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Analytical and Computational Investigations of Airfoils Undergoing High-Frequency Sinusoidal Pitch and Plunge Motions at Low Reynolds Numbers

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Analytical and Computational Investigations of Airfoils Undergoing High-Frequency Sinusoidal Pitch and Plunge Motions at Low Reynolds Numbers

4.85 37,507 ratings · 3,233 reviews
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Overview: Current interests in Micro Air Vehicle (MAV) technologies call for the development of aerodynamic-design tools that will aid in the design of more efficient platforms that will also have adequate stability and control for flight in gusty environments. Influenced largely by nature MAVs tend to be very small, have low flight speeds, and utilize flapping motions for propulsion. For these reasons the focus is, specifically, on high-frequency motions at low Reynolds numbers. Toward the goal of developing design tools, it is of interest to explore the use of elementary flow solutions for simple motions such as pitch and plunge oscillations to predict aerodynamic performance for more complex motions.;In the early part of this research, a validation effort was undertaken. Computations from the current effort were compared with experiments conducted in a parallel, collaborative effort at the Air Force Research Laboratory (AFRL). A set of pure-pitch and pure-plunge sinusoidal oscillations of the SD7003 airfoil were examined. Phase-averaged measurements using particle image velocimetry in a water tunnel were compared with computations using two flow solvers: (i) an incompressible Navier-Stokes Immersed Boundary Method and (ii) an unsteady compressible Reynolds-Averaged Navier-Stokes (RANS) solver. The motions were at a reduced frequency of k = 3.93, and pitch-angle amplitudes were chosen such that a kinematic equivalence in amplitudes of effective angle of attack (from plunge) was obtained. Plunge cases showed good qualitative agreement between computation and experiment, but in the pitch cases, the wake vorticity in the experiment was substantially different from that predicted by both computations. Further, equivalence between the pure-pitch and pure-plunge motions was not attained through matching effective angle of attack.;With the failure of pitch/plunge equivalence using equivalent amplitudes of effective angle of attack, the effort shifted to include pitch-rate and wake-effect terms through the use of analytical methods including quasi-steady thin-airfoil theory (QSTAT) and Theodorsen's theory. These theories were used to develop three analytical approaches for determining pitch motions equivalent to plunge motions. A study of variation in plunge height was then examined and followed by a study of the effect of rotation point using the RANS solver.;For the range of plunge heights studied, it was observed that kinematic matching between plunge and pitch using QSTAT gave outstanding similarities in flow field, while the matching performed using Theodorsen's theory gave the best equivalence in lift coefficients for all cases. The variation of rotation point revealed that, for the given plunge height, with rotation point in front of the mid-chord location, all three schemes matched flow-field vorticity well, and with rotation point aft of the mid-chord no scheme matched vorticity fields. However, for all rotation points (except for the mid-chord location), CFD prediction of lift coefficients from the Theodorsen matching scheme matched the lift time histories closely to CFD predictions for pure-pitch.;Combined pitch and plunge motions were then examined using kinematic parameters obtained from the three schemes. The results showed that QSTAT nearly cancels the vortices emanating from the trailing edge. Theodorsen's matching approach was successful in generating a lift that was close to constant over the entire cycle. Additionally this approach showed the presence of the reverse Karman vortex sheet through the wake. Combined pitch/plunge motions were then analyzed, computationally and experimentally, with a non-zero mean angle of attack. All computational results compared excellently with experiments, capturing vorticity production on the airfoil's surface and through the wake. Lift coefficient through a cycle was shown to tend toward a constant using Theodorsen's parameters, with the constant being dependent on the initial angle of attack. This result points to the possibility of designing an unsteady motion to match a given flight-condition requirement.

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Language Eng
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ISBN 9590434
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Gregory Z. McGowan
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Gregory Z. McGowan is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Gregory Z. McGowan enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Kenneth Wilson December 09, 2024
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Stephanie Moore
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
William King
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Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
John Gonzalez
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Brian Sanchez
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Sarah Reyes
Sarah Reyes June 11, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Mary Smith
Mary Smith August 10, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Mark Green
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I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
David Jones
David Jones December 21, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Donald Adams
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An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Eric Wilson
Eric Wilson June 23, 2025
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Ashley Perez
Ashley Perez July 26, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Stephanie King
Stephanie King July 04, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Rebecca Collins
Rebecca Collins August 02, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Nicholas Johnson
Nicholas Johnson March 28, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Barbara Garcia
Barbara Garcia August 20, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Donald Adams
Donald Adams February 14, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Margaret King
Margaret King November 19, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Donald Adams
Donald Adams May 19, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Anthony Garcia
Anthony Garcia February 15, 2024
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Donna Clark
Donna Clark February 01, 2025
An acceptable diversion. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Barbara Lewis
Barbara Lewis August 31, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Barbara Gomez
Barbara Gomez July 06, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Mark Moore
Mark Moore July 18, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Stephanie Anderson
Stephanie Anderson July 12, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Eric Hill
Eric Hill January 11, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Mark Ramirez
Mark Ramirez July 29, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Christopher Allen
Christopher Allen August 20, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Eric Wilson
Eric Wilson August 13, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
George Jones
George Jones June 19, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Joseph Anderson
Joseph Anderson May 19, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Donald Wright
Donald Wright September 16, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Richard Rodriguez
Richard Rodriguez July 29, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Sarah Roberts
Sarah Roberts February 17, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Nancy White
Nancy White March 25, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Cynthia Rivera
Cynthia Rivera August 11, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Amanda Hernandez
Amanda Hernandez October 19, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
John Harris
John Harris June 25, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Ashley Martin
Ashley Martin September 29, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
George Reyes
George Reyes March 16, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Stephanie Smith
Stephanie Smith November 10, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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