波状游动物体的推进性能及优化
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摘要
水生动物具有高效率的游动特性,蕴涵了丰富的流体力学现象。对水生动物高效游动的研究,可加深对相关自然现象及其内在规律的认识,同时为研制新一代的水下航行器提供启示。波状摆动是水生动物普遍采用的一种推进方式。本文基于无粘势流理论的面元法计算了几种波状游动物体的推进性能,并采用逐步二次规划方法对物体的摆动方式进行了优化。具体的工作和结论分述如下:
(1)基于线化涡格法求解波动板的推进性能,发展了一套对摆动方式进行优化的方法。该方法增加摆动幅值约束以消除优化问题存在的奇性,采用逐步二次规划方法以避免传统Lagrange乘子法可能得到的鞍点。采用该方法,对波动板的摆动方式进行优化。结果表明,最优解都在幅值约束边界上获得;在前缘吸力最小值对应的频率附近,效率较大;当波数增加,该频率区域内极大效率增长较为明显,同时前缘吸力相应减小,使得前缘分离的风险减弱;0次幂和2次幂组合运动(OP02)的极大效率同0次幂和1次幂组合运动(OP01)的极大效率相近,两项组合运动的极大效率要小于三项(OP012)组合运动的极大效率;波数的增加,三维效应减弱,展弦比对力能参量的影响减弱。
(2)基于点涡的非线性面元法求解二维大振幅波动板推进性能,并利用上述方法对波动板摆动方式进行优化。结果表明,当幅值减小、频率减小或者波数增加时,非线性波动板结果同线化波动板结果接近,最优解在约束的边界上获得;幅值较大且频率较大时,非线性波动板解远离线化解,最优解在幅值约束的边界内;极大效率随着频率的增加而减小,随着波数的增加而增加。
(3)基于等强度源(汇)联合等强度涡的非线性面元法求解二维波动翼形的推进性能,并利用同样的方法对波动翼形的摆动方式进行优化。结果表明,当频率和幅值较小时,优化解取在幅值约束的边界,当频率和幅值较大时,优化解不在边界上,这同非线性波动板优化结果定性一致;频率的增加,使得极大效率逐渐减小,相应的前缘吸力增加;增加波数效果相反。
Many aquatic animals have developed its outstanding swimming performance,which contain abundant ?uid mechanical phenomena. The researches on the e?cientswimming of the aquatic animals can not only make us understand the related nat-ural phenomena and its intrinsic law better, but also provide the inspiration for thenew generation of man-made underwater vessels. Waving motion is widely adopted bythe aquatic animals for propulsion. The propulsive performance of several undulatoryswimming bodies are calculated by the panel method based on the in-viscid potentialtheory in this thesis. And the undulatory motion is optimized with the sequentialquadratic programming method. The results and conclusions are as follow:
(1) The propulsive performance of the waving plate is calculated by the linearvortex lattice method, and an optimization method for the undulatory motion is de-veloped. In this method, the motion amplitude constraint is added to the optimizationproblem in order to eliminate the singularity, and the sequential quadratic program-ming method is used in order to avoid the saddle point which might be obtained by thetraditional Lagrange multiplier method. With the method, the waving plate motion isoptimized. The results reveal that, the optimum solutions are obtained on the boundaryof the amplitude constraint. The e?ciency is high when frequency is in a small stretchabout the one where the leading edge suction force is a minimum. As wave-numberincreases, the e?ciency in this range increases rapidly, and the corresponding leadingedge suction force decreases which reduce the risk of leading edge stalling. For thesame amplitude constraint, the maximum e?ciency of motion with quadratically vary-ing amplitude where the linear term does not occur (OP02) is close to that with linearlyvarying amplitude (OP01), and either of them is less than the maximum e?ciency ofmotion with quadratically varying amplitude (OP012). As frequency increases, threedimensional e?ects decreases, i.e. the in?uences of aspect ratio on the hydrodynamicquantities decrease.
(2) Propulsive performance of two dimensional waving plate with large amplitudemotion is calculated by the nonlinear vortex lattice method based on point vortexelement, and the undulatory motion is optimized by the method above. The resultsreveal that, as amplitude decreases, frequency decrease or wave- number increases,the results of nonlinear vortex lattice method are close to that of linear one, and theoptimum solutions are obtained on the boundary of the amplitude constraint. Whenamplitude and frequency are large, the results are far away from the linear one, andthe optimum solutions are achieved in the interior of the boundary. The maximum efficiency decreases as frequency increase, and increases as wave-number increases.
(3) Propulsive performance of two dimensional waving foil calculated by the non-linear vortex lattice method based on constant strength source combined with constantstrength vortex, and the undulatory motion is optimized by the same optimizationmethod. The results show that the optimum solutions are obtained on the boundary ofthe amplitude constraint when frequency or amplitude are small. And they are not onthe boundary when frequency and amplitude are large. These results are qualitativelyconsistent with that of nonlinear waving plate. As frequency increases, the maximume?ciency decreases, the corresponding leading edge suction force increases. And thee?ect of wave-number is adverse.
(1)基于线化涡格法求解波动板的推进性能,发展了一套对摆动方式进行优化的方法。该方法增加摆动幅值约束以消除优化问题存在的奇性,采用逐步二次规划方法以避免传统Lagrange乘子法可能得到的鞍点。采用该方法,对波动板的摆动方式进行优化。结果表明,最优解都在幅值约束边界上获得;在前缘吸力最小值对应的频率附近,效率较大;当波数增加,该频率区域内极大效率增长较为明显,同时前缘吸力相应减小,使得前缘分离的风险减弱;0次幂和2次幂组合运动(OP02)的极大效率同0次幂和1次幂组合运动(OP01)的极大效率相近,两项组合运动的极大效率要小于三项(OP012)组合运动的极大效率;波数的增加,三维效应减弱,展弦比对力能参量的影响减弱。
(2)基于点涡的非线性面元法求解二维大振幅波动板推进性能,并利用上述方法对波动板摆动方式进行优化。结果表明,当幅值减小、频率减小或者波数增加时,非线性波动板结果同线化波动板结果接近,最优解在约束的边界上获得;幅值较大且频率较大时,非线性波动板解远离线化解,最优解在幅值约束的边界内;极大效率随着频率的增加而减小,随着波数的增加而增加。
(3)基于等强度源(汇)联合等强度涡的非线性面元法求解二维波动翼形的推进性能,并利用同样的方法对波动翼形的摆动方式进行优化。结果表明,当频率和幅值较小时,优化解取在幅值约束的边界,当频率和幅值较大时,优化解不在边界上,这同非线性波动板优化结果定性一致;频率的增加,使得极大效率逐渐减小,相应的前缘吸力增加;增加波数效果相反。
Many aquatic animals have developed its outstanding swimming performance,which contain abundant ?uid mechanical phenomena. The researches on the e?cientswimming of the aquatic animals can not only make us understand the related nat-ural phenomena and its intrinsic law better, but also provide the inspiration for thenew generation of man-made underwater vessels. Waving motion is widely adopted bythe aquatic animals for propulsion. The propulsive performance of several undulatoryswimming bodies are calculated by the panel method based on the in-viscid potentialtheory in this thesis. And the undulatory motion is optimized with the sequentialquadratic programming method. The results and conclusions are as follow:
(1) The propulsive performance of the waving plate is calculated by the linearvortex lattice method, and an optimization method for the undulatory motion is de-veloped. In this method, the motion amplitude constraint is added to the optimizationproblem in order to eliminate the singularity, and the sequential quadratic program-ming method is used in order to avoid the saddle point which might be obtained by thetraditional Lagrange multiplier method. With the method, the waving plate motion isoptimized. The results reveal that, the optimum solutions are obtained on the boundaryof the amplitude constraint. The e?ciency is high when frequency is in a small stretchabout the one where the leading edge suction force is a minimum. As wave-numberincreases, the e?ciency in this range increases rapidly, and the corresponding leadingedge suction force decreases which reduce the risk of leading edge stalling. For thesame amplitude constraint, the maximum e?ciency of motion with quadratically vary-ing amplitude where the linear term does not occur (OP02) is close to that with linearlyvarying amplitude (OP01), and either of them is less than the maximum e?ciency ofmotion with quadratically varying amplitude (OP012). As frequency increases, threedimensional e?ects decreases, i.e. the in?uences of aspect ratio on the hydrodynamicquantities decrease.
(2) Propulsive performance of two dimensional waving plate with large amplitudemotion is calculated by the nonlinear vortex lattice method based on point vortexelement, and the undulatory motion is optimized by the method above. The resultsreveal that, as amplitude decreases, frequency decrease or wave- number increases,the results of nonlinear vortex lattice method are close to that of linear one, and theoptimum solutions are obtained on the boundary of the amplitude constraint. Whenamplitude and frequency are large, the results are far away from the linear one, andthe optimum solutions are achieved in the interior of the boundary. The maximum efficiency decreases as frequency increase, and increases as wave-number increases.
(3) Propulsive performance of two dimensional waving foil calculated by the non-linear vortex lattice method based on constant strength source combined with constantstrength vortex, and the undulatory motion is optimized by the same optimizationmethod. The results show that the optimum solutions are obtained on the boundary ofthe amplitude constraint when frequency or amplitude are small. And they are not onthe boundary when frequency and amplitude are large. These results are qualitativelyconsistent with that of nonlinear waving plate. As frequency increases, the maximume?ciency decreases, the corresponding leading edge suction force increases. And thee?ect of wave-number is adverse.
引文
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