The Integral Form Fluid Momentum Theorem on Time-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis

LIN Xian-wu; LAN Wei-yao; LI Zhi-bin; LI He

doi:10.3879/j.issn.1000-0887.2016.06.001

Volume 37 Issue 6

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2016 > 37(6): 551-566

LIN Xian-wu, LAN Wei-yao, LI Zhi-bin, LI He. The Integral Form Fluid Momentum Theorem on Time-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis[J]. Applied Mathematics and Mechanics, 2016, 37(6): 551-566. doi: 10.3879/j.issn.1000-0887.2016.06.001

Citation:

PDF( 750 KB)

The Integral Form Fluid Momentum Theorem on Time-Varying Systems and Its Application to Aerodynamic Force Coefficient Analysis

doi: 10.3879/j.issn.1000-0887.2016.06.001

¹School of Aerospace Engineering, Xiamen University,Xiamen, Fujian 361005, P.R.China;²Beijing Institute of Control Engineering, Beijing 100190, P.R.China

Funds: The National Natural Science Foundation of China(11072028；61273199)

Received Date: 2016-01-27
Rev Recd Date: 2016-04-15
Publish Date: 2016-06-15

Abstract

Abstract

To tackle the calculation problem on steady and unsteady hydrodynamic force coefficients of a moving body in viscous incompressible flow, a method for calculating hydrodynamic force coefficients in viscous flow was proposed based on the quasi-equilibrium hypothesis and the vorticity aerodynamics. Firstly, the concept of time-varying flow systems was defined, and its relationship with the space volume was clarified. Then, the momentum transport equation and the fluid momentum theorem for time-varying flow systems were developed respectively, so as to provide a basis for the further discussion. Secondly, the fluid momentum theorem was applied to a flow system enclosed in the boundary composed of the body surface and the outer fixed surface with an infinite radius, and the fluid dynamic force was related to the change of the total fluid momentum. Thirdly, the quasi-equilibrium hypothesis was proposed and the total fluid momentum was expressed as a function of the body velocity and angular velocity. At last, this function was determined with the CFD technology and the method for calculating the fluid dynamic force coefficients in viscous flow was established. The study also show that the variation of the flow system should be considered during the derivation of the fluid momentum, and consequently an additional steady fluid dynamic force would come forth. This additional steady force can be proved to be zero for the body in linear uniform motion in the ideal flow, which is in accordance with d’Alembert’s paradox and Lamb’s result. However, in the case of viscous flow, this additional steady force is not necessarily to be zero, which is in accordance with the experimental results.
- fluid momentum theorem,
- time-varying system,
- momentum transport equation,
- unsteady hydrodynamic force,
- airship

FullText(HTML)

References(28)

References

[1]	Lamb H. Hydrodynamics[M]. 6th ed. New York: Dover, 1945.
[2]	Tuckerman L B. Inertia factors of ellipsoids for use in airship design[R]. Technical Report Archive and Image Library, 1926.
[3]	Erdelyi,A.,Higher Trascendental Functions,Vol,Ⅰ-Ⅲ(1953).
[4]	Allen H J, Perkins E W. A study of effects of viscosity on flow over slender inclined bodies of revolution[R]. Technical Report Archive and Image Library, 1951.
[5]	Hopkins E J. A semi-empirical method for calculating the pitching moment of bodies of revolution at low Mach numbers[R]. Technical Report Archive and Image Library, 1951.
[6]	Jones S P, deLaurier J D. Aerodynamic estimation techniques for aerostats and airships[J]. Journal of Aircraft,1983,20(2): 120-126.
[7]	Khoury G A, Gillett J D. Airship Technology[M]. New York: Cambridge University Press, 1999.
[8]	Mueller J B, Paluszek M A, Zhao Y Y. Development of an aerodynamic model and control law design for a high altitude airship[C]//AIAA 〖STBX〗3rd “Unmanned Unlimited” Technical Conference, Workshop and Exhibit.Chicago, Illinois, 2004: 1-17.
[9]	Li Y W, Nahon M. Modeling and simulation of airship dynamics[J]. Journal of Guidance Control and Dynamics,2012,30(6): 1691-1700.
[10]	Li Y W, Nahon M, Sharf I. Airship dynamics modeling: a literature review[J]. Progress in Aerospace Sciences,2011,47(3): 217-239.
[11]	基里林〖KG-4〗·〖KG-4〗阿列克桑德拉〖KG-4〗·〖KG-4〗尼卡拉伊维奇. 现代飞艇设计导论[M]. 吴飞, 王培美, 译. 北京: 国防工业出版社, 2009.(Kirilin A K. Introduction to Modern Airship Design[M]. WU Fei, WANG Pei-mei, transl. Beijing: National Defend Industry Press, 2009.(Chinese version))
[12]	Sebbane Y B. Lighter Than Air Robots[M]. Springer, 2012.
[13]	Wu J C. Theory for aerodynamic force and moment in viscous flows[J]. AIAA Journal,1981,19(4): 432-441.
[14]	Wu J C. Elements of Vorticity Aerodynamics[M]. Shanghai: Shanghai Jiao Tong University Press, 2014.
[15]	童秉纲, 尹协远, 朱克勤. 涡运动理论[M]. 合肥: 中国科学技术大学出版社, 2009.(TONG Bing-gang, YIN Xie-yuan, ZHU Ke-qin. Vortex Motion Theory[M]. Hefei: University of Science and Technology of China Press, 2009.(in Chinese))
[16]	WU Jie-zhi, MA Hi-yang, ZHOU Ming-de. Vortical Flows[M]. Springer, 2007.
[17]	Noca F, Shiels D, Jeon D. A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives[J]. Journal of Fluids and Structures,1999,13(5): 551-578.
[18]	吴子牛, 王兵, 周睿, 徐珊姝. 空气动力学(下册)[M]. 北京: 清华大学出版社, 2008.(WU Zi-niu,WANG Bing, ZHOU Rui, XU Shan-shu. Aerodynamics(Volume Two)[M]. Beijing: Tsinghua University Press, 2008.(in Chinese))
[19]	Wu J Z, Ma H Y, Zhou M D. Vorticity and Vortex Dynamics[M]. Springer, 2006.
[20]	清华大学工程力学系. 流体力学基础[M]. 北京: 机械工业出版社, 1980.(Department of Engineering Mechanics of Tsinghua University. The Basis of Fluid Dynamics[M]. Beijing: China Machine Press, 1980.(in Chinese))
[21]	Noca F. On the evaluation of time-dependent fluid-dynamic forces on bluff bodies[D]. PhD Thesis. Pasadena: California Institute of Technology, 1997.
[22]	Leal L G. Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes[M]. New York: Cambridge University Press, 2007.
[23]	Katz J, Plotkin A. Low-Speed Aerodynamics[M]. New York: Cambridge University Press, 2001.
[24]	易中, 吴萱, 周丽珍. 低速空气动力学[M]. 北京: 冶金工业出版社, 2005.(YI Zhong, WU Xuan, ZHOU Li-zhen. Low-Speed Aerodynamic[M]. Beijing: Metallurgical Industry Press, 2005.(in Chinese))
[25]	徐明友, 丁松滨. 飞行动力学[M]. 北京: 科学出版, 2003.(XU Ming-you, DING Song-bin. Flight Dynamics[M]. Beijing: Science Press, 2003.(in Chinese))
[26]	Prandtl L, Tietjens Q G. Fundamentals of Hydro- and Aeromechanics[M]. New York: Dover Publications, 1957.
[27]	Anderson J D. Fundamentals of Aerodynamics[M]. Boston: McGraw-Hill Higher Education, 2001: 112-114.
[28]	Batchelor G K. An Introduction to Fluid Dynamics[M]. Beijing: China Machine Press, 2004.