An Accelerated Lambda Iteration Method for Multilevel Radiative Transfer III. Noncoherent E

合集下载

物理学名词

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。

风云卫星数据和产品应用手册讲解

风云卫星数据和产品应用手册第1章概述1.1 FY-3A卫星概况风云三号A气象卫星（简称FY-3A）是我国的第二代太阳同步极轨气象卫星。

风云三号气象卫星将实现全球、全天候、多光谱、三维、定量对地观测。

风云三号星发射总质量为2450kg，发射尺寸：4.38m×2m×2m，卫星长期功耗1130W。

卫星本体由服务舱、推进舱与有效载荷舱组成。

服务舱采用中心承力筒和隔板结构，主要安装电源、测控、数管及姿轨控分系统的部件和设备、推进舱采用中心承筒和隔板结构，主要安装推进系统设备以及蓄电池组和放电调节器。

有效载荷舱隔板和构架结构，主要安装探测仪器的探测头部，舱内主要安装探测仪器的电子设备等。

风云三号A卫星有十一台遥感探测仪器。

遥感数据通过两个实时传输信道（HRPT和MPT）和一个延时传输信道（DPT）进行传输。

风云三号A卫星设计寿命为3年。

1.2 主要技术指标1.2.1 卫星轨道⑴轨道类型：近极地太阳同步轨道⑵轨道标称高度：831公里⑶轨道倾角：98.81°⑷入轨精度：半长轴偏差： |Δa|≤5公里轨道倾角偏差：|Δi|≤0.1°轨道偏心率≤0.003⑸标称轨道回归周期为5.79天⑹轨道保持偏心率：≤0.00013⑺交点地方时漂移：2年小于15分钟⑻卫星发射窗口：降交点地方时10:051.2.2 卫星姿态⑴姿态稳定方式：三轴稳定⑵三轴指向精度：≤0.3°⑶三轴测量精度：≤0.05°⑷三轴姿态稳定度：≤4×10-3 °/s1.2.3 太阳帆板对日定向跟踪1.2.4 星上记时⑴记时方式：J2000日计数和日毫秒计数⑵记时单位：1毫秒⑶时间精度(星地总精度):小于20毫秒1.2.5 遥感探测仪器性能指标1.2.5.1 可见光红外扫描辐射计(VIRR)(1)通道数、各通道波段范围、灵敏度见表1-1。

(2)空间分辨率：星下点分辨率1.1Km(3)扫描范围：±55.4°(4)扫描器转速：6线/秒(5)每条扫描线采样点数：2048(6)MTF≥0.3(7)通道配准：飞行方向/扫描方向星下点配准精度<0.5个像元(8)扫描抖动：<0.8个IFOV(9)通道信号衰减：<15%/2年(10)量化等级：10比特(11)定标精度：可见光和近红外通道：CH1、2、7、8、9 7%(反射率)CH6、10 10%(反射率)红外通道：1k(270k)。

高温气冷堆用碳毡材料导热系数测量及反问题计算

"卷第# #期 ! 第! * # !年# #月 !)
原
子ห้องสมุดไป่ตู้
能
科
学
技
术
$ % & ' ! " ( % ' # # ( % ; ' ) * # !
+ , % . /0 1 2 3 / . 2 1 / 27 1 89 2 / : 1 % & % 4 56 4 5
高温气冷堆用碳毡材料导热系数测量及反问题计算
李聪新任!成杨星团 " 姜胜耀孙艳飞
清华大学核能与新能源技术研究院先进反应堆工程与安全教育部重点实验室北京 !# * * * " !
摘要碳纤维材料已成为核能航天等领域不可或缺的重要功能材料在高温气冷堆及其相关实验中需要使用大量碳纤维保温材料但由于目前测试方法的限制相关材料物性参数测量数据严重不足尤其是缺乏高温 #* 致其使用受到限制为此清华大学核能与新能源技术研究院 * * h 以上的热物性参数研制了模拟高温气冷堆温度环境氛围的材料测试装置可提供 #@ * * h以下的材料性能测试根据该详细介绍了采用非线性导热反问题方法确定材料温度相关导热系装置一次典型实验过程的测量数据非稳态热传导原理求解反问题的简明算法该方法既数的完整过程和具体算法提出了一种依据稳态也可为其他反问题算法提供良好的迭代初值实验确定了高温气冷堆用碳毡保温材料在可单独使用将为高温气冷堆相关实验和其他特高温条件下的应用提供重要参考 #@ * * h 以下的导热系数关键词高温气冷堆碳毡保温材料高温导热系数导热反问题中图分类号 9 = B B )!!! 文献标志码 +!!! 文章编号 # * * * ? @ A B # ) * # ! # # ? # A C @ ? * A D G' ) * # !' % F Q . 7 1 ' * * * > ! " # # *' C > B " 5 5

Ansys热分析教程(全)

章节内容概述
• 第7章-续 – 例题 6 - 低压气轮机箱的热分析
• 第 8 章 - 辐射 – 辐射概念的回顾 – 基本定义 – 辐射建模的可选择方法 – 辐射矩阵模块 – 辐射分析例题 - 使用辐射矩阵模块进行热沉分析，隐式和非隐式方法。
• 第 9 章 - 相变 – 基本模型/术语 – 在 ANSYS中求解相变 – 相变例题 - 飞轮铸造分析
传导
• 传导的热流由传导的傅立叶定律决定：
q*
=
− Knn
∂T ∂n
=
heat
flow
rate
per
unit
area
in
direction
n
Where, Knn = thermal conductivity in direction n
T = temperature
∂T = thermal gradient in direction n ∂n
• 负号表示热沿梯度的反向流动(i.e., 热从热的部分流向冷的).
q*
T
dT
dn
n
对流
• 对流的热流由冷却的牛顿准则得出:
q* = hf (TS − TB ) = heat flow rate per unit area between surface and fluid
Where, hf = convective film coefficient TS = surface temperature TB = bulk fluid temperature
• 第 6 章 - 复杂的, 时间和空间变化的边界条件 – 表格化的热边界条件 (载荷) – 基本变量 – 用户定义的因变变量
章节内容概述

2046 J. Opt. Soc. Am. AVol. 20, No. 11November 2003 Martí-López et al.

Jeremy C. Hebden Department of Medical Physics and Bioengineering, University College London, 11-20 Capper Street,
London WC1E 6JA, UK
Simon R. Arridge Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
OCIS codes: 170.5280, 290.7050, 290.1990.
1. INTRODUCTION
Optical tomography (OT) deals with the problem of retrieving spatial functions of internal physical properties of a body from a set of optical measurements.1 Examples of such functions are scattering and absorption coefﬁcients (in biomedical applications) or the refractive index (in plasma physics research). Since biological tissues are relatively low absorbing in the optical window ranging from ␭ ϭ 700 nm to ␭ ϭ 1000 nm, most medical applications of OT are carried out in that range. Unfortunately, most biological tissues also strongly scatter light, which represents a serious problem for viewing the body’s internal structures and characterizing biological processes by optical methods.2–4

氨基酸的结晶

Crystallization of Amino Acids on Self-AssembledMonolayers of Rigid Thiols on GoldAlfred Y.Lee,†,‡Abraham Ulman,†,§and Allan S.Myerson*,‡Department of Chemical and Environmental Engineering,Illinois Institute of Technology, Chicago,Illinois60616,and Department of Chemical Engineering,Chemistry and Material Science,and the NSF MRSEC for Polymers at Engineered Interfaces,Polytechnic University,Brooklyn,New York11201Received March6,2002.In Final Form:May3,2002Self-assembled monolayers(SAMs)of rigid biphenyl thiols are employed as heterogeneous nucleants for the crystallization of L-alanine and DL-valine.Powder X-ray diffraction and interfacial angle measurements reveal that the L-alanine crystallographic planes corresponding to nucleation are{200}, {020},and{011}on SAMs of4′-hydroxy-(4-mercaptobiphenyl),4′-methyl-(4-mercaptobiphenyl),and4-(4-mercaptophenyl)pyridine on gold(111)surfaces,respectively.In the case of DL-valine,monolayer surfaces that act as hydrogen bond acceptors(e.g.,4′-hydroxy-(4-mercaptobiphenyl)and4-(4-mercaptophenyl)-pyridine)induce the racemic crystal to nucleate from the{020}plane whereas the nucleating plane for the4′-methyl-(4-mercaptobiphenyl)surface is the fast-growing{100}face.The observation of crystal nucleation and orientation can be attributed to the strong interfacial interactions,in particular,hydrogen bonding,between the surface functionalities of the monolayer film and the individual molecules of the crystallizing phase.Molecular modeling studies are also undertaken to examine the molecular recognition process across the interface between the surfactant monolayer and the crystallographic planes.Similar to binding studies of solvents and impurities on crystal habit surfaces,binding energies between SAMs and particular amino acid crystal faces are calculated and the results are in good agreement with the observed nucleation planes of the amino acids.In addition to L-alanine and DL-valine,the interaction of SAMs and mixed SAMs of rigid thiols on the morphology of R-glycine is examined(Kang,J.F.;Zaccaro, J.;Ulman,A.;Myerson,ngmuir2000,16,3791),and similarly the calculations are in good agreement. These results suggest that binding energy calculations can be a valid method to screen self-assembled monolayers as potential templates for nucleation and growth of organic and inorganic crystals.I.IntroductionCrystallization from solution is a two-step process: nucleation,the birth of a crystal,and crystal growth,the growth of the crystal to larger sizes.2In this process, prenucleation aggregates(or clusters)are formed by individual molecules,which become stable nuclei,upon reaching a critical size,and further grow into macroscopic crystals.Homogeneous nucleation is very rare and re-quires high supersaturation to surmount the activation barrier,∆G crit.However,for a fixed supersaturation the activation barrier can be lowered by decreasing the surface energy of the aggregate,for instance,by introducing a foreign surface or substance.3This foreign surface(or substance)includes“tailor-made”additives,4impurities,5 organic single crystals,6Langmuir monolayers7floating at the air-water interface,and self-assembled monolayers (SAMs)immersed in solution.1Tailor-made additives or auxiliaries are designer impurities that have one part which resembles the crystallizing species and another part that is chemically or structurally different from the solute molecule.4,8These additives disrupt the bonding sequence in the crystals,thereby lowering the growth rate of the affected faces as evident in the case of L-alanine where hydrophobic amino acids such as L-leucine and L-valine inhibited the development of specific crystal faces,while in the presence of hydrophilic amino acids the crystal morphology did not change.9In addition to being habit modifiers,these molecular additives can also control polymorphism,where the impurities inhibit the growth of one polymorph and,in turn,promote the growth of the other polymorph.10Nucleation promoters such as organic single crystals and self-assembled monolayers have also been used to control polymorph selectivity,based on geometric match-ing between the molecular clusters and the ledges of the crystal substrates11and interfacial hydrogen bonding between the monolayer film and solute clusters,12respec-*To whom correspondence should be addressed.Phone:312 5677010.Fax:3125677018.E-mail:myerson@.†Polytechnic University.‡Illinois Institute of Technology.§NSF MRSEC for Polymers at Engineered Interfaces.(1)Kang,J.F.;Zaccaro,J.;Ulman,A.;Myerson,ngmuir2000, 16,3791.(2)(a)Myerson,A.S.Handbook of Industrial Crystallization,2nd ed.;Butterworth-Heinemann:Boston,2002.(b)Myerson,A.S.Mo-lecular Modeling Applications in Crystallization;Cambridge Uni-versity Press:New York,1999.(c)Mullin,J.W.Crystallization,4th ed.;Butterworth-Heinemann:Boston,2001.(3)Turnbull,D.J.Chem.Phys.1949,18,198.(b)Fletcher,N.H.J. Chem.Phys.1963,38,237.(4)Weissbuch,I.;Lahav,M.;Leiserowitz,L.In Molecular Modeling Applications in Crystallization;Myerson, A.S.,Ed.;Cambridge University Press:New York,1999;p166.(5)Meenan,P.A.;Anderson,S.R.;Klug,D.L.In Handbook of Industrial Crystallization,2nd ed.;Myerson,A.S.,Ed.;Butterworth Heinemann:Boston,2002;p67.(6)Carter,P.W.;Ward,M.D.J.Am.Chem.Soc.1993,115,11521.(7)(a)Rapaport,H.;Kuzmenko,I.;Berfeld,M.;Kjaer,K.;Als-Nielsen, J.;Popovitz-Biro,R.;Weissbuch,I.;Lahav,M.;Leiserowitz,L.J.Phys. Chem.B2000,104,1399.(b)Frostman,L.M.;Ward,ngmuir 1997,13,330.(8)(a)Berkovitch-Yellin,Z.;Ariel,S.;Leiserowitz,L.J.Am.Chem. Soc.1985,105,765.(b)Addadi,L.;Weinstein,S.;Gate,E.;Weissbuch,I.;Lahav,M.J.Am.Chem.Soc.1982,104,4610.(9)Li,L.;Lechuga-Ballesteros,D.;Szkudlarek,B.A.;Rodriguez-Hornedo,N.J.Colloid Interface Sci.1994,168,8.(10)(a)Weissbuch,I.;Lahav,M.;Leiserowitz,L.Adv.Mater.1994, 6,952.(b)Davey,R.J.;Blagden,N.;Potts,G.D.;Docherty,R.J.Am. Chem.Soc.1997,119,1767.5886Langmuir2002,18,5886-589810.1021/la025704w CCC:$22.00©2002American Chemical SocietyPublished on Web06/22/2002tively.Similar to Langmuir monolayers,self-assembled monolayers can be used as an interface across which stereochemical matching13and hydrogen bonding14in-teraction can transfer order and symmetry from the monolayer surface to a growing crystal.However,SAMs and mixed SAMs15lack the mobility of molecules at an air-water interface and hence the possibility to adjust lateral positions to match a face of a nucleating crystal. This is clearly evident in the case of the SAMs of rigid biphenyl thiols,where even conformational adjustment is not possible.Recently,SAMs of4-mercaptobiphenyl have been shown to be more superior to those of al-kanethiolates and are stable model surfaces.16Further-more,the ability to engineer surface functionalities at the molecular level makes SAMs of rigid thiols very attractiveas templates for heterogeneous nucleation. Organosilane monolayer films have been used to promote nucleation and growth of calcium oxalate mono-hydrate crystals17and have been employed in“biomimetic”synthesis as observed in the oriented growth of CaCO318 and iron hydroxide crystals.19Functionalized SAMs of alkanethiols have also been shown to control the oriented growth of CaCO3.20This was also evident in the hetero-geneous nucleation and growth of malonic acid crystals21 on alkanethiolate SAMs on gold where the monolayer composition strongly influenced the orientation of the malonic acid crystals.Additionally,functionalized alkane-thiolate SAMs have enhanced the growth of protein crystals.22More recently,SAMs and mixed SAMs of rigid thiols served as templates.1It was observed that glycine nucleated in the R-form independent of the hydroxyl and pyridine surface concentration and the morphology of the glycine crystal was very sensitive to the OH and pyridine site densities.Self-assembled monolayers on solid surfaces offer many advantages for enhanced crystal nucleation.In this work, SAMs of rigid thiols on gold are employed to investigate the effects of interfacial molecular recognition on nucle-ation and growth of L-alanine and DL-valine crystals.In addition,molecular modeling techniques are employed to examine the affinity between monolayer surfaces and particular amino acid crystal faces and to gain a better understanding of the molecular recognition events oc-curring.The modeling techniques employed are similar to studies of solvent and additive interactions on crystal habit23but have never been applied to organic monolayer films as templates for nucleation.II.Experimental SectionMaterials.Anhydrous ethanol was obtained from Pharmco (Brookfield,CT).L-Alanine(CH3CH(NH2)CO2H),and DL-valine ((CH3)2CHCH(NH2)CO2H)were purchased from Aldrich and used without further purification.Distilled water purified with a Milli-Q water system(Millipore)was used.Details of the synthesis of the4′-substituted4-mercaptobiphenyl(see Figure1)are described elsewhere.24Gold Substrate and Monolayer Preparation.Glass slides were cleaned in ethanol in an ultrasonic bath at40°C for10min. The slides were next treated in a plasma chamber at an argon pressure of0.1Torr for30min.Afterward,they were mounted in the vacuum evaporator(Key High Vacuum)on a substrate holder,approximately15cm above the gold cluster.The slides were baked overnight in a vacuum(10-7Torr)at300°C.Gold (purity>99.99%)was evaporated at a rate of3-5Å/s until the film thickness reached1000Å;the evaporation rate and film thickness were monitored with a quartz crystal microbalance (TM100model from Maxtek Inc.).The gold substrates were annealed in a vacuum at300°C for18h.After cooling to room temperature,the chamber was filled with high-purity nitrogen and the gold slides were either placed into the adsorbing solution right after the ellipsometric measurement was performed or stored in a vacuum desiccator for later use.25Atomic force microscopy(AFM)studies24revealed terraces of Au(111)with typical crystalline sizes of0.5-1µm2.Monolayers were formed by overnight(∼18h)immersion of clean substrates in10µm ethanol solutions of the thiols.The substrates were removed from the solution,rinsed with copious amounts of absolute ethanol to remove unbound thiols,and blown dry with a jet of nitrogen. Contact angle measurements,IR spectroscopy,and ellipsometry showed that after1h,90%or more of the SAMs are formed.26 Thus,to ensure equilibrium SAMs,the gold substrates were left overnight in the dipping solution.Crystal Growth.Nucleation and growth experiments were carried out in Quartex jars(1oz.)at25°C.Supersaturated solutions(25%)of L-alanine and DL-valine were obtained by dissolving 4.58g and 1.95g in22.0g of Millipore water, respectively.The solutions were heated to65°C for90min in an ultrasonic bath to obtain complete dissolution.The solutions were cooled to room temperature for90min before the SAMs were carefully introduced and aligned vertically to the wall. Macrocrystals of L-alanine and DL-valine nucleated at the surfaces(11)(a)Bonafede,S.J.;Ward,M.D.J.Am.Chem.Soc.1995,117, 7853.(b)Mitchell,C.A.;Yu,L.;Ward,M.D.J.Am.Chem.Soc.2001, 123,10830.(12)Carter,P.W.;Ward,M.D.J.Am.Chem.Soc.1994,116,769.(13)(a)Landau,E.M.;Levanon,M.;Leiserowitz,L.;Lahav,M.;Sagiv, J.Nature1985,318,353.(b)Weissbuch,I.;Berfeld,M.;Bouwman,W.; Kjaer,K.;Als,J.;Lahav,M.;Leiserowitz,L.J.Am.Chem.Soc.1997, 119,933.(14)Weissbuch,I.;Popvitz,R.;Lahav,M.;Leiserowitz,L.Acta Crystallogr.1995,B51,115.(15)For a review on SAMs of thiols on gold see:(a)Ulman,A.An Introduction to Ultrathin Organic Films:From Langmuir-Blodgett to Self-Assembly;Academic Press:Boston,1991.(b)Ulman,A.Chem. Rev.1996,96,1533.(16)(a)Kang,J.F.;Ulman,A.;Liao,S.;Jordan,R.J.Am.Chem.Soc. 1998,120,9662.(b)Kang,J.F.;Jordan,R.;Ulman,ngmuir1998,14,3983.(17)Campbell,A.A.;Fryxell,G.E.;Graff,G.L.;Rieke,P.C.; Tarasevich,B.J.Scanning Microsc.1993,7(1),423.(18)Archibald,D.D.;Qadri,S.B.;Gaber,ngmuir1996,12, 538.(19)Tarasevich,B.J.;Rieke,P.C.;Liu,J.Chem.Mater.1996,8,292.(20)Aizenberg,J.;Black,A.J.;Whitesides,G.M.J.Am.Chem.Soc. 1999,121,4500.(21)Frostman,L.M.;Bader,M.M.;Ward,ngmuir1994, 10,576.(22)Ji,D.;Arnold,C.M.;Graupe,M.;Beadle,E.;Dunn,R.V.;Phan, M.N.;Villazana,R.J.;Benson,R.;Colorado,R.,Jr.;Lee,T.R.;Friedman, J.M.J.Cryst.Growth2000,218,390.(23)(a)Docherty,R.;Meenan,P.In Molecular Modeling Applications in Crystallization;Myerson,A.S.,Ed.;Cambridge University Press: New York,1999;p106.(b)Myerson,A.S.;Jang,S.M.J.Cryst.Growth 1995,156,459.(c)Walker,E.M.;Roberts,K.J.;Maginn,ngmuir 1998,14,5620.(d)Evans,J.;Lee,A.Y.;Myerson,A.S.In Crystallization and Solidification Properties of Lipids;Widlak,N.,Hartel,R.W.,Narine, S.,Eds.;AOCS Press:Champaign,IL,2001;p17.(24)Kang,J.F.;Ulman,A.;Liao,S.;Jordan,R.;Yang,G.;Liu,G. Langmuir2001,17,95.(25)(a)Jordan,R.;Ulman,A.J.Am.Chem.Soc.1998,120,243.(b) Jordan,R.;Ulman,A.;Kang,J.F.;Rafailovich,M.;Sokolov,J.J.Am. Chem.Soc.1999,121,1016.(26)Ulman,A.Acc.Chem.Res.2001,34,855.Figure1.Rigid4′-substituted4-mercaptobiphenyls.Crystallization of Amino Acids on Thiol SAMs Langmuir,Vol.18,No.15,20025887and near the edge of the substrates.Only crystals having visible SAM area around them were considered,and the rest were discarded.The chosen crystals attached to the substrates were removed from the solution and stored in a vacuum desiccator for later analysis.Due to the strong adhesion of the crystal face to the SAM surface,gold marks were often observed on the crystal face that nucleated on the SAM surface.Characterization.A Rudolph Research AutoEL ellipsometer was used to measure the thickness of the monolayer surface.The He -Ne laser (632.8nm)light fell at 70°on the sample and reflected into the analyzer.Data were taken over five to seven spots on each sample.The measured thickness of the SAMs of biphenyl thiols ranged from 12to 14Å,assuming a refractive index of 1.462for all films.Powder X-ray diffraction patterns of crystalline L -alanine and DL -valine were obtained with a Rigaku Miniflex diffractometer with Cu K R radiation (λ)1.5418Å).All samples were manually ground into fine powder and packed in glass slides for analysis.Data were collected from 5°to 50°with a step size of 0.1°.Crystal habits of L -alanine and DL -valine were indexed by measuring the interfacial angles using a two-circle optical goniometer.All possible measured interfacial angles were compared with the theoretical values derived from the unit cell parameters of L -alanine and DL -valine crystals.27,28III.Modeling SectionIII.1.General.All of the binding energy calculations,including molecular mechanics and dynamics simulations,are carried out with the program Cerius 2.The overall methodology and procedures are summarized in Figure 2.The crystal structures of each amino acid are obtained from the Cambridge Crystallographic Database (ref codes GLYCIN17,LALNIN12,and VALIDL for R -glycine,L -alanine,and DL -valine,respectively).To accurately predict the crystal morphology,molecular mechanics simulations using a suitable potential function (or force field)are performed.In this work,molecular simulations are carried out using the DREIDING 2.21force field.29The van der Waals forces are approximated with the Lennard-Jones 12-6expression,and hydrogen bonding energy is modeled using a Lennard-Jones-like 12-10expression.The Ewald summation technique is employed for the summation of long-range van der Waals and electrostatic interactions under the periodic boundary conditions,and the charge distribution within the molecule is calculated using the Gasteiger method.30ttice Energy Calculation.The lattice energy E lat,also known as the cohesive or crystal binding energy,is calculated by summing all the atom -atom interactions between a central molecule and all the surrounding molecules in the crystal.If the central molecule and the n surrounding molecules each have n ′atoms,thenwhere V kij is the interaction between atom i in the central molecule and atom j in the k th surrounding parison to the “experimental”lattice energy,V exp ,allows us to assess the accuracy of the intermolecular interactions between the molecules by the defined po-tential function.where the term 2RT represents a compensation factor for the difference between the vibrational contribution to the crystal enthalpy and gas-phase enthalpy 31and ∆H sub is the experimental sublimation energy.III.3.Morphological Predictions.The morphology of each amino acid crystal is predicted using the attach-ment energy (AE)32calculation and the Bravais -Friedel -Donnay -Harker (BFDH)law.33The habit or shape of the crystal depends on the growth rate of the faces present.Faces that are slow growing have the greatest morpho-logical importance,and conversely,faces that are fast growing have the least morphological importance and are the smallest faces on the grown crystal.The simplest morphological simulation is the BFDH law which assumes that the linear growth rate of a given crystal face is inversely proportional to the corresponding interplanar distance after taking into account the extinction conditions of the crystal space group.The attachment energy of a crystal face is the difference between the crystal energy and the slice energy.Hartman and Bennema 32found that the relative growth rate of a face is directly proportional to the attachment energy and as a result,the more negative the attachment energy (or more energy released)for a particular face,the less prominent that face is on the crystal.Conversely,faces with the lowest attachment energies are the slowest growing faces and thus have the greatest morphological importance .III.4.Molecular Modeling of SAMs of 4-Mercapto-biphenyls on a Au(111)Surface.Molecular dynamics (MD)simulations are useful techniques in gaining insights on the structural and dynamical properties of self-assembled monolayers.In contrast to molecular mechan-ics,molecular dynamics computes the forces and moves the atom in response to forces,while molecular mechanics computes the forces on the atoms and changes their position to minimize the interaction energy.Recently,MD simulations have been used to investigate the packing order and orientation of rigid 4-mercaptobiphenyl thiol monolayers on gold surfaces.Results show that hydrogen-terminated biphenylmercaptan packs in the herringbone conformation 34and suggest average tilt angles of 8°.(27)Simpson,H.J.;Marsh,R.E.Acta Crystallogr .1966,20,550.(28)Mallikarjunan,M.;Rao,S.T.Acta Crystallogr .1969,B25,296.(29)Mayo,S.L.;Olafson,B.D.;Goddard,W.A.,III J.Phys.Chem .1990,94,8897.(30)Gasteiger,J.;Marsili,M.Tetrahedron 1980,36,3219.(31)Williams,D.E.J.Phys.Chem .1966,45,3370.(32)(a)Hartman,P.;Bennema,P.J.Cryst.Growth 1980,49,145.(33)(a)Bravais,A.Etudes Crystallographiques ;Gauthier-Villars:Paris,1866.(b)Friedel,M.G.Bulletin de la Societe Francaise de Mineralogie 1907,30,326.(c)Donnay,J.D.;Harker,D.Am.Mineral.1937,22,446.Figure 2.Overall scheme showing the computational meth-odology adopted when calculating the binding energy betweenthe crystallographic plane and the monolayer surface.Elat)∑k )1n ∑i )1n ′∑j )1n ′V kij (1)V exp )-∆H sub -2RT(2)5888Langmuir,Vol.18,No.15,2002Lee et al.Based on this work,molecular mechanics simulations are performed for hydroxy-and methyl-terminated 4-mer-captobiphenyl along with 4-(4-mercaptophenyl)pyridine for binding studies with different crystallographic planes.In the periodic model,each unit cell contains four biphenyl molecules and the geometric parameters are a )10.02Å,b )42.25Å,c )10.11Åand R )138.3°, )119.9°,γ)95.7°.The length in the y -direction is set to ∼42Åto ensure two-dimensional periodicity.Also,the gold atoms are arranged in a hexagonal lattice along the XY plane with a nearest neighbor atom of 2.88Å,and the biphenyl occupied a ( 3× 3)R30°Au(111)lattice.To simulate different 4′-substituted 4-mercaptobiphenyls,minimiza-tion was carried out by fixing the biphenyl moiety and varying the substituents at the 4′-position.As a result,the simulated models yielded uniform ordered SAMs of 4′-substituted 4-mercaptobiphenyls and 4-(4-mercapto-phenyl)pyridine with identical packing structure and dynamics to those of a hydrogen-terminated monolayer of biphenylmercaptan (Figure 3).However,this is not true experimentally since adsorption of different 4′-substituted 4-mercaptobiphenyls on gold surfaces results in different monolayer structures and thus one of the main assump-tions made in this work.III.5.Binding of Crystal Habit Faces to SAMs of 4-Mercaptobiphenyls on a Au(111)Surface.Based on BFDH and attachment energy morphology prediction,crystal habit faces with the highest morphological im-portance are chosen for binding studies.The crystal surfaces of interest are cleaved and extended to a 3×3unit cell and partially fixed,allowing flexibility in the tail atoms of the amino acid molecules and a more accurate representation of the effects of SAMs of rigid thiols on the crystallographic plane in the calculation of binding energies.The crystal surface is then docked onto a 3×1×3partially fixed nonperiodic monolayer surface,and the conjugate gradient energy minimization technique is performed.Next,the crystal surface is moved to another site on the monolayer surface and the minimization calculations are again performed.This process was repeated 15-20times to obtain the global minimum.For each monolayer surface,numerous calculations are carried out with different crystallographic planes of each amino acid.The binding energy (φBE )of each crystallographic surface with the monolayer surface iswhere φIE is the minimum interaction energy of the monolayer and crystal surfaces,φM is the minimum energy of the monolayer surface in the absence of the crystal face but in the same conformation as it adopts on the surface,and φS is the minimum energy of the crystal surface with no monolayer surface present and in the same molecular conformation in which it docks on the surface.Negative values of binding energies indicate preferential binding of the crystallographic surfaces with SAMs of 4-mercaptobiphenyl.In cases where the binding energy is positive,there is a less likely chance that the particular crystal face will interact and nucleate on the monolayer surface.Thus,using this approach it is possible to screen self-assembled monolayers as possible templates for nucleation and growth of crystals.IV.Results and DiscussionIV.1.Crystallization of Amino Acids on SAMs on Gold.L -Alanine crystallizes from water in the ortho-rhombic space group P 21212(a )6.025Å,b )12.324Å,and c )5.783Å),27and the morphology of the crystals is bipyramidal,dominated by the {020},{120},{110},and {011}growth forms,35as shown in Figure 4.The crystal grown in aqueous solution is indexed by comparing the interfacial angles measured by optical goniometry and theoretical values based on the unit cell of L -alanine.Powder X-ray diffraction patterns (Figure 5)and inter-facial angle measurements reveal that L -alanine crystals nucleating on SAM surfaces crystallize in the ortho-rhombic space group with similar unit cell dimensions.However,functionalized SAMs induce the formation of L -alanine crystals in different crystallographic directions.L -Alanine crystals display the normal bipyramidal habit but are randomly oriented with the different surfaces.In methyl-terminated SAMs,L -alanine selectively nucle-ated on the {020}plane on the surface (Figure 6),whereas in 100%OH SAM surfaces,L -alanine nucleated on an unobserved {200}side face.The crystal exhibits a similar morphology as observed in aqueous solution with an appearance of a {200}face adjacent to the {110}planes (Figure 6).In both cases,the area of each crystal face is substantially larger than those of the other faces on the crystal.The SAM surfaces almost act as an additive or impurity molecule specifically interacting with the crystal face and consequently reducing the relative growth rate and modifying the habit.Crystallization of L -alanine on 4-(4-mercaptophenyl)pyridine surfaces resulted in the {011}face as the plane corresponding to nucleation (Figure 6).The preferential interaction of the monolayer with the {011}face can be attributed to hydrogen bonding at the crystal -monolayer interface.Unlike the other two sur-faces where they can serve as both hydrogen bond donors and acceptors (4′-hydroxy-4-mercaptobiphenyl)or solely as H-bond donors (4′-methyl-4-mercaptobiphenyl),the pyridine electron pair at the surface only serve as hydrogen bond acceptors.The binding of the pyridine surface and the {011}plane can be explained by the amino and methyl groups protruding out perpendicular to the plane (Figure 7)and forming N -H ‚‚‚N and C -H ‚‚‚N hydrogen bonds with the SAM surface,respectively.In contrast,the 100%(34)Ulman,A.;Kang,J.F.;Shnidman,Y.;Liao,S.;Jordan,R.;Choi,G.Y.;Zaccaro,J.;Myerson,A.S.;Rafailovich,M.;Sokolov,J.;Flesicher,C.Rev.Mol.Biotech .2000,74,175.(35)Lehmann,M.S.;Koetzle,T.F.;Hamilton,W.C.J.Am.Chem.Soc .1972.101,2657.Figure 3.Snapshots of (a)4′-methyl-4-mercaptobiphenyl,(b)4′-hydroxy-4-mercaptobiphenyl,(c)4-(4-mercaptophenyl)pyri-dine,and (d)mixed SAMs of 4′-methyl-4-mercaptobiphenyl and 4′-hydroxy-4-mercaptobiphenyl (top view).φBE )φIE -(φM +φS )(3)Crystallization of Amino Acids on Thiol SAMs Langmuir,Vol.18,No.15,20025889CH 3and 100%OH SAM surfaces do not interact as strongly with the hydrogen bond donating plane.In a similar manner,the appearance of an unobserved {200}face of L -alanine grown in aqueous solution on [Au]-S -C 6H 4-C 6H 4-OH can be attributed to hydrogen bonds forming between the two surfaces.The {200}surface contains alternating methyl (CH 3)and carboxylic groups (COO -)that form N -H ‚‚‚O and O ‚‚‚H -O with the hydroxide group of the monolayer film (Figure 7),ideal for binding with surfaces that can serve as both hydrogen bond donors and acceptors.As a result,the preferential interaction leads to the stabilization and appearance of the {200}face.The oriented nucleation of L -alanine crystals on func-tionalized SAMs arises due to the different molecular structures of each crystal face.Similar to the adsorption of additive onto a crystal face,the interaction (or binding)with the monolayer surface depends on the functional group that each crystal face possesses.As a result of preferential interactions with specific crystal faces,in-terfacial molecular recognition directs nucleation and subsequently influences the crystal growth.In addition to L -alanine,SAMs of rigid thiols are employed to investigate the possibility of inhibiting the racemic crystal and inducing the formation of one of its enantiomers.The powder X-ray diffraction pattern (Figure 8)reveals that DL -valine nucleates in the monoclinic form independent of the hydroxyl,methyl,or pyridine surface concentration and that there was no trace of conglomer-ates.DL -Valine crystallizes in the monoclinic space group P 21/c with a unit cell of dimensions a )5.21Å,b )22.10Å,c )5.41Å,and )109.2°.28Although the structural literature reports three separate space group assignments,Leiserowitz and co-workers 36have shown that two of the three space groups (P 21and P 1)are highly improbable for racemic crystals.Interfacial angle measurements and powder X-ray diffraction undertaken in this work agreed much better with the theoretical values and simulated pattern based on the unit cell of the monoclinic space group(36)Wolf,S.G.;Berkovitch-Yellin,Z.;Lahav,M.;Leiserowitz,L.Mol.Cryst.Liq.Cryst .1990,186,3.Figure 4.Crystallographic image (a)and morphology (b)of L -alanine crystal grown from aqueoussolution.Figure 5.X-ray diffractograms of L -alanine nucleated on functionalized SAMs,compared with L -alanine crystallized from aqueous solution (bottom).Indices of the crystallographic planes corresponding to the diffraction intensities of major peaks are indicated at the top.5890Langmuir,Vol.18,No.15,2002Lee et al.。

Mach_数和壁面温度对HyTRV_边界层转捩的影响

第９卷㊀第２期２０２４年３月气体物理ＰＨＹＳＩＣＳＯＦＧＡＳＥＳＶｏｌ.９㊀Ｎｏ.２Ｍａｒ.２０２４㊀㊀ＤＯＩ:１０.１９５２７/ｊ.ｃｎｋｉ.２０９６￣１６４２.１０９８Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩的影响章录兴ꎬ㊀王光学ꎬ㊀杜㊀磊ꎬ㊀余发源ꎬ㊀张怀宝(中山大学航空航天学院ꎬ广东深圳５１８１０７)ＥｆｆｅｃｔｓｏｆＭａｃｈＮｕｍｂｅｒａｎｄＷａｌｌＴｅｍｐｅｒａｔｕｒｅｏｎＨｙＴＲＶＢｏｕｎｄａｒｙＬａｙｅｒＴｒａｎｓｉｔｉｏｎＺＨＡＮＧＬｕｘｉｎｇꎬ㊀ＷＡＮＧＧｕａｎｇｘｕｅꎬ㊀ＤＵＬｅｉꎬ㊀ＹＵＦａｙｕａｎꎬ㊀ＺＨＡＮＧＨｕａｉｂａｏ(ＳｃｈｏｏｌｏｆＡｅｒｏｎａｕｔｉｃｓａｎｄＡｓｔｒｏｎａｕｔｉｃｓꎬＳｕｎＹａｔ￣ｓｅｎＵｎｉｖｅｒｓｉｔｙꎬＳｈｅｎｚｈｅｎ５１８１０７ꎬＣｈｉｎａ)摘㊀要:典型的高超声速飞行器流场存在着复杂的转捩现象ꎬ其对飞行器的性能有着显著的影响ꎮ针对ＨｙＴＲＶ这款接近真实高超声速飞行器的升力体模型ꎬ采用数值模拟方法ꎬ研究Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ转捩的影响规律ꎮ采用课题组自研软件开展数值计算ꎬＭａｃｈ数的范围为３~８ꎬ壁面温度的范围为１５０~９００Ｋꎮ首先对γ￣Ｒｅ~θｔ转捩模型和ＳＳＴ湍流模型进行了高超声速修正:将压力梯度系数修正㊁高速横流修正引入到γ￣Ｒｅ~θｔ转捩模型ꎬ并对ＳＳＴ湍流模型闭合系数β∗和β进行可压缩修正ꎻ然后开展了网格无关性验证ꎬ通过与实验结果对比ꎬ确认了修正后的数值方法和软件平台ꎻ最终开展Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩规律的影响研究ꎮ计算结果表明ꎬ转捩区域主要集中在上表面两侧㊁下表面中心线两侧ꎻ增大来流Ｍａｃｈ数ꎬ上下表面转捩起始位置均大幅后移ꎬ湍流区大幅缩小ꎬ但仍会存在ꎬ同时上表面层流区摩阻系数不断增大ꎬ下表面湍流区摩阻系数不断减小ꎻ升高壁面温度ꎬ上下表面转捩起始位置先前移ꎬ然后快速后移ꎬ最终湍流区先后几乎消失ꎮ关键词:转捩ꎻＨｙＴＲＶꎻ摩阻ꎻＭａｃｈ数ꎻ壁面温度㊀㊀㊀收稿日期:２０２３￣１２￣１３ꎻ修回日期:２０２４￣０１￣０２基金项目:国家重大项目(ＧＪＸＭ９２５７９)ꎻ广东省自然科学基金－面上项目(２０２３Ａ１５１５０１００３６)ꎻ中山大学中央高校基本科研业务费专项资金(２２ｑｎｔｄ０７０５)第一作者简介:章录兴(１９９８ )㊀男ꎬ硕士ꎬ主要研究方向为高超声速空气动力学ꎮＥ￣ｍａｉｌ:184****8082＠１６３.ｃｏｍ通信作者简介:张怀宝(１９８５ )㊀男ꎬ副教授ꎬ主要研究方向为空气动力学ꎮＥ￣ｍａｉｌ:ｚｈａｎｇｈｂ２８＠ｍａｉｌ.ｓｙｓｕ.ｅｄｕ.ｃｎ中图分类号:Ｖ２１１ꎻＶ４１１㊀㊀文献标志码:ＡＡｂｓｔｒａｃｔ:Ｔｈｅｒｅｉｓａｃｏｍｐｌｅｘｔｒａｎｓｉｔｉｏｎｐｈｅｎｏｍｅｎｏｎｉｎｔｈｅｆｌｏｗｆｉｅｌｄｏｆａｔｙｐｉｃａｌｈｙｐｅｒｓｏｎｉｃｖｅｈｉｃｌｅꎬｗｈｉｃｈｈａｓａｓｉｇｎｉｆｉ￣ｃａｎｔｉｍｐａｃｔｏｎｔｈｅｐｅｒｆｏｒｍａｎｃｅｏｆｔｈｅｖｅｈｉｃｌｅ.ＴｈｅｅｆｆｅｃｔｓｏｆＭａｃｈｎｕｍｂｅｒａｎｄｗａｌｌｔｅｍｐｅｒａｔｕｒｅｏｎｔｈｅｔｒａｎｓｉｔｉｏｎｏｆＨｙＴＲＶｗｅｒｅｓｔｕｄｉｅｄｂｙｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｍｅｔｈｏｄｓ.Ｔｈｅｓｅｌｆ￣ｄｅｖｅｌｏｐｅｄｓｏｆｔｗａｒｅｏｆｔｈｅｒｅｓｅａｒｃｈｇｒｏｕｐｗａｓｕｓｅｄｔｏｃａｒｒｙｏｕｔｎｕ￣ｍｅｒｉｃａｌｃａｌｃｕｌａｔｉｏｎｓ.ＴｈｅｒａｎｇｅｏｆＭａｃｈｎｕｍｂｅｒｗａｓ３~８ꎬａｎｄｔｈｅｒａｎｇｅｏｆｗａｌｌｔｅｍｐｅｒａｔｕｒｅｗａｓ１５０~９００Ｋ.Ｆｉｒｓｔｌｙꎬｔｈｅｈｙｐｅｒｓｏｎｉｃｃｏｒｒｅｃｔｉｏｎｓｏｆｔｈｅγ￣Ｒｅ~θｔｔｒａｎｓｉｔｉｏｎｍｏｄｅｌａｎｄｔｈｅＳＳＴｔｕｒｂｕｌｅｎｃｅｍｏｄｅｌｗｅｒｅｃａｒｒｉｅｄｏｕｔ.Ｔｈｅｐｒｅｓｓｕｒｅｇｒａｄｉｅｎｔｃｏｅｆｆｉｃｉｅｎｔｃｏｒｒｅｃｔｉｏｎａｎｄｔｈｅｈｉｇｈ￣ｓｐｅｅｄｃｒｏｓｓ￣ｆｌｏｗｃｏｒｒｅｃｔｉｏｎｗｅｒｅｉｎｔｒｏｄｕｃｅｄｉｎｔｏｔｈｅγ￣Ｒｅ~θｔｔｒａｎｓｉｔｉｏｎｍｏｄｅｌꎬａｎｄｔｈｅｃｏｍ￣ｐｒｅｓｓｉｂｉｌｉｔｙｃｏｒｒｅｃｔｉｏｎｓｏｆｔｈｅｃｌｏｓｕｒｅｃｏｅｆｆｉｃｉｅｎｔｓβ∗ａｎｄβｏｆｔｈｅＳＳＴｔｕｒｂｕｌｅｎｃｅｍｏｄｅｌｗｅｒｅｃａｒｒｉｅｄｏｕｔ.Ｔｈｅｎꎬｔｈｅｇｒｉｄｉｎ￣ｄｅｐｅｎｄｅｎｃｅｖｅｒｉｆｉｃａｔｉｏｎｗａｓｃａｒｒｉｅｄｏｕｔꎬａｎｄｔｈｅｍｏｄｉｆｉｅｄｎｕｍｅｒｉｃａｌｍｅｔｈｏｄａｎｄｓｏｆｔｗａｒｅｐｌａｔｆｏｒｍｗｅｒｅｃｏｎｆｉｒｍｅｄｂｙｃｏｍ￣ｐａｒｉｎｇｗｉｔｈｅｘｐｅｒｉｍｅｎｔａｌｒｅｓｕｌｔｓ.ＦｉｎａｌｌｙꎬｔｈｅｅｆｆｅｃｔｓｏｆＭａｃｈｎｕｍｂｅｒａｎｄｗａｌｌｔｅｍｐｅｒａｔｕｒｅｏｎｔｈｅｔｒａｎｓｉｔｉｏｎｌａｗｏｆｔｈｅＨｙＴＲＶｂｏｕｎｄａｒｙｌａｙｅｒｗｅｒｅｓｔｕｄｉｅｄ.Ｔｈｅｒｅｓｕｌｔｓｓｈｏｗｔｈａｔｔｈｅｔｒａｎｓｉｔｉｏｎａｒｅａｉｓｍａｉｎｌｙｃｏｎｃｅｎｔｒａｔｅｄｏｎｂｏｔｈｓｉｄｅｓｏｆｔｈｅｕｐｐｅｒｓｕｒｆａｃｅａｎｄｔｈｅｃｅｎｔｅｒｌｉｎｅｏｆｔｈｅｌｏｗｅｒｓｕｒｆａｃｅ.ＷｉｔｈｔｈｅｉｎｃｒｅａｓｅｏｆｔｈｅｉｎｃｏｍｉｎｇＭａｃｈｎｕｍｂｅｒꎬｔｈｅｓｔａｒｔｉｎｇｐｏｓｉｔｉｏｎｏｆｔｒａｎｓｉｔｉｏｎｏｎｔｈｅｕｐｐｅｒａｎｄｌｏｗｅｒｓｕｒｆａｃｅｓｉｓｇｒｅａｔｌｙｂａｃｋｗａｒｄꎬａｎｄｔｈｅｔｕｒｂｕｌｅｎｔｚｏｎｅｉｓｇｒｅａｔｌｙｒｅｄｕｃｅｄꎬｂｕｔｉｔｓｔｉｌｌｅｘ￣ｉｓｔｓ.Ａｔｔｈｅｓａｍｅｔｉｍｅꎬｔｈｅｆｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｏｆｔｈｅｌａｍｉｎａｒｆｌｏｗｚｏｎｅｏｎｔｈｅｕｐｐｅｒｓｕｒｆａｃｅｉｎｃｒｅａｓｅｓｃｏｎｔｉｎｕｏｕｓｌｙꎬａｎｄｔｈｅｆｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｏｆｔｈｅｔｕｒｂｕｌｅｎｔｚｏｎｅｏｎｔｈｅｌｏｗｅｒｓｕｒｆａｃｅｄｅｃｒｅａｓｅｓ.Ａｓｔｈｅｗａｌｌｔｅｍｐｅｒａｔｕｒｅｉｎｃｒｅａｓｅｓꎬｔｈｅｓｔａｒｔｉｎｇｐｏｓｉ￣ｔｉｏｎｏｆｔｒａｎｓｉｔｉｏｎｏｎｔｈｅｕｐｐｅｒａｎｄｌｏｗｅｒｓｕｒｆａｃｅｓｓｈｉｆｔｓｆｏｒｗａｒｄꎬｔｈｅｎｒａｐｉｄｌｙｓｈｉｆｔｓｂａｃｋｗａｒｄꎬａｎｄｆｉｎａｌｌｙｔｈｅｔｕｒｂｕｌｅｎｔｚｏｎｅａｌｍｏｓｔｄｉｓａｐｐｅａｒｓ.气体物理２０２４年㊀第９卷Ｋｅｙｗｏｒｄｓ:ｔｒａｎｓｉｔｉｏｎꎻＨｙＴＲＶꎻｆｒｉｃｔｉｏｎꎻＭａｃｈｎｕｍｂｅｒꎻｗａｌｌｔｅｍｐｅｒａｔｕｒｅ引㊀言高超声速飞行器具有突防能力强㊁打击范围广㊁响应迅速等显著优势ꎬ正逐渐成为各国空天竞争的热点[１]ꎮ高超声速飞行器边界层转捩是该类飞行器气动设计中的重要问题[２]ꎮ在边界层转捩过程中ꎬ流态由层流转变为湍流ꎬ飞行器的表面摩阻急剧增大到层流时的３~５倍ꎬ严重影响飞行器的气动性能与热防护系统ꎬ转捩还会导致飞行器壁面烧蚀㊁颤振加剧㊁飞行姿态控制难度大等一系列问题ꎬ对飞行器的飞行安全构成严重的威胁[３￣５]ꎬ开展高超声速飞行器边界层转捩研究具有十分重要的意义ꎮ影响边界层转捩的因素很多ꎬ例如ꎬＭａｃｈ数㊁Ｒｅｙｎｏｌｄｓ数㊁湍流强度㊁表面传导热等ꎮ在高超声速流动条件下ꎬ强激波㊁强逆压梯度㊁熵层等高超声速现象及其相互作用ꎬ会使得转捩流动的预测和研究难度进一步增大[６]ꎮ目前高超声速飞行器转捩数值模拟方法主要有直接数值模拟(ＤＮＳ)㊁大涡模拟(ＬＥＳ)和基于Ｒｅｙｎｏｌｄｓ平均Ｎａｖｉｅｒ￣Ｓｔｏｋｅｓ(ＲＡＮＳ)的转捩模型方法ꎬ由于前两种计算量巨大ꎬ难以推广到工程应用ꎬ基于Ｒｅｙｎｏｌｄｓ平均Ｎａｖｉｅｒ￣Ｓｔｏｋｅｓ的转捩模型在工程实践中应用最为广泛ꎬ其中γ￣Ｒｅ~θｔ转捩模型基于局部变量ꎬ与现代ＣＦＤ方法良好兼容ꎬ目前已经有多项研究尝试从一般性的流动问题拓展到高超声速流动转捩模拟[６￣９]ꎮ目前高超声速流动转捩的研究对象主要是结构相对简单的构型ꎮＭｃＤａｎｉｅｌ等[１０]研究了扩口直锥在高超声速流动条件下的转捩现象ꎮＰａｐｐ等[１１]研究了圆锥在高超声速流动条件下的转捩特性ꎮ美国和澳大利亚组织联合实施的ＨＩＦｉＲＥ计划[１２]ꎬ研究了圆锥形状的ＨＩＦｉＲＥ１和椭圆锥形的ＨＩＦｉＲＥ５的转捩问题ꎮ杨云军等[１３]采用数值模拟方法ꎬ分析了椭圆锥的转捩影响机制ꎬ并研究了Ｒｅｙｎｏｌｄｓ数对转捩特性的影响规律ꎮ另外ꎬ袁先旭等[１４]于２０１５年成功实施了圆锥体ＭＦ￣１航天模型飞行试验ꎮ以上对高超声速流动的转捩研究ꎬ都取得了比较理想的结果ꎬ然而所采用的模型都是圆锥㊁椭圆锥等简单几何外形ꎬ这与真实高超声速飞行器有较大差异ꎬ较难反映真实的转捩特性ꎮ为了有效促进对真实高超声速飞行器的转捩问题研究ꎬ中国空气动力研究与发展中心提出并设计了一款接近真实飞行器的升力体模型ꎬ即高超声速转捩研究飞行器(ｈｙｐｅｒｓｏｎｉｃｔｒａｎｓｉｔｉｏｎｒｅｓｅａｒｃｈｖｅｈｉｃｌｅꎬＨｙＴＲＶ)[１５]ꎬ模型详细的参数见参考文献[１６]ꎮＨｙＴＲＶ外形如图１所示ꎬ其整体外形较为复杂ꎬ不同区域发生转捩的情况也不尽相同ꎮ对ＨｙＴＲＶ的转捩问题研究能够显著提高对真实高超声速飞行器转捩特性的认识水平ꎮＬｉｕ等[１７]采用理论分析㊁数值模拟和风洞实验３种方法对ＨｙＴＲＶ的转捩特性进行了研究ꎻ陈坚强等[１５]分析了ＨｙＴＲＶ的边界层失稳特征ꎻＣｈｅｎ等[１８]对ＨｙＴＲＶ进行了多维线性稳定性分析ꎻＱｉ等[１９]在来流Ｍａｃｈ数６㊁攻角０ʎ的条件下对ＨｙＴＲＶ进行了直接数值模拟ꎻ万兵兵等[２０]结合风洞实验与飞行试验ꎬ利用ｅＮ方法预测了ＨｙＴＲＶ升力体横流区的转捩阵面形状ꎮ目前ꎬ相关研究主要集中在ＨｙＴＲＶ的稳定性特征及转捩预测两个方面ꎬ而对若干关键参数ꎬ特别是Ｍａｃｈ数和壁面温度对转捩的影响研究还比较少ꎮ(ａ)Ｆｒｏｎｔｖｉｅｗ(ｂ)Ｓｉｄｅｖｉｅｗ㊀㊀㊀图１㊀ＨｙＴＲＶ外形Ｆｉｇ.１㊀ＳｈａｐｅｏｆＨｙＴＲＶ基于此ꎬ本文采用数值模拟方法ꎬ应用课题组自研软件开展Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ转捩流动的影响规律研究ꎮ１㊀数值方法１.１㊀控制方程和数值方法控制方程为三维可压缩ＲＡＮＳ方程ꎬ采用结构网格技术和有限体积方法ꎬ变量插值方法采用２阶ＭＵＳＣＬ格式ꎬ通量计算采用低耗散的通量向量差分Ｒｏｅ格式ꎬ黏性项离散采用中心格式ꎬ时间推进方法采用ＬＵ￣ＳＧＳ格式ꎮ壁面采用等温㊁无滑移壁面条件ꎬ入口采用Ｒｉｅｍａｎｎ远场边界条件ꎬ出口采用零梯度外推边界条件ꎮ１.２㊀γ￣Ｒｅ~θｔ转捩模型γ￣Ｒｅ~θｔ转捩模型是Ｍｅｎｔｅｒ等[２１ꎬ２２]于２００４年提０１第２期章录兴ꎬ等:Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩的影响出的一种基于拟合公式的间歇因子转捩模型ꎬ在２００９年公布了完整的拟合公式及相关参数[２３]ꎮ许多学者也开发了相应的程序ꎬ并进行了大量的算例验证[２４￣２８]ꎬ证明了该模型具有较好的转捩预测能力ꎬ预测精度较高ꎻ通过合适的标定ꎬγ￣Ｒｅ~θｔ转捩模型可以适用于多种情况下的转捩模拟ꎮ该模型构建了关于间歇因子γ的输运方程和关于转捩动量厚度Ｒｅｙｎｏｌｄｓ数Ｒｅ~θｔ的输运方程ꎮ具体来说ꎬγ表示该位置是湍流流动的概率ꎬ取值范围为０<γ<１ꎮ关于γ的控制方程为Ə(ργ)Əｔ＋Ə(ρｕｊγ)Əｘｊ＝Ｐγ－Ｅγ＋ƏƏｘｊμ＋μｔσｆæèçöø÷ƏγƏｘｊéëêêùûúú其中ꎬＰγ为生成项ꎬＥγ为破坏项ꎮ关于Ｒｅ~θｔ的输运方程为Ə(ρＲｅ~θｔ)Əｔ＋Ə(ρｕｊＲｅ~θｔ)Əｘｊ＝Ｐθｔ＋ƏƏｘｊσθｔ(μ＋μｔ)ƏＲｅ~θｔƏｘｊéëêêùûúú其中ꎬＰθｔ为源项ꎬ其作用是使边界层外部的Ｒｅ~θｔ等于Ｒｅθｔꎬ定义式为Ｐθｔ＝ｃθｔρｔ(Ｒｅθｔ－Ｒｅ~θｔ)(１.０－Ｆθｔ)Ｒｅθｔ采用以下经验公式Ｒｅθｔ＝１１７３.５１－５８９４２８Ｔｕ＋０.２１９６Ｔｕ２æèçöø÷Ｆ(λθ)ꎬＴｕɤ０.３Ｒｅθｔ＝３３１.５０(Ｔｕ－０.５６５８)－０.６７１Ｆ(λθ)ꎬＴｕ>０.３ìîíïïïïＦ(λθ)＝１＋(１２.９８６λθ＋１２３.６６λ２θ＋４０５.６８９λ３θ)ｅ－(Ｔｕ１.５)１.５ꎬ㊀λθɤ０Ｆ(λθ)＝１＋０.２７５(１－ｅ－３５.０λθ)ｅ－(Ｔｕ０.５)ꎬλθ>０ìîíïïïï在实际计算中ꎬ通过γ￣Ｒｅ~θｔ转捩模型获得间歇因子ꎬ再通过间歇因子来控制ＳＳＴｋ￣ω湍流模型中湍动能的生成ꎮγ￣Ｒｅ~θｔ转捩模型与ＳＳＴｋ￣ω湍流模型耦合为Ə(ρｋ)Əｔ＋Ə(ρｕｊｋ)Əｘｊ＝γｅｆｆτｉｊƏｕｉƏｘｊ－ｍｉｎ(ｍａｘ(γｅｆｆꎬ０.１)ꎬ１.０)ρβ∗ｋω＋ƏƏｘｊμ＋μｔσｋæèçöø÷ƏｋƏｘｊéëêêùûúúƏ(ρω)Əｔ＋Ə(ρｕｊω)Əｘｊ＝γｖｔτｉｊƏｕｉƏｘｊ－βρω２＋ƏƏｘｊ(μ＋σωμｔ)ƏωƏｘｊéëêêùûúú＋２ρ(１－Ｆ１)σω２１ωƏｋƏｘｊƏωƏｘｊ模型中具体参数定义见文献[２３]ꎮ１.３㊀高超声速修正原始ＳＳＴ湍流模型及γ￣Ｒｅ~θｔ转捩模型都是基于不可压缩流动发展的ꎬ为了更好地预测高超声速流动转捩ꎬ本节引入了３种重要的高超声速修正方法ꎮ１.３.１㊀压力梯度修正压力梯度对边界层转捩的影响较大ꎬ在高Ｍａｃｈ数情况下ꎬ边界层厚度较大ꎬ进而影响压力梯度的大小ꎬ因此在模拟高超声速流动时应该考虑Ｍａｃｈ数对压力梯度的影响ꎮ本文采用张毅峰等[２９]提出的压力梯度修正方法ꎬ具体修正形式如下λᶄθ＝λθ１＋γᶄ－１２Ｍａｅæèçöø÷其中ꎬＭａｅ为边界层外缘Ｍａｃｈ数ꎬγᶄ为比热比ꎮ１.３.２㊀高速横流修正在原始γ￣Ｒｅ~θｔ转捩模型中ꎬ没有考虑横流不稳定性对转捩的影响ꎬ对于横流模态主导的转捩ꎬ原始转捩模型计算的结果并不理想ꎮＬａｎｇｔｒｙ等[３０]在２０１５年对γ￣Ｒｅ~θｔ转捩模型进行了低速横流修正ꎬ向星皓等[９]在Ｌａｎｇｔｒｙ低速横流修正的基础上ꎬ对高超声速椭圆锥转捩ＤＮＳ数据进行了拓展ꎬ提出了高速横流转捩判据ꎬ本文直接采用向星皓提出的高速横流转捩方法ꎮＬａｎｇｔｒｙ将横流强度引入转捩发生动量厚度Ｒｅｙｎｏｌｄｓ数输运方程中Ə(ρＲｅ~θｔ)Əｔ＋Ə(ρｕｊＲｅ~θｔ)Əｘｊ＝Ｐθｔ＋ＤＳＣＦ＋ƏƏｘｊσθｔ(μ＋μｔ)ƏＲｅ~θｔƏｘｊéëêêùûúú式中ꎬＤＳＣＦ为横流源项ꎬＬａｎｇｔｒｙ低速横流修正为ＤＳＣＦ＝ｃθｔρｔｃｃｒｏｓｓｆｌｏｗｍｉｎ(ＲｅＳＣＦ－Ｒｅ~θｔꎬ０.０)Ｆθｔ２其中ꎬＲｅＳＣＦ为低速横流判据ＲｅＳＣＦ＝θｔρＵｌｏｃａｌ０.８２æèçöø÷μ＝－３５.０８８ｌｎｈθｔæèçöø÷＋３１９.５１＋ｆ(＋ΔＨｃｒｏｓｓｆｌｏｗ)－ｆ(－ΔＨｃｒｏｓｓｆｌｏｗ)其中ꎬｈ为壁面粗糙度高度ꎬθｔ为动量厚度ꎬ１１气体物理２０２４年㊀第９卷ΔＨｃｒｏｓｓｆｌｏｗ是横流强度抬升项ꎮ向星皓提出的高速横流转捩判据ꎬ其中高速横流源项ＤＳＣＦ￣Ｈ为ＤＳＣＦ￣Ｈ＝ｃＣＦρｍｉｎ(ＲｅＳＣＦ￣Ｈ－Ｒｅ~θｔꎬ０)ＦθｔＲｅＳＣＦ￣Ｈ＝ＣＣＦ￣１ｌｎｈｌμ＋ＣＣＦ￣２＋(Ｈｃｒｏｓｓｆｌｏｗ)其中ꎬＣＣＦ￣１＝－９.６１８ꎬＣＣＦ￣２＝１２８.３３ꎻｌμ为粗糙度参考高度ꎬｌμ＝１μｍꎻｆ(Ｈｃｒｏｓｓｆｌｏｗ)为抬升函数ｆ(Ｈｃｒｏｓｓｆｌｏｗ)＝６００００.１０６６－ΔＨｃｒｏｓｓｆｌｏｗ＋５００００(０.１０６６－ΔＨｃｒｏｓｓｆｌｏｗ)２其中ꎬΔＨｃｒｏｓｓｆｌｏｗ与Ｌａｎｇｔｒｙ低速横流修正中保持一致ꎮ１.３.３㊀ＳＳＴ可压缩修正高超声速流动具有强可压缩性ꎬ所以在进行高超声速计算时ꎬ应该对湍流模型进行可压缩修正ꎮＳａｒｋａｒ[３１]提出了膨胀耗散修正ꎬ对ＳＳＴ湍流模型中的闭合系数β∗ꎬβ进行了可压缩修正ꎬＷｉｌｃｏｘ[３２]在Ｓａｒｋａｒ修正的基础上考虑了可压缩生成项产生时的延迟效应ꎬ使得可压缩修正在湍流Ｍａｃｈ数较小的近壁面关闭ꎬ在湍流Ｍａｃｈ数较大的自由剪切层打开ꎬ本文采用Ｗｉｌｃｏｘ提出的可压缩性修正β∗＝β∗０[１＋ξ∗Ｆ(Ｍａｔ)]β＝β０－β∗０ξ∗Ｆ(Ｍａｔ)其中ꎬβ０ꎬβ∗均为原始模型中的系数ꎬξ∗＝１.５ꎮＦ(Ｍａｔ)＝[Ｍａｔ－Ｍａｔ０]Ｈ(Ｍａｔ－Ｍａｔ０)Ｍａｔ０＝１/４ꎬＨ(ｘ)＝０ꎬｘɤ０１ꎬｘ>０{其中ꎬＭａｔ＝２ｋ/ａ为湍流Ｍａｃｈ数ꎬａ为当地声速ꎮ２㊀网格无关性验证及数值方法确认２.１㊀网格无关性验证计算采用３套网格ꎬ考虑到ＨｙＴＲＶ的几何对称性ꎬ生成３套半模网格ꎬ第１层网格高度为１ˑ１０－６ｍꎬ确保ｙ＋<１ꎬ流向ˑ法向ˑ周向的网格数分别为:网格１是３０１ˑ２０１ˑ２０１ꎬ网格２是３０１ˑ３０１ˑ２０１ꎬ网格３是４０１ˑ３８１ˑ２８１ꎮ全模下表面如图２所示ꎬ选取ｙ/Ｌ＝０中心线和ｘ/Ｌ＝０.５处ꎬ对比３套网格的表面摩阻系数ꎬ计算结果如图３所示ꎮ采用网格１时ꎬ表面摩阻系数分布与另外两个结果存在明显差异ꎻ而采用网格２和网格３时ꎬ表面摩阻系数曲线基本重合ꎬ表明在流向㊁法向和周向均满足网格无关性ꎬ后续数值计算采用网格２ꎮ图２㊀截取位置示意图Ｆｉｇ.２㊀Ｓｃｈｅｍａｔｉｃｄｉａｇｒａｍｏｆｔｈｅｉｎｔｅｒｃｅｐｔｉｏｎｌｏｃａｔｉｏｎ(ａ)Ｓｕｒｆａｃｅｆｒｉｃｔｉｏｎａｔｙ/Ｌ＝０(ｂ)Ｓｕｒｆａｃｅｆｒｉｃｔｉｏｎａｔｘ/Ｌ＝０.５图３㊀采用３套网格计算得到的摩阻对比Ｆｉｇ.３㊀Ｃｏｍｐａｒｉｓｏｎｏｆｔｈｅｆｒｉｃｔｉｏｎｄｒａｇｃａｌｃｕｌａｔｅｄｕｓｉｎｇｔｈｒｅｅｓｅｔｓｏｆｇｒｉｄｓ２.２㊀数值方法和自研软件的确认采用修正后的转捩模型对ＨｙＴＲＶ开展计算ꎬ计算工况为Ｍａ＝６ꎬ来流温度Ｔɕ＝９７Ｋꎬ单位２１第２期章录兴ꎬ等:Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩的影响Ｒｅｙｎｏｌｄｓ数为Ｒｅ＝１.１ˑ１０７/ｍꎬ攻角α＝０ʎꎬ来流湍流度ＦＳＴＩ＝０.８％ꎬ壁面温度Ｔ＝３００Ｋꎮ为方便对比分析ꎬ计算结果与参考结果均采用上下对称形式布置ꎬ例如ꎬ图４是模型下表面计算结果与实验结果对比:对于下表面两侧转捩的起始位置ꎬ高超声速修正前的转捩位置在ｘ＝０.６８ｍ附近ꎬ高超声速修正后的计算结果与实验结果吻合良好ꎬ均在ｘ＝０.６０ｍ附近ꎬ并且湍流边界层区域形状基本一致ꎬ说明修正后的转捩模型能够较好地预测ＨｙＴＲＶ转捩的位置ꎮ(ａ)Ｃａｌｃｕｌａｔｉｏｎｏｆｔｈｅｆｒｉｃｔｉｏｎｄｉｓｔｒｉｂｕｔｉｏｎ(ｂｅｆｏｒｅｈｙｐｅｒｓｏｎｉｃｃｏｒｒｅｃｔｉｏｎ)(ｂ)Ｃａｌｃｕｌａｔｉｏｎｏｆｔｈｅｆｒｉｃｔｉｏｎｄｉｓｔｒｉｂｕｔｉｏｎ(ａｆｔｅｒｈｙｐｅｒｓｏｎｉｃｃｏｒｒｅｃｔｉｏｎ)(ｃ)Ｅｘｐｅｒｉｍｅｎｔａｌｒｅｓｕｌｔｓｏｆｔｈｅｈｅａｔｆｌｕｘｄｉｓｔｒｉｂｕｔｉｏｎ[１７]图４㊀下表面计算结果和实验结果对比Ｆｉｇ.４㊀Ｃｏｍｐａｒｉｓｏｎｏｆｔｈｅｃａｌｃｕｌａｔｅｄａｎｄｅｘｐｅｒｉｍｅｎｔａｌｒｅｓｕｌｔｓｏｎｔｈｅｌｏｗｅｒｓｕｒｆａｃｅ３㊀ＨｙＴＲＶ转捩的基本流动特性计算工况采用Ｍａ＝６ꎬ攻角α＝０ʎꎬ来流湍流度ＦＳＴＩ＝０.６％ꎬ分析ＨｙＴＲＶ转捩的基本流动特性ꎮ从图５可以看出ꎬ模型两侧和顶端均出现高压区ꎬ高压区之间为低压区ꎬ横截面上存在周向压力梯度ꎬ流动从高压区向低压区汇集ꎬ从而在下表面中心线附近和上表面两侧腰部区域均形成流向涡结构(见图６)ꎬ沿流动方向ꎬ高压区域逐渐扩大ꎬ流向涡结构的影响范围也越大ꎮ在流向涡结构的边缘位置ꎬ壁面附近的低速流体被抬升到外壁面区域ꎬ外壁面区域的高速流体又被带入到近壁面区域ꎬ进而导致流向涡结构边缘处壁面的摩阻显著增加ꎬ最终诱发转捩ꎬ这些流动特征与文献[１５]的结果一致ꎮ图７显示了上下表面摩阻的分布情况ꎬ其中上表面两侧区域在ｘ/Ｌ＝０.８０附近ꎬ摩阻显著增加ꎬ出现明显的转捩现象ꎬ转捩区域分布在两侧边缘位置ꎻ而下表面两侧区域在ｘ/Ｌ＝０.７５附近ꎬ也出现明显的转捩ꎬ转捩区域相对集中在中心线两侧ꎮ图５㊀不同截面位置处的压力云图Ｆｉｇ.５㊀Ｐｒｅｓｓｕｒｅｃｏｎｔｏｕｒｓａｔｄｉｆｆｅｒｅｎｔｃｒｏｓｓ￣ｓｅｃｔｉｏｎｌｏｃａｔｉｏｎｓ图６㊀不同截面位置处的流向速度云图Ｆｉｇ.６㊀Ｓｔｒｅａｍｗｉｓｅｖｅｌｏｃｉｔｙｃｏｎｔｏｕｒｓａｔｄｉｆｆｅｒｅｎｔｃｒｏｓｓ￣ｓｅｃｔｉｏｎｌｏｃａｔｉｏｎｓ３１气体物理２０２４年㊀第９卷(ａ)Ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀(ｂ)Ｌｏｗｅｒｓｕｒｆａｃｅ图７㊀上下表面摩阻分布云图Ｆｉｇ.７㊀Ｆｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｃｏｎｔｏｕｒｓｏｎｔｈｅｕｐｐｅｒａｎｄｌｏｗｅｒｓｕｒｆａｃｅｓ４㊀不同Ｍａｃｈ数对ＨｙＴＲＶ转捩的影响保持来流湍流度ＦＳＴＩ＝０.６％不变ꎬＭａｃｈ数变化范围为３~８ꎮ图８是不同Ｍａｃｈ数条件下ＨｙＴＲＶ上下表面的摩阻分布云图ꎬ从图中可知ꎬ随着Ｍａｃｈ数的增加ꎬ上下表面的湍流区域均逐渐减少ꎬ其中上表面两侧转捩起始位置由ｘ/Ｌ＝０.５６附近后移至ｘ/Ｌ＝０.９２附近ꎬ下表面两侧转捩起始位置由ｘ/Ｌ＝０.４８附近后移至ｘ/Ｌ＝０.９９附近ꎬ上下表面两侧转捩起始位置均大幅后移ꎬ说明Ｍａｃｈ数对ＨｙＴＲＶ转捩的影响很大ꎮｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ａ)Ｍａ＝３ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｂ)Ｍａ＝４ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｃ)Ｍａ＝５４１第２期章录兴ꎬ等:Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩的影响ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｄ)Ｍａ＝６ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｅ)Ｍａ＝７ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｆ)Ｍａ＝８图８㊀不同Ｍａｃｈ数条件下摩阻系数分布云图Ｆｉｇ.８㊀ＦｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｃｏｎｔｏｕｒｓａｔｄｉｆｆｅｒｅｎｔＭａｃｈｎｕｍｂｅｒｓ上表面选取图７中ｚ/Ｌ＝０.１２的位置ꎬ下表面选取ｚ/Ｌ＝０.１０的位置进行分析ꎮ从图９中可以分析出ꎬ随着Ｍａｃｈ数的增加ꎬ上表面转捩起始位置不断后移ꎬ当Ｍａｃｈ数增加到７时ꎬ由于湍流区的缩小ꎬ此处位置不再发生转捩ꎬ此外ꎬＭａｃｈ数越高层流区摩阻系数越大ꎻ下表面转捩起始位置也不断后移ꎬ当Ｍａｃｈ数增加到８时ꎬ此处位置不再发生转捩ꎬ此外ꎬＭａｃｈ数越高ꎬ湍流区的摩阻系数越小ꎬ这些结论与关于来流Ｍａｃｈ数对转捩位置影响的普遍研究结论一致ꎮ(ａ)Ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀(ｂ)Ｌｏｗｅｒｓｕｒｆａｃｅ图９㊀不同位置摩阻系数随Ｍａｃｈ数的变化Ｆｉｇ.９㊀ＶａｒｉａｔｉｏｎｏｆｆｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｗｉｔｈＭａｃｈｎｕｍｂｅｒａｔｄｉｆｆｅｒｅｎｔｌｏｃａｔｉｏｎｓ５１气体物理２０２４年㊀第９卷５㊀不同壁面温度对ＨｙＴＲＶ转捩的影响保持来流湍流度ＦＳＴＩ＝０.６％及Ｍａ＝６不变ꎬ壁面温度的变化范围为１５０~９００Ｋꎮ图１０是不同壁面温度条件下ＨｙＴＲＶ上下表面的摩阻分布云图ꎬ可以看出随着壁面温度的增加ꎬ上表面两侧湍流区域先是缓慢扩大ꎬ在壁面温度为５００Ｋ时湍流区域快速缩小ꎬ增加到９００Ｋ时ꎬ已无明显湍流区域ꎻ下表面两侧湍流区域先是无明显变化ꎬ同样当壁面温度升高到５００Ｋ时ꎬ湍流区域快速缩小ꎬ当壁面温度升高到７００Ｋ时ꎬ两侧已经无明显的湍流区域ꎬ相比上表面两侧湍流区域ꎬ下表面湍流区域消失得更早ꎮ由此可以得出壁面温度对转捩的产生有较大的影响ꎬ壁面温度增加到一定程度将导致ＨｙＴＲＶ没有明显的转捩现象ꎮｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ａ)Ｔ＝１５０Ｋｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｂ)Ｔ＝２００Ｋｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｃ)Ｔ＝３００Ｋｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｄ)Ｔ＝５００Ｋ６１第２期章录兴ꎬ等:Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩的影响ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｅ)Ｔ＝７００Ｋｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀ｌｏｗｅｒｓｕｒｆａｃｅ(ｆ)Ｔ＝９００Ｋ图１０㊀不同壁面温度条件下摩阻系数分布云图Ｆｉｇ.１０㊀Ｆｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｃｏｎｔｏｕｒｓａｔｄｉｆｆｅｒｅｎｔｗａｌｌｔｅｍｐｅｒａｔｕｒｅｃｏｎｄｉｔｉｏｎｓ上表面选取ｚ/Ｌ＝０.１２５的位置ꎬ下表面选取ｚ/Ｌ＝０.１００的位置进行分析ꎮ从图１１中可以分析出ꎬ随着壁面温度的增加ꎬ上表面转捩起始位置先前移ꎬ当壁面温度增加到５００Ｋ时ꎬ转捩起始位置后移ꎬ转捩区长度逐渐增加ꎬ层流区域的摩阻系数逐渐增加ꎬ当壁面温度增加到７００Ｋ时ꎬ该位置已不再出现转捩ꎻ下表面转捩起始位置先小幅后移ꎬ当壁面温度增加到３００Ｋ时ꎬ转捩起始位置开始后移ꎬ当壁面温度增加到７００Ｋ时ꎬ由于湍流区域的减小ꎬ该位置不再发生转捩ꎮ(ａ)Ｕｐｐｅｒｓｕｒｆａｃｅ㊀㊀㊀㊀㊀(ｂ)Ｌｏｗｅｒｓｕｒｆａｃｅ图１１㊀不同位置摩阻系数随壁面温度的变化Ｆｉｇ.１１㊀Ｖａｒｉａｔｉｏｎｏｆｆｒｉｃｔｉｏｎｃｏｅｆｆｉｃｉｅｎｔｗｉｔｈｗａｌｌｔｅｍｐｅｒａｔｕｒｅａｔｄｉｆｆｅｒｅｎｔｌｏｃａｔｉｏｎｓ为进一步分析壁面温度的影响ꎬ本文分别在上下表面湍流区选取一点(０.９ꎬ０.０２９ꎬ０.１４)ꎬ(０.９７ꎬ－０.３４ꎬ０.１２)ꎬ分析边界层湍动能剖面ꎬ结果如图１２所示ꎮ从图中可以看到ꎬ随着壁面温度升高ꎬ边界层厚度先略微变厚ꎬ再变薄ꎬ当壁面温度升高到７００Ｋ时ꎬ边界层厚度迅速降低ꎮ这些结果与转捩位置先前移再后移的结论相符合ꎬ因为边界层厚度会影响不稳定波的时间和空间尺度ꎬ边界层厚度低时ꎬ不稳定波增长速度变慢ꎬ延迟转捩发生ꎮ需要指出的是ꎬ仅采用当前使用的方法ꎬ无法从更深层７１气体物理２０２４年㊀第９卷次揭示转捩反转的流动机理ꎬ而须另外借助稳定性分析方法ꎬ例如ꎬ使用ｅＮ方法开展基于模态的稳定性研究ꎮ文献[３３]采用该手段研究了大掠角平板钝三角翼随壁温比变化出现转捩反转的内在机理:壁温比升高促进横流模态和第１模态扰动增长ꎬ抑制第２模态发展ꎬ在第１㊁２模态联合作用影响下ꎬ出现转捩反转现象ꎮ我们将在后续开展进一步研究ꎮ(ａ)Ｕｐｐｅｒｓｕｒｆａｃｅ(ｂ)Ｌｏｗｅｒｓｕｒｆａｃｅ图１２㊀不同位置湍动能剖面随壁面温度的变化Ｆｉｇ.１２㊀Ｖａｒｉａｔｉｏｎｏｆｔｕｒｂｕｌｅｎｔｋｉｎｅｔｉｃｅｎｅｒｇｙｗｉｔｈｗａｌｌｔｅｍｐｅｒａｔｕｒｅａｔｄｉｆｆｅｒｅｎｔｌｏｃａｔｉｏｎｓ６㊀结论针对ＨｙＴＲＶ转捩问题ꎬ在Ｍａｃｈ数Ｍａ＝３~８ꎬ壁面温度Ｔ＝１５０~９００Ｋ的条件下ꎬ基于课题组自研软件ꎬ对γ￣Ｒｅ~θｔ转捩模型和ＳＳＴ湍流模型进行了高超声速修正ꎬ研究了Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ转捩的影响ꎬ得出以下结论:１)经过高超声速修正后的γ￣Ｒｅ~θｔ转捩模型和ＳＳＴ湍流模型能够较为准确地预测ＨｙＴＲＶ转捩位置ꎬ并且湍流边界层区域形状与实验结果基本一致ꎻＨｙＴＲＶ存在多个不同的转捩区域ꎬ上表面两侧转捩区域分布在两侧边缘位置ꎬ下表面两侧转捩区域分布在中心线两侧ꎮ２)Ｍａｃｈ数的增加会导致上下表面转捩起始位置均大幅后移ꎬ湍流区大幅缩小ꎬ但当Ｍａｃｈ数增加到８时ꎬ湍流区仍然存在ꎬ并没有消失ꎻ上表面层流区摩阻不断增加ꎬ下表面湍流区摩阻不断减小ꎮ３)壁面温度的增加会导致上下表面转捩起始位置先前移ꎬ再后移ꎬ这与边界层厚度变化规律一致ꎬ当壁面温度增加到７００Ｋ时ꎬ下表面湍流区已经基本消失ꎬ当壁面温度增加到９００Ｋ时ꎬ上表面湍流区也基本消失ꎻ上表面在层流区域的摩阻系数逐渐增大ꎬ在湍流区的摩阻系数逐渐减小ꎮ致谢㊀感谢中国空气动力研究与发展中心和空天飞行空气动力科学与技术全国重点实验室提供的ＨｙＴＲＶ模型数据和实验数据ꎮ参考文献(Ｒｅｆｅｒｅｎｃｅｓ)[１]㊀ＯｂｅｒｉｎｇＩＩＩＨꎬＨｅｉｎｒｉｃｈｓＲＬ.Ｍｉｓｓｉｌｅｄｅｆｅｎｓｅｆｏｒｇｒｅａｔｐｏｗｅｒｃｏｎｆｌｉｃｔ:ｏｕｔｍａｎｅｕｖｅｒｉｎｇｔｈｅＣｈｉｎａｔｈｒｅａｔ[Ｊ].Ｓｔｒａ￣ｔｅｇｉｃＳｔｕｄｉｅｓＱｕａｒｔｅｒｌｙꎬ２０１９ꎬ３(４):３７￣５６. [２]ＣｈｅｎｇＣꎬＷｕＪＨꎬＺｈａｎｇＹＬꎬｅｔａｌ.Ａｅｒｏｄｙｎａｍｉｃｓａｎｄｄｙｎａｍｉｃｓｔａｂｉｌｉｔｙｏｆｍｉｃｒｏ￣ａｉｒ￣ｖｅｈｉｃｌｅｗｉｔｈｆｏｕｒｆｌａｐｐｉｎｇｗｉｎｇｓｉｎｈｏｖｅｒｉｎｇｆｌｉｇｈｔ[Ｊ].ＡｄｖａｎｃｅｓｉｎＡｅｒｏｄｙｎａｍｉｃｓꎬ２０２０ꎬ２(３):５.[３]ＢｅｒｔｉｎＪＪꎬＣｕｍｍｉｎｇｓＲＭ.Ｆｉｆｔｙｙｅａｒｓｏｆｈｙｐｅｒｓｏｎｉｃｓ:ｗｈｅｒｅｗｅᶄｖｅｂｅｅｎꎬｗｈｅｒｅｗｅᶄｒｅｇｏｉｎｇ[Ｊ].ＰｒｏｇｒｅｓｓｉｎＡｅｒｏｓｐａｃｅＳｃｉｅｎｃｅｓꎬ２００３ꎬ３９(６/７):５１１￣５３６. [４]陈坚强ꎬ涂国华ꎬ张毅锋ꎬ等.高超声速边界层转捩研究现状与发展趋势[Ｊ].空气动力学学报ꎬ２０１７ꎬ３５(３):３１１￣３３７.ＣｈｅｎＪＱꎬＴｕＧＨꎬＺｈａｎｇＹＦꎬｅｔａｌ.Ｈｙｐｅｒｓｎｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎ:ｗｈａｔｗｅｋｎｏｗꎬｗｈｅｒｅｓｈａｌｌｗｅｇｏ[Ｊ].ＡｃｔａＡｅｒｏｄｙｎａｍｉｃａＳｉｎｉｃａꎬ２０１７ꎬ３５(３):３１１￣３３７(ｉｎＣｈｉｎｅｓｅ).[５]段毅ꎬ姚世勇ꎬ李思怡ꎬ等.高超声速边界层转捩的若干问题及工程应用研究进展综述[Ｊ].空气动力学学报ꎬ２０２０ꎬ３８(２):３９１￣４０３.ＤｕａｎＹꎬＹａｏＳＹꎬＬｉＳＹꎬｅｔａｌ.Ｒｅｖｉｅｗｏｆｐｒｏｇｒｅｓｓｉｎｓｏｍｅｉｓｓｕｅｓａｎｄｅｎｇｉｎｅｅｒｉｎｇａｐｐｌｉｃａｔｉｏｎｏｆｈｙｐｅｒｓｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎ[Ｊ].ＡｃｔａＡｅｒｏｄｙｎａｍｉｃａＳｉｎｉｃａꎬ２０２０ꎬ３８(２):３９１￣４０３(ｉｎＣｈｉｎｅｓｅ).[６]ＺｈａｎｇＹＦꎬＺｈａｎｇＹＲꎬＣｈｅｎＪＱꎬｅｔａｌ.Ｎｕｍｅｒｉｃａｌｓｉ￣８１第２期章录兴ꎬ等:Ｍａｃｈ数和壁面温度对ＨｙＴＲＶ边界层转捩的影响ｍｕｌａｔｉｏｎｓｏｆｈｙｐｅｒｓｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎｂａｓｅｄｏｎｔｈｅｆｌｏｗｓｏｌｖｅｒｃｈａｎｔ２.０[Ｒ].ＡＩＡＡ２０１７￣２４０９ꎬ２０１７. [７]ＫｒａｕｓｅＭꎬＢｅｈｒＭꎬＢａｌｌｍａｎｎＪ.Ｍｏｄｅｌｉｎｇｏｆｔｒａｎｓｉｔｉｏｎｅｆｆｅｃｔｓｉｎｈｙｐｅｒｓｏｎｉｃｉｎｔａｋｅｆｌｏｗｓｕｓｉｎｇａｃｏｒｒｅｌａｔｉｏｎ￣ｂａｓｅｄｉｎｔｅｒｍｉｔｔｅｎｃｙｍｏｄｅｌ[Ｒ].ＡＩＡＡ２００８￣２５９８ꎬ２００８. [８]ＹｉＭＲꎬＺｈａｏＨＹꎬＬｅＪＬ.Ｈｙｐｅｒｓｏｎｉｃｎａｔｕｒａｌａｎｄｆｏｒｃｅｄｔｒａｎｓｉｔｉｏｎｓｉｍｕｌａｔｉｏｎｂｙｃｏｒｒｅｌａｔｉｏｎ￣ｂａｓｅｄｉｎｔｅｒｍｉｔ￣ｔｅｎｃｙ[Ｒ].ＡＩＡＡ２０１７￣２３３７ꎬ２０１７.[９]向星皓ꎬ张毅锋ꎬ袁先旭ꎬ等.Ｃ￣γ￣Ｒｅθ高超声速三维边界层转捩预测模型[Ｊ].航空学报ꎬ２０２１ꎬ４２(９):６２５７１１.ＸｉａｎｇＸＨꎬＺｈａｎｇＹＦꎬＹｕａｎＸＸꎬｅｔａｌ.Ｃ￣γ￣Ｒｅθｍｏｄｅｌｆｏｒｈｙｐｅｒｓｏｎｉｃｔｈｒｅｅ￣ｄｉｍｅｎｓｉｏｎａｌｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎｐｒｅｄｉｃｔｉｏｎ[Ｊ].ＡｃｔａＡｅｒｏｎａｕｔｉｃａｅｔＡｓｔｒｏｎａｕｔｉｃａＳｉｎｉｃａꎬ２０２１ꎬ４２(９):６２５７１１(ｉｎＣｈｉｎｅｓｅ).[１０]ＭｃＤａｎｉｅｌＲＤꎬＮａｎｃｅＲＰꎬＨａｓｓａｎＨＡ.Ｔｒａｎｓｉｔｉｏｎｏｎｓｅｔｐｒｅｄｉｃｔｉｏｎｆｏｒｈｉｇｈ￣ｓｐｅｅｄｆｌｏｗ[Ｊ].ＪｏｕｒｎａｌｏｆＳｐａｃｅｃｒａｆｔａｎｄＲｏｃｋｅｔｓꎬ２０００ꎬ３７(３):３０４￣３０９.[１１]ＰａｐｐＪＬꎬＤａｓｈＳＭ.Ｒａｐｉｄｅｎｇｉｎｅｅｒｉｎｇａｐｐｒｏａｃｈｔｏｍｏｄｅｌｉｎｇｈｙｐｅｒｓｏｎｉｃｌａｍｉｎａｒ￣ｔｏ￣ｔｕｒｂｕｌｅｎｔｔｒａｎｓｉｔｉｏｎａｌｆｌｏｗｓ[Ｊ].ＪｏｕｒｎａｌｏｆＳｐａｃｅｃｒａｆｔａｎｄＲｏｃｋｅｔｓꎬ２００５ꎬ４２(３):４６７￣４７５.[１２]ＪｕｌｉａｎｏＴＪꎬＳｃｈｎｅｉｄｅｒＳＰ.ＩｎｓｔａｂｉｌｉｔｙａｎｄｔｒａｎｓｉｔｉｏｎｏｎｔｈｅＨＩＦｉＲＥ￣５ｉｎａＭａｃｈ￣６ｑｕｉｅｔｔｕｎｎｅｌ[Ｒ].ＡＩＡＡ２０１０￣５００４ꎬ２０１０.[１３]杨云军ꎬ马汉东ꎬ周伟江.高超声速流动转捩的数值研究[Ｊ].宇航学报ꎬ２００６ꎬ２７(１):８５￣８８.ＹａｎｇＹＪꎬＭａＨＤꎬＺｈｏｕＷＪ.Ｎｕｍｅｒｉｃａｌｒｅｓｅａｒｃｈｏｎｓｕｐｅｒｓｏｎｉｃｆｌｏｗｔｒａｎｓｉｔｉｏｎ[Ｊ].ＪｏｕｒｎａｌｏｆＡｓｔｒｏｎａｕｔｉｃｓꎬ２００６ꎬ２７(１):８５￣８８(ｉｎＣｈｉｎｅｓｅ).[１４]袁先旭ꎬ何琨ꎬ陈坚强ꎬ等.ＭＦ￣１模型飞行试验转捩结果初步分析[Ｊ].空气动力学学报ꎬ２０１８ꎬ３６(２):２８６￣２９３.ＹｕａｎＸＸꎬＨｅＫꎬＣｈｅｎＪＱꎬｅｔａｌ.ＰｒｅｌｉｍｉｎａｒｙｔｒａｎｓｉｔｉｏｎｒｅｓｅａｒｃｈａｎａｌｙｓｉｓｏｆＭＦ￣１[Ｊ].ＡｃｔａＡｅｒｏｄｙｎａｍｉｃａＳｉｎｉｃａꎬ２０１８ꎬ３６(２):２８６￣２９３(ｉｎＣｈｉｎｅｓｅ).[１５]陈坚强ꎬ涂国华ꎬ万兵兵ꎬ等.ＨｙＴＲＶ流场特征与边界层稳定性特征分析[Ｊ].航空学报ꎬ２０２１ꎬ４２(６):１２４３１７.ＣｈｅｎＪＱꎬＴｕＧＨꎬＷａｎＢＢꎬｅｔａｌ.Ｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｆｌｏｗｆｉｅｌｄａｎｄｂｏｕｎｄａｒｙ￣ｌａｙｅｒｓｔａｂｉｌｉｔｙｏｆＨｙＴＲＶ[Ｊ].ＡｃｔａＡｅｒｏｎａｕｔｉｃａｅｔＡｓｔｒｏｎａｕｔｉｃａＳｉｎｉｃａꎬ２０２１ꎬ４２(６):１２４３１７(ｉｎＣｈｉｎｅｓｅ).[１６]陈坚强ꎬ刘深深ꎬ刘智勇ꎬ等.用于高超声速边界层转捩研究的标模气动布局及设计方法.中国:１０９９６９３７４Ｂ[Ｐ].２０２１￣０５￣１８.ＣｈｅｎＪＱꎬＬｉｕＳＳꎬＬｉｕＺＹꎬｅｔａｌ.Ｓｔａｎｄａｒｄｍｏｄｅｌａｅｒｏ￣ｄｙｎａｍｉｃｌａｙｏｕｔａｎｄｄｅｓｉｇｎｍｅｔｈｏｄｆｏｒｈｙｐｅｒｓｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎｒｅｓｅａｒｃｈ.ＣＮꎬ１０９９６９３７４Ｂ[Ｐ].２０２１￣０５￣１８(ｉｎＣｈｉｎｅｓｅ).[１７]ＬｉｕＳＳꎬＹｕａｎＸＸꎬＬｉｕＺＹꎬｅｔａｌ.Ｄｅｓｉｇｎａｎｄｔｒａｎｓｉｔｉｏｎｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆａｓｔａｎｄａｒｄｍｏｄｅｌｆｏｒｈｙｐｅｒｓｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎｒｅｓｅａｒｃｈ[Ｊ].ＡｃｔａＭｅｃｈａｎｉｃａＳｉｎｉｃａꎬ２０２１ꎬ３７(１１):１６３７￣１６４７.[１８]ＣｈｅｎＸꎬＤｏｎｇＳＷꎬＴｕＧＨꎬｅｔａｌ.Ｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎ￣ｓｉｔｉｏｎａｎｄｌｉｎｅａｒｍｏｄａｌｉｎｓｔａｂｉｌｉｔｉｅｓｏｆｈｙｐｅｒｓｏｎｉｃｆｌｏｗｏｖｅｒａｌｉｆｔｉｎｇｂｏｄｙ[Ｊ].ＪｏｕｒｎａｌｏｆＦｌｕｉｄＭｅｃｈａｎｉｃｓꎬ２０２２ꎬ９３８(４０８):Ａ８.[１９]ＱｉＨꎬＬｉＸＬꎬＹｕＣＰꎬｅｔａｌ.Ｄｉｒｅｃｔｎｕｍｅｒｉｃａｌｓｉｍｕｌａｔｉｏｎｏｆｈｙｐｅｒｓｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎｏｖｅｒａｌｉｆｔｉｎｇ￣ｂｏｄｙｍｏｄｅｌＨｙＴＲＶ[Ｊ].ＡｄｖａｎｃｅｓｉｎＡｅｒｏｄｙｎａｍｉｃｓꎬ２０２１ꎬ３(１):３１.[２０]万兵兵ꎬ陈曦ꎬ陈坚强ꎬ等.三维边界层转捩预测ＨｙＴＥＮ软件在高超声速典型标模中的应用[Ｊ].空天技术ꎬ２０２３(１):１５０￣１５８.ＷａｎＢＢꎬＣｈｅｎＸꎬＣｈｅｎＪＱꎬｅｔａｌ.ＡｐｐｌｉｃａｔｉｏｎｓｏｆＨｙＴＥＮｓｏｆｔｗａｒｅｆｏｒｐｒｅｄｉｃｔｉｎｇｔｈｒｅｅ￣ｄｉｍｅｎｓｉｏｎａｌｂｏｕｎｄａｒｙ￣ｌａｙｅｒｔｒａｎｓｉｔｉｏｎｉｎｔｙｐｉｃａｌｈｙｐｅｒｓｏｎｉｃｍｏｄｅｌｓ[Ｊ].ＡｅｒｏｓｐａｃｅＴｅｃｈｎｏｌｏｇｙꎬ２０２３(１):１５０￣１５８(ｉｎＣｈｉｎｅｓｅ). [２１]ＭｅｎｔｅｒＦＲꎬＬａｎｇｔｒｙＲＢꎬＬｉｋｋｉＳＲꎬｅｔａｌ.Ａｃｏｒｒｅｌａｔｉｏｎ￣ｂａｓｅｄｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｕｓｉｎｇｌｏｃａｌｖａｒｉａｂｌｅｓＰａｒｔⅠ:ｍｏｄｅｌｆｏｒｍｕｌａｔｉｏｎ[Ｊ].ＪｏｕｒｎａｌｏｆＴｕｒｂｏｍａｃｈｉｎｅｒｙꎬ２００６ꎬ１２８(３):４１３￣４２２.[２２]ＬａｎｇｔｒｙＲＢꎬＭｅｎｔｅｒＦＲꎬＬｉｋｋｉＳＲꎬｅｔａｌ.Ａｃｏｒｒｅｌａｔｉｏｎ￣ｂａｓｅｄｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｕｓｉｎｇｌｏｃａｌｖａｒｉａｂｌｅｓＰａｒｔⅡ:ｔｅｓｔｃａｓｅｓａｎｄｉｎｄｕｓｔｒｉａｌａｐｐｌｉｃａｔｉｏｎｓ[Ｊ].ＪｏｕｒｎａｌｏｆＴｕｒ￣ｂｏｍａｃｈｉｎｅｒｙꎬ２００６ꎬ１２８(３):４２３￣４３４.[２３]ＬａｎｇｔｒｙＲＢꎬＭｅｎｔｅｒＦＲ.Ｃｏｒｒｅｌａｔｉｏｎ￣ｂａｓｅｄｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｉｎｇｆｏｒｕｎｓｔｒｕｃｔｕｒｅｄｐａｒａｌｌｅｌｉｚｅｄｃｏｍｐｕｔａｔｉｏｎａｌｆｌｕｉｄｄｙｎａｍｉｃｓｃｏｄｅｓ[Ｊ].ＡＩＡＡＪｏｕｒｎａｌꎬ２００９ꎬ４７(１２):２８９４￣２９０６.[２４]孟德虹ꎬ张玉伦ꎬ王光学ꎬ等.γ￣Ｒｅθ转捩模型在二维低速问题中的应用[Ｊ].航空学报ꎬ２０１１ꎬ３２(５):７９２￣８０１.ＭｅｎｇＤＨꎬＺｈａｎｇＹＬꎬＷａｎｇＧＸꎬｅｔａｌ.Ａｐｐｌｉｃａｔｉｏｎｏｆγ￣Ｒｅθｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｔｏｔｗｏ￣ｄｉｍｅｎｓｉｏｎａｌｌｏｗｓｐｅｅｄｆｌｏｗｓ[Ｊ].ＡｃｔａＡｅｒｏｎａｕｔｉｃａｅｔＡｓｔｒｏｎａｕｔｉｃａＳｉｎｉｃａꎬ２０１１ꎬ３２(５):７９２￣８０１(ｉｎＣｈｉｎｅｓｅ).[２５]牟斌ꎬ江雄ꎬ肖中云ꎬ等.γ￣Ｒｅθ转捩模型的标定与应用[Ｊ].空气动力学学报ꎬ２０１３ꎬ３１(１):１０３￣１０９.ＭｏｕＢꎬＪｉａｎｇＸꎬＸｉａｏＺＹꎬｅｔａｌ.Ｉｍｐｌｅｍｅｎｔａｔｉｏｎａｎｄｃａｌｉｂｅｒａｔｉｏｎｏｆγ￣Ｒｅθｔｒａｎｓｉｔｉｏｎｍｏｄｅｌ[Ｊ].ＡｃｔａＡｅｒｏｄｙ￣ｎａｍｉｃａＳｉｎｉｃａꎬ２０１３ꎬ３１(１):１０３￣１０９(ｉｎＣｈｉｎｅｓｅ). [２６]郭隽ꎬ刘丽平ꎬ徐晶磊ꎬ等.γ￣Ｒｅ~θｔ转捩模型在跨声速涡轮叶栅中的应用[Ｊ].推进技术ꎬ２０１８ꎬ３９(９):１９９４￣２００１.９１气体物理２０２４年㊀第９卷ＧｕｏＪꎬＬｉｕＬＰꎬＸｕＪＬꎬｅｔａｌ.Ａｐｐｌｉｃａｔｉｏｎｏｆγ￣Ｒｅ~θｔｔｒａｎ￣ｓｉｔｉｏｎｍｏｄｅｌｉｎｔｒａｎｓｏｎｉｃｔｕｒｂｉｎｅｃａｓｃａｄｅｓ[Ｊ].ＪｏｕｒｎａｌｏｆＰｒｏｐｕｌｓｉｏｎＴｅｃｈｎｏｌｏｇｙꎬ２０１８ꎬ３９(９):１９９４￣２００１(ｉｎＣｈｉｎｅｓｅ).[２７]郑赟ꎬ李虹杨ꎬ刘大响.γ￣Ｒｅθ转捩模型在高超声速下的应用及分析[Ｊ].推进技术ꎬ２０１４ꎬ３５(３):２９６￣３０４.ＺｈｅｎｇＹꎬＬｉＨＹꎬＬｉｕＤＸ.Ａｐｐｌｉｃａｔｉｏｎａｎｄａｎａｌｙｓｉｓｏｆγ￣Ｒｅθｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｉｎｈｙｐｅｒｓｏｎｉｃｆｌｏｗ[Ｊ].ＪｏｕｒｎａｌｏｆＰｒｏｐｕｌｓｉｏｎＴｅｃｈｎｏｌｏｇｙꎬ２０１４ꎬ３５(３):２９６￣３０４(ｉｎＣｈｉ￣ｎｅｓｅ).[２８]孔维萱ꎬ阎超ꎬ赵瑞.γ￣Ｒｅθ模式应用于高速边界层转捩的研究[Ｊ].空气动力学学报ꎬ２０１３ꎬ３１(１):１２０￣１２６.ＫｏｎｇＷＸꎬＹａｎＣꎬＺｈａｏＲ.γ￣Ｒｅθｍｏｄｅｌｒｅｓｅａｒｃｈｆｏｒｈｉｇｈ￣ｓｐｅｅｄｂｏｕｎｄａｒｙｌａｙｅｒｔｒａｎｓｉｔｉｏｎ[Ｊ].ＡｃｔａＡｅｒｏｄｙ￣ｎａｍｉｃａＳｉｎｉｃａꎬ２０１３ꎬ３１(１):１２０￣１２６(ｉｎＣｈｉｎｅｓｅ). [２９]张毅锋ꎬ何琨ꎬ张益荣ꎬ等.Ｍｅｎｔｅｒ转捩模型在高超声速流动模拟中的改进及验证[Ｊ].宇航学报ꎬ２０１６ꎬ３７(４):３９７￣４０２.ＺｈａｎｇＹＦꎬＨｅＫꎬＺｈａｎｇＹＲꎬｅｔａｌ.ＩｍｐｒｏｖｅｍｅｎｔａｎｄｖａｌｉｄａｔｉｏｎｏｆＭｅｎｔｅｒᶄｓｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｆｏｒｈｙｐｅｒｓｏｎｉｃｆｌｏｗｓｉｍｕｌａｔｉｏｎ[Ｊ].ＪｏｕｒｎａｌｏｆＡｓｔｒｏｎａｕｔｉｃｓꎬ２０１６ꎬ３７(４):３９７￣４０２(ｉｎＣｈｉｎｅｓｅ).[３０]ＬａｎｇｔｒｙＲＢꎬＳｅｎｇｕｐｔａＫꎬＹｅｈＤＴꎬｅｔａｌ.Ｅｘｔｅｎｄｉｎｇｔｈｅγ￣Ｒｅθｔｃｏｒｒｅｌａｔｉｏｎｂａｓｅｄｔｒａｎｓｉｔｉｏｎｍｏｄｅｌｆｏｒｃｒｏｓｓｆｌｏｗｅｆｆｅｃｔｓ(Ｉｎｖｉｔｅｄ)[Ｒ].ＡＩＡＡ２０１５￣２４７４ꎬ２０１５. [３１]ＳａｒｋａｒＳ.Ｔｈｅｐｒｅｓｓｕｒｅ￣ｄｉｌａｔａｔｉｏｎｃｏｒｒｅｌａｔｉｏｎｉｎｃｏｍｐｒｅｓｓｉ￣ｂｌｅｆｌｏｗｓ[Ｊ].ＰｈｙｓｉｃｓｏｆＦｌｕｉｄｓＡꎬ１９９２ꎬ４(１２):２６７４￣２６８２.[３２]ＷｉｌｃｏｘＤＣ.Ｄｉｌａｔａｔｉｏｎ￣ｄｉｓｓｉｐａｔｉｏｎｃｏｒｒｅｃｔｉｏｎｓｆｏｒａｄｖａｎｃｅｄｔｕｒｂｕｌｅｎｃｅｍｏｄｅｌｓ[Ｊ].ＡＩＡＡＪｏｕｒｎａｌꎬ１９９２ꎬ３０(１１):２６３９￣２６４６.[３３]马祎蕾ꎬ余平ꎬ姚世勇.壁温对钝三角翼边界层稳定性及转捩影响[Ｊ].空气动力学学报ꎬ２０２０ꎬ３８(６):１０１７￣１０２６.ＭａＹＬꎬＹｕＰꎬＹａｏＳＹ.Ｅｆｆｅｃｔｏｆｗａｌｌｔｅｍｐｅｒａｔｕｒｅｏｎｓｔａｂｉｌｉｔｙａｎｄｔｒａｎｓｉｔｉｏｎｏｆｈｙｐｅｒｓｏｎｉｃｂｏｕｎｄａｒｙｌａｙｅｒｏｎａｂｌｕｎｔｄｅｌｔａｗｉｎｇ[Ｊ].ＡｃｔａＡｅｒｏｄｙｎａｍｉｃａＳｉｎｉｃａꎬ２０２０ꎬ３８(６):１０１７￣１０２６(ｉｎＣｈｉｎｅｓｅ).０２。

稳定的高功率激光系统在高级引力波探测器中的应用

Stabilized high-power laser system forthe gravitational wave detector advancedLIGOP.Kwee,1,∗C.Bogan,2K.Danzmann,1,2M.Frede,4H.Kim,1P.King,5J.P¨o ld,1O.Puncken,3R.L.Savage,5F.Seifert,5P.Wessels,3L.Winkelmann,3and B.Willke21Max-Planck-Institut f¨u r Gravitationsphysik(Albert-Einstein-Institut),Hannover,Germany2Leibniz Universit¨a t Hannover,Hannover,Germany3Laser Zentrum Hannover e.V.,Hannover,Germany4neoLASE GmbH,Hannover,Germany5LIGO Laboratory,California Institute of Technology,Pasadena,California,USA*patrick.kwee@aei.mpg.deAbstract:An ultra-stable,high-power cw Nd:Y AG laser system,devel-oped for the ground-based gravitational wave detector Advanced LIGO(Laser Interferometer Gravitational-Wave Observatory),was comprehen-sively ser power,frequency,beam pointing and beamquality were simultaneously stabilized using different active and passiveschemes.The output beam,the performance of the stabilization,and thecross-coupling between different stabilization feedback control loops werecharacterized and found to fulﬁll most design requirements.The employedstabilization schemes and the achieved performance are of relevance tomany high-precision optical experiments.©2012Optical Society of AmericaOCIS codes:(140.3425)Laser stabilization;(120.3180)Interferometry.References and links1.S.Rowan and J.Hough,“Gravitational wave detection by interferometry(ground and space),”Living Rev.Rel-ativity3,1–3(2000).2.P.R.Saulson,Fundamentals of Interferometric Gravitational Wave Detectors(World Scientiﬁc,1994).3.G.M.Harry,“Advanced LIGO:the next generation of gravitational wave detectors,”Class.Quantum Grav.27,084006(2010).4. B.Willke,“Stabilized lasers for advanced gravitational wave detectors,”Laser Photon.Rev.4,780–794(2010).5.P.Kwee,“Laser characterization and stabilization for precision interferometry,”Ph.D.thesis,Universit¨a t Han-nover(2010).6.K.Somiya,Y.Chen,S.Kawamura,and N.Mio,“Frequency noise and intensity noise of next-generationgravitational-wave detectors with RF/DC readout schemes,”Phys.Rev.D73,122005(2006).7. B.Willke,P.King,R.Savage,and P.Fritschel,“Pre-stabilized laser design requirements,”internal technicalreport T050036-v4,LIGO Scientiﬁc Collaboration(2009).8.L.Winkelmann,O.Puncken,R.Kluzik,C.Veltkamp,P.Kwee,J.Poeld,C.Bogan,B.Willke,M.Frede,J.Neu-mann,P.Wessels,and D.Kracht,“Injection-locked single-frequency laser with an output power of220W,”Appl.Phys.B102,529–538(2011).9.T.J.Kane and R.L.Byer,“Monolithic,unidirectional single-mode Nd:Y AG ring laser,”Opt.Lett.10,65–67(1985).10.I.Freitag,A.T¨u nnermann,and H.Welling,“Power scaling of diode-pumped monolithic Nd:Y AG lasers to outputpowers of several watts,”mun.115,511–515(1995).11.M.Frede,B.Schulz,R.Wilhelm,P.Kwee,F.Seifert,B.Willke,and D.Kracht,“Fundamental mode,single-frequency laser ampliﬁer for gravitational wave detectors,”Opt.Express15,459–465(2007).#161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 1061712. A.D.Farinas,E.K.Gustafson,and R.L.Byer,“Frequency and intensity noise in an injection-locked,solid-statelaser,”J.Opt.Soc.Am.B12,328–334(1995).13.R.Bork,M.Aronsson,D.Barker,J.Batch,J.Heefner,A.Ivanov,R.McCarthy,V.Sandberg,and K.Thorne,“New control and data acquisition system in the Advanced LIGO project,”Proc.of Industrial Control And Large Experimental Physics Control System(ICALEPSC)conference(2011).14.“Experimental physics and industrial control system,”/epics/.15.P.Kwee and B.Willke,“Automatic laser beam characterization of monolithic Nd:Y AG nonplanar ring lasers,”Appl.Opt.47,6022–6032(2008).16.P.Kwee,F.Seifert,B.Willke,and K.Danzmann,“Laser beam quality and pointing measurement with an opticalresonator,”Rev.Sci.Instrum.78,073103(2007).17. A.R¨u diger,R.Schilling,L.Schnupp,W.Winkler,H.Billing,and K.Maischberger,“A mode selector to suppressﬂuctuations in laser beam geometry,”Opt.Acta28,641–658(1981).18. B.Willke,N.Uehara,E.K.Gustafson,R.L.Byer,P.J.King,S.U.Seel,and R.L.Savage,“Spatial and temporalﬁltering of a10-W Nd:Y AG laser with a Fabry-Perot ring-cavity premode cleaner,”Opt.Lett.23,1704–1706 (1998).19.J.H.P¨o ld,“Stabilization of the Advanced LIGO200W laser,”Diploma thesis,Leibniz Universit¨a t Hannover(2009).20. E.D.Black,“An introduction to Pound-Drever-Hall laser frequency stabilization,”Am.J.Phys.69,79–87(2001).21.R.W.P.Drever,J.L.Hall,F.V.Kowalski,J.Hough,G.M.Ford,A.J.Munley,and H.Ward,“Laser phase andfrequency stabilization using an optical resonator,”Appl.Phys.B31,97–105(1983).22. A.Bullington,ntz,M.Fejer,and R.Byer,“Modal frequency degeneracy in thermally loaded optical res-onators,”Appl.Opt.47,2840–2851(2008).23.G.Mueller,“Beam jitter coupling in Advanced LIGO,”Opt.Express13,7118–7132(2005).24.V.Delaubert,N.Treps,ssen,C.C.Harb,C.Fabre,m,and H.-A.Bachor,“TEM10homodynedetection as an optimal small-displacement and tilt-measurement scheme,”Phys.Rev.A74,053823(2006). 25.P.Kwee,B.Willke,and K.Danzmann,“Laser power noise detection at the quantum-noise limit of32A pho-tocurrent,”Opt.Lett.36,3563–3565(2011).26. A.Araya,N.Mio,K.Tsubono,K.Suehiro,S.Telada,M.Ohashi,and M.Fujimoto,“Optical mode cleaner withsuspended mirrors,”Appl.Opt.36,1446–1453(1997).27.P.Kwee,B.Willke,and K.Danzmann,“Shot-noise-limited laser power stabilization with a high-power photodi-ode array,”Opt.Lett.34,2912–2914(2009).28. ntz,P.Fritschel,H.Rong,E.Daw,and G.Gonz´a lez,“Quantum-limited optical phase detection at the10−10rad level,”J.Opt.Soc.Am.A19,91–100(2002).1.IntroductionInterferometric gravitational wave detectors[1,2]perform one of the most precise differential length measurements ever.Their goal is to directly detect the faint signals of gravitational waves emitted by astrophysical sources.The Advanced LIGO(Laser Interferometer Gravitational-Wave Observatory)[3]project is currently installing three second-generation,ground-based detectors at two observatory sites in the USA.The4kilometer-long baseline Michelson inter-ferometers have an anticipated tenfold better sensitivity than theirﬁrst-generation counterparts (Inital LIGO)and will presumably reach a strain sensitivity between10−24and10−23Hz−1/2.One key technology necessary to reach this extreme sensitivity are ultra-stable high-power laser systems[4,5].A high laser output power is required to reach a high signal-to-quantum-noise ratio,since the effect of quantum noise at high frequencies in the gravitational wave readout is reduced with increasing circulating laser power in the interferometer.In addition to quantum noise,technical laser noise coupling to the gravitational wave channel is a major noise source[6].Thus it is important to reduce the coupling of laser noise,e.g.by optical design or by exploiting symmetries,and to reduce laser noise itself by various active and passive stabilization schemes.In this article,we report on the pre-stabilized laser(PSL)of the Advanced LIGO detector. The PSL is based on a high-power solid-state laser that is comprehensively stabilized.One laser system was set up at the Albert-Einstein-Institute(AEI)in Hannover,Germany,the so called PSL reference system.Another identical PSL has already been installed at one Advanced LIGO site,the one near Livingston,LA,USA,and two more PSLs will be installed at the second #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10618site at Hanford,WA,USA.We have characterized the reference PSL and theﬁrst observatory PSL.For this we measured various beam parameters and noise levels of the output beam in the gravitational wave detection frequency band from about10Hz to10kHz,measured the performance of the active and passive stabilization schemes,and determined upper bounds for the cross coupling between different control loops.At the time of writing the PSL reference system has been operated continuously for more than18months,and continues to operate reliably.The reference system delivered a continuous-wave,single-frequency laser beam at1064nm wavelength with a maximum power of150W with99.5%in the TEM00mode.The active and passive stabilization schemes efﬁciently re-duced the technical laser noise by several orders of magnitude such that most design require-ments[5,7]were fulﬁlled.In the gravitational wave detection frequency band the relative power noise was as low as2×10−8Hz−1/2,relative beam pointingﬂuctuations were as low as1×10−7Hz−1/2,and an in-loop measurement of the frequency noise was consistent with the maximum acceptable frequency noise of about0.1HzHz−1/2.The cross couplings between the control loops were,in general,rather small or at the expected levels.Thus we were able to optimize each loop individually and observed no instabilities due to cross couplings.This stabilized laser system is an indispensable part of Advanced LIGO and fulﬁlled nearly all design goals concerning the maximum acceptable noise levels of the different beam pa-rameters right after installation.Furthermore all or a subset of the implemented stabilization schemes might be of interest for many other high-precision optical experiments that are limited by laser noise.Besides gravitational wave detectors,stabilized laser systems are used e.g.in the ﬁeld of optical frequency standards,macroscopic quantum objects,precision spectroscopy and optical traps.In the following section the laser system,the stabilization scheme and the characterization methods are described(Section2).Then,the results of the characterization(Section3)and the conclusions(Section4)are presented.ser system and stabilizationThe PSL consists of the laser,developed and fabricated by Laser Zentrum Hannover e.V.(LZH) and neoLASE,and the stabilization,developed and integrated by AEI.The optical components of the PSL are on a commercial optical table,occupying a space of about1.5×3.5m2,in a clean,dust-free environment.At the observatory sites the optical table is located in an acoustically isolated cleanroom.Most of the required electronics,the laser diodes for pumping the laser,and water chillers for cooling components on the optical table are placed outside of this cleanroom.The laser itself consists of three stages(Fig.1).An almostﬁnal version of the laser,the so-called engineering prototype,is described in detail in[8].The primary focus of this article is the stabilization and characterization of the PSL.Thus only a rough overview of the laser and the minor modiﬁcations implemented between engineering prototype and reference system are given in the following.Theﬁrst stage,the master laser,is a commercial non-planar ring-oscillator[9,10](NPRO) manufactured by InnoLight GmbH in Hannover,Germany.This solid-state laser uses a Nd:Y AG crystal as the laser medium and resonator at the same time.The NPRO is pumped by laser diodes at808nm and delivers an output power of2W.An internal power stabilization,called the noise eater,suppresses the relaxation oscillation at around1MHz.Due to its monolithic res-onator,the laser has exceptional intrinsic frequency stability.The two subsequent laser stages, used for power scaling,inherit the frequency stability of the master laser.The second stage(medium-power ampliﬁer)is a single-pass ampliﬁer[11]with an output power of35W.The seed laser beam from the NPRO stage passes through four Nd:YVO4crys-#161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10619power stabilizationFig.1.Pre-stabilized laser system of Advanced LIGO.The three-staged laser(NPRO,medium power ampliﬁer,high power oscillator)and the stabilization scheme(pre-mode-cleaner,power and frequency stabilization)are shown.The input-mode-cleaner is not partof the PSL but closely related.NPRO,non-planar ring oscillator;EOM,electro-optic mod-ulator;FI,Faraday isolator;AOM,acousto-optic modulator.tals which are longitudinally pumped byﬁber-coupled laser diodes at808nm.The third stage is an injection-locked ring oscillator[8]with an output power of about220W, called the high-power oscillator(HPO).Four Nd:Y AG crystals are used as the active media. Each is longitudinally pumped by sevenﬁber-coupled laser diodes at808nm.The oscillator is injection-locked[12]to the previous laser stage using a feedback control loop.A broadband EOM(electro-optic modulator)placed between the NPRO and the medium-power ampliﬁer is used to generate the required phase modulation sidebands at35.5MHz.Thus the high output power and good beam quality of this last stage is combined with the good frequency stability of the previous stages.The reference system features some minor modiﬁcations compared to the engineering proto-type[8]concerning the optics:The external halo aperture was integrated into the laser system permanently improving the beam quality.Additionally,a few minor designﬂaws related to the mechanical structure and the optical layout were engineered out.This did not degrade the output performance,nor the characteristics of the locked laser.In general the PSL is designed to be operated in two different power modes.In high-power mode all three laser stages are engaged with a power of about160W at the PSL output.In low-power mode the high-power oscillator is turned off and a shutter inside the laser resonator is closed.The beam of the medium-power stage is reﬂected at the output coupler of the high power stage leaving a residual power of about13W at the PSL output.This low-power mode will be used in the early commissioning phase and in the low-frequency-optimized operation mode of Advanced LIGO and is not discussed further in this article.The stabilization has three sections(Fig.1:PMC,PD2,reference cavity):A passive resonator, the so called pre-mode-cleaner(PMC),is used toﬁlter the laser beam spatially and temporally (see subsection2.1).Two pick-off beams at the PMC are used for the active power stabilization (see subsection2.2)and the active frequency pre-stabilization,respectively(see subsection2.3).In general most stabilization feedback control loops of the PSL are implemented using analog electronics.A real-time computer system(Control and Data Acquisition Systems,CDS,[13]) which is common to many other subsystems of Advanced LIGO,is utilized to control and mon-itor important parameters of the analog electronics.The lock acquisition of various loops,a few #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10620slow digital control loops,and the data acquisition are implemented using this computer sys-tem.Many signals are recorded at different sampling rates ranging from16Hz to33kHz for diagnostics,monitoring and vetoing of gravitational wave signals.In total four real-time pro-cesses are used to control different aspects of the laser system.The Experimental Physics and Industrial Control System(EPICS)[14]and its associated user tools are used to communicate with the real-time software modules.The PSL contains a permanent,dedicated diagnostic instrument,the so called diagnostic breadboard(DBB,not shown in Fig.1)[15].This instrument is used to analyze two different beams,pick-off beams of the medium power stage and of the HPO.Two shutters are used to multiplex these to the DBB.We are able to measureﬂuctuations in power,frequency and beam pointing in an automated way with this instrument.In addition the beam quality quantiﬁed by the higher order mode content of the beam was measured using a modescan technique[16].The DBB is controlled by one real-time process of the CDS.In contrast to most of the other control loops in the PSL,all DBB control loops were implemented digitally.We used this instrument during the characterization of the laser system to measure the mentioned laser beam parameters of the HPO.In addition we temporarily placed an identical copy of the DBB downstream of the PMC to characterize the output beam of the PSL reference system.2.1.Pre-mode-cleanerA key component of the stabilization scheme is the passive ring resonator,called the pre-mode-cleaner(PMC)[17,18].It functions to suppress higher-order transverse modes,to improve the beam quality and the pointing stability of the laser beam,and toﬁlter powerﬂuctuations at radio frequencies.The beam transmitted through this resonator is the output beam of the PSL, and it is delivered to the subsequent subsystems of the gravitational wave detector.We developed and used a computer program[19]to model theﬁlter effects of the PMC as a function of various resonator parameters in order to aid its design.This led to a resonator with a bow-tie conﬁguration consisting of four low-loss mirrors glued to an aluminum spacer. The optical round-trip length is2m with a free spectral range(FSR)of150MHz.The inci-dence angle of the horizontally polarized laser beam is6◦.Theﬂat input and output coupling mirrors have a power transmission of2.4%and the two concave high reﬂectivity mirrors(3m radius of curvature)have a transmission of68ppm.The measured bandwidth was,as expected, 560kHz which corresponds to aﬁnesse of133and a power build-up factor of42.The Gaussian input/output beam had a waist radius of about568µm and the measured acquired round-trip Gouy phase was about1.7rad which is equivalent to0.27FSR.One TEM00resonance frequency of the PMC is stabilized to the laser frequency.The Pound-Drever-Hall(PDH)[20,21]sensing scheme is used to generate error signals,reusing the phase modulation sidebands at35.5MHz created between NPRO and medium power ampliﬁer for the injection locking.The signal of the photodetector PD1,placed in reﬂection of the PMC, is demodulated at35.5MHz.This photodetector consists of a1mm InGaAs photodiode and a transimpedance ampliﬁer.A piezo-electric element(PZT)between one of the curved mirrors and the spacer is used as a fast actuator to control the round-trip length and thereby the reso-nance frequencies of the PMC.With a maximum voltage of382V we were able to change the round-trip length by about2.4µm.An analog feedback control loop with a bandwidth of about 7kHz is used to stabilize the PMC resonance frequency to the laser frequency.In addition,the electronics is able to automatically bring the PMC into resonance with the laser(lock acquisition).For this process a125ms period ramp signal with an amplitude cor-responding to about one FSR is applied to the PZT of the PMC.The average power on pho-todetector PD1is monitored and as soon as the power drops below a given threshold the logic considers the PMC as resonant and closes the analog control loop.This lock acquisition proce-#161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10621dure took an average of about65ms and is automatically repeated as soon as the PMC goes off resonance.One real-time process of CDS is dedicated to control the PMC electronics.This includes parameters such as the proportional gain of the loop or lock acquisition parameters.In addition to the PZT actuator,two heating foils,delivering a maximum total heating power of14W,are attached to the aluminum spacer to control its temperature and thereby the roundtrip length on timescales longer than3s.We measured a heating and cooling1/e time constant of about2h with a range of4.5K which corresponds to about197FSR.During maintenance periods we heat the spacer with7W to reach a spacer temperature of about2.3K above room temperature in order to optimize the dynamic range of this actuator.A digital control loop uses this heater as an actuator to off-load the PZT actuator allowing compensation for slow room temperature and laser frequency drifts.The PMC is placed inside a pressure-tight tank at atmospheric pressure for acoustic shield-ing,to avoid contamination of the resonator mirrors and to minimize optical path length changes induced by atmospheric pressure variations.We used only low-outgassing materials and fabri-cated the PMC in a cleanroom in order to keep the initial mirror contamination to a minimum and to sustain a high long-term throughput.The PMCﬁlters the laser beam and improves the beam quality of the laser by suppress-ing higher order transverse modes[17].The acquired round-trip Gouy phase of the PMC was chosen in such a way that the resonance frequencies of higher order TEM modes are clearly separated from the TEM00resonance frequency.Thus these modes are not resonant and are mainly reﬂected by the PMC,whereas the TEM00mode is transmitted.However,during the design phase we underestimated the thermal effects in the PMC such that at nominal circu-lating power the round-trip Gouy-phase is close to0.25FSR and the resonance of the TEM40 mode is close to that of the TEM00mode.To characterize the mode-cleaning performance we measured the beam quality upstream and downstream of the PMC with the two independent DBBs.At150W in the transmitted beam,the circulating power in the PMC is about6.4kW and the intensity at the mirror surface can be as high as1.8×1010W m−2.At these power levels even small absorptions in the mirror coatings cause thermal effects which slightly change the mirror curvature[22].To estimate these thermal effects we analyzed the transmitted beam as a function of the circulating power using the DBB.In particular we measured the mode content of the LG10and TEM40mode.Changes of the PMC eigenmode waist size showed up as variations of the LG10mode content.A power dependence of the round-trip Gouy phase caused a variation of the power within the TEM40mode since its resonance frequency is close to a TEM00mode resonance and thus the suppression of this mode depends strongly on the Gouy phase.We adjusted the input power to the PMC such that the transmitted power ranged from100W to 150W corresponding to a circulating power between4.2kW and6.4kW.We used our PMC computer simulation to deduce the power dependence of the eigenmode waist size and the round-trip Gouy phase.The results are given in section3.1.At all circulating power levels,however,the TEM10and TEM01modes are strongly sup-pressed by the PMC and thus beam pointingﬂuctuations are reduced.Pointingﬂuctuations can be expressed toﬁrst order as powerﬂuctuations of the TEM10and TEM01modes[23,24].The PMC reduces theﬁeld amplitude of these modes and thus the pointingﬂuctuations by a factor of about61according to the measuredﬁnesse and round-trip Gouy phase.To keep beam point-ingﬂuctuations small is important since they couple to the gravitational wave channel by small differential misalignments of the interferometer optics.Thus stringent design requirements,at the10−6Hz−1/2level for relative pointing,were set.To verify the pointing suppression effect of the PMC we used DBBs to measure the beam pointingﬂuctuations upstream and downstream #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10622Fig.2.Detailed schematic of the power noise sensor setup for theﬁrst power stabilizationloop.This setup corresponds to PD2in the overview in Fig.1.λ/2,waveplate;PBS,polar-izing beam splitter;BD,glassﬁlters used as beam dump;PD,single element photodetector;QPD,quadrant photodetector.of the PMC.The resonator design has an even number of nearly normal-incidence reﬂections.Thus the resonance frequencies of horizontal and vertical polarized light are almost identical and the PMC does not act as polarizer.Therefore we use a thin-ﬁlm polarizer upstream of the PMC to reach the required purity of larger than100:1in horizontal polarization.Finally the PMC reduces technical powerﬂuctuations at radio frequencies(RF).A good power stability between9MHz and100MHz is necessary as the phase modulated light in-jected into the interferometer is used to sense several degrees of freedom of the interferometer that need to be controlled.Power noise around these phase modulation sidebands would be a noise source for the respective stabilization loop.The PMC has a bandwidth(HWHM)of about 560kHz and acts toﬁrst order as a low-passﬁlter for powerﬂuctuations with a-3dB corner frequency at this frequency.To verify that the suppression of RF powerﬂuctuations is sufﬁ-cient to fulﬁll the design requirements,we measured the relative power noise up to100MHz downstream of the PMC with a dedicated experiment involving the optical ac coupling tech-nique[25].In addition the PMC serves the very important purpose of deﬁning the spatial laser mode for the downstream subsystem,namely the input optics(IO)subsystem.The IO subsystem is responsible,among other things,to further stabilize the laser beam with the suspended input mode cleaner[26]before the beam will be injected into the interferometer.Modiﬁcations of beam alignment or beam size of the laser system,which were and might be unavoidable,e.g., due to maintenance,do not propagate downstream of the PMC toﬁrst order due to its mode-cleaning effect.Furthermore we beneﬁt from a similar isolating effect for the active power and frequency stabilization by using the beams transmitted through the curved high-reﬂectivity mirrors of the PMC.2.2.Power stabilizationThe passiveﬁltering effect of the PMC reduces powerﬂuctuations signiﬁcantly only above the PMC bandwidth.In the detection band from about10Hz to10kHz good power stability is required sinceﬂuctuations couple via the radiation pressure imbalance and the dark-fringe offset to the gravitational wave channel.Thus two cascaded active control loops,theﬁrst and second power stabilization loop,are used to reduce powerﬂuctuations which are mainly caused by the HPO stage.Theﬁrst loop uses a low-noise photodetector(PD2,see Figs.1and2)at one pick-off port #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10623of the PMC to measure the powerﬂuctuations downstream of the PMC.An analog electronics feedback control loop and an AOM(acousto-optic modulator)as actuator,located upstream of the PMC,are used to stabilize the power.Scattered light turned out to be a critical noise source for thisﬁrst loop.Thus we placed all required optical and opto-electronic components into a box to shield from scattered light(see Fig.2).The beam transmitted by the curved PMC mirror has a power of about360mW.This beam isﬁrst attenuated in the box using aλ/2waveplate and a thin-ﬁlm polarizer,such that we are able to adjust the power on the photodetectors to the optimal operation point.Afterwards the beam is split by a50:50beam splitter.The beams are directed to two identical photode-tectors,one for the control loop(PD2a,in-loop detector)and one for independent out-of-loop measurements to verify the achieved power stability(PD2b,out-of-loop detector).These pho-todetectors consist of a2mm InGaAs photodiode(PerkinElmer C30642GH),a transimpedance ampliﬁer and an integrated signal-conditioningﬁlter.At the chosen operation point a power of about4mW illuminates each photodetector generating a photocurrent of about3mA.Thus the shot noise is at a relative power noise of10−8Hz−1/2.The signal conditioningﬁlter has a gain of0.2at very low frequencies(<70mHz)and ampliﬁes the photodetector signal in the im-portant frequency range between3.3Hz and120Hz by about52dB.This signal conditioning ﬁlter reduces the electronics noise requirements on all subsequent stages,but has the drawback that the range between3.3Hz and120Hz is limited to maximum peak-to-peak relative power ﬂuctuations of5×10−3.Thus the signal-conditioned channel is in its designed operation range only when the power stabilization loop is closed and therefore it is not possible to measure the free running power noise using this channel due to saturation.The uncoated glass windows of the photodiodes were removed and the laser beam hits the photodiodes at an incidence angle of45◦.The residual reﬂection from the photodiode surface is dumped into a glassﬁlter(Schott BG39)at the Brewster angle.Beam positionﬂuctuations in combination with spatial inhomogeneities in the photodiode responsivity is another noise source for the power stabilization.We placed a silicon quadrant photodetector(QPD)in the box to measure the beam positionﬂuctuations of a low-power beam picked off the main beam in the box.The beam parameters,in particular the Gouy phase,at the QPD are the same as on the power sensing detectors.Thus the beam positionﬂuctuations measured with the QPD are the same as the ones on the power sensing photodetectors,assuming that the positionﬂuctuations are caused upstream of the QPD pick-off point.We used the QPD to measure beam positionﬂuctuations only for diagnostic and noise projection purposes.In a slightly modiﬁed experiment,we replaced one turning mirror in the path to the power sta-bilization box by a mirror attached to a tip/tilt PZT element.We measured the typical coupling between beam positionﬂuctuations generated by the PZT and the residual relative photocurrent ﬂuctuations measured with the out-of-the-loop photodetector.This coupling was between1m−1 and10m−1which is a typical value observed in different power stabilization experiments as well.We measured this coupling factor to be able to calculate the noise contribution in the out-of-the-loop photodetector signal due to beam positionﬂuctuations(see Subsection3.3).Since this tip/tilt actuator was only temporarily in the setup,we are not able to measure the coupling on a regular basis.Both power sensing photodetectors are connected to analog feedback control electronics.A low-pass(100mHz corner frequency)ﬁltered reference value is subtracted from one signal which is subsequently passed through several control loopﬁlter stages.With power stabilization activated,we are able to control the power on the photodetectors and thereby the PSL output power via the reference level on time scales longer than10s.The reference level and other important parameters of these electronics are controlled by one dedicated real-time process of the CDS.The actuation or control signal of the electronics is passed to an AOM driver #161737 - $15.00 USD Received 18 Jan 2012; revised 27 Feb 2012; accepted 4 Mar 2012; published 24 Apr 2012 (C) 2012 OSA7 May 2012 / Vol. 20, No. 10 / OPTICS EXPRESS 10624。

溴到硼酸酯

Journal of
Materials Chemistry C
Published on 20 November 2014. Downloaded on 08/12/2016 07:54:22.
PAPER
View Article Online
View Journal | View Issue
Cite this: J. Mater. Chem. C, 2015, 3, 861
However, these oligouorene functionalized oligomers may suﬀer from the unwanted long wavelength emission under long-term device operation, similar to polyuorene-based macromolecules.34–36
Received 26th September 2014 Accepted 17th November 2014 DOI: 10.1039/c4tc02173h /MaterialsC
Starburst 4,40,400-tris(carbazol-9-yl)triphenylamine-based deep-blue ﬂuorescent emitters with tunable oligophenyl length for solution-processed undoped organic lightemitting diodes†
Introduction
Since 1987, organic light-emitting diodes (OLEDs) have attracted tremendous attention due to their potential applications in at-panel displays and solid-state lightings.1–10 To achieve fullcolor displays, three primary RGB luminescent materials with excellent stability, eﬃciency and color purity are required. With respect to green and red counterparts, it seems to be a big challenge to develop blue emitters, especially deep-blue ones that have a Commission Internationale de l'Eclairage (CIE) y coordinate value of <0.10, because the intrinsic wide bandgap would inevitably result in ineﬃcient charge injection to an emitting layer (EML).11 Therefore, great eﬀorts should be paid to the design of deep-blue emitters to push forward the commercialization of full-color OLEDs.

[Fluent] Solver error原因及处理方法综整

5。网格划分有问题，两个三维流域交于一条线；或者二维流域交于一点；（有这个问题的，如果选用湍流模型，计算必然发散）2 L9 b9 O& n" I. u* { 6。CFD 软件和分网格软件单位不匹配，导致物理模型失真。－－－－－－－－by barggier#
q6 e9 E9 }9 S* t" r
7. 一个修改方法是：使用 fluent 的 case check，根据 fluent 的推荐修改 solver 和边界设置，有些情况可以避免粘性比大于 100000 的问题。-------------------------by mycc
( t5 A$ ~ O: A8 Q% \8 x$ P
原因: license 过期方法: 更新 license。
Fluent: 时机:在水流过毛细管的仿针的基础之上，加入了表面张力，再求解就总出现这个错误 Updating solution at time level N... Error: Too many (5895) VOF sub-timesteps. The velocity) ]9 p4 T' i8 } ^ field is probably diverging. Please check the solution," S# ], L% G/ k2 Q, J7 y @- q and reduce the time-step if necessary. Error Object: () 原因: 流体流动的特征时间小一个数量级才行$ ?1 ]' n9 i) J, V5 E1 M 方法: 应该可以先设置小的时间步迭代,之后再逐渐增加时间步长 ---------by wzg235
( Fluent:) 時機
1 在用 fluent 计算一个 3D 的动网格的列子的时候, 每一个时间步 lterate 之后都会出现这样的提示，而且不能继续 lterate

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

arXiv:astro-ph/9404019v1 8 Apr 1994A&Amanuscriptno.(willbeinsertedbyhandlater)

1.IntroductionThescatteringbyelectronsoflow-energyphotons(hν≪mec2)isimportantinastrophysicalsituationsonlyundertheratherspecialcircumstancethattheelectron-scatteringopacityisnottoomuchsmallerthanthatfromallothersources.Thomsonscatteringinthesecaseshastraditionallybeenregardedasco-herentinfrequency,andmuchworkonspectrumformationhasbeenbasedonthisassumption.However,ifthespectrumoftheobjectinquestionscontainsfeatureswithawidthlessthanorcomparabletotheelectronDopplerwidth,suchasstronglinesandcontinuumedges,thescatteringmayhavetobetreatedasnoncoherent,i.e.thechangeinthefrequencyofthescat-teredphotonbytheelectronDopplereﬀectmustbetakenintoaccount(M¨unch1948,Hummer&Mihalas1967,Auer&Miha-las1968a,1968b).Althoughthedescriptionofthisredistribu-tionprocessasaconvolutionofthemeanintensityJ(ν)witharedistributionfunctionissimpleinprinciple,itsinclusion

innumericalcalculationsleadstoconsiderablediﬃcultiesinpracticeforthreereasons.1)ThescaleoftheredistributioninfrequencyismuchlargerthantheatomicDopplerlinewidths;2)theevaluationoftheconvolutionateachfrequencyinvolvesanintegrationoverawidebandofsurroundingfrequencies;3)thiscouplingoffrequenciesconﬂictswiththebasicstrategyofapproximatelambdaiteration(ALI)methodswhichinvolveafrequency-by-frequencyevaluationoftheapproximatelambdaoperator.Thetransferequationfortwolevelsystemsaccountingfornoncoherentelectronscatteringhavebeensolvedinvariousapproximationbyanumberofworkers.Earlyworkonthisproblemwasbasedontheformulationintermsofa“reversinglayer”byChandrasekar(1948),whofoundasolutionforthecaseinwhichthereddeningofscatteredphotonsarisingfromtheComptoneﬀectwasincluded.SubsequentlyM¨unch(1948)consideredtheeﬀectsofelectronDopplerredistribution,againintermsofa“reversing-layer”model,bymeansofaFouriertransforminfrequency.Thisandotherearlyworkissumma-rizedinChapter12ofChandrasekhar(1960).Numericalsolu-tionshavebeengivenforlinesintheatmospheresofO-typestarsbyAuerandMihalas(1968a,1968b),whoassumedcom-pleteredistributionfortheatomicscattering.Rangarajanetal(1991)givesolutionsforparameterizedmodelswithbothbothpartialandcompleteredistributionintheline.Hillier(1991)andHamannetal.(1992)haveincludednon-coherentelectronscattering(NES)incomputingtheemergentlinespectraofrealisticmodelsofWolf-Rayetstars,forwhichtheeﬀectsareclearlyobservable.However,intheseworksNESisincludedonlyduringtheformalsolutionfortheemergentspectra,afterthelevelpopulationshavebeenﬁxedfromanNLTEsolutioninwhichNEShasnotbeentakenintoaccount.Inthispaperwedevelopanumericalmethodfortheso-lutiontoradiativetransferproblemsinwhichnoncoherentelectronscatteringcanplayanimportantrole.Themethodisbasedonapproximatingtheelectronscatteringredistribu-tionfunctionbyasumofexponentials.Itisshownthatonlytwoexponentialtermsgiveaveryaccurateapproximation.Theelectronscatteringemissivityasafunctionoffrequencyateachpointintheatmospherethencanbeexpressedthroughtheso-lutiontotwosimplediﬀerentialequationsinfrequencyspace.2Thecorrespondingdiﬀerenceequationscanbesolvednumeri-callybyGaussianelimination.Thisprocedureiseasilyincludedinanyiterativesolutionofthecombinedradiativetransferandstatisticalequilibriumequations.InpreviousschemesforevaluatingtheNESemissivity,thecomputingtimeforeachdepthintheatmospherescalesasNFNW,whereNFisthenumberoffrequencygridpoints,andNWisthenumberoffrequencygridpointsneededtorepresentadequatelythewidthoftheelectronredistributionfunction.ForapplicationstospectrallineswithstructureonscalesofbothatomicandelectronDopplerwidths,NWcanbeoforderof10–50orlarger.ThepresentmethodscalesmorefavorablyasCNF,whereCisasmallconstant,independentofthefre-quencygrid.Italsoautomaticallyenforcesexactconservationofphotonnumber.InthispaperwedescribeanimplementationofourmethodoftreatingnoncoherentelectronscatteringforthemultilevelALIcodeMALI(Rybicki&Hummer,1991,1992;hereafterRHI,RHII).Incontrasttopreviousmethods(Hillier1991,Hamannetal.1992),fullaccountistakenoftheeﬀectofNESonthelevelpopulations,aswellasontheemergentspectrum.AlthoughtheparticularapplicationdescribedhereistoMALI,themethodpresentedhereisquitegeneralandshouldbeeasilyadaptabletoothercodesaswell,especiallyALIcodes.ItshouldbemadeclearthatinthislatestgeneralizationofMALInoncoherentelectronscatteringistreatednotfullybyALI,butonlybymeansofordinarylambdaiteration.Thiswasnotbychoice,butresultedfromafailuretoﬁndsuit-ableapproximateelectronscatteringoperatorstouseinanALImethod.Inparticular,wetriedseveralapproximateop-eratorsbasedoncoherentscattering,whichisalreadysolvednon-iterativelyinMALI.Allofourchoiceswereeitherunstableorhadverypoorconvergenceproperties.Fortunately,formanycasesofinterest,themeannumberofphotonsscatteringsduetoelectronscatteringisverymoderate,oforderafewtens.SincethetypicalnumberofiterationsinanALIsolutioncanbeofordermanytenstoahundred,thetreat-mentofNESbyordinarylambdaiterationinthesecaseswillnotsubstantiallychangethenetnumberofiterationsrequiredforasolution.Oneshouldalsonotethatnumericalaccelera-tors,suchasNg’s(1974)method,usedinMALI,acttoimprovetheconvergenceofordinarylambdaiteration,aswellasALI.However,forproblemswithmeannumbersofscatteringsoforderofahundredormore,thepresentmethodissimplynotsuitable,andothermethodswillhavetobedeveloped.InSect.2wepresentthebasicdescriptionoftheelectronredistributionproblem.InSect.3wedeveloptheapproximateexponentialﬁttotheelectronscatteringredistributionfunc-tionandshowhowtheemissivitycanbefoundbysolvingtwodiﬀerentialequations.Wethengiveresultsillustratingtheac-curacyofourapproximationandthebasicfeaturesoftwo-leveltransferproblemsincludingelectronscatteringtreatedasco-herentandincoherentprocesses.Sect.4describestheincor-porationofourmethodintoMALIandgivesresultsforahotO-staratmosphereincludingnoncoherentelectronscattering.Asexpected,theeﬀectsonindividuallineswerequitenotice-able,asweretheeﬀectswithinafewelectronDopplerwidthsofcontinua.However,wealsofoundanunexpectedandpo-tentiallyimportanteﬀectforcertaincontinua,which,intheabsenceofnoncoherentscattering,arestronglyinabsorption.Thenscatteringofradiationfromthestrongercontinuumbe-lowtheedgeintotheothercancauseasubstantialanomalous