基于近壁相干结构的湍流减阻主动控制研究
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摘要
湍流减阻一直是流体力学研究的热点问题。鉴于近壁相干结构和湍流高摩擦阻力的密切关系，通过干扰近壁相干结构的演化来达到减阻目的的主动控制方法，因其适用范围广、减阻率大和减阻效率高等特点成为国际湍流研究的前沿课题。近年来，MEMS技术的发展为主动控制的实现提供了可能性，而MEMS系统的设计必须以对减阻机理和控制方案的深刻认识为前提。本文利用槽道湍流的直接数值模拟，对基于近壁相干结构的湍流减阻机理和控制方案进行了研究，主要工作和成果如下：
（1）从雷诺应力输运和脉动拟涡能输运的角度研究了反向控制抑制湍流的动力学机理。在雷诺应力输运中，压力相关项率先打破法向雷诺应力的输运平衡，并在湍流抑制中起着非常关键的作用。在脉动拟涡能输运中，涡量的拉伸被有效抑制，法向脉动涡量为脉动拟涡能的减小做出了重要贡献。
（2）系统地研究了壁面可测信号（流向脉动摩擦应力τ wx、展向脉动摩擦应力τ wz和脉动压力p~_w）和近壁区流向涡的内在关系。发现τ wx与下游流向涡密切相关，而τ wz则反映了正上方流向涡对壁面的影响。 p~_w和近壁区流向涡的关系较为复杂：在探测点上游，高压区（p~'_w>0）对应着流体的下扫，低压区（p ' w<0）则对应着流体的上抛；在探测点，近壁区流向涡和正下方低压区存在强相关性；而在下游，壁面压力和上抛及下扫的对应关系与上游相反，这一发现弥补了现有认识的不足。考虑到主动控制和外界对流场的干扰，通过引入随机扰动对上述关系的鲁棒性进行了考察。在随机干扰下，τ wx和近壁流向涡的关系被打破，而p~_w和τ wz仍然可以可靠地反映近壁区流向涡，该发现可用于主动控制输入信号的选取。
（3）提出了两种基于壁面局部信号τ wz和p~_w的湍流减阻主动控制新方案，并利用直接数值模拟，对“壁面吹吸”和“智能蒙皮”这两种典型致动方式下的减阻效果进行了考核。以τ wz为输入信号的控制方案，在“壁面吹吸”和“智能蒙皮”的致动方式下，分别获得了16%和5%的减阻率，以p~_w为输入信号的控制方案分别获得了11%和2%的减阻率。
总之，本文工作加深了对湍流减阻机理的认识，揭示了壁面可测信号和近壁区流向涡的关系，提出了两种基于壁面局部可测信号的主动控制新方案，为实现基于相干结构的湍流减阻主动控制提供了有价值的思路和方法。
Turbulent drag reduction is always a hot topic in fluid mechanics. Due to the closerelationship between the near-wall coherent structures and high skin-friction in wallturbulence, the active drag-reduction control has been developed by instantaneouslyinterfering with the evolution of near-wall coherent structures. Active control ofturbulent coherent structures is an attractive research issue owing to its robustperformance, great potential and high efficiency. In recent years, the development of theMEMS technology provides us the possibility for the real practical application of activeturbulence control. As a prerequisite for the design of active control systems based onMEMS, the mechanism and control schemes for drag reduction should be deeplyunderstood. In this thesis, the mechanism and control schemes for drag reduction basedon the manipulation of the near-wall coherent structures are studied via direct numericalsimulation (DNS) of turbulent channel flow. The main work and results are as thefollowing:
(1) The dynamical mechanism of turbulence suppression is explored via thetransient response of Reynolds stress and enstrophy transport to the opposition control.It is found that the balance of the Reynolds stress in the wall normal direction is firstbroken by the pressure-related term which plays a key role in the subsequent globalsuppression of turbulence. In the enstrophy transport, the stretching of the vorticity isattenuated and the wall normal vorticity makes a significant contribution to thesuppression of enstrophy.
(2) The relationship between the measurable flow quantities (streamwise andspanwise wall shear stressτ wx,τ wzand wall fluctuating pressure p~_w) and thenear-wall streamwise vortices is studied using the DNS databases of fully developedturbulent channel flow. It is found that all the three wall quantitiesτ wx, p~_wandτ wzareclosely related with the near-wall streamwise vortices.τ wxcorresponds to the sweep andejection motions induced by the downstream streamwise vortices.τ wzis the spanwisefootprint of the above vortical structures. Compared with the wall shear stress, thecorrelation between p~_wand the near-wall streamwise vortices is more complex. In theupstream of the detecting point, the high pressure region (p~_w>0) corresponds to the sweep motion on the down-wash side of the streamwise vortices, while the low pressureregion (p~_w <0)corresponds to the ejection on the up-wash side of the structure; in themiddle, a low pressure region is formed just below the streamwise vortices; in thedownstream, the correspondence between p~_wand the sweep/ejection motions is inopposite to that in the upstream. Considering the practical requirement of turbulencecontrol, a random blowing/suction at the wall is introduced to examine the robustness ofthe relationship. The results show that the relationship based onτ wxis destroyed whilep~_wandτ wzstill exhibit an excellent correspondence with the near-wall streamwisevortices.
(3) Two new control algorithms based onτ wzand p~_ware proposed for turbulencedrag reduction and realized by the two typical actuations “blowing/suction” and “smartskin”. The control schemes based onτ wzusing “blowing/suction” and “smart skin”obtained16%and5%drag reduction while the control scheme based on p~_wgets11%and2%drag reduction, respectively.
In summary, the present work has deepened our understanding of the mechanismof turbulent drag reduction. The inner relationship between the wall-measurable flowquantities and the near-wall streamwise vortices has been disclosed. Two new controlschemes based on the wall-measureable local information have been constructed. Itprovides with us valuable ideas and methods for the development of active turbulencecontrol for drag reduction based on near-wall coherent structures.
（1）从雷诺应力输运和脉动拟涡能输运的角度研究了反向控制抑制湍流的动力学机理。在雷诺应力输运中，压力相关项率先打破法向雷诺应力的输运平衡，并在湍流抑制中起着非常关键的作用。在脉动拟涡能输运中，涡量的拉伸被有效抑制，法向脉动涡量为脉动拟涡能的减小做出了重要贡献。
（2）系统地研究了壁面可测信号（流向脉动摩擦应力τ wx、展向脉动摩擦应力τ wz和脉动压力p~_w）和近壁区流向涡的内在关系。发现τ wx与下游流向涡密切相关，而τ wz则反映了正上方流向涡对壁面的影响。 p~_w和近壁区流向涡的关系较为复杂：在探测点上游，高压区（p~'_w>0）对应着流体的下扫，低压区（p ' w<0）则对应着流体的上抛；在探测点，近壁区流向涡和正下方低压区存在强相关性；而在下游，壁面压力和上抛及下扫的对应关系与上游相反，这一发现弥补了现有认识的不足。考虑到主动控制和外界对流场的干扰，通过引入随机扰动对上述关系的鲁棒性进行了考察。在随机干扰下，τ wx和近壁流向涡的关系被打破，而p~_w和τ wz仍然可以可靠地反映近壁区流向涡，该发现可用于主动控制输入信号的选取。
（3）提出了两种基于壁面局部信号τ wz和p~_w的湍流减阻主动控制新方案，并利用直接数值模拟，对“壁面吹吸”和“智能蒙皮”这两种典型致动方式下的减阻效果进行了考核。以τ wz为输入信号的控制方案，在“壁面吹吸”和“智能蒙皮”的致动方式下，分别获得了16%和5%的减阻率，以p~_w为输入信号的控制方案分别获得了11%和2%的减阻率。
总之，本文工作加深了对湍流减阻机理的认识，揭示了壁面可测信号和近壁区流向涡的关系，提出了两种基于壁面局部可测信号的主动控制新方案，为实现基于相干结构的湍流减阻主动控制提供了有价值的思路和方法。
Turbulent drag reduction is always a hot topic in fluid mechanics. Due to the closerelationship between the near-wall coherent structures and high skin-friction in wallturbulence, the active drag-reduction control has been developed by instantaneouslyinterfering with the evolution of near-wall coherent structures. Active control ofturbulent coherent structures is an attractive research issue owing to its robustperformance, great potential and high efficiency. In recent years, the development of theMEMS technology provides us the possibility for the real practical application of activeturbulence control. As a prerequisite for the design of active control systems based onMEMS, the mechanism and control schemes for drag reduction should be deeplyunderstood. In this thesis, the mechanism and control schemes for drag reduction basedon the manipulation of the near-wall coherent structures are studied via direct numericalsimulation (DNS) of turbulent channel flow. The main work and results are as thefollowing:
(1) The dynamical mechanism of turbulence suppression is explored via thetransient response of Reynolds stress and enstrophy transport to the opposition control.It is found that the balance of the Reynolds stress in the wall normal direction is firstbroken by the pressure-related term which plays a key role in the subsequent globalsuppression of turbulence. In the enstrophy transport, the stretching of the vorticity isattenuated and the wall normal vorticity makes a significant contribution to thesuppression of enstrophy.
(2) The relationship between the measurable flow quantities (streamwise andspanwise wall shear stressτ wx,τ wzand wall fluctuating pressure p~_w) and thenear-wall streamwise vortices is studied using the DNS databases of fully developedturbulent channel flow. It is found that all the three wall quantitiesτ wx, p~_wandτ wzareclosely related with the near-wall streamwise vortices.τ wxcorresponds to the sweep andejection motions induced by the downstream streamwise vortices.τ wzis the spanwisefootprint of the above vortical structures. Compared with the wall shear stress, thecorrelation between p~_wand the near-wall streamwise vortices is more complex. In theupstream of the detecting point, the high pressure region (p~_w>0) corresponds to the sweep motion on the down-wash side of the streamwise vortices, while the low pressureregion (p~_w <0)corresponds to the ejection on the up-wash side of the structure; in themiddle, a low pressure region is formed just below the streamwise vortices; in thedownstream, the correspondence between p~_wand the sweep/ejection motions is inopposite to that in the upstream. Considering the practical requirement of turbulencecontrol, a random blowing/suction at the wall is introduced to examine the robustness ofthe relationship. The results show that the relationship based onτ wxis destroyed whilep~_wandτ wzstill exhibit an excellent correspondence with the near-wall streamwisevortices.
(3) Two new control algorithms based onτ wzand p~_ware proposed for turbulencedrag reduction and realized by the two typical actuations “blowing/suction” and “smartskin”. The control schemes based onτ wzusing “blowing/suction” and “smart skin”obtained16%and5%drag reduction while the control scheme based on p~_wgets11%and2%drag reduction, respectively.
In summary, the present work has deepened our understanding of the mechanismof turbulent drag reduction. The inner relationship between the wall-measurable flowquantities and the near-wall streamwise vortices has been disclosed. Two new controlschemes based on the wall-measureable local information have been constructed. Itprovides with us valuable ideas and methods for the development of active turbulencecontrol for drag reduction based on near-wall coherent structures.
引文
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Angelis V D, Lombardi P, Banerjee S.1997. Direct numerical simulation of turbulent flow over awavy wall. Physics of Fluids,9(8):2429-2442.
Bewley T, Moin P.1994. Optimal control of turbulent channel flows. Active Control of Vibrationand Noise ASME DE75:221-227.
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Bewley T R, Temam R, Ziane M.2000. A general framework for robust control in fluid mechanics.Physica D,138:360-392.
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Bewley T R, Moin P, Temam R.2001. DNS-based predictive control of turbulence: an optimalbenchmark for feedback algorithms, Journal of Fluid Mechanics,447:179-225.
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