Electric field induced second harmonic generation on 1-D diffusion flames

generation on 1-D diffusion flames

Item Type Conference Paper

Authors Park, Jin;Son, Jinwoo;Butterworth, Thomas D.;Cha, Min Suk Eprint version Post-print

Publisher The Korean Society of Combustion

Rights This is an accepted manuscript version of a paper before final publisher editing and formatting. Archived with thanks to The Korean Society of Combustion.

Download date 2023-12-03 19:26:01

Link to Item http://hdl.handle.net/10754/686411

Electric field induced second harmonic generation on 1-D diffusion flames

Jin Park^*†, Jinwoo Son^*, Thomas D. Butterworth^**, Min Suk Cha^*

ABSTRACT

Applying an electric field to a flame mobilizes ions and electrons generated in the reaction zone, resulting in the modifications of the flame characteristics and applied field. The total electric field measurement can determine the modified flame structure and ion distribution. We employed the EFISH technique, a high spatial resolution laser diagnostic, on the counterflow diffusion flames. Here, we presented the derived space charge density and electric potential with the measured electric field results.

Key Words : Electric field, EFISH, Diffusion flame, Counterflow flame

The external electric field applied to the flame induces migration of ions and electrons by acting the Lorentz force, leading to locally amplifying or shielding the applied field. An understanding of the local electric field, 𝑬, is necessary because the electric potential, 𝑽, and the space charge density, 𝒏_𝐜, can be derived from 𝑬 by the following Eq. (1):

−𝑑^"𝑉(𝑧)

𝑑𝑧^" =𝑑𝐸(𝑧)

𝑑𝑧 = 𝑒

𝜀_#𝑛_$(𝑧) (1) However, measuring electric fields in combustion systems is challenging because the measurement methods must be non-intrusive and require high spatial resolution. Thus, we employ electric field induced second harmonic generation (EFISH), which has been recently utilized for electric field measurement in plasma environment [1-4], to measure the electric field in the flame. Since EFISH is a laser diagnostic technique with a spatial resolution of the μm order, it is sufficiently applicable to flames.

Figure 1 illustrates the experimental setup for EFISH measurement on the counterflow flame. A methane diffusion flame was tested with stoichiometric mixture fraction 𝑍_%& = 0.5

and nozzles exit velocity and curtain flow velocity are 20 cm/s. The electric field between the burners interacts with the incident beam of 1064 nm to generate a second harmonic signal of 532 nm at the focal point.

The two beams are spatially separated by a prism and collected by a photodiode and a photomultiplier tube, respectively.

Fig. 1 Schematic diagram of EFISH experiment setup on the counterflow burner (PD:

Photodiode, PMT: photomultiplier tube).

The intensity of the second harmonic signal,

𝐼"', with the Gaussian beam is given by:

𝐼_!" ∝ $𝜒^($)(𝑧) ∙ 𝑁(𝑧) ∙ 𝐸(𝑧) ∙ 𝐼_",^! ∙ -. exp(𝑖 ∙ ∆𝑘𝑥)

1 + 8 𝑥𝑧_&9^! 𝑑𝑥

' (

- (2)

Where 𝜒⁽⁾⁾ is the third order susceptibility (material-dependent), 𝑁 is the number density of molecules, 𝐸 is the electric field, 𝐼' is the intensity of the fundamental beam, 𝐿 is the laser path length exposed to the electric field,

∆𝑘 is the wave vector mismatch between fundamental beam and second harmonic wave, 𝑧+ is the Rayleigh range of the Gaussian beam, 𝑥 is the direction of propagation of the incident

picosecond Nd:YAG Laser (Ekspla, PL2251A )

convex lens f = 400 mm

long pass filter

>800 nm

burner burner

convex lens f = 400 mm

mirror applied electric field

prism oscilloscope

PD PMT

* King Abdullah University of Science and Technology (KAUST), Physical Science & Engineering Division (PSE)

** Maastricht University, Faculty of Science and Engineering

† Corresponding author, jin.park@KAUST.edu.sa

beam, and 𝑧 is the direction of the electric field vector. The highly distorted 𝑁 and 𝜒⁽⁾⁾ in the high-temperature reaction zone make it difficult to quantify the EFISH signal measured in the flame as electric field intensity. In this regard, we have proposed a calibration method that does not require information on 𝑁 and 𝜒⁽⁾⁾ [5]. Our basic idea was comparing two EFISH signals: one is measured with the superposition of the external electric field and space charge generated electric field; and another signal is measured only with the electric field by space charge. To realize this approach, the applied external field needs to be eliminated in a very short time. However, in our previous work, the delay between the measurement times of the two signals was 5 μs, which was too long to freeze the space charge distribution. If the delay is too long, not only the distribution of existing ions is changed, but also newly generated electrons and ions are supplied from the reaction zone. Moreover, we didn’t consider the laser path length exposed to the electric filed, 𝐿, in the proposed calibration method. Simplifying Eq. 2 to make the effect of L on the EFISH signal conspicuous:

𝐼_!" ∝ $𝜒^($)(𝑧) ∙ 𝑁(𝑧) ∙ 𝐸(𝑧) ∙ 𝐼_"∙2 ∙ sin (∆𝑘 ∙ 𝐿)

∆𝑘 3

!

(3)

Thus, we developed an improved calibration method that reflect 𝐿 overlooked in the previous calibration method.

Fig. 2 Voltage curve during drop using the H/V switch. The applied voltage reaches zero 140 ns after the trigger.

First, we had to reduce the delay time short enough to freeze the ion distribution.

Accordingly, we introduced a high voltage switch (BEHLKE, HTS 301-01-GSM) between

the voltage amplifier and the burner to drop the external high voltage rapidly. The employed high voltage switch provides a delay of 140 ns as shown in Fig. 2. 140 ns is too short for the chemical time scale, so there is very little generation of electrons and ions from the flame.

As we discussed above, the flame with the applied DC has an electric field, 𝐸9⃗_,-, in which the external applied field, 𝐸9⃗_./&, and the electric field caused by the space charge, 𝐸9⃗_,00, are superimposed:

𝐸9⃗,-= 𝐸9⃗./&+ 𝐸9⃗,00 (4) In previous work, we measured and

compared EFISH signals for 𝐸9⃗,- and 𝐸9⃗,00. To properly derive the local calibration constant, 𝑐(𝑧), by comparing the two signals, it is necessary that all variables except the electric field intensity are the same. However, when measuring 𝐸9⃗_,-, 𝐿 is the burner diameter of 8 cm, and when measuring 𝐸9⃗_,00, 𝐿 is the diameter of the flame, which is 2−3 cm. Therefore, instead of comparing 𝐸9⃗_,- , and 𝐸9⃗_,00 , we compared EFISH signals for two different applied voltages of 2 and 2.5 kV.

In the tested methane counterflow diffusion flame, the electric current is saturated above 2 kV, which means that all ions and electrons generated in the flame flow through the burner as an electric current. Consequently, we can infer that the space charge densities formed under 2 and 2.5 kV conditions are almost identical. We defined the ratio of the incident beam to the second harmonic signal as 𝑆 ≡

𝐼_"1^#.3/𝐼₁. Computing the difference between the

two signals with the defined 𝑆:

𝑆_".345− 𝑆_".#45= 𝑐(𝑧) ∙ {𝐸_".345(𝑧) − 𝐸_".#45(𝑧)} (5) 𝑐(𝑧) ≡ 𝜒⁽⁾⁾(𝑧) ∙ 𝑁(𝑧) ∙2 ∙ sin(∆𝑘 ∙ 𝐿)

∆𝑘 (6) In Equation 5, 𝐸_".345(𝑧) − 𝐸_".#45(𝑧) = 0.5 kV/cm, so 𝑐(𝑧) is easily calculated as follows:

𝑐(𝑧) = 𝑆_".345− 𝑆_".#45

0.5 𝑘𝑉/𝑐𝑚 (7) Together with the obtained 𝑐(𝑧), we can quantify the EFISH signal with an electric field

0 50 100 150

0.0 2.5

Applied voltage [kV]

Time [ns]

as follows:

𝐸(𝑧) = 𝑆(𝑧)

𝑐(𝑧) (8)

Fig. 3 (a) Measured electric field profile, (b) electric potential, and (c) charge density derived by Eq. (1). 𝑧 = 0 mm is fuel nozzle side and 𝑧 = 10 mm is oxygen nozzle side.

We applied the proposed calibration method under the condition that an external positive high voltage was applied to the oxygen nozzle side. That is, positive ions move toward the fuel stream, and electrons and negative ions move toward the oxygen stream. Fig. 3 demonstrates the measured electric field by the space charge and the electric potential and charge density derived by Eq. (1). For typical hydrocarbon flames, the dominant negatively charged particles are electrons. Electrons have much higher mobility than other ions, they have a short residence time. However, before the electrons reach the burner surface, they collide with electron-affinity O2 and create abundant O2-

. Thus, a negative charge density similar to the positive charge density is observed. The peak of the charge density is approximately 1.5

× 10¹⁰ cm^-3, which is close to 1.0 × 10¹⁰ cm^-3,

which was previously predicted theoretically and measured by mass spectroscopy [6, 7].

The direction of the electric field formed between the negative ion pile and the positive ion pile is opposite to that of the external electric field, and an area of approximately 2

−8 mm corresponds to the field inversion regime. In the vicinity of the nozzle surface (i.e., 0−2, 8−10 mm region), the electric field is amplified by the space charge.

We developed an EFISH calibration method and successfully measured the total electric field of an electric field modified diffusion flame.

However, this calibration method requires many prerequisites and needs to be modified when the direction or strength of the external electric field is changed. For a comprehensive investigation, we will extend the experimental conditions from −2.5 kV to +2.5 kV.

Acknowledgement

The research reported in this publication was funded by King Abdullah University of Science and Technology (KAUST), under award number BAS/1/1384-01-01.

References

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015011.

[3] Cui, Yingzhe, Chijie Zhuang, and Rong Zeng.

"Electric field measurements under DC corona discharges in ambient air by electric field induced second harmonic generation." Applied Physics Letters 115.24 (2019): 244101.

[4] Orr, Keegan, et al. "Measurements of electric field in an atmospheric pressure helium plasma jet by the E-FISH method." Plasma Sources Science and Technology 29.3 (2020):

035019.

0 2 4 6 8 10

-1.0x10¹⁰ 0.0 1.0x10¹⁰ 2.0x10¹⁰

Charge density [cm-3]

z position [mm]

-2 0 2 4

Electric field [kV/cm]

0.0 0.5 1.0 1.5 2.0

Voltage [kV]

(a)

(b)

(c)

[5] Butterworth, Thomas D., and Min Suk Cha.

"Electric field measurement in electric-field modified flames." Proceedings of the Combustion Institute 38.4 (2021): 6651-6660.

[6] Goodings, J. M., D. K. Bohme, and Chun- Wai Ng. "Detailed ion chemistry in methane oxygen flames. I. Positive ions." Combustion and Flame 36 (1979): 27-43.

[7] Prager, J., U. Riedel, and J. Warnatz.

"Modeling ion chemistry and charged species diffusion in lean methane–oxygen flames."

Proceedings of the Combustion Institute 31.1 (2007): 1129-1137.