Schlieren Image Velocimetry of Swirl Sprays

Schlieren image velocimetry (SIV) is based on light deflection through flow heterogeneities and image cross-correlations. This is a low-cost and relatively low complexity technique that allows measurement of the droplet velocity field in a large region of a spray. A Z-type Toepler schlieren system with a high-speed camera was used to determine mean vertical and horizontal droplet velocities, as well as the cone angles of sprays produced by a pressure swirl injector with characteristic geometric constant K = 2. Different LEDs and digital filters were evaluated for edge detection and improvement of image contrast. Open software was adopted for digital image processing and velocimetry. Interrogation windows and overlaps of different sizes were tested to obtain an appropriate correlation for determination of the velocity field. The digital images were obtained with 5 × 103 fps and a resolution of 2.77 pixels/mm. Since the swirl sprays analysed presented instabilities, a number of 100 cross-correlations of images was required to reduce mean velocity fluctuations. Injection pressures varied from 0.05 to 7 bar and mass flow rates varied from 1.389 to 13.89 g/s, using water as test fluid. The wideband warm white LED with Laplacian or high-pass filters provided velocity data for a larger range of injection pressures. Mean axial velocities varied from 3.3 to 11.3 m/s, approximately, with mean horizontal velocities varying from around 0.17 to 3.3 m/s for pressures from 0.05 to 3.22 bar. The velocity data were compared to microscopic shadowgraphy results, showing a good agreement. Spray cone angles ranged from about 32.5o to 69.5°, for injection pressures from 0.05 to 7 bar, and results of triangulation with a blue LED were closer to semi-empirical data.


Introduction
Schlieren Image Velocimetry (SIV) is a technique with different variations or configurations used for measurement of Lagrangian velocities of flow heterogeneities which can originate from pressure, density, velocity or temperature gradients. To visualize these flow heterogeneities, optical imaging techniques such as shadowgraphy or schlieren can be utilized. Recently, SIV methods have found broader applications due to their relatively reduced experimental complexity, low cost, easy implementation and wide range of problems that can be analyzed.
Currently, the three main flow velocity measurement techniques are Phase Doppler Anemometry (PDA), Particle Image Velocimetry (PIV) and Microscopic Shadowgraphy (Elserfy et al. 2021;Klinner and Willert 2022;Qavi and Jiang 2022). Each technique has limiting factors for application, e.g., the measurement areas. The PDA technique provides point values of the flow velocity, and the investigated areas are on the order of the crosssection of a laser beam, ~ 1 mm 2 . The Microscopic Shadowgraphy technique yields velocity values of a few droplets within a relatively small field of view ~ 25-100 mm 2 . Consequently, the determination of the entire field of spray velocities using PDA or Microscopic Shadowgraphy techniques requires a sweep along the spray. The PIV technique, on the other hand, can provide the velocity field of a spray on a larger area, generally in the order of a few cm 2 , which is, in general, sufficient to cover the interest area of sprays produced by most injectors used in combustion. Several studies indicate a good agreement of droplet velocities measured by these three techniques (Ghaemi et al. 2010;Goldsworthy et al. 2011;Lee et al. 2013).
Flow velocimetry by schlieren and shadowgraphy optical systems with various configurations was compared with Particle Image Velocimetry (PIV) (Biswas and Qiao 2017;Ozawa et al. 2020). These authors verified that shadowgraphy results were closer to PIV data. On the other hand, Bharti et al. (2022) investigated the performance of knife light cutting in a Z-type Toepler system, and concluded that the best results are found for a schlieren method with 65% of light obstruction. Nevertheless, the ideal velocimetry system for a given application will depend not only on the optical system parameters, but also on the test fluid refractive index. A scheme of the Z-Toepler optical system used in the present work is shown in Fig. 1.
The contrast of an image obtained by a schlieren system (Settles 2001) can be calculated by: where f 2 is the focal length of the second mirror, a is the unobstructed height of the light source image formed in the focal region, n 0 is the medium refractive index, L is the extension of the medium in the direction of propagation of the light rays and n∕ y is the angular deflection by a ray of light as it passes through the test object. Jonassen et al. (2006) obtained the contrast sensitivity using a schlieren Toepler method: where γ is the percentage of the light beam cut by the knife. If there is no obstruction of light, as in shadowgraphy, then the sensitivity is lower.
(1) C = f 2 a L n 0 n y (2) S = f 2 a 1 − ∕100 Therefore, the contrast and sensitivity of a schlieren method depend on four key parameters: the focal length of the mirrors, height of the unobstructed light source, percentage of light cut by the knife and refractive index of the test object. Thus, these four parameters should be taken into account in order to reproduce the operating conditions of a given study.
The Z-Toepler optical arrangement with a knife is a schlieren method. When the knife is removed, the array becomes a shadowgraphy system. A knife increases image contrast and system sensitivity by blocking a fraction the light that passes through the test region. However, in the velocimetry of sprays, the increase in the contrast makes the air within and around the spray visible. Since the Z-Toepler method integrates the images of droplets with the surrounding air, it generates a blurred image. Therefore, an optical array configuration without a knife was adopted in order to improve image correlation and velocity calculation.
Tests of fluids with different refractive indexes, such as oxygen and methane gases, using a same optical arrangement, will produce images with different sensitivities and contrasts. Normally, to obtain images of a subsonic flow of oxygen gas using a Z-Toepler optical system with 1.5 m focal length mirrors, a 50% cut-off of the light may be necessary. In a subsonic flow of methane under the same conditions, the use of a knife is not necessary, and shadowgraphy is sufficient to observe the flow. In other words, a shadowgraph of an oxygen subsonic flow at ambient conditions presents low contrast and sensitivity whereas for a methane gas flow, a shadowgraph will provide good contrast and sensitivity.
A spray contains droplets of different sizes. The SIV method uses the heterogeneities formed by groups of droplets within small flow regions. The average droplet velocity is calculated from a correlation between sequential images of the heterogeneity. Each spray image is divided in windows with overlaps of different sizes. A given overlap, in general, shows droplets of different sizes and small droplets within a window are indicated by a single pixel while large droplets occupy more than one pixel.
A PIV system creates a laser sheet across the spray which scatters the light whereas a SIV system uses a collimated light beam. Consequently, a PIV system with the same resolution of a SIV system in terms of pixels/mm yields a lower resolution in terms of lp/mm (lp = line pairs). The resolution based on pixels/mm depends on the magnification factor and the camera sensor, while the number of lines per mm depends on the quality of optical components, magnification, light source, camera sensor, etc. A low resolution (pixels/mm) is not desired, however the adoption of a high resolution will imply a small field area. On the other hand, the utilization of high fps values of the digital camera reduces the number of pixels available for imaging. In the present case fps = 5 kHz was required to measure droplet velocities in all operating conditions and, consequently, the image size was 300 × 300 pixels.
Therefore, the main objective of this work is to develop a SIV method capable to provide the velocity field of droplets in large areas of a spray. The performance of the SIV method is improved by using specific light sources and digital filters. The proposed technique presents lower cost and its application is less complex than the PIV technique.
The lighting used in the experiment is not only related to the sensitivity of the schlieren technique, but also to the resolution of the images. Digital processing can be used regardless of the technique adopted to obtain the flow image. Since liquid water was atomized by a pressure swirl injector in this work, it was not necessary to cut the light in the Z-Toepler arrangement to capture the droplet images and, therefore, the shadowgraphy configuration was adopted in all the tests.
Regarding the limitations of optical velocimetry methods such as SIV and PIV, the two main parameters are image resolution (pixels/mm) and frame rate (fps) of the cameras used for imaging. Normally, in high-speed cameras the frame rate is inversely proportional to the image size. Therefore, to adjust the camera fps to the fluid velocity, the size of the investigated area is usually reduced or objective lenses are attached to the camera in order to reduce the size of the test object on the camera sensor. Traditional PIV methods normally require a resolution of 10 pixels/mm and time between images of 1 μs. Wills et al. (2020) developed a SIV methodology that was able to determine the flow velocity in a wind tunnel using images with resolution of 4.5 pixels/mm and 1 × 10 5 fps.
This paper investigates the influences of light wavelength and digital filters on contrast, sensitivity and resolution of a SIV method applied to spray analysis. Monochromatic and wideband LEDs are compared and spray digital images are pre-processed using edge detection filters and a high-pass filter. An open software is adopted for image cross-correlation and velocity calculation, and different interrogation and overlap window sizes are tested. A comparison between SIV and Microscopic Shadowgraphy data will be performed. Spray cone angles and mean axial and horizontal velocity fields of spray droplets formed by a pressure swirl injector are determined for different operational conditions.

Literature Review
A short review of the literature on application and development of SIV methods is presented in this section, considering optical arrangements, image processing methods and velocimetry software.

Schlieren Optical Methods
Toepler, Focusing Schlieren and Background Oriented Schlieren (BOS) arrangements are among the most used SIV systems. Toepler methods also can have different configurations for SIV: one-mirror, lens and Z-type. Jonassen et al. (2006) measured turbulent flow velocities using Toepler SIV and carried out one of the first studies with different optical configurations and, according to the authors, the best results were obtained using LED light sources. Biswas and Qiao (2017) studied a high-velocity helium jet with a Z-type Toepler method using vertical and horizontal knife orientations and shadowgraphy. Their results were similar to laser PIV data for both shadowgraphy and the schlieren method with the knife in horizontal position and cut fraction of 40%. Gena et al. (2020) used a Toepler one-mirror optical array to measure the velocities of the human thermal plume. They verified that quantitative schlieren results had good agreement with hot-wire anemometer and thermistor data measured at discrete points along the plume. Nematollahi et al. (2020) developed a SIV system using a modified Toepler Z-type arrangement, for the diagnostic of organic Rankine cycles in subsonic and supersonic flow regimes and obtained results similar to PIV data. Wang et al. (2021a, b) also used a Toepler Z-type array to study the flow velocities in hydrogen and methane flame ignition processes. Rong et al. (2021) used a one-mirror optical system combined with a color filter to detect and measure the velocity of pollutants emitted in the atmospheric air.
Concerning Toepler optical systems, Z-type configurations allow work distances far from the mirrors, what makes them attractive for studies of sprays, plasmas, flames, wind and shock tunnels. Toepler systems using only one mirror present a higher sensitivity, equal to twice the focal length (2X), while Z-type Toepler systems show a sensitivity proportional to the focal length (1X) (Settles 2001). Besides, systems with only one mirror have lower costs than systems with two mirrors, and in the case of systems using large mirrors, over 0.5 m diameter, their values can be very high. However, in one-mirror systems the test object must be close to the mirror, what can be a limiting factor when two-phase or reactive flows are analysed. Toepler systems using only lenses are advantageous for investigating small scale flows, since they can provide a higher spatial resolution compared to systems with mirrors. For example, Kim et al. (2020) adopted a Toepler lens system to visualize bacteria-size particles within droplets.
A focusing schlieren optical system was developed by Fu and Wu (2001) to perform velocimetry by correlation of images of buoyant flows generated from gas explosion ejection and gas fires. Hargather et al. (2011) used a focusing schlieren system for studies of supersonic flows in wind tunnels. However, they verified that Toepler methods provided better velocimetry results than focusing schlieren. One important aspect of their work was the improvement of the SIV by LED lighting. According to the authors, LED application enables intense lighting, with good light distribution from a small source when compared to traditional lamps. The focusing schlieren systems present an advantage over Toepler methods because they may provide three-dimensional images of the flow, while Toepler methods are limited to two-dimensional analysis.
BOS is the most versatile method of all schlieren systems. The recent wide utilization of this method lies in two main factors, the first is the simplicity and low cost of its components, BOS systems can be used for flow velocity analysis using smartphones (Aguirre-Pablo et al. 2017;Settles 2018). And the second reason is with regard to the possibility of obtaining the analysis of large areas, such as a helicopter in flight (Raffel 1 3 2015) or shock waves from explosive tests (Winter and Hargather 2019). However, BOS does not present the same sensitivity as Toepler methods and small gradients in temperature, pressure or density may not be observed. Goldhahn and Seume (2007) pointed out that the determining factors in the sensitivity of the BOS technique are the camera resolution, the software used and the increase in the focal length of the camera's lens and the camera proximity of the test fluid.

Schlieren Image Processing
Digital filters have been used to improve the quality of schlieren images since the initial utilization of digital cameras. For schlieren velocimetry applications, filters were first used by Fu (2001). The most common filters for processing schlieren images are the gray scale conversion of color images, edge detection, noise reduction, contrast balance, background subtraction and high-pass. Biswas and Qiao (2017) have studied different types of filters and the best results were obtained with noise removal, contrast balance and Laplacian filters.

PIV and SIV Software
The first velocity estimates by schlieren images were related to shock waves. Ernest Mach utilized the optical arrangement developed by his contemporary August Toepler to visualize shock waves in flows (Krehl and Engemann 1995). The first measurement of velocity in a flow using a Schlieren optical array and a high-speed conventional camera was performed by Townend (1936) whereas the first application of a schlieren system for velocimetry with a high-speed digital camera and a commercial PIV software was made by Fu (2001).
Due to the development of low-cost and high-speed cameras and computers with high data processing capacity, there has been a growing increase in the development and use of the SIV technique. Among the software used in velocimetry, the following stand out: (i) traditional PIV-commercial or open and free code; (ii) specific correlation velocimetry software developed for schlieren images; iii) codes that use machine learning and artificial intelligence to calculate flow velocity.
Currently, conventional PIV software programs are the most commonly used for SIV. The advantage of using these PIV software packages is their long-time improvement and their ability to measure the many parameters of interest in fluid mechanics.
The pioneering work in software development for SIV was that of Hargather et al. (2011) who developed a Matlab code using the "normxcorr2" function. Wills et al. (2020) adapted a PIV code with the normxcorr2 function, and determined the velocity of supersonic flows using images with a resolution of 4.5 pixels/mm. Wang et al. (2021a, b) developed and optimized a schlieren motion estimation (SME) algorithm capable of calculating the velocity in flaming ignition processes. Cai et al. (2021) developed a powerful BOS method capable of measuring the threedimensional field of pressure and velocity that uses neural networks to perform flow tomography. Znamenskaya and Doroshchenko (Znamenskaya and Doroshchenko 2021), developed an edge detection method using machine learning, enabling the calculation of supersonic velocities in shock tubes.
In the present work, the OpenPIV software (Ben-Gida et al. 2020), in MATLAB version, was adopted. This software package contains toolboxes for calculation of different flow characteristics, including mean and turbulent velocity fields, vorticities, auto-correlations and energy terms.

Experimental Setup
This section describes the experimental setup and test conditions for the present spray studies. The experimental setup is comprised by the test bench, injector and optical system.

Test Bench
The bench used for tests contains tanks of fluids, nitrogen pressuring tank, rotameters, valves, datalogger, pressure transducers, thermocouples and feed lines for testing different fluids, as shown in Fig. 2. A Novus pressure transmitter, HUBA 510 model, with accuracy of 0.5%, was used for measurement of injection pressure, whereas an OMEL 3P model rotameter with 2% accuracy relative to the reading was utilized for measurement of liquid flow rates. Triplicate data were used to determine liquid flow rates, as described in Sect. 3.3.

Injector
Injectors are used to atomize a fluid in order to increase its surface area and, therefore, to augment vaporization, mixing and burning rates. During the atomization process the fluid surface area gradually increases due to the breakdown of larger droplets and ligaments into  (Lefebvre and Mcdonell 2017). There are many types of injectors which are employed according to several criteria such as atomization efficiency, operational range, stability, availability and application history. Pressure swirl injectors are widely used in internal combustion engines (Huang et al. 2020), rocket engines (Kang 2018) and gas turbine engines (Alajmi et al. 2019).
The pressure swirl injector utilized in this work comprises a vortex chamber, tangential inlets, convergent section and exit nozzle, as shown in Fig. 3. Fluid (water) is injected through the tangential inlets into the vortex chamber and forms an air core along the injector axis due to the high tangential velocity of the fluid. The liquid flow at the nozzle exit forms a rotating hollow conical film, then the rotating film becomes unstable, undergoes a primary breakup forms ligaments of liquid and relatively large droplets which then breakup to form small droplets through a secondary atomization process. The pressure swirl injector used for tests has a characteristic geometric constant K = 2 and its main dimensions were depicted in Fig. 3. The geometric constant K is a design parameter of pressure swirl injectors and affects atomization performance, discharge coefficient and spray angle (Bazarov et al. 2004). It is given by K = r s R∕A e , where r s is the radius of the injector nozzle, R is the radial distance from the center of the vortex chamber to the radius of the tangential inlet hole and A e is the inlet area. Additional details about the present injector design are given by (Fischer 2019).

Optical System
A Z-type schlieren Toepler system was mounted on an aluminum optical table, as seen in Figs. 1 and 2, and the test region with injector, spray and collection system is located at the middle of the table. Two mirrors with diameters of 300 mm were placed at the ends of the optical table. The mirrors present optical surface quality of 40 -20 scratch-dig and focal length of 1500 mm. To record the spray images, a Fastec TX3 high-speed camera was used, with 5 kfps and shutter of 2 μs.
Three Thorlabs LEDs were used as light sources: (i) M375L4 monochromatic LED with wavelength centered in the region of 375 nm, corresponding to ultraviolet color; (ii) M430L4 monochromatic LED with wavelength centered in the region of 430 nm, corresponding to blue color; (iii) MWWHL4 LED with wavelengths in the region from 400 to 800 nm, corresponding to warm white color of 3000 K. Spectra of the light sources were recorded by an Ocean Optics Flame UV-VIS spectrometer and are shown in Fig. 4.   Fig. 3 Pressure swirl injector used for tests Spray images with 300 × 300 pixels and their histograms were obtained using the aforementioned LEDs, as depicted in Fig. 5. No type of correction or filter was used in these images. The image colors do not correspond to the LED colors, since there is interaction between light and camera lens. Figure 5a shows a spray image obtained with the blue LED, however Fig. 5d shows that the maximum peak of its histogram corresponds to the green color. In the case of ultraviolet light the image histogram, showed in Fig. 5e, presents spikes in blue and green colors. The warm white LED yields an orange color, as seen in Fig. 5c, whereas the histogram in Fig. 5f shows three spikes in red, green and blue.

Test Conditions
Tests were performed for 10 different injection pressures (gauge), from about 0 to 7.2 bar. Figure 6 shows the measured mass flow rates versus injection pressures, using triplicate data. A fitting curve for the mass flow rate, ṁ = 5.768ΔP 0.438 g/s, was obtained with a relatively high correlation R 2 = 0.999.
Spray images for each injection pressure were obtained with the three LEDs previously described and are shown in Fig. 7. At the lowest pressure considered (ΔP ~ 0 in Test 1) the water mass flow rate is very small, caused by the liquid column weight, and there is formation of a few droplets. In Test 2, ΔP ~ 0.16 bar, the mass flow rate is 2.78 g/s and there appears an onion-like structure adjacent to the nozzle exit and, below this "onion", there is formation of a spray cone. In Test 3, ΔP ~ 0.44 bar, the mass flow rate is 4.17 g/s, and the "onion" size increases and the spray cone angle decrease in relation to Test 2. The spray cone angle decreases in Test 3 but increases in the next Tests with increasing injection pressures. The onion structure disappears in Test 4 and there is formation of a conical liquid film which breakups to produce a hollow spray cone.

Image Pre-processing
Image pre-processing was carried out by the GIMP program, a free and open-source image creation and editing program. It allows the conversion of images, application of digital filters for edge detection and high frequency filtering. Initially, all the images were converted to gray scale, then were pre-processed with different filters (Team GIMP 2019). Figure 8 shows the pre-processed images with different filters and their histograms for Test 5, where a warm white 3000 K light source was used.
A Gaussian filter was applied to the spray images in order to detect droplet and spray cone edges, as seen in Fig. 8a. The filtered image presented a white background with spray details in black, and its histogram shows a spike of white pixels, as presented in Fig. 8d. A Laplacian filter was also applied to the spray images to detect droplet and spray cone edges,  Fig. 8b. This filter produced an image with black background and spray details in white, and its histogram presents a spike of black pixels, as depicted in Fig. 8e. A highpass filter was used to eliminate high frequencies in the spray images, as shown in Fig. 8c. These high frequencies originate from sudden changes in brightness or color in neighboring pixels. The high-pass filter produced an image with gray background and droplet and spray cone details in black, and its histogram has spikes of black and gray pixels, as seen in Fig. 8f.

Spray Image Correlation
In the PIV technique, small tracking particles are used for measurement of flow velocities. Usually, particles of titanium dioxide, TiO 2, or alumina, Al 2 O 3 , are used with average sizes of the order of micra. In the SIV technique, the particles are the flow heterogeneities which can have different sizes. For example, in the case of sprays, the tracking particles are droplets and ligaments generated by the atomization process, and these particles can have sizes varying from microns to millimeters. Figure 9a shows an illustration of image correlation used in the PIV technique, with two sequential images at times t 1 and t 2 . The correlation between images yields the displacements of the trace particles. Figure 9b shows an illustration of a SIV image The non-uniformity of droplet and ligament shapes affects the size of the interrogation windows used to obtain the image correlation and, therefore, to calculate the particle velocities. In the SIV technique larger particles need larger interrogation windows to be analyzed. The images in the present study have sizes of 300 × 300 pixels, and the interrogation window size best suited to calculate image correlations was 64 × 64, since it allowed to identify the particle shapes and correlations in relatively short times.
OpenPIV software adopts a cross-correlation algorithm that yields a map of displacement vectors to correlate two sequential PIV images. The output data, in pixels of displacement, is transformed into physical units (m/s) by using the scale (magnification) and time interval ∆t. The algorithm is applied to sub-image rectangular or square interrogation windows, using a FFT-based cross-correlation algorithm to process sequential pairs of PIV images to yield the velocity field maps consequently sizes are typically of 2 n × 2 m sizes (64 × 16, 32 × 32, etc.) (Ben-Gida et al. 2020). The value of spacing/overlap controls the grid spatial resolution at which the vertical and horizontal velocity components are estimated. Use of larger sizes of interrogation windows decreases the resolution of the calculated velocity field, however it is less affected by the background noise.

Results and Discussion
Initially, the Z-Toepler schlieren optical system was adjusted to obtain the spray images. The system sensitivity increased with the knife-edge cut-off. However, the increased sensitivity made the surrounding air also visible, thus affecting the droplet velocity measurements. Therefore, a knife-edge cut-off of 0%, corresponding to shadowgraphy, was selected for all the tests.

Axial Velocity Measurements
Three steps were required to calculate the mean axial velocity field, as shown in Fig. 10. Hundreds of sequential images were taken by the high-speed camera with time interval of 1/fps = 19.79 ms, and shutter of 2 μs. The origin (z = 0) of the spray axis was set 10 mm below the nozzle exit, in order to locate interrogation windows to obtain image correlations. Above this position droplets are not formed yet. Figure 10a shows a pre-processed spray image of Test 4, using a high-pass filter, with ΔP = 0.96 bar and ṁ = 5.55 g/s. Figure 10b presents velocities calculated from two sequential images by the OpenPIV software. Figure 10c depicts the mean axial velocity field along the spray, from 100 sequential images, obtained with help of the Spatial and Temporal Analysis Toolbox of OpenPIV software. The calculated mean axial velocity field is not Fig. 9 Illustration of image correlations in the PIV and SIV techniques using interrogation windows with different scales and number of pixels 1 3 perfectly symmetrical and is located below the film breakup region. The maximum mean axial droplet velocity was approximately 6.46 m/s. The spray of a pressure swirl injector in general has a hollow cone shape and outside this cone there are no droplets. However, there is a mist around the spray due to air recirculation. This mist presents very low average velocities and, consequently, this is the main reason for the drastic decrease in measured droplet velocities in the spray boundary by the SIV system.
Normally, in the development or application of SIV techniques, their results are compared with data obtained by other techniques. For example, Hargather and Settles (Hargather and Settles 2010;Settles and Hargather 2017) have compared flow velocities in a wind tunnel measured by a SIV system with results from a Pitot tube and from conventional PIV. Their results showed a good agreement among SIV and the other measurement techniques. In the present work, a microscopic shadowgraphy system was used for determination of individual droplet velocities and comparison with SIV results.
The microscopy system comprised a Fastec HS-7 high speed camera, a Navitar 6000 superzoom lens and a Titan TL telecentric light source from Edmund Optics. A zoom magnification of 3.71 was adopted with lighting and work distances equal to 300 mm. Calibration of the shadowgraph microsocopy system was performed with a Thorlabs R1L1S1N multi-target for resolution and distortion measurements. The calculated resolution was 57 lp/mm using the USAF 1951 target and no significant distortions were observed using a concentric circles target. Sequential spray images obtained by microscopic shadowgraphy are depicted in Fig. 11. The original images are shown in Fig. 11a, b, while Fig. 11c, d show the processed images in which the red particles were chosen to determine the average droplet velocities. For each test condition, velocities of one thousand droplets were determined by the microscopic shadowgraphy method. The calculated values are compared to the SIV method data, as will be shown in the Results section. Figure 12 presents the mean axial velocity field of droplets in Test 5, as calculated by the OpenPIV software. Figure 12a, b and c show the calculated mean axial velocities using interrogation windows of 64 × 64 with overlaps of 32 × 32, 16 × 16 and 8 × 8, respectively. As seen in Fig. 12, larger overlaps provide velocity fields of lower resolution. However, the maximum mean axial velocity in this case was not significantly affected by the overlap size. Maximum mean axial droplet velocity for Test 5 was approximately 7.35 m/s, larger than the value found for Test 4, as expected, since larger injection pressures yield larger Fig. 10 Mean axial velocity distribution: a pre-processed image of Test 4 with a high-pass filter; b instantaneous axial velocity; c mean axial velocity using 100 image correlations flow velocities. The axial velocity field is not fully symmetrical since the film breakup process is not uniform, droplet sizes and velocities are not uniform and there are two inlet channels in the injector that provide a non-uniform mass distribution.

Light Sources and Digital Filters
Correlation maps of signal/noise were investigated to verify the influences of light source and filter on the determination of the droplet mean axial velocities. Figure 13 shows signal/noise ratios of Test 5 using different light sources and different digital filters. The signal/noise values were normalized by their maximum values. According to Adrian (1990, 1991), an image cross-correlation can be assumed true if the ratio between the values of the most intense peak and the second most intense peak of signal/noise, PPR = C max ∕C 2 , is larger than 2. The calculated ratios for different LEDs have indicated that the warm white LED produces the best results, since the second peak is much lower than the higher peak, when compared to the other LEDs tested. Next, the effects of digital filters were investigated using the warm white LED, and the high-pass filter presented the best results, as seen in Fig. 13f which shows basically a single peak, similar results for other test conditions. The raw images, as shown in Fig. 7, were used to determine the signal/noise ratios using the different LEDs, as depicted in Fig. 13 a, b, c. The highest signal/ noise ratio was obtained by the warm white LED. Therefore, the images obtained with the white warm LED were chosen for digital filtering.
The operational conditions affect the determination of velocities by PIV or SIV systems. A mist is formed by the spray and its amount increases for larger injection pressures. This mist surrounds the test region and can present velocities in the opposite direction of the larger spray droplets. A Z-Toepler system visualizes all the droplets and the mist in the test region, therefore its inability to differentiate between mist and droplets limits the efficiency of the optical method.
Consequently, tests were performed with different LEDs and digital filters to determine the best SIV configuration for most operational conditions. Table 1 shows the maximum injection pressures and maximum axial velocities which can be measured 50 mm after the spray breakup region using the different LEDs and filters.

Fig. 13
Signal-noise maps for Test 5 using different LEDs and filters

3
The results presented on Table 1 and showed in Fig. 12 are similar, indicating that a warm white LED with Laplacian and high-pass filters can improve the measurement range. Monochromatic LEDs are known to increase image resolution (Hollows 2013), since polychromatic light sources are subject to chromatic aberration. Shorter wavelengths (ultraviolet) can produce a better contrast than longer wavelengths (infrared), thus it should be expected that ultraviolet monochromatic LED would produce the best results for the present work. However, the wideband emission white warm LED (400-750 nm) yielded higher signal-noise ratio and allowed the imaging of a larger range of droplet velocities. A similar result was found by Jonassen et al. (2006) who verified that wideband emission LEDs produced better results in the SIV than laser light sources.

Average Droplet Velocities
PIV and SIV systems require averaging on several pairs of images to calculate flow or droplet velocity distributions. In general, sprays contain droplets of different sizes, shapes and velocities, which vary in time at any point inside the spray. Consequently, the instantaneous velocity of a single pair of images may not provide reliable information for characterization of the spray velocity field. Figure 14 shows the mean axial velocity of droplets for Test 6 ( ΔP = 2.32 bar, ṁ = 8.33 g/s) using different numbers of pairs of images.
The sprays analyzed are not axisymmetric or steady since a pressure swirl injector does not have a uniform mass flow distribution (Fischer 2019) and there are liquid film  Figure 14d shows that the mean velocity field obtained with one hundred pairs of images is similar to that obtained with fifty pairs of images. Therefore, 100 pairs of images were adopted for spray analysis in the present work A Z-Toepler system obtains projections of droplet velocities in the z-y plane, yielding the vertical and horizontal velocity components. These horizontal and vertical components can be used to calculate the tangential, radial and axial components of the droplet velocities. The vertical component (z-component) corresponds to the axial droplet velocity. The radial component is equal to axial velocity multiplied by the tangent of the spray semiangle and the tangential component is equal to the horizontal component at the spray axis position. The droplet velocity field on the x-y plane can be assumed as radial if the tangential droplet velocity component is negligible compared to the radial velocity component. Figure 15 depicts a scheme of a uniform radial flow of droplets from a spray ring with infinitesimal thickness (spray cross-section). The droplet velocity y-component obtained by the optical system is represented by the red arrow in Fig. 15 and its theoretical profile is a straight line with tan (β) = V r /R where V r is the radial component of the droplet velocity and R is the radius of the spray cross-section. Figure 16 shows the measured horizontal components (y-components) of droplet velocities for different injection pressures and mass flow rates, using 100 pairs of images. The plots are not symmetrical since the spray is not symmetrical and also the tangential components of the droplet velocities are not zero. However, the tangential component of the liquid film velocity is reduced when its distance to the nozzle axis increases, assuming a liquid flow with constant angular momentum. After the liquid film breaks up, the tangential velocities of the spray droplets are also reduced by the still air drag. On the right side of Fig. 16a-c, the droplets have positive y-component velocities, whereas on the left side the droplets present negative y-component velocities. The mean y-component velocity fields observed in the present work are similar to the ones found using PIV (Durdina et al. 2012(Durdina et al. , 2014Xie et al. 2014;Rajamanickam and Basu 2017;Zhang et al. 2017;Danh et al. 2019;Petry et al. 2022).

Spray Cone Angle
The spray cone angle is an important characteristic that indicates the spreading and the volume occupied by a spray. To determine spray cone angles, a triangle was positioned adjacent to the nozzle exit on the spray images, and the triangle base was located 50 mm below the nozzle, as seen in Fig. 17. The same procedure was adopted for all the sprays, including fully hollow cones and sprays with onion-like structures. Figure 18 shows spray cone angles as a function of the injection pressures, for different LEDS and digital filters. The experimental data were compared to the semi-empirical curve of Rizk and Lefebvre (1987) for spray cone angles of pressure swirl injectors: where K is the characteristic geometric parameter, d s is the discharge orifice diameter, ρ is liquid density and μ L is liquid dynamic viscosity. Measured cone angles did not show a good agreement with the semi-empirical curve for lower pressures, due to the presence of a onion-like structure. A similar behavior was observed by Reddy and Mishra (2008) who investigated the transition between solid cones and developing hollow cones. Figure 18a shows that the blue LED yields the best agreement with the semi-empirical curve. Figure 18b depicts the effects of edge detection and high-pass filters on measured cone angles, using the warm white LED. Spray cone angles with the three filters showed a like behavior and were relatively close to the semi-empirical curve by Rizk and Lefebvre.

Influence of Injection Pressure on Axial and Radial Velocities
The profiles of mean axial velocity as a function of radial distance are shown in Fig. 19. Velocity data were obtained at points located 50 mm below the nozzle exit orifice, from spray images using a white warm LED and applying a high-pass digital filter. Droplet velocities show a non-linear increase with injection pressures and are approximately constant along the spray width at z = 50 mm. Droplet velocities decay rapidly along the spray edges at a 20 mm radius, approximately. Figure 20 presents fit curves for droplet velocities measured at r = 0 mm and z = 50 mm, using spray images obtained by the Toepler system and processed with Laplacian and high-pass filters. The fit curves presented, respectively, pressure exponents n = 0.431 and n = 0.433 which are close to the calculated pressure exponent for the mass flow rate, n = 0.438, as depicted in Fig. 6. The fit curve using the Laplacian filter is slightly higher than the fit curve using the high-pass filter and shows a similar behavior to the cone angle measurements.  Velocity data obtained by Microscopic Shadowgraphy are also depicted in Fig. 20. The root mean square errors (RMSE) for the measured velocities by the Toepler system, with images processed by high pass and Laplacian filters, with respect to the shadow microscopy data are, respectively, ± 0.171 and ± 0.622 m/s, indicating that the high pass filtered data present the best agreement with the shadow microscopy data. The errors for velocity determination using a microscopic shadowgraphy method were estimated by the edge detection limits of a droplet (Lee et al. 2013). In the present optical system, the edge detection limits were within a variation of 4 pixels. Then, the velocity calculation error was determined dividing the distance corresponding to the 4 pixels by the time interval of two sequential images. Therefore, the minimum error was ± 0.03 m/s for Test 2 and the maximum error was ± 0.13 m/s for Test 7. The droplet velocities measured by the SIV method using low-resolution images show a good agreement with data obtained by a shadow microscopic system using high-resolution images. Additionally, the SIV method allows a relatively rapid determination of the droplet velocity field in large areas of a spray. Figure 21 presents the profiles of the y-component of droplet velocities for different injection pressures, measured at z = 50 mm below the nozzle exit. These profiles are approximately linear and close to zero near the origin and present maximum and minimum values near the edge of the spray cone. As the axial velocities, the y-component of droplet velocities increase significantly with injection pressures. Once the spray cone angles increase with the feed pressures there is a larger spreading of the horizontal velocity profiles for higher pressures.

Conclusions
This work described a schlieren image velocimetry (SIV) method that allows measurement of the droplet velocity field in a large region of a spray. A Z-type Toepler schlieren system was used to determine the vertical and horizontal mean droplet velocities and cone angles of sprays produced by a pressure swirl injector with a characteristic geometric constant K = 2. The velocity data were compared to microscopic shadowgraphy results, showing a good agreement. Digital images were obtained by a high-speed camera with a resolution of 2.77 pixels/mm and 5 × 10 3 fps. Several LEDs and digital filters were evaluated for improvement of image contrast and edge detection. An open software (OpenPIV) was adopted and interrogation windows and overlaps of different sizes were compared to obtain appropriate correlation and resolution for droplet velocity calculations. Wideband emission LEDs presented better results than monochromatic LEDs, with higher signal/ noise ratios, and allowed image cross-correlations and velocity measurements for a larger range of injection pressures. Spray cone angles were also determined using different light sources and filters. The blue LED, without using a digital filter, provided the best agreement between experimental and theoretical data, when compared to the other LEDs tested. High-pass and Gaussian filters, using a white warm LED, showed similar results and a slightly better agreement with theoretical data than the Laplacian filter. Larger interrogation windows of 64 × 64 pixels combined with small overlaps of 8 × 8 pixels yielded the best resolutions for the velocity fields. Since the sprays presented instabilities, a number of 100 cross-correlations of images was required to reduce fluctuations of the mean droplet velocities. Injection pressures varied from 0.05 to 7 bar and mass flow rates varied from 1.389 to 13.89 g/s, using water as test fluid. Spray cone angles ranged from about 32.5 o to 69.5°, for injection pressures from 0.05 to 7 bar, using triangulation and a blue LED as light source. Mean axial velocities varied from 3.3 to 11.3 m/s, approximately, with mean horizontal velocities varying from around 0.17 to 3.3 m/s for pressures from 0.05 to 3.22 bar. Velocities calculated using a wideband LED light source in the Z-Toepler optical system and high-pass filtered images presented the best agreement with microscopic shadowgraphy results.