Equipment used in the laboratory test, as shown in Figure 1, could be classified into three main categories: the air supply system, fuel system, and imaging and detection system.

The airflow generation in this setup involved using a Gebhardt company centrifugal blower, operating at a speed of 2,750 rpm, with the capacity to generate up to 35% of a cubic meter per second (Figure 2A). The LS company employs a converter (Figure 2B) capable of modulating the blower’s speed to control and adjust flow rates within the channel. This converter achieves different channel velocities by altering the motor’s input frequency, ranging from 0 to 60 Hz, changing the engine’s speed from 0 to 2,750 rpm, and the flow speed from 0 to approximately 53 m/s.

The primary structure of the wind tunnel was crafted from Plexiglas. It possessed a cross-section measuring 50 × 80 mm and extended over a length of 60 cm. The transparent nature of Plexiglas enables optical measurements during testing. The Plexiglas sheet was 2-mm-thick, and the nozzle was positioned 30 cm into the channel. The initial 30 cm of the channel streamlined and smoothed the flow (Figure 2C).

A honeycomb composed of hexagonal aluminum cells (Figure 2D) was employed to enhance flow stability and minimize vertical velocity components. These hexagonal cells comprised multiple tubes that effectively reduced the intrusion of large-scale eddies into the airflow. The honeycomb structure utilized in this study was 35-mm-long and was characterized by 6-mm regular hexagons.

To ensure the stability of the channel and prevent unwanted vibrations, two solid Plexiglass base holders with a cross-section of 20 × 20 mm were employed. Additionally, 100 × 100 mm Plexiglass sheets were used to maintain balance on the base and table. Furthermore, a support holder was covered with fiber and polystyrene to prevent vibrations in the blower.

Injecting a liquid jet vertically into the air stream requires a specific route for fuel injection at the desired speed by the jet supply system. Due to natural fuel limitations, water was used as a fluid injected into the stream. Injections of fluid into the transverse airflow at the desired speed required increased pressure behind the fluid using a pressurized tank (Figure 3A). The tanker was partially filled with liquid and pressurized by a gas. We could then adjust the flow rate in the nozzle outlet using a regulator valve. A flow meter was used to obtain the rate of the fluid jet in the nozzle outlet. The outlet speed of the nozzle was easily calculated by measuring the inlet flow and the nozzle area. The Besta Company made the flowmeter used, in the range of 0.16–1.6 L per minute (Figure 3B). The nozzle used here was a simple orifice, and was circular and elliptical in different dimensions (Figure 3C). Four configurations for the nozzle outlet were considered. In two cases, the nozzle outlet was circular with diameters of 1 and 2 mm, and in the other two cases, elliptical nozzles with major and minor radii of 1 and 2, and 1 and 4 mm, respectively, were constructed. These nozzles were fabricated using a super drill and wire cutter and were specifically designed for this paper. When the smaller diameter faced the wind direction, the aspect ratio was less than 1, and when the same nozzle had its larger diameter facing the wind, the aspect ratio became greater than 1. Thus, depending on its orientation relative to the wind, two aspect ratios smaller and greater than 1 could be achieved with a single nozzle.

In this study, shadowgraphy was used to detect crossflow. We required detection and imaging systems to capture relatively good-quality images for crossflow analysis. The camera used in this test was a Casio EX-F1 camera that can take pictures at 1,200 frames per second.

This study used 25-micron-long time exposure photography, which is the maximum time that could be achieved with the present camera. Due to the low time exposure, it needed a vital light source, as explained in the following paragraphs. The most important effect of the time exposure on the photographs was that the lower the number, the less light the camera sensor needed. For example, if the droplets were flowing, they could be depicted with a relatively low resolution with low lightning time.

For a light source, a projector with an Onomat 1000-W bulb was used due to the type of lens mounted on it and the surrounding protections; its light output was relatively uniform (Figure 4A). To measure the speed of the incoming air, a hot wire anemometer model 1,340, manufactured by Tess Corporation with an error of less than 3% was used. (Figure 4B).

Measurement of the velocity profile in the test’s transverse section showed that this section’s velocity profile was uniform. The speed of blown air varied from 7.6 to 51.8 (ms⁻¹). The fluid tested was water; the use of water instead of fuel is routine and was used as the scavenged fluid. Since nozzles with different openings were used in this experiment, the speed of the outlet water of the nozzle was different. However, water velocity generally varied from 1.06 to 33.95. The test temperature was an ambient 25 °C (Table 1).

Because this is a study on crossflow, there are many non-dimensional numbers in the problem. The following are the dimensionless numbers used in this experiment (Ashgriz, 2011). The momentum ratio number is defined as the ratio of the liquid jet momentum to the gas momentum (liquid jet dynamic pressure to the dynamic gas pressure): q = ρ l v l 2 ρ g v g 2 (1)

In relation (1), ρ l is the liquid density, v l is the liquid velocity (jet) in the y-direction, ρ g is the density of the gas (air), and v g is the gas velocity (air) in the x-direction. The gas Weber number is defined as the force of inertia to the surface tension force: w e g = ρ g v g 2 d σ l . (2)

In relation (2), d is the diameter of the nozzle and σ l is the liquid’s surface tension.

The liquid Weber number is defined as the gas Weber number: w e l = ρ l v l 2 d σ l . (3)

The gas Reynolds number is defined as the ratio of inertia to the viscous force: R e g = ρ g v g l μ g , (4)

where l is the characteristic length and μ g is the viscosity of the air.

The liquid Reynolds number is also defined as follows: R e l = ρ l v l l μ l . (5)

Eqs 1–5 were used to obtain the Mach number for gas and liquid, as well as the Reynolds number for gas and liquid and the momentum ratio. As can be seen, the dimensionless numbers are determined after plugging the values obtained from Table 1 into these equations.

The trajectory and penetration of a liquid jet into a transverse gas flow are critical parameters for a fluid jet. They directly influence the distribution of fuel injection within the combustion chamber, the process of evaporation, and the rate of mixing with the oxidizing agent. It is also essential to design the combustion chamber to prevent the liquid jet from impacting the chamber walls. The observations from this study reveal that, when a liquid jet is injected into calm air, it maintains a straight trajectory and does not collide with the upper wall of the test section. It is important to note that these observations are based on small-scale dimensions. In larger-scale scenarios, the fluid jet may indeed deflect and not reach the upper surface of the channel.

A schematic representation of the fluid jet being sprayed into the transverse air is shown in Figure 5. The liquid separates from the surface of the jet column in the form of a liquid strip. Due to hydrodynamic instability, the liquid jet, which initially leaves the nozzle as a continuous column, becomes unstable along its length, leading to its eventual breakup into ligaments—a “column breakup.” Subsequently, the separated liquid pieces along this trajectory transform into smaller droplets that enter the combustion chamber.

Figure 6 shows the injected fluid jet in the transverse airflow for circular nozzles. The overall process of the liquid jet breaking into the airflow and forming the spray in different nozzles is the same, and, depending on the geometry used, the length of penetration and breakup will be different.

Figure 7 shows the liquid jet trajectory for the geometry of different nozzles. In each geometry, liquid velocity, and the different air velocities, several photographs were taken at the time, with a total of 2,100 photographs. To better detect the boundaries of the liquid jet column and detect the breakup point, we took the average of photographs at the same conditions using MATLAB software (Supplementary Appendix SA).

Figure 8 illustrates the impact of transverse air velocity on the penetration depth of the liquid jet. It is evident from the figure that, as the air velocity quantified by the Weber number increases, the penetration depth of the liquid jet decreases. This is due to the increased drag force caused by the higher velocity, which prompts the liquid jet to deviate from its earlier path, resulting in a reduced penetration depth.

The observed change in penetration depth aligns with findings from other studies. However, it is important to note that this study differs from previous research regarding the fluid used, which is not oil. Additionally, the velocities employed in this study are distinct. The primary objective of this research is to examine how variations in transverse air velocity affect the penetration depth of liquid jets, particularly when dealing with nozzles of different geometries.

In this research, two circular nozzles with diameters of 1 and 2 mm, two elliptical horizontal nozzles with a small diameter of 1 mm and large diameters of 2 and 4 mm, and two elliptical vertical nozzles with a small diameter of 1 mm and large diameters of 2 and 4 mm were used. Laboratory tests were first performed with a circular nozzle with a diameter of 1 mm, and then, a circular nozzle with a diameter of 2 mm was used. Oval nozzles performed another part of the laboratory tests. The results are shown in the following diagrams. As shown in Figure 9, the behavior of the liquid jet is the same for all nozzles, so the liquid jet penetration decreases with the increasing amount of transverse air velocity, assuming that other parameters are constant.

The impact of nozzle geometry on the penetration of the liquid jet can be studied while maintaining a constant Weber number and momentum ratio. Figure 10 demonstrates that the velocity of incoming air decreases for circular geometries with increasing diameter while holding the Weber number constant. Conversely, at a constant momentum ratio, the velocity of the inlet liquid increases due to the momentum ratio formula (q). With lower air velocity at a larger diameter, a reduced drag force is exerted on the liquid. The increased fluid velocity also results in higher momentum, leading to a greater penetration depth. Similar principles apply to elliptic nozzles, meaning that the penetration depth increases as the ratio of the larger to smaller diameters increases while keeping Weber’s number and momentum ratio constant. When there are the same areas but with opposite dimensions, where the smaller diameter is aligned with the flow direction and the larger diameter is oriented perpendicularly to the transverse flow, it is evident that the penetration depth is greater. In cases where the minor diameter is aligned perpendicular to the transverse flow, the airflow encounters less surface area, resulting in reduced drag force on the liquid jet and, consequently, deeper penetration of the liquid jet.

Considering the upper boundary of the liquid jet trajectory for the circular nozzle, we can determine the equation of the liquid injection trajectory using linear regression. Considering the circular nozzle with a diameter of 1 mm, the equation of the liquid jet trajectory was obtained as follows: y d = 3.94 x d 0.35 q 0.33 . (6)

As shown in Figure 11, the liquid-jet injection trajectory agrees very well with previous research, and the difference may be due to factors such as the experimental equipment, the difference between the momentum ratio, and Weber numbers.

Linear regression can also be used to obtain the elliptical nozzle injection trajectory. The direction equation for the elliptical nozzle is obtained as follows: y d e q = 2.051 x d e q 0.34 q 0.52 . (7)

A specific diameter should be used to make the jet spray trajectory dimensionless and the diameter used in the Weber number into an elliptical nozzle. For this purpose, it should be considered equivalent to the following diameter: d e q = a b , (8)

where a is a large diameter, b is a small diameter oval, and d e q is the equivalent diameter.

As mentioned, two distinct breakup processes exist for liquid jets in transverse flow: surface and column breakup. The liquid forms a continuous column between the nozzle outlet and the breakup point. Determining the exact location of this breakup is crucial for modeling fluid jets in transverse airflow. However, obtaining a precise location can be challenging, primarily due to the presence of high-density droplets. As shown in Figure 12, the length of the breakup x b and its height y b are equal to the trajectory that the liquid jet passes in the trajectory of the transverse flow to break.

To determine the breakup length, it is necessary to identify the coordinates of the breakup point by examining various combinations of momentum ratios and Weber numbers for a given nozzle. This process allows for the derivation of relevant relationships. Interestingly, the difference in breakup length is minimal when considering various values of q and Weber numbers less than 10, essentially making it a constant value for these scenarios. Similarly, another constant value can be established for different q values and Weber numbers exceeding 10. As a result, we can derive the following fixed values for the breakup length: x b d = 4.1 ± 0.5 w e < 10 x b d = 10.3 ± 0.6 w e < 10 . (9)

To obtain the height of the breakup, the height should be calculated by considering the momentum ratio and different Weber numbers. Then, the height of the breakup equation is obtained, which is as follows for the Weber number greater and smaller than 10: y b d = 10.419 x d 0.278 w e < 10 y b d = 4.77 x d 0.387 w e < 10 . (10)

Much research (Mazallon et al., 1999; Sallam et al., 2004; Zhang et al., 2013; Song et al., 2017) has demonstrated that the Weber number influences the breakup pattern of a liquid jet. The initial phase in a liquid jet’s breakup involves the formation of a strip-like ligament. The presence of vortices in the crossflow induces waves on the surface of the liquid column jet. These waves gradually grow, ultimately leading to the fragmentation of the liquid jet into ligaments. These separated segments are exposed to the dynamic air pressure, causing them to break into smaller droplets. This force leads to the dispersion of the liquid jet column, transforming it into a bean-like shape. The phenomenon where a liquid jet breaks into ligaments is commonly referred to as “column breakup” (Figure 13).

Another kind of breakup appears with the increase in the Weber number. In this kind of breakup, a hollow layer of liquid is formed as a bag shape. The time of its formation is brief because aerodynamic force overcomes surface tension, and bags change to small particles. The bag breakup is shown in Figure 14. In Part 1, bag breakup is produced and, in Part 2, changes to small particles.

The bag breakup has vanished to increase the Weber number, and small particles (much smaller than the nozzle diameter) are separated from the liquid column. This step combines a different kind of breakup called multimode breakup. In this regime, particles separate from the bottom part before the breakup because of increasing aerodynamic force (Figure 15).

As shown in Figure 16, the breakup pattern changes when increasing the Weber number while maintaining an equal momentum ratio and nozzle diameter. Specifically, Weber numbers 2, 16.6, and 62 are considered for different sections. At Weber number 2, the growth of surface instability is prolonged, allowing sufficient time for forming ligaments. In the case of Weber number 16.6, dynamic pressure increases, leading to the growth of waves on the liquid jet’s surface and resulting in a “bag breakup”. After a period, aerodynamic forces overcome surface tension, causing the bags to break and form small particles. These bags represent only a portion of the liquid jet, with the remainder transforming into ligaments or larger particles. With the Weber number increasing to 62, the aerodynamic forces applied to the column jet intensify. These forces surpass the surface tension in each segment, and particles separate from the jet’s surface. In this scenario, bag breakup is minimal and quickly transitions into small particles. A comparison of these results with previous studies is presented in Table 2.

In this article, the variance method is used to obtain the uncertainty of the test results. Considering the w function as follows, W = w x 1 , x 2 , x 3 , . . . , x n . (11)

The error propagation for the function given in relation 11 is calculated using the variance method thus: δ w = ∂ w ∂ x 1 δ x 1 2 + ∂ w ∂ x 2 δ x 2 2 + ∂ w ∂ x 3 δ x 3 2 + . . . (12)

In relation 11, all parameters from x 1 to x n are independent of each other. Uncertainty about any of the parameters can result from systematic or inherent errors. For example, the liquid trajectory is obtained from Eq. 6. Using Eq. 11, the error expression for y d function can be expressed based on all other quantities. δ y d = ∂ y d ∂ x d δ x d 2 + ∂ y d ∂ q δ q 2 1 2 . (13)

Now the error is obtained for each of the aforementioned sentences separately. δ x d = ∂ x d ∂ x δ x 2 + ∂ x d ∂ d δ d 2 1 2 (14) δ x d = 1 d δ x 2 + − x d 2 δ d 2 1 2 . (15)

The momentum ratio error (Eq. 1) can be obtained from the following equation. δ q = ∂ q ∂ ρ l δ ρ l 2 + ∂ q ∂ ρ g δ ρ g 2 + ∂ q ∂ v l δ v l 2 + ∂ q ∂ v g δ v g 2 1 2 . (16)

After derivation from relationship q and placing it in the aforementioned equation, we derive a relation as follows. δ q = v l 2 ρ g v g δ ρ l 2 + − ρ l v l 2 ρ g 2 v l 2 δ ρ g 2 + ρ l v l ρ g v g 2 δ v l 2 + ρ l v l 2 ρ g v g 3 δ v g 2 1 2 . (17)

In the aforementioned relationship, v g is the gas or air velocity obtained using a speedometer. The liquid velocity is obtained from the following equation: Q = v t = π 4 × d 2 × v l ⇒ v l = 4 v π d 2 t . (18)

The liquid velocity error can be obtained thus: δ v l = 4 π d 2 t δ v 2 + − 8 v π d 3 t δ d 2 + − 4 v π d 2 t 2 δ t 2 1 2 . (19)

To obtain the approximate error for Eq. 11, it is necessary to know the error of each of the primary quantities. All errors are shown in Table 3.

Considering the aforementioned error values, the error value y d is 2%. Similarly, the error can be obtained in each step (Zhang et al., 2013).