1、Lesson 2: Euler Eq. for Turbine Machine,LEI Jun-Yong,Pump & Compressor,Content,问题描述,假设与推导,讨论,The general principle of pump,Transformation of Energy,Liquid,Compressor,Pump,Gas,Mechanical Energy (Pressure) Storage by Fluid,一、,Trasformation,Mechanical Energy Input,Water Flow,p1, c1, H1,p: pressure,c: v
2、elocity,H: height,p2, c2, H2,Problem & Aim to?,Mechanical Energy (Pressure) Storage by Fluid,Mechanical Energy Input,N = Mw,ag=9.18 N/kgConst.,Continue,Geometry,r1 Diameter of Inlet, mm,b,bA Blade, mm,r2 Diameter of outlet, mm,Kinetic,n rotate speed, r/min,Q Capacity, m3/min,Dynamic,M torque, Nm,N P
3、ower, W,Who work out this problem?,Leonhard Euler (1707-1783),13 Babies! & 2 Marriage,Euler calculated without apparent effort, as men breathe, or eagles sustain themselves in the wind.,- Francois Arago,Simplification,3 Dimension problem is converted to 2 Dimension,二、,The Parameters,Geometry,r1 Diam
4、eter of Inlet,b,bA Blade,r2 Diameter of outlet,Kinetic,N rotate speed,Q Capacity,Dynamic,M torque,N Power,2,1,Velocity Triangle for Inlet & Outlet,u1,w1,c1,u2,w2,c2,u,w,c,叶轮圆周速度/牵连速度,相对速度,绝对速度,2,1,u2,w2,c2,(360)(转速n)/(60),角速度w,(r)(w),圆周速度u,nu,周向分量,cu,径向分量,cr,(r)(cr)(2pr)(b),(密度)(速度)(面积),质量流量G,=,=,=,
5、Gc,Continue,Force Analysis,质点系的牛顿第二定律,动量矩的变化,(dL)/(dt),M,=,受到的合力矩,(dL)=(dG)(r2cu2-r1cu1),Continue,Inlet,Outlet,Fluid (Mass) Particle System,Moment t1,t2,Channel,Angular Momentum of Fluid Particle, t1 ？, t2 ？,Inlet,Outlet,Moment t1,t2,Channel,Angular Momentum of Fluid Particle, t1, t2,Vector Product
6、(cr),Newton No.2 Law,出口速度三角形,Euler Formula,D2/D1=2.0,Force & Power,Newton No.2 Law,Blade Power Input,Blade Torque,Rotate Speed,The Logic of Derivation,Q & A,Question,Answer,三、,More Explain,Continue,Effect of Kinds of Parameters,Const.,？,Performance Curve,Function,Q,HQ,NQ,A,A/B,Distribution of Fluid
7、Energy,Pump,u1,p1,u2,p2,Hth,Impeller Reaction : W,Home Work,欧拉推导叶轮机械过程时做了哪些假设？ 推导欧拉方程 Hth=f(Q) or Hth=f(u)； 解释流体获得能头的来源； 请解释柯氏加速度（可选题，参见理论力学）,Deadline: Next Wed. Main Building 2204 Room,Solution to Home Work - 1,欧拉推导叶轮机械过程时做了哪些假设？ 各种力学物理量速度、压力没有轴向分量，因此3D问题转化为2D问题； 沿周向，各种力学量具有均一数值，因此2D问题再次被简化为1D问题； 液体没有粘性，因此不存在因粘性所导致的（内）摩擦损失； 存在无限多不具有厚度叶片，因此流体的流动方向严格与叶片相切； 稳定流动，因此各种物理量对时间的导数为0。,Deadline: Next Wed. Main Building 2204 Room,Solution to Home Work - 2,推导欧拉方程 Hth=f(Q) or Hth=f(u)；,Inlet,Outlet,Moment t1,t2,Channel,Angular Momentum of Fluid Particle, t1, t2,
