大攻角细长旋成体绕流的稳定性
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摘要
现代飞行器在做大攻角机动时常会由于前体非对称涡的出现而受到较大的侧向力和偏航力矩,研究前体非对称涡的产生机理和发展规律具有重要的学术意义和工程价值。本文通过对大攻角细长尖拱柱旋成体模型非对称涡流的数值模拟和对流场的整体稳定性、空间稳定性分析,对此问题进行了研究,目的是对非对称流动的特征和机理有更深的理解,从而对前体涡的的控制有所助益。
首先,基于一般曲线坐标系内的有限差分法发展了一套直接数值模拟的并行程序;为了进行三维整体稳定性分析,还发展了一套基于可压缩有限差分法和隐式重启Arnoldi方法的三维整体不稳定性分析方法;此外还探讨了通过对扰动场的分析研究扰动沿空间的发展规律的方法。
通过直接数值模拟,考察了不同扰动强度和扰动周向角下的流场非对称特征及相应的截面侧向力沿细长体轴向的发展规律。结果表明,在大攻角(如50°)下,靠近细长体头部处的截面侧向力系数随扰动周向角是连续变化的,而随着轴向距离的增加,这种变化曲线逐渐趋于方波的形式,且扰动越强,开始出现方波波形的截面越靠近头部。计算中也发现,Reynolds数越小,流场对头部扰动的感受性越弱,体现在流场的非对称程度变小:而侧向力随扰动周向角的变化也随Reynolds数的减小,由双周期方波变为单周期方波,最后变为单周期连续变化。
对不加扰动得到的对称的三维基本流所作的整体稳定性分析表明,非对称性的产生不是整体不稳定的结果。在实验中出现较大侧向力的攻角范围内(40°-50°),较小Reynolds数下,对称流场是整体稳定的;较大Reynolds数下,对称流场是整体不稳定的,但不稳定的特征模态不会引发流场的显著不对称。所得到的占优特征模态中,高频模态代表分离剪切层的振荡;低频模态代表主涡的涡核颤动。这两类非定常模态都在实验中有所体现。非定常直接数值模拟的结果也与整体稳定性分析的结果一致。
通过对扰动场的分析发现,扰动能量沿轴向的发展过程中,在经过起始增长区后,会进入指数增长区,最后进入非线性饱和区。由指数增长区可以得到空间增长率,且此空间增长率不随扰动强度和周向角而变化,而是由基本流的参数决定:攻角越大,空间增长率也越大;在所考虑的层流分离Reynolds数范围内,Reynolds数对空间增长率影响很小。扰动能量的非线性饱和对应着双稳态方波现象的出现。采用脉冲激励的Van der pol方程可以很好地模拟扰动量沿轴向的发展过程,而且可以解释扰动能量的指数增长现象。
Modern aircraft often endure large side force and yawing moment when performing maneuver flight at large angle of attack because of the emergency of asymmetric forebody vortex.The investigations of the formation mechanism and developing roles of the asymmetric forebody vortex flow have great importance in both academic field and engineering application areas.In this dissertation,these issues are explored by numerical simulation of the asymmetric vortex flow around a slender ogive-cylinder body and the global and spatial stability analysis of the flow field.This study aims at better understanding of the character and mechanism of the asymmetric flow field,to contribute to the control of forebody asymmetric vortex.
A parallel direct numerical simulation program has been developed,based on a finite difference method in generalized curvilinear coordinate;a three-dimensional global stability analysis method has been developed using a finite difference method for compressible flow and implicitly restarted Arnoldi method;in addition,the analysis method to investigate the spatial evolution of perturbation based on analysis of disturbance field has been discussed.
The numerical simulations in this dissertation mainly intend to investigate the asymmetric characters and the corresponding development of sectional side force along the body for different strength and circumferential angle of the disturbance.The results show that,at large angle of attack(typically 50°),the sectional side force varies continuously with the circumferential angle of the disturbance;this variation tends toward a square-wave form further downstream.With the increment of the strength of disturbance,the section where the square-wave form variation emerges gets closer to the tip.It is also found that at lower Reynolds number,the flow field is less sensitive to tip disturbance,and the asymmetry decreases;the variation of side force with the circumferential angle of disturbance turns from double periodic square-wave form to single periodic square-wave form,and at last the variation turns to be single periodic and continuous.
The global stability analysis for the symmetric three-dimensional basic flow indicates that,the asymmetry does not caused by a global instability mechanism.At the angle of attack 40°-50°(when large side force was observed in experiments),for small Reynolds number,the symmetric flow field is globally stable;for larger Reynolds number, the symmetric flow field turns to be globally unstable,but the unstable eigenvectors won't lead to large asymmetry and side force.There are two kinds of dominant eigen- vectors found:the high-frequency ones show the result of shear-layer unsteadiness;the low-frequency ones represent the fluctuation of the main vortex cores.The effects of both kinds were found in experiments,and the unsteady numerical simulation results confirm to the global stability analysis well.
The analysis of disturbance field shows that after an initial growth regime,there is an exponential growth regime of the disturbance energy along the body,followed by nonlinear growth regimes.The linear spatial growth rate can be obtained from the exponential growth regime.The growth rate is independent to the strength and circumferential angle of the disturbance,and is determined by the parameters of the basic flow:it gets larger with the angle of attack increases,and is insensitive to Reynolds number at the Reynolds number range under consideration.The nonlinear saturation of the disturbance energy is corresponding to the emergency of bistable phenomenon.The Van der pol equation under impulse excitation can be used to simulate the development of perturbation along the body,and it can also explain the exponential growth of the disturbance energy.
首先,基于一般曲线坐标系内的有限差分法发展了一套直接数值模拟的并行程序;为了进行三维整体稳定性分析,还发展了一套基于可压缩有限差分法和隐式重启Arnoldi方法的三维整体不稳定性分析方法;此外还探讨了通过对扰动场的分析研究扰动沿空间的发展规律的方法。
通过直接数值模拟,考察了不同扰动强度和扰动周向角下的流场非对称特征及相应的截面侧向力沿细长体轴向的发展规律。结果表明,在大攻角(如50°)下,靠近细长体头部处的截面侧向力系数随扰动周向角是连续变化的,而随着轴向距离的增加,这种变化曲线逐渐趋于方波的形式,且扰动越强,开始出现方波波形的截面越靠近头部。计算中也发现,Reynolds数越小,流场对头部扰动的感受性越弱,体现在流场的非对称程度变小:而侧向力随扰动周向角的变化也随Reynolds数的减小,由双周期方波变为单周期方波,最后变为单周期连续变化。
对不加扰动得到的对称的三维基本流所作的整体稳定性分析表明,非对称性的产生不是整体不稳定的结果。在实验中出现较大侧向力的攻角范围内(40°-50°),较小Reynolds数下,对称流场是整体稳定的;较大Reynolds数下,对称流场是整体不稳定的,但不稳定的特征模态不会引发流场的显著不对称。所得到的占优特征模态中,高频模态代表分离剪切层的振荡;低频模态代表主涡的涡核颤动。这两类非定常模态都在实验中有所体现。非定常直接数值模拟的结果也与整体稳定性分析的结果一致。
通过对扰动场的分析发现,扰动能量沿轴向的发展过程中,在经过起始增长区后,会进入指数增长区,最后进入非线性饱和区。由指数增长区可以得到空间增长率,且此空间增长率不随扰动强度和周向角而变化,而是由基本流的参数决定:攻角越大,空间增长率也越大;在所考虑的层流分离Reynolds数范围内,Reynolds数对空间增长率影响很小。扰动能量的非线性饱和对应着双稳态方波现象的出现。采用脉冲激励的Van der pol方程可以很好地模拟扰动量沿轴向的发展过程,而且可以解释扰动能量的指数增长现象。
Modern aircraft often endure large side force and yawing moment when performing maneuver flight at large angle of attack because of the emergency of asymmetric forebody vortex.The investigations of the formation mechanism and developing roles of the asymmetric forebody vortex flow have great importance in both academic field and engineering application areas.In this dissertation,these issues are explored by numerical simulation of the asymmetric vortex flow around a slender ogive-cylinder body and the global and spatial stability analysis of the flow field.This study aims at better understanding of the character and mechanism of the asymmetric flow field,to contribute to the control of forebody asymmetric vortex.
A parallel direct numerical simulation program has been developed,based on a finite difference method in generalized curvilinear coordinate;a three-dimensional global stability analysis method has been developed using a finite difference method for compressible flow and implicitly restarted Arnoldi method;in addition,the analysis method to investigate the spatial evolution of perturbation based on analysis of disturbance field has been discussed.
The numerical simulations in this dissertation mainly intend to investigate the asymmetric characters and the corresponding development of sectional side force along the body for different strength and circumferential angle of the disturbance.The results show that,at large angle of attack(typically 50°),the sectional side force varies continuously with the circumferential angle of the disturbance;this variation tends toward a square-wave form further downstream.With the increment of the strength of disturbance,the section where the square-wave form variation emerges gets closer to the tip.It is also found that at lower Reynolds number,the flow field is less sensitive to tip disturbance,and the asymmetry decreases;the variation of side force with the circumferential angle of disturbance turns from double periodic square-wave form to single periodic square-wave form,and at last the variation turns to be single periodic and continuous.
The global stability analysis for the symmetric three-dimensional basic flow indicates that,the asymmetry does not caused by a global instability mechanism.At the angle of attack 40°-50°(when large side force was observed in experiments),for small Reynolds number,the symmetric flow field is globally stable;for larger Reynolds number, the symmetric flow field turns to be globally unstable,but the unstable eigenvectors won't lead to large asymmetry and side force.There are two kinds of dominant eigen- vectors found:the high-frequency ones show the result of shear-layer unsteadiness;the low-frequency ones represent the fluctuation of the main vortex cores.The effects of both kinds were found in experiments,and the unsteady numerical simulation results confirm to the global stability analysis well.
The analysis of disturbance field shows that after an initial growth regime,there is an exponential growth regime of the disturbance energy along the body,followed by nonlinear growth regimes.The linear spatial growth rate can be obtained from the exponential growth regime.The growth rate is independent to the strength and circumferential angle of the disturbance,and is determined by the parameters of the basic flow:it gets larger with the angle of attack increases,and is insensitive to Reynolds number at the Reynolds number range under consideration.The nonlinear saturation of the disturbance energy is corresponding to the emergency of bistable phenomenon.The Van der pol equation under impulse excitation can be used to simulate the development of perturbation along the body,and it can also explain the exponential growth of the disturbance energy.
引文
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