流体力学课件第一章

1、2022/9/11 School of Jet PropulsionBeihang University.FLUID MECHANICS2022/9/12 Chapter 1 Introduction 1.1 Preliminary Remarks When you think about it, almost everything on this planet either is a fluid or moves within or near a fluid. -Frank M. WhiteWhat is a fluid?2022/9/13The concept of a fluidA so

2、lid can resist a shear stress(剪切应力)by a static deformation, a fluid can not.Any shear stress applied to a fluid, no matter how small, will result in motion of that fluid.The fluid moves and deforms continuously as long as the shear is applied.2022/9/14What is Fluid Mechanics Fluid Mechanics is the s

3、tudy of fluid either in motion (Fluid Dynamics 流体动力学) or at rest(Fluid Statics 流体静力学) and subsequent effects of the fluid upon the boundaries, which may be either solid surfaces or interfaces with other fluids.2022/9/15The famous collapse of the a Narrow Bridge in 1940Curved shoot (Banana shoot)Nosp

4、inSpinwhy2022/9/16Boeing 74770.764.4 19.41 (m) 395 000kgAn-225 8488.418.1 (m)600,000kg How can the airplane fly?Drag & Lift2022/9/172022/9/18The engine of a turbofan(涡扇) jet2022/9/19；2022/9/110History and Scope of Fluid MechanicsPre-history:Sailing ships with oars(橹桨) and irrigation system were both

5、 known in prehistory2022/9/111Archimedes(285-212 BC)Parallelogram law for addition of vectors Law of buoyancy2022/9/112Leonardo da Vinci(1452-1519) * Equation of conservation of mass in one-dimensional steady flow* Experimentalist* Turbulence2022/9/113Isaac Newton(1642-1727)Laws of motionLaws of vis

6、cosity of Newtonian fluid2022/9/114 18th centuryMathematicians：Euler（欧拉）： Euler equationBernoulli (伯努利) ： Bernoulli equationFrictionless(无粘) flow solutionsDAlembert（达朗贝尔）： DAlembert paradox（佯谬，疑题）Engineers： Hydraulics （水力学）relaying on experimentChannels ，Ship resistance， Pipe flows，Wave turbinePitot

7、 Venturi Torricelli Poiseuille2022/9/11519th centuryNavier (1785-1836) & Stokes (1819-1905)N-S equation viscous flow solutionReynolds (1842-1912) TurbulenceFamous experiment on transition Reynolds Number2022/9/11620th centuryLudwig Prandtl (1875-1953)Boundary theory(1904)To be the single most import

8、ant tool in modern flow analysis.The father of modern fluid mechanicsVonkarman(1881-1963)I.taylor(1886-1975)Laid foundation for the present stateof the art in fluid mechanics2022/9/1171.2 The Fluid as a Continuum (连续介质）Density(密度)Elemental volume（流体微团、流体质点）* Large enough in microscope（微观）10-9mm3 of

9、air at standard conditions contains approximately 3107 molecules.So density is essentially a point function and fluid properties can be thought of as varying continually in space .* Small enough in macroscope（宏观）.Most engineering problems are concerned with physical dimensions much larger than this

10、limiting volume.2022/9/118The elemental volume must be small enough in macroscopeSuch a fluid is called a continuum, which simply means that its variation in properties is so smooth that the differential calculus can be used to analyze the substance.2022/9/1191.3 Some Properties of fluids1.viscosity

11、(粘性)* Definition： When a fluid is sheared（剪切）, it begins to move. Subsequently, a pair of forces appear on the shear surface, which resists the shear motion of the fluid. This is called viscosityThis resistant force is shear stress.(剪切应力,内摩擦应力)In fact, this shear motion of a fluid is a kind of defor

12、mation（变形）* The nature of viscosity：For liquid is cohesion（结合）(movie) For gas is the transport of momentum（动量输运）(movie)2022/9/120m : Coefficient of viscosity (粘性系数)FT/L2n = m / r: Kinematic viscosity (运动学粘性系数)L2/TVelocity gradient* Newtonian law of viscosity(牛顿粘性定律，牛顿内摩擦定律)UUu(y)xyShear stressThe li

13、near fluid, which follow Newtonian resistance law,is called Newtonian flow. （牛顿流动、牛顿流体）The velocity gradient is in fact a kind of deformation.Real fluid (Viscous) , Ideal fluid (Inviscid & Frictionless)2022/9/1212. Compressibility(压缩性) pressible(不可压): r = constMost liquid flows are treated as pressi

14、ble.Only 1 percent increase if pressure increase by 220Compressible（可压缩）: r = r (P.T)Gases can also be treated as pressible when their velocity is less than 0.3 Ma numbers3. State Relations for Gases Perfect-gas Law（理想气体状态方程）2022/9/1224.Thermal Conductivity(热传导) : heat flux in n direction per unit a

15、reak: coefficient of thermal conductivityT: temperature n: direction of heat transfer Fouriers law of heat conduction2022/9/1231.4 Two different points of view in analyzing problems in mechanics* The Eulerian view (欧拉观点)and the Lagrangian view （拉格朗日观点） The Eulerian view is concerned with the field o

16、f flow, appropriate to fluid mechanics.The Lagrangian view follows an individual particle moving though the flow,appropriate to solid mechanics.The contrast of two frames2022/9/124* Flow classification(流动分类)According to Eulerian view, any property is function of coordinates（space） and time. In Carte

17、sian system (直角坐标系) ，it can be expressed asf(x,y,z,t)x,y,z,t: Eulerian variable component ( 欧拉变数)f: Function of only one coordinate component, one-dimensional ( 一维 1-D）. In the like manner, two-dimensional （ 二维 2-D） , three-dimensional ( 三维 3-D ) : Function of time unsteady (非定常)Otherwise steady (定常

18、) 2022/9/125OneTwo dimensionalThreeSteadyUnsteadyCompressible pressibleViscousInviscid2022/9/1261.5 Streamline(流线),Pathline(迹线) & Flowfield (流场)* What is a streamline A streamline is the line everywhere tangent to the velocity vector at a given instant.2022/9/127 A pathline is the actual path traver

19、sed by a given fluid particles.For steady flow: Streamline = Pathline* What is a pathlinePathlines in steady flowPathlines in unsteady flow2022/9/128Flow Pattern (流型、流普、流线族）Stream surface(流面)& Streamtube (流管）Flow pattern : a set of streamlinesStreamsurface: a collection of all the streamlines passin

20、g through a line which is not a streamline.Stream line can not intersect（相交），except for singularity point(奇点)Streamtube : a closed collection of streamlines.No flow across streamtube walls2022/9/129Flow field (流场) ： In a given flow situation, the properties of the fluid are functions of position and

21、 time, namely space-time distributions of the fluid properties. 2022/9/130Streamline equation(流线方程)ds - Infinitesimal (无穷小)dydxds2022/9/131Example:Given the steady two-dimensional velocity distribution u=kx,v=-ky,w=0,where k is a positive constant.Compute and plot the streamlines of the flow,including direction.Solution: Since time (t) does not appear explicitly,the motion is steady,so that streamlines,pathlines will coincide.Since w=0,the motion is two-dimensional.Integrating:Hyperbolas(双曲