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Abstract
Resonant Schlieren technique combines the variation of the refractive index of the medium with the absorption of seeded particles, thus producing high contrast images. It presents low cost and a relatively easy implementation and operation, and allows visualization of low and high-density flows. This paper describes the application of the Resonant Schlieren method to visualize a pulsed free jet of sulfur hexafluoride. A piezoelectric valve with a duty cycle of 10 Hz and pulse width of 2 ms was used to control the flow through a nozzle with 1 mm diameter. Pressures in a vacuum chamber with optical windows were varied from 20 mbar to 1 bar and the flow was seeded with iodine molecules in order to increase the gas refractive index. The Schlieren images of the expanded flows presented a high contrast and the measured pulsed jet front velocities varied from 3 to 166 m/s, from subsonic to supersonic flow regimes. Numerical simulations were performed using the lattice Boltzmann method and the theoretical results showed a good agreement with experimental data.
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1. Introduction
Visualization of low-density flows by conventional optical techniques is limited by different factors. For example, Schlieren methods and shadowgraphy are limited by the variation of the refractive index of the medium and by the characteristics of the optical components used. Consequently, at low pressure and low-density flows, the deflection of a light ray is reduced, decreasing the image contrast. To overcome this limitation, the Resonant Schlieren (RS) system combines the angular deflection produced by the refraction of light through the flow with the atomic or molecular absorption of species present in the flow. The RS technique allows to obtain higher contrast images than conventional methods [1].
The main visualization and velocimetry methods of low-density flows are electron-beam fluorescence, electric glow discharge, planar laser-induced fluorescence (PLIF), molecular tagging velocimetry and gas velocimetry based on infrared laser-induced fluorescence. The electron-beam technique produces excitation of the molecules present in the flow by an electron source [2–5]. Electric glow discharge is a technique that can use electrodes or cathodes to produce an electrical discharge within the flow. The electrical discharge produces luminescence in the flow, making it visible [6]. In the PLIF technique, a molecule in the flow is irradiated by a laser beam with a frequency equal to the resonance frequency of the molecule, therefore its energy state changes from a stable ground state to an excited state. As the excited molecule releases energy and returns to its ground state, there is light emission which allows flow visualization [7,8]. Molecular tagging velocimetry is a “time-of-flight” technique, similar to PLIF but with larger emission time. The velocity measurement can be easily performed by writing a tag line into the flow and recording its displacements after multiple time delays [9,10]. A recent method for rarefied gas velocity field measurements by means of infrared molecular tagging velocimetry was developed to determine the velocity of carbon dioxide (CO2) jets. Infrared laser-induced fluorescence utilizes the resonant vibrational energy level transitions of small gas molecules, such as CO2, to tag and trace the flow of the molecules by taking subsequent images of the infrared emission [11]. However, all techniques based on the electronic excitation of molecules in the flow are applied only in supersonic and hypersonic flows, because the light emission time is very short. In the case of subsonic flows, the displacement of the excited molecules would be imperceptible by a camera. On the other hand, the RS method can be used in subsonic, supersonic or hypersonic flow regimes.
Leonard and Keck were the first researchers to use the RS method [12]. They applied sodium vapor to increase the contrast of Schlieren images for ballistics studies. Then, the technique was used to visualize sound waves [13] and to image flames [14] and plasmas [15,16].
A significant improvement in the capacity of Schlieren techniques has occurred along the last decades, because high-speed digital cameras and fast computers have opened the possibility for quantitative use of the technique. Lemieux and Hornung used the RS technique to investigate Tollmien-Schlichting instabilities and regime transitions [17]. Other chemical elements such as lithium were used to increase the contrast in Schlieren images of hypersonic low-density flows produced in shock tunnels [18]. Bishop et al. improved the RS method to determine the density of acetylene flames without the need for prior combustion information such as temperature and pressure [19]. Bachmann et al. applied resonant Schlieren to image a column of excited Rb atoms surrounded by atoms in the ground state [20].
In recent years, there has been a great interest in the development of space propulsion systems using new propellants with higher performance and lower toxicity than conventional propellants. Sulfur hexafluoride (SF6) is a high molecular weight gas which has been considered for applications in cold gas thrusters and ion thrusters [21,22]. In cold gas systems, the propellant is stored at high pressure in a tank and, by opening a valve, the gas flows through a nozzle until it reaches supersonic speed, generating thrust. Piezoelectric valves can yield millisecond pulses with high frequency duty cycles and present lower volume and lower power consumption than solenoid valves [21].
In the present work, the RS technique is employed to visualize and determine the velocity of a pulsed free jet of sulfur hexafluoride (SF6). A duty cycle of 10 Hz with pulse width of 2 ms was produced by a piezoelectric valve. The flow was seeded with iodine (I2) in order to increase the gas refractive index. Schlieren images of the expanded flows through a vacuum chamber with optical windows were obtained for pressures ranging from 20 mbar to 1 bar. The pulsed flow was also numerically simulated using the lattice Boltzmann method and the numerical data obtained were compared to the experimental results.
2. Complex refractive index and absortion spectrum
Light speed decreases when light passes through a medium other than vacuum. Therefore, its wavelength varies in the same proportion, since the frequency of light is not affected by the change in the medium. Index of refraction of light in a medium relates the velocity of light in a vacuum, ${c_0}$, to the velocity of light in that medium, c, by $n = {c_0}/c$. The refractive index for a mixture of gases in an isotropic medium is given by the Gladstone-Dale equation:
where Ki is the specific refraction constant and ρj is the partial density of gas j in the mixture, given by ${\rho _j} = {{{p_j}} / {{R_j}}}T$, where pj is the partial pressure of gas j, Rj is the gas constant, and T is temperature [1]. The specific refraction of a given gas is given by: where NA is the Avogadro’s constant and αj is the polarizability of species j. For sulfur hexafluoride, the refractive index is ${n_{S{F_6}}} = 1.00072905$ for a pressure of 101325 Pa, temperature 288.15 K, and wavelength of 600 nm [23]. The difference in the refractive index for common gases is in the third or fourth decimal place.The definition of common gases does not include gases that absorb light in the region of the visible spectrum. To calculate the refractive index of these gases, one has to divide the refractive index into a real part and an imaginary part that arises due to the absorption of light visible [24,13].
The propagation of an electromagnetic wave through an isotropic medium is fully characterized by the complex refractive index of this medium:
where n is the real part of the refractive index, a is the absorption coefficient, given by the Lambert-Beer law, ${i^2} ={-} 1$, $\tilde{v}$ is the wavenumber, $\tilde{v} = \omega /2\pi {\nu _p}$, such that ω is the circular frequency and ${\nu _p}$ is phase velocity [25].For the specific complex refraction index $\hat{n}$ of a resonant gas to be calculated, a complex term for the polarization of the species must then be obtained, given by $\hat{\alpha } = \alpha - i\alpha ^{\prime}$. The dipole polarizability can be calculated using the following expression [26]:
Hohm [26] applied Eq. (4) for calculating the refractive index and polarizability of iodine vapor inside an electronic rovibrational transition band. Additionally, Hohm and coworkers [26,27] have used dispersive Fourier-transform spectroscopy in the visible (DFTS-VIS) to measure the complex refractive index of different gases. In the case of iodine, there was excellent agreement between measured and calculated polarizability data at T = 296.3 K and p = 36 Pa, despite the small refractivity, $(n - 1) \approx 7 \times {10^{ - 7}}$.
Assuming ideal gas behavior, p = 101325 Pa, T = 288.15 K and wavelength of 600 nm for SF6 and I2, the absolute refractivity ratio $\frac{{|{{{\hat{n}}_{{I_2}}} - 1} |}}{{|{{n_{S{F_6}}} - 1} |}} = \frac{{|{{{\hat{\alpha }}_{{I_2}}}} |}}{{|{{\alpha_{S{F_6}}}} |}} = 2.7$ was calculated. In the case of air, one obtains $\frac{{|{{{\hat{\alpha }}_{{I_2}}}} |}}{{|{{\alpha_{S{F_6}}}} |}} = 7.2$ at a wavelength of 532 nm. This difference in refractivity allows the visualization of flows by the Resonant Schlieren technique at lower pressures, where conventional Schlieren methods cannot provide flow images with a good contrast.
A numerical simulation of the absorption spectrum of the iodine seeds was performed in order to identify the strongest absorption band and, consequently, to point out the laser frequency to be adopted as source light of the Schlieren system.
An iodine molecule can present electronic, vibrational and rotational transitions. In the visible region of its electronic spectrum, iodine shows progressions of bands involving vibrational states. The electronic spectrum has a maximum absorption in the green region [28]. Figure 1 shows the simulation of an iodine absorption spectrum in the region of 15000 to 19430 cm−1 performed with the IodineSpec5 code [29]. A temperature of 298 K, pressure of 1 atm and a line width resolution of 0.1 cm−1 were considered. At the frequency of 18797 cm−1, the CW Nd-Yag laser emission coincides with a peak absorption of the iodine spectrum. The absorption intensity of the spectrum in Fig. 1 was normalized and the value –1 was attributed to the maximum absorption in the frequency region from 11200 to 19430 cm−1.
Tests were carried out to check the absorption of iodine molecules at the wavelength of laser emission. A sample of solid iodine was confined in a glass ampoule and then was heated by a heat gun, in order to promote iodine sublimation. An Ocean Optics HR 2000 spectrometer was used to record the I2 emission spectrum and the laser emission line. As seen in Fig. 2, energy absorption by the iodine molecules in the 532 nm region causes emission of anti-Stokes radiation in the 520 nm region.
3. Toepler Schlieren system
A Toepler Schlieren arrangement presents high sensitivity to small variations in the flow refractive index. A scheme of a simplified optical system using lenses is presented in Fig. 3. Arrangements with lenses have some advantages with respect to systems using mirrors, since they present less optical aberrations and a relatively easy implementation of a laser light source, which is very convenient for use in the RS method.
Fig. 3. Schlieren arrangement, where l1 and l2 are the lenses, L is flow length in the z-direction, f2 is the second lens focal distance and k is a knife.
Contrast is the difference in luminance or color that makes an object representation in an image or screen distinguishable. In visual perception of the real world, contrast is determined by the difference in the color and brightness of the object and other objects within the same field of view. In the case of a Schlieren image, using a monochromatic light source, the contrast is limited only by the difference in brightness, that is, by the amount of light that arrives at each point of a screen or camera sensor. Using the contrast equation presented by Settles [30], the image contrast for Resonant Schlieren along the y axis is given by
where h is the unobstructed height of the light source image projected onto the knife and b is the percentage of light obstructed by the knife, ranging from $0 \le b \le 1$. When b = 0 no knife is used, corresponding to the shadowgraphy technique, and when b = 1 the whole image of the light source is obstructed.The following observations can be made from Eq. (5): i) the image contrast is proportional to the focal distance of the second lens (f2); ii) contrast is inversely proportional to the unobstructed height of the light source image at the knife edge (h); and iii) contrast is proportional to the first derivative of $|{\hat{n}} |$. Gases with high refraction index, in general, present larger gradients of the refraction index. Usually, values of b vary from 0.7 to 0.8, depending on the sensitivity of the camera.
4. Experimental setup
A scheme of the experimental setup is presented in Fig. 4. The setup includes a stainless-steel expansion chamber, a Lasertechnics 203B LPV pulsed piezoelectric valve, a Tektronix TDS 2014- oscilloscope, a FG-2002C function generator, a SF6 tank with 5 bar, an iodine cell, and a valve driver to amplify the signal from the function generator to open the valve. The vacuum system comprised a mechanical pump and a diffuser pump, with pressure measurement by a Pirani portable thermovac TM 101. A CW Nd-Yag laser from Coherent brand, Verdi V-8 model, was used as a light source, with emission at 532 nm, linewidth 5 MHz and output power of 3 W. A beam expander was used to produce a parallel beam of light, using a focusing lens with a 2 m focal length. Prisms and mirrors were employed to direct the light beam and neutral density filters were used to attenuate the light beam before reaching the camera. A high-speed Phantom v2010 digital camera was used operating at 37000 fps. Schlieren images were obtained with obstruction of about 70% of the light beam. A cylindrical nozzle with exit diameter of 1 mm was located at the exit of the piezoelectric valve. The pulse width time was 2 ms with a frequency of 10 Hz.
Fig. 4. Optical Schlieren arrangement: (a) Optical components: LE - laser beam elevator, P1 and P2 - prisms, B - beam expander with lenses, L - focusing lens, M1 and M2 - flat mirrors, K - knife; and F - neutral filter; (b) Photo of the experimental arrangement.
The front velocities of the SF6 pulsed free jets were determined along the x-direction inside a vacuum chamber with pressures varying from 20 mbar to 1 bar, while the stagnation pressure of the SF6 tank was equal to 5 bar in all tests.
Iodine molecules were seeded in the SF6 flow in order to increase the fluid refraction index, once absorption of light by the iodine molecules increase the complex refractive index of the medium. Iodine was introduced into the flow through a metal ampoule heated by a thermal jacket. The flow of SF6, as it passes through the ampoule, drags the iodine molecules, and is injected by the pulsed valve into the expansion chamber. The amount of seeded molecules was controlled by the temperature of the thermal jacket, since iodine is in solid state at ambient temperature and sublimes with increasing temperature. This procedure did not yield a uniform distribution of iodine throughout the flow, but allowed to increase the contrast of the Schlieren images.
Images obtained by the high-speed digital camera were 512×512 pixels in size, with a spatial resolution of 6.7 pixels/mm, and were recorded at an interval of 27 µs with exposure time of 10 µs. The PCC software [31] was utilized to calculate the velocity of the pulsed jet flow from the instants in which the front of the pulsed flow passed at points 0 and 5 mm from the nozzle exit of the piezoelectric valve.
5. Numerical simulation
The pulsed free jet of SF6 was numerically simulated taking into account viscous effects and using the lattice Boltzmann method (LBM) [32,33]. A 3D scheme was adopted utilizing the LBM D3Q19 stencil for velocity distribution. A relaxation method was employed considering a single relaxation time (SRT) and a relaxation ratio 1.9, as suggested by Elguennouni et al. (2020) [34]. Programs for environment generation, numerical integration and visualization were written in Python language using the lbmpy library [35].
The simulations were performed in the flow development region and in the source flow region which represents the pulsed valve exit. The free region had pressures from 20 mbar to 1 bar and the source flow region had a stagnation pressure of 5 bar. The initial temperature was 298 K and the inlet pulsed flow was modeled as a sine wave with 10 Hz. In these conditions there is generation of a series of waves that propagate in space and dissipate when spread away from the source. Figure 5 shows plots of the average relative densities of the pulsed flows for several chamber pressures at different times and, as expected, the pulsed flow velocities increase for smaller chamber pressures. In Fig. 5, the background has different color scales in order to enhance the contrast.
Fig. 5. Numerical simulations of 10 Hz pulsed flows of SF6 for different chamber pressures: (a) Pc = 1 bar; (b) Pc = 0.3 bar; (c) Pc = 0.25 bar.
6. Results and discussions
Figure 6(a) shows an image with optical diffraction effects produced by laser interaction with the large number of optical elements (mirrors, lenses, windows, filters and prisms). These diffraction effects may be eliminated by light coherence reduction using an appropriate optical filter or by digital image filters. Figure 6(b) shows the Schlieren image of the flow after digital background filtering. The image of the test area without the presence of flow was used with a median filter and a contrast balance. The final result of the image processing is the visualization of the SF6 flow without any diffraction effect shown in Fig. 6(b).
Fig. 6. Schlieren images of SF6 flow. (a) Raw image; (b) Processed image. The expansion of the jets can be seen in Visualization 1.
Imaging of air subsonic flows at room temperature is not an easy task for Schlieren systems. On the other hand, subsonic flows, of SF6 can be easily visualized, due to its high refractive index compared to air. However, by decreasing the test chamber pressure through which the flow is expanded, visualization becomes increasingly difficult, until a certain pressure value when the flow cannot be visualized. The addition of iodine seeds in the SF6 flow increases the range of pressures where it is possible to visualize the flow.
Contrast enhancement of Schlieren images by iodine seeds can be verified in Fig. 7 that shows pulsed jet flows of SF6 into a chamber with pressure of 50 mbar. The raw images of the pulsed jet with and without iodine seeds are depicted, respectively, in Figs. 7(a) and 7(b), while the processed images are shown, respectively, in Figs. 7(c) and 7(d). The pulsed jet image shown in Fig. 7(c), with iodine seeds, presents a better contrast than the pulsed jet image in Fig. 7(d), without iodine seeds.
Fig. 7. Effect of iodine seeding on visualization of a pulsed jet of SF6 for Pc = 0.05 bar: (a) SF6 with iodine seeds; (b) SF6 without iodine seeds; (c) processed image of SF6 with iodine seeds; (d) processed image of SF6 without iodine seeds.
As mentioned before, the iodine molecules absorb part of the light beam, increasing the flow refraction index and, consequently, the contrast in the image increases. The contrast enhancement makes it possible to visualize low-density flows produced at low pressures. In addition, the edges of the flow are more easily identified, reducing the error associated with geometric measurements of the flow. For velocimetry of pulsed jet flows, an increase in the image contrast allows to determine the pulsed jet front position with a higher precision.
Figure 8 shows Schlieren images of SF6 pulsed jet flows at various instants with different chamber pressures. At lower pressures the flow velocity in the expansion chamber is higher, but the contrast of the images becomes increasingly worse as the air becomes rarefied.
Fig. 8. Visualization of a pulsed jet flow of SF6 at different chamber pressures: a) Pc =1 bar; b) Pc = 0.3 bar; c) Pc = 0.25 bar.
Figure 9 compares experimental and numerical data of pulsed jet front velocities as a function of the chamber pressure, Pc. Numerical data are depicted by the red curve, given by $v = 2.867P_c^{ - 1.037}$, yielding a rms error of ±3.54 m/s with respect to the experimental data. In order to calibrate distances with pixels for velocimetry, a ruler with a length of 20 mm was positioned in the test region.
The optical technique error was calculated from the detection limits of the pulsed jet front. The maximum error is ±5.55 m/s, given by the distance of 2 pixels divided by the time interval between two sequential images [36].
Measured jet front velocities varied from 3 to 166 m/s, approximately. Considering the sound speed at room temperature for SF6 equal to 138.4 m/s, the Mach number M varies from subsonic (M < 1) to supersonic (M > 1). It should be noted that there is a temperature decrease in expanding flows and, consequently, the speed of sound is reduced and the Mach number increases.
The Resonant Schlieren technique allows visualization of flows where conventional techniques cannot provide images with an appropriate contrast level. The RS technique requires seeding of molecules which can absorb light in the visible spectrum. Iodine molecules present strong absorption of light in the visible region, especially in the green wavelength. Therefore, common laser light sources with wavelength 532 nm can be used in Resonant Schlieren systems.
7. Conclusion
Visualization of a pulsed free jet of gaseous SF6 was made by the Resonant Schlieren technique using iodine seeds. A piezoelectric valve with a duty cycle of 10 Hz was used to control the pulsed flow through a cylindrical nozzle with 1 mm diameter, from a tank at 5 bar to a vacuum chamber with pressures varying from 20 mbar to 1 bar. Initially, the contrast equation of a Schlieren image was derived based on the complex refractive index. A numerical simulation of the iodine absorption spectrum was performed in order to identify the lines with highest absorption of light, consequently a 532 nm CW Nd-Yag laser was adopted as a light source. Then, a numerical simulation was made using the lattice Boltzmann method to estimate the pulsed jet front velocities. The Schlieren images obtained of flows with iodine seeds presented a higher contrast than images of flows without seeds. The front velocities of the SF6 pulsed jet flow at the nozzle exit varied from 3 to 166 m/s, ranging from subsonic to supersonic flow regimes. The numerical results have shown a good agreement with experimental data.
Funding
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (1).
Acknowledgment
The authors thank Prof. Uwe Hohm from Braunschweig University for helping with the analysis of the complex refractive index.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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