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## 10. Separation

An important observation is that fluid flow is always irreversible. It is irreversible because fluids have viscosity, and whenever velocity gradients appear in the flow there will be friction and energy dissipation due to viscous stresses. The flow can be reversible only if there are no velocity gradients anywhere, since that is the only condition under which there is no friction. However, when frictional effects are small, a flow may be approximately reversible. For instance, in the flow through a large duct where the boundary layers are very thin, viscous effects are confined to a rather small region, and the fluid friction may sometimes be neglected. This is not the case for most practical flows. In most pipe and duct flows, for example, the velocity gradients extend over the entire cross-section and frictional stresses are all important. Even if the boundary layers are thin to begin with, they can thicken rapidly under some circumstances, and the flow can separate, as in the diffuser flow shown in figure 10.1.

 Figure 10.1 Separated diffuser flow (included angle =20^o). Flow is from left to right. From Japan Society of Mechanical Engineers.

If the flow is in the direction of increasing area (this is called a diffuser flow), the effects of friction and separation are usually small, if the angle of divergence is very small. For larger angles (an included angle greater than about 7^o is sufficient), there is a possibility of flow separation, by which we mean that in some parts of the flow the fluid is actually going in a direction opposite to the bulk flow direction. Large losses can occur, as the mechanical energy of the fluid is used to drive large unsteady eddying motions which eventually dissipate into heat. This type of flow can occur for quite small angles. In contrast, when the flow is in the direction of decreasing area, as in the contraction flow shown in figure 10.2, there is very little risk of producing large separated regions, even for very large values of the included angle (up to 45^o), and generally losses are quite small.

 Figure 10.2 Flow in a contraction. Flow is from left to right.

So great care needs to be taken in considering frictional effects: sometimes they are negligible, and sometimes they are not. When separation occurs, however, frictional effects are always important. It is worth noting that sharp corners almost always produce a separated flow. The sudden expansion and contraction flows shown in figure 10.3 graphically demonstrate the problem, and these flows are clearly irreversible.

 Figure 10.3 Flow through a sudden contraction (left), and a sudden expansion (right). Flow is from left to right. From Japan Society of Mechanical Engineers.

Sharp corners typically produce a separated flow, but they are not the only cause of separation. For example, the flow over a cylinder can produce a large region of separated flow downstream of the cylinder (figure 10.4). This region is called a wake (see also figure 8.3).

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 Figure 10.4 Flow over two cylinders. From Japan Society of Mechanical Engineers.

The flow patterns over the front and back of the cylinder are quite different. In the front, the flow smoothly passes over the cylinder, but in the wake the flow is usually highly unsteady and large eddies or vortices are shed downstream. The large eddies are formed at a regular frequency and they produce pressure disturbances in the flow which we can sometimes hear as sound waves. When we talk of the wind whistling in the trees, it is the sound of eddies being shed. A Greek instrument, the Aolian harp, made use of this regular vortex shedding to produce music. The alternate shedding of vortices produces an alternating lift force, oscillating in direction and magnitude. If the frequency of the shedding couples to a natural frequency of the cylinder and its supports, large cross-stream oscillations can occur in the cylinder position. This kind of aerodynamic instability was responsible for the destruction of the Tacoma Narrows bridge, and it has led to a number of spectacular cooling tower failures in England.

Wakes almost always contain large eddying motions which are shed downstream, although they may not shed at a regular frequency. For instance, the wake of a boat often contains large eddying motions, and this region is often called a ``dead-water'' region. Similar flow patterns are observed downstream of pylons supporting a bridge.

In any case, the eddies dissipate energy. Friction is the source of the irreversibility of fluid flow: either through the formation of boundary layers over the surface, or large eddies in the wake (in thermodynamics we say that the entropy of the flow increases). In an imaginary fluid that has no friction (an inviscid fluid), there would be no drag, the entropy does not change, and the flow would be reversible. For example, a cylinder in the flow of an inviscid fluid has no vortex shedding and it has no drag, contrary to our practical experience.

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