Thesis
Vorticity transport analysis of low reynolds number translating and rotating wings
University of Iowa
Master of Science (MS), University of Iowa
Spring 2023
DOI: 10.25820/etd.007033
Abstract
An aspect ratio 9.5 rectangular wing is articulated in revolving and translating motions at a 45-degree angle of incidence and Reynolds number $Re = O(300)$. Four initial cases are considered varying two salient aspects of rotational motion. Coriolis and centripetal accelerations are present in the rotating cases and absent in the translating cases, whereas uniform and linearly-varying inflow velocity profiles are imposed on instances of the rotating and translating cases. Each case exhibits distinct leading-edge vortex (LEV) growth and behavior. For the range of displacements studied (180 deg. rotation and corresponding translational displacement) a stably attached LEV is observed when rotational accelerations and/or a linearly-varying inflow velocity profile is present; however, the inflow velocity profile has a stronger effect on stability of the LEV. LEV vorticity magnitude and lift force are significantly augmented when both factors are included (i.e. the full revolving wing case). Vorticity transport analyses are conducted in a planar control region two chords from the axis of rotation, where three-dimensional vorticity transport is shown to be important in mitigating LEV growth, and at an equivalent distance from the wing root in the translating case. The revolving wing exhibits a substantially larger leading-edge shear-layer vorticity flux than the other cases. Inspection of the Coriolis tilting term demonstrates little relevance to LEV stability. In all cases, the surface diffusive flux and shear-layer vorticity flux contributions are found to be negatively correlated. Additionally, a correlation is found between the spanwise convective flux and tilting flux contributions in all cases. Decomposition of the spanwise convective flux reveals that the tilting flux is a constituent of it, demonstrating that the two phenomena are kinematically linked. Based on this result, a significantly simplified vorticity transport equation is developed in which all of the three-dimensional transport fluxes are consolidated into a single term, providing new physical interpretation of these terms. Six additional cases, with contributions from rotational accelerations increased, or the inflow gradient decreased, elucidate the relative impact on LEV stability of both aspects of rotational motion. Exceptional LEV stability was apparent when the rotational accelerations are increased, while LEV strength and stability decreased as the intensity of the inflow gradient decreased. Spatial distributions of out-of-plane vorticity transport mechanisms emphasized the importance of spanwise flow in promoting LEV stability. Finally, the no-slip boundary condition on the suction surface was removed for the fully rotating case, and the presence surface diffusion led to decreased LEV stability, contrasting previous understanding.
Details
- Title: Subtitle
- Vorticity transport analysis of low reynolds number translating and rotating wings
- Creators
- James H Paulson
- Contributors
- James H J Buchholz (Advisor)Thierry Jardin (Committee Member)Casey Harwood (Committee Member)
- Resource Type
- Thesis
- Degree Awarded
- Master of Science (MS), University of Iowa
- Degree in
- Mechanical Engineering
- Date degree season
- Spring 2023
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.007033
- Number of pages
- xii, 85 pages
- Copyright
- Copyright 2023 James H Paulson
- Language
- English
- Date submitted
- 04/25/2023
- Date approved
- 05/10/2023
- Description illustrations
- illustrations, tables, graphs
- Description bibliographic
- Includes bibliographical references (pages 80-85).
- Public Abstract (ETD)
- It is well known that wings undergoing rotational motion experience stronger lift forces than translating wings under the same conditions, e.g. many insect wings produce insufficient lift for hovering flight in translational motion, but when flapping provide sufficient aerodynamic forces for complex maneuvers. This has been attributed to several mechanisms but primary focus has been on the presence of a leading-edge vortex (LEV), which forms at the leading-edge of the wing and increases lift performance. From a reference frame attached to a revolving wing, the fluid flow has two distinct aspects that distinguish it from a translating wing: a relative inflow velocity that varies linearly from the axis of rotation to the tip of the wing and rotational accelerations (centripetal and Coriolis) which are resultant from the rotation of the reference frame. This study systematically isolates the aspects of rotational motion to better understand how they influence the development of the leading-edge vortex. Because there are large variations in the relative impact of these effects along the span of the wing, an aspect ratio 9.5 wing at an angle of attack of 45 deg. is simulated in a rotating or translating motion. Distinct behavior can be correlated to each aspect of rotational motion, with both aspects proving to be important. To better understand the phenomena contributing to the stable LEV, a vorticity transport budget is applied. The vorticity transport budget tracks sources or sinks of circulation, tying them to physical mechanisms; the budget acts as a quantitative analytical tool from which we can better understand LEV stability. A new form of the transport equation is derived which shows that some of the previously identified mechanisms are dependent and consolidates them, resulting in a simpler equation. Insights from the four basic cases informed the selection of 6 new cases, constructed by varying the inflow gradient and rotational accelerations quantitatively, providing further insight into their impact on LEV development. These cases further strengthen the arguments made by the initial cases as well as better demonstrating the relevance of rotational accelerations. The generation of vorticity on the surface of the wing, below the LEV, has been previously shown to be an important LEV circulation-weakening mechanism, through the generation of a secondary vortex. To understand how this effects LEV stability, a no-slip or free-slip boundary condition is applied to the suction surface of the wing. The isolation of surface diffusion demonstrated that, while it was an important weakening mechanism, the presence of surface diffusion seems to destabilize the LEV, contrasting previous understanding. Again a vorticity transport budget was applied, and analysis demonstrated the importance of three-dimensionality in the LEV, both via spanwise variation in LEV strength and the presence of spanwise flow within the LEV.
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984425197802771
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