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February2005 GenerationofDynamicGridsandComputationofUnsteadyTransonicFlowsaroundAssemblies ·7·
GenerationofDynamicGridsandComputationofUnsteadyTransonicFlowsaroundAssemblies
CAIFeia,*,ZHANGLipingb
aDepartmentofAerodynamics,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,China
bSchoolofElectronicandInformationEngineering,BeijingUniversityofAeronauticsandAstronautics,Beijing100191,China（投稿时请将作者姓名和单位删掉）
（注：
英文单位名称请注意写准确，具体可上本刊网站下载中心“单位英文名称”查询，如发现本刊所给英译文有误，欢迎指正）
Received5May2009;revised11June2009;accepted16September2009
Abstract
Thecouplednumericalsimulationofflowfield,solidtemperaturefield,speciesconcentrationfieldandgasradiationtransfer/energyfieldbasedonstatisticalnarrow-bandcorrelated-k（SNBCK）model,isemployedtoaccuratelypredictaerothermodynamiccharacteristicofaircraftexhaustsystem.AseriesofmethodstoincreasecomputationalefficiencyanddescendcomputationalresourcesmakeitpossibletofinishthecalculationinPC.Theparametersofnarrow-bandmodelareevaluatedbyHITEMPline-by-linedatabase.Threeexampleshaveprovedtheaccuracyofusingthesemethodstosolveflowheattransfercoupledproblemandradiationtransfer/energyequation,whicharethecalculationoftemperaturedistributionofwater-coolingnozzleinrocketengine,thecalculationofcarbondioxideabsorptivityat4.3micronband,andthegasradiationheattransferevaluationofthecylindricalfurnace.Finally,theinnerflapstemperaturedistributionofejectingnozzlewithfloatingouterflapsiscomputed,underhigh-altitude,high-speedandafterburningconditions.Twocompletelydifferentair-inletschemesofejectingchannelalmostachievethesameeffectincoolinginnerflaps.（英文摘要应不少于150词；包含研究的目的、方法、结果和结论；通常用一般现在时，除非有明显的过去时间指示词出现）
Keywords:
transonicflow;unsteadyflow;full-potentialequation（5-8个，建议其中1-2个选自EIcontrolledterm词表）
No.2 CAIFeietal./ChineseJournalofAeronautics24（2011）xx-xx ·3·
1.Introduction*Correspondingauthor.Tel.:
+86-10-82317058.
E-mailaddress:
abc@
Foundationitem:
NationalNaturalScienceFoundationofChina（基金号）（注：
基金项目的正确英文名称请查询本刊下载中心“基金项目英文名称”）
1000-9361/$-seefrontmatter©2011ElsevierLtd.Allrightsreserved.
doi:
ThecomputationmethodofunsteadytransonicflowbasedonN-Sequationsshouldbebestaccurate,buttothree-dimensionalcomplexproblems,itcanbeachievedonlyonlargecomputers,andmoreover,theresultsarenotidealsometimes[1].Aviscous/inviscidinteractionmethodisanapplicableoneandthecomputationtimecanbereducedbytwoorders.
Themethodtosolvethefull-potentialequationovertransonicunsteadyforcesonwingshasbeendeveloped[2-3],buttoassemblies,itisnotmature,andtheresearchworksarecontinuouslycarriedon[4-5].
Thekeytocomputetheunsteadyaerodynamicforcesistogeneratedynamicgridsefficiently.Inthepresentpaper,analgebraicmethodandrapiddeformingtechniqueareusedtogeneratethree-dimensionalboundary-fitteddynamicgridsforassemblies.Theconservativefull-potentialequationissolvedbyatime-accurateapproximatefactorizationalgorithmandinternalNewtoniterations.Anintegralboundarylayermethodbasedonthedissipationintegralisusedtoaccountforviscouseffects.Thecomputationalresultsaboutunsteadytransonicforcesonwings,bodiesandcontrolsurfacesareinagreementwithexperimentaldata.（前言一般不要放图、表、公式）
2.ComputationScheme
2.1.Governingequation
2.1.1Governingequation
Theunsteadyfull-potentialequationwritteninabodyfittedcoordinatesystemisgivenby
（1）
whererisdensity,U,V,andWarethecontravariantvelocitycomponentsinthex,h,andzdirections,meanstime,andJisJacobian.（正文中不要用公式编辑器插入符号，直接敲入即可）
（公式编辑器中的行距不要改动，默认值即可）
（公式中用到小括号时，不要用公式编辑器中的括号，如，直接用键盘敲入即可如）
wherefisvelocitypotential.
2.2.Generationofgrids
Thealgebraicmethodisusedtogeneratethree-dimensionalboundary-fittedgridsforawing.Theheightofthefirstgridnexttothebodyiscontrolled,andthegridsneartothebodyarenormalized.
Towing/missilecombination,theH-Hboundary-fittedgridsforasinglewingaregeneratedatfirstinordertosimulatetheaerodynamicforcesonmissilesaccurately.Thesectionatthepositionofpylonischangedintotwooverlappinglayers.Apartialdeformingtechniqueisusedintheareaofpylon/launching/missiletogetthestaticgridsforthecombination.
Whenwithfuselage,thedeformingtechniqueisusedatthesymmetricsectiontogetthestaticgridsalso.
Tosimplifytheequation,thedynamicgridswherethefarfieldisfixedandthebodyisdynamicareappliedtounsteadyflows.Asitwillconsumemuchtimetogenerategridsonceatime-step,toaerodynamicelasticitymovementofsmallamplitude,ordinarily,thegridsareobtainedbysolvingthebalanceequationbasedonlasttime-step,butthatisstillnoteconomic.
Takingtheincompressiblepotentialflowroundacylinderforexample,thestreamfunctionis
（2）
whereaisradius,isthevelocityoffreestream.Magnifyingitsradiusto ,thenthepreviousstreamlinepassingpoint（r,q）willyieldanormaldisplacementDr
（3）
Thatisdifficultydirectlytogeneratedynamicgrids.Simplifyingfurther,thecoordinates（representedbysubscriptu）ofthedynamicgridsare
（4）
wheresubscriptsrepresentstheboundary-fittedstaticgridswhichareusedastheinitialvalues,rrepresentstheinstantaneouscoordinatethatthestaticgridsmovetowithbodies,gisthefunctionabouttheserialnumberofthegridlines.
（5）
wherebrepresentsthecorrespondingboundarypoints,frepresentsthefarfieldpoints.
3.PresentationofResult
F5wing/missileandHARWwing/fuselagearetakenforexamplesinthepresentpaper.Fig.1showsthesketchesofF5wing/missileandHARWwing/fuselagewithcontrolsurfaces.Themissileislocatedat73.5percentofhalf-span.ThetrailingedgecontrolsurfaceofHARWwing/fuselagetakesup20percentofthechord;controlsurfaceIislocatedatapositionfrom58.9%to79.4%ofhalfspan;controlsurfaceIIislocatedfrom9.6%to23.9%.Fig.2istheH-HsurfacegridsforF5wing/missile.Fig.3showstheoverlookingviewofHARWwing/fuselageassembles’C-Hgrids.
Fig.4Comparisonbetweencomputationresultandexperimentaldata[24]fortemperaturedistributionofinnerwallofnozzle.
Table5CPUtimeratioofeachterm
Computationalterm
CPUtime/%
Flowfield
32.6
Solidtemperaturefield
2.2
Speciesconcentrationfield
4.3
Radiationtransfer/energyfield
60.9
4.Conclusions
（1）Arapidmethodofthegenerationofboundary-fitteddynamicgridsisdevelopedinthispaper,andthemethodofViscous/InviscidInteractionisusedtocomputetheunsteadyaerodynamicforcesonwing/missilesandwing/bodywithcontrolsurfaces.
（2）Thecomputationresultsareinagreementwithexperimentaldata.Tounsteadyflows,ittakesnearlyonehourtocarryoutthreetimecycleswith140thousandnodes,sothismethodispowerful.Thismethodpresentedinthispaperprovidesanapplicable,efficienttoolfortheaerodynamicelasticityanalysisinthetransonicaspect.（分点总结，只写结论，其他背景、方法都不必赘述）
References
[1]MatthewsFL,RawlingsRD.Compositematerialsengineeringandscience.2nded.NewYork:
Chapman&Hall,1994.（专著）
[2]SoutisC,FleckNA.StaticcompressionfailureofcarbonfibreT800/924Ccompositeplatewithsinglehole.JournalofCompositeMaterials1990;24（5）:
536-538.（期刊论文）
[3]BasslerHJ,EiflerD.Characterisationofplasticityinducedmartensiteformationduringfatigueofausteniticsteel.In:
RieKT,PortellaPD.Low-cycleFatigueandElasto-plasticBehaviourofMaterials.Amsterdam:
ElsevierSciLtd,1998;235-240.（专著中的部分文献）
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[7]BarbantePE.Accurateandefficientmodelingofhigh-tempera-turenonequilibriumairflows.PhDthesis,vonarmanInstituteforFluidDynamics,2001.（学位论文）
[8]AhaD,MurphyP.UCIRepositoryofmachinelearningdatabases.//www.ics.uci.edu/...>.Irvine,CA:
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[9]KhalifaHE,GlauserMN.Low-mixingnozzleforpersonalventilation.USProvisionalPatentApplicationNo.60/826,929,2006.（专利文献）
注意:
上述文献如为中文文献，则只需提供其英译文，最后加上“[inChinese]”，其他格式同前。
Biographies:
（投稿时请将作者简介删掉）
LUZhiliangreceivedtheB.S.andM.S.degreesinmechanicalengineeringfromNanjingAeronauticalInstitutein1984and1987respectively,andthenbecameateacherthere.Hismainresearchinterestsare….
E-mail:
lulu213@
JohnSMITHisaPh.D.studentatschoolofautomation,BeihangUniversity.HereceivedhisB.S.degreefromWuhanUniversityin2008.Hisareaofresearchincludes…
E-mail:
wuhanujogn@
AliceS.L.ZINOBERisaprofessorandPh.D.supervisoratcollegeofmechanicalengineering,CambridgeUniversity,Cambridge,U.K.ShereceivedthePh.D.degreefromthesameuniversityin1970.Hercurrentresearchinterestsare…
E-mail:
lzlsax@
Appendix
内容为10号字
动态网格快速生成及组合体跨声速非定常气动力计算
蔡斐，张利平
（南京航空航天大学空气动力学系）
摘要:
耦合求解流场、固体温度场、组分浓度场、基于统计窄带关联k（SNBCK）模型的气体辐射传输/能量方程以求准确模拟飞行器排气系统气动热力特性。
通过一系列提高计算效率降低计算资源占用的算法，使在PC机上完成上述计算成为可能。
窄带模型参数由HITEMP逐线计算数据库计算得到。
通
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