《流体力学 Fluid Mechanics》课程PPT教学课件（双语版）第七章 粘性流体动力学基础

First suffix iof stress expresses direction of normal of surface that stress act on;second suffix j expresses direction of stress. When i=j, Fi denoting normal stress, otherwise denoting shear stress. Making them labeled on three infinitesimal surface concluding point A, then shown as figure 7-1, here assuming normal stress that outside acts on three surface along positive direction of coordinate, shear stress along negative direction Xy y XX figure 7-I stress component of viscosity fluid 11

11 First suffix of stress expresses direction of normal of surface that stress act on; second suffix expresses direction of stress.When , denoting normal stress, otherwise denoting shear stress.Making them labeled on three infinitesimal surface concluding point A, then shown as figure 7—1, here assuming normal stress that outside acts on three surface along positive direction of coordinate, shear stress along negative direction. i j i  j Fij figure 7—1 stress component of viscosity fluid y z x zz p zx  xy  pyy yz  yx  xz pxx  xy  A

粘滤动力学基础 应力的第一个下标i表示应力作用面的法线方向;第二个下 标j表示应力的方向。当=j时F代表法向应力,否则代表切 应力。将它们标注在包含A点在内的三个微元表面上,则如图 7—-1所示,这里假定外界对微元这三个表面的法向应力都沿坐标 的正向,切向应力都沿坐标的负向。 Xy PrA y X 图71粘性流体的应力分量 12

12 应力的第一个下标 表示应力作用面的法线方向；第二个下 标 表示应力的方向。当 时 代表法向应力，否则代表切 应力 。将它们标注在包含A点在内的三个微元表面上，则如图 7—1所示，这里假定外界对微元这三个表面的法向应力都沿坐标 的正向，切向应力都沿坐标的负向。 i j i  j Fij y z x zz p zx  xy  pyy yz  yx  xz pxx  xy  图 7—1 粘性流体的应力分量 A

三、 Constitutive equation Definition Equation that confirms relation of stress and deformation velocity called constitutive equation In order to establish constitutive equation of Newton fluid Stokes put forward following assumption (1)small deformation, viz. Stress and deformation velocity are linear (2 )isotropy, that is relation of stress and deformation velocity do not change with coordinate changing ()when viscosity coefficient u>0, stress state simplifies into ideal stress state Narrating as preceding, when viscosity liquid occurs relative motion de HE T=A=u (7—2)

13 二、Constitutive equation In order to establish constitutive equation of Newton fluid , Stokes put forward following assumption: (1)small deformation, viz. Stress and deformation velocity are linear. (2)isotropy, that is relation of stress and deformation velocity do not change with coordinate changing; (3)when viscosity coefficient , stress state simplifies into ideal stress state.   0 Narrating as preceding,when viscosity liquid occurs relative motion dt d dy du       （7—2） Equation that confirms relation of stress and deformation velocity called constitutive equation. Definition :

粘滤动力学基础 二、本构方程 定义: 确定应力与变形速度关系的方程叫做本构方程。 为建立牛顿流体的本构方程,斯托克斯( Stokes)提出如 下假设: (1)小变形,即应力与变形速度成线性; (2)各向同性,即应力与变形速度的关系不随坐标变换而 变化; (3)当粘性系数→>0时,应力状态简化为理想流体的应 力状态。 如前所述,当粘性流体发生相对运动时 T=U-s de (7—2)

14 二、本构方程 为建立牛顿流体的本构方程，斯托克斯 提出如 下假设： Stokes （1）小变形，即应力与变形速度成线性； （2）各向同性，即应力与变形速度的关系不随坐标变换而 变化； （3）当粘性系数 时，应力状态简化为理想流体的应 力状态。   0 如前所述，当粘性流体发生相对运动时 dt d dy du       （7—2） 确定应力与变形速度关系的方程叫做本构方程。 定义：

Due to dynamic analysis of fluid micro-group, angular deformation velocity of fluid micro-group in plane xoy da+dB d=20= 子× y taking da+dp replace de in formula(7-2) dt dt Txy=Ix=200.= uaa x ua similarly T2=T2=2ub=u (73) az au a a=x=20,=山 az a formula(7-3) called general Newton internal friction law

15 Due to dynamic analysis of fluid micro-group, angular deformation velocity of fluid micro-group in plane xoy y u x u dt d d y x z            2 taking replace in formula（7—2） dt d dt d  d                                           x u z u z u y u y u x u x z zx xz y z y yz zy x y x xy yx z             2 2 2 similarly （7—3） formula（7—3）called general Newton internal friction law