32
P. Liu
1.5 Establishment and Application of Boundary
Layer Theory
In the twentieth century, the machinery industry reached its peak and
entered an era of all-round development and perfection, which undoubtedly promoted the comprehensive and rapid development of mechanics,
and formed multi-disciplinary and multi-field research results, showing their
own unique contents and directions in theory, experiment, and application. During this period, fluid mechanics was naturally divided into three
branches: theoretical fluid mechanics, experimental fluid mechanics, and
computational fluid mechanics. According to the study medium, it can be
divided into hydrodynamics or aerodynamics. Under the guidance of basic
theory, the complex flow problems related to viscous flow (such as laminar
flow, turbulence, transition, jet, separation flow, wake, etc.) are mainly
studied, and the problems of resistance and heat exchange of objects around
flow are solved. In theory, since N-S equation was derived in 1845, people
have been searching for its exact solution. However, because the system of
equations is a non-linear system of second-order partial differential equations,
the exact solution in a general sense is mathematically difficult. It is said that
only 73 exact solutions of N-S have been found up to now, famous examples include the Couette flow (Couetteis French physicist at the end of the
nineteenth century) produced by the dragging a flat plate under no pressure,
Poiseuille flows (the fully developed laminar flow), produced by Poiseuilleis
French physiologist (1799–1869, as shown in Fig. 1.35), the Stokes (1851)
solution of the flow around a small Reynolds number sphere, etc. A lot of
problems in practice can only be solved by the approximate method.
Since the French scientist D’Alembert put forward the D’Alembert
paradox of steady flow of ideal fluid around an arbitrary three-dimensional
object in 1752, people began to doubt the classical theory based on the ideal
fluid model. By the first half of the nineteenth century, the study of ideal
potential flow theory had gradually entered a perfect stage, and the classical
hydrodynamics research was in a low ebb. Especially, the conclusion that
there was no resistance to the flow around a cylinder was obtained using this
model, which made people unable to do anything. Naturally, the N-S equation representing viscous fluid should be used to solve this problem. However,
a difficult problem is how to deal with the effect of viscous flow around an
object at the large Reynolds number. According to the accepted facts at that
time, if the Reynolds number of incoming flow calculated by velocity and
diameter of the cylinder is greater than 10 4 , the influence of viscous effect
P. Liu
1.5 Establishment and Application of Boundary
Layer Theory
In the twentieth century, the machinery industry reached its peak and
entered an era of all-round development and perfection, which undoubtedly promoted the comprehensive and rapid development of mechanics,
and formed multi-disciplinary and multi-field research results, showing their
own unique contents and directions in theory, experiment, and application. During this period, fluid mechanics was naturally divided into three
branches: theoretical fluid mechanics, experimental fluid mechanics, and
computational fluid mechanics. According to the study medium, it can be
divided into hydrodynamics or aerodynamics. Under the guidance of basic
theory, the complex flow problems related to viscous flow (such as laminar
flow, turbulence, transition, jet, separation flow, wake, etc.) are mainly
studied, and the problems of resistance and heat exchange of objects around
flow are solved. In theory, since N-S equation was derived in 1845, people
have been searching for its exact solution. However, because the system of
equations is a non-linear system of second-order partial differential equations,
the exact solution in a general sense is mathematically difficult. It is said that
only 73 exact solutions of N-S have been found up to now, famous examples include the Couette flow (Couetteis French physicist at the end of the
nineteenth century) produced by the dragging a flat plate under no pressure,
Poiseuille flows (the fully developed laminar flow), produced by Poiseuilleis
French physiologist (1799–1869, as shown in Fig. 1.35), the Stokes (1851)
solution of the flow around a small Reynolds number sphere, etc. A lot of
problems in practice can only be solved by the approximate method.
Since the French scientist D’Alembert put forward the D’Alembert
paradox of steady flow of ideal fluid around an arbitrary three-dimensional
object in 1752, people began to doubt the classical theory based on the ideal
fluid model. By the first half of the nineteenth century, the study of ideal
potential flow theory had gradually entered a perfect stage, and the classical
hydrodynamics research was in a low ebb. Especially, the conclusion that
there was no resistance to the flow around a cylinder was obtained using this
model, which made people unable to do anything. Naturally, the N-S equation representing viscous fluid should be used to solve this problem. However,
a difficult problem is how to deal with the effect of viscous flow around an
object at the large Reynolds number. According to the accepted facts at that
time, if the Reynolds number of incoming flow calculated by velocity and
diameter of the cylinder is greater than 10 4 , the influence of viscous effect