NUMERICAL UNCERTAINTIES IN TRANSONIC FLOW CALCULATIONS FOR AEROFOILS WITH BLUNT TRAILING EDGES

Numerical uncertainties are quantified for calculations of transonic flow around a divergent trailing edge (DTE) supercritical aerofoil. The Reynolds-averaged Navier–Stokes equations are solved using a linearized block implicit solution procedure and mixing-length turbulence model. This procedure has reproduced measurements around supercritical aerofoils with blunt trailing edges that have shock, boundary layer and separated regions. The present effort quantifies numerical uncertainty in these calculations using grid convergence indices which are calculated from aerodynamic coefficients, shock location, dimensions of the recirculating region in the wake of the blunt trailing edge and distributions of surface pressure coefficients. The grid convergence index is almost uniform around the aerofoil, except in the shock region and at the point where turbulence transition was fixed. The grid convergence index indicates good convergence for lift but only fair convergence for moment and drag and also confirms that drag calculations are more sensitive to numerical error. © 1997 by John Wiley and Sons, Ltd.     

钝后缘风力机翼型的环量控制研究

钝后缘风力机翼型具有结构强度高、对表面污染不敏感等优点,但其较大的阻力系数使得翼型的整体气动特性不够理想. 利用环量控制方法对钝后缘风力机翼型进行了流动控制,以改善钝后缘风力机翼型的气动特性,减弱尾迹区脱体涡强度. 通过对钝后缘风力机翼型环量控制方法进行相关的数值模拟,对比研究了环量控制方法的增升减阻效果, 研究了环量控制下翼型升阻力特性随射流动量系数的变化规律,并对不同射流动量系数下环量控制方法的气动品质因子和控制效率进行了分析. 研究结果表明:环量控制方法能够大幅提升钝后缘风力机翼型的升力系数,同时有效地降低翼型的阻力系数; 翼型的升力系数随射流动量系数的增大而增大,表现出很明显的分离控制阶段和超环量控制阶段的变化规律; 射流能耗的功率系数随射流动量系数的增大而增大,且增长速率逐渐增大;实施环量控制方法后叶片的输出功率同样随射流动量系数增大而增大,但增长速率逐渐降低. 总体来说,环量控制方法可以有效地改善钝后缘风力机翼型的气动特性以及功率输出特性,在大型风力机流动控制中具有很好的应用前景.      

Mean and turbulence measurements in the boundary layer and wake of a symmetric aerofoil

Detailed measurements of two-dimensional profiles of static pressure, mean velocity, turbulence intensity and Reynolds shear stress were carried out with conventional pressure probes and hot wire probes at preselected streamwise stations in the boundary layer and wake of a 12.5% thick, 600 mm chord two-dimensional symmetric aerofoil mounted at zero incidence in a low speed wind tunnel. The chord Reynolds number was one million and the wake measurements extended up to three chord lengths (or nearly 660 trailing edge momentum thicknesses) downstream of the trailing edge. The data indicate rapid interaction of the wall layers immediately behind the trailing edge, leading to significant changes in the flow parameters close to the trailing edge. The relaxation of the wake is preceded by initial ‘overshoot’ in the streamwise profiles of mean-flow parameters and peak values of turbulence components. Further growth of the wake towards similarity/equilibrium is discussed.     

Transonic shock oscillations on NACA0012 aerofoil

The mechanism of the origin of shock oscillations on NACA0012 aerofoils is investigated using a moving grid thin layer Navier Stokes code. The method used to understand the mechanism is to initiate the shock oscillations on an aerofoil by moving the aerofoil from a regime of steady transonic flow into a regime of periodic flow by a change in airflow incidence. The results indicate that the shock induced bubble plays a leading role in the origin of shock oscillations and the trailing edge has an affect on its amplitude. Received 1 April 1997 / Accepted 1 December 1997     

Effect of trailing edge shape on hydrodynamic damping for a hydrofoil

Flow induced vibration on a hydrofoil may be significantly reduced with a slight modification of the trailing edge without alteration of the hydrodynamic performance. Particularly, the so called Donaldson trailing edge shape gave remarkable results and is being used in a variety of industrial applications. Nevertheless, the physics behind vibration reduction is still not understood. In the present study, we have investigated the hydrodynamic damping of a 2D hydrofoil with Donaldson trailing edge shape. The results are compared with the same hydrofoil with blunt trailing edge. The tests are carried out in EPFL high speed cavitation tunnel and two piezoelectric patches are used for the hydrofoil excitation in non-intrusive way. It was found that the hydrodynamic damping is significantly increased with the Donaldson cut. Besides, as the flow velocity is increased, the hydrodynamic damping is found to remain almost constant up to the hydrofoil resonance and then increases linearly, for both tested trailing edge shapes and for both first bending and torsion modes.     

Stability of a supersonic flat-plate wake (Comparison of numerical and experimental results)

The stability of the wake downstream of a plat plate with a blunt trailing edge is numerically investigated at a supersonic freestream velocity. The calculated stability characteristics are compared with the experimental data.     

A double vortex sheet model of the viscous flow near the trailing edge of a lifting aerofoil

Classical definitions of boundary layer mass and momentum flux deficiency thicknesses can lead to gross errors when applied to measurements near a trailing edge where the flow curvature in the free stream is appreciable. This paper presents a double vortex sheet model as a development from the single vortex sheet model of Helmholtz and others. Two bound vortex sheets define a potential function which can describe a flow with the same mass and momentum flux deficiencies as the viscous regions. The bound nature of these sheets allows the modelling of the integral properties of these regions while retaining the advantages of a potential flow. The application to the flow near the trailing edge of a lifting aerofoil is given     

Computation of turbulent asymmetric wake

The development of asymmetric wake behind an aerofoil in turbulent incompressible flow has been computed using finite volume scheme for solving two-dimensional Navier-Stokes equations along with the k-ε model of turbulence. The results are compared with available experimental data. It is observed that the computed shift of the point of minimum velocity with distance is sensitive to the prescribed value of the normal component of velocity at the trailing edge of the aerofoil. Making the model constant C_u as a function of streamline curvature and changing the production term in the equation for ε, has only marginal influence on the results.     

AN UNFACTORED IMPLICIT MOVING MESH METHOD FOR THE TWO-DIMENSIONAL UNSTEADY N–S EQUATIONS

An unfactored implicit time-marching method for the solution of the unsteady two-dimensional Reynolds-averaged thin layer Navier–Stokes equations is presented. The linear system arising from each implicit step is solved by the conjugate gradient squared (CGS) method with preconditioning based on an ADI factorization. The time-marching procedure has been used with a fast transfinite interpolation method to regenerate the mesh at each time step in response to the motion of the aerofoil. The main test cases examined are from the AGARD aeroelastic configurations and involve aerofoils oscillating rigidly in pitch. These test cases have been used to investigate the effect of various parameters, such as CGS tolerance and laminar/turbulent transition location, on the accuracy and efficiency of the method. Comparisons with available experimental data have been made for these cases. In order to illustrate the application of the mesh generator and flow solver to more general flows where the aerofoil deforms, results for an NACA 0012 aerofoil with an oscillating trailing edge flap are also shown.     

Paradox of the blunt edge of an airfoil in an unsteady flow

A paradox of the blunt edge of an airfoil in an unsteady ideal flow is established, which states that the solution of the nonlinear problem of unsteady flow around a bluntedged airfoil subject to strict boundary conditions at this edge is physically meaningless. The paradox is a consequence of the adopted model of the unsteady fluid flow near the blunt edge, which assumes inflection of streamlines. It is established that the solution of the problem by local replacement of the blunt edge by a sharp edge using the hypothesis on the smoothness of streamlines near the trailing edge is physically meaningful.     

The influence of acceleration and deceleration on shock wave movement on and around aerofoils in transonic flight

This paper examines the shock wave dynamics of a biconvex aerofoil in transonic flight during acceleration and retardation. The aerofoil has a cord length of 1 m and air at infinity is at 101.325 kPa and 300 K. Using Fluent as the CFD software, constant velocity (steady state) simulations were conducted at transonic Mach numbers. The aerofoil was then accelerated at 1041m/s² (106 g), starting at Mach 0.1, and decelerated at −1041m/s², starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were found in the transonic region between the steady and the unsteady aerodynamic forces. Analysis of the flow field in this region showed that acceleration-dependent variations in the position of the shock wave on the surfaces of the aerofoil were the main reason for this. As very high accelerations were used in order to emphasize differences, which do not have many practical applications, simulations using accelerations lower than 9 g were also conducted in order to confirm the results. The acceleration-dependent behaviour of other shock waves around the aerofoil, such as the bow shock in front of the aerofoil and the trailing wave were also examined. The trailing wave followed behind the aerofoil changing position with different accelerations at the same Mach number.      

Investigation of the control of the flow around a wing using mini-flaps

The flow around an airfoil with a mini-flap mounted on the lower or upper wing surface is investigated. The results are obtained by measuring the pressure distribution over the airfoil surface and the forces acting on it for Mach and Reynolds numbers M = 0.1?0.8 and Re = (0.6?3.8) × 10⁶. It is shown that, as distinct from known devices such as Gurney flaps, blunt trailing edge, etc., for controlling the flow in the vicinity of the trailing edge of an airfoil, a mini-flap mounted on the undersurface produces gas flow from the upper to the lower surface around a sharp edge. In this case the flow pattern is considerably affected not only near the trailing edge but also over the entire airfoil. The pressure redistribution over the airfoil makes it possible to increase or decrease the wing lift. Thanks to the low hinge moment, the mini-flap can serve as an effective means of low-inertia control of the flow around a wing.     

Conservative calculations of non-isentropic transonic flows

The classical potential formulation of inviscid transonic flows is modified to account for non-isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second-order mixed-type equation derived via differentiating the momentum equations. The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge. Results for the present conservative calculations are presented for non-lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.     

Suppression of force fluctuations in flow past an aerofoil

Force fluctuations on a solid body are associated with unsteadiness in the wake, e.g. vortex shedding. Therefore, the control of force fluctuations can be realised by suppressing the flow unsteadiness. A NACA0024 aerofoil closed with a round trailing edge is chosen to represent the solid body throughout this investigation, with the Reynolds number fixed at Re = 1000 and angle of attack α ≤ 15^o, at which the uncontrolled flow is two-dimensional. A linear optimal control is calculated by analysing the distribution of sensitivity of unsteadiness to control around the entire surface of the body. The nonlinear effects of the calculated control, which can be actuated through surface-normal suction and blowing across the surface of the aerofoil, are tested through two-dimensional direct numerical simulations. It is observed that a surface-normal velocity control with a maximum magnitude less than 8% of the free stream velocity completely suppresses unsteadiness at α = 10° with an overall drag reduction of 14% and a 138% increase of lift.     

Secondary wake instabilities of a blunt trailing edge profiled body as a basis for flow control

Flow in the wake of a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, has been investigated experimentally, to identify and characterize the secondary instabilities accompanying the von Kármán vortices. The experiments, which involve laser-induced fluorescence for visualization and particle image velocimetry for quantitative measurement of the wake instabilities, cover Reynolds numbers ranging from 250 to 2,150 based on thickness of the body, to include the wake transition regime. The dominant secondary instability appears as spanwise undulations in von Kármán vortices, which evolve into pairs of counter-rotating vortices, with features resembling the instability mechanism predicted by Ryan et al. (J Fluid Mech 538:1–29, 2005). Feasibility of a flow control approach based on interaction with the secondary instability using a series of discrete trailing edge injectors has also been investigated. The control approach mitigates the adverse effects of vortex shedding in certain conditions, where it is able to amplify the secondary instability effectively.     

基于雨燕翅膀的仿生三角翼气动特性计算研究

针对低雷诺数微型飞行器的气动布局,设计出类似雨燕翅膀的一组具有不同前缘钝度的中等后掠(Λ=50?)仿生三角翼.为了定量对比研究三角翼后缘收缩产生的气动效应,设计了一组具有同等后掠的普通三角翼.为了深入研究仿生三角翼布局的前缘涡演化特性以及总体气动特性,采用数值模拟方法详细地探索了低雷诺数(Re=1.58×104)流动条...     

Energy harvesting of a heaving and forward pitching wing with a passively actuated trailing edge

This study experimentally investigates the energy harvesting capabilities of an oscillating wing with a passively actuated trailing edge. The oscillation kinematics are composed of a combined heaving and forward pitching motions, where the pitching axis is well behind the wing center of mass. Passive actuation is attained by connecting the trailing edge with the wing body using a torsion rod. The degree of flexibility of the trailing edge is represented by the Strouhal number based on the trailing edge natural frequency. The trailing edge passive response is studied for oscillation Strouhal numbers of 0.017, 0.025 and 0.033. Instantaneous aerodynamic forces are measured in a closed loop wind tunnel at a Reynolds number of 40 000, based on the free stream velocity and the wing chord length. Measured results include the effective angle of attack induced by the trailing edge actuation as well as the lift and moment during the oscillation cycle. For the imposed kinematics in this study, the pitching motion has a positive contribution to the mean power output whereas the heaving motion has a relatively small but negative contribution. Additionally, by decreasing the natural frequency of the trailing edge closer to that of the imposed oscillation frequency, the magnitude of the lift and moment forces and hence the mean power output, increases. It is found that there exists a strong correlation between mean power output and the effective angle of attack, shown through the passive trailing edge response, resulting in an increase in energy harvesting potential.     

Numerical Simulation of a Passive Control of the Flow Around an Aerofoil Using a Flexible,Self Adaptive Flaplet

Self-activated feathers are used by almost all birds to adapt their wing characteristics to delay stall or to moderate its adverse effects (e.g., during landing or sudden increase in angle of attack due to gusts). Some of the feathers are believed to pop up as a consequence of flow separation and to interact with the flow and produce beneficial modifications of the unsteady vorticity field. The use of self adaptive flaplets in aircrafts, inspired by birds feathers, requires the understanding of the physical mechanisms leading to the mentioned aerodynamic benefits and the determination of the characteristics of optimal flaps including their size, positioning and ideal fabrication material. In this framework, this numerical study is divided in two parts. Firstly, in a simplified scenario, we determine the main characteristics that render a flap mounted on an aerofoil at high angle of attack able to deliver increased lift and improved aerodynamic efficiency, by varying its length, position and its natural frequency. Later on, a detailed direct numerical simulation analysis is used to understand the origin of the aerodynamic benefits introduced by the flaplet movement induced by the interaction with the flow field. The parametric study that has been carried out, reveals that an optimal flap can deliver a mean lift increase of about 20% on a NACA0020 aerofoil at an incidence of 20 ^o degrees. The results obtained from the direct numerical simulation of the flow field around the aerofoil equipped with the optimal flap at a chord Reynolds number of 2 × 10⁴ shows that the flaplet movement is mainly induced by a cyclic passage of a large recirculation bubble on the aerofoil suction side. In turns, when the flap is pushed downward, the induced plane jet displaces the trailing edge vortices further downstream, away from the wing, moderating the downforce generated by those vortices and regularising the shedding cycle that appears to be much more organised when the optimal flaplet configuration is selected.     

Base drag reduction by control of the three-dimensional unsteady vortical structures

The present paper deals with the wake of a 2D body equipped with a drag reduction device. The device is a 3D trailing edge consisting of alternate segments of blunt base and spanwise cavity. The aerodynamic mechanisms acting on the near wake are studied in a water tunnel from schlieren observations by thermally marking large scale structures. The results show that the efficiency of the device is directly related to the presence of longitudinal vortices. An optimization of the shapes in subsonic compressible flow had led to a decrease of more than 40% of the total drag of the profile.     

General perspectives on model construction and evaluation for stochastic estimation,with application to a blunt trailing edge wake

The technique of stochastic estimation is examined as a specific application of linear least squares modelling. Factors that are relevant to the objectives of estimation in fluids, such as the number of sensors, the use of multiple time lags, and the strength of linear correlations, are discussed in the context of a general regression formulation. We consolidate the established findings of several research fields in order to outline clearly the potential pitfalls and reasonable performance expectations of these empirical strategies. Experimental measurements of velocity and fluctuating pressure in the wake of a blunt trailing edge body are used for quantitative illustration of key considerations for model construction and performance evaluation. It is emphasized that estimator accuracy is influenced strongly by the physical relationships among the measured variables, in addition to their correlation with the estimated variable. The evaluation of several performance metrics on an independent test set provides valuable information for the selection of a suitably complex model. In particular, “variance inflation” is interpreted as an indicator of the potential amplification of noise by a stochastic estimator.