Zepeng Cheng
(, ), Chong Pan
(, ), Jiangsheng Wang
(, )
{"title":"量化涡旋不稳定性对翼尖涡旋平均速度场统计的影响","authors":"Zepeng Cheng \n (, ), Chong Pan \n (, ), Jiangsheng Wang \n (, )","doi":"10.1007/s10409-024-24085-x","DOIUrl":null,"url":null,"abstract":"<div><p>During its evolution to the far field, the wingtip vortex exhibits complex instability behaviors such as long-wave/short-wave instability and vortex wandering. However, the quantification influence of vortex instability on its velocity field statistics has not been well investigated. To this end, experimental measurements of a canonical wingtip vortex generated by an elliptical wing under various angles of attack and Reynolds numbers were conducted using particle image velocimetry. It is found that the streamwise variation of wandering amplitude presents an exponential growth within the middle-to-far wake region and asymptotically saturates to 10<sup>−1</sup><i>b</i> in the far wake, which differs from the previous report of a linear growth trend in the near-wake region. Further, two average methods, i.e., time average (TA) and ensemble average (EA), were adopted to compare the velocity field statistics. In both TA- and EA-obtained flow fields, the vortex radius <i>r</i><sub><i>c</i></sub>, peak vorticity <span>\\(\\Omega_{x}^{p}\\)</span>, and vortex circulation <i>Γ</i> all demonstrate a power-law scaling with respect to the streamwise location, i.e., <span>\\(r_{c}\\propto x^{k_{r}},\\Omega_{x}^{p}\\propto x^{-k_{\\omega}}\\)</span>, and <span>\\(\\Gamma\\propto x^{-k_{\\Gamma}}\\)</span>, respectively. For a full rolling-up wingtip vortex in the middle-to-far wake region, the fact that <i>k</i><sub><i>Γ</i></sub> = <i>k</i><sub><i>ω</i></sub> − 2<i>k</i><sub><i>r</i></sub> demonstrates that the vortex circulation can be scaled as <span>\\(\\Gamma=\\Omega_{x}^{p}(r_{c})^{2}\\)</span>. On the other hand, TA overestimates the decay rate of peak vorticity <i>k</i><sub><i>ω</i></sub> and the growth rate of vortex radius <i>k</i><sub><i>r</i></sub>. Furthermore, the TA-introduced bias level of the peak vorticity and vortex radius is found to be scaled with an empirical scaling between the wandering amplitude by a power law, respectively. These findings provide significant practical value for detecting wake vortex in wake vortex spacing systems.</p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"40 11","pages":""},"PeriodicalIF":3.8000,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantifying the influence of vortex instability on mean velocity field statistics of wingtip vortex\",\"authors\":\"Zepeng Cheng \\n (, ), Chong Pan \\n (, ), Jiangsheng Wang \\n (, )\",\"doi\":\"10.1007/s10409-024-24085-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>During its evolution to the far field, the wingtip vortex exhibits complex instability behaviors such as long-wave/short-wave instability and vortex wandering. However, the quantification influence of vortex instability on its velocity field statistics has not been well investigated. To this end, experimental measurements of a canonical wingtip vortex generated by an elliptical wing under various angles of attack and Reynolds numbers were conducted using particle image velocimetry. It is found that the streamwise variation of wandering amplitude presents an exponential growth within the middle-to-far wake region and asymptotically saturates to 10<sup>−1</sup><i>b</i> in the far wake, which differs from the previous report of a linear growth trend in the near-wake region. Further, two average methods, i.e., time average (TA) and ensemble average (EA), were adopted to compare the velocity field statistics. In both TA- and EA-obtained flow fields, the vortex radius <i>r</i><sub><i>c</i></sub>, peak vorticity <span>\\\\(\\\\Omega_{x}^{p}\\\\)</span>, and vortex circulation <i>Γ</i> all demonstrate a power-law scaling with respect to the streamwise location, i.e., <span>\\\\(r_{c}\\\\propto x^{k_{r}},\\\\Omega_{x}^{p}\\\\propto x^{-k_{\\\\omega}}\\\\)</span>, and <span>\\\\(\\\\Gamma\\\\propto x^{-k_{\\\\Gamma}}\\\\)</span>, respectively. For a full rolling-up wingtip vortex in the middle-to-far wake region, the fact that <i>k</i><sub><i>Γ</i></sub> = <i>k</i><sub><i>ω</i></sub> − 2<i>k</i><sub><i>r</i></sub> demonstrates that the vortex circulation can be scaled as <span>\\\\(\\\\Gamma=\\\\Omega_{x}^{p}(r_{c})^{2}\\\\)</span>. On the other hand, TA overestimates the decay rate of peak vorticity <i>k</i><sub><i>ω</i></sub> and the growth rate of vortex radius <i>k</i><sub><i>r</i></sub>. Furthermore, the TA-introduced bias level of the peak vorticity and vortex radius is found to be scaled with an empirical scaling between the wandering amplitude by a power law, respectively. 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Quantifying the influence of vortex instability on mean velocity field statistics of wingtip vortex
During its evolution to the far field, the wingtip vortex exhibits complex instability behaviors such as long-wave/short-wave instability and vortex wandering. However, the quantification influence of vortex instability on its velocity field statistics has not been well investigated. To this end, experimental measurements of a canonical wingtip vortex generated by an elliptical wing under various angles of attack and Reynolds numbers were conducted using particle image velocimetry. It is found that the streamwise variation of wandering amplitude presents an exponential growth within the middle-to-far wake region and asymptotically saturates to 10−1b in the far wake, which differs from the previous report of a linear growth trend in the near-wake region. Further, two average methods, i.e., time average (TA) and ensemble average (EA), were adopted to compare the velocity field statistics. In both TA- and EA-obtained flow fields, the vortex radius rc, peak vorticity \(\Omega_{x}^{p}\), and vortex circulation Γ all demonstrate a power-law scaling with respect to the streamwise location, i.e., \(r_{c}\propto x^{k_{r}},\Omega_{x}^{p}\propto x^{-k_{\omega}}\), and \(\Gamma\propto x^{-k_{\Gamma}}\), respectively. For a full rolling-up wingtip vortex in the middle-to-far wake region, the fact that kΓ = kω − 2kr demonstrates that the vortex circulation can be scaled as \(\Gamma=\Omega_{x}^{p}(r_{c})^{2}\). On the other hand, TA overestimates the decay rate of peak vorticity kω and the growth rate of vortex radius kr. Furthermore, the TA-introduced bias level of the peak vorticity and vortex radius is found to be scaled with an empirical scaling between the wandering amplitude by a power law, respectively. These findings provide significant practical value for detecting wake vortex in wake vortex spacing systems.
期刊介绍:
Acta Mechanica Sinica, sponsored by the Chinese Society of Theoretical and Applied Mechanics, promotes scientific exchanges and collaboration among Chinese scientists in China and abroad. It features high quality, original papers in all aspects of mechanics and mechanical sciences.
Not only does the journal explore the classical subdivisions of theoretical and applied mechanics such as solid and fluid mechanics, it also explores recently emerging areas such as biomechanics and nanomechanics. In addition, the journal investigates analytical, computational, and experimental progresses in all areas of mechanics. Lastly, it encourages research in interdisciplinary subjects, serving as a bridge between mechanics and other branches of engineering and the sciences.
In addition to research papers, Acta Mechanica Sinica publishes reviews, notes, experimental techniques, scientific events, and other special topics of interest.
Related subjects » Classical Continuum Physics - Computational Intelligence and Complexity - Mechanics