Flow resistance is a wide-ranging problem. The fuel consumption of a car at high speed mainly comes from air resistance rather than ground frictional resistance. The reason why smog can be "suspended" in the air is also due to flow resistance. These all illustrate the importance of air resistance.
01
Pressure differential resistance and frictional resistance
From the point of view of force, the resistance of the object is the direct action of the fluid on its surface. What is perpendicular to the surface of the object is the pressure of the fluid, and the resistance generated by it is called differential pressure resistance; what is parallel to the surface of the object is the viscous shear force of the fluid, and the resistance generated by it is called frictional resistance. Apart from these two forces, there is no other force. Therefore, the total resistance of an object is the resultant force of pressure difference resistance and friction resistance. The pressure difference resistance is closely related to the shape of the object, and the friction resistance is mainly related to the surface area of the object.
Some places say that in addition to pressure difference resistance and friction resistance, there are induced resistance, shock wave resistance, etc., which is a misunderstanding. In fact, both induced resistance and shock wave resistance can be attributed to pressure difference resistance and friction resistance (mainly pressure difference resistance).
02
shape resistance posterior resistance
It has been known since ancient times that objects moving in a fluid will experience resistance, and the resistance is closely related to the shape of the object. But the original theory of fluid mechanics came to the opposite conclusion. Based on the laws of fluid motion of Euler and Bernoulli, if the viscosity of the fluid is ignored, the fluid will not produce resistance to objects of any shape moving in it.
It seems that the resistance is completely caused by viscosity, but the viscosity of air is very small, and the frictional resistance produced by it is much smaller than the aerodynamic resistance measured actually. This contradiction is known in history as "D'Alembert's Paradox" because it was proposed by the French mathematician D'Alembert.
It was not until Prandtl put forward the boundary layer theory that people really realized the essence of flow resistance. Pressure difference resistance is the main component of aerodynamic resistance, while for general objects, pressure difference resistance is mainly due to boundary layer separation.
Early people (maybe many people think so now) based on some kind of "common sense", believed that the shape of the front part of the object determines the size of the resistance, and the resistance will be small if the front part is sharper. With the boundary layer theory, it is more important to discover the shape of the rear of the object. Because the shape of the back of the object determines where the boundary layer separates and thus the pressure distribution on the surface of the object.
Common fish and birds are relatively perfect streamlined bodies, with round heads and pointed tails.
03
Shape resistance Front resistance
Although the shape of the rear of the object is decisive for the amount of drag, the shape of the front is also important. For example, if the front of the object is square, the fluid will separate early at the sharp corners, and the carefully designed shape of the rear will lose its meaning. For the trucks currently running on the highway, the shape optimization that has been achieved is mainly concentrated on the front part, and the rear part is limited by the shape of the container, so less work has been done. For objects moving at transonic speed, the shock wave will generate additional resistance, so the front part is designed into a very pointed shape, so that the cone angle of the shock wave is smaller to reduce resistance.
04
Shock wave resistance
When the incoming flow speed approaches or exceeds the speed of sound, shock waves will be generated, which will bring additional shock wave resistance. In essence, shock wave resistance is also a kind of pressure difference resistance, which is caused by insufficient pressure recovery in the rear half of the object due to the existence of shock waves. Neglecting the viscous loss, when there is no shock wave, the deceleration of the airflow in the second half of the object corresponds to a pressure rise Δp1; when there is a shock wave, the airflow partially loses part of the mechanical energy when passing through the shock wave, and the pressure rise Δp2 corresponding to the same deceleration is will be smaller than Δp1. Therefore, when there is a shock wave, the pressure in the rear half of the object is a little lower, which is the source of the shock wave resistance. Making the front edge of the object sharp can reduce the shock cone angle, thereby reducing the loss caused by the shock wave, and also reducing the shock wave resistance. When the ship travels on the water surface, it will generate surface waves and also have wave resistance, so it should be made pointed, while the submarine traveling underwater is rounded.
Using energy loss to explain shock wave resistance is not direct enough. After all, the pressure and viscous force on the surface of an object are the factors that directly determine the magnitude of resistance. Next, the shock wave resistance is explained by the change of the surface pressure of the object.
05
Effect of shape and surface quality on drag
Reducing resistance is an eternal theme of fluid mechanics. The use of streamlines can effectively reduce the differential pressure resistance, mainly because there is no boundary layer separation on the surface of a well-designed streamlined body, thereby reducing the differential pressure resistance.
In addition to shape, the surface roughness of an object also affects drag. Generally, the smoother the surface, the smaller the frictional resistance, but sometimes the surface of the object is intentionally rough, so that the boundary layer becomes turbulent to inhibit separation, thereby significantly reducing the pressure differential resistance.
06
Summarize
When analyzing the aerodynamic resistance of an object, the habit of fluid mechanics is to divide it according to the form of force. The resistance caused by the pressure acting vertically on the surface of the object is called differential pressure resistance, while the resistance caused by the friction force parallel to the surface of the object is called frictional resistance. Since there is no force other than these two forces on the surface of an object, any kind of resistance is either pressure difference resistance or friction resistance, or both.
The pressure difference resistance caused by flow separation and the pressure difference resistance caused by shock wave are the biggest factors affecting the aerodynamic resistance of objects.
Subsonic low-resistance objects have round heads and pointed tails, while supersonic low-resistance objects have pointed ends.
