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.     

Performance Improvement of a Supercritical Airfoil by a Multi-point Optimized Shock Control Channel

A shock control channel (SCC) is a flow control method introduced here to control the shock wave/boundarylayer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. An SCC transfers an appropriate amount of mass and momentum from downstream of the shock wave location to its upstream to decrease the pressure gradient across the shock wave and as a result the shock-wave strength is reduced. Here, a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of the SCC. This flow control method is implemented 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 the SCC. The solver is validated against experimental works studying effect of cavities in transonic airfoils. It is shown that the application of an SCC improves the average aerodynamic efficiency in a range of off-design conditions by 13.2% in comparison with the original airfoil. The SCC is shown to be an effective tool also for higher angle of attack at transonic flows. 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.     

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.     

Adjoint‐based airfoil optimization with discretization error control

In this article, we develop a new airfoil shape optimization algorithm based on higher‐order adaptive DG methods with control of the discretization error. Each flow solution in the optimization loop is computed on a sequence of goal‐oriented h‐refined or hp‐refined meshes until the error estimation of the discretization error in a flow‐related target quantity (including the drag and lift coefficients) is below a prescribed tolerance. Discrete adjoint solutions are computed and employed for the multi‐target error estimation and adaptive mesh refinement. Furthermore, discrete adjoint solutions are employed for evaluating the gradients of the objective function used in the CGs optimization algorithm. Furthermore, an extension of the adjoint‐based gradient evaluation to the case of target lift flow computations is employed. The proposed algorithm is demonstrated on an inviscid transonic flow around the RAE2822, where the shape is optimized to minimize the drag at a given constant lift and airfoil thickness. The effect of the accuracy of the underlying flow solutions on the quality of the optimized airfoil shapes is investigated. Copyright © 2014 John Wiley & Sons, Ltd.     

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。     

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.     

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 asymmetric pulsed periodic energy supply on aerodynamic characteristics of airfoils

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of local pulsed periodic energy supply is considered. The numerical solution of two-dimensional unsteady equations of gas dynamics allowed determining the changes in the flow structure near a symmetric airfoil and its aerodynamic characteristics depending on the magnitude of energy in the case of its asymmetric (with respect to the airfoil) supply. The results obtained are compared with the calculated data for the flow around the airfoil at different angles of attack without energy supply. With the use of energy supply, a prescribed lift force can be obtained with a substantially lower wave drag of the airfoil, as compared with the flow around the airfoil at an angle of attack. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 70–76, November–December, 2007.     

Effect of one-sided unsteady energy supply on aerodynamic characteristics of airfoils in a transonic flow

The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of one-sided pulsed-periodic energy supply is studied. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil at different angles of attack and the aerodynamic characteristics of the airfoil as functions of the amount of energy supplied asymmetrically (with respect to the airfoil) are determined. The results obtained are compared with the data calculated for the flow past the airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. The moment characteristics of the airfoil are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 82–87, November–December, 2008.     

Robust design of natural laminar flow supercritical airfoil by multi-objective evolution method

A transonic, high Reynolds number natural laminar flow airfoil is designed and studied. The γ-θ transition model is combined with the shear stress transport(SST)k-w turbulence model to predict the transition region for a laminar-turbulent boundary layer. The non-uniform free-form deformation(NFFD) method based on the non-uniform rational B-spline(NURBS) basis function is introduced to the airfoil parameterization.The non-dominated sorting genetic algorithm-II(NSGA-II) is used as the search algorithm, and the surrogate model based on the Kriging models is introduced to improve the efficiency of the optimization system. The optimization system is set up based on the above technologies, and the robust design about the uncertainty of the Mach number is carried out for NASA0412 airfoil. The optimized airfoil is analyzed and compared with the original airfoil. The results show that natural laminar flow can be achieved on a supercritical airfoil to improve the aerodynamic characteristic of airfoils.     

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.     

On the Design of Lifting Airfoils with High Critical Mach Number Using Full Potential Theory

 We wish to construct airfoils that have the highest free-stream Mach number for a given set of geometric constraints for which the flow is nowhere supersonic. Nonlifting airfoils that maximize the critical Mach number for a given cross-sectional area are known to possess long sonic segments at their critical speed. To construct lifting airfoils, we proceed under the conjecture that an airfoil with a high value of has the longest possible arc length of sonic velocity over its upper and lower surface. In Kropinski et al. (1995) the lifting problem was tackled in transonic small-disturbance theory. In this paper we numerically construct lifting airfoils with high using the full potential theory and we show that these airfoils have significantly higher than some standard airfoils. We also construct airfoils with higher values of the lift coefficient, by relaxing the speed constraint on the lower surface of the airfoil to have a value less than sonic. Received 13 May 1996 accepted 12 September 1996)     

基于PCE方法的翼型不确定性分析及稳健设计

由于能够获得一个既经济又对参数变化不敏感的设计结果,稳健型设计在工程设计中备受关注. 不确定性分析是稳健型设计的关键. 因此研究了基于混沌多项式的不确定性分析方法,并将其与CFD 方法结合,对计算空气动力学设计中的不确定性影响进行了量化分析. 首先以RAE2822 翼型为算例,对其跨音速马赫数不确定影响进行了分析,研究了多项式阶次对计算的影响,分析了平均流场和方差. 接着结合超临界翼型的马赫数稳健型设计验证了混沌多项式方法在稳健型设计中的有效性. 优化结果表明,稳健型优化后的翼型阻力系数明显降低,同时对于马赫数的敏感性显著减小. 通过分析表明混沌多项式方法能够大幅提高稳健型优化设计效率,能很好地应用于气动稳定性设计.      

基于PCE方法的翼型不确定性分析及稳健设计简

由于能够获得一个既经济又对参数变化不敏感的设计结果,稳健型设计在工程设计中备受关注. 不确定性分析是稳健型设计的关键. 因此研究了基于混沌多项式的不确定性分析方法,并将其与CFD 方法结合,对计算空气动力学设计中的不确定性影响进行了量化分析. 首先以RAE2822 翼型为算例,对其跨音速马赫数不确定影响进行了分析,研究了多项式阶次对计算的影响,分析了平均流场和方差. 接着结合超临界翼型的马赫数稳健型设计验证了混沌多项式方法在稳健型设计中的有效性. 优化结果表明,稳健型优化后的翼型阻力系数明显降低,同时对于马赫数的敏感性显著减小. 通过分析表明混沌多项式方法能够大幅提高稳健型优化设计效率,能很好地应用于气动稳定性设计.     

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.     

Unsteady transonic aerodynamic loadings on the airfoil caused by heaving,pitching oscillations and control surface

An implicit upwind finite volume solver for the Euler equations using the improved flux-splitting method is established and used to calculate the transonic flow past the airfoils with heaving, pitching oscillations and the control surface. Results are given for the NACA64A-10 airfoil which is in harmonic heaving and pitching oscillation and with the control surface in the transonic flow field. Some computational results are compared with the experiment data and the good agreements are shown in the paper.     

Turbulence model and numerical scheme assessment for buffet computations

The prediction of shock‐induced oscillations over transonic rigid airfoils is important for a better understanding of the buffeting phenomenon. The unsteady resolution of the Navier–Stokes equations is performed with various transport‐equation turbulence models in which corrections are added for non‐equilibrium flows. The lack of numerical efficiency due to the CFL stability condition is circumvented by the use of a wall law approach and a dual time stepping method. Moreover, various numerical schemes are used to try and be independent of the numerical discretization. Comparisons are made with the experimental results obtained for the supercritical RA16SC1 airfoil. They show the interest in using the SST correction or realizability conditions to get correct predictions of the frequency, amplitude and pressure fluctuations over the airfoil. Copyright © 2004 John Wiley & Sons, Ltd.     

An improved nonlinear reduced-order modeling for transonic aeroelastic systems

In this study, an improved nonlinear reduced-order model composed of a linear part and a nonlinear part is explored for transonic aeroelastic systems. The linear part is identified via the eigensystem realization algorithm and the nonlinear part is obtained via the Levenberg–Marquardt algorithm. The impulsive signal is chosen as the training signal for the linear part and the sinusoidal signal is used to determine the order of the linear part. The training signal for the nonlinear part is selected as the filtered white Gaussian noise with the maximal amplitude and frequency range to be designed via the aeroelastic responses. An NACA64A010 airfoil and an NACA0012 airfoil are taken as illustrative examples to demonstrate the performance of the presented reduced-order model in modeling transonic aerodynamic forces. The aeroelastic behaviors of the two airfoils are obtained via computational fluid dynamics to solve the Euler equation and the Navier–Stokes equation, respectively. The numerical results demonstrate that the presented reduced-order model can successfully predict the nonlinear aerodynamic forces with and without viscous flows. Moreover, the presented reduced-order model is capable of capturing the flutter velocity and modeling complex aeroelastic behaviors, including limit-cycle oscillations, beat phenomena and nodal-shaped oscillations at the transonic Mach numbers with high accuracy.     

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。     

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.