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.     

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.     

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.     

Nonlinear effects caused by pulsed periodic supply of energy in the vicinity of a symmetric airfoil in a transonic flow

Changes in the structure of a transonic flow around a symmetric airfoil and a decrease in the wave drag of the latter, depending on the energy-supply period and on localization and shape of the energy-supply zone, are considered by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. Energy addition to the gas ahead of the closing shock wave in an immediate vicinity of the contour in zones extended along the contour is found to significantly reduce the wave drag of the airfoil. The nature of this decrease in drag is clarified. The existence of a limiting frequency of energy supply is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 64–71, May–June, 2006.     

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.     

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.     

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the prac-ticability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disinte-grates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17%occurs with a triangular shape, while the max-imum increase in aerodynamic efficiency (lift-to-drag ratio) of around 10%happens with a rectangular shape at an angle of attack of 2.26?.     

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.     

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.     

Conservation of the resultant force vector in the plane of the angle of attack for slender star-shaped bodies in supersonic flows

At high supersonic flight speeds bodies with a star-shaped transverse and power-law longitudinal contour are optimal from the standpoint of wave drag [1–3]. In most of the subsequent experimental [4–6] and theoretical [6–9] studies only conical star-shaped bodies have been considered. For these bodies in certain flow regimes ascent of the Ferri point has been noted [10]. In [11] the boundary-value problem for elongated star-shaped bodies with a power-law longitudinal contour was solved for the case of supersonic flow. The present paper deals with the flow past these bodies at an angle of attack. It is found that for arbitrary star-shaped bodies with any longitudinal (in particular, conical) profile the aerodynamic forces can be reduced to a wave drag and a lift force, the lateral force on these bodies being equal to zero for any position of the transverse contour.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–141, November–December, 1989.     

Numerical modeling of transonic buffeting and its control by means of tangential jet blowing

Flow past the airfoil of a civil aircraft wing is numerically modeled in the transonic buffeting regimes. The characteristics of unsteady self-oscillations of the shock on the upper surface of the airfoil are studied. To suppress them a technique of controlling the flow is proposed. It consists in blowing a jet tangent to the upper surface of the airfoil from a small-size slot nozzle. The calculations are carried out within the framework of the unsteady Reynolds equations.     

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.     

Controlling buffet through local mechanical action and heat addition near a lambda-shaped shock

Unsteady transonic flow past a two-dimensional airfoil with heat and momentum addition is numerically investigated. The flow analysis is based on the solution of the unsteady Reynolds equations closed by the k-ω SST turbulence model. The equations are integrated using the finite volume method. Several positions and shapes of the heat and momentum addition zones are considered for the purpose of determining an optimal means for controlling buffet. It is established that the most considerable variations in the buffet parameters are achieved when heat addition and mechanical action are realized on the upper wing surface. The thermal energy supply always increases the buffet frequency, while the mechanical action can both increase and reduce it.     

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.     

Aerodynamic drag of a pair of bodies in transonic and supersonic flow

The aerodynamic characteristics of models of pairs of bodies on the flow acceleration and deceleration intervals are investigated experimentally at transonic and supersonic flow velocities. The dependence of the drag coefficient of the pair model on the relative drag of the leading body is determined for supersonic velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 152–156, May–June, 1990.     

Effect of energy release in shock layer on supersonic flight

The problem of supersonic flow past an elongated axisymmetric body in the presence of an energy release zone between the surface of the body and the shock wave is considered. By means of such zones it is possible to modify the aerodynamic characteristics of the body and influence its flight by decreasing or increasing the drag coefficient (see, for example, [1, 2]) or by creating an additional lift force or aerodynamic moment [3]. A simple model of steady-state flow past a body with an energy source is used to determine what parameters the source should have to permit the maximization of the controlling force (in the present case the lift) for a given energy consumption per unit time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 142–151, July–August, 1990.In conclusion, the author wishes to thank V. P. Stulov for his interest in the work.     

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.     

Dynamic stall behavior from unsteady force measurements

A direct force measurement technique employing piezoelectric load cells is used to experimentally investigate a two-dimensional airfoil (NACA 0012) undergoing dynamic stall. The load cells are installed at each end of the airfoil and give the force response in two directions in the plane normal to the airfoil axis during oscillations. Experiments are carried out at a Reynolds number based on the airfoil chord equal to 7.7×10⁴, and at four reduced frequencies, k=0.005, 0.01, 0.02, and 0.04. Phase-averaged lift of the airfoil undergoing dynamic stall is presented. It is observed that hysteresis loops of the lift occur both when the airfoil is pitched to exceed its static stall limit and when it is still within its static stall limit, and they grow in size with increasing k at the same pitching mean angle of attack and pitching amplitude. Both the lift and the drag induced by the pitching motion are further analyzed using the methods of higher order correlation analysis and continuous wavelet transforms to undercover their nonlinear and nonstationary features, in addition to classical FFT-based spectral analysis. The results are quantitatively illustrated by an energy partition analysis. It is found that the unsteady lift and drag show opposite trends when the airfoil undergoes transition from the pre-stall regime to the full-stall regime. The degree of nonlinearity of the lift increases, and the lift show a nonstationary feature in the light-stall regime, while the nonlinearity of the drag decreases, and the drag shows nonstationary feature in both the light-stall and the full-stall regimes. Furthermore, the lift and the drag have significant nonlinear interactions as shown by the correlation analysis in the light-stall regime.     

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.     

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。