二维非定常涡量空气动力学模型初探
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摘要
涡动力学是研究非定常空气动力学的一个有力切入点。历史上诞生过许多不同的非定常涡动力学模型,在一定的前提条件和假设下,这些模型简化为涡系运动模型。由于理论研究和实际应用的需要,非定常空气动力学模型的研究变得尤为重要。
本文的目的就是要探索和建立二维非定常涡量空气动力学简化模型,使其能够模拟刚性翼型非定常运动的流场情况,并计算其气动力。本文在二维、单连通域、不可压、无粘的前提下,基于涡动力学理论,建立了非定常空气动力学简化模型,并对非定常空气动力学机理进行了探索性研究。
首先,本文忽略粘性扩散的影响,建立了二维非定常涡系模型,并应用其对平板和弧形板在空气中的自由落体运动做出模拟。模拟结果表明:当假设只有翼型的左右尖端处发生分离,并且平板和弧形板的流场左右对称的时候,在下降的初始阶段和后期,虚拟质量力和脱落涡作用力分别是气动力的主要贡献者;当远端涡以无穷远处来流的速度传导时,气动力只和靠近板的尾迹有关;板的弧度越大,运动一定时间后,板所受到的空气阻力越大,最后进行匀速运动的速度越小,其原因和新脱落的点涡运动速度有关;平板在自由落体的后期经历的气动力、速度和脱落涡的剧烈波动,源于尾迹的不规则运动。
其次,本文通过建立涡层在保形变换前后的守恒原则,设计了不需要迭代的保形变换方法,实现任意单独的光滑边界凸翼型与单位圆之间的保形变换。本文的保形变换方法在具体实现时,表现出效率高和精度高的优点,在变换多种翼型和计算若干简单形状的虚拟质量时,计算结果和理论值吻合良好。
最后,本文从涡层的角度重新推导了翼型虚拟质量计算公式。
Vorticity dynamics is a good break point when researching unsteady aerodynamics. In the history, there have been different kinds of unsteady vorticty aerodynamics model simplifying flow field into vortex system. In need of theoretical research and practical application, the study of unsteady aerodynamics model has become particularly important.
The purpose of this paper is to explore and establish a model for two-dimensional unsteady vorticity aerodynamics, so as to simulate the unsteady flow field around rigid wing sections, and to calculate aerodynamic force. Based on vorticity dynamics theory, a two-dimensional simplified model for unsteady aerodynamics in inviscous incompressible flow has been established in single-connected domain. And the mechanism of unsteady aerodynamic has been researched preliminarily.
First of all, the impact of diffusion has been neglected, and a two-dimensional unsteady vortex system model has been built. Simulating of free-falling motions of plates of different curvature in the air has been conducted. The result showed that: supposing that the separation took place at the left and the right edges only, and that the flow fields were symmetrical, during the preliminary stage and the later period of falling, virtual mass force and wake induced force was the major aerodynamic force respectively; when the far vortex moved at the same speed as the flow far away, the aerodynamic force totally came from wake near the plate; the greater curvature the plate was of, the smaller velocity would it move at finally, which had something to do with the velocity of the newly shedding vortex; in the later period of falling, the fluctuation of aerodynamic force, velocity and the vortex shedding were related with the irregularity of the wakes.
Secondly, based on the conservation of vortex sheet before and after conformal mapping,an iteration-free conformal mapping method was designed, with which single-airfoil could be transformed into an unit circle. This method has showed high efficiency and accuracy while transforming a variety of airfoils to an unit circle, and calculating virtual masses of several simple shapes.
Finally, in view of vortex sheet, the formula of virtual mass has been re-derived.
本文的目的就是要探索和建立二维非定常涡量空气动力学简化模型,使其能够模拟刚性翼型非定常运动的流场情况,并计算其气动力。本文在二维、单连通域、不可压、无粘的前提下,基于涡动力学理论,建立了非定常空气动力学简化模型,并对非定常空气动力学机理进行了探索性研究。
首先,本文忽略粘性扩散的影响,建立了二维非定常涡系模型,并应用其对平板和弧形板在空气中的自由落体运动做出模拟。模拟结果表明:当假设只有翼型的左右尖端处发生分离,并且平板和弧形板的流场左右对称的时候,在下降的初始阶段和后期,虚拟质量力和脱落涡作用力分别是气动力的主要贡献者;当远端涡以无穷远处来流的速度传导时,气动力只和靠近板的尾迹有关;板的弧度越大,运动一定时间后,板所受到的空气阻力越大,最后进行匀速运动的速度越小,其原因和新脱落的点涡运动速度有关;平板在自由落体的后期经历的气动力、速度和脱落涡的剧烈波动,源于尾迹的不规则运动。
其次,本文通过建立涡层在保形变换前后的守恒原则,设计了不需要迭代的保形变换方法,实现任意单独的光滑边界凸翼型与单位圆之间的保形变换。本文的保形变换方法在具体实现时,表现出效率高和精度高的优点,在变换多种翼型和计算若干简单形状的虚拟质量时,计算结果和理论值吻合良好。
最后,本文从涡层的角度重新推导了翼型虚拟质量计算公式。
Vorticity dynamics is a good break point when researching unsteady aerodynamics. In the history, there have been different kinds of unsteady vorticty aerodynamics model simplifying flow field into vortex system. In need of theoretical research and practical application, the study of unsteady aerodynamics model has become particularly important.
The purpose of this paper is to explore and establish a model for two-dimensional unsteady vorticity aerodynamics, so as to simulate the unsteady flow field around rigid wing sections, and to calculate aerodynamic force. Based on vorticity dynamics theory, a two-dimensional simplified model for unsteady aerodynamics in inviscous incompressible flow has been established in single-connected domain. And the mechanism of unsteady aerodynamic has been researched preliminarily.
First of all, the impact of diffusion has been neglected, and a two-dimensional unsteady vortex system model has been built. Simulating of free-falling motions of plates of different curvature in the air has been conducted. The result showed that: supposing that the separation took place at the left and the right edges only, and that the flow fields were symmetrical, during the preliminary stage and the later period of falling, virtual mass force and wake induced force was the major aerodynamic force respectively; when the far vortex moved at the same speed as the flow far away, the aerodynamic force totally came from wake near the plate; the greater curvature the plate was of, the smaller velocity would it move at finally, which had something to do with the velocity of the newly shedding vortex; in the later period of falling, the fluctuation of aerodynamic force, velocity and the vortex shedding were related with the irregularity of the wakes.
Secondly, based on the conservation of vortex sheet before and after conformal mapping,an iteration-free conformal mapping method was designed, with which single-airfoil could be transformed into an unit circle. This method has showed high efficiency and accuracy while transforming a variety of airfoils to an unit circle, and calculating virtual masses of several simple shapes.
Finally, in view of vortex sheet, the formula of virtual mass has been re-derived.
引文
[1]吴子牛等.空气动力学[M].北京:清华大学出版社, 2008,4.
[2] Wu J. C.. Elements of Vorticity Aerodynamics[M].北京:清华大学出版社, 2005,6.
[3] Sears,W.R.. Unsteady Motion of Airfoils With Boundary-Layer Separation[J]. AIAA J. Vol. 14, No. 2, Feb. 1976.
[4] Basu B. C. &Hancock G. J.. The Unsteady Motion of a Two-Dimensional Aerofoil in Incompressible Inviscid Flow[J]. J. Fluid Mech vol.87, 1987, 159-178.
[5] Giesing J. P.. Vorticity And Kutta Condition for Unsteady Multienergy Flows[J]. J. of Applied Mechanics, Vol.36, No.3, 1969.
[6] Poling D. R.. And Telionis D. P.. The Response of Airfoils to Periodic Distrubances-The Unsteady Potential Flow With Lift[J]. J. Aircraft Vol. 5, No. 2, 1986.
[7] Hsu A. T. And Wu, J. C.. Vortex Flow Model for the Blade-Vorter Interaction Problem [J]. AIAA J. Vol.26, No.5, 1988, Pp621-623.
[8] K. D. Jones & M. F. Platzer. Numerical Computation of Flapping-Wing Propulsion and Power Extraction[Meeting Paper]. AIAA, Jan. 1997, 6-9.
[9] Nowak, L. M.. Computational Investigations of a NACA 0012 Airfoil in Low Reynolds Number Flows[Master's Thesis]. Naval Postgraduate School, Monterey, CA, Sept. 1992.
[10] Ellington C.P., Leading-edge vortices in insect flight[J]. Nature, 1996, 384: 626-630.
[11]余永亮.昆虫前飞拍翼非定常空气动力学的理论模化研究[D]. 2004,6.
[12] Milne-Thomson. Theoretical Hydrodynamics[M]. London: The Macmeillan Press Ltd, 1979.
[13] Sedov L. I.. Two-Dimensional Problem in Hydrodynamics and Aerodynamics[M]. Interscience Publishers, 1965.
[14]刘丹,王晓亮,单雪雄.平流层飞艇的附加质量及其对飞艇运动的影响[J].计算机仿真, 2006, 23.
[15] Theodorsen T. and Garrick I. E.. General Potential Theory of Arbitrary Wing Sections[J]. NACA TR, 1933, 452.
[16] Von Karman T. and Trefftz E. Potential-stromung um gegebene Ttagflachenquerschnitte[J]. Zeitschrift fur Flugtechnische Moforluftsch, 1918, 9:111~116.
[17] James R. M.. A New Look at Two-Dimensional Incompressible Airfoil Theory[J]. MDC, 1971, J0918.
[18] Batchelor G. K.. An Introduction to Fluid Dynamics. Cambridge, 1967.
[19]莫叶.复变函数论[M].山东:山东科技出版社, 1980.
[20]潘锦珊.气体动力学基础[M].北京:国防工业出版社, 1989.
[21]吴望一.流体力学[M].北京:北京大学出版社, 1982.
[22]航空气动力手册[M].北京:国防工业出版社, 1990.
[23] Manoochehr M. Koochesfahani. Vortical Patterns in the Wake of an Oscillating Airfoil[J]. California Institute of Technology. AIAA JOURNAL VOL. 27, NO. 9, 1989
[2] Wu J. C.. Elements of Vorticity Aerodynamics[M].北京:清华大学出版社, 2005,6.
[3] Sears,W.R.. Unsteady Motion of Airfoils With Boundary-Layer Separation[J]. AIAA J. Vol. 14, No. 2, Feb. 1976.
[4] Basu B. C. &Hancock G. J.. The Unsteady Motion of a Two-Dimensional Aerofoil in Incompressible Inviscid Flow[J]. J. Fluid Mech vol.87, 1987, 159-178.
[5] Giesing J. P.. Vorticity And Kutta Condition for Unsteady Multienergy Flows[J]. J. of Applied Mechanics, Vol.36, No.3, 1969.
[6] Poling D. R.. And Telionis D. P.. The Response of Airfoils to Periodic Distrubances-The Unsteady Potential Flow With Lift[J]. J. Aircraft Vol. 5, No. 2, 1986.
[7] Hsu A. T. And Wu, J. C.. Vortex Flow Model for the Blade-Vorter Interaction Problem [J]. AIAA J. Vol.26, No.5, 1988, Pp621-623.
[8] K. D. Jones & M. F. Platzer. Numerical Computation of Flapping-Wing Propulsion and Power Extraction[Meeting Paper]. AIAA, Jan. 1997, 6-9.
[9] Nowak, L. M.. Computational Investigations of a NACA 0012 Airfoil in Low Reynolds Number Flows[Master's Thesis]. Naval Postgraduate School, Monterey, CA, Sept. 1992.
[10] Ellington C.P., Leading-edge vortices in insect flight[J]. Nature, 1996, 384: 626-630.
[11]余永亮.昆虫前飞拍翼非定常空气动力学的理论模化研究[D]. 2004,6.
[12] Milne-Thomson. Theoretical Hydrodynamics[M]. London: The Macmeillan Press Ltd, 1979.
[13] Sedov L. I.. Two-Dimensional Problem in Hydrodynamics and Aerodynamics[M]. Interscience Publishers, 1965.
[14]刘丹,王晓亮,单雪雄.平流层飞艇的附加质量及其对飞艇运动的影响[J].计算机仿真, 2006, 23.
[15] Theodorsen T. and Garrick I. E.. General Potential Theory of Arbitrary Wing Sections[J]. NACA TR, 1933, 452.
[16] Von Karman T. and Trefftz E. Potential-stromung um gegebene Ttagflachenquerschnitte[J]. Zeitschrift fur Flugtechnische Moforluftsch, 1918, 9:111~116.
[17] James R. M.. A New Look at Two-Dimensional Incompressible Airfoil Theory[J]. MDC, 1971, J0918.
[18] Batchelor G. K.. An Introduction to Fluid Dynamics. Cambridge, 1967.
[19]莫叶.复变函数论[M].山东:山东科技出版社, 1980.
[20]潘锦珊.气体动力学基础[M].北京:国防工业出版社, 1989.
[21]吴望一.流体力学[M].北京:北京大学出版社, 1982.
[22]航空气动力手册[M].北京:国防工业出版社, 1990.
[23] Manoochehr M. Koochesfahani. Vortical Patterns in the Wake of an Oscillating Airfoil[J]. California Institute of Technology. AIAA JOURNAL VOL. 27, NO. 9, 1989
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