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Aviation History
1952
1952 - 0037.PDF
4 January 1952 9 perspective, the Vampire intake (96 per cent) had a low position- ratio and a direct inlet; cases such as the Meteor (88 per cent) and Attacker (85 per cent)—these being values converted to constant plenum-chamber conditions—were dominated by the plenum- chamber loss; on the other hand, turboprop intakes (82 per cent in a typical case) had the blade-root loss which was 8 to 10 per cent for the average airscrew, and also a high position ratio. No radical change in the picture was to be expected up to sonic flight speed since the relevant flow field in most cases was wholly subsonic. At supersonic speeds, the deceleration to compressor velocity had to take place in part through a shock system in which further loss was incurred. At speeds only slightly above a Mach number of 1.0, it might be that this loss would add to the subsonic losses without further complication. Later, the interference effects between shock-wave and boundary layer were likely to become important. Whatever the outcome, the experimental and analytical methods which had been used in the past might be expected to prove useful and reliable in exploring the future. The lecturer then took the opportunity briefly to present the details of a simple semi-empirical theory of intake loss for sub- O IO 20 30 40 50 ANGLE OF SWEEPBACK OF ENTRY Fig. 2. Calculated approach losses for wing root intakes with entries of constant area Ax. Shading indicates body wall. Body length ahead of entry=A^A\. Vo/V^l-O. cr=0-OOS. sonic intakes of the direct or fully-ducted type. The approach, so far as he was aware, had not been given before, and it provided a method of estimating the loss characteristic—and hence the ram efficiency—of a new design over the range of flight conditions from climb (F0/Fi = i.o) through level flight (V0IVi=2.o) up to the highest velocity ratio which avoided boundary layer separa tion ahead of the entry. If the additional lip losses in ground run ning were known, the complete characteristic from V0I V\=0 could be constructed. Important design-values such as the velocity ratio for optimum ram-efficiency or the limiting value for stable flow in twin-intake systems were easily derived. Considering the flow into an intake as shown diagrammatically in Fig. 1, the length l\ represented the approach length, or length of wetted surface ahead of the entry, whilst the length fc represented the enclosed duct from entry to compressor inlet position. It was assumed that the flow was incompressible, free from separations and fully mixed throughout, i.e., the speed and direction were uniform across any section normal to the axis of the duct. At an arbitrary section (velocity V, total stream tube area A) the friction force on an element of wetted surface was dF=lQVhfPdx, where c; was the skin friction coefficient, and P was the length of wall round the section in contact with the flow (inside the duct P=total perimeter). The equivalent pressure drop was SF i„i/i, Pdx> and the loss of total head in the intake was given by an integration of this pressure drop over the full length. Hence if A H was the total head loss, and q± the mean dynamic head at entry IQVI2, AH n1 + i2 /vy Pdx = J. Cf yj — « Its relationship to 1x A Hjqi was termed the intake loss coefficient, the ram efficiency r % was: AH. /F„y (2) A loss coefficient of 0.1 corresponded to about 2 per cent loss of thrust. The integration was considered in two parts. Inside the duct the equation of continuity could be used to substitute known areas for velocities. On the external approach, the velocity varied in some such way as that shown in the diagram. Since (a) it was known from experimental evidence that the pre-entry retardation took place in a short distance ahead of the entry, and (b) the effects of a stagnation region near the nose of a fuselage and the excess velocity on the shoulder would largely cancel, it followed that the friction loss on the approach was not greatly different from what it would be if the velocity was uniformly V„. The assumption was therefore made that the velocity on the approach could be replaced by a constant value V=kt V0 in which k was an empirical constant, the value of which was near 1.0. Assuming further that cf was constant, the integration in equation (1) gave in which SjAi was the position ration and / was a duct integral denned by: \+h(AxyPdx (4) \AJ~T The value of / was calculated from the shape of the duct. For a circular pipe of constant diameter, T_ length diameter which led to a well-known formula for the pipe loss. Equation (3) was the loss equation for an intake without bound ary layer by-pass in fully turbulent flow. In analysing model tests, it might be necessary to distinguish between the values of friction coefficient for the approach and duct, because of the possibility of laminar flow on the approach. Further, if a by-pass was present, this reduced the effective position ratio by a factor representing the by-pass efficiency. Writing <t> for the ratio of cf on the approach to that in the duct, and JJD for the by-pass efficiency, gave the more general form: where J=k4> (1 — rjt) S/Ai. The corresponding ram efficiency 4,'" *-*r* [•m<v) 1 (6) The loss coefficient formula was well substantiated by the results of low-speed model tests on intakes both with and without boundary layer by-passes. In compressible flow, the equation became, to a first approximation: Direct experimental confirmation of this form was, however, required. Leading-Edge Intakes Going on to consider the intake in the wing leading edge, Dr. Seddon observed that, on a straight-winged aircraft, the wing leading edge provided an alternative region of pitot pressure for the designer who was unable to find room for an entry in the nose. Even if the intake was in the wing root, it was normally less affected by the fuselage boundary-layer than one which was built on to the side of the body. But with the use of swept wings came a new problem. Did the efficiency of the leading edge intake alter with sweep-back ? By analogy with a yawed pitot-tube, the inter nal pressure might be expected to fall off with increasing angle. In fact, if the entry velocity ratio was near unity, sweep-back as such had no effect on intake efficiency. But at high forward speed, when the air was retarded in front of the entry, the pitot-tube analogy held. This could be explained in the way illustrated in Fig. 2. The effective entry was the first completely closed section normal to the line of flight (A-A in the diagram) because it was here that the air had finally decelerated to duct speed. Hence all wetted sur faces ahead of this section counted as external approach area S, and boundary layer generated on these surfaces (indicated by arrows in the diagram) was in a similar category to that which came from wetted area on the fuselage. This meant that the swept leading-edge intake had a non-zero position-ratio, and therefore gave a lower ram efficiency than a similar un-swept intake. The amount of loss depended not only on the angle of sweep-
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