五孔动力探针文献翻译

合集下载

五孔探针测量原理

五孔探针测量原理引言：五孔探针是一种广泛应用于流体力学中的测量工具，常用于测量流体的速度、压力和温度等参数。

它通过测量流体中不同位置处的静压和总压差异来计算出流体的速度和压力。

本文将详细介绍五孔探针测量原理。

一、五孔探针的组成：五孔探针由五个小孔组成，分别为中心孔和四个对称分布的边缘孔。

中心孔通常用于测量总压，而边缘孔则用于测量静压。

二、测量原理：五孔探针的测量原理基于流体的流动动力学基本方程，包括连续性方程、动量方程和能量方程。

1.连续性方程：连续性方程描述了流体在稳态条件下流动的特性。

根据连续性方程，流体在相同截面积上的质量流量相等。

通过测量中心孔和边缘孔处的流体速度，可以计算出质量流量。

2.动量方程：动量方程描述了流体在外力作用下运动的特性。

根据动量方程，流体在流动过程中会受到静压、动压和惯性力等力的作用。

通过测量不同位置处的静压差异，可以计算出流体的速度和压力。

3.能量方程：能量方程描述了流体在流动过程中能量守恒的特性。

根据能量方程，流体在流动过程中会发生动能和静能的转化。

通过测量中心孔和边缘孔处的总压差异，可以计算出流体的速度和压力。

三、五孔探针的使用：五孔探针通常通过流场中的定点测量来获取流体的动态参数。

在实际使用中，先通过中心孔测量总压，并通过边缘孔测量静压。

然后利用测得的总压和静压数据，使用测量原理中的公式计算出流体的速度和压力。

四、五孔探针的应用：五孔探针广泛应用于飞行器气动力学、流体力学实验研究、空气动力学优化设计等领域。

它能够提供精确的流场数据，为相关领域的研究和分析提供重要依据。

结论：五孔探针通过测量流体中不同位置处的静压和总压差异来计算出流体的速度和压力。

它采用连续性方程、动量方程和能量方程等流体力学基本方程，通过测量中心孔和边缘孔的参数来计算流体的动态参数。

五孔探针在飞行器气动力学、流体力学实验研究和空气动力学优化设计等领域得到广泛应用，并具有重要的实际价值。

常用仪器仪表中英文对照

常用仪器仪表中英文对照光线示波器 light beam oscillograph光学高温计 optical pyrometer光学显微镜 optical microscope光谱仪器 optical spectrum instrument吊车秤 crane weigher地中衡 platform weigher字符图形显示器 character and graphic display位移测量仪表 displacement measuring instrument巡检测装置 data logger波纹管 bellowsX射线衍射仪 X-ray diffractometerX射线荧光光谱仪 X-ray fluorescence spectrometer力测量仪表 force measuring instrument孔板 orifice plate文丘里管 venturi tube水表 water meter加速度仪 accelerometer可编程序控制器 programmable controller平衡机 balancing machine皮托管 Pitot tube皮带秤 belt weigher长度测量工具 dimensional measuring instrument长度传感器 linear transducer厚度计 thickness gauge差热分析仪 differential thermal analyzer扇形磁场质谱计 sector magnetic field mass spectrometer 料斗秤 hopper weigher核磁共振波谱仪 nuclear magnetic resonance spectrometer 气相色谱仪 gas chromatograph浮球调节阀 float adjusting valve真空计 vacuum gauge动圈仪表 moving-coil instrument基地式调节仪表 local-mounted controller密度计 densitometer液位计 liquid level meter组装式仪表 package system热流计 heat-flow meter热量计 heat flux meter热电阻 resistance temperature热电偶 thermocouple膜片和膜盒 diaphragm and diaphragm capsule调节阀 regulating valve噪声计 noise meter应变仪 strain measuring instrument湿度计 hygrometer声级计 sound lever meter黏度计 viscosimeter转矩测量仪表 torque measuring instrument转速测量仪表 tachometer露点仪 dew-point meter变送器 transmitter减压阀 pressure reducing valve测功器 dynamometer紫外和可见光分光光度计 ultraviolet-visible spectrometer 顺序控制器 sequence controller微处理器 microprocessor温度调节仪表 temperature controller煤气表 gas meter节流阀 throttle valve电子自动平衡仪表 electronic self-balance instrument电子秤 electronic weigher电子微探针 electron microprobe电子显微镜 electron microscope弹簧管 bourdon tube数字式显示仪表 digital display instrument光线示波器 light beam oscillograph光学高温计 optical pyrometer光学显微镜 optical microscope光谱仪器 optical spectrum instrument吊车秤 crane weigher地中衡 platform weigher字符图形显示器 character and graphic display位移测量仪表 displacement measuring instrument巡检测装置 data logger波纹管 bellowsX射线衍射仪 X-ray diffractometerX射线荧光光谱仪 X-ray fluorescence spectrometer 力测量仪表 force measuring instrument孔板 orifice plate文丘里管 venturi tube水表 water meter加速度仪 accelerometer可编程序控制器 programmable controller平衡机 balancing machine皮托管 Pitot tube皮带秤 belt weigher长度测量工具 dimensional measuring instrument长度传感器 linear transducer厚度计 thickness gauge差热分析仪 differential thermal analyzer扇形磁场质谱计 sector magnetic field mass spectrometer 料斗秤 hopper weigher核磁共振波谱仪 nuclear magnetic resonance spectrometer 气相色谱仪 gas chromatograph浮球调节阀 float adjusting valve真空计 vacuum gauge动圈仪表 moving-coil instrument基地式调节仪表 local-mounted controller密度计 densitometer液位计 liquid level meter组装式仪表 package system热流计 heat-flow meter热量计 heat flux meter热电阻 resistance temperature热电偶 thermocouple膜片和膜盒 diaphragm and diaphragm capsule调节阀 regulating valve噪声计 noise meter应变仪 strain measuring instrument湿度计 hygrometer声级计 sound lever meter黏度计 viscosimeter转矩测量仪表 torque measuring instrument转速测量仪表 tachometer露点仪 dew-point meter变送器 transmitter减压阀 pressure reducing valve测功器 dynamometer紫外和可见光分光光度计 ultraviolet-visible spectrometer 顺序控制器 sequence controller微处理器 microprocessor温度调节仪表 temperature controller煤气表 gas meter节流阀 throttle valve电子自动平衡仪表 electronic self-balance instrument电子秤 electronic weigher电子微探针 electron microprobe电子显微镜 electron microscope弹簧管 bourdon tube数字式显示仪表 digital display instrument。

Shrinkwrapping and the taming of hyperbolic 3-manifolds

a rX iv:mat h /47161v3[mat h.GT]22O ct25SHRINKWRAPPING AND THE TAMING OF HYPERBOLIC 3–MANIFOLDS DANNY CALEGARI AND DAVID GABAI 0.I NTRODUCTION During the period 1960–1980,Ahlfors,Bers,Kra,Marden,Maskit,Sullivan,Thurston and many others developed the theory of geometrically ﬁnite ends of hy-perbolic 3–manifolds.It remained to understand those ends which are not geo-metrically ﬁnite;such ends are called geometrically inﬁnite .Around 1978William Thurston gave a conjectural description of geometrically inﬁnite ends of complete hyperbolic 3–manifolds.An example of a geometrically inﬁnite end is given by an inﬁnite cyclic covering space of a closed hyperbolic 3-manifold which ﬁbers over the circle.Such an end has cross sections of uniformly bounded area.By contrast,the area of sections of geometrically ﬁnite ends grow exponentially in the distance from the convex core.For the sake of clarity we will assume throughout this introduction that N =H 3/Γwhere Γis parabolic free.Precise statements of the parabolic case will be given in §7.Thurston’s idea was formalized by Bonahon [Bo]and Canary [Ca]with the fol-lowing.Deﬁnition 0.1.An end E of a hyperbolic 3-manifold N is simply degenerate if it has a closed neighborhood of the form S ×[0,∞)where S is a closed surface,and there exists a sequence {S i }of CAT (−1)surfaces exiting E which are homotopic to S ×0in E .This means that there exists a sequence of maps f i :S →N such that the induced path metrics induce CAT (−1)structures on the S i ’s,f (S i )⊂S ×[i,∞)and f is homotopic to a homeomorphism onto S ×0via a homotopy supported in S ×[0,∞).Here by CAT (−1),we mean as usual a geodesic metric space for which geo-desic triangles are “thinner”than comparison triangles in hyperbolic space.If themetrics pulled back by the f i are smooth,this is equivalent to the condition that the Riemannian curvature is bounded above by −1.See [BH]for a reference.Note that by Gauss–Bonnet,the area of a CAT (−1)surface can be estimated from its Euler characteristic;it follows that a simply degenerate end has cross sections of uniformly bounded area,just like the end of a cyclic cover of a manifold ﬁbering over the circle.Francis Bonahon [Bo]observed that geometrically inﬁnite ends are exactly those ends possessing an exiting sequence of closed geodesics.This will be our working deﬁnition of such ends throughout this paper.2DANNY CALEGARI AND DAVID GABAIThe following is our main result.Theorem0.2.An end E of a complete hyperbolic3-manifold N withﬁnitely generated fundamental group is simply degenerate if there exists a sequence of closed geodesics exit-ing E.Consequently we have,Theorem0.3.Let N be a complete hyperbolic3-manifold withﬁnitely generated funda-mental group.Then every end of N is geometrically tame,i.e.it is either geometrically ﬁnite or simply degenerate.In1974Marden[Ma]showed that a geometricallyﬁnite hyperbolic3-manifold is topologically tame,i.e.is the interior of a compact3-manifold.He asked whether all complete hyperbolic3-manifolds withﬁnitely generated fundamental group are topologically tame.This question is now known as the Tame Ends Conjecture or Marden Conjecture.Theorem0.4.If N is a complete hyperbolic3-manifold withﬁnitely generated funda-mental group,then N is topologically tame.Ian Agol[Ag]has independently proven Theorem0.4.There have been many important steps towards Theorem0.2.The seminal re-sult was obtained by Thurston([T],Theorem9.2)who proved Theorems0.3and 0.4for certain algebraic limits of quasi Fuchsian groups.Bonahon[Bo]estab-lished Theorems0.2and0.4whenπ1(N)is freely indecomposible and Canary [Ca]proved that topological tameness implies geometrical tameness.Results in the direction of0.4were also obtained by Canary-Minsky[CaM],Kleineidam–Souto[KS],Evans[Ev],Brock–Bromberg–Evans–Souto[BBES],Ohshika,Brock–Souto[BS]and Souto[So].Thurstonﬁrst discovered how to obtain analytic conclusions from the existence of exiting sequences of CAT(−1)surfaces.Thurston’s work as generalized by Bonahon[Bo]and Canary[Ca]combined with Theorem0.2yields a positive proof of the Ahlfors’Measure Conjecture[A2].Theorem0.5.IfΓis aﬁnitely generated Kleinian group,then the limit set LΓis either S2∞or has Lebesgue measure zero.If LΓ=S2∞,thenΓacts ergodically on S2∞.Theorem0.5is one of the many analytical consequences of our main result. Indeed Theorem0.2implies that a complete hyperbolic3-manifold N withﬁnitely generated fundamental group is analytically tame as deﬁned by Canary[Ca].It follows from Canary that the various results of§9[Ca]hold for N.Our main result is the last step needed to prove the following monumental result,the other parts being established by Alhfors,Bers,Kra,Marden,Maskit, Mostow,Prasad,Sullivan,Thurston,Minsky,Masur–Minsky,Brock–Canary–Minsky, Ohshika,Kleineidam–Souto,Lecuire,Kim–Lecuire–Ohshika,Hossein–Souto and Rees.See[Mi]and[BCM].Theorem0.6(Classiﬁcation Theorem).If N is a complete hyperbolic3-manifold with ﬁnitely generated fundamental group,then N is determined up to isometry by its topolog-ical type,the conformal boundary of its geometricallyﬁnite ends and the ending lamina-tions of its geometrically inﬁnite ends.SHRINKWRAPPING AND THE TAMING OF HYPERBOLIC3–MANIFOLDS3 The following result was conjectured by Bers,Sullivan and Thurston.Theorem0.4is one of many results,many of them recent,needed to build a proof.Major contributions were made by Alhfors,Bers,Kra,Marden,Maskit,Mostow,Prasad, Sullivan,Thurston,Minsky,Masur–Minsky,Brock–Canary–Minsky,Ohshika,Kleineidam–Souto,Lecuire,Kim–Lecuire–Ohshika,Hossein–Souto,Rees,Bromberg and Brock–Bromberg.Theorem0.7(Density Theorem).If N=H3/Γis a completeﬁnitely generated3-manifold withﬁnitely generated fundamental group,thenΓis the algebraic limit of geo-metricallyﬁnite Kleinian groups.The main technical innovation of this paper is a new technique called shrinkwrap-ping for producing CAT(−1)surfaces in hyperbolic3-manifolds.Historically,such surfaces have been immensely important in the study of hyperbolic3-manifolds,e.g.see[T],[Bo],[Ca]and[CaM].Given a locallyﬁnite set∆of pairwise disjoint simple closed curves in the3-manifold N,we say that the embedded surface S⊂N is2-incompressible rel.∆ifevery compressing disc for S meets∆at least twice.Here is a sample theorem. Theorem0.8(Existence of shrinkwrapped surface).Let M be a complete,orientable, parabolic free hyperbolic3–manifold,and letΓbe aﬁnite collection of pairwise disjoint sim-ple closed geodesics in M.Further,let S⊂M\Γbe a closed embedded2–incompressible surface rel.Γwhich is either nonseparating in M or separates some component ofΓfrom another.Then S is homotopic to a CAT(−1)surface T via a homotopyF:S×[0,1]→Msuch that(1)F(S×0)=S(2)F(S×t)=S t is an embedding disjoint fromΓfor0≤t<1(3)F(S×1)=T(4)If T′is any other surface with these properties,then area(T)≤area(T′)We say that T is obtained from S by shrinkwrapping rel.Γ,or ifΓis understood,T is obtained from S by shrinkwrapping.In fact,we prove the stronger result that T isΓ–minimal(to be deﬁned in§1)which implies in particular that it is intrinsically CAT(−1)Here is the main technical result of this paper.Theorem0.9.Let E be an end of the complete orientable hyperbolic3-manifold N withﬁnitely generated fundamental group.Let C be a3-dimensional compact core of N,∂E Cthe component of∂C facing E and g=genus(∂E C).If there exists a sequence of closed geodesics exiting E,then there exists a sequence{S i}of CAT(−1)surfaces of genus g exit-ing E such that each{S i}is homologically separating in E.That is,each S i homologically separates∂E C from E.Theorem0.4can now be deduced from Theorem0.9and Souto[So];however,we prove that Theorem0.9implies Theorem0.4using only3-manifold topologyand elementary hyperbolic geometry.The proof of Theorem0.9blends elementary aspects of minimal surface theory, hyperbolic geometry,and3-manifold topology.The method will be demonstrated4DANNY CALEGARI AND DAVID GABAIin§4where we give a proof of Canary’s theorem.Theﬁrst time reader is urged to begin with that section.This paper is organized as follows.In§1and§2we establish the shrinkwrap-ping technique forﬁnding CAT(−1)surfaces in hyperbolic3-manifolds.In§3we prove the existence ofǫ-separated simple geodesics exiting the end of parabolic free manifolds.In§4we prove Canary’s theorem.This proof will model the proof of the general case.The general strategy will be outlined at the end of that section. In§5we develop the topological theory of end reductions in3-manifolds.In§6we give the proofs of our main results.In§7we give the necessary embellishments of our methods to state and prove our results in the case of manifolds with parabolic cusps.Notation0.10.If X⊂Y,then N(X)denotes a regular neighborhood of X in Y and int(X)denotes the interior of X.If X is a topological space,then|X|denotes the number of components of X.If A,B are topological subspaces of a third space, then A\B denotes the intersection of A with the complement of B. Acknowledgements0.11.Theﬁrst author is grateful to Nick Makarov for some useful analytic discussions.The second author is grateful to Michael Freedman for many long conversations in Fall1996which introduced him to the Tame Ends con-jecture.He thanks Francis Bonahon,Yair Minsky and Jeff Brock for their interest and helpful comments.Part of this research was carried out while he was visiting Nara Women’s University,the Technion and the Institute for Advanced Study.He thanks them for their hospitality.We thank the referees for their many thoughtful suggestions and comments.1.S HRINKWRAPPINGIn this section,we introduce a new technical tool forﬁnding CAT(−1)surfaces in hyperbolic3–manifolds,called shrinkwrapping.Roughly speaking,given a col-lection of simple closed geodesicsΓin a hyperbolic3–manifold M and an embed-ded surface S⊂M\Γ,a surface T⊂M is obtained from S by shrinkwrapping S rel.Γif it homotopic to S,can be approximated by an isotopy from S supported in M\Γ,and is least area subject to these constraints.Given mild topological conditions on M,Γ,S(namely2–incompressibility,to be deﬁned below)the shrinkwrapped surface exists,and is CAT(−1)with respect to the path metric induced by the Riemannian metric on M.We use some basic analytical tools throughout this section,including the Gauss–Bonnet formula,the coarea formula,and the Arzela–Ascoli theorem.At a number of points we must invoke results from the literature to establish existence of min-imal surfaces([MSY]),existence of limits with area and curvature control([CiSc]), and regularity of the shrinkwrapped surfaces alongΓ([Ri],[Fre]).General refer-ences are[CM],[Js][Fed]and[B].1.1.Geometry of surfaces.For convenience,we state some elementary but fun-damental lemmas concerning curvature of(smooth)surfaces in Riemannian3-manifolds.We use the following standard terms to refer to different kinds of minimal sur-faces:Deﬁnition1.1.A smooth surfaceΣin a Riemannian3-manifold is minimal if it is a critical point for area with respect to all smooth compactly supported variations.SHRINKWRAPPING AND THE TAMING OF HYPERBOLIC3–MANIFOLDS5 It is locally least area(also called stable)if it is a local minimum for area with respect to all smooth,compactly supported variations.A closed,embedded surface is globally least area if it is an absolute minimum for area amongst all smooth surfaces in its isotopy class.Note that we do not require that our minimal or locally least area surfaces are complete.Any subsurface of a globally least area surface is locally least area,and a locally least area surface is minimal.A smooth surface is minimal iff its mean curvature vectorﬁeld vanishes identically.For more details,consult[CM],especially chapter 5.The intrinsic curvature of a minimal surface is controlled by the geometry of the ambient manifold.The following lemma is formula5.6on page100of[CM]. Lemma1.2(Monotonicity of curvature).LetΣbe a minimal surface in a Riemannian manifold M.Let KΣdenote the curvature ofΣ,and K M the sectional curvature of M. Then restricted to the tangent space TΣ,1KΣ=K M−6DANNY CALEGARI AND DAVID GABAIfor smallǫ,whereφ(·,0)=Id|∂Σ,andφ(∂Σ,t)for small t is the boundary inΣof the tubular t neighborhood of∂Σ.Then∂Σκdl=−da1a3in the complete simply–connected Riemannian2–manifold of con-stant sectional curvatureκ,where the edges a i a j and a j satisfylength(a i a j)=length(a j)Given a point x∈a1a2on one of the edges of a1a2a3,there is a corresponding point a1a1xa toSHRINKWRAPPING AND THE TAMING OF HYPERBOLIC3–MANIFOLDS7 Deﬁnition1.8(Γ–minimal surfaces).Letκ∈R be given.Let M be a complete Riemannian3–manifold with sectional curvature bounded above byκ,and letΓbe an embedded collection of simple closed geodesics in M.An immersionψ:S→MisΓ–minimal if it is smooth with mean curvature0in M\Γ,and is metrically CAT(κ)with respect to the path metric induced byψfrom the Riemannian metric on M.Notice by Lemma1.2that a smooth surface S with mean curvature0in M is CAT(κ),so a minimal surface(in the usual sense)is an example of aΓ–minimal surface.1.3.Statement of shrinkwrapping theorem.Deﬁnition1.9(2–incompressibility).An embedded surface S in a3–manifold M disjoint from a collectionΓof simple closed curves is said to be2–incompressible rel.Γif any essential compressing disk for S must intersectΓin at least two points.If Γis understood,we say S is2–incompressible.Theorem1.10(Existence of shrinkwrapped surface).Let M be a complete,orientable, parabolic free hyperbolic3–manifold,and letΓbe aﬁnite collection of pairwise disjoint sim-ple closed geodesics in M.Further,let S⊂M\Γbe a closed embedded2–incompressible surface rel.Γwhich is either nonseparating in M or separates some component ofΓfrom another.Then S is homotopic to aΓ–minimal surface T via a homotopyF:S×[0,1]→Msuch that(1)F(S×0)=S(2)F(S×t)=S t is an embedding disjoint fromΓfor0≤t<1(3)F(S×1)=T(4)If T′is any other surface with these properties,then area(T)≤area(T′)We say that T is obtained from S by shrinkwrapping rel.Γ,or ifΓis understood,T is obtained from S by shrinkwrapping.The remainder of this section will be taken up with the proof of Theorem1.10. Remark1.11.In fact,for our applications,the property we want to use of our surface T is that we can estimate its diameter(rel.the thin part of M)from its Euler characteristic.This follows from a Gauss–Bonnet estimate and the bounded diameter lemma(Lemma1.15,to be proved below).In fact,our argument will show directly that the surface T satisﬁes Gauss–Bonnet;the fact that it is CAT(−1) is logically superﬂuous for the purposes of this paper.1.4.Deforming metrics along geodesics.Deﬁnition1.12(δ–separation).LetΓbe a collection of disjoint simple geodesics in a Riemannian manifold M.The collectionΓisδ–separated if any pathα:I→M with endpoints onΓand satisfyinglength(α(I))≤δ8DANNY CALEGARI AND DAVID GABAIis homotopic rel.endpoints intoΓ.The supremum of suchδis called the separation constant ofΓ.The collectionΓis weaklyδ–separated ifdist(γ,γ′)>δwheneverγ,γ′are distinct components ofΓ.The supremum of suchδis called the weak separation constant ofΓ.Deﬁnition1.13(Neighborhood and tube neighborhood).Let r>0be given.For a point x∈M,we let N r(x)denote the closed ball of radius r about x,and let N<r(x),∂N r(x)denote respectively the interior and the boundary of N r(x).For a closed geodesicγin M,we let N r(γ)denote the closed tube of radius r aboutγ, and let N<r(γ),∂N r(γ)denote respectively the interior and the boundary of N r(γ). IfΓdenotes a union of geodesicsγi,then we use the shorthand notationN r(Γ)= γi N r(γi)Remark1.14.Topologically,∂N r(x)is a sphere and∂N r(γ)is a torus,for sufﬁ-ciently small r.Similarly,N r(x)is a closed ball,and N r(γ)is a closed solid torus. IfΓisδ–separated,then Nδ/2(Γ)is a union of solid tori.Lemma1.15(Bounded Diameter Lemma).Let M be a complete hyperbolic3–manifold. LetΓbe a disjoint collection ofδ–separated embedded geodesics.Letǫ>0be a Margulis constant for dimension3,and let M≤ǫdenote the subset of M where the injectivity radius is at mostǫ.If S⊂M\Γis a2–incompressibleΓ–minimal surface,then there is a con-stant C=C(χ(S),ǫ,δ)∈R and n=n(χ(S),ǫ,δ)∈Z such that for each component S i of S∩(M\M≤ǫ),we havediam(S i)≤CFurthermore,S can only intersect at most n components of M≤ǫ.Proof.Since S is2–incompressible,any point x∈S either lies in M≤ǫ,or is the center of an embedded m–disk in S,wherem=min(ǫ/2,δ/2)Since S is CAT(−1),Gauss–Bonnet implies that the area of an embedded m–disk in S has area at least2π(cosh(m)−1)>πm2.This implies that if x∈S∩M\M≤ǫthenarea(S∩N m(x))≥πm2The proof now follows by a standard covering argument.A surface S satisfying the conclusion of the Bounded Diameter Lemma is some-times said to have diameter bounded by C modulo M≤ǫ.Remark1.16.Note that ifǫis a Margulis constant,then M≤ǫconsists of Margulis tubes and cusps.Note that the same argument shows that,away from the thin part of M and anǫneighborhood ofΓ,the diameter of S can be bounded by a constant depending only onχ(S)andǫ.The basic idea in the proof of Theorem1.10is to search for a least area repre-sentative of the isotopy class of the surface S,subject to the constraint that the track of this isotopy does not crossΓ.Unfortunately,M\Γis not complete,so the prospects for doing minimal surface theory in this manifold are remote.To rem-edy this,we deform the metric on M in a neighborhood ofΓin such a way thatSHRINKWRAPPING AND THE TAMING OF HYPERBOLIC3–MANIFOLDS9 we can guarantee the existence of a least area surface representative with respect to the deformed metric,and then take a limit of such surfaces under a sequence of smaller and smaller such metric deformations.We describe the deformations of interest below.In fact,for technical reasons which will become apparent in§1.8,the defor-mations described below are not quite adequate for our purposes,and we must consider metrics which are deformed twice—ﬁrstly,a mild deformation which satisﬁes curvature pinching−1≤K≤0,and which is totally Euclidean in a neighborhood ofΓ,and secondly a deformation analogous to the kind described below in Deﬁnition1.17,which is supported in this totally Euclidean neighbor-hood.Since the reason for this“double perturbation”will not be apparent until §1.8,we postpone discussion of such deformations until that time.Deﬁnition1.17(Deforming metrics).Letδ>0be such thatΓisδ–separated. Choose some small r with r<δ/2.For t∈[0,1)we deﬁne a family of Riemannian metrics g t on M in the following manner.The metrics g t agree with the hyperbolic metric away from someﬁxed tubular neighborhood N r(Γ).Leth:N r(1−t)(Γ)→[0,r(1−t)]be the function whose value at a point p is the hyperbolic distance from p to Γ.We deﬁne a metric g t on M which agrees with the hyperbolic metric outside N r(1−t)(Γ),and on N r(1−t)(Γ)is conformally equivalent to the hyperbolic metric, as follows.Letφ:[0,1]→[0,1]be a C∞bump function,which is equal to1on the interval[1/3,2/3],which is equal to0on the intervals[0,1/4]and[3/4,1],and which is strictly increasing on[1/4,1/3]and strictly decreasing on[2/3,3/4].Then deﬁne the ratiog t length elementr(1−t) We are really only interested in the behaviour of the metrics g t as t→1.As such,the choice of r is irrelevant.However,for convenience,we willﬁx some small r throughout the remainder of§1.The deformed metrics g t have the following properties:Lemma1.18(Metric properties).The g t metric satisﬁes the following properties:(1)For each t there is an f(t)satisfying r(1−t)/4<f(t)<3r(1−t)/4such thatthe union of tori∂N f(t)(Γ)are totally geodesic for the g t metric(2)For each componentγi and each t,the metric g t restricted to N r(γi)admits afamily of isometries which preserveγi and acts transitively on the unit normal bundle(in M)toγi(3)The area of a disk cross–section on N r(1−t)is O((1−t)2).(4)The metric g t dominates the hyperbolic metric on2–planes.That is,for all2–vectorsν,the g t area ofνis at least as large as the hyperbolic area ofνProof.Statement(2)follows from the fact that the deﬁnition of g t has the desired symmetries.Statements(3)and(4)follow from the fact that the ratio of the g t metric to the hyperbolic metric is pinched between1and3.Now,a radially sym-metric circle linkingΓof radius s has length2πcosh(s)in the hyperbolic metric, and therefore has length2πcosh(s)(1+2φ(s/r(1−t)))10DANNY CALEGARI AND DAVID GABAIin the g t metric.For sufﬁciently small(butﬁxed)r,this function of s has a local minimum on the interval[r(1−t)/4,3r(1−t)/4].It follows that the family of radially symmetric tori linking a component ofΓhas a local minimum for area in the interval[r(1−t)/4,3r(1−t)/4].By property(2),such a torus must be totally geodesic for the g t metric. Notation1.19.We denote length of an arcα:I→M with respect to the g t metricas lengtht (α(I)),and area of a surfaceψ:R→M with respect to the g t metric asarea t(ψ(R)).1.5.Constructing the homotopy.As aﬁrst approximation,we wish to construct surfaces in M\Γwhich are globally least area with respect to the g t metric.There are various tools for constructing least area surfaces in Riemannian3-manifolds under various conditions,and subject to various constraints.Typically one works in closed3-manifolds,but if one wants to work in3-manifolds with boundary,the “correct”boundary condition to impose is mean convexity.A co-oriented surface in a Riemannian3-manifold is said to be mean convex if the mean curvature vec-tor of the surface always points to the negative side of the surface,where it does not vanish.Totally geodesic surfaces and other minimal surfaces are examples of mean convex surfaces,with respect to any co-orientation.Such surfaces act as bar-riers for minimal surfaces,in the following sense:suppose that S1is a mean convex surface,and S2is a minimal surface.Suppose further that S2is on the negative side of S1.Then if S2and S1are tangent,they are equal.One should stress that this barrier property is local.See[MSY]for a more thorough discussion of barrier surfaces.Lemma1.20(Minimal surface exists).Let M,Γ,S be as in the statement of Theo-rem1.10.Let f(t)be as in Lemma1.18,so that∂N f(t)(Γ)is totally geodesic with re-spect to the g t metric.Then for each t,there exists an embedded surface S t isotopic in M\N f(t)(Γ)to S,and which is globally g t–least area among all such surfaces.Proof.Note that with respect to the g t metrics,the surfaces∂N f(t)(Γ)described in Lemma1.18are totally geodesic,and therefore act as barrier surfaces.We remove the tubular neighborhoods ofΓbounded by these totally geodesic surfaces,and denote the result M\N f(t)(Γ)by M′throughout the remainder of this proof.We assume,after a small isotopy if necessary,that S does not intersect N f(t)for any t,and therefore we can(and do)think of S as a surface in M′.Notice that M′is a complete Riemannian manifold with totally geodesic boundary.We will construct the surface S t in M′,in the same isotopy class as S(also in M′).If there exists a lower bound on the injectivity radius in M′with respect to the g t metric,then the main theorem of[MSY]implies that either such a globally least area surface S t can be found,or S is the boundary of a twisted I–bundle over a closed surface in M′,or else S can be homotoped off every compact set in M′.First we show that these last two possibilities cannot occur.If S is nonseparating in M,then it intersects some essential loopβwith algebraic intersection number 1.It follows that S cannot be homotoped offβ,and does not bound an I–bundle. Similarly,ifγ1,γ2are distinct geodesics ofΓseparated from each other by S,then theγi’s can be joined by an arcαwhich has algebraic intersection number1with the surface S.The same is true of any S′homotopic to S;it follows that S cannot be homotoped off the arcα,nor does it bound an I–bundle disjoint fromΓ,and therefore does not bound an I–bundle in M′.SHRINKWRAPPING AND THE TAMING OF HYPERBOLIC3–MANIFOLDS11 Now suppose that the injectivity radius on M′is not bounded below.We use the following trick.Let g′t be obtained from the metric g t by perturbing it on the complement of some enormous compact region E so that it has aﬂaring end there, and such that there is a barrier g′t-minimal surface close to∂E,separating the com-plement of E in M′from S.Then by[MSY]there is a globally g′t least area surface S′t,contained in the compact subset of M′bounded by this barrier surface.Since S′t must either intersectβorα,by the Bounded Diameter Lemma1.15,unless the hyperbolic area of S′t∩E is very large,the diameter of S′t in E is much smaller than the distance fromαorβto∂E.Since by hypothesis,S′t is least area for the g′t metric,its restriction to E has hyperbolic area less than the hyperbolic area of S, and therefore there is an a priori upper bound on its diameter in E.By choosing E big enough,we see that S′t is contained in the interior of E,where g t and g′t agree. Thus S′t is globally least area for the g t metric in M′,and therefore S t=S′t exists for any t.The bounded diameter lemma easily implies the following:Lemma1.21(Compact set).There is aﬁxed compact set E⊂M such that the surfaces S t constructed in Lemma1.20are all contained in E.Proof.Since the hyperbolic areas of the S t are all uniformly bounded(by e.g. the hyperbolic area of S)and are2–incompressible rel.Γ,they have uniformly bounded diameter away fromΓoutside of Margulis tubes.Since for homological reasons they must intersect the compact setsαorβ,they can intersect at most ﬁnitely many Margulis tubes.It follows that they are all contained in aﬁxed bounded neighborhood E ofαorβ,containingΓ.To extract good limits of sequences of minimal surfaces,one generally needs a priori bounds on the area and the total curvature of the limiting surfaces.Here for a surface S,the total curvature of S is just the integral of the absolute value of the(Gauss)curvature over S.For minimal surfaces of aﬁxed topological type in a manifold with sectional curvature bounded above,a curvature bound follows from an area bound by Gauss–Bonnet.However,our surfaces S t are minimal with respect to the g t metrics,which have no uniform upper bound on their sectional curvature,so we must work slightly harder to show that the the S t have uniformly bounded total curvature.More precisely,we show that their restrictions to the complement of anyﬁxed tubular neighborhood Nǫ(Γ)have uniformly bounded total curvature.Lemma1.22(Finite total curvature).Let S t be the surfaces constructed in Lemma1.20. Fix some small,positiveǫ.Then the subsurfacesS′t:=S t∩M\Nǫ(Γ)have uniformly bounded total curvature.Proof.Having chosenǫ,we choose t large enough so that r(1−t)<ǫ/2.Observeﬁrstly that each S t has g t area less that the g t area of S,and therefore hyperbolic area less that the hyperbolic area of S for sufﬁciently large t.Letτt,s=S t∩∂N s(Γ)for small s.By the coarea formula(see[Fed],[CM]page 8)we can estimatearea(S t∩(Nǫ(Γ)\Nǫ/2(Γ)))≥ ǫǫ/2length(τt,s)ds12DANNY CALEGARI AND DAVID GABAIIf the integral of geodesic curvature along a componentσofτt,ǫis large,then the length of the curves obtained by isotopingσinto S t∩Nǫ(Γ)grows very rapidly, by the deﬁnition of geodesic curvature.Since there is an a priori bound on the hyperbolic area of S t,it follows that there cannot be any long components ofτt,s with big integral geodesic curvature.More precisely,consider a long componentσofτt,s.For l∈[0,ǫ/2]the boundaryσl of the l-neighborhood ofσin S t∩Nǫ(Γ)is contained in Nǫ(Γ)\Nǫ/2(Γ).If the integral of the geodesic curvature alongσl were sufﬁciently large for every l,then the derivative of the length of theσl would be large for every l,and therefore the lengths of theσl would be large for all l∈[ǫ/4,ǫ/2].It follows that the hyperbolic area of theǫ/2collar neighborhood ofσin S t would be very large,contrary to existence of an a priori upper bound on the total hyperbolic area of S t.This contradiction implies that for some l,the integral of the geodesic curvature alongσl can be bounded from above.To summarize,for each constant C1>0 there is a constant C2>0,such that for each componentσofτt,ǫwhich has length ≥C1there is a loopσ′⊂S t∩(Nǫ(Γ)\Nǫ/2(Γ))isotopic toσby a short isotopy,satisfyingσ′κdl≤C2On the other hand,since S t is g t minimal,there is a constant C1>0such that each componentσofτt,ǫwhich has length≤C1bounds a hyperbolic globally least area disk which is contained in M\Nǫ/2(Γ).For t sufﬁciently close to1,such a disk is contained in M\N r(1−t)(Γ),and therefore must actually be a subdisk of S t.By the coarea formula above,we can chooseǫso that length(τt,s)is a priori bounded.It follows that if S′′t is the subsurface of S t bounded by the compo-nents ofτt,s of length>C1then we have a priori upper bounds on the area of S′′t, on ∂S′′tκdl,and on−χ(S′′t).Moreover,S′′t is contained in M\N r(1−t)where the metric g t agrees with the hyperbolic metric,so the curvature K of S′′t is bounded above by−1pointwise,by Lemma1.2.By the Gauss–Bonnet formula,this gives an a priori upper bound on the total curvature of S′′t,and therefore on S′t⊂S′′t. Remark1.23.A more highbrow proof of Lemma1.22follows from Theorem1 of[S],using the fact that the surfaces S′t are locally least area for the hyperbolic metric,for t sufﬁciently close to1(depending onǫ).Lemma1.24(Limit exists).Let S t be the surfaces constructed in Lemma1.20.Then there is an increasing sequence0<t1<t2<···such that lim i→∞t i=1,and the S tconverge on compact subsets of M\Γin the C∞itopology to some T′⊂M\Γwith closure T in M.Proof.By deﬁnition,the surfaces S t have g t area bounded above by the g t area of S.Moreover,since S is disjoint fromΓ,for sufﬁciently large t,the g t area of S is equal to the hyperbolic area of S.Since the g t area dominates the hyperbolic area, it follows that the S t have hyperbolic area bounded above,and by Lemma1.22, for anyǫ,the restrictions of S t to M\Nǫ(Γ)have uniformly boundedﬁnite total curvature.。

球面压力五孔探针的校准与使用

球面压力五孔探针的校准与使用
侯敏杰
【期刊名称】《燃气涡轮试验与研究》
【年(卷),期】1997(000)002
【摘要】流场的测试广泛使用五孔探针。

通过校准，建立起探针的数学模型，可避免采用查表法，提高工作效率。

本文以球面压力五孔探针为例，对五孔探针的校准，数学模型的建立及使用方法进行了研究，对五孔探针的使用具有借鉴的意义。

【总页数】1页(P37)
【作者】侯敏杰
【作者单位】燃气涡轮研究所;燃气涡轮研究所
【正文语种】中文
【中图分类】TK05
【相关文献】
1.天线球面近场测量的探针校准近远场变换 [J], 王建;林昌禄
2.超音速条件下基于CFD的压力探针校准特性数值模拟 [J], 赵彬;赵俭
3.球面非探针校准近—远场变换 [J], 佘川飞
4.球面探针校准近—远场变换 [J], 佘川飞
5.风洞实验压力探针校准测试系统平台 [J], 苗雪冬
因版权原因，仅展示原文概要，查看原文内容请购买。

【国家自然科学基金】_五孔探针_基金支持热词逐年推荐_【万方软件创新助手】_20140802

推荐指数 1 1 1 1 1 1 1
2013年序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
科研热词轴流泵流动测量数学模型五孔探针高负荷扩压叶栅高负荷压气机非线性环量附面层抽吸附面层吸除间隙流动间隙泄漏流动间隙轴面速度试验研究计算机控制自动校准涡轮叶栅流动特性水力机械气动特性来流角度数值仿真探针旋转机构抽吸孔平面叶栅叶顶间隙压气机叶栅冲角三维分离
推荐指数 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2014年序号 1 2 3 4 5 6
2014年科研热词间隙航空航天推进系统流动特性实验研究压气机叶栅推荐指数 1 1 1 1 1 1
推荐指数 3 3 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2011年序号 1 2 3 4 5
2011年科研热词现场测试泵装置效率水泵流量大型泵站五孔探针推荐指数 1 1 1 1 1
2012年序号 1 2 3 4 5 6 7
科研热词轴面速度轴流试验环量泵叶轮五孔探针
推荐指数 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2010年序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
科研热词吸气量吸气位置高负荷扩压叶栅局部附面层吸除高负荷叶栅风洞速度环量速度分量轴流泵端壁翼刀测量气动性能最佳高度数值计算局部边界层吸除实验研究叶栅总损失压气机叶栅

五孔探针流场测试新方法

五孔探针流场测试新方法随着科学技术的不断发展，流体动力学研究在各个领域中扮演着越来越重要的角色。

流场测试作为流体动力学研究的重要手段之一，对于提高流体力学研究的精确性和可靠性起着至关重要的作用。

五孔探针是一种常用的流场测试仪器，可以实现多点同时测量流场参数，如速度、压力等。

本文将介绍一种新的五孔探针流场测试方法，旨在提高测试的精确度和效率。

一、五孔探针原理五孔探针是一种基于流场动量守恒的传感器，通过五个孔位上的压力差来测量流场中的速度场。

在理想情况下，探针的压力差与流场的速度成线性关系。

通过定标和校准，可以将压力信号转换为流场速度。

五孔探针的原理比较简单，但在实际应用中需要考虑到各种因素的影响，如探针位置、探针长度、流场扰动等。

二、传统五孔探针测试方法传统的五孔探针测试方法通常是将探针安装在流场中的其中一位置，通过数据采集系统记录各个孔位上的压力信号，并通过定标和校准将压力信号转换为流场速度。

这种方法的优点是简单易行，可以实现对流场中不同位置的多点测量，但也存在一些问题，如测量精度受到流场扰动的影响、探针安装位置的选取不当等。

三、新方法介绍为了提高五孔探针的测试精度和效率，我们提出了一种新的五孔探针流场测试方法。

该方法主要包括以下几个方面的改进：1.流场平坦度校正：在进行五孔探针测试之前，我们首先对流场进行平坦度校正。

通过引入激光测距仪等高精度测量工具，可以准确地获得流场的平坦度分布，从而避免流场扰动对测试结果的影响。

2.控制探针位置误差：在安装五孔探针时，我们将采用更加精确的定位方法，控制探针位置误差在允许范围内。

通过精确的位置控制，可以减小由于位置误差导致的测量误差。

3.流场压力校准：除了对五孔探针进行定标和校准外，我们还将对流场的压力进行校准。

通过引入高精度压力传感器，可以实现对流场压力的实时监测和修正，提高测试的准确性。

4.数据处理与分析：在数据采集完成后，我们将对采集到的数据进行进一步处理与分析。

五孔探针理论校准方法研究

３１实验校准．
图１五孔探针结构示意图
２探针使用方法
具体应用中，孔探针有３测量方法：五种
这里对实验标定方法进行简单描述。
［稿日期］２ｌ一Ｏ２收ｏ２５８［者简介］王涛（９９，，０３科年毕业于西北工业大学飞行器动力工程专业，０１２１作Ｉ７一）女２０本２１０２年就读于克莱菲尔德大学，从事现航空发动机通风冷却系统飞行试验研究工作。
ｔｔｄｉｅｓｂｌｈｅｍｅｈｏＳｆａｉｅ，ａｔｕｇｕｒｈｅｅｅｒｈＳｎｅｅｌｈｏｈｆｔｒｒｓａｃｉｅｄｄ．Ｋｅｗｏｄｆｖｅｈｏｅｐｏｂｙｒｓ：ｉ — ｌｒｅ；ｉｏｐｅｓｂｅｆｏ；ｔｏｅｉａａｉｒｔｏｎｎｃｍｒｓｉｌｌｗｈｅｒｔｃｌｃｌｂａｉ
流空间大，有条件转动探针安装机构，不适合流场实
验测量。
常用手段，最主要用途是测取气流方向。因精度高，设备简单，成本低，对环境要求低以及可远距离测量等优点，五孔探针被广泛应用。本文所采用探针如图１所
示，针为管形结构，针头部外径１５ｎ孔内径探探．ｍｒ，
值，无需调整各孔平衡，根据校准曲线可直接求取偏转角、仰角、俯速度矢量、总压、压等。静

五孔探针非对向测量法在风洞自动测试系统的...

采用非对向测量法有利于提高测试速度。
图 1 五孔探针的角度定义图 Fig. 1 Geometry of five2hole probe
非对向测量时的探针校准系数为 : α方向校准系数 Kα = ( P4 - P5) / ( P2 - P) β方向校准系数 Kβ = ( P3 - P1) / ( P2 - P) 总压校准系数 Cpt = ( P2 - P03 ) / ( P2 - P)
采用非对向测量法 ,通过自动测试系统采集到的五孔压力值 ,并结合校准曲线给出的 P 3 、Ps 和V→等气动参数 , 与半对向测量得到的测量结果
比较 , 其测量精度如何呢 ? 图 3 和图 4 给出了压气机叶栅出口流场测量时叶栅能量损失系数 ζm 和叶栅出口气流角 α 沿叶高方向的分布情况。
标以 ●号的曲线表示的是人工半对向测量结果 ,
标以 ○号的曲线表示的是自动测试系统中采用非
对向测量方法得到的测量结果。从图 3 和图 4 可
以看出 ,沿叶高方向来看 ,采用半对向测量和非对
向测量法 ,叶栅能量损失系数值和出口气流角的
变化规律基本一致。按整个测量截面质量平均的
能量损失系数 ,两种测量方法相差 5. 02 % 。叶栅
哈工大科研成果简介
纤维/ 铝复合材料固2液态一次复合挤压成形基础研究
材料科学与工程学院罗守靖胡连喜杨绮雯等
主要内容及技术指标 : 首次提出纤/ 维铝复合材料固2液态一次复合挤压成形新工艺 ,采用理论分析、试验研究和数值模拟相结合的方法 ,对该新工艺进行了全面系统的研究 ,并确立了该工艺 ,获得了优质复合材料型材类制件 , 其强度和塑性等性能指标达到或高于国外同类材料水平 ,为短纤维增强金属基复合材料型材类制件的成形提供了一种先进的新途径。经济效益及社会效益 :采用该工艺制作成形复合材料制件 ,可简化材料制作成形工艺程序 ,降低制作成本 ,并提高制件的质量与性能 ,对推动金属基复合材料在国防领域中的应用 ,具有重要意义。技术水平 :国内外首创 ,未见类似报导先例。应用领域 :短纤维增强金属基复合材料及其型材类制件的制作与成形。

附录：五孔探针流场测量技术简介

2、传感器选择
根据被测量的压力范围选择适合的传感器量程。
3、数据实时采集
利用数据采集系统来采集五孔探针的压力信号，并将它实时地传送到五孔探针测试系统中，可实时地显示流场的速度和压力。
4、角度传感器和位移传感器
测量系统如果配上绝对型的轴编码器来测量探针转动角度α0 和位移传感器来测量坐标位置，可以实现角度和位置的自动测量。
探针校正曲线
3
2
1
0
-40
-20 -1 0
kδ
k2
20
40kΒιβλιοθήκη -1k2-4-2-3 δ
图2 半对向测量校准曲线
3. 非对向测量(方法1)
在根据五个压力孔测出的压力，计算出Kα和Kβ,然后根据Kα和Kβ在五孔探针特性网图Kα、Kβ=f(α,
β)中查出α和β。
Kα
=
( p2
−
p3 − p1 p1 ) + ( p2
ρ(k3 − k1 )
（1－5）
ps
=
p2
+ k2
p2 k2
− p4 − k4
（1－6）
p0
=
ps
+
ρ 2
v2
=
ps
+
p3 k3
− p1 − k1
p0 − ps =
p2 − p4 k2 − k4
=
p3 − p1 k3 − k1
（1－8）
(1-8)可以用来相互校对动压头，检验测量是否正确。
11
（1－7）
5、实时测量软件处理系统
利用压力传感器测量得到的压力 P1~5，通过非对向测量方法，可以获得基于探针坐标系下地三维速度 V’，α’，β’，并可以实时地显示基于探针系的气流速度和气流角度；再通过轴编码器测量探针转动的角度 α0，就可以获得世界坐标系统下的气流速度和角度。

五孔探针技术在压缩机测试中的应用

５结语
在离心压缩机基本级调节试验研究中应用该系统，极大地提高工作效率，降低试验成本，使研究手段真正上升了一个台阶，保证了试验精度
和水平。
接应用校正的结果进行计算。
一 —
●
Ｊ．．—— Ｊ一 — —— ． —Ｊ．． —— ．一 —Ｉ —
大提高工作效率；
针对气流测量时的不同方法，校正也可分为
对向和非对向两种方法。鉴于压缩机基本级试验的过程和实际结构条件，校正采用了非对向校正方法。即沿轴线转动五孔探针，使对孔连接的压差传感器平衡时，根据预先标定得到的五孔探针校正特性曲线和孔１、３、２、４各感受的压力值，可计算得到气流偏转角度和校正系数，从而据此求得气流速度。此次五孔探针的校正是在某标准风洞上进行的。通过全方位校准，得到校准速度系数、校
准侧滑角（仰角等特性参数。俯校准时，在某一Ｍａ数下，固定一个仰角，
３）可同时进行多路压力测量数据采集；
改变一组侧滑角，记录５个感应孔的压力值，联机处理出对应的校准压力系数，并给出电子可
查格式。典型校正曲线见图３。在使用时可以直
差压传感器、ＡＤ模块、ＰＣ微机及配套软件包构成，采用自选通道方式进行工作，使流场测量成为简单、方便、快速、
高精度的智能化测量过程。关键词：测量系统；五孔探针；智能化；工程实用中图分类号：Ｈ８４文献标识码：Ａ文章编号：１７－８１０１ｏ．７ —２Ｔ１６２４０（１）５０９０２

五孔探针在涡轮导向器出口流场测量中的应用

ａｐｉｄｔｈａｕｅｎｆａｔｒｉｅｎｚｌｕｌｔｆｗｆｅｄｎｄｔｅｇｏｅｕｔａｅｂｅｎｇｔｎｐｌｏｔｅｍｅｓｒｍｅｔｕｂｎｏｚｅｏｔｏｉｌ，ａｈｏｄｒｓｌｓｈｖｅｏｔ．ｅｏｅｌｅＫｅｒｓ：５ｏｅｐｏｅ；ａａｐｏｅｓｎｔｒｎｏｚｅ；ｏｆｅｄｍｅｓｅｎｙｗｏｄ－ｈｌｒｂｄｔｒｃｓｉｇ；ｕｂｉｅｎｚｌｆｗｌａｕｒｍｅｔｌｉ
ｃｕｅｏｈｆｅｔｆｂｕｄａｙｌｙｒａｄｓｃｎａｙｆｗ．Ｉｉａｕｅｙｕｉｇ５ｏｅｐｒｂｓａｌ．Ｉａｓｆｔｅｅｆｃｓｏｏｎｒａｅｎｅｏｄｒｏｌｔｓｍｅｓｒｄｂｓｎ－ｈｌｏｅｕｕｌｙｎｔｉａｅ，ａｗｉｅｙａｌａｌｔｄｏａａｐｏｅｓｎｆ５ｈｌｒｂａｅｎｄｖｌｐｄｎａｃ－ｈｓｐｐｒｄｌｐｐｉｂｅｍｅｈｏｆｄｔｒｃｓｉｇｏ－ｏｅｐｏｅｈｓｂｅｅｅｏｅ，ａｄａｃｌｕｃ
数分布。这样一方面可准确评价导向器的性能指标和设计水平．一方面可验证涡轮气动设计模型．另提
高设计能力。以前常用三孑压力探针测量导向器出口流场，Ｌ但严格来讲．三孔探针只适用于二维流场的测量。由
中图分类号：Ｖ２．６４１０文章标识码：Ａ文章编号：１７ — ６０（００４０４ — ５６２２２２１）０ — ０４０

一种大来流角度下五孔探针的分区插值方法[发明专利]

专利名称：一种大来流角度下五孔探针的分区插值方法专利类型：发明专利
发明人：陆华伟,路子平,王龙,王宇,田志涛,孔晓治,辛建池申请号：CN202010744265.8
申请日：20200729
公开号：CN111896211A
公开日：
20201106
专利内容由知识产权出版社提供
摘要：本发明提供一种大来流角度下五孔探针的分区插值方法，包括获取内区插值文件和外区插值文件；获取五孔探针采集到的五孔压力值，根据五孔压力值确定插值分区模式，所述插值分区模式分为内区模式和外区模式；当插值分区模式为内区模式时，基于所述内区插值文件对所述五孔压力值进行处理，得到流场的总压和静压；当插值分区模式为外区模式时，基于外区插值文件对所述五孔压力值进行处理，得到流场的总压和静压；基于流场的总压和静压计算得到流场的流速。

当探头来流角度过大时，探头部分区域的气流会发生附面层分离，处在分离区中的感压孔将失效，从而导致测量不准。

采用本发明方法可以克服上述问题，将探头适应的来流角度范围由±30°提升至±45°。

申请人：大连海事大学
地址：116026 辽宁省大连市高新园区凌海路1号
国籍：CN
代理机构：大连东方专利代理有限责任公司
代理人：李馨
更多信息请下载全文后查看。

(位移传感器专业英语维基百科555timerIC

555 timer IC第五页The 555 has three operating modes:▪ mode: in this mode, the 555 functions as a "one-shot" pulse generator. Applications include timers, missing pulse detection, bouncefree switches, touch switches, frequencydivider, capacitance measurement, (PWM) and so on.▪: free running mode: the 555 can operate as an . Uses include and lamp flashers, pulse generation, logic clocks, tone generation, security alarms, and so on. Selecting a as timing resistor allows the use of the 555 in a temperature sensor: the period of the output pulse is determined by the temperature. The use of a microprocessor based circuit can then convert the pulse period to temperature, linearize it and even provide calibration means.▪ mode or : the 555 can operate as a , if the DIS pin is not connected and no capacitor is used. Uses include bounce-free latched switches.▪[]Usage[]MonostableSchematic of a 555 in monostable modeThe relationships of the trigger signal, the voltage on C and the pulse width in monostable modeIn the monostable mode, the 555 timer acts as a "one-shot" pulse generator. The pulse begins when the 555 timer receives a signal at the trigger input that falls below a third of the voltage supply. The width of the output pulse is determined by the time constant of an RC network, which consists of a (C) and a (R). The output pulse ends when the voltage on the capacitor equals 2/3 of the supply voltage. The output pulse width can be lengthened or shortened to the need of the specific application by adjusting the values of R and C.The output pulse width of time t, which is the time it takes to charge C to 2/3 of the supply voltage, is given bywhere t is in seconds, R is in and C is in .While using the timer IC in monostable mode, the main disadvantage is that the time span between the two triggering pulses must be greater than the RC time constant.[]BistableSchematic of a 555 in bistable modeIn bistable mode, the 555 timer acts as a basic flip-flop. The trigger and reset inputs (pins 2 and 4 respectively on a 555) are held high via while the threshold input (pin 6) is simply grounded. Thus configured, pulling the trigger momentarily to ground acts as a 'set' and transitions the output pin (pin 3) to Vcc (high state). Pulling the reset input to ground acts as a 'reset' and transitions the output pin to ground (low state). No capacitors are required in a bistable configuration. Pin 5 (control) is connected to ground via a small-value capacitor (usually to uF); pin 7 (discharge) is left floating.[]AstableStandard 555 astable circuitIn astable mode, the 555 timer puts out a continuous stream of rectangular pulses having a specified frequency. Resistor R1 is connected between V CC and the discharge pin (pin 7) and another resistor (R2) is connected between the discharge pin (pin 7), and the trigger (pin 2) and threshold (pin 6) pins that share a common node. Hence the capacitor is charged throughR1 and R2, and discharged only through R2, since pin 7 has low impedance to ground during output low intervals of the cycle, therefore discharging the capacitor.In the astable mode, the frequency of the pulse stream depends on the values of R1, R2 and C: The high time from each pulse is given by:and the low time from each pulse is given by:where R1 and R2 are the values of the resistors in and C is the value of the capacitor in .The power capability of R1 must be greater than .Particularly with bipolar 555s, low values of R1 must be avoided so that the output stayssaturated near zero volts during discharge, as assumed by the above equation. Otherwise the output low time will be greater than calculated above.To achieve a of less than 50% a diode can be added in parallel with R2 towards the capacitor.This bypasses R2 during the high part of the cycle so that the high interval depends only on R1 and C.Other Types Of Timers[]556 Dual timerInternal block diagramThe dual version is called 556. It features two complete 555s in a 14 pin DIL package.[]558 Quad timerThe quad version is called 558 and has 16 pins. To fit four 555s into a 16 pin package the control, voltage, and reset lines are shared by all four modules. Each module's discharge and threshold are wired together internally and called timing.[]Joystick interface circuit using the 558 quad timerThe used a quad timer 558 in monostable (or "one-shot") mode to interface up to four "game paddles" or two to the host computer.A similar circuit was used in the . In the joystick interface circuit of the IBM PC, the (C) of theRC network was generally a 10 nF〔farad〕capacitorApplicationTraffic Lights ProjectThe 555 timer IC is connected for , the clock pulses are fed to the 4017 IC via the 10K resistor. The 4017 is a 10 stage counter, therefore the sequence of the traffic lights is spread over 10 clock pulses, 4on red, 1 on red & amber, 4 on green and 1 on amber.We need red on for 5 pulses, so we connect the red LED to pin 12 which is on for the first 5 stages of the counter. The green and yellow LEDs are connected to the nescessary counter outputs, asboth LEDs need to be on for more than one count, we use diodes to avoid a short circuit situation between outputs.The capacitor and resistor on pin 15 of the 4017 are used to reset the counter to zero (red LED on) at initial power up.Electronic Dice ProjectThe 555 timer IC is connected for Astable Operation, the clock pulses are fed to the 4017 IC via the 10K resistor. The 4017 is a 10 stage counter, output 6 (pin 5) is connected to RESET (pin 15), thus giving us a 6 stage counter , outputs 0 to 5.6 of the LEDs are connected as 3 pairs, thus requiring 4 different signals, these signals come from the 4 transistors, which in turn are connected to the nescessary outputs of the 4017. Where a transistor is operated from more than one output, diodes are used to avoid a short circuit situation between outputs.Pin 13 of the 4017 (INHIBIT) is connected to +ve via a 100K resistor to stop the counter from advancing, however pressing the ROLL button will connect pin 13 to -ve and allow the counter to advance, hence, throwing the dice.4017：Divide-by-8 Counter/Divider with 8 Decoded OutputsKnight Rider Lights ProjectThe 555 timer IC is connected for Astable Operation, the clock pulses are fed to the 4017 IC via the 10K resistor. The 4017 is a 10 stage counter, each of the outputs is connected to the appropriate LED, as some LEDs need to be on for more than one count, we use diodes to avoid a short circuit situation between outputs.The capacitor and resistor on pin 15 of the 4017 are used to reset the counter to zero at initial power up.The ULN2001N used on the bulb version is a seven channel Darlington Driver IC, a small signal on one of the inputs is enough to drive the bulb on the output.Whats the difference between Monostable and Astable in IC 555?A monostable has one stable state.The stable state of a 555 in that configuration is with its output low. It will stay low until it receives a trigger, upon which it produces one high output pulse.An astable has no stable states. The states change continuously.In a 555 that means the output alternates between low and high. The 555 will start doing this as soon as power is applied to it.A good site which explains the 555's operation in detail is。

适用复杂流场五孔探针的研制与校准

Ｄ
一
ｍ
Ⅲ
应用五孑探针测量三维流场有ｌＬ一种方法，ａ对向测量法．．．ｂ半对向测量法非对向测量法。向以及半对向测量法虽然很直观，对探针校准工作和处理实验数据量较少，但需要复杂的转动机构以及长时间找孑与孑之间的压力平ＬＬ衡，不适于测点数大的流场测量。非对向测量法操作简单，无需调整各孑平衡，Ｌ直接采集五孑压Ｌ力值，据校准曲线即可求取偏转角、仰角、根俯各分速度值、总压、静压。但在这种方法中，探针校准和实验数据处理的工作量大。尤其在对复杂流场测试中，对多马赫数条件下建立的数学模型具有较高的数值精度要求。以研制的球头五孑球探针为例，Ｌ阐述了五孑探针数学模型的建立以及使用方法，并以非Ｌ对向测量法为基础，利用计算机进行数据实时采集和处理，以提高流场测试精度和效率，为下步对复杂流场的测量提供依据１五孑探针校准与模型建立Ｌ１１孑探针结构．五Ｌ这里所研制的五孑球探针如图１示，Ｌ所由球形的探针头、探针杆，水平盘和测压接头组成。球形探针头上有五个感压孑，Ｌ各感压孑的分Ｌ布位置及编号如图２示，每个孑经过位于探所Ｌ针杆内的细管与探针尾部对应的测压接头相连。水平盘固定在杆上，随着探针一起转动，调节水平盘可以确定探头的位置。试验时，Ｌ五孑探针实际测量的是五个测压孑感受的压力ＰＰｌＰＰ，４而这五个压力ＬＯ，，２，３Ｐ，决定了气流的总压、、静压马赫数、流方向。气通过校准建立起五孑探针的数学模型，这样就可Ｌ避免采用查表法，提高了工作效率，并使流场测量的实时处理过程成为可能。球形五孑探针的校准是在亚音速吹风式Ｌ射流校准风洞上进行的，通过调节气流的流量来调节其马赫数。气流在喷管出口的锥形区域内形成均匀的射流核心区，五孑探针的头部置Ｌ

5 PIN SCAN说明书

•UnpackingOpen the box, remove the projectorfrom the packing and place it on aflat, horizontal surface.Unpack the standard accessoriessupplied with the fixture.Inspect thelamp change label (1) and replace itwith one of the optional languageversions if necessary.Make sure that the label is neverremoved,as it displays importantsafety information.•Connecting to the electrical power supplyThe operations described in this heading must be carried out by a licensed electrician.The projector must be wired up to the electrical power supply using the special socketconnector provided (4).It is good policy to connect projectors to the power supply by way of dedicatedswitches, so that each can be turned on and off individually from a remote station.The projector is designed to operate at the voltage and frequency indicated on theelectrical data plate (5).Check that these two values correspond to the mains voltageand frequency.IMPORTANT:the projector must be connected to a power supply circuithaving a proper earth system (Class I appliance).• Connecting the control signalsRS 232/423(PMX) - DMX 512•Fitting the lampRefer to the directions for replacement of the lamp given under heading 4 MAIN-TENANCE.•Installing the projectorThe projector can be placed on the floor on the rubber feet (2) or installed on the ceil-ing or wall using the holes (3) in the base.Make certain that the anchorage is stable before positioning the projector.•Minimum distance from target objectsThe projector must be positioned in such a way thatobjects struck by the beam are located at least 1.3m (4’3”) from the lens.•Minimum distance of inflammable materials from any part of the fixture:m 0.1 (4”).IMPORTANT:For better and more reliable operation of the fixture, the ambienttemperature must not exceed 35°C (95°F).Protection factor IP 20:the fixture isprotected against penetration of solid bodies more than 12mm (0.5”) in diameter (firstdigit 2), but can be damaged by spray, jet, drip or rain water (second digit 0).231POWER SUPPLY AND INTERFACE2Projectors are wired up to the controller and one to the next using two-corescreened cable and Cannon 5 pin XLR type plug/socket connectors.To connect a DMX line, a terminating plug (8) with a 100Ωresistor wired betweenpins 2 and 3 must be fitted to the last projector connected in series;the plug is notrequired when using an RS232/423(PMX) signal.INSTALLING THE PROJECTOR1IMPORTANT:Read carefully.It is essential for the correct and safe use of theequipment that erectors and operators should be fully conversant with theinformation and instructions given in this manual.INSTRUCTION MANUAL ENGLISH(4’ 3”)1.3 m12V - 100WNL45MainsThe wires must not come into contact with each other or with the metalcasing of the plug.The casing of the plug/socket must be connected to the screen and to pin 1of the connectors.Having completed the operations described above, press the on/off switch (7).Check that the lamp comes on and the auto-reset sequence starts.SIGNALSCREENSIGNAL54321DMX 512SIGNALSCREENSIGNALRS232/423 (PMX)12345561 DIMMER / STOPPER / STROBE2 PAN 3TILTCHANNEL FUNCTIONS AND OPTIONS3•Projector address codesA single PIN SCAN projector utilizes 3 control channels.To ensure that the different projectors are addressed correctly by the controller, a code must be assigned to each one.The operation is carried out on each PIN SCAN by setting the microswitch-es as indicated in the table below.Setting the TEST switch to the ON position for a few seconds with the projector powered-up, an auto-reset routine is carried out.Leaving the TEST switch at the ON position for a longer period, a full self-test program will be completed;once the operation has terminated, return the switch to the OFF position.CHANNELFUNCTIONON Pan direction change.OFF ON Tilt direction changeOFF11 12OPTION FUNCTION S T P A N T I L TOPTIONSSelect the options by setting the microswitches as indicated.12345678910BIT%EFFETTO244-25595.5-100APERTO14054.7STROBO LENTO APERTO0.0CHIUSO24395.0STROBO VELOCE 128-13950.0-54.2• DIMMER / STOPPER / STROBE - channel 112345678910BIT %25512810050.00.0• TILT - channel 3Operation with option 12 OFFOperation with option 12 ONT A N I L T12345678910T A N I L T7• Changing fusesTo change the fuses, press the tab (8pull out the fuse holder (10).rating as indicated on the label (10attached to the holder (9).holder and push in to engage the tab (8).• Routine cleaningTo maintain the light output of the projector undiminished, parts that tend to accumu-late dust and grease must be cleaned periodically.To remove dirt from the reflector and filter use a soft cloth moistened with any liquid detergent suitable for cleaning glass.CAUTION:Do not use solvents or alcoholIMPORTANT:isolate the projector from the electrical power supply before commencing maintenance work of any description.The maximum temperature on the outer surface of the projector under normal operating conditions is 100°C (212°F).After switching off, do not remove any part of the projector for at least 10 minutes;once this time has elapsed, the risk of a lamp exploding is practically zero.If the lamp needs changing, wait a further 15 minutes to avoid the risk of burns.MAINTENANCE4ENGLISHCAUTION:- When fitting a new lamp read the manufacturer's instructions carefully.- The lamp must always be changed without delay if damaged or deformed by heat.•Only use 12V halogen lamps with a maximum power of 100W madewith low pressure technology.TROUBLESHOOTING5CoolingForced ventilation cooling system using axial flow fan.Housing•Extruded die-cast aluminium.•Epoxy powder coated finish.Operating positionWill function in any position.Weight and dimensionsWeight:5.8 kg (12 lbs 12 ozs).Power supply•100-120V 50/60Hz •200-240V 50/60HzLamps•12V 90W (Halostar).To be used with special Clay Paky pencil beam parabola (2.5°).•12V/50-75-100W (Halospot).Built-in reflector with different beam apertures.Power consumption150VA max.(consumption varies in relation to the lamp).ChannelsN.3 control channels.Inputs•RS232/423(PMX)•DMX512Moving body•Movement generated by two microstepping motors with full micro-processor control.•Range of adjustment:- PAN = 360°- TILT = 227°•Resolution:- PAN = ±1.41°- TILT = ±0.89°TECHNICAL DATA6(9.1”)230(9.1”)230(7.5”)190。

亚声速气流中五孔探针的校准及应用

朋。ｌ
Ｆｉｇ，５
因此．通过排架后部的旗准杆找到其与风洞试验段轴线之间的角度关系“。．冉通过校准得到的ａｒ值．吖以无需得知探引‘与Ｉ孔洞轴线之间的角度盖系．便可求出点流向角度．具体公式蛐Ｆ：
ＹⅡｗ蚰出ｃｍｔｈ呲Ｉｏｎ蛐‰ｒｄｌｆｔｅｎＲｔＭ¨ｈｎｕｍｈｍ
ｍ５十目日＃＆ｆｄ自＆№Ｉｍ“
筏准曲线表明．ｎ或？每增加ｌ６．Ｃｏ（口）增加约ｏ．０８３，根据线性方法拟合得出的校准曲线与原始数据的误差为０００３３左右，则探针的角鹱测丘！误差约为＝００，１。。对于结冰引导飙洞ｚＣ流０５。的点流向来可知：△口一Ｋ１。（。十口』．＋口＝ＫｈＣ。＋口Ｐ一口ｄ说．±０．０４。的角度测量误差是满足要求的。同时也说哪．在小角度范围内．采用线性离散模喇对五孔探探针排架在结冰引导风ｉ｜司巾的安装见图６。由于：口ｐ一鲥一口ｒ＋口
ｎｍ
时一％∽他Ⅲ们∞船¨”“…¨” ¨
等焉篡篙％臻篙㈣兰播糍燃撼糍糍裟～
００
４结冰引导风洞测试结果
常规的风涮点流向ｊｊ！｜】吐方法中．需要将测址值进行探针安装偏角厦ＪＪ兀ｌ：浸蔗修ｊＥ后卅能得出真吏的点流向数据。由Ｊ结冰引导风洞ｉ式验段截面尺寸小，
无法对五孔探针与风嗣轴线之问的安装角进行测量．
机构为手动．ｏ及口控制机构由伺服电机驱动．角度
调竹范围为±１５。．角度控制精度００１。．校准装置及
支撑机构见用２。
州。Ｉ
Ｆｉｇ３
１’ｐｉ咖ｄ■●－ｈｒｆｌｏｒ瑚［帅ｄ㈣抖ｍ¨州ｆｎＩｎｌ｝ⅢＥ
Ｉ目３“＂ｔ
Ｊ王女＊＾Ⅲ《☆ｍ４
根据线性离散模型提供的方法，可知：
Ｋ。。一口Ｐ一（ｒ
ｏ，）／２
目２Ⅳ＂＆ｔ＃ｔⅡ｛悼ｍ日
寰ｌ探针控准结果

五孔探针在气流速度测量中的应用

气动探针是一种利用气流绕流探针时的压力分布和各孔所测的压力差来测量总、静压进而计算流体方向、速度等的气动测量装置。早期出现的三孔探针主要用于测量二维流场，五孔探针可以用于测取三维流场总、静压和方向等复合气动参数，结构如图 1 所示（图中 1-5 为五孔探针五孔位置，α 表示偏转角，β 表示俯仰角）。五孔探针应用范围广泛，例如在航天航空领域中，飞机翼型附近的复杂流场，对相关流速的测量至关重要，在流体机械领域，对涡轮叶片尾缘处气流的流向参数测量[4-6]，压缩机进出口气速的测量[7] 等，都会利用五孔探针进行测量。
论上分析了探针前正激波、斜激波对测量参数的影响，提出测量数据的修正方法；并在 Laval 喷管实验平台中使
用五孔探针对气流速度进行了测量，测量结果具有较高的精度，满足工程使用要求，验证了五孔探针对气流速度
测量校核和使用方法的准确性。研究结果不仅拓宽了五孔探针的应用范围，而且对相关的测量研究有重要的工程
图 1 五孔探针示意图
五孔探针在 Ma<0.3 的低速流场中的应用已经很成熟，但是当 Ma>0.3 时，流体可压缩性的影响逐渐增大，五孔探针测定的数据需要进一步处理才能反映实际流场的情况。本文使用五孔探针对气流速度测量及校核进行了完整研究，特别是对五孔探针在高速流场测量中的应用进行了深入的探究，并对 Laval 尾部进行了速度测量实验验证。
的研究。对五孔探针在 Ma>0.3 的高速气流速度测量中的应用进行了研究，探讨了五孔探针在高速气流中的标定
和测量方法，设计加工了锥形五孔探针，并在标准风洞 0.3>Ma>1 的高速流场中对其进行了标定，获得了相应的
标定校核结果；通过实验分析了 Ma>0.3 时气流的可压缩性对气流速度测量结果的影响；针对超音速流场，从理

五孔探针结构和校准

五孔探针结构和校准五孔探针是一种常用于气体动力学实验中的测量工具。

五孔探针的结构很简单，包含五个小孔以及相关的电路和测量器件。

在实际应用中，为了保证探针的准确性和精度，需要对探针进行校准。

五孔探针的结构五孔探针主要由五个小孔以及相关的电路和测量器件组成。

小孔通常位于探针的前端，可以是圆形或椭圆形。

小孔的布置方式取决于实验需要测量的量、所测量气体的流动特性以及探针的物理设计。

五个小孔主要分布在探针的两个不同面上，通常为三个小孔在一个面上，另外两个小孔在另一个面上，通过这种方式可以提高探针的测量精度。

此外，探针的外壳还包括了卡箍和电缆，用于安装和连接。

探针的电路中包括侵式和非侵式两种类型，以及不同类型的测量器件。

除了常规的压力、温度和速度传感器外，电路中还包含了数据处理器和数据记录器等设备。

五孔探针的校准五孔探针的校准是确保探针测量结果准确性的关键环节。

探针的校准主要包括两个方面：一是对探针小孔的准确位置和大小进行校准；二是对整个探针的性能进行综合测试，以确保探针在实际应用中的测量数据可靠。

小孔的校准是通过先进的仪器和计算方法实现的。

在校准过程中，探针的小孔被放置在一个已知流量的环境中，并测量小孔内的静压。

根据流量、小孔尺寸和静压之间的关系，可以用数学模型来计算小孔的位置和大小。

这样可以确保探针的精度和准确性。

整个探针的性能测试通常包括以下测量：风速、质量通量、温度、静压和动压等。

这些测量可以通过不同的方法来实现：例如，风速测量可以使用热线测量和全固态计（Solid State Probe）测量，而温度传感器可以使用热电偶和红外线传感器等。

在校准过程中，还需要注意探针的环境和工作条件，例如气体的密度、温度和湍流程度等。

这些因素将影响探针的测量性能和准确性。

因此，在进行校准前，需要对实验室和探针的工作条件进行检查和维护。

总结五孔探针是一种常用的气体动力学测量工具。

这种探针的结构简单，但在实际应用中需要经过专业的校准才能确保测量数据的精度和准确性。