gradients during initialization and early kernel formation. Since further evolution of the kernel occurred close to the streamwise axis of the domain, the grid was clustered in that region. Additionally, the estimated crossflow turbulence at the inlet of the facility was estimated to be low (e.g., 5%), therefore no turbulence closure was employed and the iterative grid resolution refinement ensured that the initial flame kernel structure and its propagation characteristics were well resolved. It was determined that the reported grid resolution of 30 lm was sufficient to resolve the kernel structure in the near-field and further refinement showed no measurable difference in the kernels growth and propagation. No-slip, adiabatic, boundary conditions were imposed on the cylinder and channel walls, and a characteristic non-reflecting

boundary condition was used for the outflow. Characteristics based inflow was employed with a 33 m/s cross-flow of air at 300 K and 1 atm, approximating the experimental conditions. The details of the electrical energy discharge process were not modeled. Rather, given the short duration of the capacitive discharge, the energy deposition was modeled as an instantaneous process in the simulations. The spark channel energized by this instantaneous discharge was approximated as a cylindrical volume of high-temperature, high-pressure gas along the full length of the axis between the electrodes. A nominal diameter of 1.2 mm was chosen for this initial spark kernel volume, and the sensitivity of the results to the spark diameter were investigated. Thus, the energy density in the initial kernel is determined by the energy rise due to the spark (above the background air value) and the assumed volume. Based on the instantaneous deposition approximation, air density was assumed for the kernel region prior to the energy discharge. These two properties: energy density and mass density, along with the assumption of thermal equilibrium in the spark volume, provide most of the conditions required to define the initial state of the kernel. The initial temperature and pressure can be determined from these two densities if the chemical composition is specified. The initial kernel properties were calculated assuming chemical equilibrium using the NASA CEA [35], with thermodynamic constants valid up to 20,000 K. The sensitivity of the spark kernel evolution to the initial composition is one of the issues explored in the Results section. This high-temperature spark volume was then introduced into the channel cross flow (Fig. 8), and allowed to develop for 200 ls. This time period was considered sufficient to compare with experimental observations. A fully compressible Navier– Stokes solver that has been well established for shock flows [36– 38], was employed in this study. The governing mass, momentum, species, and energy conservation equations are, respectively:

@ q @ qui þ ¼0 @t @xi

ð3Þ

@ @ @p @ s quj þ qui uj þ  ij ¼ 0 @t @xi @xj @xi

ð4Þ

  @ qY k @ @Y þ qY k ui  qDk;m k ¼ x_ k @xi @t @xi

k ¼ 1 . . . Ns

Ns X @ qet @ @T @Y þ qui et þ k þ q hk Dk;m k @xi @xi @t @xi k¼1

! 

ð5Þ

@ @p ui sij  ¼0 @xj @t

Fig. 7. Representation of the computational grid, zoomed in (a) top view and (b) side view, displaying one third of the nodes.

ð6Þ

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20

10

15 10

5

5 0

0 −5

−5

−10 −15

−10 −10

−5

0

5

10

−20

Fig. 8. Velocity field through test section mid-plane, overlaid on vertical velocity contours, taken prior to spark deposition.

where q is the mass density, ui is the velocity component in the i-th direction, p is the static pressure, and T the temperature. _ k ; hk ; Dk;m are the k-th species mass fraction, mass reaction rate, Y k; x enthalpy, and diffusion coefficient, respectively. Finally, sij is the viscous stress, et is the total energy, and k is the heat conduction coefficient. A hybrid integration scheme was used where upwind fluxes were computed using MUSCL-reconstruction and central fluxes were evaluated using fourth-order MacCormack integration. This approach allowed for the shock produced by the spark discharge to be resolved while appropriately calculating the flux in the rest of the flow. An 11 species, 30-step plasma air chemistry was derived from previous studies [39–42] examining weakly-ionized plasmas. This mechanism is optimized for high temperature gases (up to 20,000 K) and will sufficiently capture the plasma evolution for our purposes. The chemical source terms were calculated using fourth-order Euler integration. 3. Results and discussion

relatively uniform across the exit, and, as expected, the hot region is centered in the middle of the flow, which is consistent with the placement of the electrodes at the center of the channel upstream. The hot gas has expanded to reach the side walls of the rectangular channel, but does not extend completely to the top and bottom walls. The wall temperatures were not measured during this experiment; therefore, the edges are shown as black to provide a border to the figure. Moreover, the temperature profile is wider in the horizontal dimension. This is due in part to the enhanced mixing caused by the wake behind the vertical electrodes. Additionally, the horizontal surfaces of the electrodes block expansion of the spark kernel in the vertical direction, as will be described later. The efficiency with which the electrical energy supplied to the electrodes is deposited into the flow (Eq. (7)) was estimated to be above 90% for the range of flow velocities and turbulence intensities investigated; see Table 1.

gdep ¼

Ethermal Eelectrical

ð7Þ

Previous work [8] also showed little change in energy deposition due to turbulence in flowing systems for spark durations of tens of microseconds. The flowfield dynamics likely have little effect on the energy deposition because the spark duration is much shorter than any characteristic flow time here (or in most practical devices). The energy deposition is also quite high, higher than values often reported in the literature [43]. The short duration of the discharge is one reason the energy deposition into the gas is this high, as the hot plasma channel contacts the electrodes for only a short duration, limiting the heat transfer to those surfaces. Short duration discharges also have been estimated to have low radiation losses [11]. Reduced losses may also be a result of using low resistance electrodes and having the gap situated far from a wall where heat transfer could occur. The manner in which the electrical energy is measured here also plays a role. The fast response electrical probes were located very close to the spark gap, thereby improving the measurement accuracy of the supplied electrical energy. Since the measured electrical and deposited energies were nearly the same, the supplied energy was used to initialize the numerical model.

3.1. Energy deposition measurements 3.2. Numerical kernel initialization Accurate energy deposition data are essential for the physical understanding of the kernel development process and to provide initial conditions for the numerical modeling effort. As noted above, the electrical energy supplied to the electrodes was near 0.25 J. The amount of energy deposited into the flow was calculated from the calorimeter data using Eq. (2). Example profiles of velocity ðu2 Þ and temperature increase ðT 2  T 1 Þ obtained at the exit of the flow calorimeter are shown in Fig. 9. The velocity is 8

30 25

6

20

20

30 25

15

20 4

15 10

2 5

10

15 10

5

5

0 0

5

10 15

0

As discussed in Section 2.2, the deposited energy and the density are not sufficient to fully define the initial state of the kernel; the initial temperature and pressure also depend on the kernel’s chemical composition. The sensitivity to the initial composition was explored by examining various initial conditions in a uniform, no flow, constant pressure (1 atm) simulation. The evolution of the kernel composition and temperature were compared for three arbitrary cases with the same total energy and ratio of atomic nuclei, i.e. N:O = 3.76:1, but with different initial temperatures and compositions: (1) a 20,000 K case with a high concentrations þ þ of O and N þ 2 ; (2) an 18,000 K case with significant O and N 2 levels; þ and (3) a 14,000 K case with high concentrations of O and N þ . Figure 10 shows the mass fractions of NO and N þ as a function of time progression for these three cases. Initially, the mass fractions for

0

0 0

5

Table 1 Deposition efficiency measurements for three flow conditions.

10 15

Fig. 9. Examples of measured velocity and temperature profiles at the calorimeter exit plane.

Flow velocity (m/s)

Turbulence (u0 =u)

gdeposition (%)

8 33 8

0.05 0.05 0.26

97 96 93

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10 0

10 0 14,000 K

14,000 K 10

10 −5

0.5

−1

0.4

20,000 K

20,000 K

0.3

10 −2 18,000 K 10

10 −3 NO 10 −15 −10 10

10

−8

10

−6

N+ 10 −4 10 −10

di=0.8mm

0.2

18,000 K

−10

di=1.2mm

0.1 0

10

−8

10

0

50

100

150

200

−6

Fig. 10. Concentration relaxation for NO and N þ at three different initial conditions.

the different cases are several order of magnitude apart. However, within 1 ls after the energy is deposited, the mass fractions approach similar levels (15–21% for N þ and 1–8 ppb for NO). This suggests that the high chemical reaction rates at these conditions lead to a rapid approach to quasi-equilibrium for most of the radical species. Thus, we expect the numerical simulations to be relatively insensitive to the initial composition chosen for the kernel, at least for convective time scales of interest in the current experiments, as long as the deposited energy is specified. While the above results do not include the effect of pressure rise in the kernel, the increase in reaction rates at high pressure would encourage even faster equilibration. The chosen value for the initial kernel diameter (1.2 mm) was based on the estimates of the final spark channel width. The sensitivity of the kernel development to the assumed kernel diameter was also addressed by conducting simulations for different diameters, while keeping the total energy deposited constant. The initial kernel energy density varies inversely with the kernel’s initial diameter. The conditions in the kernel, following energy deposition at t ¼ 0 for two channel diameters are presented in Table 2. Numerical results for these two initial kernel diameters (the nominal value and one 33% smaller) are shown in Fig. 11, where the kernel volume is plotted as a function of time after the discharge. Here the volume is defined by all regions where the temperature is above 600 K (the background air temperature is 300 K). The kernel volume grows rapidly in the first 10–20 ls, with the larger initial diameter producing a just slightly larger volume. After 50 ls, the smaller diameter case has a slightly larger volume, possibly due to the faster expansion velocity associated with the higher initial pressure for the smaller volume. Overall however, the kernel volume is essentially the same for both initial diameters. Thus,

Fig. 11. Simulation results of kernel volume development for two initial kernel diameters.

we conclude that the modeled simulation is not very sensitive to the initial diameter choice; it is more important to know the correct kernel energy in order to predict the kernel development accurately. The initial rapid rise in kernel size observed in Fig. 11 is due to a pressure-driven expansion resulting from the high initial pressure in the kernel. The volume increase slows drastically within 10 ls when the kernel front reaches the edge of the electrodes. The kernel then begins to interact with the edges, allowing the shock front to decouple from the kernel, and the compression wave continues to propagate outwards as shown in Fig. 12. Kernel growth progresses somewhat steadily thereafter, with observed undulations in the volume caused by pressure waves reflected from the test section walls. 3.3. Kernel evolution 3.3.1. Structure and size: experiments Example schlieren images of the spark kernel evolving in air are shown in Fig. 13. Here, the nominal flow velocity was 33 m/s with a turbulence intensity of 5%. The camera was set to a framing rate of 250 Hz with an exposure time of 33 ls. Delays between the spark discharge and camera shutter opening were varied between 60 and 210 ls in steps of 10 ls, and approximately 500 images were gathered for each delay time. The bright intensities in the first several images (up to 100 ls) are due to visible emission from the plasma kernel. The dim light visible in the images represents the density gradients in the flow. At each delay time, edge tracking was performed to identify the outline of the density gradient

10

200 180

Table 2 Numerical kernel conditions at t ¼ 0, for two channel diameters.

5 160

T (K) p (MPa)

vN 2 vO2 vN vO vNO vNþ2 vOþ2 vN þ vOþ vNOþ ve

1.2 mm

0.8 mm

9592 5.52 1.67E01

17,772 13.74 8.70E04

1.66E04

8.17E06

5.83E01 2.38E01 6.99E03 2.07E04

5.78E01 1.65E01 1.91E04 3.78E04

2.61E06

5.50E06

1.21E03 3.30E04 7.09E04 2.46E03

1.09E01 1.85E02 1.31E04 1.28E01

140

0

120 −5

100 80

−10 −10

−5

0

5

10

Fig. 12. Simulation results showing spark kernel pressure distribution at 8 ls.

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60μs

140μs

6000 5000 4000 3000

80μs

160μs

2000 1000 0

100μs

120μs

180μs

200μs

Fig. 13. Representative set of sequenced images from high speed schlieren recording of kernel development; times represent the delay between the spark breakdown and the image, with the image exposure lasting 33 ls. The green contours are added to emphasize the schlieren intensity distribution. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

50

100

150

200

250

Fig. 14. Calculated temperature evolution of kernel between 60 ls and 300 ls following the spark discharge.

based on the assumed toroidal kernel geometry, specifically an annular disk with the central hole encompassing one-third of the diameter. Since the kernel volume increases, it should be accompanied by a decrease in kernel temperature, because the only source of kernel growth at these long delays is entrainment of surrounding air. An estimate of the temperature history of the kernel was produced from the volume change. First, the kernels were assumed to be uniform in temperature, contain most of the deposited energy, and have a pressure equal to the test section pressure (roughly 1 atm) after these long delays. Then, with the pressure and volume specific energy of the kernel established, the temperature was obtained assuming the kernels were in chemical equilibrium. An equilibrium code (NASA CEA [35]) was used to provide a relationship between kernel temperature and its enthalpy and composition (which includes all the important air plasma species), while Eq. (8) relates these to the other kernel parameters.

DhðT kernel Þ ¼ features. This was accomplished by converting the gray-scale data to binary images using a calibrated intensity threshold. This threshold was held constant for all images since it represents a specific density gradient in the schlieren images. The resulting edges denote the interface between the spark kernel and the ambient flow, and are included as the green contour shown in Fig. 13. The structure of the kernels can be inferred from these lineof-sight integrated images based on emission location and fine features in the schlieren images. The kernel develops from its initial near-cylindrical shape into a toroid like shape as it expands. For example, this can be recognized by the two-lobe structure in the kernel appearing around 80 ls. This emission located at the leading and trailing edges, encompassed by schlieren light, suggests two hot regions as seen in this profile view. This conversion to a toroidal kernel has been observed in previous studies [33] as a result of entrained air near the electrodes following the initial pressure expansion. The images at these two times also show that the light emitted by the high temperature kernel is more pronounced in the downstream lobe of the kernel. This suggests that high temperatures survive longer in this region compared to the upstream portion of the kernel. Using this interpretation of the kernel geometry, the volume of the kernel was estimated for each delay time. First, the total area contained within the schlieren-defined boundaries was determined for each image, with 500 images analyzed at each delay time. Then, a corresponding solid of revolution was determined

0

Edep ðp=RT kernel ÞV

ð8Þ

where, p; R; V; Edep , and T kernel are the pressure, specific gas constant, kernel volume, deposited energy, and uniform kernel temperature, respectively. The results are shown in Fig. 14 and indicate a significant decrease in the temperature of the kernel within the first 100 ls. The kernel temperature nearly stabilizes 130–150 ls after the spark is created (at a value of 1000–2000 K based on the assumed kernel geometry). The error bars were generated from the propagation of uncertainties in the kernel dimension measurements. 3.3.2. Structure and size: simulations Comparison of the simulations and experimental results provide a means to further assess the ability of the numerical approach. First, we focus on the kernel geometry. Figure 15 shows instantaneous temperature iso-surfaces for 600 K gas, representing the boundary of the kernel at three times after the energy is deposited. While the results shortly after the energy is deposited reveal a cylindrical spark kernel, the later image clearly shows the evolution to a toroidal kernel, appearing by 100 ls, in good agreement with the experimental imaging results (Fig. 13). Additionally, the effect of the electrodes on the kernel structure is evident later, when the portion of the kernel that initially propagated upstream reverses direction (due to crossflow motion) through the electrode region, leading to a breakup of the upstream side of the kernel. Next, we compare the evolution of the kernel sizes between the experiments and simulations, as this method has been used to

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1.2 1 0.8 0.6 0.4 Fig. 15. Computed visualizations of the convecting kernel at 6.5 ls, 103 ls and 209 ls.

71μs

Schlieren Computational

0.2 0

146μs

0

50

100

150

200

250

Fig. 17. Kernel cross sectional areas from experimental and computational results.

4.5

103μs

400

175μs 4

200

3.5 0 3 −200

121μs

209μs

2.5 −400

2 1

Fig. 16. Line-of-sight integrated realizations of the spark kernel density gradient at six delay times, with kernel area highlighted.

validate previous numerical results [26,33]. Since the experimental volumes described above are only estimates obtained from the line-of-sight schlieren images, based on assumptions about the kernel shape, a more direct comparison with the computational predictions can be obtained by using the total kernel projected areas obtained from the schlieren images. To produce a corresponding value from the numerical results, snapshots from the simulations were reduced to line-of-sight integrated images based on the predicted kernel density gradients. Figure 16 shows the calculated instantaneous images of the integrated density gradient at six delay times. The same edge tracking analysis used for the experimental data was applied to the computational images to generate the edge contours shown in this figure. A comparison between the measured and calculated kernel areas is shown in Fig. 17. The experimental results show a moderate increase (about 25%) in mean area from 60 to 210 ls. The error bars were generated using the standard deviations calculated from the area distributions of the 500 images obtained at each point. The areas determined from the 2D simulated density gradients agree well with the experimental data. Both show the same relative increase in the projected kernel area, though the simulation results are a little lower than the experimental data. The larger experimental areas may be due to the edge detection threshold choice or the failure of the image processing method applied to the numerical results to completely model the optical setup of the schlieren experiment. Though there are no corresponding experimental data for comparison, the simulation results in Fig. 11 show the most rapid growth in kernel size occurs in the first 10–20 ls.

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Fig. 18. Velocity vector field of test section mid-plane at 8 ls, overlaid on vertical velocity contours. The inset image highlights the region of interest.

The good agreement between the experimental and numerical results, in both kernel shape and size, is evidence that the current simulation approach using the simple energy deposition initialization condition can properly predict the initial development of the kernel. 3.3.3. Velocity, temperature, and composition Further aspects of the spark kernel evolution can be understood by examining the numerical results for the velocity and scalar fields. For example, the formation of the toroid can be understood by examining the computed velocity fields. Figure 18 shows the velocity field in a vertical test section mid-plane through the electrodes and kernel at 8 ls. When the expanding pressure wave (seen in Fig. 12) moves beyond the edges of the electrode, air is drawn downward along the vertical electrode surfaces. Thus cold surrounding air is entrained into the central region of the expanding kernel. In Fig. 18, this is evident in the zoomed portion of the flowfield at the edge of the electrode. The vertical velocity magnitude, indicated by color contours, highlight the net flow of gas down the electrodes. The resulting vorticity from this inflow persists as the kernel develops, continuing the entrainment of cold air into the center of the kernel producing the toroidal shape. This entrainment is the primary reason the kernel grows after the first 30–50 ls and the source of the rapid drop in temperature observed in the experiments (Fig. 14). The combined schlieren and emission imaging measurements show that the high temperature (low density and high emission intensity) portions of spark kernel persist predominantly in the leading edge of the kernel. This part of the kernel convects away

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Fig. 19. Time progression of spark kernel in simulation. Fig. 20. Temperature, O radical concentration, and equilibrium O concentrations plotted for streamwise locations shown in Fig. 19.

from the electrodes first. To examine this in the simulations, temperature data was extracted from the numerical results and shown in Fig. 19 for three delays after spark initiation. The figure presents 2D slices of temperature passing through the center plane of the electrodes. Convection of the kernel downstream (rightward), as well as the rapid temperature decay, can be observed. The upstream portion of the kernel passes through the electrode gap (at 103 ls) and interacts with the strong vortical motions induced at the electrode edges. This causes the trailing edge of the kernel to cool rapidly due to mixing with the surrounding air. Later (209 ls), the downstream portion of the kernel contains the only large region of hot gas along this center plane, since the rest of the central region consists primarily of entrained air. To examine the kernel conditions in more detail, Fig. 20 presents temperature and O atom mole fraction along the 1D line segments depicted in Fig. 19. The O atom was chosen specifically as it is known to have a significant impact on ignition of hydrocarbon fuels [21]. As might be expected, regions with the highest temperatures also contain the peak O levels. For comparison, equilibrium O mole fractions were calculated for the local temperature at locations along the line to explore the degree of non-equilibrium. Early after the discharge in the central region of the cylindrical kernel, the O atom levels are approximately close to the equilibrium value. As the temperature drops off at the kernel edges, however, the O atom concentration is well above its equilibrium value. This trend toward super-equilibrium O levels becomes more evident later in the process. For example at 209 ls, the O atom levels are more than an order-of-magnitude above equilibrium, even in the hottest regions. For regions in the center of the toroidal kernel, where temperatures are close to 320 K, the O mole fractions are above 1000 ppm. As the hot kernel fluid mixes with the entrained air, the O recombination reaction rates drop drastically. For example, at 320 K, the time required for recombination reactions to reduce the observed O levels by a factor of 5 exceed 200 ls. The persistence of the O radicals in the cooler regions could therefore have a significant impact on ignition in non-premixed conditions. Even as the peak kernel temperatures drop with further entrainment, the O atoms could still provide a source of ignition when the kernel encounters a flammable mixture. While the spatially averaged temperatures inferred from the schlieren area measurements (Fig. 14) are not analogous to the

spatially resolved temperatures profiles from the simulations (Fig. 20), there are some general observations that can be drawn from their comparison. First, both show a significant drop in kernel temperature at early times. Second, between 100 ls and 200 ls, the temperature decline is less pronounced. Third, at later times (100–200 ls), the peak temperatures from the simulations are 2500–2800 K, while the bulk averaged experimental results are 1300–2400 K. As should be expected, the peak values are higher than the averaged values. Given the large uncertainties in the experimental results and the simplifying assumptions on which they are based, the observed agreement is good. The similarity between the trends in the experimental estimates and the simulation temperatures not only helps to validate the modeling approach, but it also suggests the utility of the approach used here to provide estimates of the average kernel temperatures later in the process. 4. Conclusions The evolution of a high energy spark kernel was investigated experimentally and numerically. Electrical discharge profiles were measured to accurately quantify the spark kernel energy deposition. High deposition efficiency (>90%) is attributed to the short duration discharge (<1 ls). High speed schlieren imaging was conducted to observe the development of the kernel from the time of energy deposition to 300 ls. A computational model for the spark development was implemented with the initial deposition simplified to an instantaneous event, requiring only the test geometry and energy (from measurements) as an input. The simulation results were compared to the measurements of the shape, size, and temperature of the kernel, and their evolution up to 200 ls. In the simulations, evolution of the kernel after a few microseconds is only weakly dependent on the assumed initial kernel diameter and composition. The decreased energy density associated with a larger initial kernel size produces a lower pressure and weaker initial expansion, which eventually matches the expansion produced by a smaller kernel with the same deposited energy. Similarly, at the initial high temperatures, fast reaction rates result in

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later compositions that are only weakly dependent to the assumed initial composition. Good agreement was observed between the experimental and numerical results indicating that the kernel initialization approach proposed here is valid for short duration discharges, and removes the need for accurate knowledge of the temporal and spatial profiles of the deposited discharge energy. The computational results showed that rapid early expansion draws colder surrounding air along the electrodes into the core of the developing kernel, which leads to rapid mixing in this region and the transition to a toroidal kernel. The convecting cross stream causes the upstream side of the kernel to experience higher mixing and cooling. Thus, the hotter downstream lobe would likely be the dominant source of ignition if such a kernel was produced initially in a non-flammable mixture. As the hot kernel gases mix with surrounding air, O recombination rates drop rapidly. Significant superequilibrium O levels were observed (thousands of ppm) even in regions that have cooled to temperatures below 800 K, which would normally be unlikely to produce ignition. However, the superequilibrium O can significantly enhance ignition reactions. While the current simulations examined air discharges, this computational approach for modeling kernel development can also be applied to premixed ignition environments. However, it will require that appropriate chemical mechanisms be available that include the high temperature species and reactions which would be expected in the kernel. This simplified approach to spark modeling has been shown to accurately capture the appropriate spark development and therefore can reduce computational costs for analogous ignition studies. Furthermore, the presented experimental measurements provide a good data set for future comparisons of capacitive discharge spark kernel development in a nonflammable flow. Acknowledgments The authors gratefully acknowledge support for this work from Pratt and Whitney (PW) through the PW-Georgia Tech Center of Excellence. References [1] [2] [3] [4] [5]

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