工程流体力学第五章all.ppt

Chapter 5 Boundary Layer (BL),5.1 Introduction,* DAlembert Paradox（佯谬，疑题）: A body immersed in a frictionless fluid has zero drag.,2,or,3,Boundary layer (边界层),Although frictional effects in slightly viscous fluid are indeed present, they are confined to a thin layer near the surface of the body, and the rest of the flow can be considered inviscid. (1904, Prandtl),Ludwig Prandtl(1875-1953),第三届国际数学大会 德国海登堡 （论粘性很小的流体运动）,5.2 Three Thicknesses of a Boundary Layer,2. Displacement Thickness (排移厚度，位移厚度）,1. BL Thickness d (名义厚度，厚度）,The locus of points where the velocity u parallel to the plate reaches 99 percent of the external velocity U.,5,3. Momentum Thickness （动量厚度，动量损失厚度）,5.3 Momentum Integral Relation for flat-plate BL (平板边界层动量积分方程),U=const p=const,Steady & incompressible,RTT,8,Momentum equation:,Continuity:,速度积分法求阻力,10,BC:,11,12,The thickness of a flat plate BL:,Estimate,13,Shape factor (形状因子),14,Drag coefficient(阻力系数),Homework: P7.9, P7.10, P7.11,Skin-friction coefficient (表面摩擦系数),15,5.4 Boundary Layer Equation,2-D,steady,incompressible,neglect body force N-S equations,16,Euler Equation,17,Reynolds stress(雷诺应力),Prandtls Boundary Layer Equation,18,5.5 Blasius Solution of Laminar Flat-Plate Boundary Layer,Prandtls student,similarity,Coordinate transformation （坐标变换）,Blasius 1908,19,Blasius equation,（吴望一流体力学下册）,20,21,Blasius Solution vs Experimental results,22,5.6 Boundary Layers Separation,s1,23,Critical point,Favorable pressure gradient(顺压梯度),Adverse pressure gradient(逆压梯度),Separation(分离),s2,s3,s4,s5,24,5.7 Turbulent Boundary Layer,Inertia force / viscous force,Turbulence,25,26,Reynolds Equation,We can analyze the turbulent flow by recognizing that the velocities and pressures comprise of an average and a fluctuating part. This representation was first suggested by Reynolds and is called the “Reynolds deco