[Paper Review] Megahertz Schlieren Imaging of Shock Structure and Sound Waves in Under-Expanded, Impinging Jets

Christian Willert, Daniel Edgington-Mitchell+1 more|arXiv (Cornell University)|Oct 15, 2010

Aerodynamics and Acoustics in Jet Flows6 references3 citations

TL;DR

This study presents megahertz-rate Schlieren imaging of under-expanded, impinging jets using a pulsed high-power LED light source, enabling time-resolved visualization of shock structures and sound waves at frame rates up to 1 MHz. The method reveals helical jet instabilities at low pressure ratios (2.0–2.5), Mach disk formation at higher ratios (3.0–5.0), and asymmetric acoustic radiation linked to jet structure, with superior image quality and repeatability compared to xenon flashes or lasers.

ABSTRACT

The accompanying fluid dynamics videos visualize the temporal evolution of shock structures and sound waves in and around an under-expanded jet that is impinging on a rigid surface at varying pressure ratios. The recordings were obtained at frame rates of 500 kHz to 1 Mhz using a novel pulsed illumination source based on a high power light emitting diode (LED) which is operated in pulsed current mode synchronized to the camera frame rate.

Motivation & Objective

• To enable high-speed, time-resolved visualization of unsteady shock structures and sound waves in under-expanded, impinging jets.
• To overcome limitations of conventional xenon flash or laser illumination by developing a high-repetition-rate, stable, and speckle-free light source for Schlieren imaging.
• To investigate the influence of nozzle pressure ratio (2.0–5.0) on jet structure, shock dynamics, and acoustic wave radiation in impinging flows.
• To compare the performance of pulsed high-power LEDs against traditional light sources in terms of image quality, repeatability, and temporal resolution.
• To analyze the relationship between jet instability modes (e.g., helical motion) and asymmetric acoustic radiation in impinging supersonic jets.

Proposed method

• Employed a high-power pulsed LED (Luminus Phlatlight CBT-120, green) operated in burst mode at up to 120 A with 500 ns pulse width and 200 ns rise time, yielding effective light pulses of ~300 ns.
• Synchronized the LED pulse train to a high-speed camera (Shimadzu HPV-1, 312×260 pixels) at frame rates of 500 kHz to 1 MHz for stroboscopic imaging.
• Used a conventional Schlieren optical setup with a single mirror and knife-edge, illuminated by nearly monochromatic green light to reduce speckle and enhance contrast.
• Applied contrast enhancement by subtracting the average image from each frame to suppress static features (e.g., mirror blemishes) and highlight unsteady flow structures.
• Captured four sequences at fixed plate distance (x/D = 4) and nozzle diameter D = 5 mm, with nozzle pressure ratios of 2.0, 2.5, 3.0, and 5.0.
• Generated pseudo-colored, contrast-enhanced visualizations for improved feature visibility while preserving temporal fidelity.

Experimental results

Research questions

• RQ1 How do shock structures and unsteady instabilities evolve in under-expanded jets impinging on a flat plate at nozzle pressure ratios from 2.0 to 5.0?
• RQ2 What is the role of jet helical instability in generating asymmetric acoustic radiation during impingement?
• RQ3 How does the use of a pulsed high-power LED compare to xenon flash or laser sources in terms of image quality, temporal resolution, and speckle suppression for Schlieren imaging?
• RQ4 At what pressure ratio does Mach disk formation become prominent, and how does it affect downstream turbulence and acoustic wave propagation?
• RQ5 How does the jet’s structural symmetry (e.g., helical vs. axisymmetric) influence the directivity and intensity of radiated sound waves?

Key findings

• At nozzle pressure ratios of 2.0 and 2.5, weak shocks near the jet exit exhibited gyration, indicating a helical instability mode in the jet core.
• Shear layer instabilities were clearly visible on the jet boundary at all pressure ratios, with increasing bowing of the shear layer at higher pressure ratios (3.0 and 5.0).
• Mach disks formed at the jet core for pressure ratios ≥3.0, with the shock position and spacing increasing with pressure ratio, and no observed gyration at these higher ratios.
• A slip line formed around the Mach disk edges, generating internal shear layers and increasing turbulence intensity immediately downstream.
• Acoustic waves radiated asymmetrically at pressure ratios 2.0 and 2.5, correlating with the helical jet structure and asymmetric impingement on the plate.
• At higher pressure ratios (3.0 and 5.0), the acoustic radiation pattern became more symmetric, consistent with the more stable, axisymmetric jet structure and Mach disk formation.