Chapter 5 Boundary Layer (BL) 5.1 Introduction D'Alembert Paradox(佯谬,疑题): A body immersed in a frictionless fluid has zero drag au a ou au l-+1 p ax 2 Ox- Oy
Chapter 5 Boundary Layer (BL) 5.1 Introduction * D’Alembert Paradox（佯谬，疑题）: A body immersed in a frictionless fluid has zero drag. + + = − + 2 2 2 2 1 y u x u x p X y u v x u u
+一=X ~,2 p、ox2oy Inviscid 0 or Ox- ay 0 2
2 = 0 + + = − + 2 2 2 2 1 y u x u x p X y u v x u u Inviscid x p X y u v x u u = − + 1 0 2 2 2 2 = + y u x u or = 0 = y u
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) 第三届国际数学大会 德国海登堡 (论性很小的流体运动) Ludwig Prandtl(1875-1953)
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 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 2 Displacement Thickness 8*(排移厚度,移厚度) U
5.2 Three Thicknesses of a Boundary Layer 2. Displacement Thickness * (排移厚度，位移厚度） d U y u x 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
U real ud ldeal s Udy=pU △m= !- pU=pr(-Mb=DU「(1-p rea PU8-8
5 u dy d * 0 udy d y U = 0 udy 0 Udy = U − 0 0 Udy udy ( ) = − 0 U u dy * U = − 0 1 dy U u U = − 0 * 1 dy U u m real = m ideal = m = ( ) * m real = U −