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
流体力学(英文课件)chap3
4
子 在 川 上 曰 ： 逝 者 如 斯 夫 ！
人不能两次踏进同一条河流
Fluid Mechanics 2010 Chapter 3
5
子 在 川 上 曰 ： 逝 者 如 斯 夫 ！
请君试问东流水， 请君试问东流水，别意与之谁短长 问君能有几多愁？ 问君能有几多愁？恰似一江春水向东流 君不见黄河之水天上来， 君不见黄河之水天上来，奔流到海不复回 飞流直下三千尺， 飞流直下三千尺，疑是银河落九天 沧海横流， 沧海横流，方显英雄本色 风乍起，吹皱一池春水 风乍起， 大风起兮云飞扬 忽如一夜春风来， 忽如一夜春风来，千树万树莉花开 海水朝朝朝朝朝朝朝落 浮云长长长长长长长消
10级称为狂风，24.5—28.4m/s，特征是树木可被吹倒，一般建 级称为狂风， 级称为狂风 ，特征是树木可被吹倒， 筑物遭破坏； 筑物遭破坏； 11级称为暴风，28.5—32.6m/s，特征是大树可被吹倒，一般建 级称为暴风， 级称为暴风 ，特征是大树可被吹倒， 筑物遭严重破坏； 筑物遭严重破坏； 12级称为飓风，>32.6m/s，在陆地少见，其摧毁力很大。 级称为飓风， Fluid Mechanics 2010 Chapter 3 其摧毁力很大。 级称为飓风 ，在陆地少见，
Eulerian description:
The flow parameters are functions of both space and time. Quantities such as velocity and acceleration are functions of both space and time. In Cartesian coordinates the velocity and the acceleration are expressed as:
流体力学课件
am , ds 0
am ds
3 重力场中的平衡流体 重力场下
f x f y 0, f z g
w fz z
w g z
dw g dz
w gz
所以
dp dw gdz
F dxdydz( f x i f y j f z k )
以x方向的平衡为例：
质量力： dxdydzfx 表面力： pdydz p' dydz
p 是坐标的连续函数， 由泰勒公式并略去二阶以上无穷小 p p' p dx x p dxdydzfx pdydz ( p dx)dydz 0 Fxi 0 x
2)试管轴线与水平线夹角α
答案
h
( z1 , p1 )
( z 2 , p2 )
4 静压强的表示方法与度量
以绝对真空为压力起点的表示方法 －绝对压力 以大气压力为压力起点的表示方法 －相对压力 、表压力 表示绝对压力小于一个大气压力的压力范围 -真空度
0
0.1Mpa
绝对压力
相对压力
真空度
０
压力单位：
Pa N / m2
b( gh1 L / 2 gh2 L / 3) / cos G / 2 bgL(h1 / 2 h2 / 3) / cos G / 2
T 3 1000 9.8 2(1 / 2 1.73 / 3) / 0.5 pA 9800 / 2
h1
6 流体的相对平衡 例： 由
1 p p0 ( 2 r 2 gz) 2
流体力学英文版1
For instance, 1) rarefied gas flow 稀薄气体(e.g., as
encountered in flights into the upper reaches of
the atmosphere);
2) micro-scale channel flows (in MEMS and even NEMS, etc. )
δ V*～10−9 mm3
10
In a continuum, volume of a fluid particle or element satisfy (连续介质中的流体质点、流体微团满足下 列条件):
Large enough in microscope（微观足够大), Small enough in macroscope（宏观足够小）, i.e. 10−9 mm3 of air at standard conditions contains approximately 3× 107 molecules.
– primary unit
Quantity
SI Unit
Dimension
Length
Meter,
L
Mass
Kilogram,
M
Time
Second,
T
Temperature
Kelvin,
θ
15
z Secondary quantity – 导出量
or secondary dimension 导出量纲
pathlines
2
1.1 Definition of a fluid
Fluid is a substance that deforms ( 变形) continuously under the application of a shear (tangential) stress no matter how small or large the shear stress may be.
流体力学(英文课件)chap5
分 量 形 式
u x u x u x u x 1 p ux uy uz X t x y z x
4 equations for 4 quantities
u y
ux
u y
uy
u y
uz
u y
1 p y 1 p Z z u z 0 z Y
16
4. Incompressible 2. The Navier-Stokes Equations (3) Ideal Fluid Flow
p xx dx)dydz zx dxdy ( zx zx dz)dxdy x z yx du yx dxdz ( yx dy)dxdz dxdydz x y dt
E
z
F p yy
yz
xz p xx
A G
H
1. index: normal vector on face 2. index: direction of force
xy
D
yx
B
O x 图3-21
zx p zz
y
zy
C
p xx xy xz yx p yy yz p zz zx zy
1 p az Z z
Fluid Mechanics 2010 CN Chapter 4
10
4 - 1 理 想 流 体 的 运 动 方 程
欧拉运动微分方程
1、采用六面体微元分析法
2、加速度中含当地加速度和迁移加速度
3、x轴方向：
p dx p dx p dydz p dydz X dxdydz dxdydzax x 2 x 2
流体力学 英文课件第3章
D2=10 in
3.5 The Linear Momentum Equation (动量方程) （ Newton’s Second Law ）
ds ( i AiV i )out ( i AiV i )in dt i i
1-D in & out steady RTT
x
Example: A fixed control volume of a streamtube in steady flow has a uniform inlet (1,A1,V1 )and a uniform exit (2,A2,V2) . Find the net force on the control volume.
Solution:
F m(V 2 V 1) m 1 A1V 1 2 A2V 2
F x m(V2 x V1x ) m(V 2 V 1 cos )
2
V1
V2
F y m(V2 y V1 y ) mV 1 sin
In the like manner
(d )out ( AVdt )out
s
ds
t
t+dt t t+dt
d s d cv 1 [(d )out (d )in] dt dt dt
d s d cv [( AV )out ( AV )in] dt dt
s
t t+dt
t
t+dt
: any property of fluid (m, mV , H , E )
d dm
:The amount of per unit mass
流体力学(英文课件)chap7
Fluid Mechanics 2010 luid Mechanics 2010 CN Chapter 6
3
第 六 章 层 流 紊 流 及 其 能 量 损 失
研究 对象 以不可压缩流体的管流为主 能量损失
Energy Loss 卧 式 水 泵 及 其 管 路
Incompressible pipe flow
Basics of Fluid Mechanics Chapter 6: § 1 to 3
Laminar Flow
Marc Henn
Ph.D., Mechanical Engineer
Contents 6.1 Laminar and turbulent flow state 6.2 Friction losses in developed flows 6.3 Laminar developed pipe flow
11
6.1.1 Pipe flow with Head loss
Fluid Mechanics 2010 CN Chapter 6
12
第 六 章 层 流 紊 流 及 其 能 量 损 失
Experimental set-up
Energy line Hydraulic grade line
两种损失：沿程阻力（损失）、局部阻力（损失） 两种损失：沿程阻力（损失）、局部阻力（损失） ）、局部阻力
Fluid Mechanics 2010 CN Chapter 6
5
第 六 章 层 流 紊 流 及 其 能 量 损 失
能量损失
Fluid Mechanics 2010 CN Chapter 6
6
第 六 章 层 流 紊 流 及 其 能 量 损 失
流体力学中科大 英文版
Distinction between a gas and a liquid (2)
● VAPOR: – Gas whose T and P very near the liquid phase
– Steam is a vapor, state near that of water
● GAS: – Super-heated vapor, far away from liquid phase – Volume of gas or vapor greatly affected by ΔT and ΔP ● Thermodynamics
– Irrigation -- sedimentation
– Meteorology -- oceanography
第12页，共57页。
Scope of Fluid Mechanics (2)
Used in the design of:
– Water supply system – Dam spillways – Shock absorbers, brakes – ships, submarines – Aircrafts, rockets
-- breakwaters, marinas -- computer disk drives
-- pumps, HVAC systems -- artificial organs
Yatchs
hang gliders
第13页，共57页。
As fish habitat...
第14页，共57页。
For reptile habitat...
第37页，共57页。
Historical development (2) ● Newton (1642-1727): laws of motion, law of
流体力学英语
流体动力学 fluid dynamics 说明连续介质力学mechanics of continuous 说明介质 medium 说明流体质点 fluid particle 说明无粘性流体nonviscous fluid, inviscid 说明连续介质假设continuous medium hypothesis 说明流体运动学 fluid kinematics 说明水静力学 hydrostatics 说明液体静力学 hydrostatics 说明支配方程 governing equation 说明伯努利方程 Bernoulli equation 说明伯努利定理 Bernonlli theorem 说明毕奥-萨伐尔定律 Biot-Savart law 说明欧拉方程 Euler equation 说明亥姆霍兹定理 Helmholtz theorem 说明开尔文定理 Kelvin theorem 说明涡片 vortex sheet 说明库塔-茹可夫斯基条件 Kutta-Zhoukowski condition 说明布拉休斯解 Blasius solution 说明达朗贝尔佯廖 d''''Alembert paradox 说明雷诺数 Reynolds number 说明施特鲁哈尔数 Strouhal number 说明随体导数 material derivative 说明不可压缩流体 incompressible fluid 说明质量守恒conservation of mass 说明动量守恒conservation of momentum 说明能量守恒conservation of energy 说明动量方程 momentum equation 说明能量方程 energy equation 说明控制体积 control volume 说明液体静压 hydrostatic pressure 说明涡量拟能 enstrophy 说明压差 differential pressure 说明流[动] flow 说明流线 stream line 说明流面 stream surface 说明流管 stream tube 说明迹线path, path line 说明流场 flow field 说明流态 flow regime 说明流动参量 flow parameter 说明流量flow rate, flow discharge 说明涡旋 vortex 说明涡量 vorticity 说明涡丝 vortex filament 说明涡线 vortex line 说明涡面 vortex surface 说明涡层 vortex layer 说明涡环 vortex ring 说明涡对 vortex pair 说明涡管 vortex tube 说明涡街 vortex street 说明卡门涡街 Karman vortex street 说明马蹄涡 horseshoe vortex 说明对流涡胞 convective cell 说明卷筒涡胞 roll cell 说明涡 eddy 说明涡粘性 eddy viscosity 说明环流 circulation 说明环量 circulation 说明速度环量 velocity circulation 说明偶极子 doublet, dipole 说明驻点 stagnation point 说明总压[力] total pressure 说明总压头 total head 说明静压头 static head 说明总焓 total enthalpy 说明能量输运 energy transport 说明速度剖面 velocity profile 说明库埃特流 Couette flow 说明单相流single phase flow 说明单组份流 single-component flow 说明均匀流 uniform flow 说明非均匀流 nonuniform flow 说明二维流 two-dimensional flow 说明三维流 three-dimensional flow 说明准定常流 quasi-steady flow 说明非定常流unsteady flow, non-steady flow 说明暂态流 transient flow 说明周期流 periodic flow 说明振荡流 oscillatory flow 说明分层流 stratified flow 说明无旋流 irrotational flow 说明有旋流 rotational flow 说明轴对称流 axisymmetric flow 说明不可压缩性 incompressibility 说明不可压缩流[动] incompressible flow 说明浮体 floating body 说明定倾中心 metacenter 说明阻力 drag, resistance 说明减阻 drag reduction 说明表面力 surface force 说明表面张力 surface tension 说明毛细[管]作用 capillarity 说明来流 incoming flow 说明自由流 free stream 说明自由流线free stream line 说明外流 external flow 说明进口 entrance, inlet 说明出口 exit, outlet 说明扰动 disturbance, perturbation 说明分布 distribution 说明传播 propagation 说明色散 dispersion 说明弥散 dispersion 说明附加质量added mass ,associated mass 说明收缩 contraction 说明镜象法 image method 说明无量纲参数 dimensionless parameter 说明几何相似 geometric similarity 说明运动相似 kinematic similarity 说明动力相似[性] dynamic similarity 说明平面流 plane flow 说明势 potential 说明势流 potential flow 说明速度势 velocity potential 说明复势 complex potential 说明复速度 complex velocity 说明流函数 stream function 说明源 source 说明汇 sink 说明速度[水]头 velocity head 说明拐角流 corner flow 说明空泡流 cavity flow 说明超空泡 supercavity 说明超空泡流 supercavity flow 说明空气动力学 aerodynamics 说明低速空气动力学 low-speed aerodynamics 说明高速空气动力学 high-speed aerodynamics 说明气动热力学 aerothermodynamics 说明亚声速流[动] subsonic flow 说明跨声速流[动] transonic flow 说明超声速流[动] supersonic flow 说明锥形流 conical flow 说明楔流 wedge flow 说明叶栅流 cascade flow 说明非平衡流[动] non-equilibrium flow 说明细长体 slender body 说明细长度 slenderness 说明钝头体 bluff body 说明钝体 blunt body 说明翼型 airfoil 说明翼弦 chord 说明薄翼理论 thin-airfoil theory 说明构型 configuration 说明后缘 trailing edge 说明迎角angle of attack 说明失速 stall 说明脱体激波detached shock wave 说明波阻 wave drag 说明诱导阻力 induced drag 说明诱导速度 induced velocity 说明临界雷诺数 critical Reynolds number 说明前缘涡leading edge vortex 说明附着涡 bound vortex 说明约束涡 confined vortex 说明气动中心 aerodynamic center 说明气动力 aerodynamic force 说明气动噪声 aerodynamic noise 说明气动加热 aerodynamic heating 说明离解 dissociation 说明地面效应 ground effect 说明气体动力学 gas dynamics 说明稀疏波 rarefaction wave 说明热状态方程thermal equation of state 说明喷管 Nozzle 说明普朗特-迈耶流 Prandtl-Meyer flow 说明瑞利流 Rayleigh flow 说明可压缩流[动] compressible flow 说明可压缩流体 compressible fluid 说明绝热流 adiabatic flow 说明非绝热流 diabatic flow 说明未扰动流 undisturbed flow 说明等熵流 isentropic flow 说明匀熵流 homoentropic flow 说明兰金-于戈尼奥条件 Rankine-Hugoniot condition 说明状态方程equation of state 说明量热状态方程caloric equation of state 说明完全气体 perfect gas 说明拉瓦尔喷管 Laval nozzle 说明马赫角 Mach angle 说明马赫锥 Mach cone 说明马赫线 Mach line 说明马赫数 Mach number 说明马赫波 Mach wave 说明当地马赫数local Mach number 说明冲击波 shock wave 说明激波 shock wave 说明正激波normal shock wave 说明斜激波oblique shock wave 说明头波 bow wave 说明附体激波 attached shock wave 说明激波阵面 shock front 说明激波层 shock layer 说明压缩波 compression wave 说明反射 reflection 说明折射 refraction 说明散射 scattering 说明衍射 diffraction 说明绕射 diffraction 说明出口压力 exit pressure 说明超压[强] over pressure 说明反压 back pressure 说明爆炸 explosion 说明爆轰 detonation 说明缓燃 deflagration 说明水动力学 hydrodynamics 说明液体动力学 hydrodynamics 说明泰勒不稳定性 Taylor instability 说明盖斯特纳波 Gerstner wave 说明斯托克斯波 Stokes wave 说明瑞利数 Rayleigh number 说明自由面 free surface 说明波速wave speed, wave velocity 说明波高 wave height 说明波列 wave train 说明波群 wave group 说明波能 wave energy 说明表面波 surface wave 说明表面张力波 capillary wave 说明规则波 regular wave 说明不规则波 irregular wave 说明浅水波shallow water wave 说明深水波deep water wave 说明重力波 gravity wave 说明椭圆余弦波 cnoidal wave 说明潮波 tidal wave 说明涌波 surge wave 说明破碎波 breaking wave 说明船波 ship wave 说明非线性波 nonlinear wave 说明孤立子 soliton 说明水动[力]噪声 hydrodynamic noise 说明水击 water hammer 说明空化 cavitation 说明空化数 cavitation number 说明空蚀 cavitation damage 说明超空化流 supercavitating flow 说明水翼 hydrofoil 说明水力学 hydraulics 说明洪水波 flood wave 说明涟漪 ripple 说明消能 energy dissipation 说明海洋水动力学 marine hydrodynamics 说明谢齐公式 Chezy formula 说明欧拉数 Euler number 说明弗劳德数 Froude number 说明水力半径 hydraulic radius 说明水力坡度 hvdraulic slope 说明高度水头 elevating head 说明水头损失 head loss 说明水位 water level 说明水跃 hydraulic jump 说明含水层 aquifer 说明排水 drainage 说明排放量 discharge 说明壅水曲线back water curve 说明压[强水]头 pressure head 说明过水断面 flow cross-section 说明明槽流open channel flow 说明孔流 orifice flow 说明无压流free surface flow 说明有压流 pressure flow 说明缓流 subcritical flow 说明急流 supercritical flow 说明渐变流gradually varied flow 说明急变流rapidly varied flow 说明临界流 critical flow 说明异重流density current, gravity flow 说明堰流 weir flow 说明掺气流 aerated flow 说明含沙流 sediment-laden stream 说明降水曲线 dropdown curve 说明沉积物 sediment, deposit 说明沉[降堆]积 sedimentation, deposition 说明沉降速度 settling velocity 说明流动稳定性 flow stability 说明不稳定性 instability 说明奥尔-索末菲方程 Orr-Sommerfeld equation 说明涡量方程 vorticity equation 说明泊肃叶流 Poiseuille flow 说明奥辛流 Oseen flow 说明剪切流 shear flow 说明粘性流[动] viscous flow 说明层流 laminar flow 说明分离流 separated flow 说明二次流 secondary flow 说明近场流 near field flow 说明远场流far field flow 说明滞止流 stagnation flow 说明尾流 wake [flow] 说明回流 back flow 说明反流 reverse flow 说明射流 jet 说明自由射流 free jet 说明管流pipe flow, tube flow 说明内流 internal flow 说明拟序结构 coherent structure 说明猝发过程 bursting process 说明表观粘度 apparent viscosity 说明运动粘性 kinematic viscosity 说明动力粘性 dynamic viscosity 说明泊 poise 说明厘泊 centipoise 说明厘沱 centistoke 说明剪切层 shear layer 说明次层 sublayer 说明流动分离 flow separation 说明层流分离 laminar separation 说明湍流分离 turbulent separation 说明分离点 separation point 说明附着点 attachment point 说明再附 reattachment 说明再层流化 relaminarization 说明起动涡 starting vortex 说明驻涡 standing vortex 说明涡旋破碎 vortex breakdown 说明涡旋脱落 vortex shedding 说明压[力]降 pressure drop 说明压差阻力 pressure drag 说明压力能 pressure energy 说明型阻 profile drag 说明滑移速度 slip velocity 说明无滑移条件 non-slip condition 说明壁剪应力skin friction, frictional drag 说明壁剪切速度 friction velocity 说明磨擦损失 friction loss 说明磨擦因子 friction factor 说明耗散 dissipation 说明滞后 lag 说明相似性解 similar solution 说明局域相似 local similarity 说明气体润滑 gas lubrication 说明液体动力润滑 hydrodynamic lubrication 说明浆体 slurry 说明泰勒数 Taylor number 说明纳维-斯托克斯方程 Navier-Stokes equation 说明牛顿流体 Newtonian fluid 说明边界层理论boundary later theory 说明边界层方程boundary layer equation 说明边界层 boundary layer 说明附面层 boundary layer 说明层流边界层laminar boundary layer 说明湍流边界层turbulent boundary layer 说明温度边界层thermal boundary layer 说明边界层转捩boundary layer transition 说明边界层分离boundary layer separation 说明边界层厚度boundary layer thickness 说明位移厚度 displacement thickness 说明动量厚度 momentum thickness 说明能量厚度 energy thickness 说明焓厚度 enthalpy thickness 说明注入 injection 说明吸出 suction 说明泰勒涡 Taylor vortex 说明速度亏损律velocity defect law 说明形状因子 shape factor 说明测速法 anemometry 说明粘度测定法 visco[si] metry 说明流动显示 flow visualization 说明油烟显示 oil smoke visualization 说明孔板流量计 orifice meter 说明频率响应 frequency response 说明油膜显示 oil film visualization 说明阴影法 shadow method 说明纹影法 schlieren method 说明烟丝法smoke wire method 说明丝线法 tuft method 说明氢泡法 nydrogen bubble method 说明相似理论 similarity theory 说明相似律 similarity law 说明部分相似 partial similarity 说明定理pi theorem, Buckingham theorem 说明静[态]校准 static calibration 说明动态校准 dynamic calibration 说明风洞 wind tunnel 说明激波管 shock tube 说明激波管风洞shock tube wind tunnel 说明水洞 water tunnel 说明拖曳水池 towing tank 说明旋臂水池rotating arm basin 说明扩散段 diffuser 说明测压孔 pressure tap 说明皮托管 pitot tube 说明普雷斯顿管 preston tube 说明斯坦顿管 Stanton tube 说明文丘里管 Venturi tube 说明U形管 U-tube 说明压强计 manometer 说明微压计 micromanometer 说明多管压强计 multiple manometer 说明静压管 static [pressure]tube 说明流速计 anemometer 说明风速管Pitot- static tube 说明激光多普勒测速计laser Doppler anemometer,laser Doppler velocimeter 说明热线流速计 hot-wire anemometer 说明热膜流速计hot- film anemometer 说明流量计 flow meter 说明粘度计 visco[si] meter 说明涡量计 vorticity meter 说明传感器 transducer, sensor 说明压强传感器 pressure transducer 说明热敏电阻 thermistor 说明示踪物 tracer 说明时间线 time line 说明脉线 streak line 说明尺度效应 scale effect 说明壁效应 wall effect 说明堵塞 blockage 说明堵寒效应 blockage effect 说明动态响应 dynamic response 说明响应频率 response frequency 说明底压 base pressure 说明菲克定律 Fick law 说明巴塞特力 Basset force 说明埃克特数 Eckert number 说明格拉斯霍夫数 Grashof number 说明努塞特数 Nusselt number 说明普朗特数 prandtl number 说明雷诺比拟 Reynolds analogy 说明施密特数 schmidt number 说明斯坦顿数 Stanton number 说明对流 convection 说明自由对流natural convection, free convec-tion 说明强迫对流 forced convection 说明热对流 heat convection 说明质量传递 mass transfer 说明传质系数 mass transfer coefficient 说明热量传递 heat transfer 说明传热系数heat transfer coefficient 说明对流传热 convective heat transfer 说明辐射传热 radiative heat transfer 说明动量交换 momentum transfer 说明能量传递 energy transfer 说明传导 conduction 说明热传导conductive heat transfer 说明热交换 heat exchange 说明临界热通量 critical heat flux 说明浓度 concentration 说明扩散 diffusion 说明扩散性 diffusivity 说明扩散率 diffusivity 说明扩散速度 diffusion velocity 说明分子扩散 molecular diffusion 说明沸腾 boiling 说明蒸发 evaporation 说明气化 gasification 说明凝结 condensation 说明成核 nucleation 说明计算流体力学computational fluid mechanics 说明多重尺度问题multiple scale problem 说明伯格斯方程 Burgers equation 说明对流扩散方程convection diffusion equation 说明KDU方程 KDV equation 说明修正微分方程 modified differential equation 说明拉克斯等价定理Lax equivalence theorem 说明数值模拟 numerical simulation 说明大涡模拟large eddy simulation 说明数值粘性 numerical viscosity 说明非线性不稳定性 nonlinear instability 说明希尔特稳定性分析 Hirt stability analysis 说明相容条件 consistency condition 说明CFL条件Courant- Friedrichs- Lewy condition ,CFL condition 说明狄里克雷边界条件Dirichlet boundary condition 说明熵条件 entropy condition 说明远场边界条件far field boundary condition 说明流入边界条件 inflow boundary condition 说明无反射边界条件nonreflecting boundary condition 说明数值边界条件numerical boundary condition 说明流出边界条件 outflow boundary condition 说明冯.诺伊曼条件von Neumann condition 说明近似因子分解法approximate factorization method 说明人工压缩 artificial compression 说明人工粘性 artificial viscosity 说明边界元法boundary element method 说明配置方法 collocation method 说明能量法 energy method 说明有限体积法finite volume method 说明流体网格法fluid in cell method,FLIC method 说明通量校正传输法flux-corrected transport method 说明通量矢量分解法flux vector splitting method 说明伽辽金法 Galerkin method 说明积分方法 integral method 说明标记网格法marker and cell method, MAC method 说明特征线法method of characteristics 说明直线法method of lines 说明矩量法 moment method 说明多重网格法 multi- grid method 说明板块法 panel method 说明质点网格法particle in cell method, PIC method 说明质点法 particle method 说明预估校正法 predictor-corrector method 说明投影法 projection method 说明准谱法 pseudo-spectral method 说明随机选取法random choice method 说明激波捕捉法 shock-capturing method 说明激波拟合法 shock-fitting method 说明谱方法 spectral method 说明稀疏矩阵分解法split coefficient matrix method 说明不定常法 time-dependent method 说明时间分步法 time splitting method 说明变分法 variational method 说明涡方法 vortex method 说明隐格式 implicit scheme 说明显格式 explicit scheme 说明交替方向隐格式alternating direction implicit scheme, ADI scheme 说明反扩散差分格式anti-diffusion difference scheme 说明紧差分格式compact difference scheme 说明守恒差分格式conservation difference scheme 说明克兰克-尼科尔森格式 Crank-Nicolson scheme 说明杜福特-弗兰克尔格式 Dufort-Frankel scheme 说明指数格式 exponential scheme 说明戈本诺夫格式 Godunov scheme 说明高分辨率格式high resolution scheme 说明拉克斯-温德罗夫格式 Lax-Wendroff scheme 说明蛙跳格式 leap-frog scheme 说明单调差分格式 monotone difference scheme 说明保单调差分格式monotonicity preserving diffe-rence scheme 说明穆曼-科尔格式 Murman-Cole scheme 说明半隐格式 semi-implicit scheme 说明斜迎风格式 skew-upstream scheme 说明全变差下降格式total variation decreasing scheme TVD scheme 说明迎风格式upstream scheme , upwind scheme 说明计算区域 computational domain 说明物理区域 physical domain 说明影响域domain of influence 说明依赖域 domain of dependence 说明区域分解 domain decomposition 说明维数分解 dimensional split 说明物理解 physical solution 说明弱解 weak solution 说明黎曼解算子 Riemann solver 说明守恒型 conservation form 说明弱守恒型weak conservation form 说明强守恒型strong conservation form 说明散度型 divergence form 说明贴体曲线坐标body- fitted curvilinear coordi-nates 说明[自]适应网格[self-] adaptive mesh 说明适应网格生成 adaptive grid generation 说明自动网格生成 automatic grid generation 说明数值网格生成numerical grid generation 说明交错网格 staggered mesh 说明网格雷诺数 cell Reynolds number 说明数植扩散 numerical diffusion 说明数值耗散 numerical dissipation 说明数值色散 numerical dispersion 说明数值通量 numerical flux 说明放大因子 amplification factor 说明放大矩阵 amplification matrix 说明阻尼误差 damping error 说明离散涡 discrete vortex 说明熵通量 entropy flux 说明熵函数 entropy function 说明分步法fractional step method 说明。
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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..
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8.1 Introduction
We will focus our attention on this category of flows.
High-Re-number flows can be subdivided into three major categories:
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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
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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
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Outline
8.1 Introduction 8.2 Separation
8.3 Flow around immersed bodies