Bluff body wakes with free, fixed, and discontinuous separation at low Reynolds numbers and low aspect ratio

Some comparative experimental results are presented of bluff body wakes with free, fixed, and discontinuous separation. The particular examples considered are a circular cylinder, a plain blunt trailing edge aerofoil and a segemented blunt trailing edge aerofoil. The evolution of the near wake and vortex shedding modes are compared and 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     

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.      

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.      

Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness δ^* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 × 512 × 64 (∼ 8.4×10⁶) and 512 × 1024 × 128 (∼ 6.7×10⁷) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Kármán, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed. Received 4 March 1999 and accepted 27 October 2000     

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.     

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 IMPROVED NAVIER–STOKES PROCEDURE FOR ANALYSIS OF TWO-DIMENSIONAL AEROFOILS IN LAMINAR AND TURBULENT FLOWS

An accurate and robust Navier–Stokes procedure to predict the complex flow about an aerofoil has been developed. Much improvement over existing methods is achieved in various aspects of the solution procedure. The computational grid generated by conformal mapping, which is not only orthogonal but aligned with the inviscid streamlines, keeps the equations simple and minimizes the error due to false diffusion. Formal second-order accuracy is ensured by employing the QUICK scheme for the convective derivatives in the full Navier–Stokes and turbulence transport equations. To treat the separated region properly and to better resolve the flow field in the wake, the two-layer k–ε turbulence model is incorporated. The onset of transition is triggered in a unique fashion to warrant the smooth transition to turbulent flow. Sample calculations for various aerofoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, C_Lmax, the velocity fields and the Reynolds stress profiles, are found to be in excellent agreement with the data. © 1997 John Wiley & Sons, Ltd.     

Unsteady supersonic flow over an oscillatory aerofoil using a second-order TVD scheme

The unsteady flow over an oscillatory NACA0012 aerofoil has been simulated by the calculation with Euler equations. The equations are discretized by an implicit Euler in time, and a second-order space-accurate TVD scheme based on flux vector splitting with van Leer's limiter. Modified eigenvalues are proposed to overcome the slope discontinuities of split eigenvalues at Mach = 0·0 and ± 1·0, and to generate a bow shock in front of the aerofoil. A moving grid system around the aerofoil is generated by Sorenson's boundary fitted co-ordinates for each time step. The calculations have been done for two angles of attack θ = 5·0° sin (ωt) and θ = 3·0° + 3·0° sin (ωt) for the free-stream Mach numbers 2·0 and 3·0. The results show that pressure and Mach cells flow along characteristic lines. To examine unsteady effects, the responses of wall pressure and normal force coefficients are analysed by a Fourier series expansion.     

Investigation of Advanced Turbulence Models for the Flow in a Generic Wing-Body Junction

The predictive performance of several turbulence models, among them formulations based on non-linear stress-strain relationships and on stress-transport equations, is examined in a collaborative university-industry study directed towards a generic wing-body junction. The geometry consists of a variation of the symmetric NACA 0020 aerofoil mounted on a flat plate, with the oncoming stream aligned with the aerofoil's symmetry plane. The dominant feature of this flow is a pronounced horseshoe vortex evolving in the junction region following separation ahead of the aerofoil's leading edge. This case is one of 6 forming a broad programme of turbulence-model validation by UMIST, Loughborough University, BAE Systems, Aircraft Research Association, Rolls-Royce plc and DERA. Key aspects of this collaboration were a high level of interaction between the partners, the use of common grids and boundary conditions, and numerical verifications aimed at maximizing confidence in the validity of the computational solutions. In total, 12 turbulence models were studied by four partners. Model performance is judged by comparing solutions with experimental data for pressure fields on the plane wall and around the aerofoil; for velocity, turbulence energy, shear stress and streamwise normal stress in the upstream symmetry plane; and for velocity, turbulence energy and shear stress in cross-flow planes downstream of the aerofoil leading edge. The emphasis of the study is on the structure of the horseshoe vortex and its effects on the forward flow. The main finding of the study is that, for this particular 3D flow, second-moment closure offers predictive advantages over the other models examined, especially in terms of the far-field structure of the horse-shoe vortex, although no model achieves close agreement with the experimental data in respect of both mean flow and turbulence quantities. This revised version was published online in July 2006 with corrections to the Cover Date.     

绕振荡水翼流动及其转捩特性的数值计算研究简

通过对比标准k-ω SST 湍流模型和基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型对绕振荡NACA66 水翼流动的数值计算结果与实验结果,对水翼振荡过程的水动力特性和流场结构变化进行了分析研究. 结果表明：与标准k-ω SST 湍流模型的数值计算结果相比,基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型能有效预测绕振荡翼型流场结构和水动力特性,捕捉流场边界层发生的流动分离和转捩现象;绕振荡水翼的流动过程可分为5 个特征阶段,当来流攻角较小时,在水翼前缘发生层流向湍流的转捩现象,水翼动力特征曲线出现变化拐点;随着来流攻角的增大,顺时针尾缘涡逐渐形成并向水翼前缘发展;当攻角较大时,前缘涡分离导致动力失速,水翼的动力特征曲线出现大幅波动;水翼处于顺时针向下旋转阶段,绕水翼的流动状态逐渐由湍流过渡为层流.     

A vertex-centred finite volume method with shock detection

This paper introduces a vertex-centred finite volume method for compressible viscous flow incorporating a new shock detection procedure. The discretization is designed to be robust and accurate on the highly stretched and curved meshes necessary for resolving turbulent boundary layers around the leading edge of an aerofoil. Details of the method are described for two-dimensional problems and the natural extension of three-dimensional multiblock meshes is discussed. The shock detection procedure is used to limit the range of the shock-capturing dissipation specifically to regions containing shocks. For transonic turbulent flow this is shown to improve the boundary layer representation significantly.     

绕振荡水翼流动及其转捩特性的数值计算研究

通过对比标准k-ω SST 湍流模型和基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型对绕振荡NACA66 水翼流动的数值计算结果与实验结果,对水翼振荡过程的水动力特性和流场结构变化进行了分析研究. 结果表明:与标准k-ω SST 湍流模型的数值计算结果相比,基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型能有效预测绕振荡翼型流场结构和水动力特性,捕捉流场边界层发生的流动分离和转捩现象;绕振荡水翼的流动过程可分为5 个特征阶段,当来流攻角较小时,在水翼前缘发生层流向湍流的转捩现象,水翼动力特征曲线出现变化拐点;随着来流攻角的增大,顺时针尾缘涡逐渐形成并向水翼前缘发展;当攻角较大时,前缘涡分离导致动力失速,水翼的动力特征曲线出现大幅波动;水翼处于顺时针向下旋转阶段,绕水翼的流动状态逐渐由湍流过渡为层流.      

A numerical method for the calculation of incompressible,steady, separated flows around aerofoils

The present work deals with the numerical calculation of the incompressible turbulent flow around aerofoils. An orthogonal curvilinear grid of ‘C’ type is used for the solution of the time averaged equations and Reynolds stresses are modelled according to the κ-ε turbulence model. PISO and SIMPLE algorithms are used to solve the strongly coupled system of the derived finite volume equations and convergence is improved by applying the method of variable local underrelaxation factors. Comparisons between the calculated and measured pressure distributions are presented for NACA 0012 and NACA 4412 wing sections. The formation of separation bubbles according to calculations is also shown.     

非定常空化流动涡旋运动及其流体动力特性

采用大涡模拟方法对绕水翼云状空化的水动力特性和非定常流场结构进行研究. 基于实验结果对数值方法进行验证,分析空化与流场内部涡旋结构之间的相互作用以及对水翼动力特性的影响. 研究结果表明:大涡模拟方法可以准确模拟绕水翼流动的非定常过程. 在无空化条件下,升阻力系数存在斯特劳哈数St = 0.85 的主频波动,这是由水翼尾部涡旋结构的发展脱落引起的;在云状空化条件下,升阻力系数存在St = 0.34 的高能量密度低频波动,这是由大规模云状空泡团的发展和脱落引起的;云状空化阶段的升阻力系数在St = 0.5~1.5 的范围内都存在较高的波动,这是由于空化现象对水翼尾缘涡旋结构的发展和脱落产生影响,在不同发展阶段,空化现象不同程度地降低尾缘涡旋结构脱落频率.      

Combined method of calculating supersonic ideal-gas flow over a wing with a supersonic blunt leading edge

A combined numerical method, based on the successive calculation of the flow regions near the blunt leading edge and center of a wing, is proposed on the assumption that the angle of attack and the relative thickness and bluntness radius of the leading edge are small. The flow in the neighborhood of the leading edge of the wing is assumed to be identical to that on the windward surface of a slender body coinciding in shape with the surface of the blunt nose of the wing and is numerically determined in accordance with [1]. The flow parameters near the center of the wing are calculated within the framework of the law of plane sections [2]. In both regions the equations of motion of the gas are integrated by the Godunov method. The flow fields around elliptic cones are obtained within the framework of the combined method and the method of [3], A comparative analysis of the results of the calculations makes it possible to estimate the region of applicability of the method proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 159–164, January–February, 1989.The authors wish to express their gratitude to A. A. Gladkov for discussing their work, and to G. P. Voskresenskii, O. V. Ivanov, and V. A. Stebunov for making available a program for calculating supersonic flow over a wing with a detached shock.