An ill-posed inverse problem of a wing with locally given velocity data and its analysis

Using locally given vertical velocity data around a wing, an inverse formulation is presented to solve a lifting problem. The inverse problem is expressed by a Fredholm integral equation of the first kind. In this paper, the kernel of the integral equation gives a Hilbert–Schmidt integral operator, and therefore the occurrence of ill-posedness in the sense of stability cannot be avoided in a normal topology. This difficulty is solved by using the regularization method for ill-posed problems. A composition mapping is introduced so that local velocity data can be available for this inverse problem. In this paper, the ill-posed inverse problem of a wing is studied using the Landweber–Friedman's regularization method within the framework of linear potential theory. A numerical example demonstrates that only with locally given velocity data is the regularization method accurate and suitable for the present physical problem of an inverse mathematical formulation. Therefore, the lifting problem can be solved by using a locally given fluid velocity instead of a wing geometry. Received: April 13, 2000 / Accepted: April 20, 2000     

二维水翼流体力学反问题的数值模拟

水翼(机翼)的反设计一直是人们研究的热门课题,本文对定常反问题进行了研究.将翼型NACA2412作为计算对象.首先给出翼型的下半部形状,以及上表面的从正问题中计算出来的速度分布.在变分原理的基础上,用有限元方法对水翼进行了数值计算.结果表明,本文理论正确,方法可行.     

A dissipative free-surface approach for an underwater body in a uniform stream

A dissipative free-surface approach is applied to the potential flow problem with respect to a hydrofoil in a two-dimensional uniform stream. A dissipative source-based panel method is developed for a NACA foil problem with its trailing edge being a stagnation point, and also for a symmetric Joukowski foil problem with its trailing edge being a non-stagnation point. To facilitate the understanding of the further application of the dissipative free-surface approach, an underwater mathematical body model is presented. Numerical simulation with respect to the body in a three-dimensional uniform stream is provided from an analytic formulation obtained by the dissipative free-surface technique.     

水翼涡激振动的数值模拟研究

对二维水翼结构进行流固耦合运动分析,利用大涡模拟方法计算高雷诺数下水翼绕流场,流场力作用于二自由度刚体上导致周期性的垂荡和转动,龙格库塔法求解刚体水翼的运动方程,位移参数作为下一时间步流场计算的边界条件,具体通过编译自定义函数控制刚体运动和流场网格变化。探讨了初始攻角、刚心位置以及来流速度对水翼振动的影响,发现在来流速度增大至某一数值时水翼发生了颤振现象,并在时域与频域上对颤振的发生机理进行深入探讨。     

电磁力控制翼型三维绕流场特性的数值研究

在弦长雷诺数Re_L=2.97×10~6下,采用脱体涡模拟方法对弱电解质中电磁力作用下翼型绕流场特性进行了数值模拟,研究了电磁力作用控制翼型失速攻角时绕流场中三维流动特性及失速问题的规律和机理。结果表明:电磁力作用可有效改善翼型周围的流场结构,显著减小翼型绕流场三维特性,并使翼型表面流体动能增加,当电磁力作用足够大时,其表面涡量转变为正向涡量。同时,电磁力作用可增加翼型升力,减小阻力,显著减小升阻力脉动特性,提高翼型升阻比,还可以显著延缓翼型失速特性,增加失速攻角,提高工作性能。     

粒子群算法在翼型剖面优化中的应用

为设计出具有良好升阻比性能的翼型剖面,采用智能优化领域新兴的粒子群优化算法(PSO)结合面元法对翼型进行优化设计。文中给出了PSO算法的数学模型及其在翼型优化设计中的主要计算过程,并以Naca66mod翼型为原型进行设计。获取了翼型优化过程中每一步处的翼型剖面形状、翼型表面压力系数分布以及翼型的升力系数、阻力系数和最大厚度比,结果分析表明经过优化后的翼型与原型相比,具有升力系数增加,阻力系数减小这一有利的特征改变。同时采用CFD方法对两种翼型进行数值模拟计算,获得同上的结论,进而验证了PSO方法在翼型优化设计中的可行性。     

基于求解速度势通量的指定压力分布二维翼型设计方法

为了提升翼型的水动力和空泡等性能,指定压力分布的翼型剖面设计的方法多数集中在给定攻角下的翼型剖面的设计,该方法存在计算量较大,收敛性不理想,特别是推广到三维问题时,上述问题尤为突出,限制了翼型设计的进一步发展。文章以势流理论面元方法为基础,通过求解指定压力分布条件下翼型表面的速度势通量,获得翼型表面形状的修正量,并将修正量分解为攻角的变化以及剖面自身的变化两部分,从而得到了翼型唯一的设计攻角和翼型剖面几何（厚度分布、拱度分布）。文中采用上述方法对二维翼型问题进行了设计验证,表明该方法可以设计任意指定压力分布的翼型剖面,理论上该方法可以用于全三维翼型的设计问题。     

三维水翼升力线理论(英文)

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.     

Hydrodynamic response of a passive shape-adaptive composite hydrofoil

The primary objective of this paper is to present cavitation tunnel tests performed on an optimised shape-adaptive composite hydrofoil and compare the results to other composite hydrofoils. The optimised composite hydrofoil was designed based on prior literature and was manufactured using an optimised ply orientation schedule and a pre-twist. In the same experiment schedule a composite hydrofoil that has a ply orientation that is opposite to the optimised hydrofoil was also tested. In addition to the cavitation tunnel experiments, the paper also presents results predicted from FEA and CFD simulations for the optimised hydrofoil and compares the results from numerical methods to experiments. The results show that the optimised hydrofoil has an improved L/D ratio and a delayed stall phenomenon compared to other hydrofoils. Furthermore, due to the pre-twisted optimised geometry, the hydrofoil does not suffer from loss of lift at low angles of attack. The experimental results demonstrated the importance of characterising the performance of flexible shape-adaptive hydrofoils based on the actual velocity of the flow in addition to the conventional characterisation based on Reynold's number. Additional numerical simulations were performed to investigate the hydrofoils observed load dependant deformation behaviour. These results clearly show that for the same Reynold's number, the hydrofoil can have an appreciably different response if the flow velocity is different.     

水翼艇纵向运动多变量鲁棒控制

为了提高水翼艇纵向运动控制的鲁棒性,采用MIMO闭环增益成形算法设计了鲁棒控制器.给出了水翼艇纵向运动传递函数形式的数学模型,通过镜像映射方法将不稳定模型转换成稳定的数学模型.仿真结果表明,所设计的鲁棒控制器将纵摇角降至了原来的25%并对模型摄动具有鲁棒性.     

The effect of finite depth on 2D and 3D cavitating hydrofoils

The iterative numerical method that has been developed for cavitating hydrofoils and surface piercing bodies moving inside a numerical towing tank is modified and extended to the case of fully submerged, both two- and three-dimensional cavitating hydrofoils in water of finite depth, and the effects of subcritical speed, critical speed and supercritical speed are investigated in detail. The iterative numerical method based on Green’s theorem allows separating the cavitating hydrofoil problem, the free surface problem and finite bottom problem both in two and three dimensions. The cavitating hydrofoil surface, the free surface and the surface of finite bottom are modeled with constant strength dipole and constant strength source panels. While the kinematic boundary condition is applied on the hydrofoil surface, a dynamic condition is applied with a cavity closure condition on the cavity surface. The source strengths on the free surface are expressed in terms of perturbation potential by applying the linearized free surface conditions. No radiation condition is enforced for downstream and transverse boundaries. The source strengths on the bottom surface are zero because of vanishing normal velocity. The method is applied to 2D and 3D cavitating hydrofoils, and the effect of finite bottom on lift and drag coefficients, cavity number and wave elevation is investigated.     

涂层对空化流动特性影响的实验研究

利用实验的方法研究了涂层对绕水翼空化流动特性的影响。分别针对喷涂环氧涂层和氟碳涂层的 Clark-Y 型水翼,采用高速摄像装置观察了不同空化阶段的空化流动形态。研究结果表明：（1）在初生空化阶段,当σ=1.82时,沿环氧涂层水翼表面展向排列着初生空泡,而氟碳涂层水翼还处于无空化状态,说明相对于环氧涂层,氟碳涂层对空化现象的产生有一定的抑制作用,氟碳涂层水翼初生空化数为1.50;（2）在片状附着型阶段,当σ小于1.63时,绕环氧涂层水翼的空化先于氟碳涂层水翼发展至片状空化,绕水翼空化流动产生大量分散空泡,沿水翼表面向后运动过程中逐渐长大,在高压区溃灭后形成小空泡并以马蹄涡形式继续运动。同一空化数下,绕环氧涂层水翼空化流动的空泡长度大于氟碳涂层水翼。但随空化数降低,两者空泡长度逐渐接近,说明环氧涂层在片状空化阶段对空化的抑制作用逐渐增强;（3）σ=0.87时空化发展至云状空化阶段,空化流动伴随周期性的云状空泡的脱落,绕环氧涂层水翼的空化流动周期及无量纲空化面积均小于氟碳涂层水翼,说明涂层对空化的非定常变化也有一定的抑制作用,且环氧涂层强于氟碳涂层。     

基于混合迭代法的二维水翼空泡性能分析(英文)

In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length (CSCL) iteration and cavity shape for fixed cavitation number (CSCN) iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.     

Cavitation passive control on immersed bodies

This paper introduces a new idea of controlling cavitation around a hydrofoil through a passive cavitation controller called artificial cavitation bubble generator (ACG). Cyclic processes, namely, growth and implosion of bubbles around an immersed body, are the main reasons for the destruction and erosion of the said body. This paper aims to create a condition in which the cavitation bubbles reach a steady-state situation and prevent the occurrence of the cyclic processes. For this purpose, the ACG is placed on the surface of an immersed body, in particular, the suction surface of a 2D hydrofoil. A simulation was performed with an implicit finite volume scheme based on a SIMPLE algorithm associated with the multiphase and cavitation model. The modified k-ε RNG turbulence model equipped with a modification of the turbulent viscosity was applied to overcome the turbulence closure problem. Numerical simulation of water flow over the hydrofoil equipped with the ACG shows that a low-pressure recirculation area is produced behind the ACG and artificially generates stationary cavitation bubbles. The location, shape, and size of this ACG are the crucial parameters in creating a proper control. Results show that the cavitation bubble is controlled well with a well-designed ACG.     

解三维水翼绕流的下潜涡环栅格法

在包含于机翼表面内的某次表面及尾涡面上分布法向偶极子,在翼面上满足物面边界条件,建立了解三维机翼绕流的下潜涡环栅格法.考虑到非线性的自由液面边界条件,用下潜涡环栅格法求解水翼绕流问题.通过算例验证了方法的正确性和程序的可靠性.本方法可用于水翼及水下安定翼和各种舵的水动力计算.     

The applicability of hydrofoils as a ship control device

Centrifugal forces are commonly created when ships turn, which may cause a ship to capsize in a critical situation. A mathematical model has been developed to optimize the stability coefficients for ship, with the aim to prevent capsizing and to increase ship maneuverability in high-speed water craft. This model can be used to develop algorithms for control system improvement. The mathematical model presented in this paper optimized the use of multipurpose hydrofoils to reduce heeling and the trimming moment, maintaining an upright ship’s position and lessening the resistance via transverse force. Conventionally, the trimming and heeling of a ship are controlled using ballast water; however, under variable sea conditions it is sometimes difficult to control a ship’s motion using ballast water. In this case, a hydrofoil would be more stable and maneuverable than a ballast tank controlled vessel. A movable hydrofoil could theoretically be adapted from moveable aerofoil technology. This study proves the merit of further investigation into this possibility.     

A minimization theory in Hilbert space and its application to two-dimensional cavity flow with a numerical study

A minimization theory, which is based on the Hilbert space theory, is proposed and applied to two-dimensional cavity flow past a strut with the assumption of potential flow. That is, the minimization of the cavity drag of the strut on the cavity flow is studied with the help of the optimization theory proposed. To accelerate the optimization process, the Euler beam theory is introduced to generate a small variation in the strut. The introduction of the Euler beam theory makes the mathematical formulation for the present theory ill-conditioned. To overcome this condition, the Tikhonov regularization and the Morozov's discrepancy principle are used to regularize the present optimal theory. From the numerical study, it is shown that the proposed minimization theory is able to find an optimized shape for the given strut and corresponding optimized cavity drag. Received: June 22, 2000 / Accepted: January 30, 2001     

基于多目标粒子群算法的翼剖面优化设计

船舶桨舵等装置均有水翼剖面组成,为了得到水动力性能更好的桨舵装置,需要对水翼进行优化设计。基于iSIGHT优化平台,采用粒子群优化算法,以保证水翼剖面升阻比和改善水翼表面压力分布为优化目标,进行多目标水翼优化。通过改变水翼剖面的拱度分布和厚度分布进行优化设计。优化后得到的最优剖面相对于原始剖面,明显增加了剖面的最小压力系数,并适当提高了升阻比,从而提高了水翼剖面的空泡性能和升力性能。因此,验证了利用多目标粒子群算法进行翼型优化设计的可行性。     

基于完全耦合算法的绕水翼流固耦合特性研究

基于完全耦合算法对绕二维NACA0009水翼流固耦合特性进行了数值模拟研究。采用Theodorsen模型和Munch模型对刚性和弹性水翼的水弹性响应进行了数值计算,分析了流体与结构的相互作用关系,研究了影响结构水弹性响应和流固耦合特性的因素。研究结果表明:考虑了流体黏性的Munch模型与基于势流理论的Theodorsen模型对气动弹性响应的数值计算结果基本一致,而Theodorsen模型由于没有考虑流体黏性在一定程度上低估了结构的水弹性响应。结构的惯性、阻尼和刚度力矩与流体的相应附加载荷均处于同一数量级,故流体与结构的相互作用不可忽略,尤其对于弹性水翼,流体的惯性、附加阻尼作用增大,流固耦合算法的数值稳定性对流固耦合特性的计算结果影响将更大。外部激励频率为非共振频率时,结构的刚度作用是影响水弹性响应的主要因素,外部激励频率为共振频率时,流体的附加阻尼和附加刚度作用减弱,除结构的刚度作用外,流体与结构的惯性作用对水弹性响应和流固耦合特性的影响也较大。     

绕水翼非定常空化流动的涡动力学分析

文章采用数值方法对绕水翼的非定常空化流动进行了流动计算,并采用涡动力学方法对非定常空化流场特性进行了分析。计算中,采用基于当地涡旋修正的湍流模型封闭控制方程,通过实验对该计算结果进行验证;采用涡量法分析了空化的发生和发展对涡量输运过程的影响。结果表明:基于当地涡旋修正的湍流模型可以准确地模拟水翼周围非定常空化流场结构;水翼空化流场具有强烈的非定常特性,空化的发展和流场中的涡结构有着紧密的联系;反向射流的作用会导致附着空穴尾缘附近速度梯度的非定常变化,是导致涡量产生和消失的重要因素;空化区域内部水气两相的质量交换会导致流场内体积变化率的变化,使得空化区域内部流体的非正压性显著增强,上述两者导致空化区域内部的涡量分布呈现强烈的非定常特性;空化现象引起的水气两相之间的相互转换以及对湍流的作用都是影响涡结构空间分布的重要因素。