Steady supersonic flow past an almost straight wedge with large vertex angle

This paper studies the problem on the steady supersonic flow at the constant speed past an almost straight wedge with a piecewise smooth boundary. It is well known that if each vertex angle of the straight wedge is less than an extreme angle determined by the shock polar, the shock wave is attached to the tip of the wedge and constant states on both side of the shock are supersonic. This paper is devoted to generalizing this result. Under the hypotheses that each vertex angle is less than the extreme angle and the total variation of tangent angle along each edge is sufficiently small, a sequence of approximate solutions constructed by a modified Glimm scheme is proved to be convergent to a global weak solution of the steady problem. A sequence of the corresponding approximate leading shock fronts issuing from the tip is shown to be convergent to the leading shock front of the obtained solution. The regularity of the leading shock front is established and the asymptotic behaviour of the obtained solution at infinity is also studied.     

Effect of the wing shape on the thrust of flapping wing

Simulations of harmonically oscillating wings were performed using two-dimensional and three-dimensional boundary element method computer programs: the corresponding hydrodynamic forces were obtained by assuming potential flow. The maximum thickness of symmetric 4-digit NACA airfoils was varied in order to assess the effect of changing the foil shape on the generated thrust. It was found that the thrust coefficient per unit of wing mass decreases in magnitude when the thickness increases. The result indicates that, if the wing mass is fixed, its thickness has to be minimised in order to maximise the generated thrust. Another important finding is the dependence on the motion frequency, i.e. for a fixed foil thickness the thrust coefficient per unit of wing mass increases with the motion frequency. However, when the foil thickness becomes larger, the motion frequency effect on the generated thrust becomes less pertinent, i.e. the thrust range for a slender foil is larger than that of a thicker one over the same motion frequency range. The three-dimensional effect due to the wing spanwise shape was also investigated by changing the wing sweep angle and the influence on the generated thrust was insignificant within the range of investigated parameters. The outcome reinforces the idea that the function of swept wings for low-speed flyers, such as birds, is mainly structural as the sweep angle can be related to a desired aeroelastic response of the oscillating wing.     

The optimal conical twist of a delta wing

The problem of reducing the drag of a wing at a specified lift in a supersonic flow is investigated. A solution for a delta wing is obtained in a simplified formulation of the optimization problem and a theoretical analysis. It is shown that the optimal conical wing is formed by elements of elliptical cones and planes. Numerical modelling of the flow of a non-viscous non-heat-conducting gas past the wing is performed, and the results of the theoretical analysis and direct optimization are compared. ©2012     

About singularities at angular points of a trailing edge under the Joukowskii–Kutta Condition

The linear problem for the velocity potential around a slightly curved thin finite wing is considered under the Joukowskii–Kutta hypothesis. The exponents of possible singularities of solutions at angular points on wing's trailing edge are expressed in terms of eigenvalues of mixed boundary value problems for the Beltrami–Laplace operator on the hemisphere and the semicircle. These singularities have a structure such that the circulation function turns out to be continuous in interior angular points of the trailing edge. In the case of trapezoidal shape of the wing ends there occur square-root singularities of the velocity field at the trailing edge endpoints and the same singularities, of course, are extended along the lateral sides of the wake behind the wing. It is proved that for any angular point on the trailing edge the exponents of all above-mentioned singularities form a countable set in the upper complex half-plane with the only accumulation point at infinity. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Global existence of shock for the supersonic Euler flow past a curved 2-D wedge

In this paper, we study the global existence of the supersonic shock for the steady supersonic Euler flow past a curved 2-D wedge. By using the method of characteristic, we show that the shock exists globally and the flow between the shock and wedge is continuous provided the wedge is a small perturbation of a straight wedge under a weighted global Sobolev norm and the vertex angle is less than the extreme angle.     

Investigation on the effect of trailing edge ejection on a turbine cascade

This paper presents a detailed experimental and numerical investigation for a turbine cascade with different trailing edge ejection. The numerical simulation is based on Three-Dimensional Navier–Stokes equations coupled with an effective ejection model, where a high resolution non-oscillatory scheme, LU-SGS implicit algorithm and Baldwin-Lomax turbulence model are employed. The experiments presented in this paper focused on a transonic turbine cascade performance with different ejection to validate the numerical simulation results. The results show that the blowing ratio has a small effect on the Mach number distribution and exit flow angle with two slot types. However the energy loss coefficient increases initially, and subsequently has a decrease tendency with the increasing of blowing ratio. The ejection from the symmetry slot blows away the vortex at the blade trailing edge and strengthens the mixing between the wake and main flow. The ejection from the pressure side cutback only clears up the vortex near the slot surface, and has small effect on the flow field near the trailing edge.     

The choice of the system of geometric parameters of an optimized wing

A direct optimization method is used to determine the form of the wing which enables the aerodynamic performance to be improved for a given lift in the supersonic flow of ideal gas. The flow around the wing and its characteristics are calculated within the framework of a model based on Euler's equations. On the basis of a local analysis of the load distribution on the wing, a method is proposed for choosing the system of geometric parameters which ensures rapid convergence to the optimum. It is shown that one of the parameters of the system (the angle of rotation of the wing panel relative to the central chord) has a very slight influence on the aerodynamic characteristics of the wing.     

The topology of the sectional streamlines

The unsteady, three-dimensional full Navier-Stokes equations are solved using a Beam-Warming implicit algorithm in this paper. Computations of the flow over a 76° sweep delta wing at 36.5° angle of attack is presented. The sectional streamlines are depicted and the evolution of the instantaneous crossflow topology of the leading-edge vortex is analyzed. It is found that, along the axis, the topology of the primary vortex alters several times starting from stable focus near the apex to unstable focus, and lasts back to stable focus near wake edge; The stable limit cycle and unstable limit cycle are shown in this evolution. These various altering topologies stem from the stretching and compression of the vortex core.     

Supersonic flow onto a solid wedge

We consider the problem of two‐dimensional supersonic flow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock emanating from the corner. The weak shock is observed in supersonic flights. A longstanding natural conjecture is that the strong shock is unstable in some sense. We resolve this issue by showing that a sharp wedge will eventually produce weak shocks at the tip when accelerated to a supersonic speed. More precisely, we prove that for upstream state as initial data in the entire domain, the time‐dependent solution is self‐similar, with a weak shock at the tip of the wedge. We construct analytic solutions for self‐similar potential flow, both isothermal and isentropic with arbitrary γ ≥ 1. In the process of constructing the self‐similar solution, we develop a large number of theoretical tools for these elliptic regions. These tools allow us to establish large‐data results rather than a small perturbation. We show that the wave pattern persists as long as the weak shock is supersonic‐supersonic; when this is no longer true, numerics show a physical change of behavior. In addition, we obtain rather detailed information about the elliptic region, including analyticity as well as bounds for velocity components and shock tangents. © 2007 Wiley Periodicals, Inc.     

A Numerical and Asymptotic Investigation of Boundary-layer Wake Evolution

The evolution of four characteristically different velocityprofiles in the boundary layer at a trailing edge is studiedboth numerically and analytically; the complete wake flow iscomputed using a finite difference procedure and this is comparedwith asymptotic expansions of the flow in both the near wakeand the far wake. Two of the profiles have direct applicationto physical situations which include the flow in the wake ofa finite flat plate and the flow in the free shear layer downstreamof the point of separation of a supersonic stream from a planewall. The other two profiles demonstrate the structural changeswhich occur in the near wake when part of the initial profileis on the point of separation.     

Homogeneous/Heterogeneous Condensation in Transonic Steam Turbine Stages Including Rotor/Stator Interaction

In this numerical investigation we simulate condensing flows typical for the last stages in low pressure steam turbines of large power plants. The main fluid dynamical characteristics are unsteadiness, high free stream turbulence, complex rotor/stator interaction and metastable conditions of the working fluid, leading to partial phase transition and polydispersed two‐phase flow in the transonic regime. Here we focus on a model for simulation of the condensation process which includes simultaneous homogeneous and heterogeneous nucleation. This model is applied to a turbine stage, consisting of one rotor and one stator. We found that the reduction of thermodynamic nonequilibrium by natural or artificial seeding with heterogeneous nuclei can reduce the thermodynamic losses, but after exceeding a certain limit the efficiency may be lower compared with pure homogeneous condensation.     

On transcritical states in viscous flow passing the edge of a horizontal plate

This contribution puts forward some recent advances in the rigorous (asymptotic) theory of gravity- (and capillarity-)driven shallow flow of a viscous liquid past a horizontal plate, originating in jet impingement oblique to it. Hence, our concern is twofold: with steady developed flow over the distance from the jet centre to the trailing edge of the plate, referred to as a pronounced hydraulic jump blurred by viscous diffusion; with the predominantly inviscid transcritical limit arising near the edge due to scale reduction given an intrinsic expansive singularity taking place there. In the latter situation envisaged briefly, condensing nonlinear inertial effects, weak time dependence, and (very) weak streamline curvature as the essential ingredients into a distinguished limit demonstrates the generation of a weak (transcritical) hydraulic jump by a plate-mounted obstacle. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global Existence of a Shock for the Supersonic Flow Past a Curved Wedge

This note is devoted to the study of the global existence of a shock wave for the supersonic flow past a curved wedge. When the curved wedge is a small perturbation of a straight wedge and the angle of the wedge is less than some critical value, we show that a shock attached at the wedge will exist globally.     

The conical deformation of a delta wing with sonic leading edges

The optimal conical deformation of a delta wing with sonic leading edges is determined in a linear formulation of the problem. The drag of the wing caused by the creation of the lifting force is taken as the objective function. It is established that a superelliptical distribution of the local angle of attack over the wing span corresponds to the minimum drag. A representation in the form of a hypergeometric function is found for the directrix of the wing in a cross section. The results obtained are compared with the results of a numerical investigation within the Euler model.     

Die Begriffe Auftrieb,Widerstand und Zirkulation bei Schaufeln von Strömungsgittern

Summary The force on a wing of a cascade can be divided in the two components lift and drag like the force on a single wing. The magnitude and direction of the lift component are calculated. The change of the flow direction is caused not only by the lift but also by the drag. Approximately the flow can be calculated as the field of vortices with a circulation corresponding to cascade wings without drag.      

Mixed Convection Flow Past a Horizontal Plate: The Trailing Edge

The mixed convection flow past a horizontal plate which is aligned under a small angle of attack to a uniform free stream will be considered in the limit of large Reynolds number and small Richardson number close to the trailing edge. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

风力机叶尖涡尾迹结构PIV测量研究

空气动力研究与发展中心低速空气动力研究所依托工程型大风洞（实验段直径3.2 m）,采用高分辨率CCD相机（4 008像素×2 672像素）,针对旋转状态下的风力机叶片尾流开展大视场（单个观测区域达到570 mm×380 mm）PIV(particle image velocimetry)测量,以NREL UAE Phase Ⅵ风力机叶片1/8缩比模型为实验对象,获取了叶尖涡产生、发展的流动数据,为研究风力机叶尖涡结构和流动机理研究提供重要的基础数据．观测结果表明,叶尖涡从后缘脱落后首先有一个短时间的向内运动,然后随着尾流的膨胀向外运动,其涡强度则先是短时间内降低,然后随着涡的卷起而增强,从而形成一个强大的叶尖涡．在实验观察范围内叶尖涡在来流方向的迁移规律近似线性．     

Numerical study of the viscous hypersonic flow over a blunt delta wing

A previously developed two-dimensional Navier-Stokes solver is extended to three dimensions. The hypersonic steady flow of an perfect gas (with a constant adiabatic index) over a delta wing with a spherical nose and a cylindrical leading edge is computed as an example. The characteristic features of the flow are analyzed. Pressure, heat flux, and friction coefficient distributions are computed in the shock layer and on the wing surface. The results are compared with available numerical and experimental data.     

Comparison of analytical and numerical solution for optimal vortex diffuser design

The contribution deals with optimization of wing tip devices, so called vortex diffusers. A comparison is given between an analytical approach for obtaining the optimal circulation loading and the results of a numerical investigation using a lifting line method. The purpose of most wing tip devices is to reduce the induced drag of the main wing by converting vortex energy into thrust. In order to achieve an optimal design, a variational formulation originally proposed by Betz and Prandtl for air screws is applied to the circulation distribution of the diffuser blades. In extension to the inviscid formulation, a viscous correction is applied in order to account for frictional forces. In an effort to validate the analytical results, a comparison is given with numerical solutions from a lifting line method. The loading of the diffuser blades is parametrized and optimized with respect to resulting thrust by use of a quasi-Newton gradient method. Comparison shows that, knowing the velocity distribution in the near wake of the wing, considerable decrease of induced drag may be achieved making use of vortex diffusers. Although actual circulation loading may differ between the analytical and numerical estimation, resulting thrust agrees within a few percent. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

带有球凹/球凸的旋转通道内流动结构和强化换热的数值研究

对带有凹坑和凸包的内流通道在不同旋转数下的对流换热特性进行了数值分析,探讨了Coriolis力对通道中流场和换热特征的影响．研究发现,随着旋转数增加,通道前缘呈现出较弱的流动冲击,但存在较大的尾迹和延迟的流动再附着,后缘凹坑内部有一较小旋涡和较强射流使得后缘传热得到强化,最高可达60%．总体Nusselt数随着旋转数的增加先减小而后增大.