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Rotation Invariant Vortices for Flow Visualization.

Tobias Günther, Maik Schulze, Holger Theisel

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    We introduce rotation-invariant vortex definitions for rotating flows, improving accuracy over traditional Galilean-invariant methods for mechanical systems like pumps and ventilators.

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    Area of Science:

    • Fluid dynamics
    • Mechanical engineering
    • Vortex dynamics

    Background:

    • Vortex identification is crucial for analyzing complex fluid flows.
    • Existing vortex definitions often lack invariance under the rotations inherent in many mechanical systems.
    • Traditional methods like Galilean invariance are insufficient for flows induced by rotating machinery.

    Purpose of the Study:

    • To develop a new class of rotation-invariant vortex definitions.
    • To adapt existing Galilean-invariant vortex criteria (Sujudi-Haimes, Lambda-2, Q) to be rotation-invariant.
    • To demonstrate the improved performance of these new definitions in rotating flow scenarios.

    Main Methods:

    • Enforcing rotation invariance instead of Galilean invariance for vortex definitions.
    • Developing a general method to transform Galilean-invariant concepts to rotation-invariant ones by modifying the Jacobian matrix.
    • Applying rotation-invariant versions of Sujudi-Haimes, Lambda-2, and Q criteria to artificial and real rotating flows.

    Main Results:

    • Successfully derived rotation-invariant versions of key vortex identification criteria.
    • Demonstrated that rotation-invariant vortices provide superior results compared to Galilean-invariant counterparts in rotating flows.
    • Validated the approach on diverse artificial and real-world rotating flow examples.

    Conclusions:

    • The proposed rotation-invariant vortex definitions offer a more accurate and robust method for analyzing flows from rotating mechanical parts.
    • This new framework enhances the understanding and prediction of vortex structures in systems such as pumps, ventilators, and helicopters.
    • The general transformation approach provides a valuable tool for extending other vortex identification methods to rotation-invariant applications.