Purdue University Graduate School
2021.4.23 Rajendran-PhD.pdf (8.23 MB)


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posted on 2021-05-07, 17:00 authored by Lalit RajendranLalit Rajendran

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 using a nanosecond-duration pulse of several kilovolts, and leads to a rapid heat release and a complex three-dimensional flow field. 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.

Background-Oriented Schlieren (BOS) is a quantitative variant of schlieren imaging and measures density gradients in a flow field by tracking the apparent distortion of a target dot pattern. The distortion is estimated by cross-correlation, and the density gradients can be integrated spatially to obtain the density field. Owing to the simple setup and ease of use, BOS has been applied widely, and is becoming the preferred density measurement technique. However, there are several unaddressed limitations with potential for improvement, especially for application to complex flow fields such as those induced by plasma actuators.

This thesis presents a series of developments aimed at improving the various aspects of the BOS measurement chain to provide an overall improvement in the accuracy, precision, spatial resolution and dynamic range. A brief summary of the contributions are:

1) a synthetic image generation methodology to perform error and uncertainty analysis for PIV/BOS experiments,

2) an uncertainty quantification methodology to report local, instantaneous, a-posteriori uncertainty bounds on the density field, by propagating displacement uncertainties through the measurement chain,

3) an improved displacement uncertainty estimation method using a meta-uncertainty framework whereby uncertainties estimated by different methods are combined based on the sensitivities to image perturbations,

4) the development of a Weighted Least Squares-based density integration methodology to reduce the sensitivity of the density estimation procedure to measurement noise.

5) a tracking-based processing algorithm to improve the accuracy, precision and spatial resolution of the measurements,

6) a theoretical model of the measurement process to demonstrate the effect of density gradients on the position uncertainty, and an uncertainty quantification methodology for tracking-based BOS,

Then the improvements to BOS are applied to perform a detailed characterization of the flow induced by a filamentary surface plasma discharge to develop a reduced-order model for the length and time scales of the induced flow. The measurements show that the induced flow consists of a hot gas kernel filled with vorticity in a vortex ring that expands and cools over time. A reduced-order model is developed to describe the induced flow and applying the model to the experimental data reveals that the vortex ring's properties govern the time scale associated with the kernel dynamics. The model predictions for the actuator-induced flow length and time scales can guide the choice of filament spacing and pulse frequencies for practical multi-pulse ns-SDBD configurations.


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Degree Type

  • Doctor of Philosophy


  • Aeronautics and Astronautics

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Sally P. M. Bane

Advisor/Supervisor/Committee co-chair

Pavlos P. Vlachos

Additional Committee Member 2

John P. Sullivan

Additional Committee Member 3

Carson D. Slabaugh