A vortex method for separated flow around an airfoil with a detached spoiler

A discrete vortex method based on no-slip condition is developed for simulating unsteady separated flows around an airfoil with a detached spoiler. For flow separated at each sharp edge, such as the spoiler tips and the trailing edge of the airfoil, a vortex sheet is used to feed discrete vortices at each time step. The length, inclination and strength of each sheet is determined by the continuity equation, the momentum principle and a Kutta pressure condition such that the flow, net force and pressure difference across the vortex sheet are all zero. The separation on the airfoil upper surface is simulated by discrete vortices shed from a fixed separation point. The flow patterns behind a detached spoiler at different time steps are obtained and compared with those of the conventional spoiler. Reasonable agreements are found between the predicted pressure distributions and experimental measurements. The computed results show that base-venting changes the flow field around the spoiler and reduces the adverse effect in lift experienced by the airfoil when the spoiler undergoes a rapid deployment.     

Boundary element simulation of inviscid flow around an oscillatory foil with vortex sheet

The dynamic performance of a rigid foil with harmonic vertical and rotational motions in fluid flow has been studied through velocity potential theory. A boundary element based time stepping scheme is introduced to simulate the flow around the foil and the vortex wake. The body surface condition is satisfied on the exact foil surface and the motion and deformation of the wake sheet shed at the trailing edge is tracked. Kelvin condition is satisfied and a Kutta condition for the unsteady motion is proposed to circumvent the singularity at the trailing edge. Point vortex, which is reduced from wake vortex dipole, is introduced to approximate the vorticity. The performance of foil NACA0012 with harmonic vertical and rotational motions are studied extensively; the propulsion/swimming mode, energy harvesting mode and the flying mode are analysed in detail.     

Singularities in BIEs for the Laplace equation; Joukowski trailing-edge conjecture revisited

The paper deals with trailing-edge issues connected with the analysis of three-dimensional incompressible quasi-potential flows (i.e. flows that are potential everywhere, except for a zero-thickness vortex layer, called the wake). Specifically, following the Joukowski conjecture of smooth flow at the trailing edge, all the trailing-edge conditions that are required to avoid singularities in the boundary integral representation for the velocity, in a quasi-potential incompressible flow around a wing, are identified. In particular, these include the Kondrat'ev and Oleinik singularity as well as the vortex-line and the edge-jet singularities of Epton. Also, following Mangler and Smith, the behavior of the wake geometry at the trailing edge is determined, using the Kutta condition of no pressure discontinuity at the trailing edge. Specific theoretical issues are addressed which include (1) the relationship between Joukowski conjecture and Kutta condition, and (2) identification of those trailing-edge conditions that are necessary to assure the uniqueness of the solution (as opposite to relationships that are automatically satisfied by the solution). Regarding the first issue, in the main body of the paper, the Joukowski conjecture and the Kutta condition are used as if they were independent assumptions; then, in Appendix A, it is shown that the Kutta condition need not be invoked as a separate assumption since it may be obtained as a consequence of the governing equations and of the Joukowski conjecture. In order to clarify the second issue, the theoretical analysis is coupled with a numerical one. In particular, the conditions necessary to insure uniqueness are inferred (not proven) through numerical experimentation: only the no-vortex-line condition appears to be necessary to insure uniqueness. This is accomplished by using a piecewise-cubic boundary-element method for quasi-potential flows that is an extension of a high-order formulation introduced by the authors and their collaborators (the order of the formulation is adequate to address all the theoretical trailing-edge conditions uncovered). The emphasis is on steady flows in simply connected regions; however, some issues related to unsteady flows in multiply connected regions are also examined. Finally, several open problems that require additional work are identified.     

A panel method computation for oscillating aerofoil in compressible flow

A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity. The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.     

Aerodynamic forces and flow structures of an airfoil in some unsteady motions at small Reynolds number

Summary The aerodynamic forces and flow structures of a NACA 0012 airfoil in some unsteady motions at small Reynolds number (Re=100) are studied by numerically solving the Navier-Stokes equations. These motions include airfoil acceleration and deceleration from one translational speed to another and rapidly pitching up in constant freestream (equivalent to pitching up during translational motion at constant speed). It is shown that at small Reynolds number (Re=100), when the airfoil is performing fast acceleration or deceleration from one speed to another, a large aerodynamic force can be generated during and for a time period after the acceleration or deceleration; a large aerodynamic force can also be generated when the airfoil is performing a fast pitching motion in a constant freestream. In these fast unsteady motions, an airfoil in low Re flow can produce a large aerodynamic force as effective as in large Re flow, or the effect of unsteady motion dominates the Reynolds number effect. During the fast unsteady motion of the airfoil, new layers of strong vorticity are formed near the upper and lower surfaces of the airfoil under the previously existing thick vorticity layers, and it is the generation and motion of the new vorticity layers that is mainly responsible for the generation of the large aerodynamic force; the large-scale structure and movement of the newly produced vorticity layers are similar to that of high Re flow.     

Oscillating cascade unsteady aerodynamics including separated flow effects

A mathematical model is developed to predict the effect of flow separation on the unsteady aerodynamic lift and moment acting on a two-dimensional flat plate cascade which is harmonically oscillating in a subsonic flow field. The unsteady flow is considered to be a small perturbation to the uniform steady flow, with the steady flow assumed to separate at a specified fixed position on the airfoil suction surface. This formulation does not require the difference in the upwash velocity across the airfoil in the separated flow region to be determined before calculating the unsteady pressure difference across the chordline of the airfoils, thereby eliminating the assumption that the upwash difference is zero at the trailing edge when the steady flow is separated. Results obtained demonstrate that although flow separation decreases bending mode stability, it does not result in bending mode flutter. However, flow separation can result in torsion mode flutter, with this instability being a function of the location of both the separation point and the elastic axis.     

A flat plate in a rotating,stratified flow

Summary The boundary layer over a flat plate of semi-infinite extent in a stratified and rotating flow grows forward from the trailing edge, and is characterized by an intrinsic length scaleL, which represents the distance from the trailing edge at which vortex stretching becomes just as important in the boundary layer as baroclinic vorticity production. Near the trailing edge, the layer is essentially the layer in a purely stratified flow; far upstream (manyL), it is an Ekman layer. The boundary layer entrains no fluid, but induces at its edge a transverse velocity component which drives an higher-order streamwise outer flow. If the flow is bounded above and below by horizontal planes, the Wiener-Hopf solution for this outer flow indicates that the disturbance decays rapidly downstream, but the transverse velocity component is non-zero far upstream.     

Compressible dynamic stall vorticity flux control using a dynamic camber airfoil

This study reports control of compressible dynamic stall through management of its unsteady vorticity using a variable droop leading edge (VDLE) airfoil. Through dynamic adaptation of the airfoil edge incidence, the formation of a dynamic stall vortex was virtually eliminated for Mach numbers of up to 0.4. Consequently, the leading edge vorticity flux was redistributed enabling retention of the dynamic lift. Of even greater importance was the fact that the drag and pitching moment coefficients were reduced by nearly 50%. The camber variations introduced when the leading edge was drooped are explained to be the source of this benefit. Analysis of the peak vorticity flux levels allowed the determination of minimum necessary airfoil adaptation schedule.     

Boundary element analysis of wave-current interaction around a large structure

A numerical approach for wave-current interaction around a large structure is investigated, based on potential flow theory, linear waves and small current velocity approximation. The velocity potential in a wave-current coexisting field is separated into a steady current potential and an unsteady wave potential. The boundary element method was then employed to compute the unsteady wave potential with effects of both a uniform current and a large body taken into consideration. It is demonstrated that the steady current potential can be expressed as the sum of a uniform current and a steady disturbance due to the presence of the object. The variation of current velocity in the vicinity of the object is then calculated by using a surface vorticity boundary integral meethod. Boundary element analysis is also used for the numerical solutions of the surface vorticity method. Substituting both unsteady wave potential and current velocity into the first-order dynamic surface boundary condition, the water surface elevation around a large structure in a wave-current coexisting field can then be obtained. Comparisons of numerical predictions with experimental results ar also made; qualitative good agreements are obtained.     

Prediction of incidence effects on oscillating airfoil aerodynamics by a locally analytical method

A complete mathematical model is formulated to analyse the effects of mean flow incidence angle on the unsteady aerodynamics of an oscillating airfoil in an incompressible flow field. A velocity potential formulation is utilized. The steady flow is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating airfoil. The numerical solution technique for both the steady and unsteady flow fields is based on a locally analytical method. In this method, analytical solutions are incorporated into the numerical technique, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual local computational grid elements. This flow model and locally analytic numerical solution method are then verified through the excellent correlation obtained with the Theodorsen oscillating flat plate and Sears transverse gust classical solutions. The effects of mean flow incidence on the steady and oscillating airfoil aerodynamics are then investigated.     

On unsteady airfoil-vortex interaction

Summary An experimental investigation on unsteady airfoil-vortex interaction has been done. The incident vortex, to interact with a downstream airfoil (NACA 0018, chord lengthc=20 mm), is generated by a square cylinder (side lengthD=20 mm). The square cylinder and airfoil are arranged in tandem and the spacing ratioL/D of the central distance to the side length is set a constant value of 4.625. The free stream Mach numbers are varied between 0.153 and 0.750, whereas the free stream Reynolds numbers (based on the side lengthD) are varied between 0.713×10⁵ and 3.44×10⁵.It is found that as the incident vortex approaches the airfoil, the circulation and scale are decreased until it arrives at a position near the leading edge of the airfoil. During this stage, some circulation of the incident vortex is transferred to the secondary vortex generated on the airfoil opposite to the surface that the incident vortex approaches. Thus, circulation and scale of the secondary vortex are increased. However, after the incident vortex goes further downstream, no circulation of the incident vortex is transferred to the secondary vortex effectively. As the result, both of the incident vortex and secondary vortex decay due to the viscous dissipation through the interaction with the boundary layer of the airfoil. The locus of the incident vortex is deviated in such a way that it goes away from the airfoil. The streamwise position of the secondary vortex is adjusted by the incident vortex, orvice versa, so as to meet each other just behind the trailing edge of the airfoil.With 8 Figures     

Uniqueness of the bounded flow solution in aerodynamics

We discuss uniqueness for steady incompressible inviscid flows past a body with a sharp trailing edge TE, with particular regard to multiconnected (toroidal) 3D wing configurations. Boundedness of the velocity field at TE is enforced by means of a singularity removal principal (Kutta condition). The resulting bounded flow solution is unique for 2D airfoils and 3D conventional wings. For toroidal bodies the flow depends on the available eigensolution which, however, has no direct influence on the lift. In this multiconnected case uniqueness of the bounded solution is shown to depend on the topology of the trailing edge.     

基于变弯度技术和协同射流的混合流动控制技术研究

现代飞机强调高速巡航特性且兼顾隐身特性,因此翼型往往采用厚度较小,前缘半径不大,弯度不大的薄翼型。这类翼型的低速气动性能较差,容易失速,限制了这类飞机的短距起降特性和载重能力,因此需要借助流动控制技术来改善低速特性。该文讨论新型的协同射流主动流动控制技术,同变弯度技术包括后缘变弯和前缘下垂技术等被动流动控制技术相结合,探索混合流动控制技术的流动控制机理和控制效果。基于数值模拟的结果发现:仅采用单一的流动控制技术在薄翼型上得到的控制效果有限,而将协同射流同变弯度技术结合的混合流动控制技术可同时发挥不同流动控制技术的优点(例如协同射流引起的后缘失速的推迟,下垂前缘带来的前缘失速推迟,后缘襟翼带来的零升迎角减小)。该文提供的混合流动控制方案可以将薄翼型的最大升力系数提升至C_Lmax=3.3127,相对原始构型提升了96%,具有广阔的工程应用前景。     

基于数论网格法与Morris法的翼型气动特性敏感性分析

针对在风力机翼型气动特性敏感性分析中计算效率较低的问题，提出了一种基于数论网格（number theoretic net，NT-net）法与Morris法的翼型气动特性敏感性分析方法。首先，构建了拟合精度较高的翼型参数化模型；其次，阐述了NT-net法的计算原理，采用NT-net法对翼型参数化模型的多项式系数进行抽样；然后，以风力机翼型S832为研究对象，采用Morris法进行翼型气动特性的全局敏感性分析；最后，进一步分析在特定工况下风力机翼型参数化模型的多项式系数对翼型外形及气动特性的影响。结果表明：影响翼型气动特性的主要因素依次为翼型的最大相对厚度和最大相对弯度、前缘半径和后缘厚度；当来流攻角较小时，最大相对厚度和最大相对弯度取适当的较小值、前缘半径取适当的较大值可有效增强该工况下风力机翼型的气动特性，同时也验证了NT-net法的计算效率更高。研究结果为风力机翼型气动设计提供了理论参考。     

Microtab对翼型跨音速抖振始发特性的影响

研究了microtab对翼型跨音速抖振始发特性的影响。采用SST湍流模型对RANS方程进行封闭,以NACA0012翼型为对象,用CFD方法计算了在其后缘附近安装microtab后,翼型的跨音速流场。对比分析了在翼型后缘附近的上表面、下表面单独安装和上下表面对称安装microtab后,对翼型跨音速抖振始发特性的影响,并研究了microtab的高度和弦向安装位置对跨音速抖振边界的控制作用。结果表明：在翼型后缘附近的上表面加装microtab能够提高抖振始发攻角,并且随着microtab高度的增加,抖振始发攻角有增大的趋势。在翼型后缘附近的下表面加装microtab能够提高抖振始发时的升力系数,且抖振始发时的升力系数随着microtab高度的增加而增大。microtab的弦向安装位置的变化对于抖振始发攻角影响较小,但是对抖振始发时的升力系数有明显的影响。         

Unsteady panel method for flapping foil

A computer program based on a potential-flow panel method was developed to evaluate the hydrodynamic forces acting on a harmonically heaving and pitching two-dimensional rigid foil. A new formulation of the unsteady Kutta condition, postulating a finite pressure difference at the trailing edge of the oscillating foil, is proposed and implemented in the numerical procedure. A comparison with published experimental data [Anderson JM, Streitlien K, Barrett DS, Triantafyllou MS. Oscillating foils of high propulsive efficiency. J Fluid Mech 1998;360(1):41–72; Read DA, Hover FS, Triantafyllou MS. Forces on oscillating foils for propulsion and maneuvering. J Fluids Struct 2003;17(1):163–83; Schouveiler L, Hover FS, Triantafyllou MS. Performance of flapping foil propulsion. J Fluids Struct 2005;20(7):949–59] showed good agreement with the computational results. The analysis of the experimental results indicates clearly that robust computational procedures are necessary for reliable data processing in terms of calibration, noise removal, correction factors, etc. The proposed two-dimensional approach to the problem is currently being developed as a three-dimensional procedure that will address the unsteady flow effects such as inertia-related ones that are currently omitted.     

某跨音速高压涡轮非定常流动数值模拟研究

通过求解三维非定常雷诺平均N-S方程模拟某跨音速高压涡轮非定常流场,研究涡轮内非定常流动特征。通过对静子尾迹及静子尾缘激波和转子叶排之间的相互干涉过程进行详细分析,发现定常/非定常模拟方法获得的涡轮总体性能参数基本一致但流场存在较大差异。静子尾迹是导致涡轮流场非定常性的重要因素之一:在转子叶栅通道中部和下部,静子尾迹和转子叶片附面层及下通道涡发生明显干涉,并导致通道中下部损失周期性波动幅度较大,此外尾迹和下通道涡间的干涉作用在转子尾缘处诱导出高频脱落涡。静子尾缘激波也是导致涡轮流场非定常性的原因之一,激波和转子叶片作用形成复杂的波系结构,对涡轮流场影响显著:一方面激波/附面层干涉导致转子和静子的吸力面产生周期性变化的高温区域;另一方面激波撞击叶片导致叶片表面的气流在激波后出现分离,对转子静压分布产生影响,使得转子叶片表面载荷出现明显的非定常性,进而导致涡轮输出功的周期性波动十分剧烈。     

A numerical method for the analysis of flexible bodies in unsteady viscous flows

A two‐dimensional numerical model for unsteady viscous flow around flexible bodies is developed. Bodies are represented by distributed body forces. The body force density is found at every time‐step so as to adjust the velocity within the computational cells occupied by the body to a prescribed value. The method combines certain ideas from the immersed boundary method and the volume of fluid method. The main advantage of this method is that the computations can be effected on a Cartesian grid, without having to fit the grid to the body surface. This is particularly useful in the case of flexible bodies, in which case the surface of the object changes dynamically, and in the case of multiple bodies moving relatively to each other. The capabilities of the model are demonstrated through the study of the flow around a flapping flexible airfoil. The novelty of this method is that the surface of the airfoil is modelled as an active flexible skin that actually drives the flow. The accuracy and fidelity of the model are validated by reproducing well‐established results for vortex shedding from a stationary as well as oscillating rigid cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

The motion of the free-surface separation point during the initial stage of horizontal impulsive displacement of a floating circular cylinder

The initial stage of unsteady two-dimensional flow caused by the impulsive horizontal motion of a floating circular cylinder is investigated by using methods of asymptotic analysis. Initially the cylinder is half-submerged and the liquid free surface is flat and horizontal. The liquid is of infinite depth. Then the cylinder suddenly starts to move horizontally with a speed given as a function of time. The liquid is assumed ideal and incompressible and its flow potential. The initial flow is provided by pressure-impulse theory, with an account of a possible separation of the liquid free surface from the trailing face of the rigid surface of the cylinder. The initial position of the separation point on the surface of the moving body is determined by using the condition that the fluid velocity is finite at the separation point (Kutta condition). The motion of the separation point along the surface of the cylinder is numerically determined with the help of the second-order outer solution of the problem and the Kutta condition at the moving separation point. It is shown that the length of the wetted part of the cylinder surface increases at a rate proportional to the speed of the cylinder. The speed of the separation point depends on the Froude number. The pressure on the wetted part of the cylinder can be below the atmospheric pressure for relatively high speed.