柔性体与流体耦合运动的数值模拟和实验研究
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摘要
单个和多个柔性体在运动流体中的流固耦合问题广泛存在于生物运动和人类生产、生活中。这一类流固耦合问题的研究同时涉及到流体力学、材料力学、结构动力学、计算力学和实验力学等学科的知识,具有较大的研究难度。对这些问题的深入研究可以帮助提炼成熟有效的流固耦合数值、理论研究方法,积累实验数据,为人类进一步认识自然界提供理论基础,为工程和国防应用提供技术支持。
本文开发了一种计算“柔性体-流体”耦合运动的二维数值模拟算法,并利用该算法对单个及多个柔性体在均匀来流和卡门涡街中的运动进行了数值模拟计算,分析了各控制参数对柔性体运动及力学性能的影响机制。此外,本文还利用旗帜吹风和丝线摆动实验对计算结果进行了比较验证。最后,本文以两串行排列圆柱为研究对象对低雷诺数下多个钝体绕流的流场结构进行了实验观察和分析。
本文主要内容和结论包括：
1.单个柔性体在均匀来流中的流固耦合运动研究。利用流固耦合程序模拟了均匀来流中悬臂梁的运动,考察了流体诱导的柔性体摆动频率、振幅和受力情况随来流速度的变化规律,得出了不同密度比柔性体的临界稳定速度。在低速风洞中进行了旗帜吹风实验,验证了数值结果的正确性。
2.均匀来流中相同长度并行排列柔性体耦合运动的研究。对运动流体中两个并行排列柔性体的耦合运动进行了数值模拟和实验研究,分析了排列间距对临界稳定速度,运动耦合模态,摆动频率、振幅,尾涡结构和柔性体受力情况的影响。研究结果表明,两并排柔性体在流体中的稳定临界速度随排列间距的增加先减小后增加。速度超过临界速度以后,两柔性体可能呈现同向摆动、反向摆动、过渡状态和解耦这几种运动耦合模式。相同间距下,流速较低时两旗帜以高于单个旗帜的频率反向摆动,流速较高时则以较低的频率同向摆动。相同流速下,间距较小时两旗帜同向摆动,间距较大时反向摆动。值得指出的是,介于同向和反向摆动模态之间存在一个过渡状态,实验和计算都证实在过渡状态柔性体的运动频谱中同时含有两个主频率。
3.不同排列方式柔性体耦合运动的数值模拟。通过对不同方式排列的两相同柔性体,长短不一的柔性体,柔性体和平板等组合的耦合运动的数值模拟,本文考察了各种排列方式下间距对物体耦合运动模式和受力情况的影响机制。计算结果表明,近距离串行排列时上游丝线的摆动振幅和所受阻力都减小,下游丝线受到的阻力则明显增大。近距离交错排列时,两个柔性体的摆动振幅和阻力都减小,这可能是鱼群游动采用菱形排列方式的一个原因。将短柔性体和平板摆放在柔性体侧边和下游时,也会抑制柔性体的摆动幅度。
4.柔性体与圆柱的耦合作用。在肥皂膜水洞中进行了丝线在圆柱前后的流动显示实验,并根据实验结果利用面元法计算了丝线在卡门涡街中受到的阻力系数。实验结果表明丝线在圆柱上游时摆动振幅变大,频率变低；在圆柱下游卡门涡街中时,则以圆柱的脱涡频率同步摆动。相关数值计算结果表明丝线具有从卡门涡街中汲取能量,获得推力的能力。以不同相位差在卡门涡街中运动时丝线受到的阻力系数有明显变化。当丝线向着涡心运动时受到推力作用,避开涡心穿行时则仍然受到平均阻力的作用。
5.串行排列圆柱的低Re数实验研究。在水平肥皂膜水洞中观察了串行排列圆柱周围的流场结构。实验结果显示随排列间距逐渐增大,流场结构依次呈现单钝体(SBB),剪切层再附(SLR),同步脱涡(SVS)和二次涡形成(SVF)模态。本文首次报道了SVF模态以及在尾迹中形成的二次涡,并通过数值计算分析了SVF模态形成的机理。实验观察和数值模拟结果都表明,随排列间距增大或减小各模态之间的转换存在回滞现象。
The interactions between moving fluid and one or multiply deformable bodies are commonly exhibited in animal kinematics, people's everyday life and various industry applications. This kind of fluid-flexible-structure coupling phenomena proves to be research challenge by involving many disciplines, including fluid dynamics, material mechanics, structural dynamics, computational mechanics and experimental mechanics. Studying these problems and collecting experimental data help researchers develop practical and efficient fluid-solid coupling numerical and theoretical methods. The research on the coupling kinematics of one or multiply flexible bodies in fluid flow can not only make us understand the nature better, but also provide technical supports for engineering application and national defense.
In this dissertation, we developed a two-dimensional numerical method to study flexible-structure-fluid coupling problems. Using this method, we studied the flow-induced flapping of single and multiple deformable bodies and analyzed the dependence of the coupling mode and mechanical properties on each governing parameter. In addition, this paper verified the numerical results through the flapping experiments of flags and filaments. Finally, we studied the flow field structure around two tandem cylinders at low Reynolds number both experimentally and numerically.
The main content and conclusions are as follow:
1. Fluid-solid coupling flapping of a flexible body in a uniform flow.
We simulated the kinematics of a cantilever beam in a moving flow using our in-house program, and investigated the flow-induced flapping frequency, amplitude and forces with different parameters. The critical velocities for different density ratios were calculated. Furthermore, we verified the accuracy of our numerical results through a flag flapping experiment in a low speed wind tunnel.
2. The coupling flapping of two side by side identical flexible bodies in a uniform flow.
We investigated the coupling flapping of two side by side flexible bodies in a moving flow numerically and experimentally, and summarized the affect of the arranging distance on the coupling mode, flapping frequency and amplitude, wake structure and forces of the two objects. The results revealed that, with the increasing distance, the critical velocities for two side by side flexible bodies would decrease first and then increase to the same value as in the case of a single flexible body in flow. There are four different coupling modes:in phase flapping, out of phase flapping, transition and decoupled modes. For a same distance, when the flow speed is relatively low the two flexible bodies flap in phase with a high frequency. Oppositely, they flap out of phase with a much lower frequency when the flow speed is high. Under fixed flow velocity condition, the two flexible bodies flap in phase when the distance is small and out of phase when the distance is large. One thing worth of mentioning is that, both our numerical and experimental results proved that a transition state exists between the in phase and out of phase modes, in which the flapping of the flexible bodies involves two frequencies.
3. Numerical study on the coupling of two bodies in other arrangements.
By simulating the interactions of two identical flexible bodies, two different flexible bodies, a flexible body and a rigid plate arranged in different manners, this paper studied the influencing mechanism of the distance on the coupling mode and drag coefficients. Our numerical results revealed that when two flexible bodies are set in line with a small distance, the flapping amplitude and the drag coefficient of the upstream body are decreased and those of the downstream body are increased obviously. The drags on both bodies decrease when two flexible bodies are closely stagger positioned. This might be a reason for fish schooling in diamond arrangement. We can also depress the body flapping by setting a short flexible body or a rigid plate either along the side or at the near downstream.
4. Flapping of a filament in the bow wake and in the downstream of a cylinder.
The experiments of a filament flapping in front or behind a cylinder were conducted in a flow film tunnel. Based on the experimental kinematic information we calculated the forces of the filament in uniform flow and in a Karman vortex street. The experimental results showed that, in the bow wake in front of a cylinder the filament will flap with larger amplitude and lower frequency than those in a free stream. In the Karman vortex street behind the cylinder, the filament flaps synchronously with the vortices. Numerical results revealed that the filament has the ability to derive energy and achieve thrust from the Karman vortex street. The drag coefficient depends strongly on the phase relation between the filament movement and the Karman vortex street. When the filament moves toward the vortices centers, it suffers a thrust. When it slaloms between vortices, a drag is presented.
5. Experimental investigation on two tandem cylinders at low Reynolds number.
We conducted experiments on two tandem cylinders in a horizontal flow film tunnel and investigated the single bluff-body (SBB), shear layer reattachment (SLR), synchronization of vortex shedding (SVS) and second vortex formation (SVF) modes with increasing distance. The SVF mode is first presented in this research and the formation of the secondary vortex in this mode was analyzed numerically. We also confirmed.the mode transitions hysteresis when the distance is increasing or decreasing continuously.
本文开发了一种计算“柔性体-流体”耦合运动的二维数值模拟算法,并利用该算法对单个及多个柔性体在均匀来流和卡门涡街中的运动进行了数值模拟计算,分析了各控制参数对柔性体运动及力学性能的影响机制。此外,本文还利用旗帜吹风和丝线摆动实验对计算结果进行了比较验证。最后,本文以两串行排列圆柱为研究对象对低雷诺数下多个钝体绕流的流场结构进行了实验观察和分析。
本文主要内容和结论包括：
1.单个柔性体在均匀来流中的流固耦合运动研究。利用流固耦合程序模拟了均匀来流中悬臂梁的运动,考察了流体诱导的柔性体摆动频率、振幅和受力情况随来流速度的变化规律,得出了不同密度比柔性体的临界稳定速度。在低速风洞中进行了旗帜吹风实验,验证了数值结果的正确性。
2.均匀来流中相同长度并行排列柔性体耦合运动的研究。对运动流体中两个并行排列柔性体的耦合运动进行了数值模拟和实验研究,分析了排列间距对临界稳定速度,运动耦合模态,摆动频率、振幅,尾涡结构和柔性体受力情况的影响。研究结果表明,两并排柔性体在流体中的稳定临界速度随排列间距的增加先减小后增加。速度超过临界速度以后,两柔性体可能呈现同向摆动、反向摆动、过渡状态和解耦这几种运动耦合模式。相同间距下,流速较低时两旗帜以高于单个旗帜的频率反向摆动,流速较高时则以较低的频率同向摆动。相同流速下,间距较小时两旗帜同向摆动,间距较大时反向摆动。值得指出的是,介于同向和反向摆动模态之间存在一个过渡状态,实验和计算都证实在过渡状态柔性体的运动频谱中同时含有两个主频率。
3.不同排列方式柔性体耦合运动的数值模拟。通过对不同方式排列的两相同柔性体,长短不一的柔性体,柔性体和平板等组合的耦合运动的数值模拟,本文考察了各种排列方式下间距对物体耦合运动模式和受力情况的影响机制。计算结果表明,近距离串行排列时上游丝线的摆动振幅和所受阻力都减小,下游丝线受到的阻力则明显增大。近距离交错排列时,两个柔性体的摆动振幅和阻力都减小,这可能是鱼群游动采用菱形排列方式的一个原因。将短柔性体和平板摆放在柔性体侧边和下游时,也会抑制柔性体的摆动幅度。
4.柔性体与圆柱的耦合作用。在肥皂膜水洞中进行了丝线在圆柱前后的流动显示实验,并根据实验结果利用面元法计算了丝线在卡门涡街中受到的阻力系数。实验结果表明丝线在圆柱上游时摆动振幅变大,频率变低；在圆柱下游卡门涡街中时,则以圆柱的脱涡频率同步摆动。相关数值计算结果表明丝线具有从卡门涡街中汲取能量,获得推力的能力。以不同相位差在卡门涡街中运动时丝线受到的阻力系数有明显变化。当丝线向着涡心运动时受到推力作用,避开涡心穿行时则仍然受到平均阻力的作用。
5.串行排列圆柱的低Re数实验研究。在水平肥皂膜水洞中观察了串行排列圆柱周围的流场结构。实验结果显示随排列间距逐渐增大,流场结构依次呈现单钝体(SBB),剪切层再附(SLR),同步脱涡(SVS)和二次涡形成(SVF)模态。本文首次报道了SVF模态以及在尾迹中形成的二次涡,并通过数值计算分析了SVF模态形成的机理。实验观察和数值模拟结果都表明,随排列间距增大或减小各模态之间的转换存在回滞现象。
The interactions between moving fluid and one or multiply deformable bodies are commonly exhibited in animal kinematics, people's everyday life and various industry applications. This kind of fluid-flexible-structure coupling phenomena proves to be research challenge by involving many disciplines, including fluid dynamics, material mechanics, structural dynamics, computational mechanics and experimental mechanics. Studying these problems and collecting experimental data help researchers develop practical and efficient fluid-solid coupling numerical and theoretical methods. The research on the coupling kinematics of one or multiply flexible bodies in fluid flow can not only make us understand the nature better, but also provide technical supports for engineering application and national defense.
In this dissertation, we developed a two-dimensional numerical method to study flexible-structure-fluid coupling problems. Using this method, we studied the flow-induced flapping of single and multiple deformable bodies and analyzed the dependence of the coupling mode and mechanical properties on each governing parameter. In addition, this paper verified the numerical results through the flapping experiments of flags and filaments. Finally, we studied the flow field structure around two tandem cylinders at low Reynolds number both experimentally and numerically.
The main content and conclusions are as follow:
1. Fluid-solid coupling flapping of a flexible body in a uniform flow.
We simulated the kinematics of a cantilever beam in a moving flow using our in-house program, and investigated the flow-induced flapping frequency, amplitude and forces with different parameters. The critical velocities for different density ratios were calculated. Furthermore, we verified the accuracy of our numerical results through a flag flapping experiment in a low speed wind tunnel.
2. The coupling flapping of two side by side identical flexible bodies in a uniform flow.
We investigated the coupling flapping of two side by side flexible bodies in a moving flow numerically and experimentally, and summarized the affect of the arranging distance on the coupling mode, flapping frequency and amplitude, wake structure and forces of the two objects. The results revealed that, with the increasing distance, the critical velocities for two side by side flexible bodies would decrease first and then increase to the same value as in the case of a single flexible body in flow. There are four different coupling modes:in phase flapping, out of phase flapping, transition and decoupled modes. For a same distance, when the flow speed is relatively low the two flexible bodies flap in phase with a high frequency. Oppositely, they flap out of phase with a much lower frequency when the flow speed is high. Under fixed flow velocity condition, the two flexible bodies flap in phase when the distance is small and out of phase when the distance is large. One thing worth of mentioning is that, both our numerical and experimental results proved that a transition state exists between the in phase and out of phase modes, in which the flapping of the flexible bodies involves two frequencies.
3. Numerical study on the coupling of two bodies in other arrangements.
By simulating the interactions of two identical flexible bodies, two different flexible bodies, a flexible body and a rigid plate arranged in different manners, this paper studied the influencing mechanism of the distance on the coupling mode and drag coefficients. Our numerical results revealed that when two flexible bodies are set in line with a small distance, the flapping amplitude and the drag coefficient of the upstream body are decreased and those of the downstream body are increased obviously. The drags on both bodies decrease when two flexible bodies are closely stagger positioned. This might be a reason for fish schooling in diamond arrangement. We can also depress the body flapping by setting a short flexible body or a rigid plate either along the side or at the near downstream.
4. Flapping of a filament in the bow wake and in the downstream of a cylinder.
The experiments of a filament flapping in front or behind a cylinder were conducted in a flow film tunnel. Based on the experimental kinematic information we calculated the forces of the filament in uniform flow and in a Karman vortex street. The experimental results showed that, in the bow wake in front of a cylinder the filament will flap with larger amplitude and lower frequency than those in a free stream. In the Karman vortex street behind the cylinder, the filament flaps synchronously with the vortices. Numerical results revealed that the filament has the ability to derive energy and achieve thrust from the Karman vortex street. The drag coefficient depends strongly on the phase relation between the filament movement and the Karman vortex street. When the filament moves toward the vortices centers, it suffers a thrust. When it slaloms between vortices, a drag is presented.
5. Experimental investigation on two tandem cylinders at low Reynolds number.
We conducted experiments on two tandem cylinders in a horizontal flow film tunnel and investigated the single bluff-body (SBB), shear layer reattachment (SLR), synchronization of vortex shedding (SVS) and second vortex formation (SVF) modes with increasing distance. The SVF mode is first presented in this research and the formation of the secondary vortex in this mode was analyzed numerically. We also confirmed.the mode transitions hysteresis when the distance is increasing or decreasing continuously.
引文
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