流体力学英文课件
(流体力学与传热英文课件)Pressure drop and loss due to friction
The equation(1.4-10) is the equation usually used to calculate skin friction loss in straight pipe.
For laminar flow only, combining Eqs. (1.4-20 ) and (1.4-10) .gives
f 16 Re
64
Re
(1.4-22 )
It is not possible to predict theoretically the Fanning friction factor f for turbulent flow as was done for laminar flow.
1.4.3 Turbulent Flow in Pipes and Channels
Although the problem has not been completely solved, useful relationships are available.
• For turbulent flow the friction factor must be determined empirically, and it not only depends upon the Reynolds number but also on surface roughness of the pipe.
L R
Rearranging equation (1.4-2 ) gives
w
Rp 2L
Substituting from equation above into equation (1.4-7) gives
fV 2 w /2R V p 2//2 2 L4D L pf V 2 2
大学物理：第五章 流体力学 (Fluid Mechanics)
Aneurysm(动脉瘤)
若处动脉的半径增大N倍 血液流速就缩小N2倍 病灶处的压强大幅度上降 由于该处血管壁薄，使血 管容易破裂。
上海交通大学 物理系
Atherosclerosis（动脉粥样硬化）
动脉病变从内膜开始。一 般先有脂质和复合糖类积 聚、出血及血栓形成，纤 维组织增生及钙质沉着， 并有动脉中层的逐渐蜕变 和钙化，病变常累及弹性 及大中等肌性动脉，
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? hB=0.5m
P0
?
0
1 2
v
2 c
ghc
Pc
1 2
v
2 A
ghA
PA
vc 2ghA 6 m / s
B,C点
1 2
v
2 c
ghc
Pc
1 2
v
2 B
ghB
PB
SBvB SCvC
PB P0 0.85g
PB P0 ghD
hD 0.85m
上海交通大学 物理系
一柱形容器，高1m、截面积为5x10-2 m2，储满水 ，在容器底部有一面积为2x10-4 m2 的水龙头，问 使容器中的水流尽需多少时间？
度变小，压强变大
压力
上海交通大学 物理系
马格纳斯效应
上海交通大学 物理系
机翼受到的举力
Q：用机翼上、下的流速变化，讨论其受到的升力，是否合理
上海交通大学 物理系
上海交通大学 物理系
压强的范围
太阳中心 地球中心 实验室能维持的最大压强 最深的海沟 尖鞋跟对地板 汽车轮胎 海平面的大气压 正常的血压 最好的实验室真空
四、液流连续原理(Principle of continuity of flow)
汪志明版流体力学英文版chap8
§ 8.1 Equation of Tubular Flow
With solid wall condition, the mechanical energy equation in steady volumetric force field is:
2 2 ~ ~ ~ U c T dA U c T dA h Tw T dA 2 2 A2 A1 A3
The fellow equation is gotten by using integral median theory,
Chapter 8 One-Dimensional Tubular Flow
§ 8.1 Equation of Tubular Flow 1) Flow Type There are two kinds of flow type basically: laminar flow, which streamline is dependent, turbulent flow,which streamline disturb each other. ' The upper critical Reynolds Re c number is gained when laminar flow translate turbulent flow. The lower critical Reynolds Re c number is gained when turbulent flow translate laminar flow.
§ 8.1 Equation of Tubular Flow
Determine flow type laminar flow Re Re c ' Re c Re Re c transition flow Re Re turbulent flow c The empirical lower critical Reynolds number is between 2000 and 2320 for tubular flow. The upper critical Reynolds number is usually determined by actually flowing condition.
流体力学英文版第二章静力学——Hydrostatic
δFs = −
∂pˆi + ∂p ˆj + ∂p kˆ ∂x ∂y ∂z
δxδyδz = −∇pδxδyδz
6 / 32
Basic equation for pressure field
Notes
Besides the surface forces, the body force due to the weight of the
δxδz
It is simplified to
∂p
δFy
=
− δxδyδz ∂y
Similarly, for the x and z directions, the resultant surface forces are
∂p
∂p
δFx
=
− δxδyδz, ∂x
δFz
=
− ∂z
δxδyδz
In the vector form, it can be expressed as
element is
δFv = −ρgδxδyδzkˆ
The whole resultant force acting on the rectangular element of fluid can be expressed as
δF = δFs + δFv = −∇pδxδyδz − ρgδxδyδzkˆ = δma
Figure 4: Face and body forces acting on a rectangular element
5 / 32
Basic equation for pressure field
Notes
In the y direction
∂p δy
流体力学_英文课件第1章
∂T q = −k ∂n
q: heat flux in n direction per unit area
k: coefficient of thermal conductivity T: temperature n: direction of heat transfer
1.3 The Fluid as a Continuum (连续介质 连续介质） 连续介质
Turbulence Famous experiment on transition Reynolds Number
20th century
Ludwig Prandtl (1875-1953)
Boundary layer theory(1904)
To be the single most important tool in modern flow analysis.
Shear stress
y
U U
du τ∝ dy
Velocity gradient
u(y)
x
du τ =µ dy
The velocity gradient is comparable to deformation.
This kind of linear fluid is called Newtonian fluid. （牛顿流体 牛顿流体） 牛顿流体
陆利蓬 李秋实 王洪伟 景晓东 邹正平 李志平 （4-5 班） （1-3班）
Grades:
30% homework + 70% final exam
Contents
Chapter 1………Introduction (6 hours) Chapter 2………Fluid Statics (4 hours) Chapter 3………Integral Relations (12 hours) Chapter 4………Differential Relations (8 hours) Chapter 5………Boundary Layer (6 hours) Chapter 6………Flow Compressibility (2 hours) Chapter 7………Vorticity (4 hours) Summary (2 hours)
流体力学 英文课件第5章
u u′ = U
η′ =
y
δ
1 0
1 =
1 1 0
y η= νx U
δ ≈ 5.5 νx
U
u = φ (η ) U
18
Put
u = φ (η ) into boundary layer equation U 吴望一《流体力学》下册） （吴望一《流体力学》下册）
′′ + 1 ( φ (η )d η )φ ′ = 0 φ 2 ∫
2
u = a + by + cy
BC:
y =0 u =0
y = δ u ≈U
∂u ≈0 ∂y
a = 0, b =
2U
δ
,c = -
U
δ2
u 2y y2 = − 2 U δ δ
0 ≤ y ≤ δ (x)
10
θ = ∫0
δ
δ
u u (1− )dy U U
u 2y y2 = − 2 U δ δ
θ =∫ (
f ′(η) =
u U
0.0 1.0 … 5.0 8.0
0.0 0.32979 … 0.99155 1.00000 1.00000
δ
5.0 = x Rex
δ * .721
x = Rex
θ 0.664
x = Rex
1.328 0.664 CD = Cf = Re L Rex
∞
δ
δ* H= ≈ 2.59 θ
U =U V = 0
(Inviscid Flow)
dU 1 dP U =− dx ρ dx
16
Euler Equation U ∂U + V ∂U = − 1 dP ∂x ∂y ρ ∂x
流体力学英语
流体力学英语B本构方程constitutive equation壁面摩擦速度friction velocity壁面剪应力skin friction壁面摩擦阻力friction drag边界层boundary layer边界层方程boundary layer equation 边界层分离boundary layer separation 边界层厚度boundary layer thickness 边界层理论boundary layer theory边界层转捩boundary layer transition 表面波surface wave表面力surface force表面张力surface tension波wave波前wave front波数wave number波阵面wave front波高wave height波谷trough波节node波能wave energy波群wave group波速wave speed, wave velocity 波阻wave drag伯努利定理Bernoulli theorem伯努利方程Bernoulli equation泊肃叶流动Poiseulle flow不规则波irregular wave不可压缩流动incompressible flow不可压缩流体incompressible fluid不可压缩性incompressibility布拉休斯解Blasius solution部分相似partial similarity背压back pressureC测速法anemometry层流laminar layerAadded mass 附加质量adiabatic flow 绝热流aerodynamicforce气动力aerodynamics 空气动力学airfoil 翼型anemometer 流速计anemometry 测速法angle ofattack攻角angle ofattack迎角attached point 附着点attachedshock wave附体激波attachedvortex附着涡axisymmetricflow轴对称流Bback flow 反压（背压）back flow 回流Bernoulliequation伯努利方程Bernoullitheorem伯努利定理Blasiussolution布拉休斯解blockage 堵塞blockageeffect堵塞效应bluff body 钝头体blunt body 钝体boundarylayer边界层层流边界层laminar boundary layer 超声速流动supersonic flow潮波tidal wave冲击波shock wave出口压力exit pressure船波ship wave次层sublayer猝发过程bursting processD达朗贝尔佯谬d’Alembert paradox当地马赫数local mach number等熵流动isentropic flow动力相似dynamic similarity动力粘性dynamic viscosity动量方程momentum equation 动量厚度momentum thickness 动量守恒conservation堵塞blockage堵塞效应blockage effect对流convection钝体blunt body钝头体bluff body多管压强计multiple manometerE二次流Secondary flow二维流动Two dimensional flowF反流reverse flow反射reflection boundarylayer附面层boundarylayer equation边界层方程boundarylayerseparation边界层分离boundarylayer theory边界层理论boundarylayerthickness边界层厚度boundarylayertransition边界层转捩burstingprocess猝发过程Ccapillarity 毛细（管）作用chord 翼弦circulation 环量circulation 环流coefficient of viscosity粘性系数coherentstructure拟序结构coherentstructure相干结构complexpotential复势complexvelocity复速度compressibleflow可压缩流compressiblefluid可压缩流体compressionwave压缩波反压（背压）back flow非定常流动unsteady flow非均匀流动nonuniform flow非牛顿流体non-Newtonian fluid非牛顿流体力学non-Newtonian fluid mechanics 非线性波nonlinear wave非线性不稳定性nonlinear instability分离点separation point分离流separated flow分子扩散molecular diffusion风洞wind tunnel风速管pitot-static tube浮体floating body弗劳德数Froude number复势complex potential复速度complex velocity附加质量added mass附面层boundary layer附体激波attached shock wave附着点attached point附着涡attached vortexG高超声速流动hypersonic高速空气动力学high-speed aerodynamics 攻角angle of attack孤立子soliton拐角流动corner flow管流pipe flow规则波regular waveH亥姆霍兹定理Helmholtz theorem焓厚度enthalpy thickness耗散dissipation computational fluid mechanics计算流体力学conservation 动量守恒conservationof energy能量守恒conservationof mass质量守恒continuousmediumhypothesis连续介质假设constitutiveequation本构方程controlvolume控制体积convection 对流corner flow 拐角流动Coutte flow 库埃特流criticalReynoldsnumber临界雷诺数Dd’Alembertparadox达朗贝尔佯谬deep waterwave深水波detachedshock wave脱体激波differentialpressure压差diffraction 绕射diffusion 扩散diffusivity 扩散性dimensionless parameter无量纲参数dispersion 色散displacement 位移厚宏观力学macroscopic mechanics环量circulation环流circulation回流back flow汇sinkJ迹线path, pathline激波shock wave激波阵面shock front几何相似geometric similarity计算流体力学computational fluid mechanics 剪切层shear layer剪切流shear flow减阻drag reduction近场流near field flow静压管static(pressure)tube静压头static head镜象法image method局部相似local similarity绝热流adiabatic flow均匀流uniform flowK卡门涡街Karman vortex street可压缩流compressible flow可压缩流体compressible fluid空气动力学aerodynamics孔板流量计orifice meter控制方程governing equation控制体积control volume库埃特流Coutte flow跨声速流transonic flow扩散diffusion扩散性diffusivity thickness 度dissipation 耗散dissociation 离解disturbance, perturbation扰动doublet,dipole偶极子dragreduction减阻drag,resistance阻力dynamicsimilary动力相似dynamicviscosity动力粘性Eeddy 涡团eddy current 涡流eddy viscosity涡粘性energyequation能量方程energytransfer能量传递energytransport能量输运enstrophy 涡量拟能enthalpythickness焓厚度equation ofstate状态方程Eulerequation欧拉方程Euler number 欧拉数exit pressure 出口压力external flow 外流库塔－儒可夫斯基条件Kutta-Zhukowski condition科尔莫戈罗夫长度Kolmogorov lengthL拉瓦尔喷管Laval nozzle兰金－于戈尼奥条件Rankine-Hugoniot condition雷诺数Reynolds number离解dissociation连续介质假设continuous medium hypothesis 连续介质力学mechanics of continuous medium 临界雷诺数critical Reynolds number流场flow field流动参量flow parameter流动分离flow separation流动稳定性flow stability流动显示flow visualization流管stream tube流函数stream function流量flowrate, flow discharge流量计flowmeter流面stream surface流速计anemometer流体动力学fluid dynamics流体运动学fluid kinematics流体质点fluid particle流线streamlineM马赫波Mach wave马赫角Mach angle马赫数Mach number马赫线Mach lineFfar field boundarycondition远场边界条件far field flow 远场流floating body 浮体flow field 流场flow parameter流动参量flowseparation流动分离flow stability 流动稳定性flowvisualization流动显示flowmeter 流量计flowrate, flow discharge 流量fluiddynamics流体动力学fluidkinematics流体运动学fluid particle 流体质点free jet 自由射流free stream 自由流freestreamline自由流线free surface 自由面friction drag 壁面摩擦阻力friction loss 摩擦损失frictionvelocity壁面摩擦速度frictionvelocity摩擦速度Froudenumber弗劳德数马蹄涡horseshoe vortex脉线streak line毛细（管）作用capillarity幂律流体power law fluid摩擦速度friction velocity摩擦损失friction lossN纳维—斯托克斯方程Navier-Stokes equation 内流internal flow能量传递energy transfer能量方程energy equation能量守恒conservation of energy 能量输运energy transport 拟序结构coherent structure粘度测定法viscometry粘度计viscometer粘性流（动）viscous flow粘性流体viscous fluid粘性系数coefficient of viscosity 牛顿流体Newtonian fluid O欧拉方程Euler equation欧拉数Euler number偶极子doublet, dipoleP喷管nozzle皮托管Pitot tube平面流plane flow普朗特—迈耶流动Prandtl-Meyer flowGgas dynamics 气体动力学geometricsimilarity几何相似governing equation控制方程governing equation支配方程gravity wave 重力波HHelmholtz theorem亥姆霍兹定理high-speed aerodynamics高速空气动力学homoentropic flow均熵流horseshoe vortex马蹄涡hot-filmanemometer热膜流速计hot-wire anemometer热线流速计hydraulicradius水力半径hydrodynamic pressure液体动力学hydrodynamics水动力学hydrogen bubblemethod氢泡法hydrostatic pressure液体静压hydrostatics 水静力学hypersonic 高超声速流动普朗特数Prandtl numberQ气动力aerodynamic force气体动力学gas dynamics前缘涡leading edge vortex浅水波shallow water wave氢泡法hydrogen bubble methodR染色线streakline扰动disturbance, perturbation绕射diffraction热膜流速计hot-film anemometer热线流速计hot-wire anemometer热状态方程thermal equation of state儒可夫斯基变换Zhoukowski transformation S三维流three-dimensional flow色散dispersion射流jet深水波deep water wave失速stall施特鲁哈尔数Strouhal number失踪物tracer势potential势流potential flow数值模拟numerical simulation水动力学hydrodynamics水静力学hydrostatics水力半径hydraulic radiusIimage method 镜象法incompressibility不可压缩性incompressible flow不可压缩流动incompressible fluid不可压缩流体induced drag 诱导阻力inducedvelocity诱导速度injection 注入internal flow 内流inviscid fluid 无粘性流体irregularwave不规则波irrotationalflow无旋流isentropicflow等熵流动Jjet 射流KKarmanvortexstreet卡门涡街kinematicsimilarity运动相似kinematicviscosity运动粘性Kolmogorov length科尔莫戈罗夫长度Kutta-Zhukowskicondition库塔－儒可夫斯基条件水位water level速度环量velocity circulation 速度亏损律velocity deflect law 速度剖面velocity profile速度势velocity potential速度型velocity profile随体导数material derivativeT条纹线streakline湍流turbulence, turbulent flow 湍流边界层turbulent boundary flow 脱体激波detached shock waveW外流external flow完全气体perfect gas微压计micromanometer尾流wake未扰动波undisturbed flow位移厚度displacement thickness文丘里管Venturi tube纹影法schlieren method涡团eddy涡对vortex pair涡管vortex tube涡环vortex ring涡街vortex street涡量vorticity涡量方程vorticity equation涡量拟能enstrophy涡流eddy current涡面vortex surface涡片vortex sheet涡丝vortex filamentLlaminarboundarylayer层流边界层laminar layer 层流Laval nozzle 拉瓦尔喷管leading edgevortex前缘涡local mach number当地马赫数localsimilarity局部相似MMach angle 马赫角Mach line 马赫线Mach number 马赫数Mach wave 马赫波macroscopic mechanics宏观力学manometer 压强计materialderivative随体导数mechanics of continuous medium连续介质力学micromanometer微压计moleculardiffusion分子扩散momentumequation动量方程momentum 动量涡线vortex line涡旋脱落vortex shedding涡粘性eddy viscosity无滑移条件non-slip condition无量纲参数dimensionless parameter 无粘性流体inviscid fluid 无旋流irrotational flowX吸出suction稀疏波rarefaction wave细长体slender body相干结构coherent structure相似理论similarity theory相似律similarity law相似性解similar solution楔流wedge flow斜激波oblique shock wave形阻profile dragU形管U-tube形状因子shape factorY压差differential pressure压（力）降pressure drop压力能pressure energy压强表pressure gage压强计manometer压缩波compression wave亚声速流subsonic flow液体动力学hydrodynamic pressure 液体静压hydrostatic pressure翼弦chord翼型airfoil阴影法shadow method thickness 厚度multiple manometer多管压强计NNavier-Stokes equation纳维—斯托克斯方程near fieldflow近场流Newtonianfluid牛顿流体node 波节nonlinearinstability非线性不稳定性nonlinearwave非线性波non-Newtonian fluid非牛顿流体non-Newtonian fluid mechanics非牛顿流体力学non-slipcondition无滑移条件nonuniformflow非均匀流动normalshockwave正激波nozzle 喷管numericalsimulation数值模拟Ooblique shockwave斜激波orifice meter 孔板流量计迎角angle of attack 有旋流rotational flow 诱导速度induced velocity诱导阻力induced drag源source远场边界条件far field boundary condition 远场流far field flow 均熵流homoentropic flow运动粘性kinematic viscosity运动相似kinematic similarityZ再附reattachment折射refraction正激波normal shockwave支配方程governing equation滞止状态stagnation condition质量守恒conservation of mass重力波gravity wave轴对称流axisymmetric flow注入injection驻点stagnation point状态方程equation of state准定常流quasi-steady flow自由流free stream自由流线free streamline自由面free surface自由射流free jet总压total pressure总压头total head总焓total enthalpy阻力drag, resistancePpartialsimilarity部分相似path,pathline迹线perfect gas 完全气体pipe flow 管流Pitot tube 皮托管pitot-static tube风速管plane flow 平面流Poiseulle flow泊肃叶流动potential 势potentialflow势流power lawfluid幂律流体Prandtlnumber普朗特数Prandtl-Meyer flow普朗特—迈耶流动pressuredrop压（力）降pressureenergy压力能pressuregage压强表profile drag 形阻Qquasi-steadyflow准定常流RRankine-H ugoniot condition 兰金－于戈尼奥条件rarefactionwave稀疏波reattachment再附reflection 反射refraction 折射regular wave规则波reverseflow反流Reynoldsnumber雷诺数rotationalflow有旋流Sschlierenmethod纹影法secondaryflow二次流separatedflow分离流separationpoint分离点shadowmethod阴影法shallow waterwave浅水波shape factor 形状因子shear flow 剪切流shear layer 剪切层ship wave 船波shock front 激波阵面shock wave 冲击波shock wave 激波similar 相似性solution 解similarity law 相似律similarity theory 相似理论sink 汇skin friction 壁面剪应力slender body 细长体soliton 孤立子source 源stagnation condition 滞止状态stagnationpoint驻点stall 失速static head 静压头static(pressure)tube静压管streak line 脉线streakline 染色线streakline 条纹线streamfunction流函数streamsurface流面stream tube 流管streamline 流线Strouhal number 施特鲁哈尔数sublayer 次层subsonic flow 亚声速流suction 吸出supersonic flow 超声速流动surface force 表面力surface tension 表面张力surface wave 表面波Tthermal equation of state 热状态方程three-dimensional flow三维流tidal wave 潮波total enthalpy 总焓total head 总压头total pressure 总压tracer 失踪物transonic flow 跨声速流trough 波谷turbulence, turbulent flow湍流turbulent boundary flow 湍流边界层two dimensional flow 二维流动Uundisturbed flow 未扰动波uniform flow 均匀流unsteady flow 非定常流动U-tube U形管Vvelocity circulation 速度环量velocity deflect law 速度亏损律velocitypotential速度势velocity profile 速度剖面velocity 速度型profileVenturi tube 文丘里管viscometer 粘度计viscometry 粘度测定法viscous flow 粘性流（动）viscous fluid 粘性流体vortexfilament涡丝vortex line 涡线vortex pair 涡对vortex ring 涡环vortex shedding 涡旋脱落vortex sheet 涡片vortex street 涡街vortex surface 涡面vortex tube 涡管vorticity 涡量vorticity equation 涡量方程Wwake 尾流water level 水位wave 波wave drag 波阻wave energy 波能wave front 波前wave front 波阵面wave group 波群wave height 波高wave number 波数wave speed,wave velocity波速wedge flow 楔流wind tunnel 风洞ZZhoukowski transformatio n 儒可夫斯基变换。
计算流体力学课件-part1
2024/2/28
19
❖Computational Fluid Dynamics
计算流体流体力学
第二讲 典型模型方程的数学性质
模型方程的概念
➢完整方程
连续方程
动量方程
能量方程
2024/2/28
20
❖Computational Fluid Dynamics
沿特征线，扰动波的幅值不变，传播速度为c
则在t>0时，传播过程如下图：
2024/2/28
27
❖Computational Fluid Dynamics
计算流体流体力学
第二讲 典型模型方程的数学性质
模型方程的特征
➢单波方程
➢c>0时，传播沿x正向 ➢C<0时，传播沿x负向 ❖扰动波以有限速度传播是双曲型方程的重要 特征（波形和波幅可能会变化，此处为什么不 变？）
如何表达初始形状三角形
如何存储数据 如何积分
数值积分，HOW？
如何显示结果
TECPLOT
尝试改变几个常数，看看结果有何变化，常数反映了什么？
2024/2/28
22Biblioteka ❖Computational Fluid Dynamics
回顾
控制方程
模型方程
➢NS ➢EULER ➢Impressible NS ➢RANS
➢单波方程可以模拟EULER方程的一些特征
2024/2/28
28
❖Computational Fluid Dynamics
计算流体流体力学
第二讲 典型模型方程的数学性质
模型方程的特征
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2013-11-15
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8.1 Introduction
The study of external flows is of importance to the engineers in the analysis of flow around an aircraft, turbine blades, automobiles, buildings, smokestacks, bridge abutments, and so on. To discuss the external flows, we can divided the flows into low-Re-number flows (Re < 5, or so) and high-Renumber flows (Re >1000).
The separation on the flat surface occurs as the flow is approaching a stagnation region where the velocity is low and the pressure is high
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8.1 Introduction In the study of external flows, the drag and lift are interested, the details of the flow field are seldom of interest. • Drag(阻力) (曳力) : the force of the flow exerts in the direction of the flow Projected area (projected of plane • Lift(升力): the force on athe flow exerts normal to the Drag force normal direction of the flow.of to the direction the flow)
The flow can become significantly influenced by the presence of a boundary or another object. These flows should not be discussed in this curriculum.
8.2 Separation
Separation occurs when the main stream flow leaves the body, resulting in a separated region of flow. For blunt bodies, separation is unavoidable at high Re numbers and its effect must be understood.
the laminar and turbulent boundary layers. The boundary layer that develops on a plane streamlined surface is usually sufficiently thin that the curvature of the surface can be ignored, so the problem can be treated as a flat plate. Outside the boundary layer there exists an inviscid, freestream flow. 2013-11-15 9
For due to the The boundary layer near The separated region is For blunt body, the flow Shear stresses streamlined body,region This the stagnation point is aflow simply leaves the region may separate from the viscosity are concentrated closes; wake eventually in the the wake body and form a streamlined body atthe main the laminar the thin boundary layer, the intoformed. boundary layer, keeps diffusion separated region. trailing and undergoes transition flow the edge. separated region, and and eventually downstream to a turbulent disappears as its area wake. Outside these regions boundary layer.approximateexceedingly large. the flow is becomes by an inviscid flow.
• Low-Re number flows, called stokes flows, seldom occur in engineering application (lubrication flow and flow in porous media) and is not discussed in this curriculum. We will direct our attention to high-Re-number flows in this curriculum only.
abrupt change in geometry, separation will occur at, or near, the abrupt change. reattachment will occur at some location.
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8.2 Separation
Downstream of the Upstream of the separation separation point, the xpoint, the x-component component velocity near the velocity near the wall is in the wall is in the negative xpositive x-direction, so u/y direction, so u/y at the at the wall is positive. wall must be negative. Consider the flow on the flat surface just before the step, the region near the forward separation point is enlarged..
4
•
2013-11-15
8.1 Introduction
We will focus our attention on this category of flows.
High-Re-number flows can be subdivided into three major categories:
2013-11-
If the flow in the boundary layer on a For streamlined object, the streamlined bodythe separated can region is be determined, insignificantly small or nonexistent, so it is need to study drag can be calculated.
•
•
•
Incompressible immersed flows (involving such automobiles, helicopters, submarines, and buildings); Flows of liquids that involve a free surface as a ship or a bridge abutment; Compressible flows involving high-speed object (V > 100 m/s) such as aircraft, missiles, and bullets.
drag coefficient : C D FD
Lift force
lift coefficient :
1 V 2 A 2 FL CL 1 V 2 A 2
2013-11-15
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8.1 Introduction
For blunt object, the drag on a blunt is dominated by the flow in the separated region, hence there is little interest in studying the boundary layer growth on the front part of a blunt body and the associated viscous shear at the wall. The interest is focused on the empirical data that provide the drag coefficient.
Chapter 8:
External flows
2013-11-15
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Outline
8.1 Introduction 8.2 Separation
8.3 Flow around immersed bodies