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Journal of Visualization

, Volume 21, Issue 4, pp 533–542 | Cite as

Flow visualization of the non-parallel jet-vortex interaction

  • Samantha Houser
  • Ikechukwu Okafor
  • Vrishank Raghav
  • Ajit Yoganathan
Regular Paper
  • 141 Downloads

Abstract

The jet–vortex interaction is observed in settings ranging from aeronautics to physiology. In aeronautics, it presents as a parallel interaction of the jet exhaust and aircraft wing-tip vortex, and in the diseased state of the heart called aortic regurgitation, the interaction between blood flows is characterized by a non-parallel interaction. While there is substantial research into the mechanisms of the parallel interaction, there is comparatively limited scientific material focused on the non-parallel interaction. The objective of this study was to characterize three distinct orientations (30°, 60° and 90°) of the non-parallel jet–vortex interaction in a simplified flow loop. The ratio of the jet Reynolds number to the vortex ring Reynolds number was used to define four levels of jet strength. Flow visualization and particle image velocimetry were used to qualitatively and quantitatively describe how the flow structures interacted, and the energy dissipation rate of each condition was calculated. It was determined that as the relative jet strength increases, the vortex ring dissipates more rapidly and the energy dissipation rate increases. This information provides a basis for the understanding of a vortex ring’s interaction with an impinging jet. When the angle between the jet and vortex ring flows is perpendicular, the energy dissipation rate decreased from 6.1 W at the highest jet strength to 0.3 W at the lowest jet strength, while at an angle of 30° the energy dissipation rate decreased from 51.8 to 10.3 W. This finding contradicts the expected result, which potentiates further studies of various non-parallel arrangements.

Graphical Abstract

Keywords

Non-parallel Vortex Jet Interaction Visualization 

1 Introduction

The interaction between a vortex ring and a jet under a variety of circumstances has been studied, most commonly as a parallel interaction. The interaction between the wing-tip vortex and the exhaust jet of an aircraft is a parallel jet–vortex phenomenon that has been studied experimentally (Ferreira Gago et al. 2002; Wang and M. Q. Zaman 2002; Margaris et al. 2008) and numerically (Ilea and Hoffmann 2011; Depommier et al. 2011). Vortices are formed off the wing tips due to the pressure difference on either side of the wing, which can cause drag and potentially dangerous turbulence in the wake of the aircraft. In an attempt to minimize this turbulence, manipulation of the jet engine location and angle is a reasonable solution; however, simplified experiments must be conducted beforehand to create a basic understanding of this interaction, as noted by Wang and M. Q. Zaman (2002). Margaris et al. (2008) accomplished this by studying the interaction of a single trailing vortex with a coaxial cold jet, and the following parameters were considered: ratio of jet to vortex strength, jet to vortex distance, jet inclination angle and Reynolds number. It was determined that an increased amount of jet turbulence is entrained into the vortex as the ratio of jet to vortex strength decreased and jet to vortex distance decreased, and that these effects were delayed when the jet was angled away from the wing tip (Margaris et al. 2008).

Unlike the parallel jet–vortex interaction, the non-parallel interaction between a vortex and a jet is a topic that requires further investigation. In this case, simplified studies do not exist, which prevents more in-depth investigations into phenomena that are characterized by this interaction. A prime example of this can be observed in human physiology, in a diseased cardiac state known as aortic regurgitation. Aortic regurgitation is defined as a backflow of blood through the aortic valve into the left ventricle during diastole, or passive filling, and this backflow is characterized by a steady jet (Hamirani et al. 2012). The vortex that this jet interacts with is formed from the passive flow of blood through the mitral valve into the left ventricle during diastole. Increased left ventricular volume and hypertrophy (i.e. ventricular disease) can develop over time, and this worsens as the strength of regurgitation increases (Bekeredjian and Grayburn 2005). The extent of this interaction is also potentially affected by various aorto-mitral configurations, or angles between the regurgitant jet and the vortex (Goetz et al. 2005). Although there is substantial clinical understanding of this disease, it is also important to study the fluid mechanical properties of this type of interaction.

A comprehensive study of multiple jet–vortex orifice angles would provide a basis for any future investigations into specific non-parallel jet–vortex phenomena, including the example of aortic regurgitation. Hence, the objective of this study was to characterize the non-parallel interaction between a steady jet and a vortex. We hypothesize that increased jet strength and increased interaction angle would result in increased vortical destruction and increased energy dissipation.

2 Materials and methods

2.1 Experimental setup

The jets and vortices studied herein were established within a closed flow loop (Fig. 1). The loop consisted of a semi-infinite chamber where the jet and vortex ring interacted. The diameter of the orifice of the jet and the vortex ring flows were 4 and 25.4 mm, respectively. The L/D ratio, or ratio of the length of fluid ejected to the diameter, was 3.0. This is also referred to as the formation number, as proposed by Gharib et al. (1998). Reynolds number, shown in Eq. 1, was utilized to determine the flow conditions in this study,
$$Re = \frac{\rho u L}{\mu }$$
(1)
where Re is the Reynolds number, ρ is the density of the working fluid, u is the velocity, L is the pipe diameter and μ is the dynamic viscosity of the working fluid. The vortex ring entrance length was calculated using Eq. 2. Although it is more commonly used for steady flow situations, the use of this equation was justified based on the work of He and Ku (1994). Equation 2 was defined as follows:
$$\frac{{l_{\text{e}} }}{L} = 4.4Re^{{\left( {\frac{1}{6}} \right)}}$$
(2)
where Re is the Reynolds number, L is the diameter and le is the entrance length. le was found to be 470 mm. The entrance length ensured the formation of fully developed flow before ejection.
Fig. 1

Experimental setup of jet–vortex interaction flow loop

A programmable pulsatile pump (ViVitro SuperPump) allowed for controlled, isolated vortex rings to be ejected into the chamber, as shown in Fig. 2. The flow profile for vortex ring ejection is shown in Fig. 3. A steady pump (Dayton Compact Submersible Pump) provided the constant jet flow. Two passive mechanical valves were utilized to ensure unidirectional flow. Two flow probes provided real-time flow information. The jet flow was monitored by a probe (Transonic Systems Inc., ME 10 PXN) with inner diameter of 9.5 mm, and resolution of ± 1 mL/min at 10 Hz. A larger probe (Transonic Systems Inc., ME 25 PXN), with an inner diameter of 25.4 mm and a resolution of ± 10 mL/min at 10 Hz, was used for the vortex ring flow. All acquired data was read into a custom LabVIEW System Design Software, which was also used as the master controller of the experimental system.
Fig. 2

The pulsatile pump position over time, interval of data collection shown in red, pause interval shown in blue. Time points A, B, and C (occurring at 3.3, 3.5, and 3.7 s, respectively) represent the time points of data displayed later in this work

Fig. 3

Vortex flow rate over time

To cover a range of non-parallel angles of interaction between the jet and vortex, angles (ϴ) 90°, 60°, and 30° were studied (Fig. 4). The distance from the ejection orifice required for complete vortex ring formation was determined according to Gharib et al. (1998), and the jet orifice was placed the same distance radially. The region of interest was digitally calibrated by taking an image of a 6 × 6 mm checker-patterned sheet in the mid-plane of the vortex ring axis, which provided calibrated measurements that could be applied to all flow visualization data.
Fig. 4

Area of interest, with three angles (ϴ) between jet and vortex ring centerlines. Star represents the distance for optimal vortex ring formation

2.2 Flow conditions

Reynolds number was used to describe the strengths of the two flows studied in this work, which allowed for a comparison of the inertial forces of the jet to those of the vortex. The vortex ring Reynolds number was held constant for all trials with a Reynolds number of 4200, while the Reynolds number of the jet was varied. Reynolds numbers were computed as shown:
$$Re_{J} = \frac{{u_{J} L_{J} }}{{v_{J} }}$$
(3)
$$\text{Re}_{V} = \frac{{u_{V} L_{V} }}{{v_{V} }} = \frac{\varGamma }{{v_{V} }}$$
(4)
where \(Re_{J}\) is the jet Reynolds number, \(Re_{V}\) is the vortex ring Reynolds number, u is velocity, L is diameter of the pipe, Г is circulation, and v is kinematic viscosity of the working fluid. The derivation of the vortex ring Reynolds number based on circulation was used from Glezer (1988). J and V subscripts denote jet and vortex, respectively.
A dimensionless variable representing the strength of the jet relative to the strength of the vortex, α, was computed using the following equation:
$$\alpha = \frac{{Re_{J} }}{{Re_{V} }}$$
(5)
where α is the ratio of the jet Reynolds number to the vortex ring Reynolds number, or relative jet strength. Four levels of relative jet strength were studied (Table 1). To focus on the interaction between a single vortex ring and a jet, an ideal vortex ring was created that was laminar and had minimal trailing vortices, with a formation number of 3.0. An in-depth explanation of the differences between various vortex rings and their corresponding formation numbers can be found in Gharib et al. (1998), while Glezer (1988) discusses the differences between laminar and turbulent vortex rings. Using the process outlined in Gharib et al. (1998), this resulted in a vortex ring Reynolds number of 4200. The relative jet strength ratios (α) studied included cases where the jet strength is less than, equal to, and greater than the vortex ring strength.
Table 1

Flow rates and reynolds numbers of jet and vortex ring for all trials

Jet flow rate (L/min)

Jet reynolds number

Time-average vortex ring flow Rate (L/min)

Vortex reynolds number

Relative jet strength (α)

0.36

~ 2100

4.43

~ 4200

0.5

0.72

~ 4200

4.43

~ 4200

1.0

0.90

~ 5200

4.43

~ 4200

1.25

1.08

~ 6300

4.43

~ 4200

1.50

2.3 Flow visualization

Color flow visualization provides valuable qualitative data because it allows fluid tracking over time and reveals the relative concentration of dye in a certain area due to color intensity. Water-based dyes (Bright Dyes®, Miamisburg, OH, 106053 FWT Red 50 Dye, 106002 Standard Blue Dye) were used to visualize the flows, and 3 mL of a 1% dye solution was injected into each flow. Jet fluid was colored red while vortex ring fluid was colored blue. A color high-speed camera (GoPro, Hero4, San Mateo, CA) was used to acquire the images at 240 fps. The wide-angle mode was disabled to prevent distortion of the images.

2.4 Particle image velocimetry

Digital particle image velocimetry (PIV) was used to capture the jet/vortex interaction within the semi-infinite medium. The fluid inside the flow loop was seeded with fluorescent particles (PMMA with RhB dye, 1–20 µm, Dantec Dynamics; Copenhagen, Denmark) which were illuminated using a laser sheet of 1 mm thickness generated from a Nd:YAG laser (New Wave laser, 532 nm, ESI Inc.; Portland, OR). The particles were imaged with a CCD camera (LaVision, Göttingen, Germany, Imager ProX, 1600 × 1200 pixels). A high-pass filter (cut-off wavelength of 580 nm) was used to minimize laser reflections, improving the signal-to-noise ratio. Data were acquired for 50 cycles of data at 10 time points, at approximately 10 Hz. The data were processed using DaVis 8.0 (LaVision). The two-dimensional measurements from PIV were used to visualize the changes in vorticity during interaction, as well as to calculate energy dissipation rate, or EDR (Eq. 6). These equations took place in Tecplot 360, and the area of EDR integration for each case is outlined in Fig. 5.
Fig. 5

Images of jet (various configurations) and vortex ring in the absence of the opposing flow. Dotted line represents area of interest for the calculation of EDR. Leading edge of vortex denoted by arrow

$${\text{EDR}} = \mu \overline{{\left[ {\left( {\frac{\partial u}{\partial x}} \right)^{2} + \left( {\frac{\partial v}{\partial y}} \right)^{2} + 0.5 \left( {\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}} \right)^{2} } \right]}}$$
(6)

3 Results and discussion

With PIV data, it is difficult to distinguish the origin of fluid after the interaction, or how quickly fluid dissipates from its origin flow structure into the ambient fluid. For this reason, colored dye flow visualization was used in conjunction with PIV data to provide a more full characterization of the interaction. Both flow visualization and PIV images were taken at the time points during the interval of data collection illustrated in Fig. 2. Figure 5 displays the jets and vortex ring without interaction. Representative flow visualization images are provided for the lowest and highest relative jet strengths in Figs. 6, 7. Electronic Supplemental Material 1 and 2 display footage of the interactions in Figs. 6, 7, respectively.
Fig. 6

Comparison of all three angles (ϴ) at the lowest jet strength (α = 0.50), time points A, B, and C

Fig. 7

Comparison of all three angles (ϴ) at the highest jet strength (α = 1.50), time points A, B, and C

3.1 Flow visualization

Linear, monotonic changes were observed across all relative jet strengths, therefore only the highest and lowest cases are described thereafter. It was apparent that at the lowest relative jet strength (α = 0.5) shown in Fig. 6, there was less vortical breakdown over time as the angle between the flows decreased (moving from columns 1 to 3). This occurred to a reduced extent at the highest relative jet strength (α = 1.5) shown in Fig. 7. As the angle decreased, the vortical structure was maintained and more fluid from the jet flow was entrained in the vortex ring. This was potentially due to the increasingly parallel flow directions that allowed the jet to better enter the vortex ring (at the gap between the rings and the centerline flow) instead of colliding perpendicularly with the rings. It can be noted that the blue dye color intensity within the vortex ring remained highest at the lowest relative jet strength case (Fig. 6), signifying that less of the vortex ring dissipated due to its interaction with the jet, while in the highest relative jet strength case (Fig. 7) the color intensity decreases more rapidly. An interesting observation is that, in the lowest relative jet strength case (Fig. 6) at angles 30° and 60° (columns 2 and 3), the jet trajectory seems to be pushed upward after initial interaction with the vortex ring. This is less apparent in the highest relative jet strength case (Fig. 7). For all cases, it is important to note that changes in the lower portion of the vortex ring could have been affected not only by the jet, but also by the bottom wall of the chamber.

Through comparison of the two relative jet strengths, it was apparent that as α increased, the structure of the vortex ring deteriorated more quickly after initial contact with the jet. This is most visible when the jet is angled 30° from the vortex ring (column 3); at the lowest relative jet strength (Fig. 6), there existed a relatively unaffected vortical structure at time point C, but for the highest relative jet strength (Fig. 7) the vortex ring was considerably dissipated. Therefore, it is apparent that with greater jet strength, the vortex ring dissipated more rapidly.

The electronic supplemental material provides more full visualization of the interactions studied. It was observed in Electronic Supplemental Material 1 (ESM1) that as the angle of interaction decreased less vortical breakdown occurred over time. The leading edge of the vortex ring, as described in Fig. 5, remains largely unperturbed with jet interaction in the 60° and 30° angles cases of ESM1. As the vortex ring moves through the chamber, no fluid crosses the plane created by the leading edge for these cases. However, in the 90° case, the leading edge was quickly penetrated by the jet flow, leading to rapid loss of vortex ring integrity. This trend in leading edge preservation was not observed in the highest jet flow rate case (ESM2). However, both ESM1 and ESM2 exhibit greater vorticity preservation with increased interaction angle. In ESM1, the entrainment of jet fluid into the vortex ring is apparent, most clearly in the 60° and 30° angles cases. When comparing ESM1 to ESM2, it is apparent that as the jet strength increases, the vortical structure dissipated more rapidly regardless of interaction angle. Another interesting observation that is exclusively explained by the electronic supplemental material is that there is some entrainment of surrounding fluid into the jet. The jet flow widens downstream, indicating that surrounding fluid is being pulled into the jet flow. This is more apparent in the highest jet flow rate case (ESM2).

3.2 Particle image velocimetry

To illustrate quantitative changes over time, vorticity color maps for the highest and lowest relative jet strengths were created from PIV data (Figs. 8, 9). As the angle between the flows decreased (moving from columns 1–3), it can be observed that more of the vortical structure is maintained after interaction with the jet, and that the vorticity within the vortex ring cores increase. When comparing the lowest (Fig. 8) and highest relative jet strengths (Fig. 9), it is apparent that less vorticity of the vortex ring was maintained after interaction as the strength of the jet increased. At 90° and 60° angles for the highest relative jet strength case, there is little to no trace of any vortical structure in time point C—drastically different from the structures seen in these angles for the lowest relative jet strength.
Fig. 8

Vorticity magnitude of all angles at the lowest jet strength (α = 0.5), time points A, B, and C

Fig. 9

Vorticity magnitude of all angles at the highest jet strength (α = 1.5), time points A, B, and C

Figure 10 displays the overall EDR of each α condition at all orifice angle conditions. These EDR values were obtained with a spatial–temporal integration, integrating over the specific area outlined in Fig. 5 and summing these values over all timepoints. It is apparent that as the strength of the jet increased, more energy loss occurred in the system over time. This is consistent with the qualitative flow visualization data as well as findings from other works (Stugaard et al. 2015; Okafor et al. 2017). Interestingly, however, the EDR differed greatly between orifice arrangements, but consistently across every jet strength. The 90° arrangement allowed for greatly lowered EDR than the 60° and 30° arrangements, while the 60° angle had a slightly greater EDR than the 30° angle in the higher three jet strength conditions. The drastic differences between the fully perpendicular orientation and the other orientations of jet to vortex ring flow imply that the angle has a large impact on the EDR of this interaction. This contradicts what was seen in the PIV visualizations, because the increased conservation of fluid within the vortex ring at smaller orifice angles would suggest a decreased EDR for these conditions. One potential explanation for this discrepancy is that the increased interaction time for the acute angles (30° and 60°) allowed for more energy dissipation in general. This is reflected in Fig. 10, since this represents a sum of the EDR for all timepoints. Nevertheless, further investigation of the differences in EDR among various non-parallel angles is necessary to fully understand this interaction and support this novel finding.
Fig. 10

Energy dissipation rate (W/m2) for all angles and jet strengths

4 Limitations

A few limitations to this study are to be mentioned. First, the inclusion of an impinging wall was not ideal for a fully simplified study of the interaction between a jet and a vortex ring; an infinite space could have provided more reliable data, especially when visualizing the lower vortex ring in the area of interest. It can be noted in the flow visualization data that much of the jet fluid remains near the bottom of the chamber and is not effectively removed from the area of interaction. This would be preventable in an infinite space set-up. However, the inclusion of a wall could prove useful when comparing this data to aortic regurgitation data, since the lateral wall of the left ventricle is located close to the location of interaction within the heart.

Second, the quality of flow visualization data was somewhat reduced due to the technique of addition of colored dye to the flows. In some cases, there was an insufficient mixing of the dye with the flow, resulting in a lack of uniformity of color through both the jet flow and each vortex. This could be amended by allowing a longer entrance length after dye injection, or through the use of pre-dyed fluid. The same amount of dye was injected for each trial, regardless of the jet flow rate. This resulted in a less intense color for the higher jet flow rates, creating the appearance of ambient fluid entrainment. Future studies using this flow visualization method would benefit from using pre-dyed fluid or making appropriate additions of dye volume for higher flow rates.

Third, the nature of a vortex ring is three-dimensional; therefore, the results of this two-dimensional study must be interpreted as only valid in the plane of study. While the EDR calculation was dependent on time, the values were smoothed across all time points, which could have detracted from the accuracy of the data. Future studies should explore beyond the limited range of Reynolds numbers studied in this work, to provide more breadth of data of this interaction.

5 Conclusion

By creating a simplified non-parallel arrangement of a jet and a vortex ring, it was possible to provide insight into the basic fluid mechanical properties of this interaction. Through analysis of flow visualization and PIV data, along with the calculated of an EDR, it was determined that relative jet strength is positively correlated with both vortical breakdown and energy dissipation. Additionally, a decreased angle of interaction between the jet and vortex ring greatly decreased structural breakdown of the vortex, and also led to entrainment of the jet fluid at low relative jet strengths. However, a fully perpendicular angle of interaction allowed for the least EDR among the angle conditions, which will require further investigation. In conclusion, not only is this information valuable within the fluid mechanics field, but it can also provide a stepping stone to a greater understanding of phenomena that include this interaction.

Supplementary material

12650_2018_478_MOESM1_ESM.mp4 (11.4 mb)
Supplementary material 1 (MP4 11682 kb) ESM_1: Comparison of all three angles (ϴ) at the lowest jet strength (α = 0.50)
12650_2018_478_MOESM2_ESM.mp4 (7.8 mb)
Supplementary material 2 (MP4 7957 kb) ESM_2: Comparison of all three angles (ϴ) at the highest jet strength (α = 1.50)

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Copyright information

© The Visualization Society of Japan 2018

Authors and Affiliations

  • Samantha Houser
    • 1
  • Ikechukwu Okafor
    • 2
    • 3
  • Vrishank Raghav
    • 1
    • 4
  • Ajit Yoganathan
    • 1
    • 2
  1. 1.Wallace H. Coulter Department of Biomedical EngineeringGeorgia Institute of Technology, Emory UniversityAtlantaUSA
  2. 2.School of Chemical and Biomolecular EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Biomedical Engineering Practice, ExponentPhiladelphiaUSA
  4. 4.Department of Aerospace EngineeringAuburn UniversityAuburnUSA

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