The Multi-point Optimization of Shock Control Bump with Constant-Lift Constraint Enhanced with Suction and Blowing for a Supercritical Airfoil

Both shock control bump (SCB) and suction and blowing are flow control methods used to control the shock wave/boundary layer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. A SCB uses a small local surface deformation to reduce the shock-wave strength, while suction decreases the boundary-layer thickness and blowing delays the flow separation. Here a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of SCB and suction and blowing. These flow control methods are used separately or together on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow equations are solved using Roe’s averages scheme and a gradient-based adjoint algorithm is used to find the optimum location and shape of all devices. It is shown that the simultaneous application of blowing and SCB (hybrid blowing/SCB) improves the average aerodynamic efficiency at off-design conditions by 18.2 % in comparison with the clean airfoil, while this increase is only 16.9 % for the hybrid suction/SCB. We have also studied the SWBLI and how the optimization algorithm makes the flow wave structure and interactions of the shock wave with the boundary layer favorable.     

The application of the gradient-based adjoint multi-point optimization of single and double shock control bumps for transonic airfoils

A shock control bump (SCB) is a flow control method that uses local small deformations in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB that are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and NACA-64-A010, over a wide range of off-design Mach numbers. All results are compared with the usual single-point optimization. We use numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm to find the optimum location and shape of the SCB. We show that the application of SCBs may increase the aerodynamic performance of an RAE-2822 airfoil by 21.9 and by 22.8 % for a NACA-64-A010 airfoil compared to the no-bump design in a particular flight condition. We have also investigated the simultaneous usage of two bumps for the upper and the lower surfaces of the airfoil. This has resulted in a 26.1 % improvement for the RAE-2822 compared to the clean airfoil in one flight condition.     

Kriging‐based optimization applied to flow control

The automatic optimization of flow control devices is a delicate issue because of the drastic computational time related to unsteady high‐fidelity flow analyses and the possible multimodality of the objective function. Thus, we experiment in this article the use of kriging‐based algorithms to optimize flow control parameters because these methods have shown their efficiency for global optimization at moderate cost. Navier–Stokes simulations, carried out for different control parameters, are used to build iteratively a kriging model. At each step, a statistical analysis is performed to enrich the model with new simulation results by exploring the most promising areas, until optimal flow control parameters are found. This approach is validated and demonstrated on two problems, including comparisons with similar studies: the control of the flow around an oscillatory rotating cylinder and the reduction of the intensity of a shock wave for a transonic airfoil by adding a bump to the airfoil profile. Copyright © 2011 John Wiley & Sons, Ltd.     

Criterial analysis of the effect of vibrations of an airfoil surface element on the transonic flow structure

A criterial analysis of the effect of forced vibrations of airfoil surface elements on the shock wave structure of a transonic flow around the airfoil is performed. The parameter responsible for regimes of interaction of vibrationally moving zones of the airfoil with the closing shock wave is determined. The influence of this parameter on the wave drag of the airfoil is studied.     

跨音速翼型上的激波／边界层干扰自适应控制计算

在激波区使用自适应壁对跨音速翼型的激波／边界层的相互作用（干扰）进行控制，可改变机翼的气动性能，这种被动控制可通过在翼型的激波区开一凹腔，其上覆盖一弹性橡胶膜柔壁来，本文给出用Ｎａｖｉｅｒ－Ｓｔｏｋｅｒ方程数值模拟这一自适应控制翼型的跨音速粘性绕流，提出了一个适应于本特殊情况（物面边界局部地区在求解过程中有变化）的处理办法。并探讨了自适应柔壁对当代跨音速翼绕流的影响。     

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accu-rate Fourier time spectral method (TSM) is examined and compared with a conventional 2nd-order backward differ-ence formula (BDF) method for periodic unsteady flows. In particular, detailed error analysis based on numerical com-putations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth sub-sonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the predic-tion of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higher-order harmonic contents to the local pressure fluctuations, a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method. The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.     

Analysis of High-order Explicit LES Dynamic Modeling Applied to Airfoil Flows

A high-order low dissipative numerical framework is discussed to tackle simultaneously the modeling of unresolved sub-grid scale flow turbulence and the capturing of shock waves. The flows around two different airfoil profiles are simulated using a Spectral Difference discretisation scheme. First, a transitional, almost incompressible, low Reynolds number flow over a Selig-Donovan 7003 airfoil. Second, a high Reynolds number flow over a RAE2822 airfoil under transonic conditions. These flows feature both laminar and turbulent flow physics and are thus particularly challenging for turbulence sub-grid scale modeling. The accuracy of the recently developed Spectral Element Dynamic Model, specifically capable of detecting spatial under-resolution in high-order flow simulations, is evaluated. Concerning the test in transonic conditions, the additional complexity due to the presence of shock waves has been handled using an artificial viscosity shock-capturing technique based on bulk viscosity. To mitigate the impact of the shock-capturing on turbulence dissipation, it was necessary to combine the high-order modal-type shock detection with a usual sensor measuring the local flow compressibility.

     

Effect of Localization of Pulsed Energy Addition on the Wave Drag of an Airfoil in a Transonic Flow

The possibility of controlling the aerodynamic characteristics of airfoils with the help of local pulsed-periodic energy addition into the flow near the airfoil contour at transonic flight regimes is considered. By means of the numerical solution of two-dimensional unsteady equations of gas dynamics, changes in the flow structure and wave drag of a symmetric airfoil due to changes in localization and shape of energy-addition zones are examined. It is shown that the considered method of controlling airfoil characteristics in transonic flow regimes is rather promising. For a zero angle of attack, the greatest decrease in wave drag is obtained with energy addition at the trailing edge of the airfoil.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 60–67, September–October, 2005.     

超临界翼型跨音速特性实验研究

针对新设计的超临界翼型,采用风洞实验方法验证和评估了其气动特性。在增压连续式跨音速风洞(NF-6风洞)开展了超临界翼型跨音速特性的实验研究,验证了该翼型设计的压力分布曲线特点。激波位置和波后压力平台区长度表明设计结果和实验结果基本一致,揭示了超临界翼型跨音速的气动特性;阻力发散马赫数达到期望的设计指标,探讨了雷诺数对该翼型气动特性的影响。最后采用升华法实现了翼型表面流动特性的显示。结果表明转捩点约在16%弦长位置。     

Resonant phenomena in a transonic flow around an airfoil with pulsed periodic energy supply

Interaction of a pulsed periodic source of energy with a closing shock wave arising near airfoils in transonic flight is studied. The evolution of the shock-wave structure of the flow around a symmetric airfoil is examined by solving two-dimensional unsteady gas-dynamic equations, and a resonant mechanism of interaction is found, which leads to considerable (by an order of magnitude) reduction of the wave drag of the airfoil.     

Forced oscillations of airfoil flows

The effect of background flow oscillations on a transonic airfoil (NACA 0012) flow was investigated experimentally. The oscillations were generated by means of a rotating plate placed downstream of the airfoil. Owing to the expansion and compression waves generated at the plate, the flow over the airfoil flow was drastically disturbed. This resulted in the presence of high intensity oscillations of a shock wave and a separation bubble on the suction surface of the airfoil. For relatively large values of the airfoil angle of attack, weak shock waves (transonic sound waves) were periodically shed upstream of the airfoil.This work was supported by Commission of the European Communities (Communit's Action for Cooperation in Science and Technology with Central and Eastern European Countries).The authors wish to thank Mr P. Koperski for his effective assistance in taking the photographs.     

INTERFERENCE OF SHOCK AND BOUNDARY LAYER IN SUPERSONIC FLOW

激波与物面边界层的干扰涉及可压缩流动的稳定性、转捩、分离等问题,直接影响到飞行器的阻力、表面热防护和飞行性能等工程技术问题。首先总结了前人对于激波与边界层的干扰所做的工作,之后重点研究和对比分析了超声速与跨声速流动中,正激波、斜激波以及头部激波对于飞行器层流和湍流边界层的干扰影响。激波强度的不同对边界层干扰作用不同,在强干扰情况下将会引起边界层分离和翼型失速。     

翼型跨音速流动计算和外形设计的变域变分有限元方法

在气体动力学问题研究中经常会碰到诸如激波、翼型设计等未知界面问题。未知界面的存在为该类问题的理论分析和数值求解带来了很大困难。刘高联针对未知界面问题发展了一种变域变分有限元方法,该方法将未知界面看作是一个变化区域的边界,采用变域变分将未知界面结合在变分泛函中,使其与求解流场的控制方程结合起来,从而将未知界面的求解和流场的求解完全耦合进行,因而是一种处理未知界面的独特工具,极适合于气动外形的设计求解。本文运用变域变分有限元方法对翼型跨音速流动正、反命题进行了数值研究。由于在跨音速翼型绕流中存在激波,所以为了得到压缩激波解,采用了“人工密度”办法。几个算例均得到了满意的计算结果和设计结果,证明了本文方法的有效性和优越性。     

振动翼型和襟翼的绕流特性研究

用数值模拟手段详细地研究了振动翼型和襟翼的绕流问题,数值模拟的出发方程为Euler和N-S方程,格式为Bcam-Warming格式的改进型。数值实验主要针对流场的二大特性进行的,即振动对激波的影响和振动对分离的抑制作用,结果表明:(1)随翼型或襟翼的振动激波强度和位置也相应地变化但这一变化滞后于攻角的变化;(2)振幅加大激波强度的变化和激波运动范围也加大;(3)振动频率越高对激波的影响反而较低频时要小;(4)流动条件的不同可使升力回线的走向发生变化;(5)振动对分离有明显的抑制作用。     

Far nonlinear field of a nonlifting airfoil for a generalised equation of transonic flow

The transonic flow equation [1] for plane unsteady irrotational idealgas flows is extended to the case of subsonic, transonic or supersonic flows in a region with an almost constant value of the velocity using orthogonal flow coordinates (family of equipotential lines and streamlines). A solution for the nonlinear far field of steady transonic flow past an airfoil has been obtained for the transonic equation [2]. In this paper it is obtained for a generalized transonic equation and its asymptotic expansion is given. In using difference methods of calculating the flow past an airfoil in the transonic regime a knowledge of the nonlinear field makes it possible to reduce the dimensions of the calculation region (near field) as compared with the region determined by the far field of the linear theory.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–91, January–February, 1986.     

Frequency lock-in phenomenon for oscillating airfoils in buffeting flows

Navier-Stokes based computer simulations are conducted to determine the aerodynamic flow field response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation in transonic buffeting flows, and also in pre-buffet flow conditions. Shock buffet is the term for the self-sustained shock oscillations that are observed for certain combinations of Mach number and steady mean flow angle of attack even in the absence of structural motion. The shock buffet frequencies are typically on the order of the elastic structural frequencies, and therefore may be a contributor to transonic aeroelastic response phenomena, including limit-cycle oscillations. Numerical simulations indicate that the pre-shock-buffet flow natural frequency increases with mean angle of attack, while the flow damping decreases and approaches zero at the onset of buffet. Airfoil harmonic heave motions are prescribed to study the interaction between the flow fields induced by the shock buffet and airfoil motion, respectively. At pre-shock-buffet conditions the flow response is predominantly at the airfoil motion frequency, with some smaller response at multiplies of this frequency. At shock buffet conditions, a key effect of prescribed airfoil motions on the buffeting flow is to create the possibility of a lock-in phenomenon, in which the shock buffet frequency is synchronized to the prescribed airfoil motion frequency for certain combinations of airfoil motion frequencies and amplitudes. Aerodynamic gain-phase models for the lock-in region, as well as for the pre-shock-buffet conditions are suggested, and also a possible relationship between the lock-in mechanism and limit-cycle oscillation is discussed.     

Controlling Transonic Flow around Airfoils by Means of Local Pulsed Addition of Energy

The influence of local pulsed-periodic addition of energy into a supersonic region on the flow structure and wave drag of an airfoil in transonic flow regimes is considered by methods of mathematical modeling. The study reveals significant prospects of the considered method of controlling airfoil performance in transonic flow regimes, including wave-drag reduction.     

基于自适应直角网格的二维全速势方程有限体积解法A finite volume method for 2D Full-Potential equation on adaptive Cartesian grids

为满足亚声速和跨声速飞机概念设计中快速气动计算的需求,研究和发展一种基于自适应直角网格的非线性全速势方程有限体积解法。要点如下。（1）在几何自适应直角网格的基础上,使用结合单元融合的网格切割算法处理物面边界,提出一种修正非贴体切割网格的方法。（2）采用隐式格式结合GM RES算法求解该非线性位流方程,针对流场的自适应来捕捉激波。（3）采用镜像法处理物面边界处的无穿透条件,并提出解析的方法来修正镜像单元的值。（4）针对直角网格的特点,提出在库塔线上插入库塔单元的方法施加库塔条件。NACA0012翼型绕流的算例结果表明,该方法用于亚声速和跨声速气动计算能得到令人满意的结果,且自动化程度高、收敛速度快。     

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 10⁶ are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.