Noninvasive Imaging of a Liquid Jet

Liquid jets emanating into quiescent air are fundamental and found in a wide variety of applications including ink-jet printing, manufacturing, irrigation, consumer products, and entertainment [1–4]. Improved characterization of liquid jets is necessary to better understand jet phenomena in these applications and assess the response to varying liquid flow conditions. High-quality experimental data that are temporally and spatially resolved can also be used to validate high fidelity simulations of liquid jets; these data have recently been identified to be lacking in the literature [5–7].

Jets dynamics are influenced by a multitude of factors that can lead to instabilities along the gas–liquid interface. For example, falling liquid jets exhibit a two-phase flow when exiting into atmospheric air and the gas–liquid interface is driven by capillary instabilities [8,9]. These instabilities cause sinusoidal perturbations and growing surface deformations that lead to jet bulging, and eventual breakup of the jet into individual droplets. Liquid jets are affected by gravitational forces through a decreasing diameter as the liquid falls from a vertical nozzle, referred to as necking [10]. This phenomenon holds true until the instabilities start to dominate the surface.

Surface tension also causes the pressure in the jet to be larger than in the surrounding air. This pressure varies within the jet and reaches a maximum where the jet radius is the smallest [10]. Since liquid flows from high to low pressure, the liquid migrates from high curvature liquid regions (higher pressure) to low curvature liquid regions (lower pressure) and forms bulges by pulling in the liquid from above and below the high curvature areas. The bulges grow until the radius of the jet above and below the bulge becomes zero, forming large droplets with smaller satellite droplets between them. Wicking around the liquid nozzle exit, due to capillary effects, is also an important liquid jet characteristic.

Liquid jets, atomization, and drop formation have been analyzed using a variety of nonintrusive experimental techniques including flash photography [1], high-intensity strobe light imaging [11,12], shadowgraphy [5,9,13,14], backlit imaging [15,16], holography [13], laser induced fluorescence [6,7], and X-ray imaging [8,17]. The liquid jet between the nozzle and initial breakup region distorts the light that passes through it, making measurements difficult for optical and laser diagnostics.

Backlit imaging is an optical method that is very similar to shadowgraphy in that the flow is illuminated from behind using a single light source, and the shadow that is cast on the imaging system shows the presence or absence of liquid. Shadowgraphy, however, uses collimated optics to achieve parallel light rays through the field of interest, whereas backlit imaging omits collimating optics so the setup is less expensive and easier to configure [18–20].

X-ray flow visualization provides another noninvasive method to characterize optically opaque fluid flows, like those found in perturbed liquid jets [21], but X-rays demonstrate minimal refraction and scattering events when passing through two-phase flows. For example, a synchrotron X-ray source utilizes line-of-sight measurements of X-ray absorption [22], and can penetrate the dense liquid region to provide high spatial and temporal resolution of the liquid jet.

Several techniques have been used at synchrotron light sources to probe multiphase flows, and they have recently been reviewed by Heindel [22]. Focused beam radiography is performed with synchrotron X-ray beams at facilities like the Advanced Photon Source at Argonne National Laboratory [23,24]. Focused beam techniques use monochromatic X-rays to measure the X-ray absorption in a small region of interest through which the X-ray is passing. These data are converted to a projected density of liquid using Beer–Lambert's law. Although focused beam measurements are point measurements, they can achieve high temporal and spatial resolution along a single line of sight. For example, Duke et al. [25] were able to achieve a 5 μm spatial resolution and 3.6 μs temporal resolution when quantifying nozzle cavitation with focused beam measurements.

A second synchrotron high-speed X-ray technique used in liquid analysis is white beam imaging. These measurements use the unfocused polychromatic emission from the synchrotron to achieve the high X-ray flux needed for high-speed two-dimensional (2D) radiographic images. Once the highly collimated X-ray beam passes through the flow of interest, it is captured by a scintillator detector that fluoresces visible light proportional to the amount of absorbed X-ray energy, which is in turn related to the liquid optical depth through which the beam has passed. Hence, in dense fluid regions like a liquid jet, more X-rays are absorbed in the center of the liquid jet and less are absorbed near the edges. The scintillator emission is then imaged with visible light optics and cameras. The resulting image is a 2D projected X-ray absorption map of the 3D flow. White beam imaging has recently been used to observe fluid flow structures in an atomized spray with a spatial resolution of the order of microns at frame rates up to 100 kHz [26,27].

The focus of this paper is on a small-scale liquid jet exiting a circular nozzle, with varying jet exit Reynolds numbers, before the breakup process occurs. The purpose of this work is to characterize the pure liquid jet, both quantitatively and qualitatively, using three different imaging modes of backlit imaging, white beam X-ray imaging, and focused beam X-ray radiography. Data from each imaging method are then compared to assess their usefulness.

The back-illuminated or backlit (BL) imaging setup used in this study consisted of a high intensity light emitting diode (LED) panel coupled with a high-speed camera (Fig. 1). The LED panel was an Advanced Illumination MicroBrite^TM (Rochester, VT) red LED backlight with nominal wavelengths of 625 nm, and provided a uniform 8.75 cm (vertical) by 18.5 cm (horizontal) light source. It was mounted ∼200 mm (8 in.) behind the center of the liquid needle.

The camera used in the BL system was a Photron FASTCAM SA-Z (San Diego, CA) with a Nikon AF Nikkor 180 mm f/2.8D IF-Ed lens coupled with a Nikon TC-14A 1.4× teleconverter (Tokyo, Japan) for an effective focal length of 252 mm. A red bandpass filter (Midwest Optical Systems BP635, Palatine, IL) on the lens allowed for about 95.7% transmission of the 625 nm spectrum while rejecting nearly 100% of the light outside the range 580–680 nm. The camera was located so the front of the lens was ∼1350 mm (53 in.) from the center of the liquid needle. The camera was aligned with the exit of the liquid needle using a laser level.

The entire BL imaging system was surrounded by a black fleece fabric shroud to minimize artifacts and reflections from ambient light. The aperture, frame rate, and exposure were selected to maximize depth of field and maximize the usage of the camera's dynamic range while minimizing motion blur in the images. This was determined to be an aperture of f/11 (f/15.4 effective due to the teleconverter), a frame rate of 10 kHz, an exposure of 99 μs, an image size of 1024 × 1024 pixels, and an effective pixel size of 90 μm.

The X-ray images obtained for this study were acquired at the 7-BM beamline of the Advanced Photon Source (APS) at Argonne National Laboratory. This beamline utilizes a synchrotron bending magnet for the X-ray source that provided a nearly collimated, polychromatic X-ray beam [28]. Two types of X-ray measurement techniques were used: full-field imaging with a polychromatic white beam (WB), and focused beam (FB) measurements with a monochromatic X-ray beam (see Fig. 2). Details of the X-ray techniques are summarized in a recent review paper [22] and the references cited therein.

where ε is the linear absorption coefficient of the liquid (in mm⁻¹), I₀ is the X-ray intensity of the beam before the liquid jet, and I(t) is the X-ray intensity at the detector at the given instant in time, t, which was recorded with a PIN diode at a rate of 6.25 MHz for 10 s, and then binned to an effective rate of 270 kHz (the repetition rate of the synchrotron). Note that I₀ was obtained by recording positive-intrinsic-negative (PIN) diode readings outside the liquid jet region.

WB imaging provides a 2D projection with a larger field of view (but still much smaller than BL imaging). At the 7-BM beamline at APS, the WB X-ray beam size is approximately 8 mm × 6 mm, but with the camera settings used in this study, the acquired image size was 4.9 mm × 3.4 mm. WB imaging is less accurate in determining the EPL because the beam is polychromatic and a correct determination of ε requires detailed spectral modeling [22], making it better suited for qualitative analysis of the liquid jet morphology. After passing through the liquid jet, the X-rays illuminate a cerium doped yttrium aluminum garnet (YAG(Ce)) scintillator, which converts the X-rays to visible light. The light from the scintillator is reflected off a mirror (to keep the optical equipment out of the X-ray beam), and then imaged with a high-speed camera using a 105 mm–50 mm macro-coupled lens pair with a combined 2.1 magnification. The high-speed camera used for WB imaging in this study was a Photron FASTCAM Mini AX50 (San Diego, CA) operated at 10 kHz, an exposure of 1.05 μs, an image size of 352 × 512 pixels, and an effective pixel size of 9.5 μm.

The BL data were analyzed using standard matlab image analysis functions to binarize the image. Hence, the BL images only show the presence or absence of liquid in the projected image. These images are then used to identify the left-most and right-most liquid boundary, from which the difference provides an estimate of the maximum projected liquid jet width as a function of axial location in each image.

The WB images were more challenging to process because they show a grayscale variation based on projected liquid thickness. Additionally, regions of abrupt density variation can also show phase contrast imaging effects [22], which can introduce noise and blur the boundary if a simple binarization is utilized. The WB images were processed using binarization and edge detection to determine an accurate, continuous jet boundary. Figure 3 provides a schematic representation of the process. Binarization first converted the original grayscale WB image to a binary black and white image. The threshold was set at 0.75 to differentiate between the liquid and the background; however, the phase contrast effects introduced noise and blurred boundaries. Edge detection was then used to identify the liquid jet boundary by using a sharp grayscale gradient. This can give an image with multiple edges at higher liquid Reynolds numbers (due to surface contours and phase contrast image effects). The original identified edges may also provide a discontinuous, overlapping boundary as shown in Fig. 3.

Both binarization and edge detection added noise, but when used together, this was minimized. Edge detection provided a starting pixel location to test for a more accurate liquid jet edge. This location was used in the binarized image to control for noise. If the number of white pixels in a 15-pixel section rightwards of the first left edge pixel was less than or equal to 4, then the first edge pixel was recorded as the left boundary. If the count was greater than 4, the starting pixel was shifted to the next edge pixel and the white pixel count was repeated. This process resulted in an image that has a single continuous liquid jet boundary with a width of one pixel (right image in Fig. 3). The resulting identified left and right boundaries are then used to determine jet width at various axial locations.

Since FB radiography uses a probe much smaller than the jet width (5 μm × 6 μm), data were acquired in a raster-scanned method at specified axial locations in the spanwise (width) direction. More data points were captured near the liquid jet boundaries. Equation (1) was then used to determine the instantaneous EPL, where the absorption coefficient, ε, was determined from the NIST XCOM database for an X-ray energy of 8 keV [29]. The instantaneous EPL was then averaged at each spanwise location to produce a profile of the liquid jet thickness at each axial location. Assuming the liquid jet was axisymmetric, the maximum EPL can be approximated as the liquid jet thickness.

Following Kastengren et al. [23], the uncertainty in the absorption coefficient used in Beer–Lambert's law is approximately 1.5%, and the uncertainty in the measurement positions are ±20 μm in the axial direction (x) and ±5 μm in the spanwise direction (y). The overall uncertainty in the equivalent path length measurement is estimated to be ±1.5%.

The liquid needle used in this work to produce a liquid jet was the same liquid needle used in several previous airblast atomization studies [30–33]; however, in those studies, the liquid needle was part of a two-fluid coaxial atomizer. In this study, the same gas and liquid flow paths were present, but the gas flow was not used and only the liquid needle had fluid flowing through it. The liquid needle was a circular tube with an inner diameter of d_l = 2.1 mm and an outer diameter at the liquid exit of D_l = 2.7 mm. Both d_l and D_l were measured using X-ray WB imaging, which can penetrate the fully assembled aluminum airblast atomizer. The liquid (distilled water) entered the L = 110 mm long needle from a constant pressure 114 L (30 gal) liquid reservoir, which provided a constant liquid flowrate over an extended time period before the reservoir was refilled. An electronic proportioning valve and liquid flowmeter, both connected to a data acquisition system, ensured a constant liquid flowrate at a given setpoint using a proportional-integral-derivative (PID) controller. The L/d_l ratio of the liquid needle was fixed at L/d_l = 52.4, making the flow fully developed at the needle exit.

Three different flow conditions were tested in this study, and quantitative data were gathered from the liquid needle tip (x = 0 mm) to x = 35 mm (before liquid breakup), where x is the axial coordinate in the flow direction whose origin is at the needle exit. The liquid for BL imaging was filtered distilled water at room temperature. The liquid for WB imaging was filtered distilled water with ∼5% by mass of potassium iodide salt (KI) and 0.5% by mass of sodium bromide salt (NaBr) to increase X-ray attenuation, which has been shown to have negligible effects on density, viscosity, and flow behavior [34,35]. The liquid for FB data collection was filtered distilled water only (no added salts) because the X-ray attenuation coefficient of distilled water is precisely known, which increased the accuracy of the EPL calculations. The X-ray absorption at the photon energy used for FB data (8 keV) is also sufficiently large such that added contrast is not needed.

where d_l was the inner diameter of the liquid needle (d_l = 2.1 mm), U_l was the mean liquid velocity at the liquid needle exit, and ν_l was the kinematic viscosity of water at 25 °C. The fixed Reynolds numbers encompassed laminar (U_l = 0.099 L/min, Re_l = 1100), transitional (U_l = 0.385 L/min, Re_l = 4400), and turbulent (U_l = 0.99 L/min, Re_l = 11,200) liquid jets.

The liquid flowmeter had an accuracy of ±2% of full scale and the overall uncertainty in the Reynolds number was estimated to be ±2.4%, assuming there was no error in the tabulated fluid properties.

Figure 4 shows sample single frames from the high-speed videos obtained through BL imaging, while Supplemental Material on the ASME Digital Collection shows the high-speed video for these conditions played back at 0.2% of real speed (frame rate of 20 Hz).

The given camera and lens settings produced an image that is over 60 mm in length, with portions of the image cropped to focus on a region just below the nozzle exit.

As the LED light passes through the liquid jet, it is reflected, refracted, and diffracted away from its original path wherever liquid is present, creating a shadow that is captured by the high-speed camera. Note the high curvature of the liquid jet (particularly for Re_l = 1100) creates a liquid lens [36], focusing light to the center of the liquid stream, which results in the dark outline and bright center of the liquid jet. As the Reynolds number increases, surface fluctuations disrupt the light path and dark regions appear on the surface of the liquid jet. The surface fluctuations increase with increasing flowrate and more are observed when the liquid jet is turbulent (Re_l = 11,200).

Although difficult to view in the qualitative BL images, the laminar liquid jet wicks up the outside of the liquid needle at the exit, producing a liquid width that is larger than the needle ID (this will be confirmed below). The laminar flow also thins as it moves downstream due to the acceleration of the jet from gravity. These flow features are more difficult to visualize in the transitional and turbulent flow cases.

Backlit imaging is a simple method to provide a wide field of view of optically accessible flows, and shows the presence or absence of liquid. For the liquid jet, the average jet width as a function of axial location can easily be determined through image analysis; these measures are provided in the “Imaging Modality Comparisons” section. Furthermore, if a different lens combination and camera position are used, closeup regions of the liquid jet could be captured, but this was not done in this study.

Figure 5 shows WB X-ray images of pure liquid jets exiting from the liquid nozzle. The figure shows representative snapshots of all three flow conditions side-by-side. The Supplemental Material on the ASME Digital Collection shows the high-speed video for these conditions played back at 0.1% or 0.2% of real speed (frame rate of 10 or 20 Hz, respectively). WB X-ray images cover the entire region between x = 0 mm and x = 31 mm, but they have to be acquired in a checkerboard fashion because the X-ray beam has a limited size [26]. This did, however, allow for closeup images of these regions. In Fig. 5, only the top, middle, and bottom sections are shown. Each WB image encompasses a projected area of 4.9 mm × 3.4 mm. The different gray scales in the water region outside the nozzle exit plane indicate different water thicknesses, where darker regions are associated with more water. Beam hardening effects could also be present, which are artifacts of polychromatic X-ray beams passing through dense material [21,37].

Figure 5(a) shows the nozzle exit for the laminar condition. The striped bars represent the liquid needle location and size. As observed in the videos of Supplemental Material on the ASME Digital Collection, water wicks around the needle tip, causing the water exit diameter to expand to a diameter greater than the d_l = 2.1 mm needle ID. Similar observations were recorded when the liquid needle was used in an airblast atomizer [26,38].

The laminar flow condition (Re_l = 1100) experiences the most physical change due to gravitational effects. It begins to neck immediately after wicking and continues with increasing axial distance. The WB images show the smooth necking pattern ending around x = 13 mm, where bulging starts and continues through x = 31 mm as shown in Fig. 5(c). Figure 5(b) shows the state of the laminar flow where the initial bulge formations are observed. The surface instabilities start around x = 13 mm (about five to six nozzle diameters from the exit) and grow into large bulges and long sinusoidal waves as shown in Fig. 5(c). This behavior is the precursor to drop formation [10]. The bulge formation was not observed when doing BL imaging, which was completed at a different laboratory location while still using the same liquid needle. The water used in WB imaging, however, had small amounts of potassium iodide and sodium bromide salt added to increase the X-ray absorption. Although others have indicated these small amounts of added salts have negligible effects on density, viscosity, and flow behavior [34,35], they may have modified the surface tension enough to enhance surface perturbations that lead to bulge formation. Furthermore, the PID controller was modified between the APS and Iowa State University (ISU) experiments. At APS, the controller allowed a small error in the flowrate before adjustments were made, while at ISU, the controller was more aggressive in changing the valve settings to hold the flowrate at a tighter tolerance. Finally, due to space limitations, the liquid jet at APS was expelled into an exhaust system that pulled a slight suction to minimize splashing. The suction promotes a small gas flow parallel to the liquid jet, which could also enhance surface perturbations.

The smooth necking and long wavelength variations in the laminar flow also differed from that observed for transitional and turbulent flow. The transitional flow (Re_l = 4400) necks slightly, as shown in Fig. 5(d), but the surface perturbations make visual confirmation of necking in the WB videos or still images difficult (but they are quantified below with FB radiography). The surface perturbations begin as low amplitude waves after exiting the nozzle, as shown in Fig. 5(d), but then increase in amplitude further downstream as shown by the long surface wave in Fig. 5(f).

Figure 5(g) shows the turbulent liquid jet (Re_l = 11,200) immediately after exiting the nozzle. This visual has been described as a “wrinkle structure” and is caused by the combination of turbulent eddies within the jet, and the shear force between the fast-moving liquid jet and the still air [17]. The magnitude of the wrinkles decreases downstream and give way to larger-scale surface waves as observed in Fig. 5(h), which has also been demonstrated by Lin et al. [17]. This is likely due to the small wrinkle structures dissipating as the surface waves grow. As shown in Fig. 5(i), the perturbations in the flow grow significantly in amplitude as the jet flows downstream (cf. Fig. 5(h)).

All of the turbulent WB images show enhanced features that were not found in the laminar or transitional conditions. In Fig. 5(g), there are abrupt changes in the grayscale that are adjacent to each other in the projected image. The different grayscales show various amounts of fluid in those regions; a lighter shade represents a smaller amount of liquid and a darker shade represents more liquid that is either thicker or multiple liquid sections that are overlapped. The abrupt change in fluid thickness also promotes phase contrast effects that outline the surface variations. These features demonstrate the advantage of the WB imaging technique compared to BL imaging to capture different surface characteristics through the amount of X-ray absorption in the liquid. Figures 5(h) and 5(i) also show layers in the liquid jet, demonstrating the overall asymmetric nature of the turbulent jet.

Focused beam radiography uses an X-ray beam with a small cross section (5 μm × 6 μm) making it an effective point-source measurement that can acquire data at high temporal resolutions (270 kHz in this study). Figure 6 shows a small sample data stream from FB radiography. Since the beam location is fixed in space, the liquid needle is positioned using vertical and horizontal translation stages, such that the beam for the data in Fig. 6 is located at axial location x = 15 mm and spanwise location y = 1.15 mm for Re_l = 11,200—this is near the edge of the turbulent liquid jet. FB radiography also uses a monochromatic X-ray beam, so Eq. (1) is used with the precise X-ray linear absorption coefficient for water to determine the instantaneous EPL at the given location. When EPL = 0, there is no water in the beam path. As the wrinkled structure of the liquid jet edge passes through the beam location, the rapid variations in liquid thickness are captured.

The EPL values like those in Fig. 6 are averaged over a 10 s data acquisition time to determine the average EPL at the given (x, y) coordinate. Recording data spanwise across the liquid jet produces a profile of the average liquid jet thickness like that shown in Fig. 7. When the liquid jet is laminar at x = 0.1 mm from the liquid needle exit, the maximum normalized average EPL is greater than 1, meaning the jet thickness is wider than the ID of the liquid needle. This verifies the wicking inferred from the BL images and observed in the WB image (Fig. 5(a)). The transitional and turbulent maximum normalized average EPLs are slightly above or below 1, indicating little to no wicking occurs at the higher liquid velocities. These quantitative data support the WB observations in Figs. 5(d) and 5(g) that show the transitional and turbulent jets leave the nozzle with a diameter equal to or less than the nozzle diameter. The wicking in the laminar flow condition is likely caused by capillary effects and the lower velocity allowing the water to wick around the nozzle tip.

where y is the spanwise coordinate, h is the spanwise offset of where the maximum EPL occurs, EPL is the chord length at the given spanwise location, and EPL_max is the maximum EPL for the given conditions. Two circular profiles using Eq. (3) are shown on Fig. 7, one for Re_l = 1100 with h = 0 (circle A) and one for Re_l = 11,200 with h = 0 (circle B). The data for Re_l = 1100 follow circle A almost identically, while for Re_l = 11,200, there is a small shift from Circle B on the right-hand side. This shows that the axisymmetric flow assumption at the liquid needle exit is valid, particularly for laminar flow.

Figure 8 shows the nondimensional EPL at various axial locations for the turbulent flow condition. At all axial locations, the data approach EPL = 0 asymptotically on both the left and right side of the liquid jet; this is more apparent with increasing distance from the needle exit. Because of surface perturbations due to shear forces between the quiescent air and fast-moving liquid jet, the instantaneous EPL is not constant near the jet edge (see, for example, Fig. 6), and the average EPL asymptotes to 0 as the FB moves away for the liquid region. This is most significant at x = 35 mm where large surface fluctuations are observed in both the BL and WB imaging. Note, however, the interior EPL profile still follows that of a circle, as shown by the inscribed circle at X = 35 mm where EPL_max is offset from the center of the liquid needle (h is the offset distance). The rightward shift of the data as x increases is most likely caused by the possible slight misalignment in the nozzle vertical position, which is estimated to be of the order of ∼0.75 deg.

Figure 9 compares the available visual information and detail that is available from each of the three imaging modes used in this study. BL imaging provides the largest field of view (Fig. 9(a)) and is limited only by the LED area and camera position and lens setup. A large liquid jet region is visible, and subregions could be identified and magnified through camera positioning and lenses. Local liquid thickness, however, is difficult to infer and jet width is one of the few available quantitative measures.

WB image size is limited by the cross section of the X-ray beam at APS, but more detail of the liquid jet is available (Figs. 9(b)–9(d)), where the darker regions imply more projected liquid. Variation in grayscale can be correlated to optical depth, which is the product of ε and EPL in Eq. (1) [31]; however, because the X-ray beam is polychromatic and beam hardening may be present, ε is not known precisely and quantifying the EPL is a challenge. Following the procedure outlined in Fig. 3, the liquid jet width can be determined from the WD images.

Focused beam radiography, and the use of Eq. (1), produces a time series of the local EPL (Fig. 9(f)). The temporal and spatial resolution of these data are very high [24,28,39]. The instantaneous EPL at a given location can be averaged to produce an average EPL. Raster scanning across the liquid jet produces the profile of the average liquid thickness in the beam direction (Fig. 9(g)). The raster scanning is then done at several axial locations to get a complete picture of the liquid jet.

Assuming the liquid jet, on average, is axisymmetric, the maximum EPL determined from FB radiography can be compared to width measures from BL and WB imaging. Figure 10 shows this comparison for Re_l = 1100. As visually observed (e.g., Figs. 4 and 5), the flow is very smooth and consistent and the assumption of axisymmetric flow is valid. The maximum average EPL and jet widths from each imaging mode compare well. The error bars represent ±1 standard deviation of all the measurements. Note that for the FB measurements, the error bars are smaller than the size of the symbols. Near the jet exit (x/d_l near 0), nondimensionalized measured values are greater than 1, confirming the wicking observations and the liquid jet diameter is larger than the liquid needle ID near the needle exit. The maximum EPL or width then decreases as the downstream distance increases, indicating necking is prevalent.

Increasing the Reynolds number to Re_l = 4400 (Fig. 11), the three imaging modes again compare well. The nondimensionalized FB data starts near 1 and then decreases slightly as the liquid jet travels downstream, indicating there is minimal wicking and only slight necking. The BL and WB values are larger than the FB data in all cases, but the error bars are much larger and overlap to some extent. Both the BL and WB widths compare well. In both cases, the instantaneous width from these imaging modes produce the maximum extent of the liquid jet. The average width from BL and WB imaging is then the average maximum possible jet width. When there are surface fluctuations, BL and WB imaging will record the presence or absence of liquid near the jet edge, whereas FB radiography produces the actual EPL (e.g., Fig. 6). Hence, when comparing the average maximum EPL from FB radiography to the average width from BL and WB imaging, the FB data will always produce smaller measurements if the jet is not smooth.

As shown in Fig. 12, when Re_l = 11,200 (turbulent liquid jet), the BL and WB imaging compare well but predict larger jet widths than the maximum EPL from FB radiography. This is again because, when measuring jet width from the BL and WB images, the maximum extent is recorded. In contrast, if the chord length is very small and intermittent near the jet edge, the FB measurement will provide the actual average chord length. For example, if Fig. 6 was the FB signal at the edge of the liquid jet, BL and WB width measures would specify a threshold and any value above the threshold would be all liquid while everything below would be all gas. With a threshold representing a small amount of liquid (a small EPL), the average from BL and WB imaging would be larger than the actual signal average from FB radiography. This is reflected in Fig. 12.

Comparing standard deviations between the three imaging modes can provide an assessment of the preciseness of the measurement. The standard deviation from FB radiography where the maximum EPL is recorded is compared to the standard deviation from the BL and WB width measures in Fig. 13, where the standard deviation is normalized with the liquid needle ID. In general, the normalized standard deviation increases with axial distance from the jet exit because surface fluctuations grow with increasing axial distance. The exception to this trend are the FB measures of the laminar jet that are very small due to the stable flow of the laminar jet. Two other observations are apparent in Fig. 13. First, the standard deviation for Re_l = 1100 is approximately a factor of 5 smaller than the values for Re_l = 4400 and 11,200, which are similar. Once the flow exiting the liquid is no longer laminar, the surface perturbations cause similar measurement fluctuations. Second, the standard deviations for FB radiography are an order of magnitude smaller (or more) than those produced with WB or BL imaging, which are very similar to each other. Hence, FB radiography is more precise.

This study used backlit imaging, white beam X-ray imaging, and focused beam X-ray radiography to characterize liquid jets, both qualitatively and quantitatively. Three liquid Reynolds numbers were imaged, encompassing laminar (Re_l = 1100), transitional (Re_l = 4400), and turbulent (Re_l = 11,200) flow exiting a liquid needle. It was shown that the laminar condition had wicking around the liquid needle, whereas transitional and turbulent jets did not. The laminar condition also experienced significant necking, as expected. The transitional condition showed perturbations beginning near the nozzle exit and growing downstream. The turbulent condition demonstrated a “wrinkle structure” caused by the combination of turbulence eddies within the jet and the shear force between the jet and the air.

Backlit imaging was fairly easy to acquire and provided a large field of view, from which liquid jet width could be quantified. White beam X-ray image had a much smaller field of view but provided additional information through grayscale variations on the jet surface. Jet width was also measured. Focused beam X-ray radiography is a point measurement and provided high spatial and temporal resolution, but had much more involved data acquisition and analysis methods. The focused beam data also had much smaller standard deviations, even when the liquid flow was turbulent.

These data can be used to provide benchmark flow conditions for those testing computational fluid dynamics codes. Both qualitative and quantitative comparisons can be made to validate simulations.

Some of the analysis provided in this work was completed by Dr. Julie Bothell, Dr. Danyu Li, and Mr. Timothy Dahlstrom; their input is greatly appreciated. The views and conclusions contained herein are those of the authors only and should not be interpreted as representing those of ONR, the U.S. Navy, or the U.S. Government. The X-ray data were gathered at the 7-BM beamline of the Advanced Photon Source, a U.S. Department of Energy (DOE) laboratory.

• Office of Naval Research (Award Nos. N00014-16-1-2617 and N00014-18-1-2319; Funder ID: 10.13039/100000006).

• Office of Science by Argonne National Laboratory (Award No. DE-AC02-06CH11357; Funder ID: 10.13039/100006132).

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.