Development of Image-Based Density Diagnostics with Background-Oriented Schlieren and Application to Plasma Induced Flow

Lalit Kishore Rajendran, Purdue University

Abstract

There is growing interest in the use of nanosecond surface dielectric barrier discharge (ns-SDBD) actuators for high-speed (supersonic/hypersonic) flow control. A plasma discharge is created in these actuators using a nanosecond-duration pulse of several kilovolts to deposit energy rapidly in the electrode gap which causes the electrical breakdown. This creates a rapid heat release, which leads to the formation of a shock wave and the development of a complex three-dimensional flow field that is not fully understood. Actuators based on ns-SDBDs have been applied to high-speed flow control problems such as shock-boundary layer interactions (SBLI), but the results have been mixed and the control authority of the actuator is not well established. This is because, although a general idea of the flow features induced by a ns-SDBD exists, the effect of the actuator geometry (such as the filament spacing) and the operating parameters (such as the pulse frequency) on the induced flow are not well understood and play a critical role in flow control applications. Even the flow field induced by a single pulse of a ns-SDBD is not entirely understood at a more fundamental level, in contrast to the well-characterized AC-driven SDBD. The flow field induced by ns-DBDs is on much shorter time scales(by almost an order of magnitude) and involves large spatiotemporal gradients in the velocity and temperature fields, posing a significant experimental challenge. Majority of the past work has been limited to qualitative visualizations such as schlieren imaging, and detailed measurements of the induced flow are required to develop a mechanistic model of the actuator performance, such as the heating and vorticity production, and to develop design rules to guide the development and deployment of these actuators. Background-Oriented Schlieren (BOS) is a recently developed optical flow diagnostic that is a quantitative variant of schlieren imaging and can be used to measure the density and temperature fields of the actuator induced flow. BOS measures density gradients in a flow field by tracking the apparent distortion of a target dot pattern. Since density and refractive index are proportional for fluids, density gradients in a flow are associated with refractive index gradients, and an object viewed through a variable density medium will appear distorted due to the refraction of light rays traversing the medium. The distortion of the dot pattern is typically estimated by cross-correlating an image of the dot pattern without the density gradients (called the reference image) with a distorted image viewed through the density gradients (called the gradient image). The density gradients can be integrated spatially to obtain the density field, generally by solving the Poisson equation using different computational procedures. Owing to the simple setup and ease of use, BOS has been applied widely in laboratory scale experiments as well as in large scale experiments and rugged industrial facilities, and is becoming the preferred method of density measurement in fluid flows. However, BOS features several unaddressed limitations with potential for improvement, especially for application to complex flow fields such as those induced by plasma actuators. Some of the limitations are: 1) low spatial resolution due to the large window-sized used in crosscorrelation algorithms, 2) lack of an uncertainty quantification methodology, and 3) the density integration procedure using the Poisson solver is very sensitive to noise. Further, since BOS comprises several factors like the dot pattern, illumination, density gradients, optical system and the processing algorithms, each of these factors contribute to the final measurement error/uncertainty in a complex manner.

Degree

Ph.D.

Advisors

Vlachos, Purdue University.

Subject Area

Optics|Fluid mechanics|Mathematics|Mechanics

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