一种新型有压力梯度的平面层流边界层理论——机械能耗损积分法  

A New Theory of Laminal Plane Boundary Layer with Pressure Gradient

作　　者：荣深涛[1] 

机构地区：[1]北方交通大学土木建筑工程学院,北京100044

出　　处：《北方交通大学学报》2003年第4期1-5,共5页Journal of Northern Jiaotong University

基　　金：国家自然科学基金资助项目(19771070)

摘　　要：提出了一种新的有压力梯度的层流平面边界层理论,可称为机械能耗损积分法,它是由两部分理论所组成的:第一部分包括不可压缩流体的应力微分方程以及从中导出的层流平面边界层流速与切应力分布的理论公式,式中包括一无因次型参数或相似准则P,P的数值表征不同层流平面边界层的流速与切应力分布.第二部分包括动量与动能积分方程以及由它们导出的机械能耗散积分方程和层流平面边界层厚度的理论公式.本理论同所有积分法一样,采用了横向流速为零的假定,但扬弃了普兰特假定,因而其压力梯度的使用范围不受约束,对忽略横向流所导致的理论误差,利用机械能耗损系数进行了修正,因而可取得较高的精度.对零攻角层流平面边界层的试算表明:其型参数P=-1,其流速分布与半槽道流相似,存在一顺压梯度而非现有理论所假定的为零压梯度,所有计算结果与实验比较在未修正前其误差不超过5%,在修正之后不超过1%.本理论采用了微分法与积分法各自的优点,是分析严谨、结构简便、计算精确的适用于任意压力梯度的层流平面边界层理论,其计算方法还可推广应用于湍流平面边界层.A new theory is proposed for laminal plane baundary layer with pressure gradient, which is formed by the following two portions. The first is the theoretical formular of the ralative volocity distribution with its dimensionless simular criterial or shape parameter P, which is derived from the stress differential equation of the uncompressible flow by using of the hypothesis of transverse energy conservation, every numerical number of P represents a typical volocity distribution of laminar plane boundary layer. The secondary is the theoretical formnlae of the thickness of the laminar plane boundary layer derived from the mechanical energy lose integration equation without using Prandtl hypothesis. The numerical number of shape parameter of a zero_attack_angle laminar plane boundary layer is equel to P=-1 determined by the experiement data, the velocity distribition curve is similar to a semi_channel flow. The formula of the thickness of the laminar boundary layer δ and the shear stress τ on plane after correction by transverse energy lose coefficlent are perfect coincident with experiment data.

关 键 词：流体力学 层流 边界层 型参数 相似准则 

分 类 号：O357.4[理学—流体力学]