Jet-stirred homogeneous isotropic turbulent water tank for bubble and droplet fragmentation

Among the different setups mentioned, we focus here on jet-stirred turbulence facilities, which can produce a large HIT region and a relatively high Re_λ.⁶ Typically, jet-stirred facilities are either based on a jet array located on one side of the facility^3,27,28 or on two jet arrays facing each other.^2,6,24 These facilities can be operated with continuous flow jets,²⁹ or the jets can be operated in a random fashion via actuators.²⁷ Compared to the continuous flow jets, the randomly actuated jet scheme is normally used to prevent strong secondary flows and to produce low anisotropy levels with a larger HIT volume.^6,25,27,28 Even in these facilities, however, some degree of anisotropy can sometimes be present,² but this seems to depend on the geometry of the jet array and the test section. So, it seems that it is the aim of the experiment that should guide the optimal jet configuration: a single jet array, for example, is convenient for studying turbulence near boundaries,²⁷ whereas two sets of jet arrays facing each other are better for applications requiring a weaker mean flow and a larger HIT region.^6,26

In this work, we present a jet facility designed to investigate topology changes of droplets and bubbles dispersed in HIT. Under the action of turbulence forcing, droplets can deform and eventually break due to dynamic pressure gradients across the interface. Breakage of droplets and bubbles by turbulence is a crucial phenomenon that still requires complete and satisfactory understanding:^30–32 with this facility, we plan to generate a consistent dataset that can lead to further investigation on this problem of fundamental importance for a number of industrial and environmental applications.

Combining these features is intricate, and a high Re_λ does not imply a high ɛ, as shown in Table I. In addition, such flows have a complex three-dimensional nature that might require robust and time-resolved optical measurement techniques. Hence, the facility must be designed to allow optical access from multiple cameras for employing non-intrusive and non-invasive 3D visualization techniques. This requirement adds complexity, as the geometry must ensure flow visibility while minimizing any potential interference for the turbulence. To the best of our knowledge, the only facility capable of approximating these conditions is the vertical tunnel presented by Masuk et al.,²⁸ which can generate nearly HIT with high values of ɛ.

Herein, we describe a new octagonal water tank with intense turbulence driven by two facing jet arrays operated with continuous flow. The facility is capable of producing outstanding Re_λ and ɛ while keeping good isotropy levels and a weak mean flow. With this setup, we can tune the jet velocity and the distance between jet arrays, thereby using ɛ scaling and decay in our favor to optimize the turbulence characteristics in the tank center. These characteristics fit our main objective of examining droplet deformation and breakup in HIT. The necessity to support computational results with experimental evidence is crucial, particularly in the study of complex multiphase flows, as highlighted by Ref. 39. This approach is essential because computational methods, while powerful, often have inherent limitations and uncertainties, especially when simulating multiphase flows that involve droplet and bubble fragmentation.^37,40 The present experimental facility addresses these challenges by providing a robust platform to investigate the fragmentation dynamics of bubbles and droplets over a broad range of internal droplet viscosity and We. This comprehensive range enables the facility to capture the essential physics governing fragmentation processes while adhering to the fundamental assumptions outlined in the Kolmogorov–Hinze framework for droplet/bubble breakup in turbulent flows. Moreover, while the current research emphasis is on understanding the behavior of droplets and bubbles in turbulence, the versatility of the new facility extends its applicability beyond this specific focus. It is suitable for a variety of single-phase and multiphase flow studies,⁴¹ potentially providing high-fidelity experimental data necessary to improve the predictive capabilities of computational approaches.

In this paper, we describe the principal characteristics of the new water tank. Three-dimensional flow statistics were retrieved from optical measurements using four high-speed cameras; we used the Shake-The-Box (STB) method⁴² for the 3D-Lagrangian particle tracking (LPT). The facility components, turbulence generation, and imaging system are presented in Sec. II. In Sec. III, we describe the 3D measurement techniques, and in Sec. IV, we discuss velocity statistics, turbulence intensity, and turbulence scaling. Section V exhibits examples of multiphase experiments conducted in the facility. Finally, we draw the conclusions and outlook of this work in Sec. VI.

The current facility was designed to produce high-intensity turbulence in homogeneous and isotropic conditions. The facility can be used for multiple applications, and our main object of study was the deformation and breakup of oil droplets in HIT. In this section, we describe the facility’s main components and the imaging system.

We present the main loop schematic in Fig. 1. The water flow was driven by a 5.5 kW centrifugal pump with a maximum flow rate of 18.5 m³/h (GRUNDFOS NB32-160/177). Water was stored in a 0.9 m³ reservoir made of 10 mm thick polyvinyl chloride (PVC) plates. A gate valve connected the reservoir to the pump suction pipe (not visible in the schematic). We added flanged expansion joints in the suction and discharge pipes to absorb part of the pump vibrations. The main line was composed of PVC pipes with an internal diameter of 100 mm to reduce pressure losses. Three ball valves assisted in the flow control; the upper left valve in Fig. 1 worked as a bypass.

The flow was then directed to a pressure vessel, which served as a calming reservoir and divided the main flow into 24 flexible pipes that fed the two facing jet arrays. The cylindrical pressure vessel made of polyamide 6 (PA6) was 6 cm thick, 45 cm long, and had an internal diameter of 29 cm. A pair of 3 cm thick PA6 plates was used as end plates; the plates contained an inner cavity to place the sealing gaskets. We reinforced the structure by enclosing the lids with a steel frame. Six threaded rods (M16) were used to tighten the vessel, allowing us to open the component for cleaning. The vessel upheld internal pressures up to 5 bars. We connected 24 flexible pipes of 8 mm internal diameter to the top lid through push-to-connect fittings. The flexible pipes could withstand an internal pressure of 12 bars. All 24 pipes had the same length (2.5 m long) and were positioned with a similar bending radius and height to avoid unequal pressure losses and, consequently, a nonuniform flow distribution. Although some velocity variation between jets in the arrays can persist, no significant effect was visible in the tank center (the flow characteristics are presented in Sec. IV A).

From the pressure vessel, the flow headed through the flexible pipes to the jet arrays connected to the test section (blue arrows in Fig. 1). The octagonal acrylic tank is described in Sec. II B. The flow exited the test section through four flexible pipes mounted horizontally (red arrows in Fig. 1). The four pipes had the same length (3 m), internal diameter (50 mm), and a similar curvature, so the outflow was homogeneously distributed. Otherwise, an unequal flow in the outlet pipes would influence the flow characteristics within the test section. Note that the test section has four vertically mounted exits that were not used (the upper exits are visible in Fig. 4). We decided to use only the horizontal exits because the pressure inside the tank was very close to the atmospheric pressure, and the water did not flow through the upper exit. Using only the horizontal exits resulted in a small anisotropy in the yz-plane, as discussed at the end of Sec. IV A, but was still preferred over an uneven outlet flow distribution.

The test section was constructed from 25 mm thick cast acrylic in an octagonal shape to facilitate optical access. Its hydraulic diameter was D_h ≈ 21 cm. Figure 2 shows an illustration of the octagonal tank. We had optical access along 80 cm in the central section. Flanges on both sides allowed us to open the facility for cleaning and maintenance. We included a window in the top center of the section, which is convenient for placing a calibration target in the tank but limits the optical access in the top/bottom walls.

The water entered the test section through the jet arrays and exited through four flexible pipes mounted horizontally (visible in Figs. 1 and 4). The turbulence was generated by two opposite jet arrays connected to the test section ends. Each array contained N rigid pipes connected to the pressure vessel’s flexible pipes through push-to-connect fittings. Different jet array lids could be manufactured to change the jet spacing, M, or the jet disposition; Fig. 2 shows a typical jet array lid geometry with N = 12. We used rigid pipes for the jets with two inner diameters: d = 6 and 7 mm. A compression nut set fixed the rigid pipes in the end lids, allowing us to linearly slide the pipes and control the distance between arrays, 2x*, without compromising the sealing. We controlled the turbulence in the center by changing x* or tuning the pump flow rate. Every jet released flows with initial jet velocity, V_jet, ranging from 2 to 14 m/s, yielding jet Reynolds numbers, Re_jet, from 12 000 to 100 000. In summary, we can change N, M, x*, d, and V_jet to modify the turbulence characteristics in the facility. The current jet array scheme is simple and cheap to manufacture, as we only need to make new lids to change M or N. The limitation is the space available for the jets: for example, with M < 2.5 cm, we would lack space to screw the pipes’ connections. In such cases, a 3D-printed array (as in Masuk et al.²⁸) would be a better solution, although more costly.

A relevant aspect of this facility is that the turbulence is generated by continuously operated jets. Generally, jet-stirred facilities operate with randomly actuated jets, known for reducing secondary flows, producing a larger HIT volume, smaller mean flow, and, arguably, lower anisotropy. One drawback of random jets would be producing weaker turbulence; this, however, remains dubious, as more stirring does not mean better mixing, and turning on more simultaneous jets can potentially weaken the turbulence.²⁷ Withal, few facilities showed a non-negligible anisotropy even when operating under stochastic forcing,² which is indicative that the influence of the jet array geometry is yet to be fully understood.

Oil droplets were injected from the bottom center of the tank, as visible in Fig. 2. The strong turbulence posed a challenge to control the droplet injection diameter, as velocity fluctuations could drag the droplets from the needle before they fully developed. We achieved more stable initial conditions by employing the technique introduced by Tomiyama et al.⁴⁵  Figure 3 presents a schematic of the injection system. It consisted of two pipelines, one with oil and the other with water, that merged into a single pipe after a manifold. We used the syringe pump Baxter Flo-Gard GSP with a controllable flow rate to inject the oil into one pipe. Water was supplied to the other pipe by a small reservoir placed 1.2 m over the test section (the absolute pressure within the test section was less than 1.1 bar). A valve downstream of the reservoir aided in controlling the water flow rate. The slightly higher pressure in the injection system pipes softly pushed the droplets into the test section, additionally hindering the strong initial deformations from the pinch-off process. In addition, we added a cylindrical shield around the needle tip to prevent the turbulence from breaking the droplets before they fully leave the needle.

The image acquisition consisted of six high-speed cameras, model Phantom VEO 340L, with a resolution of 2560 × 1600 pixels and a 10 μm pixel pitch; the main components of the imaging system were the same as those presented in Giurgiu et al.⁴⁶ The cameras were equipped with 100 mm focal length Tokina macro objectives and mounted in Scheimpflug condition. The optical magnification was ∼0.6, and the extent of the measured domain was ∼4 × 4 × 4 cm³. Throughout this work, we used four cameras to retrieve the single-phase turbulence statistics (setup shown in Fig. 4). The setup with six cameras is recommended for the two-phase measurements: using more cameras allows capturing more tracers near the interface²⁸ and fosters better quality of the 3D shape reconstruction.⁴⁷ Image acquisition and processing were done using the LaVision software DaVis 10.2.1.

We used different illumination systems for the single- and two-phase cases. For single-phase measurements, we used a dual-cavity laser Nd:YAG Litron LD25-527, synchronized with the cameras by a LaVision Programmable Timing Unit X (PTU X). For the two-phase case, we used dedicated LEDs from PHLOX (HSC Backlight) opposing each camera. The first setup was advantageous for the LPT—we were able to detect more particle trajectories per unit of volume. However, the laser was inadequate for droplet visualization as the interfaces reflected the laser sheet and cast shadows in the measurement volume. With the backlight system, one can obtain a sharper projection of the droplet silhouette and still track the particle shadows.^28,48

In both cases, the water was seeded with 20 μm polyamide particles (1.03 g/cm³ density). The ratio between particle diameter and the Kolmogorov length scale, η, was of $O$(0.1–1). The seeding particles could be treated as tracers as their response time was much smaller than the Kolmogorov time scale, τ_η (St ≈ 8 × 10⁻⁴, where the Stokes number is the ratio between particle response time and τ_η⁴⁹). The laser sheet illuminated the seeding particles from the test section bottom wall, entering with an angle to deviate from the droplet injection components. We used a set of lenses and mirrors to adjust the sheet thickness to about 4 cm and illuminate the tank center.

Simultaneously with the camera recordings, we monitored the pressure inside the vessel with a WIKA A-10 absolute pressure transducer (an accuracy of ±0.5% times the measured value) and the temperature with an RTD PT1000 from the IFM model TA2115 (an accuracy of ±[0.3 + 0.1% × measured value]). Both sensors were connected to the pressure vessel top lid, as indicated in Fig. 1. We measured the total flow rate with an Endress+Hauser Promag 10 electromagnetic flowmeter, which has an accuracy of ±0.75% times the measured value. Straight pipes of seven and four diameters long were placed upstream and downstream of the flowmeter, granting fully developed flow conditions at the electrode plane. Sensor data were collected by a National Instruments acquisition system composed of a cDAQ-9174 CompactDAQ chassis and one NI-9203 current input module. We used the software LabVIEW to monitor and record the data.

Two different measurements were conducted in similar measurement volumes: (1) Single-phase velocity data were measured via 3D-LPT using the Shake-The-Box method,⁴² and (2) the 3D interface topology was obtained with the Visual Hull method.^47,50 Preceding the measurements, we conducted the geometrical calibration using a two-level LaVision calibration target model 058-5. The target was placed through the top window and moved to three planes (z = −10, 0, 10 mm) using a linear actuator with 0.01 μm resolution (model: BM17.25 Micrometer Head). The mapping functions were obtained from the target images using a third-order polynomial in DaVis, with fit errors below 0.3 pixels. Note that the resolution of the linear actuator was sufficient to set the position of the z-planes, and the geometrical calibration only gives the initial 2D–3D mapping functions. Calibration targets have limited accuracy for 3D measurements due to the number and size of markers and external factors such as vibrations or physical interaction with the setup.⁵¹ In 3D-LPT measurements, the mapping functions are normally refined with the volume self-calibration (VSC) method.⁵² In our case, flow images were acquired with low particle image density for an initial VSC, yielding average disparities below 0.05 voxel. Afterward, we added more tracers to attain a higher particle concentration, repeated the VSC, and started the experiments.

Single-phase velocity statistics were obtained via the Shake-The-Box method with the camera configuration shown in Fig. 4. We used four cameras with the laser illumination system to acquire the flow images. The camera acquisition frequency ranged from 1.25 to 4 kHz and was adjusted to keep the average particle displacement below 10 $px̄$ (where $px̄$ is the normalized camera pixel length scaled by the magnification).⁵¹ For every measurement set, we acquired 1000 loops of 50 consecutive frames with five seconds of delay between loops using the recording-loop mode in DaVis to ensure the convergence of the turbulent quantities. From 5000 to 10 000 particles were tracked per frame; most trajectories extended over the entire recording (50 frames long), with trajectories shorter than ten frames deleted to filter out outliers and possible ghost tracks.⁵³ Flow rate and temperature data were simultaneously recorded. We repeated the VSC after every 200 loops to preserve a precise calibration. The raw particle images were then pre-processed in DaVis with a sliding minimum subtraction and a spatial normalization with the local average. We obtained the particle trajectories with the STB method, setting the allowed triangulation to 1.0 voxel and adding a second pass (backward in time) to complement the tracks.⁵¹ The data were exported from DaVis and post-processed in an in-house binning MATLAB code for the single-point statistics or used in the Lagrangian form for the two-point statistics.

To obtain time-resolved and averaged statistics on the droplet dynamics, we needed to simultaneously reconstruct the droplet topology and identify the surrounding flow structures with the 3D-LPT. The multiphase experiments were conducted with five high-speed cameras and the backlight illumination system. Compared to the single-phase setup from Fig. 4, we moved camera No. 4 to the bottom diagonal opposing camera No. 2 and added a fifth camera opposing camera No. 1. Then, cameras Nos. 1, 2, 4, and 5 were slightly rotated along the y-axis to open space for the LED panels; we carefully mounted these cameras in Scheimpflug condition. The bubble or droplet images were acquired after the initial VSC with an acquisition frequency of 2 kHz (we repeated the VSC after every ten recordings). Using the injection system shown in Fig. 3, we favored having a single bubble/droplet in the measurement volume to increase the number of visible particles and reduce turbulence modulation effects by the dispersed phase. The recorded images were pre-processed to segment the dispersed phase and seeding particles. We then used the visual hull method^47,50 to retrieve the interface shape and STB for the particle trajectories. The reconstructed object data were exported to an in-house MATLAB code and converted to a volumetric binary image. The volume of the bubbles/droplets was obtained by counting the number of voxels of each 3D object. We used this volume to calculate the droplet equivalent diameter, D_eq = (6V/π)^1/3. Other geometrical features, such as aspect ratio, semi-axes length/orientation, and center of mass, can also be retrieved; connecting the center of mass between frames determined the dispersed phase trajectory.

The uncertainties for the trajectories reconstructed with STB were extracted directly from the DaVis software. The uncertainties are based on linear regression analysis methods that calculate the confidence bands of every trajectory, providing the instantaneous uncertainty δ of the position, velocity, and acceleration for every tracked particle (we refer the reader to Ref. 53 for more details).

We conducted a series of experiments to characterize the turbulence in our facility. The principal inquiries were about the mean flow, homogeneity, and isotropy (Sec. IV A), energy dissipation rate (Sec. IV B), and turbulence scaling (Sec. IV C).

The instantaneous velocity field, U_i, was decomposed into the temporal mean velocity plus the fluctuation velocity, $Ui=Uī+ui$⁠. Throughout this work, subscripts i = (1, 2, 3) represent directions (x, y, z) in the coordinate system x = {x, y, z}, the overbar $(⋯̄)$ is the time average, and ⟨⋯⟩ stands for the ensemble average. Figure 5 depicts the variation of $Uī$ and the fluctuation velocity root mean square, $ui′=⟨ui2⟩1/2$⁠, along the x and y axes. The profiles over the z-direction had a similar trend (not shown here). The experiment was conducted with V_jet = 8 m/s, N = 12, and x* = 36 cm. The velocity profiles suggested a homogeneous turbulence region within a volume of at least 4 × 4 × 4 cm³, with the inhomogeneity factor, $IH=1−u1,min′/u1,max′$⁠,²⁹ lower than 7%. Furthermore, the mean velocities were less than 10% of the respective fluctuations. The mean flow strength can be further quantified by the ratio of its kinetic energy to the average turbulent kinetic energy, $m*=(Ū⋅Ū)/(u1′2+u2′2+u3′2)$⁠.²⁷ Variano and Cowen²⁷ suggested that mean flow effects are negligible for m* <5%. In the case reported in Fig. 5, we found m* = 2.78%.

In conjunction with the homogeneity condition, the turbulence should ideally be isotropic. For the setup reported in Fig. 5, the isotropy ratios were $u1′/u2′=1.09$ and $u2′/u3′=0.98$⁠. However, the anisotropy and the mean flow strength were noticeably higher for the configuration with N = 4, M = 5 cm, and x* = 40 cm (⁠$u1′/u2′≈1.73$⁠, $u2′/u3′≈1.02$⁠, and m* = 7.14%). Results for different jet array configurations are summarized in Table II. The isotropy condition can also be verified with the anisotropic components of the Reynolds stress tensor, τ_ij = ⟨u_iu_j⟩, which should be zero in isotropic turbulence.^1,29 In Fig. 6, we present the three off-diagonal components of τ_ij normalized by the turbulent kinetic energy, k = ⟨u_iu_i⟩/2, obtained from the experiments previously reported in Fig. 5. The normalized values were within ±2.5%, indicating that the turbulence was nearly isotropic. Furthermore, the τ₂₃ component showed higher values compared to the others, and we speculate that this small anisotropy in the yz-plane developed from the outlet pipes being only in the xz-plane. The yz-anisotropy could be reduced by adding exit pipes in the xy-plane, provided the flow distribution is uniform (which was not the case in our experiment, as there was no flow through the upper exit due to the tank’s low internal pressure).

One known issue of using jets operating with continuous flow is the presence of a mean shear/strain.^16,18,23 To verify how strong the mean shear is in the current setup, we calculated the mean strain rate factor, MSRF, similarly to Refs. 2 and 24. The factor in the streamwise direction was defined by the ratio of the mean flow strain to the fluctuating velocity strain, $MSRF=⟨(∂U1̄/∂x1)/s112̄1/2⟩$⁠, where s_ij = 0.5(∂u_i/∂x_j + ∂u_j/∂x_i) is the fluctuating strain-rate tensor. In the setup with N = 12, we estimated MSRF to be between 0.04 and 0.05, which is comparable with the low values found in random actuated jet arrays.^2,24 The mean strain, however, became significant when reducing the distance between arrays (Table II) and reached MSRF = 0.35 at x* = 10 cm.

In a different array configuration with N = 4 and V_jet = 14 m/s, where we reached ɛ > 1 m² s⁻³ but with elevated anisotropy and inhomogeneity. For this case, even at an acquisition frequency of 4 kHz, the average particle displacement was relatively high (⁠$∼20px̄$⁠) and might have debilitated the accuracy of the STB.⁴² From the different setups summarized in Table II, we recommend the configuration with N = 12 as it exhibited better isotropy and weaker mean flow compared to the other cases. It is noteworthy that adopting randomly actuated jets would improve $u1′/u2′$⁠, weaken secondary flows, and expand the HIT region but with the cost of potentially weakening the energy dissipation rate, u′, and Re_λ.

Figure 8 shows the autocovariance for the case with V_jet = 5 m/s, N = 12, M = 3.1 cm, and x* = 36 cm. Since the measurement volume was not sufficiently large for R to reach its asymptotic limit at zero in all cases, we extrapolated R until its first zero-crossing by fitting an exponential curve. This method provides only a rough estimation, as no universal models exist to predict R(r > L).^6,57 A better alternative would be fitting the model function to f(r) in the inertial range as in Refs. 6 and 25. However, since we opted for calculating R directly from the 3D trajectories instead of using the e_i projections to calculate f, this model function was not applicable. Table II displays the estimated L for different configurations. Since we have some degree of large-scale anisotropy, the longitudinal integral scale in the streamwise direction, L_11,x, is expected to be larger than L_11,y and L_11,z, and the integral scale L taken from arbitrary projections likely falls between those.

Figure 9 presents how u′ decays with x*/d. While the scaling with x*⁻¹ was confirmed for most data points, the model underpredicted u′ when adopting C₀ = 0.28 and B = 5.8 as in a single round jet.^29,58 This discrepancy suggests that the coefficients were not suitable for the current setup, likely due to effects such as interactions between the opposing jets, confinement, or interactions between the outflow and the jets. A more accurate prediction was obtained by adopting C₀B = 2.5. We cannot discuss the values of C₀ and B individually, as particular measurements would be necessary to estimate them. It is also noteworthy that the point at x*/d = 14.3 deviated from the scaling, potentially due to its location outside the self-similar region, where the linear scaling does not hold,¹ or the presence of a negative virtual origin, which could shift the model’s straight line to lower values near the jets.

The authors adopted C_ɛ = 0.73, C₀ = 0.28, K = 3.31, and B = 5.47 for cases with co-flow⁵⁹ or B = 5.8 without co-flow.⁵⁸ As discussed previously, we found different coefficients in our facility: K = 1.16, C₀B = 2.5, and C_ɛ ≈ 0.43 (average value from the 12 jets configuration in Table II). The experimental results on the decay of ɛ along x*/d are displayed in Fig. 11. The dashed and dotted-dashed lines correspond to Eq. (9) using the coefficients from Tan et al.²⁹ and the ones found in the current work. The experimental data from Tan et al.²⁹ for a continuous single jet array are also included; most of their experiments were for a jet array in a co-flow arrangement, but we only show the case without co-flow.

Overall, Eq. (9) also provided a reasonable prediction of ɛ for the opposing jet array configuration; of course, the constants had to be adapted to fit the characteristics of the new facility. Although further investigation of the variables from Eq. (9), such as analyzing a broader range of d, is still necessary, our results support the ideas presented by Tan et al.²⁹ These scalings can be especially useful in the initial design stages of a facility, where, for a threshold ɛ, one can estimate the necessary pumping power based on a range of V_jet, d, and N.

As a last characterization of the turbulence scaling, we report the scale separation over the Reynolds number, similar to Bang and Pujara.²⁵ Here, the Reynolds number was based on large-scale eddies, Re_L = u₀L/ν, considering u₀ ≈ u′. The turbulence parameters, normalized by the respective Kolmogorov scales, are expected to follow the scaling laws: $L/η∼ReL3/4$⁠, $λ/η∼ReL1/4$⁠, $τL/τη∼ReL1/2$⁠, and $u′/uη∼ReL1/4$⁠.^1,57 The integral time scale and the Taylor microscale were not measured, so we indirectly calculated these quantities as τ_L = L/u′ and $λ=u′15ν/ε$⁠. Figure 12 exhibits the scale separation for all cases reported in Table II. The experimental data showed overall good agreement with the classic scaling laws. The largest discrepancies were observed for the integral scales, likely due to biases introduced by the methods used to estimate L.

We provide here examples of two-phase flow measurements in the jet-stirred facility obtained with the techniques described in Sec. III B. Figure 13 exhibits the procedure to retrieve the coupled statistics: the raw images had the intensity inverted and the dispersed phase discretized using threshold segmentation and excluding small objects [see the binary image in Fig. 13(b)]. The particle images were pre-processed with a sliding minimum subtraction, a Gaussian smoothing, and multiplied by the inverse of Fig. 13(b) to remove the dispersed phase [Fig. 13(a)]. Then, the particle images were processed with STB to obtain the trajectories surrounding the dispersed phase. The 3D interface was reconstructed from binary dispersed phase images using the visual hull technique, similar to Ref. 47. Finally, the reconstructed bubbles/droplets and the flow field were regrouped so the interaction between phases could be investigated.

Flow statistics near the interface can be extracted by considering only the trajectories within a given search diameter from the bubble/droplet center of mass, D_s.⁶⁰ The more particles tracked inside the search diameter, the more reliable the flow statistics should be close to the interface. A high particle concentration also yields a finer resolution when converting the STB trajectories to time-resolved Eulerian data, which can be done with techniques such as the Vortex-In-Cell (VIC#).⁶¹ In Fig. 14, we report the typical particle concentration around bubbles and the influence of the number of cameras; the data were collected from 35 bubble breakup events. Figure 14(a) shows a reconstruction example of a bubble (D_eq = 7.4 mm) with more than 700 particles within D_s = 3D_eq.

For D_s = 3D_eq, the cases with three, four, and five cameras had an average number of tracked particles of 357, 467, and 503. The respective bulk number of trajectories was 4356 ± 605, 6762 ± 842, and 7214 ± 944 in a measurement volume of 40 × 50 × 28 mm³ (average concentrations of 0.08, 0.12, and 0.13 particles/mm³). The average values over different search diameters are presented in Fig. 14(b). Overall, there was a good gain from three to four cameras but little difference between four and five cameras. The latter seemed to have slightly more particles close to the interface. Figure 14(c) shows the probability density function (pdf) of the distance between particles and interface, l_p. Here, the influence of the number of cameras was barely visible. In all cases, the closest particles were less than 1 mm from the interface, and most particles were concentrated between 10 and 25 mm away.

Noteworthy, we achieved this number of trajectories with a relatively low particle image density, ppp, of less than 0.01 in all cases. Over this value, there was a significant increase in the background noise due to the out-of-focus particle shadow, affecting the STB accuracy and limiting the number of reconstructed particles. One alternative to further increase the ppp and obtain more trajectories in the bubble vicinity would be using techniques developed for high-concentration particle shadow tracking, such as the OpenLPT.⁶² 

Along with having a good resolution of the flow near the bubble/droplet, we also need to estimate the local interface response to turbulent fluctuations. An approach to represent the local deformation was recently reported by Qi et al.,⁶³ which used the nearest neighbor algorithm to estimate the displacement of each vertex on the 3D-object surface in relation to the vertices in the previous time instant; we refer to the reader to Ref. 63 for a description of all steps. Here, we used the averaged distance of each vertex to the k-nearest neighbor vertices. The local displacement was then divided by the time delay between consecutive frames to obtain the interface velocity, u_f. The method only provides the interface velocity projected in the direction normal to the surface, which can be a limitation when measuring the deformation of oil droplets. For droplets with a high inner viscosity, the stretching of fluid particles can produce thin filaments before the breakup.^31,64 This filament stretching process might be linked with a tangential deformation and cannot be quantified by the nearest neighbor approach.

Figure 15 presents examples of the deformation evolution during the breakup of one air bubble (a) and one oil droplet (b). The experiments were done with the N = 12 jet array configuration at different velocities. In this setup, the bubble and the droplet were in the inertial range (D_eq = 6.1 mm and D_eq = 7.0 mm), assuming they did not modulate the turbulence. For the droplet case, we used an oil from DL Chemical (PB-300) with a kinematic viscosity of 36 mm²/s, a density of 826 kg/m³, and an interfacial tension of 29.5 mN/m. The interfacial tension was measured using the pendant drop technique.

In Fig. 15(c), the deformation was represented by the standard deviation of the local deformation velocity, $σuf$⁠, normalized with the eddy turnover velocity at the bubble/droplet scales, $uε,D=C2(εDeq)1/3$⁠, in line with the KH framework. The energy dissipation rate was estimated from the velocity of the surrounding particles within a search diameter of 4D_eq. We used ɛ to calculate u_ɛ,D, τ_η, and We for every breakup case. From the events shown in Fig. 15, we had ⟨ɛ⟩ = 0.21 m² s⁻³ (u_ɛ,D = 0.16 m/s, τ_η = 2.0 ms) during the bubble breakup and ⟨ɛ⟩ = 0.09 m² s⁻³ (u_ɛ,D = 0.12 m/s, τ_η = 3.2 ms) during the droplet breakup.

The bubble breakup followed a similar time scale separation as discussed by Qi et al.⁶³ The bubble stayed in a low-deformed state for a long period until about −14τ_η, when the interface velocity started to slowly increase and resulted in a less spherical shape [see snapshots in Fig. 15(a)]. This slow deformation growth lasted until −2τ_η and was potentially linked to an inertial deformation stage⁶³ driven by the surrounding flow. Then, after −2τ_η, the bubble underwent a sudden interfacial velocity increase until t/τ_η = 0, when the breakup occurred. This steeper profile of $σuf$ portrayed the neck formation and the subsequent fast inward deformation that led to the filament rupture, a mechanism likely related to capillary-driven deformations.^63,65,66 Note that local deformations became faster than the eddy turnover velocity, indicating that this deformation stage was not allied with the local turbulence at the bubble scale.

The deformation evolution in the droplet breakup differed considerably from the bubble case. The already stretched droplet stayed in a highly deformed state for more than 15τ_η and rotated following surrounding vortical structures. Although highly deformed, $σuf$ remained similar to u_ɛ,D during the whole process. Distinctly from the bubble case, the interface velocity did not undergo a sudden increase right before the breakage. The lack of abrupt changes in $σuf$ is attributed to viscous effects and the internal flow’s resistance to external forces and interface responses. In most observed breakups with We ≈ 1, the oil filaments rupturing resembled the ones resulting from the Rayleigh–Plateau instability in liquid jets.⁶⁷ 

The example from Fig. 15(b) also features a common challenge of such 3D measurements: the limited time window in which the dispersed phase remains in the field of view. In the experiments with high-viscosity oils, the droplets often entered the measurement volume in an already highly deformed state [as in Fig. 15(b)] or left it before breaking. To predict the available observation time in the current facility, we calculated the typical time lag at which the bubble displacement was comparable to the measurement volume size. This time lag was estimated by dividing the characteristic length of the measurement volume (⁠$L≈40$ mm) by the bubble’s absolute velocity. We obtained the bubble velocity data from 35 breakup events by computing the 3D trajectories of the mother and daughter bubbles. Figure 16 shows the pdf of the time lag, indicating the available observation time. The average time lag was 119.2 ms. Note that the pdf represents the extreme case where we had the most intense turbulence (V_jet = 8 m/s) and strong buoyancy effects since the only bubbles were analyzed (the time lag in the y-direction is 10% shorter than in x and z). We emphasize that the pdf was retrieved from a limited dataset and should be treated as a rough estimation.

The observation times until breakage of the examples shown in Sec. V B were also included in Fig. 16 (blue and red markers). For the bubble case, a period of 46 ms was sufficient to capture the deformation evolution from a nearly spherical state until the breakage. In contrast, a residence time of 56 ms was not enough for us to observe the initial deformation stage of the droplet. In both cases, the total observation time counting the residence time of the daughter bubbles/droplets was 60 ms (bubble) and 112 ms (droplet). Note that the droplet measurements are usually taken at a lower jet velocity to have a We similar to the bubbles, as the oil had a lower interfacial tension. Combined with the lower buoyancy, one can expect an overall longer observation time for droplets compared to Fig. 16. The main difficulties then are related to the slower breakup process and the filament stretching (we observed filaments extending over more than 2 cm), and capturing the complete process within the measurement volume is rare. In conclusion, the wide range of time and length scales present in the breakup process imposes a considerable challenge related to equipment/technique limitations, especially when dealing with 3D measurements. Thus, the quest is to choose an optimal combination of acquisition frequency and measurement volume size to resolve the most relevant scales of a given object of study.

We presented a new jet-stirred turbulent tank designed for multiphase flow experiments at high Reynolds numbers and correspondingly high energy dissipation rates. The facility is composed of two arrays of jets facing each other, with the jets continuously fed. The jets generate turbulence within an octagonal acrylic tank constructed to allow optical access for multiple high-speed cameras. This facility was specifically designed for conducting 3D measurements of multiphase flows, with a primary emphasis on studying the deformation and breakup of droplets/bubbles dispersed within turbulence.

Our objective is to establish a comprehensive database concerning these interface dynamics, which hold relevance across various environmental and industrial applications. To achieve this, it is crucial for the turbulence to exhibit preferential characteristics: homogeneity, isotropy, and a high Reynolds number, thereby replicating the foundational assumptions of the Kolmogorov–Hinze framework in a controlled manner.

Toward this end, we conducted a quantitative three-dimensional analysis of the turbulence characteristics within our facility. We have shown that the facing jet array configuration engenders homogeneous turbulence with minimal anisotropy in the central region of the facility, encompassing a volume dimension conducive to tracking and characterizing the interface of discrete phases. In particular, the apparatus operates with Reynolds numbers reaching up to 800, with a 10% degree of anisotropy. Finally, we presented examples of 3D topology reconstruction coupled with particle tracking under HIT conditions, confirming the capability of this new facility for multiphase flow measurements.

The authors wish to acknowledge Mr. Werner Jandl and Mr. Yigit Kücük for their help with the facility design and construction, and Vlad Giurgiu for his assistance and useful discussions. The authors acknowledge TU Wien Bibliothek for financial support through its Open Access Funding Programme. The funding from the Faculty of Mechanical and Industrial Engineering, TU Wien, Sonderprojekt No. A230719_UP_E322 is also gratefully acknowledged.

The authors have no conflicts to disclose.

Leonel Beckedorff: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Giuseppe C. A. Caridi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Alfredo Soldati: Conceptualization (equal); Funding acquisition (lead); Project administration (equal); Resources (lead); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.