According to the principle of inertia (see Laws of the movement of Newton), no energy is necessary to maintain the rectilinear motion uniform of a body in the vacuum . In a fluid, liquid or gas, a resistance or forces trailed is opposed to the movement of the body and it is the work of this force which involves a consumption of energy. If the movement were accelerated, it would also be necessary to take account of the added mass.

General information

General formula

The trail of an obstacle $F\_x\; \backslash ,$ always depends on the density of the fluid $\backslash \; rho\; \backslash ,$, its speed $V\; \backslash ,$ far from the obstacle and of a surface $A\; \backslash ,$ selected according to the obstacle (it is often the Master-couple, surfaces seen by the flow). If in fact the only variables intervene, the dimensional Analyze watch which the formula cannot be written, except for a factor, which

This formula, imposed by dimensional coherence, reveals a surface, a grouping of variables which is interpreted like the dynamic Pression and the Coefficient of drag without dimension $C\_x\; \backslash ,$.

In general, this force depends on other physical sizes, which often corresponds to the fact that the trail is not proportional to the square speed. The formula keeps the same form exactly but the coefficient of drag depends on these sizes through other numbers without dimensions. Except exceptions, it depends on the incidence of the flow and viscosity through the Reynolds number. For rather important speeds, it also depends on compressibility through the Mach number. In more particular cases, it depends on various physical parameters which can be taken into account effectively by using other numbers without dimensions which are often of simple reports/ratios lengths.

Various types of trail

In all the cases, there exists a trailed friction related to the differences in speeds between the fluid nets; those cause a dissipation of the mechanical energy which is transformed into heat. It is essential for a thin body like a plane plate.

The more one body deviates from a plate, plus this trail of friction becomes negligible in front of the form drag or trailed pressure related to a fall of Pression to the downstream of the obstacle. It is the case of a car.

With the downstream of a wing of finished scale lines of swirls consuming energy appear which are at the origin of an induced trailed by the Portance.

As of the Transsonique is formed a Shock wave (for an idea on the phenomenon, to see Supersonique) which slows down the flow brutally. This deceleration still corresponds to a loss of energy, work of the trailed wave .

In what follows, one will arbitrarily consider the case of a flow compared to a fixed obstacle (as in a blower).

Trail of friction

Speed varies between zero on the obstacle and its value far from this one. One thus observes variations speed which tend to being attenuated by the Viscosité of the fluid according to a phenomenon similar to a solid friction resulting in a heating.

For the very low speeds, corresponding to very a small number of Reynolds, viscosity is dominating. The coefficient of drag is then inversely proportional to the Reynolds number, the force being consequently proportional at the speed and not to its square.

The more the Reynolds number increases, the more viscosity with evil to slow down the general flow. The zone of variation speeds imposed by the condition of not-slip on the wall narrows and forms a Boundary layer which concentrates the main part of the viscous effects. At the beginning, the flow is Laminaire there: the fluid nets follow the shape of the obstacle wisely. Starting from a zone of transition, the flow becomes turbulent, the particles contained in the boundary layer having erratic trajectories. It is then thicker and dissipates more energy than the laminar layer.

In aeronautics, it thus appears desirable to push back as much as possible this transition but, in certain cases, it is necessary to find a compromise with the maintenance of turbulence intended to prevent separation at the origin of the form drag.

Form drag

The trail of friction represents the essence of the trail of a thin obstacle. As soon as the obstacle has a certain thickness superimposes a form drag which quickly becomes dominating on a bluff body.

Case of a bluff body

For the very weak Reynolds, the fluid is accelerated with the upstream and idle with the back. According to the Theorem of Bernoulli, the pressure decreases then increases to find the same values as with the upstream. More precisely, the paradox of Alembert appears: without viscosity there would be no trail. Actually viscosity maintains the cohesion of the fluid and, when it becomes negligible in the Reynolds relatively high, he occurs an separation which involves a separation of the flow. Indeed one can then consider that the boundary layer is rather thin so that the pressure roughly has there the same value as in the close healthy fluid (it is the principle of simplifications of the theory of the boundary layer). In addition, in the vicinity most immediate of the wall, the speed is very low there. That makes it possible the relatively high pressure to accelerate the boundary layer with the upstream and to make it ebb upstream in its downstream part. With the meeting of the healthy fluid coming from the upstream a swirl starts then which dissipates energy. With a symmetrical bluff body, like a cylinder with circular section, one obtains two symmetrical swirls then. A weak increase speed privileges one of both and, when its diameter becomes about the diameter of the cylinder, it is detached to be replaced by a swirl located on other side, which gives rise to a Allée from swirls of Karman. New increases in the Reynolds number transform the swirling wake into a turbulent wake. In all the cases, swirling or turbulent, speeds of the fluid particles are increased, which involves a fall of the pressure and consumes energy.

Thus is born the form drag which corresponds less one overpressure to the upstream that with a depression with the downstream related to an separation.

Case of a shaped body

As long as the swirls are not detached, they remain locked up in a zone surrounded by the healthy flow where the viscosity of the fluid is negligible. A manner of reducing the trail consists in solidifying this zone by the addition to the obstacle of an appendix. This makes it possible to increase the speed to which separation occurs.

A wing of plane is at the same time shaped and thin, this last characteristic bringing it closer to a plate. Thus, the form drag can be controlled with the incidences not too high. There exists nevertheless an incidence beyond which a swirl is created on the suction face, which involves unhooking with a significant growth of the trail and a reduction in the bearing pressure.

Induced trail

A wing of finished scale creates a induced Traînée by the bearing pressure via tip vortexes. Those are related to the equalization of the pressures coming from the under-surface and the suction face.

Trail of wave

In the shock waves the rate of the flow falls brutally so that its normal component with the shock passes from supersonic to the subsonic one, which results in a new type of trail corresponding to a new consumption of energy.

In the Transonic phase , the shock wave located on the suction face is at the origin of a phenomenon similar to the separation which, in addition to the increase in the trail, causes an instability.

In the Supersonic phase , this phenomenon disappears but it is replaced, for a traditional profile of wing with leading edge rounded, by a new term of trail related to a detached shock wave.

See too

• atmospheric Aérodynamisme
• Trailed, Trailed gravitational condensation
• Trailed
• Trailed electric