Drag Reduction by Riblets amp; Sharkskin Denticles: A
Numerical Study
A DISSERTATION
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL
OF THE UNIVERSITY OF MINNESOTA BY
Aaron Boomsma
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Professor Fotis Sotiropoulos
July, 2015
Acknowledgements
I would like to thank my adviser Professor Fotis Sotiropoulos for his support, guidance, and patience over the past five years. Professor Sotiropoulos is a visionary and has a drive for excellence. I am inspired to foster these traits in my own life. I also would like to thank the committee members, Professors Terry Simon, Ellen Longmire, and Sean Garrick. I sincerely appreciate their time, effort, and valuable feedback.
This dissertation would not be possible without the members of our research group,
Mohammad Hajit, Toni Calderer, Saurabh Chawdhary, Daniel Foti, Xiaolei Yang, Dionysus Angelidis, Trung Le Bao, Ali Khosronejad, amp; Seokoo Kang. I couldnrsquo;t have asked for a better research group. The technical expertise of every member was instrumental in my research. Irsquo;m looking forward to a future with them as colleagues and friends.
I would like to thank George Lauder and Li Wen of the Lauder Laboratory for the opportunity to collaborate and for the denticle CAD model. I would also like to thank the staff at Sandia National Labs for their collaboration. During my Ph.D., I was fortunate to travel to the Sandia National Laboratory and use the RedMesa supercomputer. RedMesa was an integral part of my research. I particularly appreciate the mentorship of David Maniaci. I also want to express my gratitude to my coworkers at TSI Inc. for their encouragement as Irsquo;ve finished this dissertation. I have felt welcomed and appreciated, and Irsquo;m looking forward towards a future of development and innovation at TSI.
I would like to thank my father and mother, Steve and Julie Boomsma, for their tremendous support and sacrifice. They have expressed confidence in me from the very beginning. I love them both very much. I am thankful for my wife, Amanda Boomsma. She has shared the burdens of this Ph.D. and has selflessly set her goals aside so that I could work towards mine. Lastly, I want to thank my Lord and savior, Jesus Christ. He is my rock and my salvation.
This research was made possible through a grant from the United States Department of Energy. Computational resources were provided by the Sandia National Laboratory and the Minnesota Supercomputing Institute.
Abstract
Riblet films are a passive method of turbulent boundary layer control that can reduce viscous drag. They have been studied with great detail for over 30 years. Although common riblet applications include flows with Adverse Pressure Gradients (APG), nearly all research thus far has been performed in channel flows. Recent research has provided motivation to study riblets in more complicated turbulent flows with claims that riblet drag reduction can double in mild APG common to airfoils at moderate angles of attack. Therefore, in this study, we compare drag reduction by scalloped riblet films between riblets in a zero pressure gradient and those in a mild APG using high-resolution large eddy simulations. In order to gain a fundamental understanding of the relationship between drag reduction and pressure gradient, we simulated several different riblet sizes that encompassed a broad range of s (riblet width in wall units), similarly to many experimental studies. We found that there was only a slight improvement in drag reduction for riblets in the mild APG. We also observed that peak values of streamwise turbulence intensity, turbulent kinetic energy, and streamwise vorticity scale with riblet width. Primary Reynolds shear stresses and turbulence kinetic energy production however scale with the ability of the riblet to reduce skin-friction.
Another turbulent roughness of similar shape and size to riblets is sharkskin. The hydrodynamic function of sharkskin has been under investigation for the past 30 years. Current literature conflicts on whether sharkskin is able to reduce skin friction similarly to riblets. To contribute insights toward reconciling these conflicting views, Direct Numerical Simulations (DNS) are carried out to obtain detailed flow fields around realistic denticles. A sharp interface immersed boundary method is employed to simulate two arrangements of actual sharkskin denticles (from Isurus oxyrinchus) in a turbulent boundary layer at Retau; asymp; 180. For comparison, turbulent flow over drag-reducing scalloped riblets is also simulated with similar flow conditions and with the same numerical method. Although the denticles resemble riblets, both sharkskin arrangements increase total drag by 44-50%, while the riblets reduce drag by 5%. Analysis of the simulated flow fields shows that the turbulent flow around denticles is highly three-dimensional and separated, with 25% of the total drag being form drag. The complex three-dimensional shape of the denticles gives rise to a mean flow dominated by strong secondary flows in sharp contrast with the mean flow generated by riblets, which is largely two-dimensional. The so resulting threedimensionality of sharkskin flows leads to an increase in the magnitude of the turbulence statistics near the denticles, which further contributes to increasing the total drag. The simulations also show that, at least for the simulated arrangements, sharkskin, in sharp contrast with drag-reducing riblets, is unable to isolate high shear stress near denticle ridges causing a significant
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肋条减阻和鲨鱼表皮凸起减阻的数值模拟
明尼苏达州大学研究生院学位论文
Aaron Boomsma
符合授予哲学博士学位的部分要求
Fotis Sotiropoulos 教授
2015年7月
致谢
我要感谢我的导师Fotis Sotiropoulos 教授五年多以来给予我的支持、引导和耐心。Sotiropoulos 教授是一个追求卓越和富有远见的人。在我自己的生活中，我也被激励着去培养这些品质。我还要感谢委员会的成员，Terry Simon，Ellen Longmire， 和 Sean Garrick 教授。我真心的感谢他们为我所花费的时间和精力，以及给予我的有价值的反馈。
如果没有我们课题组的成员，Mohammad Hajit，Toni Calderer， Saurabh Chawdhary，Daniel Foti， Xiaolei Yang， Dionysus Angelidis， Trung Le Bao， Ali Khosronejad 和Seokoo Kang，我不可能完成这篇论文。在他们之外，我不能找到一个更好的课题组了。每一个成员的专业技术都对我的研究有所帮助。我希望在将来能够和他们继续做朋友和同事。
我要感谢兰黛实验室的George Lauder 和 Li Wen所提供的合作机会以及在建立鲨鱼表皮凸起的CAD模型上给予的帮助。我还要感谢桑迪亚国家实验室的成员提供的帮助。在我攻读博士学位期间，我很幸运能够参观桑迪亚国家实验室并使用RedMesa 超级计算机。RedMesa 是我整个研究中不可缺少的一部分。我特别感激David Maniaci的指导。我想对TSI公司的同事对我完成论文所提出的鼓励表示感谢。在那里，我受到了欢迎和赞赏，我也希望将来能够在TSI公司有所发展和创新。
我要感谢我的父亲Steve和我的母亲Julie Boomsma所做出的大力支持和奉献，他们从一开始就对我表示了极大的信任。我很爱他们。感谢我的妻子Amanda Boomsma。她和我一起承担了我的攻读学位的负担，她为了我能够专心攻读博士学位而无私的将她的梦想搁在一边。最后，我要感谢真主Jesus Christ，他是我的罄石，我的拯救。
这项研究获得了美国能源部的资助。明尼苏达州超级计算研究所和桑迪亚国家实验室提供了计算资源。
摘要
肋条薄膜是减少湍流边界层粘性阻力的一种被动减阻方法。这种方法已经被详细研究了30多年。尽管通常的肋条应用在包括逆压梯度（APG）流动中，但是几乎迄今为止所有的研究都是在管道流动中得到验证的。最近的研究结果为研究肋条在更加复杂的湍流中获得比在温和的APG和中等攻角的机翼条件下成倍的减阻效果提供了动机。因此，在本课题中，我们使用高分辨率的大涡模拟比较了在零压力梯度和中等压力梯度下扇形肋条薄膜的减阻效果。为了得到减阻效果和压力梯度的基本关系，我们模拟了几组不同s （沟槽宽度）尺寸的肋条的减阻效果，模拟结果与实验得出的结论基本吻合。我们发现在中等APG条件下，肋条的减阻效果只增加了一点。我们还观察到顺流方向的湍流强度的平均值，湍流动能，和顺流方向的漩涡面积和肋条宽度有关系。初始的雷诺剪切应力和湍流动能产生的范围对肋条减少表面摩擦力的能力有影响。
另外一种湍流状态下的拥有相似形状和尺寸的肋条的粗糙面是鲨鱼皮。对鲨鱼皮的水动力学作用已经有了超过30年的调查研究。目前的文献对于鲨鱼皮能否像肋条一样减少表面的摩擦仍然有不同看法。为了消除这种分歧，直接数值模拟(DNS)被用于获得真实鲨鱼表皮凸起周围的流场细节。在 Retau; asymp; 180的湍流边界层条件下，采用一种尖锐表面浸入边界的方法模拟真实鲨鱼皮（灰鲭鲨）凸起的两种状态。为了能够比较结果的差异，在试验中采用相同的数值模拟方法模拟同种流动状态下的湍流流过扇形减阻肋条的情况。尽管鲨鱼表皮凸起与减阻肋条相似，但两种状态下的鲨鱼表皮的总阻力都增加了44-50%，而肋条却减少了5%的阻力。分析模拟流场发现，凸起周围的湍流是高度立体和分离的，形成了总阻力的25%。凸起复杂的三维形状产生了一种由强烈的二维流动主导的流动，这种流动与肋条所产生的大型二维流动形成了强烈的对比。所以鲨鱼皮表面的三维流动导致了凸起附近湍流统计的量级增加，这进一步导致了总阻力的增加。模拟结果还显示，至少在模拟条件下，与减阻肋条不同的是，鲨鱼皮不能隔绝凸起附近的高剪切应力，导致相当一部分凸起表面暴露在高剪切应力下。
最后，我们推断鲨鱼表皮的作用可能和扰流器防止分流相似。为了证明上述推论， 我们在有无鲨鱼皮两种情况下模拟了稳定泡沫分离的上游部分。使用大涡模拟，我们的研究显示鲨鱼皮恶化了弱分离区，同时，扩大了泡沫分离的边界。这种现象的原因是凸起的作用类似于阻流器而不是漩涡发生器。实际上，我们的研究结果表明泡沫分离发生在第二排凸起之后并且湍流损失的动能不可恢复。顺流方向的湍流强度与基线相比是有所下降的。最后，以目前的研究结果来看，并没有发现带有凸起的鲨鱼皮在管道流动中能够降低回流。
目录
摘要 ii
第1章
文献综述
很多实际流动的的表面都很粗糙。粗糙度的形状和尺寸根据一些参数的不同而有很大差异，粗糙度的大小对边界层和无滑移边界状态的减阻有很大的影响。早期针对粗糙度的调查研究是出于管道流动的摩擦损失。对管道流动中压力损失的早期研究者包括 Hagen [19]， Darcy [20]，和 Weisbach [21]。因此，今天的流体机械工程师对管道流阻力达西-韦斯巴赫方程和达西摩擦因子非常熟悉。其中尤为重要的是Nikuradse [1]所做的工作。Nikuradse系统的研究了在各种粗
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