化工流体流动与传热课件

2024/5/161东北石油大学东北石油大学化化 学学 化工化工 学学 院院版权所有：大庆石油学院化学化工学院 Copyright 2004 Daqing Petroleum Institute。All rights reserved。化工流体流动与传热化工流体流动与传热2023/8/31东北石油大学化东北石油大学化 学学 化工化工 学学 院版权所有：院版权所有：22024/5/162主讲主讲：余兰兰2023/8/32主讲：余兰兰化工流体流动与传热主讲：余兰兰化工流体流动与传热(第二章第二章)32024/5/163New Words And Expressionsfluidshear stressesincompressiblecompressiblesolid boundariespotential flowirrotational flowfrictionmechanical energyboundary layervelocity-gradient shear-stress fields流体流体剪应力剪应力不可压缩的不可压缩的可压缩的可压缩的固体壁面固体壁面势流势流无旋流无旋流摩擦摩擦机械能机械能边界层边界层速度梯度速度梯度剪应力场剪应力场2023/8/33New Words And Express42024/5/164turbulencevelocity fieldsteadyone-dimensional flowvectorcomponents scalareddieslaminar flowrheological behavior of fluidsNewtonian fluidsnon-Newtonian fluids 湍流湍流速度场速度场稳定的稳定的一维流动一维流动矢量矢量分量分量标量标量漩涡漩涡 层流层流流体流变性质流体流变性质牛顿型流体牛顿型流体非牛顿型流体非牛顿型流体2023/8/34turbulence湍流湍流52024/5/165threshold shear stressBingham plasticspseudoplastic fluiddilatant fluidshear-rate-thinningshear-rate-thickeningtime-dependent flowthixotropic liquidsrheopectic substancesviscositycritical velocityturbulent flow剪切应力的临界值剪切应力的临界值宾哈姆塑性流体宾哈姆塑性流体假塑性流体假塑性流体涨塑性流体涨塑性流体剪切速率递减剪切速率递减剪切速率递增剪切速率递增时变流时变流摇溶性液体摇溶性液体震凝性物质震凝性物质粘度粘度临界速度临界速度湍流湍流2023/8/35threshold shear stres62024/5/166the diameter of the tubedensityaverage linear velocitygroupReynolds numbervelocity fluctuationsqualitative and quantitativewall turbulencefree turbulencediameterpotential energyboundary layersthe bulk fluid velocitythe viscous sublayer管径管径密度密度平均线速率平均线速率群组群组雷诺准数雷诺准数脉动速度脉动速度定性和定量定性和定量壁面湍流壁面湍流自由湍流自由湍流直径直径势能势能边界层边界层主流体速度主流体速度粘滞底层粘滞底层2023/8/36the diameter of the t72024/5/167缓冲层缓冲层湍流层湍流层过渡过渡湍流强度湍流强度过渡长度过渡长度二维的二维的速度梯度速度梯度动量动量 漩涡漩涡尾流尾流剪应力剪应力压力损失压力损失边界层分离边界层分离the buffer layerthe turbulent zonetransitionintensity of turbulencetransition lengthtwo-dimensionalvelocity gradientsmomentumvorticeswakeshear stressespressure loss inboundary-layer separation2023/8/37缓冲层缓冲层the buffer layer82024/5/168the mass-balancecontinuity equationsthe linear-and angular-momentum-balance the mechanical-energy balance vectortensorstreamlines质量守恒质量守恒连续性方程式连续性方程式线性动量守恒和角动量守恒线性动量守恒和角动量守恒机械能守恒机械能守恒矢量矢量张量张量流线流线2023/8/38the mass-balance质量守恒质量守恒92024/5/169 Chapter 2 Fluid Flow2.1 Fluid Statics and Its Applications 2023/8/39 Chapter 2 Fluid Fl102024/5/1610Nature of Fluids uAn attempt to change the shape of a mass of fluid results in layers of fluid sliding over one another until a new shape is attained l流体是不能永久抵抗形变的物质。流体是不能永久抵抗形变的物质。l若想改变一定质量流体的形状，将导致流体中层与若想改变一定质量流体的形状，将导致流体中层与层之间相互滑动直至获得新的形状。层之间相互滑动直至获得新的形状。uA fluid is a substance that does not permanently resist distortion2023/8/310Nature of Fluids An 112024/5/1611uDuring the change in shape，shear stresses exist，the magnitudes of which depend upon the viscosity of the fluid and the rate of sliding，but when a final shape has been reached，all shear stresses will have disappeared u在变形时，存在剪应力，其大小取决于流体在变形时，存在剪应力，其大小取决于流体的黏度和滑动的速率，当最终形状确定后，的黏度和滑动的速率，当最终形状确定后，剪应力消失。剪应力消失。2023/8/311During the change in122024/5/1612v处于平衡的流体与剪应力无关。处于平衡的流体与剪应力无关。vA fluid in equilibrium is free from shear stressesv在给定的温度和压力下，流体的密度是常数，在工程上通在给定的温度和压力下，流体的密度是常数，在工程上通常以磅常以磅/立方英尺或公斤立方英尺或公斤/立方米来测量。立方米来测量。vAt a given temperature and pressure，a fluid possesses a definite density，which in engineering practice is usually measured in pounds per cubic foot or kilograms per cubic meter 2023/8/312处于平衡的流体与剪应力无关。处于平衡的流体与剪应力无关。A flui132024/5/1613vIf the density is but little affected by moderate changes in temperature and pressure，the fluid is said to be incompressible，and if the density is sensitive to changes in these variables，the fluid is said to be compressible v如果温度和压力轻度改变时对密度的影响很小，将该流体如果温度和压力轻度改变时对密度的影响很小，将该流体称为不可压缩的；若密度受这些变量的影响很大，则称称为不可压缩的；若密度受这些变量的影响很大，则称该流体为可压缩的。该流体为可压缩的。2023/8/313If the density is bu142024/5/16142.2 Fluid-Flow Phenomena 流动流体的行为在很大程度上取决于流体是否流动流体的行为在很大程度上取决于流体是否受固体边界的影响。受固体边界的影响。The behavior of a flowing fluid depends strongly on whether or not the fluid is under the influence of solid boundaries.1.Potential flow 2.2.1 Fluid flow2023/8/3142.2 Fluid-Flow Pheno152024/5/1615A moving fluid uninfluenced by stationary solid walls is not subject to shear,and shear stresses do not exist within it.不受固定固体壁面影响的流动流体就不受剪切力作不受固定固体壁面影响的流动流体就不受剪切力作用，且其内部不存在剪切应力。用，且其内部不存在剪切应力。2023/8/315A moving fluid uninf162024/5/1616The flow of incompressible fluids with no shear is called potential flow and is completely described by the principles of Newtonian mechanics and conservation of mass.无剪切力的不可压缩流体的流动称为无剪切力的不可压缩流体的流动称为“势流势流”，完全由牛，完全由牛顿力学和质量守恒原理来描述。顿力学和质量守恒原理来描述。vThe mathematical theory of potential flow is highly developed but is outside the scope of this bookv势流的数学理论已被深入研究，但不属于本书的范围。势流的数学理论已被深入研究，但不属于本书的范围。2023/8/316The flow of incompre172024/5/1617Potential flow has two important characteristics:v(1)neither circulations nor eddies can form within the stream,so that potential flow is also called irrotational flow,and v(2)friction cannot develop,so that there is no dissipation of mechanical energy into heat.v势流有两个重要的特征：势流有两个重要的特征：v（2）没有摩擦，因此没有机械能损耗变热的情况。）没有摩擦，因此没有机械能损耗变热的情况。v（1）在流动流体内不能生成漩涡，因此势流也称为无旋流）在流动流体内不能生成漩涡，因此势流也称为无旋流2023/8/317Potential flow has t182024/5/1618vA fundamental principle of fluid mechanics,originally stated by Prandtl in 1904,is that except for fluids moving at low velocities or possessing high viscosities,the effect of the solid boundary on the flow is confined to a layer of the fluid immediately adjacent to the solid wall.vPrandtl 在在1904年最先提出的流体力学基本原理中说，年最先提出的流体力学基本原理中说，除低速流动或黏度很大的流体外，固体边界对流动的影除低速流动或黏度很大的流体外，固体边界对流动的影响仅限于紧挨固体壁面的流体层内。响仅限于紧挨固体壁面的流体层内。2.Boundary layer2023/8/318A fundamental princi192024/5/1619v此流体层称为边界层，剪切力仅存在于这部分流体中。在此流体层称为边界层，剪切力仅存在于这部分流体中。在边界层之外，则是势流。边界层之外，则是势流。vThis layer is called the boundary layer,and shear forces are confined to this part of the fluid.Outside the boundary layer,potential flow survives.vMost technical flow processes are best studied by considering the fluid stream as two parts,the boundary layer and the remaining fluid.v对于大多数工艺流动过程，是将流体看作两部分对于大多数工艺流动过程，是将流体看作两部分边界层边界层及其以外的流体，进行了深入的研究。及其以外的流体，进行了深入的研究。2023/8/319此流体层称为边界层，剪切力仅存在于这部分此流体层称为边界层，剪切力仅存在于这部分202024/5/1620vIn some situations,the boundary layer may be neglected,and in others,such as flow through pipes,the boundary layer fills the entire channel,and there is no potential flow.v在在某某些些情情况况下下可可以以忽忽略略边边界界层层，而而在在另另外外一一些些时时候候边边界界层层充充满整个通道（像通过管道的流动），就没有势流。满整个通道（像通过管道的流动），就没有势流。vWithin the current of an incompressible fluid under the influence of solid boundaries,four important effects appear:v在在受受固固体体边边界界影影响响的的不不可可压压缩缩流流体体的的流流动动中中，有有四四个个重重要要的影响因素：的影响因素：2023/8/320In some situations,212024/5/1621l(1)the coupling of velocity-gradient and shear-stress fields,v（1）速度梯度与剪应力场的关系；）速度梯度与剪应力场的关系；v（2）湍流的开始；）湍流的开始；v（3）边界层的生成与发展；）边界层的生成与发展；v（4）边界层的分离。）边界层的分离。v(2)the onset of turbulence,v(3)the formation and growth of boundary layers,andv(4)the separation of boundary layers from contact with the solid boundary.2023/8/321(1)the coupling of 222024/5/16223.The Velocity FielduWhen a stream of fluid is flowing in bulk past a solid wall，the fluid adheres to the solid at the actual interface between solid and fluid u当流体大量流过固体壁面时，与固体紧挨着的流体当流体大量流过固体壁面时，与固体紧挨着的流体粘附在固体表面上。粘附在固体表面上。2023/8/3223.The Velocity Fiel232024/5/1623uThe adhesion is a result of the force fields at the boundary，which are also responsible for the interfacial tension between solid and fluid v这个粘附是力场在边界作用的结果，也与固体和流体间的界这个粘附是力场在边界作用的结果，也与固体和流体间的界面拉力有关。面拉力有关。vIf，therefore，the wall is at rest in the reference frame chosen for the solid-fluid system，the velocity of the fluid at the interface is zero u因此，若认为固体壁面相对于流体是静止的，则在界面上因此，若认为固体壁面相对于流体是静止的，则在界面上流体的速度为零。流体的速度为零。2023/8/323The adhesion is a re242024/5/1624uSince at distances away from the solid the velocity is finite，there must be variations in velocity from point to point in the flowing stream v因为距固体壁面一定距离处的速度是一定值，所以在流体因为距固体壁面一定距离处的速度是一定值，所以在流体中的速度逐点变化。中的速度逐点变化。vTherefore，the velocity at any point is a function of the space coordinates of that point，and a velocity field exists in the space occupied by the fluid v因此，任一点的流速是该点空间坐标的函数，且在流体中因此，任一点的流速是该点空间坐标的函数，且在流体中存在速度场。存在速度场。2023/8/324Since at distances a252024/5/16254.Laminar FlowvAt low velocities fluids tend to flow without lateral mixing，and adjacent layers slide past one another like playing cards v流体在低速流动时，没有横向混合，相邻层间就像扑克牌那流体在低速流动时，没有横向混合，相邻层间就像扑克牌那样互相滑过。样互相滑过。2023/8/3254.Laminar FlowAt lo262024/5/1626vThere are neither cross-currents nor eddiesv既没有横向流也没有漩涡。既没有横向流也没有漩涡。vThis regime is called laminar flowv这种情况称为层流。这种情况称为层流。vAt higher velocities turbulence appears，and eddies form，which，as discussed later，lead to lateral mixingv在较高流速下，出现湍流，形成引起横向混合的漩涡，将在在较高流速下，出现湍流，形成引起横向混合的漩涡，将在后面讨论。后面讨论。2023/8/326There are neither cr272024/5/16272.2.2 Newtonian and non-Newtonian FluidsvThe fact that at each point in a flowing fluid both a rate of shear and a shear stress exist suggests that these quantities may be related.v在流动流体中任一点上同时存在速度梯度和剪切应在流动流体中任一点上同时存在速度梯度和剪切应力这个事实提醒我们这些量之间可能是有联系的。力这个事实提醒我们这些量之间可能是有联系的。1.Newtonian and non-Newtonian Fluids2023/8/3272.2.2 Newtonian and 282024/5/1628vIn fact they are,the science of rheology deals with their coupling and the complex relations between them.v事实上的确如此，流变学论述它们之间的联系以及复杂关系。事实上的确如此，流变学论述它们之间的联系以及复杂关系。vFigure 2-1 shows several examples of the rheological behavior of fluids.v图图2-1示出流体流变性质的几个例子。示出流体流变性质的几个例子。2023/8/328In fact they are,th292024/5/1629Figure 2-1 Shear stress versus velocity gradient for Newtonian and non-Newtonian fluids2023/8/329Figure 2-1 Shear st302024/5/1630vThe curves are plots of shear stress vs.rate of shear and apply at constant temperature and pressure.v这些曲线是剪切应力对速度梯度作图的结果，适用于恒温恒压条件。vThe simplest behavior is that shown by curve A,which is a straight line passing through the origin.v最简单的特性如曲线最简单的特性如曲线A所示，这是一条过原点的直线所示，这是一条过原点的直线2023/8/330The curves are plots312024/5/1631lFluids following this simple linearity are called Newtonian fluids.vGases,true solutions,and noncolloidal liquids are Newtonian.v气体、实际溶液以及非胶体液体都是牛顿型的。气体、实际溶液以及非胶体液体都是牛顿型的。v遵循这个简单直线的流体称为牛顿型流体。遵循这个简单直线的流体称为牛顿型流体。2023/8/331Fluids following thi322024/5/1632v图图2-1中其他曲线表示非牛顿型流体的流变性质。中其他曲线表示非牛顿型流体的流变性质。vThe other curves shown in Fig.2-1 represent the rheological behavior of liquids called non-Newtonian.lSome liquids,e.g.,sewage sludge,do not flow at all until a threshold shear stress,denoted by ,is attained and then flow linearly at shear stresses greater than .v某些液体，如污泥浆，在其剪切应力达到临界值（记作某些液体，如污泥浆，在其剪切应力达到临界值（记作0）以前根本不流动，超过此值，流动中剪切应力则从以前根本不流动，超过此值，流动中剪切应力则从0起线性起线性增长。增长。2023/8/332图图2-1中其他曲线表示非牛顿型流体的流变中其他曲线表示非牛顿型流体的流变332024/5/1633lCurve B is an example of this relation.Liquids acting this way are called Bingham plastics.l曲线曲线B是这个关系的例子。这类液体称为宾哈姆塑性流体。是这个关系的例子。这类液体称为宾哈姆塑性流体。vLine C represents a pseudoplastic fluid.vC线表示假塑性（或拟塑性）流体。线表示假塑性（或拟塑性）流体。vThe curve passes through the origin,is concave downward at low shears,and becomes linear at high shears.v该线通过原点，在低剪切力时凹边向下，高剪切力时则成直该线通过原点，在低剪切力时凹边向下，高剪切力时则成直线。线。2023/8/333Curve B is an exampl342024/5/1634lRubber latex is an example of such a fluid.l乳胶就是这样一种流体。乳胶就是这样一种流体。lCurve D represents a dilatant fluid.The curve is concave upward at low shears and becomes linear at high shears.l曲线曲线D代表涨塑性流体，在低剪切力时凹边向上，高剪切力代表涨塑性流体，在低剪切力时凹边向上，高剪切力时也成直线。时也成直线。2023/8/334Rubber latex is an e352024/5/1635lQuicksand and some sand-filled emulsions show this behavior.l流沙以及某些充满沙子的乳浊液表现出这种性质。流沙以及某些充满沙子的乳浊液表现出这种性质。vPseudo plastics are said to be shear-rate-thinning and dilatant fluids shear-rate-thickening.v假假塑塑性性流流体体称称为为剪剪切切速速率率递递减减型型流流体体，涨涨塑塑性性流流体体称称为为剪剪切速率递增型流体。切速率递增型流体。2023/8/335Quicksand and some s362024/5/16362.Viscosity lIn a Newtonian fluid the shear rate obviously is proportional to the shear stress.l在牛顿型流体中，剪切速率显然是与剪切应力成正比的。在牛顿型流体中，剪切速率显然是与剪切应力成正比的。2023/8/3362.Viscosity In a Ne372024/5/1637lThe proportionality constant is called the viscosity and is defined by the equationl比例常数比例常数称为黏度，其定义由方程（称为黏度，其定义由方程（2-1）给出：）给出：（2-1）2023/8/337The proportionality 382024/5/16383.TurbulencelThe distinction between laminar and turbulent flow was first demonstrated in a classic experiment by Osborne Reynolds,reported in 1883.l层流与湍流的区别由层流与湍流的区别由Osborne Reynolds在在1883年首先从年首先从试验中发现。试验中发现。vThe equipment used by Reynolds is shown in Fig.2-2.vReynolds所用的设备示于图所用的设备示于图2-2。(1)Turbulence2023/8/3383.TurbulenceThe dis392024/5/1639 Figure 2-2 Reynolds experiment2023/8/339402024/5/1640vReynolds found that,at low flow rates,the jet of colored water flowed intact along with the mainstream and no cross mixing occurred.lReynolds发现，在低流速下，染色水流与主流体一起流发现，在低流速下，染色水流与主流体一起流动，不受任何影响，不发生横向混合。动，不受任何影响，不发生横向混合。lThe behavior of the color band showed clearly that the water was flowing in parallel straight lines and that the flow was laminar.l染色水的特征表明水是以平行直线的方式流动，即层流。染色水的特征表明水是以平行直线的方式流动，即层流。2023/8/340Reynolds found that,412024/5/1641vWhen the flow rate was increased,a velocity,called the critical velocity was reached at which the thread of color disappeared and the color diffused uniformly throughout the entire cross section of the stream of water.l当流速增加，达到一个临界速度时，染色水流消失，而颜色当流速增加，达到一个临界速度时，染色水流消失，而颜色在整个水流中均匀地扩散。在整个水流中均匀地扩散。2023/8/341When the flow rate w422024/5/1642lThis behavior of the colored water showed that the water no longer flowed in laminar motion but moved erratically in the form of crosscurrents and eddies.l染色水流的这个特征表明水不再是层流流动，而是以涡流和染色水流的这个特征表明水不再是层流流动，而是以涡流和漩涡的形式不稳定地移动。漩涡的形式不稳定地移动。vThis type of motion is turbulent flow.l这个运动类型称为湍流。这个运动类型称为湍流。2023/8/342This behavior of the432024/5/1643 (2)Reynolds Number and Transition from Laminar to Turbulent Flow2023/8/343 (2)Reynolds Number442024/5/1644uReynolds studied the conditions under which one type of flow changes into the other and found that the critical velocity,at which laminar flow changes into turbulent flow,depends on four quantities:vReynolds研究了流动类型转变的条件，并发现了临界速度，研究了流动类型转变的条件，并发现了临界速度，在此值下层流变为湍流。在此值下层流变为湍流。v该值与该值与4个量有关：管径、液体的黏度、密度和平均线速度。个量有关：管径、液体的黏度、密度和平均线速度。vthe diameter of the tube,and the viscosity,density,and average linear velocity of the liquid.2023/8/344Reynolds studied the452024/5/1645lFurthermore,he found that these four factors can be combined into one group and that the change in kind of flow occurs at a definite value of the group.l进而，他又发现这进而，他又发现这4个因素可被组成一个数群，该数群在某个因素可被组成一个数群，该数群在某一定值时，流动的类型发生变化。一定值时，流动的类型发生变化。vThe grouping of variables so found wasv这些变量的组合形式为这些变量的组合形式为2023/8/345Furthermore,he foun462024/5/1646 （2-2）where d=diameter of tube u=average velocity of liquid =density of liquid =viscosity of liquid2023/8/346 （2-2）where d=d472024/5/1647vThe dimensionless group of variables defined by Eq.(2-2)is called the Reynolds number，Re.v由方程（由方程（2-2）定义的这些变量的无因次数群称为雷）定义的这些变量的无因次数群称为雷诺准数。诺准数。v It is one of the named dimensionless groups listed in Appendix 5.v它是附录它是附录5中所列的无因次数群之一。中所列的无因次数群之一。2023/8/347The dimensionless gr482024/5/1648vIts magnitude is independent of the units used,provided the units are consistent.v它的值与所使用的单位制无关，只要单位一致即可。它的值与所使用的单位制无关，只要单位一致即可。vAdditional observations have shown that the transition from laminar to turbulent flow actually may occur over a wide range of Reynolds numbers.v另外的观察表明，由层流到湍流的过渡可以发生在一个较大另外的观察表明，由层流到湍流的过渡可以发生在一个较大的雷诺数范围内。的雷诺数范围内。2023/8/348Its magnitude is ind492024/5/1649vLaminar flow is always encountered at Reynolds numbers below 2,100,but it can persist up to Reynolds numbers of several thousand under special conditions of well-rounded tube entrance and very quiet liquid in the tank.v雷诺数低于雷诺数低于2100时，总是层流流动，但在管口很圆，箱内时，总是层流流动，但在管口很圆，箱内液体很平静的特殊条件下，在雷诺数达到几千时仍可保持液体很平静的特殊条件下，在雷诺数达到几千时仍可保持层流。层流。2023/8/349Laminar flow is alwa502024/5/1650vUnder ordinary conditions of flow,the flow is turbulent at Reynolds numbers above about 4,000.v在通常的流动条件下，雷诺数大于在通常的流动条件下，雷诺数大于4000时就是湍流流动。时就是湍流流动。v Between 2,100 and 4,000 a transition,or dip,region is found,where the type of flow may be either laminar or turbulent,depending upon conditions at the entrance of the tube and on the distance from the entrance.v在在2100和和4000之之间间是是过过渡渡区区，流流动动类类型型不不是是层层流流就就是是湍湍流流，取决于管口的条件以及到管口的距离。取决于管口的条件以及到管口的距离。2023/8/350Under ordinary condi512024/5/1651vReynolds experiments were conducted with water,but they have long since been shown to apply to other liquids and also to gases.v雷诺实验中用的是水，但也适用于其他液体雷诺实验中用的是水，但也适用于其他液体和气体。和气体。2023/8/351Reynolds experiment522024/5/1652(3)Nature of TurbulencevBecause of its importance in many branches of engineering,turbulent flow has been extensively investigated in recent years,and a large literature has accumulated on this subject.v由于湍流在许多工程学科中的重要性，近些年来人们已对由于湍流在许多工程学科中的重要性，近些年来人们已对其进行了广泛的研究，发表了许多文章。其进行了广泛的研究，发表了许多文章。2023/8/352(3)Nature of Turbule532024/5/1653uThe first kind of turbulence is called wall turbulence and the second kind free turbulence.vWall turbulence appears when the fluid flows through closed or open channels or past solid shapes immersed in the stream.v前一种湍流称为壁面湍流，后一种称为自由湍流。前一种湍流称为壁面湍流，后一种称为自由湍流。v流体在封闭或敞开的流道中流动时，或流过浸没在流体中的流体在封闭或敞开的流道中流动时，或流过浸没在流体中的固体时出现壁面湍流。固体时出现壁面湍流。()Types of Turbulence2023/8/353The first kind of tu542024/5/1654uFree turbulence appears in the flow of a jet into a mass of stagnant fluid or when a boundary layer separates from a solid wall and flows through the bulk of the fluid.u在一射流流入大量停滞流体内，或一边界层从固体壁面分离在一射流流入大量停滞流体内，或一边界层从固体壁面分离流入流体主流中时，发生自由湍流。流入流体主流中时，发生自由湍流。2023/8/354Free turbulence appe552024/5/1655vLarge eddies are continually formed.They break down into smaller eddies,which in turn evolve still smaller ones.Finally,the smallest eddies disappear.v大漩涡不断形成，破碎成较小的漩涡，又依次变成更小的。大漩涡不断形成，破碎成较小的漩涡，又依次变成更小的。最终，最小的漩涡消失最终，最小的漩涡消失 vTurbulent flow consists of a mass of eddies of various sizes coexisting in the flowing stream.v共存于流动流体中的大量大大小小的漩涡构成了湍流流动。共存于流动流体中的大量大大小小的漩涡构成了湍流流动。()Eddies in Turbulence2023/8/355Large eddies are con562024/5/1656vAny given eddy possesses a definite amount of mechanical energy,much like that of a small spinning top.v任何指定的漩涡都具有一定量的机械能，很像旋转的小陀螺。任何指定的漩涡都具有一定量的机械能，很像旋转的小陀螺。vThe energy of the largest eddies is supplied by the potential energy of the bulk flow of the fluid.v最大漩涡的能量来自流体主流中的势能。最大漩涡的能量来自流体主流中的势能。()Energy in Turbulence2023/8/356Any given eddy posse572024/5/16572.2.3 Flow in Boundary Layers vA boundary layer is defined as that part of a moving fluid in which the fluid motion is influenced by the presence of a solid boundary.v所谓边界层，就是流动流体中受固体边界影响的部所谓边界层，就是流动流体中受固体边界影响的部分。分。1.Boundary layer2023/8/3572.2.3 Flow in Bounda582024/5/1658v图图2-3中所示为平行于一薄板流动的流体形成边界层的示例。中所示为平行于一薄板流动的流体形成边界层的示例。vAs a specific example of boundary-layer formation consider the flow of fluid parallel with a thin plate,as shown in Fig.2-3.2023/8/358图图2-3中所示为平行于一薄板流动的流体形中所示为平行于一薄板流动的流体形592024/5/1659Figure 2-3 Prandtl boundary layer2023/8/359Figure 2-3 Prandtl 602024/5/1660lIn Fig.2-3 the dotted line OL is so drawn that the velocity changes are confined between this line and the trace of the wall.l在图在图2-3中的虚线中的虚线OL表明速度仅在该线与壁面之间变化。表明速度仅在该线与壁面之间变化。vBecause the velocity lines are asymptotic with respect to distance from the plate,it is assumed,in order to locate the dotted line definitely,that the line passes through all points where the velocity is 99 percent of the bulk fluid velocity u.v由于速度曲线相对遇到平板的距离呈渐近线变化，为了明确虚线的位由于速度曲线相对遇到平板的距离呈渐近线变化，为了明确虚线的位置，假定该线上各点的速度均等于主流体速度置，假定该线上各点的速度均等于主流体速度u 的的99%。2023/8/360In Fig.2-3 the dott612024/5/1661lLine OL represents an imaginary surface which separates the fluid stream into two parts:vone in which the fluid velocity is constant and the other in which the velocity varies from zero at the wall to a velocity substantially equal to that of the undisturbed fluid.vOL线代表一个设想的面，该面将流体分为两部分：线代表一个设想的面，该面将流体分为两部分：v一部分流体的速度是常数，另一部分的速度由壁面处的零变一部分流体的速度是常数，另一部分的速度由壁面处的零变化至基本上等于不受干扰流体的速度。化至基本上等于不受干扰流体的速度。2023/8/361Line OL represents a622024/5/1662lThis imaginary surface separates the fluid that is directly affected by the plate from that in which the local velocity is constant and equal to the initial velocity of the approach fluid.v这个假想面将流体分成速度直接受壁面影响的和局部速度为这个假想面将流体分成速度直接受壁面影响的和局部速度为常数并且与流入的流体最初速度相等的两类流体。常数并且与流入的流体最初速度相等的两类流体。vThe zone,or layer,between the dotted line and the plate