流体机械04讲-流体机械速度三角形分析与欧拉方程_486101757

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速度三角形的定义 Definition Of Velocity Triangle
工作机的进、出口速度三角形
Velocity Triangle of Working Machine’s Inlet and Outlet
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K K K K K K 径向分量(radial component) 轴向分量(axial component) 圆周分量(circumferential component)
vr , wr
vz , wz
vu , wu
在旋转的流体机械中，只有径向分量和轴向分量对通过叶轮的流量有贡献
In rotary fluid machinery, only radial component and axial component make contribution to flow rate through impeller
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几种典型水轮机的轴面投影
Axial Region Projections of Several Typical Turbines
辐流式(FL) Radial Flow Type
轴流式(ZL) Axial Flow Type
叶片形状及图示方法
Blade Shape and Graphic Method
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流体机械的能量转化过程
Energy Transformation Process of Fluid Machinery
流体能
Fluid Energy
水轮机Turbine
机械能
Mechanical Energy
来流 Incoming Flow
来流 Incoming Flow Vu=0
vK = uK + wK Absolute velocity and relative velocity have relation represented as below:
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速度三角形的定义 Definition Of Velocity Triangle
Pascal
2
4
6
Pascal
8
10
12
14
16
18
Time / s
7000
6000
5000
4000
3000
5
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速度三角形的定义 Definition Of Velocity Triangle
β2e β2
水斗式水轮机的进、出口速度三角形
Velocity Triangle of Inlet and Outlet of Scoop-type Turbine
4 x 10 0 -0.5 -1 -1.5 -2 -2.5 -3
(r,z)坐标 (r,z) Coordinate
1.轴面（子午面）——过叶轮轴心线的平面 ·Axial region (meridian plane): Plan through axial lead of impeller 2.平面投影图——在垂直于转轮轴线平面上的投影 ·plan projection drawing: Projection on the plane against to axial cord of impeller 3.轴面投影图——用轴面投影（旋转投影）法得到的在轴面上的投影 ·Axial region projection drawing: Projection on the axial region got through axial region projection (Revolved rejection) method 4.轴面截线——用轴面投影法得到的轴面与叶轮的交线 ·Axial region transversal: Intersection of axial region and impeller wheel got through axial region projection method 5.叶轮叶片形状的表示法——轴面截线族（正、背面） ·Representation of shape of impeller wheel blade : Axial region transversal group (pressure & suction side)
Vu=0 出流 Efferent Flow
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Vu=0 出流 Efferent Flow
机械能
Mechanical Energy
水泵Pump
王正伟 13601363209
流体能
Fluid Energy
2
1
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叶片形状及图示方法
Blade Shape and Graphic Method
在旋转的流体机械中，将这径向分量和轴向分量合成
K K In rotary fluid machinery, compose radial component and axial component together
引入wK轴m 面=速wK度r ：+
vKm wz
,
wmK vm
=
K vr
+
K vz
Wu
由于牵连速度为圆周方向，因此各速度分量间存在如下关系：
如何表示空间叶片的形状？
How to represent the shape of space blade?
两个二维平面 Two Two-dimension Plan
平面投影图 Plan Projection Drawing
轴面投影图 Pinacoidal Projection Drawing
(r,θ)坐标 (r,θ) Coordinate
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混流式(HL) Mixed-flow Type
贯流式(GL) Tubular Fl源自文库w Type
斜流式(XL) Diagonal-flow Type
冲击式(CJ)－平面投影图
Impulse Type Plan Projection Drawing
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4.1 流体机械的能量转化过程 Energy transformation process of fluid machinery 4.2 叶片形状及图示方法 Blade shape and graphic method 4.3 几种典型水轮机的轴面投影 Pinacoidal projections of several typical turbines 4.4 展开流面 Developed stream surface 4.5 过流流面 Cross‐section 4.6 速度三角形的定义 Definition of velocity triangle 4.7 叶片式流体机械欧拉方程 Euler equation of vane type fluid machinery 4.8 叶片式流体机械的反击度 Reactiondegree of vanetypefluid machinery 4.9 不同工作条件下的速度三角形－自学分析 Self study and analyze: velocity triangle under different operating conditions
Vu=0
叶片 Blade：M=0→M≠0
导叶 Guide Vane:
部分压能→动能 Partial Pressure Energy→Kinetic Energy
Vu≠0
Vu≠0
导叶 Guide Vane:
部分动能→压能 Partial Kinetic Energy→Pressure Energy
叶片 Blade: 动量矩M≠0→M=0
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混流式水轮机中的绝对与相对运动 Absolute Velocity And Relative Velocity
Inside Mixed-Flow Turbine
0-导叶出口
Guide Vane Outlet
1-转轮进口
Impeller Inlet
2-转轮出口
Impeller Outlet
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速度三角形的定义 Definition Of Velocity Triangle
·在流体机械旋转叶轮内的流动区域中任取一点，考察该点流体的运动速度 Take any point in flowing area of fluid machinery rotating impeller; observe kinematic velocity of fluid on this point. ·观察者站在相对于地球静止的固定坐标系下观察到的为绝对速度 Absolute velocity is observed when observer stands on stable fixed coordinate relative to the earth. ·观察者站在与叶轮一起旋转的相对坐标系下观察到的是相对速度 Relative velocity is observed when observer stands on relative coordinate rotating with impellers. ·观察者可以非常清楚地观察流体在转轮内的运动状态 Observer can observe fluid motion state inside impeller wheel clearly. ·绝对速度和相对速度间存在如下关系：
·This curve’s rotating around the axial makes the revolution surface called cross section ·过流断面的面积确定了轴面速度的平均值
·The area of cross section determines average meridional velocity
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速度三角形的定义 Definition Of Velocity Triangle
在旋转机械中，往往将各速度在柱坐标系下分解成 In rotary, velocity is usually resoluted in column coordinate
Velocity of following runs along circumferential direction,
Therefore velocity components have relation as belowing
K vr
=
K wr
K vz
=
K wz
K vu
=
K wu
+ uK
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a-点的轴面投影 Axial Region Projection Of Point
b-轴面流线
Axial Region Streamline
c-导叶
Guide Vane
d-相对运动迹线 Relative Velocity Trace Line
e-转轮叶片
Impeller Wheel Blade
f-绝对运动迹线 Absolute Velocity Trace Line
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过流断面 Flow Stream Cross Surface
·在轴面上作若干轴面流线
·Make several axial region streamlines on an axial region ·再作一曲线与所有轴面流线正交
·And then make a curve orthogonal to all streamlines ·该曲线绕轴旋转一周形成的回转面称为过流断面
展开流面 Developed Stream Surface
轴面流线 Axial Region Streamline
旋转流面 Revolved Stream Surface
流面展开 Stream Surface Development
1.流线 2.轴面流线 3.旋转流面 4.两类流面 5.过流断面
Streamline Axial Region Streamline Revolved Stream Surface Two Kinds Of Stream Surfaces Cross Section