Is the fluid boundary layer real?

In simple terms, a boundary layer is the definition of a certain flow phenomenon. When the air flow through an object, the gas molecules on the surface of the object will be stuck by the wall due to the presence of viscosity, and the velocity will drop to 0. Gas molecules that are very close to the surface collide with these gas molecules with a velocity of 0 or other slowed down, resulting in a slowdown.

The farther away from the surface, the lower the probability and effect of such a collision, and the closer the velocity of the gas molecules is to the velocity of the incoming flow. In this way, a flow region is formed above the surface of the object with a gradual increase in velocity from 0 to the incoming velocity, which is called the boundary layer in hydrodynamics. Flow within the boundary layer is important for understanding many hydrodynamic problems, such as stall and frictional resistance, so it has always been a hot topic of research.

Concepts are all set by people, I circle a piece of land, give the name "A", you ask me whether "A" exists or not, of course mine exists, he does not exist, can I name him, and then, I found a problem, because the concepts of points and lines in geometry are also named, but they only exist in the human brain, and there is no entity in the real world. It can be said that they do not exist. And if you think about it, the concepts of points and lines in geometry can always be applied in the real world.

The concept of dots and lines is actually a description of the world, an abstraction, which is essentially the first in the objective world, and is an abstract concept that deletes the properties of objective things that cannot express the geometric nature. I think the boundary layer is also the same concept, the birth of the boundary layer is not born from the need for a simple description of the objective world (such as "my bicycle", just to describe the bicycle that already exists), but to simplify the calculation of fluid mechanics, it itself is a mathematical assumption introduced in the study of mathematical models, it is abstracted from the objective world, but it does not really exist in the objective world. Further, we can see the image of the "boundary layer" in the experiment, I think the "boundary layer" in the diagram is still different from the boundary layer in the mathematical model, just like a straight wooden stick and a line segment are different, the line segment can replace the wooden stick when studying the geometric relationship, and in the fluid mechanics model, the boundary layer of the mathematical assumption replaces the physical object of the "boundary layer" in **.

The boundary layer would be better served by a different name like a stick. <>

The boundary layer is a thin flowing layer that is not negligible in the flow of high Reynolds number and is close to the surface of the object, also known as the flow boundary layer and the surface layer. This concept was first proposed by the German Ludwig Prandtl, the founder of modern fluid mechanics, in 1904. Since then, boundary layer research has become an important topic and field in fluid mechanics.

In the boundary layer, the fluid that is close to the surface of the object is completely adhered to the surface of the object due to the gravitational force of the molecules, and the relative velocity with the object is zero. From the outward facing, the fluid velocity rapidly increases to the local free flow velocity, which corresponds to the velocity of the ideal flow around the stream, and is generally of the same order of magnitude as the incoming velocity. Therefore, the normal direction gradient of velocity to the perpendicular surface is very large, even if the viscosity of the fluid is not large, such as air, water, etc., the viscous force is still very large relative to the inertial force, which plays a significant role, so it is a viscous flow.

Outside the boundary layer, the velocity gradient is small, the viscous forces are negligible, and the flow can be considered as an aviscous or ideal flow. At high Reynolds numbers, the boundary layer is very thin, much less thick than the length along the flow direction, and the Navier-Stokes equation can be simplified to the boundary layer equation based on the magnitude comparison of the scale and velocity rate of change. When solving the high Reynolds number winding flow problem, the flow can be divided into two parts: viscous flow in the boundary layer and ideal flow outside the boundary layer, which can be solved iteratively respectively.

The boundary layer is divided into laminar flow, turbulent flow, mixed flow, low velocity (incompressible), high velocity (compressible), and two-dimensional and three-dimensional. Since viscosity is closely related to heat conduction, there is a temperature boundary layer in addition to the velocity boundary layer in high-speed flows. <>

Before the boundary layer of the fluid was proposed, the fluid was thought to be described in terms of an inviscous Euler model. However, the results derived from this are very different from the actual project. The most famous is d'Alembert's paradox.

That is, if the fluid passes around the cylinder, there is no resistance. Plante's boundary layer theory is an epoch-making milestone in fluid mechanics. Based on experimental observations, he pointed out that in the thin layer where the fluid is in contact with the solid, there is a velocity shear layer, called the boundary layer.

The viscous action is only present in this thin layer, and the main stream area outside the thin layer can be disregarded as the viscous effect. It is precisely because of the shear stress and dissipation of such a boundary layer that the frictional resistance of the object in the fluid will occur.

There are many complex flow phenomena along with the boundary layer. It mainly includes the separation of the boundary layer and the transition of the boundary layer. The separation of the boundary layer means that the velocity of the fluid on the surface of the boundary layer is blocked to 0 under the dual action of reverse pressure gradient and viscosity.

The boundary layer will leave the solid surface and form a free-shear layer into the main flow zone. The separation of the boundary layer can greatly change the distribution of the entire flow field. This is one of the main reasons for the complexity of the flow field in the turbine.

Another phenomenon is the transition of the boundary layer. That is, the transition from laminar to turbulent boundary layers. The morphology and properties of the laminar boundary layer and the turbulent boundary layer are completely different.

The effect of the separation on the blending of fluids is also different. Especially in turbines, boundary layer transitions are frequent due to large shear and large inverse pressure gradients.

The essential difference between laminar flow and turbulent flow is the presence or absence of radial pulsation, which can be judged by the Reynolds number re.

re is defined as the ratio of the inertial force to the viscous force per unit mass of the fluid.

The Reynolds number of laminar flow is relatively small, and the viscous force dominates, even if there is a strong disturbance to the water, the disturbance will be attenuated due to the viscosity of the fluid, and the flow can still maintain a laminar flow state.

The Reynolds number of turbulent flow is large, and the inertial force is stronger than the viscous force, so there will be pulsating motion, and there is macroscopic mixing along the main flow direction and the cross flow direction.

The above is from "Fluid Mechanics", Wang Huimin, Hohai University Press.

Concept: The boundary layer is a thin flowing layer with non-negligible viscous force that adheres to the surface of the object in the flow of high Reynolds number, also known as the flowing boundary layer and the attached surface layer. Its thickness is:

Starting from the object surface (where the local velocity is zero), follow the normal direction to the distance between locations where the velocity is equal to the local free flow velocity u (strictly speaking, equal to or .

Why it matters: Controlling the adverse effects of the boundary layer. For example, in applications (e.g. for aeronautical aircraft), the transition and separation of laminar boundary layers causes wing drag (increase) or lift (or even stall) to reduce the force of the wing, so early on efforts were made to smooth the wing surface and to design a "laminar wing profile" to maintain the laminar boundary layer. However, this control is limited, so many methods of manual control of the boundary layer have been adopted to affect the structure of the boundary layer, so as to avoid the separation of air flow in the boundary layer, and reduce the resistance and increase the lifting force.

Experiments and theories have yielded several effective methods for local acceleration of the fluid: to move part of the object surface, and blow out the fluid through the nozzle hole (slit) on the object surface to increase the energy of surface stagnation (Fig. 9); Through the slit on the object surface, the stagnant current is sucked away and the boundary layer is thinned to inhibit the separation. Injection with different gases to accelerate the stagnant flow; Change the shape of the wing.

19.There are five factors that determine whether the boundary layer on the surface of an object belongs to a laminar or turbulent boundary layer: , air flow through+

Hello dear! <>

We are glad to answer for you: The five factors of whether the boundary layer on the surface of an object belongs to a laminar edge crack boundary layer or a turbulent boundary layer include: object surface shape, air velocity, air density, object surface roughness, air viscosity, and waxinessWhen the surface shape of the object is smooth, the air velocity is relatively low, the air density is high, the surface roughness of the object is small, and the air viscosity is large, the laminar boundary layer is usually formed.

However, when the surface shape of the sliding object is complex, the air velocity is high, the air density is low, the surface roughness of the object is large, and the air viscosity is small, the turbulent boundary layer is usually formed.

The friction of the earth's surface through the ground creates resistance to the horizontal movement of the air, which slows down the airflow close to the ground, and the effect of this resistance on the airflow weakens with altitude, and only at altitudes above 300 500m above the surface is the wind not affected by the rough layer of the earth's surface.

Able to flow at gradient wind speeds.

Different surface roughness has different gradient wind heights, also known as atmospheric boundary layer heights, HT is used to represent the height above the atmospheric boundary layer, the flow of wind is not affected by the rough layer of the ground, and the wind flows freely along the isobars in a laminar manner, which is called gradient wind.

Gradient Wind The height at which the flow starts is called the gradient wind height.

Since the surface of the pipe wall is rough and the fluid has a certain viscosity, it can be concluded that the velocity of the fluid very close to the wall is not equal to the incoming velocity of the fluid. Its velocity gradually increases from zero to a given velocity of the incoming flow in the direction of the wall along its normal (i.e., the direction of the perpendicular wall). So the fluid near the wall will have a thin area, which is called the boundary layer.

There is a certain distribution of fluid velocity in the boundary layer (generally assumed to be logarithmic distribution), and the flow state also has a certain variation, generally the closest to the wall is the laminar flow zone, that is, the turbulent transition zone, and finally the turbulent zone.

Because there are no smooth solids and no ideal fluids, there is a boundary layer for near-wall flows. However, not all boundary layers have a significant impact on flow, and most of them are negligible.

When a fluid flows around an object, the boundary layer at the front end or upstream of the object is generally the laminar boundary layer. Laminar boundary layer along a surface. Due to the variation in the outflow velocity, it differs from the slab, but the velocity distribution is broadly similar.

The velocity gradient of the object surface is large, so the shear stress is also large. The shear stress on the object surface is:

where is the hydrodynamic viscosity coefficient. If we calculate 0, we can find the frictional resistance coefficient and frictional resistance of the object surface. However, these calculations can only be used before the separation point.

In the case of a rotationally symmetrical flow, it can be transformed into a two-dimensional form by a transformation formula, such as the Mangler transformation, and the existing two-dimensional solution can be used. Three-dimensional calculations around any object are much more complex than two-dimensional, so they can only be solved numerically.