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Aviation History
1926
1926 - 0202.PDF
SUPPLEMENT TO FLIGHT 28 THE AIRCRAFT ENGINEER MARCH 25, 1926 resulting combined streamlines constructed ]ust as resultant velocities can be graphically determined. From Bernouilli's equation (see Lamb's Hydrodynamics p. 21), it can be shown that the total head at any point of a streamline is constant. Algebraically, P -j- \ i> V2 = a constant, where P = pressure /> = fluid density V = velocity. It will be remembered that we are dealing with an incom- pressible fluid so that density is independent of pressure. It is plain that this introduces a very important limitation to the possible velocities if flow is to be conformable. By con- formable is meant conforming to the shape of the body. As the velocity along the streamline rises, the pressure necessarily falls, and should the velocity rise to such a figure that the pressure to satisfy Bernouilli's equation would have to fall by an amount greater than the initial fluid pressure, an absolute negative pressure would be required to maintain conformable flow. A negative pressure is plainly impossible in an incompressible fluid hence such phenomena as cavitation in water. It will also be obvious that the application of analyses for the " ideal" (i.e. incompressible, inviscid) medium will onlv apply to air if the actual compressibility effects in air are negligible, or in other words, if the pressure changes are only such as to produce a negligible change of density. We shall have to return to this point in a later article in discussing high speed phenomena such as are found with fast running large diameter propellers. For the moment, however, it is sufficient to emphasise the importance of gradual changes of curvature to avoid giving rise to high velocities where there are violent changes of curvature. The potential or pressure system normal to the streamlines can equally be plotted and where the flow is conformable to a body it will be found that the pressures on the body will balance out— the body will be in equilibrium. If the fluid were viscous (sticky)—capable of giving rise to forces tangential to the surface of the body—the simple intro- duction of the body for the " closed " circuit streamlines would be impossible. There must now be a finite velocity gradient between the surface of the body and the external streamlines. This boundary layer is known to be extremely thin and to effect a negligible change in the external stream lines around the greater part of the body. An idea of what happens in this boundary layer may be gathered by imagining the layer represented by a thin layer of dough placed between the palms of the two hands. Now, if the hands be moved relatively to one another, e.g., one forwards and the other backwards, the dough will roll up into a number of rollers. I have not tried this experiment, and I cannot guarantee its success in practice ; it presents, nevertheless, a good picture of the relative movement of the sticky air and the body rolling up the air in the boundary layer. A somewhat similar phenomenon can be seen in the rollers forming in shoal water due to the friction between the water and the sand. The energy of these rollers has to be accounted for, and the force associated with its production is usually known as skin friction, and one is forced to the conclusion that very little else is known about it. Various expressions based on experi- ment are extant which purport to assess this form in terms of length and velocity. Velocity in this instance is the mean velocity of the total stream, or alternatively the velocity of the body through still air. The most popular of these is Zahm's. I do not give the form of the expression as it does not appear to me to represent anything but an empirical formula for the actual experimental forms used within a limited velocity range. An infinitely thin lamina is unfor- tunately not a practicable possibility; consequently, all such experiments are obscured by " form " resistance. Even if it were practicable; so far as I know—and I am quite open to correction—it remains to be demonstrated that an expres- sman containing only the above variables is applicable to any form of body, particularly in the presence of cyclic flow.* * It is perhaps as well to mention that this somewhat crude attempt atpicturing certain aerodynamic phenomena is part of a series of articles on performance and that fuller or more accurate representation w'ould be out ofplace. Reference should be made to Lanchester's " Aerodynamics " and "The Flying Machine", Proceedings—Institute Automobile Engineers, 1915(separately published) and particularly to ISairstow's paper " Skin Friction and the subsequent discussion—Journal It. Ae. Soc. January 1925 ". When the streamlines meet a body they must diverge, and after passing round the body must meet again. If the condition of continuous curvature is to be maintained it is plain that the divergence and the closure must be cusplike. If the presentation of the body is to be changed under flight conditions (change of incidence), there must be movement of the forward stagnation point. This demands the removal of the forward cusp in favour of a rounded nose of curvature gradually increasing towards the. normal stagnation point. Very little can be done with the movement of the aft stagnation point. For obvious reasons, the back cannot be so rounded as to make any appreciable difference to the high velocities in the trailing edge region, the prime cause of the breakdown of conformable flow as change from normal presentation takes place. If we leave the body as it now is, the familiar Joukowsky streamline form will be easily recog- nised. The cusped rear end is, however, a practical nuisance —in fact, anything but an approximation is almost a practical impossibility. Fortunately, experimental evidence such as the tests on wing forms, airship bodies and the like, indicate that within reason the closure of the trailing part of the body at a finite angle has a negligible effect on the resistance. There are two possible explanations for this : firstly, towards the end of the cusp the pressures are so nearly normal to the stream that their component resistance parallel to the stream is a very small part of the total pressure over this part of the body. A second possible additional explanation is that the cumulative effect of the boundary layer rollers tends to cause the streamlines to break away just before the end of the tail is reached, this region shedding a periodic stream of eddies whose energy is partly (mainly ?) derived from the boundary layer rollers. Pictures of such flow (ref. Bairstow's Applied Aerodynamics, p. 340) shows this phenomenon for bodies with finite trailing edges (Figs. 174 and 175.) I have not seen experimental flow patterns for Joukowsky cusped forms, but if the difference of resistance is negligible, it is hard to believe that similar non-conformable flow and eddy-making would not be present at the tail. As a natural consequence, it would follow that the form of the tail in the non-conforming region was of minor importance, or even that it could be cut off altogether. Some struts which had been so mutilated were included in a series tested at the National Physical Laboratory in 1912, at the instance of Mr. Alec Ogilvie (a full description was published in the issue of FLIGHT, for June 15, 1912). The results were very favourable. Unfortunately, these tests were carried out at fairly low VI (though VI =2-5 is well towards a stable type of flow.) I do not know of any further experiments in this direction, although owing to certain practical advantages I used this form for interplane struts and for fuselages on several machines about this period. The full scale evidence (of course, largely negative and of doubtful qualitative value) did not indicate that at higher values of VI the favourable resistance coefficient was not realised. In addition, some experiments on aerofoils carried out at the Royal Aircraft Establishment (see R. & M. 928) indicate that blunting the trailing edge of wing sections does not sensibly increase their resistance, whilst a more extensive and systematic series of experiments carried out by Boulton & Paul, Ltd., in their wind channel at Norwich at VI = 30 seems to show that truncation can be carried to considerable lengths with slight effect on aerodynamic properties. It does not, of course, follow that these suggestions are valid at speeds where compressibility becomes important. Nearly all readers will, I think, understand that the term " bodies," which I have used from time to time in this article does not refer to aeroplane bodies in particular, but to any solid object placed in the stream of flow. I have referred to a change in attitude as affecting the flow round bodies, but made no mention of lift. In fact, the types of flow discussed do not srive rise to lift and conformable flow in the " ideal " fluid could not cause lift. It must now be imagined that the figures represent a section of a wing of infinite span and the flow around it. As the span is infinite, every section normal to the span will have the same flow pattern. If we consider a wing section and plot the streamlines in an " ideal " fluid by the sink and source and translational method (the com- plexity of the actual process may be gathered from Taylor's
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