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Session: Novel experimental measurement methods IV
Session starts: Wednesday 05 November, 15:40
Presentation starts: 16:20
Room: Lecture room A

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Andrew Tanious (School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, AL10 9AB, UK)
Zhengzhong Sun (School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, AL10 9AB, UK)
Andreas Papoutsakis (School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, AL10 9AB, UK)
Hongwei Wu (School of Physics, Engineering and Computer Science, University of Hertfordshire, Hatfield, AL10 9AB, UK)

Abstract:
Abstract Vortex rings are fundamental structures in fluid dynamics with diverse applications in propulsion, flow control, and thermal management. In this study, gaseous vortex rings are generated in air using a novel speaker-cavity box generator, composed of a 250W speaker woofer mounted onto an acrylic box with a 40 mm diameter orifice and visualised through a dual-camera Z-type Schlieren Image Velocimetry (SIV) setup, enabling high-speed flow field capture without particle seeding. Experiments varied the diaphragm triggering frequency ranging from 1 Hz to 50 Hz, revealing that vortex ring translational velocity increases with frequency culminating in a 128% velocity gain at 50 Hz compared to 1 Hz. Optimisation of the inter-camera triggering delay of 25 μs was found to maximise measurement accuracy. Optical flow analysis of Schlieren images quantified both velocity and vorticity fields, confirming peak vorticity at the ring core, in agreement with theoretical predictions. This study demonstrates repeatable, air-based vortex ring generation and characterisation, offering potential applications such as cooling of electronic devices. Future work will optimise orifice diameter and extend SIV analysis into turbulent regimes. Introduction Vortex rings are a fundamental phenomenon in fluid dynamics, characterised by their toroidal structure and complex flow patterns. A vortex ring is formed when a fluid is impulsively forced through an outlet such as an orifice or a nozzle, creating a self-propagating ring of vorticity. Vortex rings have been extensively studied and utilised in various applications, including mixing stratified liquids [1], underwater propulsion [2], enhanced drug delivery [3], flow control [4], and heat transfer [5]. Several mechanisms have been developed to generate and analyse vortex rings which include solenoid valve devices [6], oscillating diaphragm actuators [7], and piston cylinder generators [8]. A defining characteristic of vortex rings is their translational velocity (U_tr), which is commonly analysed using their circulation, impulse, and kinetic energy. Krieg and Mohseni [9] developed an approach predicting U_tr within 4–5% error for stabilised rings, showing converging nozzles yield 30% higher U_tr than tube nozzles at identical piston velocities, valid post-pinch-off. Classical models (e.g., Fraenkel’s) align with experiments (<5% error) when disturbances are minimised, with core radii exceeding inviscid estimates by ~30% and stable diameters (82–91 mm) observed across Reynolds numbers (2270<〖Re〗_Γ< 6790). Universal velocity ratios (~0.93U for drag vortices) and factors like viscosity, nozzle geometry, and core dynamics reconcile discrepancies between inviscid theories and viscous-dominated regimes [10]. Another core characteristic is the ring’s vorticity distribution. Vorticity dynamics in vortex rings reveal critical insights into their formation and evolution. Ren et al. [11] identified two early-stage vortical structures: a laminar vortex ring encircled by a wrapping structure, which disintegrates into turbulent hairpin vortices [12]. Limbourg and Nedic [8] found orifice-generated rings exhibit lower formation numbers (L_O⁄D_o ≈2.0) versus nozzle-generated rings, with radial velocity amplifying vorticity to increase total circulation by 2.4 times. Universal parameters (α≈0.33,β≈1.8,γ≈1.9) and stepwise vorticity accumulation underscore distinct formation mechanisms, including earlier circulation saturation in orifice configurations due to enhanced vorticity dynamics. Visualisation of vortex ring flow fields relies on techniques like Particle Image Velocimetry (PIV), including 3D methods (Tomographic [13], Multiplane [14], Holographic PIV[15]) and 2D systems. Emerging Schlieren Image Velocimetry (SIV), tested by Ukai [16] using the Schlieren Motion Estimation (SME) method on turbulent heated air, proves effective without seeding particles, instead leveraging natural flow eddies as tracers [17]. Validated in jet plumes [18] and convective airflows [19], SIV has advantages over PIV by eliminating seeding and capturing velocity and temperature fields simultaneously, increasing its practicality in complex flow analyses. Current vortex ring research predominantly focuses on liquid mediums, mainly water, using piston-cylinder mechanisms [13], with limited exploration of air-based vortex rings for applications like electronics cooling. Additionally, studies on vortex ring repeatability and the use of SIV for flow analysis are scarce. Addressing these gaps, this study investigates gaseous vortex rings in air, generated via a novel speaker cavity box generation system to ensure repeatable characteristics. SIV is applied to analyse flow fields at varying diaphragm vibration frequencies, with results detailing translational velocity, velocity fields, and vorticity to advance understanding of air-based vortex dynamics. Experimental Setup In the current work, gaseous vortex rings were generated using a vortex ring generator comprising a 250W speaker woofer mounted onto a 200 mm × 200 mm × 50 mm acrylic cavity box with a wall thickness of 6 mm, with a 40 mm diameter orifice for vortex ejection. The speaker was driven by square waveform signals supplied by a function generator and then amplified using an acoustic amplifier, producing vortex rings at the signal’s rising edge. These emerged from the orifice on the side opposite the vibrating diaphragm as shown in Figure 1(a). Visualisation was achieved using a Z-type Schlieren setup, consisting of a 40W Luftvis LED light source, two identical 100 mm diameter parabolic mirrors, a razor blade knife-edge, and two Photron Mini UX-50 high-speed cameras. Cold compressed air was introduced via an air spray duster to create density gradients inside the rings due to the temperature variation, leveraging refractive index differences as per the Gladstone-Dale law [20]. To overcome high-speed camera resolution limits, a modified Schlieren system with a dual-camera configuration was implemented as depicted in Figure 1(b). A beam splitter directed light to two synchronised cameras, with adjustable inter-camera triggering delays in the range (5–50 µs), increasing effective frame rate at the highest resolution of the cameras’ sensors. A custom algorithm was developed to align successive frames from both cameras for accurate comparison. The velocity and vorticity fields of the vortex rings were analysed using optical flow method. A MATLAB-based tracking algorithm was developed to compute translational velocity through tracking the front edge of vortex ring along the centreline of the ring across successive frames, with experiments conducted over square waveform signals with triggering frequencies from 1–50 Hz to assess the influence on vortex characteristics. Results and Discussion In the present study, the evolution and early formation of the vortex rings are visualised through the dual camera schlieren technique at different frequencies. The typical formation sequence of the vortex rings at a triggering frequency of 2Hz can be seen at Figure 2. The effect of the triggering frequency of the speaker vibrating diaphragm is investigated through the variation of the frequency in the range (1-50Hz). The results, as shown in Figure 3, indicate that while the vortex ring velocity increases with the increased frequency due to the acceleration of the vibrating diaphragm at higher frequencies, the rate of increase gradually slows down as the frequency rises. The maximum velocity increase reaches 128% at 50Hz compared to 1Hz. The effect of the inter-camera triggering delay on the accuracy of the results is also investigated as it is varied ranging from 5 µs to 50 µs. At a constant triggering frequency, as the inter-camera triggering delay is increased, the instantaneous average velocity decreases. The highest measurement accuracy is achieved at 25 µs. Figure 4 shows a sample plot of the vorticity vector field for a vortex ring captured at a triggering frequency of 2Hz with a triggering delay of 25 µs. As can be seen from Figure 4, the highest vorticity of the vortex ring is located at the centre of the ring core which agrees with the literature findings. Conclusion This study pioneers the use of a speaker-driven vortex generator with dual-camera Schlieren Image Velocimetry (SIV) for air-based vortex ring analysis, achieving particle-free, high-resolution flow characterisation, a key advancement over conventional liquid-focused, particle-seeded methods. Results show that increasing the diaphragm triggering frequency significantly enhances translational velocity, with a 128% increase at 50 Hz compared to 1 Hz. The dual-camera setup captured high-speed dynamics effectively, while optical flow analysis confirmed peak vorticity at the ring core, aligning with the literature. Demonstrated repeatability underscores potential applications like electronics cooling. Future work will optimise orifice diameter and extend SIV to turbulent regimes, bridging inviscid models and viscous behaviour.