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1、適用于氣動(dòng)彈性的小波非定常氣動(dòng)力降階方法劉曉燕,楊超,吳志剛(北京航空航天大學(xué)航空科學(xué)與工程學(xué)院,北京100191)Wavelet2basedReduced2orderMethodforUnsteadyAerodynamicsApplicabletoAeroelasticityLiuXiaoyan,YangChao,WuZhigang(SchoolofAeronauticScienceandEngineering,BeijingUniversityofAeronauticsandAstronauti
2、cs,Beijing100191,China)摘要:發(fā)展非定常氣動(dòng)力模型降階技術(shù)旨在縮減計(jì)算耗費(fèi)并且使得計(jì)算流體力學(xué)信息能夠應(yīng)用于氣動(dòng)伺服彈性以及設(shè)計(jì)優(yōu)化當(dāng)中。采用小波方法建立基于Volterra級(jí)數(shù)的非定常氣動(dòng)力降階模型。在模型識(shí)別過(guò)程中,激勵(lì)是光滑連續(xù)的且以零階保持方式進(jìn)行離散,采樣頻率選擇二的整數(shù)冪次。近似的一階Volterra核基于Haar尺度函數(shù)族展開,鑒于Volterra核在系統(tǒng)響應(yīng)中的衰減特性,可在合適的有限時(shí)長(zhǎng)截?cái)嘁浑A核。為了獲得一階核的各項(xiàng)展開系數(shù),需要求解由輸入/輸出數(shù)據(jù)組成的超
3、定方程,其中涉及到奇異值分解算法。為了驗(yàn)證小波方法的有效性,算例選取了二維的NACA64a010翼型。數(shù)值仿真結(jié)果表明該方法能夠比較準(zhǔn)確地預(yù)測(cè)結(jié)構(gòu)小擾動(dòng)引起的非定常氣動(dòng)力響應(yīng)且能描述一定的非線性現(xiàn)象。關(guān)鍵詞:氣動(dòng)彈性;氣動(dòng)力降階模型;小波;Volterra級(jí)數(shù);超定方程;零階保持中圖分類號(hào):V211147文獻(xiàn)標(biāo)識(shí)碼: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氣動(dòng)伺服彈性(Aeroservoelasticity,ASE)系統(tǒng)可以看做是氣動(dòng)、結(jié)構(gòu)和控制3個(gè)環(huán)節(jié)相互耦合的閉環(huán)系統(tǒng),其中需要建立便于主動(dòng)控制系統(tǒng)設(shè)計(jì)的氣動(dòng)力低階模型,因而非定常氣動(dòng)力的預(yù)測(cè)就顯得尤為
