The interaction of vortex rings with thin wire mesh screens is investigated using laser-induced fluorescence (LIF) and molecular tagging velocimetry (MTV). The existence of vortex shedding from individual wires of the porous screens, suggested by prior works, is shown and compared to flow visualization results. A range of interaction Reynolds numbers and screen porosities are studied to determine the conditions affecting the interaction. Transmitted vortex (TV) ring formation is shown to be a function of vortex shedding and the shedding Reynolds number, but not a function of porosity. Screen porosity is shown to affect the TV convective speed but did not impact the formation behaviors. Three major flow regimes existed for the interaction: TV formation with no vortex shedding, TV formation with visible vortex shedding, and no downstream formation with strong shed vortices.

## Introduction

Vortex rings are fundamental flow structures found in nature. For example, they can be found in atmospheric weather events like downbursts [1], as wall scouring mechanisms in the human heart [2], and in marine propulsion systems such as jellyfish [3,4]. In modern technology vortex rings are used for flow control synthetic jets [5], but can also present a dangerous flight condition for helicopter flight known as vortex ring state [6]. Vortex ring interaction with porous surfaces is observed in flows induced by forest fires, through filters such as those in research wind tunnels and in detection of hazardous material residue in clothing. Vortex rings are often used to investigate more complex phenomena (e.g., vortex structure interactions) because of their simplicity and repeatability. They have previously been used to study free surface behavior [7], cavitation and collapse [8], and helicopter tip vortex behavior [9]. The size and strength of vortex rings can be controlled based on formation parameters making them convenient for experiments where a concentrated vortex is being investigated. Interaction of vortex structures with porous media can provide more information about turbulent transition of flows.

The formation of vortex rings is well understood and is described in numerous analytic, computational, and experimental studies (e.g., see Refs. [317]). A limiting case of the vortex ring/porous boundary interaction is the interaction of a vortex ring with a solid boundary. The dynamics of this interaction involve the development of a boundary layer that separates from the solid boundary forming secondary vortex (SV) structures [1821]. When the solid boundary is replaced with a thin porous one, additional vortex structures are observed downstream of the porous boundaries [2225]. In some cases, a newly formed transmitted vortex (TV) ring convects downstream of the porous boundary in the direction as the impinging vortex [2225]. The interaction with a thin porous screen provides the opportunity to study a complex vortex boundary interaction, which can expand the understanding of similar natural and technological flows. The interaction exhibits complex boundary layer dynamics, regions of high vorticity, and a varying downstream flow behavior dependent on the vortex and boundary properties [2225]. A better understanding of fluid–structure interactions of this type would allow for validation of numerical models. It could also be used to understand how coherent structures in turbulent flow evolve during interaction with boundaries. The goal of this work is to show experimentally the hypothesis of Hrynuk et al. [25] and numerical study of Cheng et al. [26] that vortex shedding occurs when a vortex ring interacts with a thin porous screen, changing the formation behavior of the transmitted vortex. This work will also aim to characterize the flow behavior as a function of vortex and porous screen properties.

## Background

The works by Naaktgenboren [23] and Naaktgenboren et al. [24] investigated the interaction of vortex rings with thin porous media composed of wire mesh screens of constant wire diameter but variable porosity (ϕ). Note that ϕ is defined as the ratio of the open area to the total area of the planar surface. The interactions resulted in different dynamics as a function of vortex strength and screen porosity. When the screen porosity was high (ϕ = 0.79), meaning a greater open area, a downstream vortex formed, and convected on a similar trajectory as the impinging vortex but with a lower convective speed and more diffuse vortex core. The degree of expansion of the upstream vortex ring for these cases was a function of ϕ. Secondary vortex rings were formed on the upstream surface of the screen, similar to those observed for solid wall interactions. Stronger vortex rings were less affected by the mesh surfaces showing that vortex properties also affected interaction dynamics. In all cases, the transmitted vortex rings were found to either be laminar or to relaminarize downstream of the screens.

Adhikari and Lim [22] also investigated the interaction of vortex rings with variable vortex strength on mesh surfaces of constant wire diameter and different porosity (ϕ = 0.62, 0.81). They observed that three flow regimes existed as a function of the Reynolds number based on circulation, Re = Γ/ν. At low Reynolds numbers, i.e., a weaker vortex, the vortex ring approached the surface and radially expanded but did not pass through. As the Reynolds number was increased the vortex ring interacted with the surface, forming secondary structures upstream and a TV downstream of the screen. In the third regime, when the Reynolds number was high enough, a TV was formed but no upstream structures were observed. They concluded that the Reynolds number of the vortex ring and the porosity determine the boundaries between these regimes.

In Ref. [25], the effects of the scale of the porous boundary were investigated by holding porosity constant while varying the filament (mesh wire) diameter of the surface. This study used fluorescence flow visualization to observe the interaction. A set of screens with a nominally constant porosity (ϕ ≈ 0.65) were used with vortex rings of varied initial circulation. A wide range of commercially available wire diameters were investigated (0.0178–0.267 cm), and results showed that the wire diameter had a large effect on the formation behavior of secondary and downstream structures. Evidence of vortex shedding from the individual wires of the porous boundary showed three different flow regimes for the downstream vortex: Vortex transmission without vortex shedding from the wires, vortex transmission with shedding, and breakup of the vortex ring and transition to turbulent flow. The regimes were separated by defining an interaction Reynolds number based on both vortex and screen properties defined as
$Rei=(UcDwire)/ϕν$
(1)
which uses the vortex ring convection speed (Uc), fluid (ν) and screen properties (Dwire, ϕ).

More recently, Lim and Adhikari [27] review many of the studies previously discussed and include a review of similar fundamental vortex ring problems. While not addressed by Lim and Adhikari [27], the study by Cheng et al. [26] used lattice Boltzmann method (LBM) to perform a numerical study evaluating the results of Refs. [22] and [25]. Their study focused on screen porosity (ϕ), thickness (H), and a structural dimension (A) which corresponds to wire diameter although their wire filaments were rectangular in cross-sectional shape. Numerical results in Ref. [26] showed the presence of shed vorticity from individual wires, providing some confirmation of the hypothesis of Ref. [25]. Cheng et al. [26] also showed that screen thickness and porosity have similar effects on vortex transmission, where if ϕ is lowered or H increased then vortex transmission is inhibited. Higher ϕ (more open area) and vortex Reynolds number increased transmission of vorticity downstream which aided in the formation of a transmitted vortex. They also showed that wire diameter directly affected the stability of vortex rings and that the shed vorticity impacted the transmitted vortex behavior. However, they noted that at large wire diameter vortex impingement location relative to individual wires plays a large role on vortex transmission.

This study expands on the prior work by investigating the interaction using molecular tagging velocimetry (MTV), a molecular counterpart to particle image velocity (PIV). This method allowed for the velocity and vorticity fields near the screen surfaces to be quantified. In MTV, the laser pulse is not present when the phosphorescent molecules are imaged. As a result, laser reflection issues near surfaces, associated with PIV, are not present and near surface velocities can be measured. Near screen data were used for the observation of vortex shedding proposed in Ref. [25] and shown numerically by Cheng et al. [26]. Additionally, a wider range of screen porosities were investigated to determine the validity of the interaction Reynolds number and compare to behaviors in Ref. [26].

### Experimental Methods.

The experimental apparatus used in this work was the same system described in Ref. [25]. The facility was a 60 × 60 × 60 cm3 acrylic tank which was open to the atmosphere, Fig. 1(a). A fluid column provided the driving force and source for the fluid slug ejected to form the vortex ring. A high speed solenoid valve controlled the duration of the slug ejection (Δt). The feed column head height (Z) and solenoid open time were used in combination to vary the vortex properties. The fluid column drop during the solenoid open time was taken to be the stroke length, Ls, for an equivalent piston-driven vortex ring generator. The exit of the vortex ring generator had an inner diameter of Dgen = 2.54 cm and a sharp edge. The time history of the ejection velocity, Uj, and fluid column height, Z, are shown in Fig. 1(b) for head height z = 70 cm for the solenoid open time. The equivalent stroke to diameter ratio, an important factor in the formation properties of vortex rings, was defined as Ls/Dgen for this geometry. The stroke to diameter ratio in this work ranged between 1.4 and 1.7 depending on head height, which falls between the work of Adhikari and Lim [22] (Ls/Dgen = 1.0) and Koochesfahani and coworkers [20,21] (Ls/Dgen = 1.0, 3.0). Formation Reynolds number was defined as Ref = Uj,maxDgen/ν, where Uj,max was the maximum ejection velocity. The formation Reynolds numbers investigated in this work, and in Ref. [25], were Ref = 2300–4200, which falls in the range investigated in many prior works (e.g., see Ref. [27]).

Laser-induced fluorescence (LIF) was used for flow visualization. The feed column of the vortex generator was filled with a mixture of water and fluorescein dye (1.6 × 10−4 molar). A 100 mW solid-state CNILaser laser (532 nm) was used to illuminate the fluorescein dye on the center-plane of the vortex ring. Images for flow visualization were captured using a Pixelink PL-B776 U color camera recording at 20 Hz, which was observed to sufficiently capture the time scales of the problem. The data recording system was synchronized using a BNC 555 delay generator, which controlled the laser, camera, and solenoid timing.

The location of the vortex ring for the LIF experiments was taken to be the center of the rolled up dye and was manually located using image processing software (imagej) as it traveled through the fluid. The accuracy in the location of the vortex ring center was estimated to be ±5 pixels (or nominally ±0.03 cm). The uncertainty was estimated by closely examining LIF images near the supposed vortex center and determining visually how distinct the center of the dye pattern was. They enabled the estimation of the region in space where the vortex center was located and was taken to conservatively be a 5 pixel radius. Convection speeds, Uc, were determined locally by differentiation of a local linear fit of ±10 location data points around the time of interest. This reduced the error in the estimate of Uc due to uncertainty in the location data at the expense of rounding peaks in the velocity record. This was the same technique as was used in Ref. [25].

Molecular tagging velocimetry was used to quantify the velocity and vorticity fields for selected cases. MTV is an optical flow measurement technique that utilizes a phosphorescent chemical tracer dissolved in the fluid to measure displacements [28,29]. In this work, the chemical tracer was composed of a three chemical combination: 1.0 × 10-4 M g1β-cyclodextrin, 0.05 M cyclohexanol, and a saturated solution of 1-bromonathphalene, uniformly mixed in both the main tank and feed column. The tracer was excited into a phosphorescent state using the fourth harmonic line (266 nm) on a Continuum Powerlite Precision II Nd:YAG pulsed laser (5 Hz). A BNC 555 delay generator was used to coordinate timing of the experimental components. Multiple experimental runs were taken to increase the spatial and temporal resolution of the experiments in the following way: A series of five repeated trials were recorded, after which the solenoid opening time was delayed by 0.025 s with respect to the camera and laser signals. This was repeated until the increase in time realigned with the 5 Hz laser firing rate again, increasing the effective data recording rate to 20 Hz. The fluid inside the tank was allowed to settle for approximately 5 min between trials. Images of the flow were recorded using a PCO Dicam Pro charge-coupled device camera (1280 × 1024 pixel resolution).

While PIV relies on particles distributed through the flow, MTV uses a molecularly mixed chemical tracer that is “tagged” in a grid-intersection pattern. In this work, the tagging pattern was created using a grid of intersecting laser lines (Fig. 2). Two images of the tagged pattern, with a known time delay, were captured after the tracer was excited by the laser pulse. The displacement of each intersection was measured using a direct correlation method described by Gendrich and Koochesfahani [30]. Only a small subset of the total flow area was excited with laser grids at one time; therefore, a larger flow field was built by combining several different fields of view. MTV data collected were not defined on a regularly spaced grid, so they were remapped onto a regularly spaced grid (0.05 cm × 0.05 cm) using the methods described in Ref. [31]. Vorticity was then calculated using a second-order finite difference method on the regularly spaced data. The instantaneous error level in the MTV measurements was 0.1 pixel (95% confidence level). Given the magnification of the experiment (171 pixel/cm) and the delay time between images (1.2 ms) the resulting error level in the velocity measurements was 0.044 cm/s, or about 0.3% of the vortex formation velocity Uj. The error level in the vorticity measurements was estimated using the analysis described in Ref. [29] to be 1.18 1/s.

Because this work is an extension of Ref. [25], the focus of the MTV results were on the z = 70 cm (Ref = 4200) and z = 50 (Ref = 3800) cases. As in Ref. [25], screens were mounted on stainless steel frames located 3Dgen downstream of the vortex generator to allow the vortices to fully form before interacting with the screens. MTV measurements were taken on screens selected based on the interaction Reynolds number (Rei, Eq. (1)) defined by Hrynuk et al. [25]. The Reynolds numbers selected were: a low interaction Reynolds number (Rei = 24), which flow visualization showed no indication of vortex shedding, the highest interaction Reynolds number for which a coherent TV formed downstream (Rei = 143), and a high Reynolds number case (Rei = 373) which showed no reformation. All three screens had a nominally constant porosity of ϕ = 65%. The corresponding wire diameters for the screens were Dwire = 0.0178, 0.104, and 0.267 cm. The screens investigated with MTV are shown in Fig. 3. These screens were similar in design to all the screens tested in the study.

In addition to the MTV experiments, an expanded range of screen porosity and wire diameters were tested using LIF to expand and validate the interaction Reynolds number developed in Ref. [25]. The wire diameters of the screens tested ranged from 0.009 cm to 0.267 cm, while porosity ranged from ϕ = 35% to ϕ = 82%. In total, nine different wire diameters and seven different porosities were tested. Interaction Reynolds numbers for the cases tested ranged from Rei = 12, which should fall in a no-shedding region, to Rei = 373, which should exhibit highly turbulent behavior downstream.

## Results

### Free Vortex.

A sample case of the freely traveling vortex ring, without a screen in place, is shown in Fig. 4, where multiple time steps throughout the convection of the vortex are overlaid on one image. After forming, the vortex ring did not vary in shape or size. Tracking results for the free vortex ring are shown in Fig. 5(a) for a head height of z = 70 cm for both the LIF and MTV tracking method. These results were the baseline for comparison with other studies and the screen interaction cases. As the vortex ring formed, it expanded near the vortex generator before convecting downstream at a near constant radius. The images recorded, Fig. 4, showed that the vortices were symmetric and travelled straight downstream from the generator.

Convective velocity calculations done on the LIF tracking showed an initial acceleration phase from the generator up to a near constant velocity. The slight decrease in velocity during the acceleration of the vortex rings, near x/Dgen ≈ 1, corresponded to the closing of the solenoid and pinch off of feeding fluid. This result was expected and occurred far from the point at which the screens would be placed, which is labeled in Fig. 5 with a dashed line. Convective velocity of the vortex rings was a function of the head height (Fig. 5), with average post acceleration convective velocities of Uc = 8.56 cm/s, 6.23 cm/s, and 4.47 cm/s for head heights z = 70 cm, 50 cm, and 20 cm, respectively.

### Screen Interaction.

The three general interaction behaviors, described in Ref. [25], are shown for z = 70 in Fig. 6. This section focuses on the screens shown in Fig. 3, which were the ones investigated using both LIF and MTV. A TV was observed for some interaction Reynolds numbers and porosities while highly disturbed flow downstream was observed for other cases. When the vortex ring interacted with the screen at a low interaction Reynolds number (Rei = 24, Dwire = 0.0178 cm), secondary vortices similar to those in a vortex ring/solid wall interaction, formed on the upstream side of the screen and a laminar TV formed downstream of the screen. At larger wire diameter (Dwire = 0.104 cm), Rei = 143, the upstream secondary vortices weakened, and the TV was less uniform in appearance but still formed downstream of screen. At this Reynolds number, the TV also formed significantly further downstream than the lowest Reynolds numbers. At high Rei, the large wire screen (Dwire = 0.267 cm, Rei = 373) vortex interaction resulted in a nonuniform pattern downstream of the screen, and no TV was formed. Small rotational structures were observed downstream of the screen in the LIF images as the vortex ring passed through. This suggested that vortex shedding was occurring and was a factor in the formation of a TV. The medium wire screen, Fig. 3, was the highest Reynolds number (Rei = 143) for which a TV consistently formed.

While vortex shedding from the individual wires of the screens was the suggested factor controlling the formation of a TV during the interaction process, the existence of vortex shedding has previously only been observed using flow visualization techniques and numerical studies. The use of MTV allowed for velocity measurements close to the screen surfaces and was used to search for evidence of vortex shedding.

Figure 7 shows the MTV results for the same cases as Fig. 6, where three interaction steps were overlaid onto one image. At low Rei, Fig. 7(a), the vortex interacted with the screen formed a SV and a TV. Vorticity downstream of the screen, which eventually rolled up into the TV, appeared first as a boundary layer near the screen due to the induced flow of the impinging primary vortex (PV). For the high interaction Reynolds numbers in Fig. 7(c) (Rei = 373), the vortex shedding suggested by Hrynuk et al. [25] and Cheng et al. [26] was observed in the measured velocity and vorticity fields. Two regions of opposite sign vorticity formed downstream of each wire and convected downstream. This vortex shedding behavior was observed, to a lesser extent, at Reynolds numbers near the transition between TV formation and no TV formation, Fig. 7(b) (Rei = 143). Vorticity shed from the wires in this Reynolds number range did not initially form distinct vortices, but instead shed in what appeared to be alternating sign shear layers. There was evidence that the shear layers formed into vortices downstream of the wires, but rapidly dissipated. The lack of clear, paired shed vortices was likely a function of the time dependency of the flow near the screen, in that the primary vortex only generated the flow conditions necessary for vortex shedding for a short period of time. These results compare well with the vorticity results presented by Cheng et al. [26] for similar wire diameters.

Figure 8 shows a comparison during the interaction of both the LIF and MTV results for a series of Reynolds numbers. It should be noted that the LIF and MTV results are not shown at exactly the same scale, and Fig. 8 is shown for the purpose of comparison. At low interaction Reynolds numbers (Rei = 17, 24; Figs. 8(a) and 8(b), respectively), a strong SV with sign opposite of the associated vortex ring leg formed upstream of the screen. The peak vorticity level of the SV was on the same order as the primary vortex ring though the size of this vortex was smaller. At higher interaction Reynolds number, the interaction transitions into the paired shed vorticity, Figs. 8(c) and 8(d) (Rei = 102, 143). Small rotational regions in the fluid dye observed in the LIF results were observed to be shed vorticity in the MTV results. Similarly, larger rotations seen in LIF data were determined be discrete, repeatable vorticies, Figs. 8(e) and 8(f) (Rei = 266, 373). These results showed that the rotational regions observed in the LIF flow visualization results here and in Ref. [25] were evidence of vortex shedding occurring during the interaction. This result allowed for the use of easier flow visualization experiments to identify vortex shedding in a wider range of screens.

### Vortex Tracking and Circulation.

Flow field MTV results were used to track the vortices and to calculate the strength of the vortices as they interacted with the screen and convected downstream. An earlier example of this tracking for the free vortex was shown in Fig. 5. Circulation was calculated as the integral of vorticity within a fixed radius around the peak vorticity of each vortex structure. The integration radius was selected based on the sizes of individual structures, which varied, to fully capture the vorticity of those structures while rejecting structures or noise far from the vortex center. An integration radius of 0.2 Dgen was used for the PV and TV, while 0.04 Dgen was used for the SV, because it was more compact. Figure 9 shows the vortex tracking results along with the circulation results for three regimes: no shedding (Rei = 24), shedding with reformation (Rei = 143), and no reformation downstream flow (Rei = 373). At low Reynolds number, the PV impacted the screen and expanded radially before dissipating near the screen. The TV initially formed with a larger radius than the PV and contracted as it convected downstream. The SV orbited the PV before convecting back upstream toward the vortex generator. The SV consistently orbited the PV for all screens tested, despite weakening at higher interaction Reynolds number, Fig. 9. SV formation was observed for the interaction of a vortex rings with solid boundaries and was likely not dependent on Reynolds number except for the SV strength.

At midlevel Reynolds number (Rei = 143), the vortex structures became more difficult to track because the peak vorticity of the TV was more variable in the vorticity forming the TV. Tracking data showed that the PV at this Reynolds number expanded radially as it interacted with the screen, similar to the low Reynolds number case. This trend was also observed for the high Reynolds number case in all LIF flow visualization, so it was considered to be independent of the interaction Reynolds number. Downstream, the TV formed with a large radius before contracting and convecting downstream, although tracking became difficult due to the lack of a single well defined peak in the vorticity field associated with the TV. At high Reynolds number, Rei = 373, the shed vorticity was tracked as there was no TV in this case. The behavior upstream of the screen was similar to both lower Reynolds numbers studied. The tracked vortices traveled as a pair for a short distance but drifted apart as the overlying rotational flow from which they were formed convected them radially outward. Note that the data in Fig. 9 shows the average flow field of five repeated trials for each instance in time. The MTV data shown in Figs. 7 and 8 show an instant in time with the five repeated data sets averaged together. This suggested that shedding behavior and track of the vortices was highly repeatable.

Circulation results, Fig. 9, showed that the PV decreased in strength as it interacted with the screen at all Reynolds numbers. Similarly, the SV circulation was similar across all Reynolds numbers tested and maintained a near constant circulation throughout the interaction. For the low Reynolds number, Fig. 9(a), the TV had an initially high circulation that decreased to a near constant level (40% of the pre-interaction PV). The midlevel Reynolds number results showed an increase in circulation of the TV compared to lower the Reynolds number as it convected downstream. Circulation for this TV was approximately 65% of the PV before it impacted the screen. This increased downstream circulation was likely caused by the addition of vorticity from the shedding that was incorporated into the TV as it formed.

Tracking circulation in the shed vortices of the high Reynolds number interaction suggests that vortex shedding may have been the source of the increased circulation in the midlevel Reynolds number TV. Circulation in the positive shed vorticity exceeded 75% of the circulation of the PV, while an additional circulation generated by a negative vortex also added to the total circulation downstream. These strong vortex structures were a potentially disrupting factor that could have inhibited the formation of a TV at higher interaction Reynolds numbers. Although Refs. [23] and [24] showed that impulse and total energy decrease during the interaction, the resulting high circulation of the shed vorticity at high Rei may have an impact on the turbulence intensity of flows far downstream of the screen. In this case, more diffuse vortices like the PV have potential for their vorticity to be amplified as they pass through the screen.

### Expanded Porosity Experiments.

This study has so far expanded on the work by Hrynuk et al. [25] and Cheng et al. [26] by experimentally showing the existence of vortex shedding on the individual wires and analyzing the track and circulation of those vortices. However, the MTV results focused on only one porosity (ϕ ≈ 65%), which was used in the development of the interaction Reynolds number (Rei). Additional flow visualization data were taken after the vortex shedding behavior was observed using MTV to expand these results to a wider range of screen porosity (ϕ = 35–82%).

The distinct flow regimes discussed in Ref. [25] were developed by sorting the Reynolds number (Rei) of a series of screen-vortex interactions to determine any delineating points for vortex shedding and TV formation. It is noted that the use of the porosity in the definition of Rei developed in Ref. [25] was to account for the acceleration of the fluid through the decreased area of the screens, which was the same for all cases in that study. Evidence of vortex shedding and TV formation was somewhat subjective as the data were from flow visualization, although the three regions defined were shown in the MTV results. The observation of vortex shedding was defined as when the authors could identify coherent rotating regions in the fluid dye downstream of the screen. A cutting or “fingering” effect was not assumed to be evidence of vortex shedding. While a first assumption would suggest that the flow fields induced on the wires should produce vortex shedding for all but the lowest Reynolds numbers, MTV results showed that for lower Reynolds numbers a boundary layer formed and rolled up into the TV instead of shed vorticity. Formation of a TV is similarly qualitative, but defined by the existence of two large scale (i.e., similar in size to the initial vortex ring) counter-rotating regions of fluid dye formed within 4Dgen downstream.

The additional cases with varying porosity showed that the interaction Reynolds number no longer clearly delineated the regions of vortex shedding and TV formation. Sorting the interaction behavior by this Reynolds number definition resulted in high Rei interactions with vortex reformation and also blurred the delineation of the first appearance of vortex shedding. The results were, therefore, also analyzed based on the screen wire Reynolds number and the convection speed as Red = Uc Dwire/ν eliminating the effect of porosity from within the Reynolds number.

The results of these experiments can be sorted into four categories: No vortex pass-through, No evidence of vortex shedding with a TV forming downstream, Evidence of vortex shedding with a TV, and No TV formation. At both high and low Reynolds number, Table 1, no vortex was transmitted downstream of the screen after the interaction, though the dynamics were different. For extremely low Reynolds number (Red = 4) the vortex did not fully penetrate the screen, and thus, no TV was formed similar to previous findings [2124], while at extremely high Reynolds numbers (Red > 100) the flow downstream of the screens was highly unsteady and the TV did not form. It was interesting to note that at very low Reynolds numbers (Red < 10) the TV formed but remained very close to the screen as the convective speed was very slow. Vortex shedding was not observed at the low end of the Reynolds numbers tested (Red < 28), and highly laminar TVs were formed downstream of the screens in this range.

The range between Red = 28 and Red = 90 showed TVs form downstream of the screen, but with vortex shedding observed during the interaction. Note that Red = 90 (Rei = 143) was one of the cases tested with MTV that showed vortex shedding and reformation (Fig. 7). Above this critical Reynolds number, the TV formation behavior entered a transitional region where the TV sometimes formed and other times did not on a run-by-run basis. This transitional range was relatively compact (90 < Red < 109), but the image sequences suggested that the TV in this Reynolds range may have potentially formed far downstream outside the fields of view of data recorded. Above Red = 113, the TV consistently did not form and showed no signs of reforming at any distance downstream of the screens.

The well delineated regions shown in Table 1 suggest that the Reynolds number that characterizes the vortex transmission behavior may be the wire Reynolds number and not the interaction Reynolds number, as previously believed. Under this categorization, similar Reynolds number exhibited the same behavior regardless of screen porosity, thus the TV formation was not controlled by porosity. This is significant as the porosity, for a constant wire diameter, is a measure of the distance between the wires. The results suggest that shedding and reformation of a TV were more dependent on the wire diameter than on the wire spacing. A few selected vortex interactions are shown in Fig. 10, which shows the vortex interaction at the screen. Note that Fig. 9 shows some cases not listed in Table 1, because Table 1 shows a subset of the full data taken, which was done for ease of viewing. In particular, three porosities at Red = 55 are shown where all three exhibited vortex shedding and TV formation, but were strikingly different visually.

While porosity had little effect on the formation of a TV, it did have a notable effect on the TV behavior downstream of the screen. Cheng et al. [26] showed that low porosity suppressed the formation of a TV. However, the current set of experiments showed a TV was inhibited only for the lowest Reynolds number and porosity. The general behavior of TV suppression observed in Ref. [26] was confirmed experimentally with these results. Additionally, Naaktgenboren et al. [23,24] also showed a reduction in energy and impulse in the TV. Figure 11 shows the TV at a set location far downstream from the screen with the associated porosity and time at which the TV reached this downstream distance. The free vortex reached this downstream location the fastest, while the lowest porosity (or highest solidity) screen TV took the longest to reach this downstream point. Note that the incoming vortex properties and the Reynolds number (excluding the free vortex) were held constant in the figure. This behavior was consistent for all the cases where a similar Reynolds number could be compared at different porosities. As a result of this, the porosity was determined to most affect the convective velocity of the TV and not the formation behaviors during the interaction.

## Conclusion

The interaction of a vortex ring and thin screens of varying porosity and wire diameters was studied and characterized to determine interaction behaviors. Velocity and vorticity fields, measurements using MTV, showed the vorticity field immediately downstream of the screen transitioned from distinct shear layers, caused by the presence of the wires, to vortex shedding from the wires as the Reynolds number increased. These experimental results supported conclusions made in Refs. [25] and [26], which both showed evidence of vortex shedding. Current experimental results also showed that the transition was governed by a Reynolds number defined by the wire diameter and the pre-interaction convection speed. The data also showed that the TV was disrupted and eventually inhibited based on the same Reynolds number definition.

Expanded LIF measurements for screens of varying porosities confirmed that formation of a TV was a function of vortex shedding behavior and not of the screen porosity. The wire Reynolds number proved to be more predictive of the flow as it correctly delineated the three major regimes observed: no shedding with TV formation (Red < 28), shedding with TV formation (28 < Red < 90), and suppression of the TV and formation of turbulence (Red >113). A transitional region was also observed between Red = 90 and Red = 113 which needs further investigation as the TV formed intermittently within the measurement domain. While porosity was no longer factored into the formation behaviors of the TV, it was shown to have a direct effect on the convective speed of the TV downstream of the screen.

## Funding Data

• The National Science Foundation (NSF) (Award No. 8045882).

• The Clarkson University Honors Program.

## Nomenclature

• A =

screen filament dimension (non-circular cross section)

•
• Dgen =

vortex generator diameter

•
• Dwire =

screen wire diameter

•
• H =

screen thickness

•
• Ls =

vortex formation stroke length

•
• Red =

wire Reynolds number

•
• Ref =

formation Reynolds number

•
• Rei =

interaction Reynolds number

•
• Uc =

vortex convective velocity

•
• Uj =

vortex formation jet velocity

•
• Z =

fluid column height

•
• Γ =

circulation

•
• ν =

kinematic viscosity

•
• ϕ =

screen porosity

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