Aerodynamics In Civil Engineering

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Fig. 8.4 Upper-wing-surface pressure distributions with laminar rooftop

Fig. 8.4 Upper-wing-surface pressure distributions with laminar rooftop other hand, only modest maximum suction pressures are permissible before sonic conditions are reached. In this case, therefore, the pressure distribution is very flat. An example of the practical application of these ideas for low flight speeds is illustrated schematically in Fig. 8.5. This shows a Liebeck* aerofoil. This sort of aerofoil was used as a basis for the aerofoil designed by Lissaman* specially for the successful man-powered aircraft Gossamer Albatross and Condor. In this application high lift and low drag were paramount. Note that there is a substantial fore-portion of the aerofoil with a favourable pressure gradient, rather than a very rapid initial acceleration up to a constant-pressure region. The favourable pressure gradient ensures that the boundary layer remains laminar until the onset of the adverse pressure gradient, thereby minimizing the boundary-layer thickness at the start of the pressure rise. Incidentally, note that the maximum suction pressure in Fig. 8.5 is considerably less than that in Fig. 8.4 for the low-speed case. But, it is not, of course, suggested here that at the speeds encountered in man-powered flight the flow over the upper wing surface is close to sonic conditions.

There is some practical disadvantage with aerofoils designed for concave pressure-recovery distributions. This is illustrated in Fig. 8.6 which compares the variations of lift coefficient with angle of incidence for typical aerofoils with convex and concave pressure distributions. It is immediately plain that the concave distribution leads to much higher values of (Cz,)max. But the trailing-edge stall is much more gentle, initially at least, for the aerofoil with the convex distribution. This is a desirable

* R.H. Liebeck (1973) A class of aerofoils designed for high lift in incompressible flow. J. of Aircraft, 10, 610-617.

tp.B.S. Lissaman (1983) 'Low-Reynolds-number airfoils', Annual Review of Fluid Mechanics, 15,223-239.

Fig. 8.7 Schematic figure illustrating a modern supercritical aerofoil

feature from the viewpoint of safety. The much sharper fall in Cl seen in the case of the aerofoil with the concave pressure distribution is explained by the fact that the boundary layer is close to separation for most of the aerofoil aft of the point of minimum pressure. (Recall that the ideal Stratford distribution aims for the boundary layer to be on the verge of separation throughout the pressure recovery.) Consequently, when the angle of incidence that provokes separation is reached, any further rise in incidence sees the separation point move rapidly forward.

As indicated above, it is not really feasible to design efficient wings for aircraft cruising at high subsonic speeds without permitting a substantial region of supersonic flow to form over the upper surface. However, it is still important to minimize the wave drag as much as possible. This is achieved by tailoring the pressure distribution so as to minimize the strength of the shock-wave system that forms at the end of the supersonic-flow region. A schematic figure illustrating the main principles of modern supercritical aerofoils is shown in Fig. 8.7. This sort of aerofoil would be designed for Moo in the range of 0.75-0.80. The principles behind this design are not very dissimilar from those exemplified by the high-speed case in Fig. 8.4, in the sense that a constant pressure is maintained over as much of the upper surface as possible.

8.3 Multi-element aerofoils

At the low speeds encountered during landing and take-off, lift needs to be greatly augmented and stall avoided. Lift augmentation is usually achieved by means of flaps* of various kinds - see Fig. 8.8. The plain flap shown in Fig. 8.8a increases the camber and angle of incidence; the Fowler flap (Fig. 8.8b) increases camber, angle of

*The most complete account is given by A.D. Young (1953) 'The aerodynamic characteristics of flaps'. Aero. Res. Council, Rep. & Mem. No. 2622.

Aerofoil Young

Shroud Aerofoil chord line

(b) The split flap

Fbre-flap Main flap—

(f)The double slotted flap

The angle 8f is the flap deflection

-Position of aerofoil chord line on flap ««hen flap is retracted

Shroud Shroud lip

Air flow through slot (d) The single slotted flap incidence and wing area; and the nose flap (Fig. 8.8g) increases camber. The flaps shown in Fig. 8.8 are relatively crude devices and are likely to lead to boundary-layer separation when deployed. Modern aircraft use combinations of these devices in the form of multi-element wings - Fig. 8.9. The slots between the elements of these wings effectively suppress the adverse effects of boundary-layer separation, providing that they are appropriately designed. Multi-element aerofoils are not a new idea. The basic concept dates back to the early days of aviation with the work of Handley Page in Britain and Lachmann in Germany. Nature also exploits the concept in the wings of birds. In many species a group of small feathers, attached to the thumb-bone and known as the alula, acts as a slat.

Main aerofoil

Fig. 8.9 Schematic sketch of a four-element aerofoil

How do multi-element aerofoils greatly augment lift without suffering the adverse effects of boundary-layer separation? The conventional explanation is that, since a slot connects the high-pressure region on the lower surface of a wing to the relatively low-pressure region on the top surface, it therefore acts as a blowing type of boundary-layer control (see Section 8.4.2). This explanation is to be found in a large number of technical reports and textbooks, and as such is one of the most widespread misconceptions in aerodynamics. It can be traced back to no less an authority than Prandtl* who wrote:

The air coming out of a slot blows into the boundary layer on the top of the wing and imparts fresh momentum to the particles in it, which have been slowed down by the action of viscosity. Owing to this help the particles are able to reach the sharp rear edge without breaking away.

This conventional view of how slots work is mistaken for two reasons. Firstly, since the stagnation pressure in the air flowing over the lower surface of a wing is exactly the same as for that over the upper surface, the air passing through a slot cannot really be said to be high-energy air, nor can the slot act like a kind of nozzle. Secondly, the slat does not give the air in the slot a high velocity compared to that over the upper surface of the unmodified single-element wing. This is readily apparent from the accurate and comprehensive measurements of the flow field around a realistic multi-element aerofoil reported by Nakayama etalIn fact, as will be explained below, the slat and slot usually act to reduce the flow speed over the main aerofoil.

The flow field associated with a typical multi-element aerofoil is highly complex. Its boundary-layer system is illustrated schematically in Fig. 8.10 based on the measurements of Nakayama etal. It is noteworthy that the wake from the slot does not interact strongly with the boundary layer on the main aerofoil before reaching the trailing edge of the latter. The wake from the main aerofoil and boundary layer from the flap also remain separate entities. As might well be expected, given the complexity of the flow field, the true explanation of how multi-element aerofoils augment lift, while avoiding the detrimental effects of boundary-layer separation, is multifaceted. And, the beneficial aerodynamic action of a well-designed multi-element aerofoil is due to a number of different primary effects, that will be described in turn.*

Fig. 8.10 Typical boundary-layer behaviour for a three-element aerofoil

* L. Prandtl and O.G. Tietjens Applied Hydro- and Aeromechanics, Dover, New York, p. 227.

*A. Nakayama, H.-P. Kreplin and H.L. Morgan (1990) 'Experimental investigation of flowfield about a multielement airfoil', AlAA J., 26, 14-21.

® Many of the ideas described in the following passages are due to A.M.O. Smith (1975) ibid.

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