Discrete vortex simulation of flow
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收稿日期:2015-06-19网络出版时间:2016-1-1914:55基金项目:国家部委基金资助项目作者简介:王春旭(通信作者),男,1981年生,博士,高级工程师。
研究方向:潜艇声隐身技术。
E-mail :260848719@吴崇建,男,1960年生,博士,研究员。
研究方向:潜艇声隐身技术引用格式:王春旭,吴崇建,陈乐佳,等.流致噪声机理及预报方法研究综述[J ].中国舰船研究,2016,11(1):57-71.WANG Chunxu ,WU Chongjian ,CHEN Lejia ,et al.A comprehensive review on the mechanism of flow-induced noise and related prediction methods [J ].Chinese Journal of Ship Research ,2016,11(1):57-71.0引言流致噪声在航海、航空领域受到高度的关注,它不仅造成飞机、直升机舱室乘员感观和心理上的不适,还严重影响水下作战平台(如潜艇)的隐蔽性。
基于广泛的工程背景需要,自上世纪40年代末,流致噪声机理、预报与控制方法的研究非常活跃,并取得了丰硕的成果,很多流致噪声问题机流致噪声机理及预报方法研究综述王春旭,吴崇建,陈乐佳,邱昌林,熊济时中国舰船研究设计中心,湖北武汉430064摘要:从自由湍流噪声、壁面湍流噪声、转子噪声和空腔流动4个方面对流致噪声机理及预报方法进行综述。
对目前工程应用中的3个主要流致噪声预报方法,即Lighthill 声比拟理论、Kirchhoff 方法和涡声理论的基本原理及适用性进行详细讨论,并对流致噪声数值模拟方法进行总结。
其中,Lighthill 声比拟理论属噪声源先验理论,虽方便应用但不能描述声流相互作用基础问题;Kirchhoff 方法在运用的过程中虽不需要确切获知源的属性,但声源区的计算精度很重要;涡声理论在声流相互作用等领域有着良好的研究前景。
多段翼型流动非定常性计算研究焦予秦;范娟莉;罗淞【摘要】Numerical simulation of flow unsteadiness of the 30P-30N multi-element airfoils has been done by detached eddy simulation (DES) method based on SA turbulence model. The average of aerodynamic characteristics for unsteady flow has been calculated and compared with experimental data to validate DES method. After that, the numerical results have been carefully analyzed. The analytical results show that the method is accurate for the simulation of the flow unsteadiness of multi-element airfoil. Vorticity has changed in certain extent beneath the lower surface of slat wing while periodic vortex shedding is obvious near the trailing edge of flap. And primary cause of multi-element airfoil's noise radiation has been revealed preliminarily. The results are useful in the research on reducing noise of multi-element airfoil.%用基于SA湍流模型的DES计算方法对30P-30N多段翼型绕流的非定常性进行数值模拟.通过将非定常计算的气动特性平均值和定常实验结果比较验证了计算方法的可靠性,并对基于SA湍流模型的DES方法非定常数值模拟的结果进行分析.结果表明,所述方法正确地模拟了多段翼型流动的非定常性.缝翼下表面具有一定的涡量变化,而襟翼上表面后缘有明显的周期性的涡脱落.初步揭示了多段翼型噪声辐射的根本原因.研究结果对减小多段翼型噪声的方法研究具有一定的意义.【期刊名称】《科学技术与工程》【年(卷),期】2011(011)013【总页数】5页(P2994-2998)【关键词】多段翼型;非定常;涡脱落;噪声【作者】焦予秦;范娟莉;罗淞【作者单位】西北工业大学翼型、叶栅空气动力学国家级重点实验室,西安,710072;西北工业大学翼型、叶栅空气动力学国家级重点实验室,西安,710072;西北工业大学翼型、叶栅空气动力学国家级重点实验室,西安,710072【正文语种】中文【中图分类】V211.41当前,随着人类环境保护意识的不断增强,对飞机噪声的强制性指标要求越来越高。
基于双向流固耦合的灯柱涡激振动分析康友良;董国朝;韩艳;李振鹏【摘要】对有焊缝圆形断面的灯柱在不同风向角下的涡激振动响应进行了数值模拟研究.基于计算流体动力学方法,采用大涡模拟湍流模型,求解不可压缩流体N-S 方程.通过编写自定义程序代码UDF,对Fluent软件进行了二次开发,将求解结构振动响应的Newmark-β算法嵌入到Fluent软件中.结合\"刚性边界层运动区域+动网格运动区域\"的动网格划分策略,对灯柱结构涡激振动响应进行了双向流固耦合数值模拟.研究结果表明:当来流风速处于5.25 m/s(0°风向角工况)和6.25 m/s(90°和-90°风向角工况)附近时,会出现\"锁定\"现象;而在其他风速区间,会出现\"拍\"现象.该流固耦合计算方法捕捉到了灯柱从\"拍\"到\"锁定\"再回到\"拍\"现象的全过程.在锁定区域附近,灯柱的涡激共振位移幅值远大于在非锁定区域灯柱的涡激共振位移幅值.【期刊名称】《交通科学与工程》【年(卷),期】2019(035)003【总页数】8页(P43-50)【关键词】灯柱;涡激振动;动网格;双向流固耦合【作者】康友良;董国朝;韩艳;李振鹏【作者单位】长沙理工大学土木工程学院,湖南长沙410114;长沙理工大学土木工程学院,湖南长沙410114;长沙理工大学土木工程学院,湖南长沙410114;长沙理工大学土木工程学院,湖南长沙410114【正文语种】中文【中图分类】TU130.2521目前,在中国修建的许多特大跨桥梁上,用于照明的灯柱属于细长杆件,且对风荷载非常敏感。
轻质、低阻尼比钢材在灯柱中使用非常广泛,发生涡激振动的几率也大幅提高。
涡激共振尽管不会导致灯柱直接破坏,但它具有发生风速低、频率大的特点,会加速灯柱局部疲劳损伤,造成施工和运营安全隐患[1]。
NACA4412翼型低速绕流的定常/非定常计算对比研究闫文辉【摘要】Numerical simulation of NACA4412 airfoil around flow is implemented based on steady and unsteady computationalmethods .Convection terms and diffusion terms are calculated using Roe scheme and center difference scheme respectively .The dual-time stepping method with implicit approximate-factorization employed in time marc-hing.Two equation SST k-ωturbulence model is forfeited forsteady/unsteady computations .Computational results of steady/unsteady numerical simulations are compared with experimental data .Periodic vortex shedding behind airfoil tail is obtained using unsteady numerical simulation .Time-averaged computational results obtained by un-steady method are batter then steady computational results .%对NACA4412翼型低速绕流进行了定常/非定常数值计算。
对流项及扩散项的空间离散分别采用Roe格式和二阶中心格式,时间方向采用了二阶精度的双时间步隐式方法求解,湍流模式采用了两方程SST k-ω模式。
英文释义中文释义备注说明一、基础词汇1、直升机种类single-rotor helicopter (with tail rotor) 单旋翼带尾桨式直升机tandem rotors helicopter 纵列式双旋翼直升机side-by-side rotors helicopter 横列式双旋翼直升机coaxial rotors helicopter 共轴双旋翼式直升机tip-driven rotors helicopter 叶尖推进式直升机tilt rotors helicopter 倾转旋翼式飞机autogyro 旋翼机compound helicopter 复合式直升机2、常见作用力thrust 推力加上coefficient,即相应系数,例:升力系数lift 升力propulsion 推进力跟发动机有关的profile drag 型阻力aerodynamic drag 气动阻力drag force 阻力centrifugal force 离心力parasite drag 废阻力protuberance drag 由于机身突起物所带来的阻力nose-down/nose up moment 低头力矩/抬头力矩对于迎角来说,抬头为正,低头为负3、直升机的一些部件rotor shaft 旋转轴main rotor axis 主旋翼轴aft 尾部fairing 整流装置fuselage 机身机身包括nose-section、corss-section shape、afterbody taper、camber几个部分构成auxiliary components 辅助元件gas turbine engine 燃气涡流发动机piston engine 活塞式发动机hub 桨毂control column 驾驶杆cockpit 驾驶舱undercarriage\landing gear 起落架可以收回的起落架retraction (轮式的是wheel,雪橇式的是skid)engine nacelle 发动机舱deflector 变流装置canopy 座舱罩airframe 机身主要相对气动分析而言的概念propeller 螺旋桨(推进器)相对旋翼机而言articulated rotor 铰接式旋翼铰接articulationhingless rotor 无铰式旋翼4、数学概念equation 等式formula 公式iterative 迭代的non-dimensionalize 无因次化coefficent 系数empirical factor 经验系数dimensionless quantity 无因次量harmonic terms 各阶谐波项second harmonic control 二阶谐波控制numerical method 数值方法linearization of small perturbation 小扰动线性化polynomial 多项式vector sum 矢量和displacement 位移evaluate 求……的值5、直升机的基本参数rotor diameter 桨盘直径rotor radius 桨盘半径disc loading 单位桨盘载荷figure of merit 相对效率twist /negative 扭度/负扭center of gravity 重心angular velocity 角速度chord length 弦长spanwise width 展向宽度solidity factor 实度collective pitch 总距span 叶素全长Lock number 洛克数power-to-weight ration 功重比pitch 俯仰roll 滚转head 偏航sweepback 后掠角stiffness 刚度刚体的:rigidconing angle 锥度角angle fo incidence(attack) 迎角offset 偏置常用在挥舞铰偏置中Aspect ratio 展弦比二、直升机空气动力学1、滑流理论英文释义中文释义备注说明momentum theory滑流理论vertical flight垂直飞行hover悬停in descent/vertical descent/vertical climb下降/上升induced power/velocity诱导功率/速度outflow流出流inflow流入流disc桨盘streamtube流管线flow pattern流型steady/unstead定常/非定常downwash/upwash下洗流/上洗流kinetic energy动能compressibility effect压缩性效应tip loss叶尖损失2、叶素理论Blade Element Theory/Elementary Blade Theory 叶素理论section shape剖面inflow angle来流角airfoil翼型blade incidence桨叶迎角lift slop 升力线斜率blade span翼展(相对于旋翼而言)leading edge前缘trailing edge后缘blade桨叶沿半径从内向外分为三个部分:inboard、mid-span、tip partsnon-uniform flow非均匀来流ideal twist儒氏旋翼blade mean lift coefficient平均升力系数与升力系数不是同一个概念3、涡流理论部分英文释义中文释义备注说明tip vortex 桨尖涡vortex-ring (state) 涡环(状态)vortex的复数vortices turbulent-wake state 紊流状态wake vortices 尾迹涡vortex cylinder 涡柱面trailing vortex system 尾迹涡系wake vortices 尾迹streamwise vortices 流向涡discrete 分离的三、前飞理论部分英文释义中文释义备注说明advance ratio前进比advancing side前行桨叶retreating side后行桨叶flapping motion挥舞运动flapping hinge挥舞铰flapping coefficient挥舞系数region of reversed flow反流区Equilibrium Equation力平衡方程Coriolis force/moment哥氏力/哥氏力力矩interia force/moments惯性力restraining force约束力gravitational force/moments重力/力矩damping 阻尼mechanical damper机械阻尼器gyroscopic moment陀螺力矩crosscoupling交叉耦合oscillatory bending stress振荡弯曲应力roll moment滚转力矩resultant force/moment合力/合力矩 A be communicated to B力A传到Blead-lag hinge摆振铰feathering hinge变距铰oncoming stream direction迎流方向reference plane参考面separated flow气流分离全称:retreating blade stallblade stalling桨尖失速全称:advancing blade compressiblity dragriseazimuth angle方位角shock induced flow seperation激波-气流分离stalling characteristic失速特性free stream dynamic pressure自由来流动压boundary layer附面层asymmetry/symmetry不对称/对称flow reversl气流反向horizontal tailplane水平安定面vertical fin垂直安定面lateral/longitudinal cyclic coefficient横向/纵向周期变距headwind逆风tailwind顺风四、性能计算部分:英文释义中文释义备注说明performance assessment性能评估helicopter performance calculation直升机性能计算ground effect地面效应autorotation自转飞行high rate of climb悬停升限wind tunnel test风洞测试patrol/loiter task巡航飞行cruise speed巡航速度weight capability承重能力rate of climb 爬升率absolute ceiling绝对升限service ceiling 实用升限optimum speed 最佳速度minimum rate of descent 最小下降率maximum edurance/loiter time 最大续航时间maximum glide distance最大航行距离maximum range最大航行里程maximum speed最大速度specific range比航程dihedral action上反作用longitudinal/lateral trim equation纵向/横向配平方程shaft power轴功率power requirement需用功率induced requirement诱导功率stability 稳定性static stability静稳定dynamic stability动稳定incidence disturbance动稳定扰动的几种情况forward speed disturbance angular velocity disturbancesideslip disturbance yawing disturbancestability augmentation system增稳系统。
ABSTRACTThe sediment incipience, transport and local scour in the case of complex flows are the hot research topic in river and coastal engineering all the time. The traditional theory in which only the mean bed shear stress or sediment carrying capacity formula is considered to study sediment transport and scour is not suitable in the case of complex flows containing turbulence and large-scale vortices. With the rapid development of discrete element method, it has developed fast to use numerical model to investigate this problem from the mesoscale view, which may reveal the mechnasim of sediment motion in the case of complex flows. Using computational fluid dynamics software OpenFOAM and particle motion simulation software LIGGGHTS, a coupled fluid-particle model, in which the flow field is simulated by LES model, is presented and applied in the investigation of sediment incipience, transport and local scour.The main contents and results of this thesis are as follows.(1) The characteristics of the flow around the cylinder are studied through the dynamic one-equation LES model, the velocity profile, leeward of the cylinder and the pressure distribution are analyzed. The simulated results are verified by comparion between RNGκε-numerical results and experimental results. The simulation results show that the dynamic one-equation LES model can describe the complex flows around cylinder and the pressure distribution better.(2) The coupled fluid-particle model is applied in the investigation of three dimensional turbulence, sediment incipience and the sediment transport at the downstream of the backward-facing step flow. The model describes the mean velocity profile, the turbulence intensity and the distribution of Reynold stress well. The probabilitv of sediment incipience and the sediment flux obtained by the coupled model at the downstream of the backward-facing step agree well with the experiment. The results indicate that the turbulence and large-scale vortices induce the sediment incipience and the mean flow contributes to its transport in the case of complex flows.(3) The coupled fluid-particle model is used to verify the sediment motion and simulate the scour around the cylinder, and the scour process and depth are analyzed. The variation of flow velocity, turbulent kinetic energy and vorticity developmentduring scouring are studied. The results reveal that the horseshoe vortex and the accelerating flow contribute dominantly to local scour in front of the cylinder while the turbulent fluctuation and wake vortex results in the scour developmentbehind the cylinder.KEY WORDS:CFD-DEM coupling model, Dynamic one-equation LES model, Complex flows, Sediment transport, Local scour目录摘要 (I)ABSTRACT (II)目录 (IV)第1章绪论 (1)1.1 研究背景与意义 (1)1.2 国内外研究现状 (2)1.2.1 圆柱绕流问题研究 (2)1.2.2 泥沙输运及冲刷问题研究 (3)1.2.3 DEM在颗粒流体耦合运动中的应用 (5)1.3 本文主要研究内容 (7)第2章CFD-DEM耦合模型 (8)2.1 流体控制方程及紊流模型 (8)2.1.1 流体控制方程 (8)2.1.2 紊流模型 (8)2.1.3 数值离散方法 (10)2.2 颗粒运动数学模型 (11)2.2.1 运动控制方程 (11)2.2.2 接触模型 (12)2.2.3 计算时间步长 (14)2.3 CFD-DEM耦合模型 (15)2.3.1 耦合模型控制方程 (15)2.3.2 流体颗粒相互作用力 (16)2.3.3 耦合计算过程 (18)2.4 本章小结 (18)第3章三维水流模型验证 (19)3.1 模型设置 (19)3.1.1 算例设计及边界条件 (19)3.1.2 明渠流模拟 (20)3.2 流场结果验证及分析 (21)3.3 压力结果验证及分析 (32)3.4 本章小结 (34)第4章复杂流动下的泥沙运动模拟研究 (35)4.1 后台阶流场模拟 (35)4.1.1 时均流速剖面验证 (36)4.1.2 紊动强度及雷诺应力验证 (37)4.2 泥沙起动概率验证 (38)4.2.1 模型设置 (38)4.2.2 结果验证及分析 (39)4.3 泥沙输运模拟研究 (42)4.3.1 算例设置 (42)4.3.2 结果分析 (43)4.4 本章小结 (45)第5章圆柱周围局部冲刷模拟研究 (47)5.1 模型设置及验证 (47)5.2 局部冲刷数值模拟 (50)5.2.1 算例设置 (50)5.2.2 冲刷过程随时间变化 (51)5.2.3 冲刷坑深度分析 (52)5.3 冲刷过程流动特性变化 (53)5.3.1 流速分布变化 (53)5.3.2 紊动能变化 (58)5.3.3 涡量场变化 (60)5.3.4 局部冲刷机制分析 (61)5.4 本章小结 (62)第6章结论与展望 (63)6.1 本文主要结论 (63)6.2 工作展望 (64)参考文献 (65)发表论文和参加科研情况说明 (72)致谢 (73)第1章绪论1.1研究背景与意义水工结构物如桥墩、桩柱等处在易受侵蚀床面上时,在水流持续作用下,其周围的水流流动呈现出强烈的紊动特征,并将改变周围床面的泥沙输运能力,从而引起建筑物周围局部地形变化即“局部冲刷”。
18. 多相流模拟介绍 自然界和工程问题中会遇到大量的多相流动。物质一般具有气态、液态和固态三相,但是多相流系统中相的概念具有更为广泛的意义。在多项流动中,所谓的“相”可以定义为具有相同类别的物质,该类物质在所处的流动中具有特定的惯性响应并与流场相互作用。比如说,相同材料的固体物质颗粒如果具有不同尺寸,就可以把它们看成不同的相,因为相同尺寸粒子的集合对流场有相似的动力学响应。本章大致介绍一下Fluent中的多相流建模。第19章和第20章将会详细介绍本章所提到的内容。第20章会介绍一下融化和固化方面的内容
18.1 多相流动区域 18.2 多相系统的例子 18.3 多相建模方法 18.4 多相流模型的选择
18.1 多相流动区域 我们可以根据下面的原则对多相流分成四类: 气-液或者液液流动: o 气泡流动:连续流体中的气泡或者液泡。 o 液滴流动:连续气体中的离散流体液滴。 o slug flow: large bubbles in a continuous fluid o 分层自由面流动:由明显的分界面隔开的非混合流体流动。 气-固流动: o 充满粒子的流动:连续气体流动中有离散的固体粒子。 o 气动输运:流动模式依赖诸如固体载荷、雷诺数和粒子属性等因素。最典型的模式有沙子的流动,slug flow, packed beds, and homogeneous flow. o 流化床:consist of a vertical cylinder containing particles where gas is introduced through a distributor. The gas rising through the bed suspends the particles. Depending on the gas flow rate, bubbles appear and rise through the bed, intensifying the mixing within the bed. liquid-solid flows o slurry flow: transport of particles in liquids. The fundamental behavior of liquid-solid flows varies with the properties of the solid particles relative to those of the liquid. In slurry flows, the Stokes number (see Equation 18.4-4) is normally less than 1. When the Stokes number is larger than 1, the characteristic of the flow is liquid-solid fluidization. o hydrotransport: densely-distributed solid particles in a continuous liquid o sedimentation: a tall column initially containing a uniform dispersed mixture of particles. At the bottom, the particles will slow down and form a sludge layer. At the top, a clear interface will appear, and in the middle a constant settling zone will exist. three-phase flows (combinations of the others listed above) Each of these flow regimes is illustrated in Figure 18.1.1.
*Correspondingauthor.E-mail:aln@cowi.dk.JournalofWindEngineeringandIndustrialAerodynamics77&78(1998)591—602
Discretevortexsimulationofflowaroundfivegenericbridgedecksections
AllanLarsen*,JensH.WaltherCOWIConsultingEngineersandPlannersA/S,Parallelvej15,DK-2800Lyngby,DenmarkDanishMaritimeInstitute,Hjortekoersvej99,DK-2800Lyngby,Denmark
AbstractTwo-dimensionalviscousincompressibleflowpastfivegenericbridgedeckcrosssectionsareinvestigatedbymeansofthediscretevortexmethod.TheanalysesyieldsrootmeansquareliftcoefficientsandStrouhalnumbersforfixedcrosssectionsandaerodynamicderivativesforthecrosssectionsundergoingforcedoscillatorycrosswindandtwistingmotion.Fairagreementisestablishedbetweenthepresentsimulationsandwindtunneltestresultsreportedintheliterature.1998ElsevierScienceLtd.Allrightsreserved.
Keywords:Computationalbridgeaerodynamics;Discretevortexmethod;Vortexshedding;Aerodynamicderivatives
1.IntroductionLongspancablesupportedbridgesareoftenfoundtobesensitivetowindeffects,hence,windloadingandaeroelasticstabilitymustbeconsideredduringdesignsimilarlytootherloadingcomponentssuchasdeadload,liveloadandpossiblyearthquake.Aerodynamicdataforbridgedesignaretraditionallyobtainedfromwindtunneltests,buttheturnovertimeforplanning,actualtestingandanalysisisoftensubstantialandmaybeprohibitiveforbridgedesignstudies.Inthesecasesthedesignerisforcedtomakeuseofaerodynamicdataavailableintheliteraturebutthisapproachinvolveslargeuncertainties.AnewcomputercodeDVMFLOWbasedonthediscretevortexmethodhasbeendevelopedinordertofacilitatetheacquisitionofsatisfactoryaerodynamicdataforuseinbridgedesignstudieswithoutresortingtotimeconsumingwindtunnel
0167-6105/98/$—seefrontmatter1998ElsevierScienceLtd.Allrightsreserved.PII:S0167-6105(98)00175-5testing.TheobjectiveofDVMFLOWistoallownumericalassessmentofaerody-namicparametersforpractical2Dbluffcross-sectionscommonlyencounteredindesign.Thepresentpaperaddressestheextractionofdesiredaerodynamicdatafromdiscretevortexsimulationsanddiscussestheirsignificancetoaeroelasticanalysisofbridges.Flowsimulationsanddiscussionofresultswillbegivenwithreferencetofivegenericbridgesections.ThesesectionswereinvestigatedexperimentallybyScanlanandTomko[1]whoreportedaerodynamicderivativesforuseinflutteranalyses.
2.DiscretevortexcodeDVMFLOWAdistinctfeatureofflowpastbluffbodies,stationaryorintimedependentmotion,isthesheddingofvorticityinthewakewhichbalancesthechangeoffluidmomentumalongthebodysurface.Similarsheddingofvorticityalsooccurinthewakeofstreamlined(airfoillike)bodiesintransientmotioninapotentialflow.Thevorticityshedataninstantintimeisconvecteddownstreambutcontinuestoaffecttheaerodynamicloadsonthebody.Analyticaltreatmentofpotentialflowpaststreamlinedbodiesassumesthatthevorticalwakeisshedfromasinglepoint—thetrailingedge.Theshedvorticityisconvecteddownwindwiththespeedofthesurroundingfluidformingatrailingvortexsheet.Thissimplifiedmodelisnotvalidforviscousflowspaststationaryormovingbluffbodies.Asaconsequenceofviscositytheunsteadyvorticalwakeofabluffbodywillbeshed,notonlyatthetrailingedge,butalongtheentirebodycontour.Theshedvorticesareconvecteddownwindbylocalmeanwindspeedandviscousdiffusionbutwillalsointeracttoformlargescalecoherentstructures.AmathematicalmodelfortheflowaroundbluffbodieswasdevelopedwithintheframeworkofthediscretevortexmethodasproposedbyTurkiyyahetal.[2]forbuildingaerodynamicproblems.Thepresentalgorithm,whichtreatsviscousdiffusionbymeansof“randomwalks”asproposedbyChorin[3],wasandprogrammedforcomputerbytheco-author.TheresultingnumericalcodeDVMFLOWestablishesatwo-dimensional(2D)viscousand“gridfree”timemarchingsimulationofthevorticityequationwellsuitedforcomputationof2Dbluffbodyflows.AnoutlineofthemathematicalmodelandthesimulatedflowaboutaflatplateispresentedinRef.[4].Applicationto4selectedbridgegirdercross-sectionsandcomparisontowindtunneltestresultsarediscussedinRef.[5].TheinputtoDVMFLOWsimulationsisaboundarypanelmodelofthebluffbodycontour(thebridgedecksection).TheoutputofDVMFLOWsimulationsistime-progressionsofsurfacepressuresandsectionloads(drag,liftandmoment).Inaddition,mapsoftheinducedvelocityfieldandvortexpositionsatprescribedtimestepsareavailable.Steady-statewindloadcoefficientsareobtainedfromtimeaver-agesofsimulatedloadsonstationarypanelmodels.Aerodynamicderivativesandvortexinducedresponseareobtainedfrompostprocessingofsimulatedtimeseriesofforcedorfreeresponse.
A.Larsen,J.H.Walther/J.WindEng.Ind.Aerodyn.77&78(1998)591–602592