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1、适用于气动弹性的小波非定常气动力降阶方法刘晓燕,杨超,吴志刚(北京航空航天大学航空科学与工程学院,北京100191)Wavelet2basedReduced2orderMethodforUnsteadyAerodynamicsApplicabletoAeroelasticityLiuXiaoyan,YangChao,WuZhigang(SchoolofAeronauticScienceandEngineering,BeijingUniversityofAeronauticsandAstronauti
2、cs,Beijing100191,China)摘要:发展非定常气动力模型降阶技术旨在缩减计算耗费并且使得计算流体力学信息能够应用于气动伺服弹性以及设计优化当中。采用小波方法建立基于Volterra级数的非定常气动力降阶模型。在模型识别过程中,激励是光滑连续的且以零阶保持方式进行离散,采样频率选择二的整数幂次。近似的一阶Volterra核基于Haar尺度函数族展开,鉴于Volterra核在系统响应中的衰减特性,可在合适的有限时长截断一阶核。为了获得一阶核的各项展开系数,需要求解由输入/输出数据组成的超
3、定方程,其中涉及到奇异值分解算法。为了验证小波方法的有效性,算例选取了二维的NACA64a010翼型。数值仿真结果表明该方法能够比较准确地预测结构小扰动引起的非定常气动力响应且能描述一定的非线性现象。关键词:气动弹性;气动力降阶模型;小波;Volterra级数;超定方程;零阶保持中图分类号:V211147文献标识码:AAbstract:Thegoalbehindthedevelopmentofreduced2ordermodelsforunsteadyaerodynamicsistoreduceco
4、mputationalcostandfacilitatetheuseofcomputationalfluiddynamicsinformationinaeroservoelasticityanddesignoptimization.Inthisarticlereduced2orderaerodynamicmodelsarederivedbyutilizingwaveletapproxi2mationsofkernelsappearinginVolterraseriesrepresentations.
5、Duringtheprocessofmodelidentification,in2putexcitationissmoothandcontinuousanditisdiscretizedbyemployingazero2orderholdwithasamplingrateof2integerpower.Theapproximatedfirst2orderkernelisexpandedbasedontheHaarscaledfunctionfamily.Thefirst2orderkernelcan
6、betruncatedinaproperlylimitedtimelengthasaresultoftheVolterraker2neldecaycharacteristicinsystemresponses.InordertoobtainthecoefficientsoftheVolterrakernel,theoverdeterminedequationcomposedoftheinput/outputdatamustbesolvedviasingularvaluedecomposition.F
7、inally,anexampleofatwo2dimensionalNACA64a010airfoilvalidatesthewavelet2basedmodelingapproach.Thenumericalresultsshowthattheproposedmethodisabletopredictmoreaccuratelytheunsteadyaerody2namicresponsesduetostructuralsmall2amplitudemotionsanddescribecertai
8、nnonlinearphenomena.Keywords:aeroelasticity;reduced2orderaerodynamicmodel;wavelet;Volterraseries;overdeterminedequa2tion;zero2orderhold气动伺服弹性(Aeroservoelasticity,ASE)系统可以看做是气动、结构和控制3个环节相互耦合的闭环系统,其中需要建立便于主动控制系统设计的气动力低阶模型,因而非定常气动力的预测就显得尤为
