空气动力学英文PPTchapter-PPT文档资料
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空气动力学英文PPT(Chapter_02)
Definition of infinitesimal fluid element:
an infinitesimally small fluid element in the flow, with a differential volume.
It contains huge large amount of molecules Fixed and moving infinitesimal fluid element. Focus of our investigation for fluid flow.
Fixed control volume and moving control volume. Focus of our investigation for fluid flow.
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中英文日报导航站
2.3.2 Infinitesimal fluid element approach
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2.3.3 Molecule approach
Definition of molecule approach:
The fluid properties are defined with the use of suitable statistical averaging in the microscope wherein the fundamental laws of nature are applied directly to atoms and molecules. In summary, although many variations on the theme can be found in different texts for the derivation of the general equations of the fluid flow, the flow model can be usually be categorized under one of the approach described above.
an infinitesimally small fluid element in the flow, with a differential volume.
It contains huge large amount of molecules Fixed and moving infinitesimal fluid element. Focus of our investigation for fluid flow.
Fixed control volume and moving control volume. Focus of our investigation for fluid flow.
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中英文日报导航站
2.3.2 Infinitesimal fluid element approach
中英文日报导航站
2.3.3 Molecule approach
Definition of molecule approach:
The fluid properties are defined with the use of suitable statistical averaging in the microscope wherein the fundamental laws of nature are applied directly to atoms and molecules. In summary, although many variations on the theme can be found in different texts for the derivation of the general equations of the fluid flow, the flow model can be usually be categorized under one of the approach described above.
空气动力学英文PPT(Chapter_05)
6. As the lift per unit span is proportional to the circulation, so, the circulation is also a function of y 7. The lift distribution goes to zero at the wing tips.
c, α
will be different.
3. Concept of geometric twist. washout and washin.
α has a distribution along the span direction
4. Concept of aerodynamic twist.
α L =0 has a distribution along the span direction
α eff = α − α i
2 The local lift vector is in the direction perpendicular to the local relative wind. As a subsequence, there is a drag created by the presence of downwash.
※ The two vortices tend to drag the surrounding air with them, and this secondary movment induces a small component is called downwash(下洗）. ※ The downwash velocity combines with the freestream velocity to produce a local relative wind which is canted downward in the vicinity of each airfoil section of the wing. ※ definition of induced angle of attack
空气动力学基础(英文版)第二章
Chapter 2
Aerodynamics: Some Fundamental Principles and Equations
There is so great a difference between a fluid and a collection of solid particles that the laws of pressure and of equilibrium of fluids are very different from the laws of the pressure and equilibrium of solids . Jean Le Rond d’Alembert, 1768
(a) The control volume fixed in space : ●fixed →no change in shape or volume ●particles, therefore mass passing through boundary ●forces interacting on boundary ●energy may exchange through boundary (work, heat)
A ds A dS
C S
Where area S is bounded by the closed curve C.
The surface integral of A over S is related to the volume integral of ▽· (divergence of A) over V by divergence’ A theorem (also called Gauss Formula):
2.3.2 Infinitesimal fluid element approach
charpter1(第一章)空气动力学ppt 北京航空航天大学出版社
北京航空航天大学《空气动力学》北京市精品课2010年版本源自Folie31、连续介质的概念
从微观的角度而言，不论液体还是气体其 分子与分子之间都是存在间隙的，例如海平面 条件下，空气分子的平均自由程为 l ＝10-8 m， 但是这个距离与我们宏观上关心的物体（如飞 行器）的任何一个尺寸 L 相比较都是微乎其 微的， l / L < < 1。 当受到物体扰动时，流体或空气所表现出 的是大量分子运动体现出的宏观特性变化，如 压强、密度等，而不是个别分子的行为。
2010年版本
Folie26
1.2 作用在流体微团上的力的分类
其中 是微团体积，ρ为密度，F 为作用于 微团的彻体力， i 、j、 k分别是三个坐标方 向的单位向量，fx 、fy 、fz 分别是三个方 向的单位质量彻体力分量 。
北京航空航天大学《空气动力学》北京市精品课
2010年版本
Folie9
2、流体的易流性
流体与固体在力学上最本质的区别在于二者承受
剪应力和产生剪切变形能力上的不同，如下图所示， 固体能够靠产生一定的剪切角变形量θ来抵抗剪切应 力 θ ＝ τ / G 其中剪切应力 τ = F/A, A 为固体与平板相连
2010年版本
Folie16
4、流体的粘性
由于粘性影响，原来是均匀的气流流至平板后 直接贴着板面的一层速度降为零，称为流体与板面
间无滑移。稍外一层的气流受到层间摩擦作用速度
也下降至接近于零，但由于不紧挨板面多少有些速 度，层间的互相牵扯作用一层层向外传递，离板面 一定距离后，牵扯作用逐步消失，速度分布变为均 匀。
质量成正比的非接触力，例如重力，惯性力和磁流体具
有的电磁力等都属于质量力，也有称为体积力或彻体力， 由于质量力与质量成正比，故一般用单位质量力表示， 其向量形式为：
空气动力学讲义
Performance
Airfoils
• An airfoil is any surface, such as a wing, which provides aerodynamic force when it interacts with （相互作用） a moving stream of air.
Not be confused with an airplane’s attitude in relation to the earth’s surface, or with “angle of incidence” （安装角）
Four forces
Lift
Thrust Weight
Drag
Weight
• An example of Interference Drag is the mixing of air over landing gear struts（支柱）.
• Fairings（整流罩） and blending of shapes help reduce interference drag.
Drag can be classified into 2 broad types:
Parasite (寄生虫） Induced
Parasite Drag
• Parasite Drag is caused by any aircraft surface which deflects or interferes with the smooth airflow around the airplane. Three Types
Form Drag
Interference Drag
Skin Friction
Form Drag压差阻力
Airfoils
• An airfoil is any surface, such as a wing, which provides aerodynamic force when it interacts with （相互作用） a moving stream of air.
Not be confused with an airplane’s attitude in relation to the earth’s surface, or with “angle of incidence” （安装角）
Four forces
Lift
Thrust Weight
Drag
Weight
• An example of Interference Drag is the mixing of air over landing gear struts（支柱）.
• Fairings（整流罩） and blending of shapes help reduce interference drag.
Drag can be classified into 2 broad types:
Parasite (寄生虫） Induced
Parasite Drag
• Parasite Drag is caused by any aircraft surface which deflects or interferes with the smooth airflow around the airplane. Three Types
Form Drag
Interference Drag
Skin Friction
Form Drag压差阻力
空气动力学英文PPT(chapter9(1))精品文档26页
the pressure, density, and
density, and temperature
temperature discontinuously
continuously decrease.
increase.
中英文日报导航站 anydaily
Hence, an expansion wave is the direct antithesis of a shock wave. 因此，膨胀波是激波的一个正相反的对应物。
M
中英文日报导航站 anydaily
On the other hand, if the upstream flow is supersonic, as shown in
Fig.9.2b, the disturbances cannot work their way upstream; rather, at
some finite distances from the body, the disturbance waves pile up and
The information is propagated upstream at approximately the local speed of sound. 物体存在的信息以近似等于 当地音速的速度传播到上游 去。
If the upstream flow is subsonic , as shown in Fig.9.2a, the disturbances have no problem working their way upstream, thus giving the incoming flow plenty of time to move out of the way of the body. 如图9.2a所示，如果上游是亚音速的， 扰动可以毫不困难地传播 到远前方上游，因此，给中了英文来日流报导足航站够an的ydai时ly 间以绕过物体。
【空气动力学课件】11.1 Introduction
u V x
v 0 y
The wall boundary condition is
0 n
Once
is known, all the other value flow variables are directly
obtained as follows:
1. Calculate u and v: u x
The continuity equation for steady,two-dimensional flow is :
( u ) ( v ) 0 x y
or
u v u v 0 x x y y
,v x y
2
Substituting u
equation. For supersonic flow, Eq.11.12 is a hyperbolic partial
differential equation. For transonic flow, Eq.11.12 is mixed type equation.
Eq. 11.12 represents a combination of continuity, momentum, energy equations. In principle, it can be solved to obtain for the flow field around any two-dimensional flow. The infinite boundary condition is
Velocity potential equation
Linearized velocity
potential equaompressibilty correction Improved compressibilty Correction
空气动力学Chapter1
1 v 1 T v p T p T
§1.1 Definition of Compressible Flow
pressibility of a fluid（流体的可压缩性系数）
If no heat is added to or taken away from the fluid element ( the compression is adiabatic （绝热）), and if no other dissipative transport mechanism such as viscosity and diffusion are important (the compression is reversible （可逆）), then the compression of the fluid element takes place isentropically, and the isentropic compressibility （等熵可压缩性系数）is defined as
§1.1 Definition of Compressible Flow
pressibility of a fluid（流体的可压缩性系数）
If the temperature of the fluid element is held constant (due to some heat transfer mechanics), then the isothermal compressibility （等温可压缩性系数）is defined as
§1.1 Definition of Compressible Flow
2. Compressibility of a fluid in motion
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激波反射与干扰多种多样，在本节中我们给出如下几种常见 类型：
•马赫反射（Mach Reflection)
在给定偏转角θ的条件下，假设M1稍稍大于能在压缩拐角 处产生直的斜激波所需要的最小马赫数值，这时，在角点处 会存在一个直的入射斜激波。然而，我们知道通过激波马赫 数下降，即 M2<M1, 这一下降会使 M2小于使气流通过直的反 射激波偏转θ角度所需的最小马赫数。在这种情况下，我们由 斜激波理论可知没有直的反射激波存在。图9.17所示的常规反 射将不可能出现。实际发生的情形如图9.18所示，由角点发出 的直入射斜激波在上壁面附近弯曲，并在上壁面变成一正激 波。这个正激波保证了上壁面处的壁面边界条件。另外，由 正激波上分支出一个弯的反射激波向下游传播。如图9.18所示 的这种波型，称为马赫反射。
d M2 1dV
V
(9.32)
参照图9.23,将(9.32)式从偏角为零，马赫数为M1的区域1，积分 到偏角为θ，马赫数为M2的区域2：
d
M2
M21dV
0
V M 中1 英文日报导航站
(9.33)
将(9.39)式代入到（9.33)式，得到：
M2
M2 1 dM
反射波后的特性没有理论方法求解，可采用数值解法求解。 中英文日报导航站
马赫反射图示
中英文日报导航站
•右行、左行激波干扰 (Intescetion of right- and left-running shock waves) A:左行波 B:右行波
9.5 DTACHED SHOCK WAVE IN FRONT OF A BLUNT BODY 钝头体前的脱体激波
中英文日报导航站
Shock detachment distance ：w激ww.a波nyd脱aily.体com距离；Sonic line:音速线
9.6 PRANDTL-MEYER EXPANSION WAVES 普朗特-梅耶膨胀波
（9.43)
(M 2)(M 1) （9.43)
(M) is given by Eq. (9.42) for a calorically perfect gas.
The Prandtl-Meyer function is very impo also
tabulated in App.C.
对于量热完全气体, (M) 由(9.42)式给定。Prandtl-Meyer
函数 非常重要，它是计算通过膨胀波气体特性变化的 关键；由于其重要性，作为马赫数M的函数在附录C中 以列表形式给出。同时马赫角 作为M的函数也在附录C
中给出。
中英文日报导航站
下面我们应用以上结果给出求解图9.23 所示问题的具体步骤：
1.对于给定M1，由附录C查得(M1)。
2.由 (M 2)(M 1)计算 (M2) 。
3.根据第2步计算出的 (M2) ，查附录
C得到M2。 4.因为膨胀波是等熵的，因此p0和T0通过膨胀波保持不变。即 T0,1=T0,2, p0,1=p0,2。由(8.40)式， (8.42)式，我们有
T2 T2/T0,2 T1 T1/T0,1
1 1 [[(( 1 1))//2 2]]M M1 222
p p1 2p p2 1//p p0 0,,1 21 1 [[(( 1 1))//2 2]]M M 1 22 2/(1)
中英文日报导航站
（9.44） （9.45）
9.7 SHOCK-EXPANSION THEORY : APPLICATIONS TO SUPERSONIC AIRFOILS 激波——膨胀波理论及其对超音速翼型的应用
特别要注意：膨胀过程是一个等熵过程。 要解决的问题是：已知上游马赫数M1及其它流动特性(区域1）， 求通过偏转角θ膨胀后的下游中（英文区日域报导2航）站 的特性。
考虑一个以无限小的偏转dθ 引起的非常弱的波，如上图所示。这 个波实际上就是与上游速度夹角为μ的马赫波。我们前面已经证明 了通过斜波波前波后的切向速度分量保持不变。所以将波前速度的 大小与方向用AB矢量线段表示画在波后，就与表示波后速度大小 和方向的AC矢量线段构成一中个英三文日角报导形航站ABC。三个内角的大小如图 所示。注意,波前波后切向速度www分.an量ydai不ly.co变m 保证了CB垂直于马赫波。
空气动力学英文 PPTchapter
精品
入射激波(Incident shock wave): 点A处产生的斜激波
反射激波（Reflected shock wave): 入射激波打到水平壁面B点， 不会自动消失，而是产生另外一个由B点发出的斜激波，以保 证激波后流动满足流线与物中面英文相日切报导的航站边界条件。这个由B点发 出的斜激波就是反射激波。
M1 1[(1)/2]M2 M
（9.40)
(M)1[(M 12)/21]M2
dM M
（9.41)
(M) 被称为Prandtl-Meyer函数，其具体表达式如下：
(M ) 1 1ta 1n 1 1(M 2 1 ) ta 1n M 2 1（9.42)
因此，（9.40)的积分可以表示为：
(M 2) 中英文(日M 报导1航)站
key to calculation of changes across an expansion wave.
Because of its importance, is tabulated as a function of M
in App. C. For convenience, values of
C:激波B的折射波
D:激波A的折射波
EF:滑移线
折射：Refracted 滑移线：Slip line
中英文日报导航站
• 两左行激波干扰
两同向激波相交形成一更强的激波CD, 同时伴随一个弱反 射波CE。这一反射波是必中须英文的日报，导以航站调节保证滑移线CF分 开的4区和5区速度方向相同www。