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Aviation History
1948
1948 - 1953.PDF
NOVEMBER I8TH, 1948 FLIGHT Ramjets A Contribution to their Theory and Performance IN aeronautical report AIR. 3__.N.R.C..'1674, Demetrios Samaras! of theDivision of Mechanical Engineering, National Research Council of Canada,surveys the field of ramjet operation and offers various adductions to the opera-tional theory of this form of prime mover. In general, fundamental design require-ments for a ramjet should be (i) low ex- ternal drag, (ii) low internal drag, (iii)high combustion efficiency, including flame stability over the entire range ofoperation, (iv) easy regulation, and (v) low power plant weight. The internalflow phenomena are similar both for the subsonic and supersonic conditions, butthe external flow differs and a different configuration is required.• Considering external losses at subsonic speeds, the report states that the criticalcompressibility speed of a ducted jet has been found to be as high as that ofthe basic streamline body, and the ex- ternal drag with airflow through the bodydid not exceed that of the basic stream- line body. Tests have proved that thelength ratio (ratio of length to maximum diameter) of the nose inlet is the primaryfactor governing the maximum critical speed, and that the effect of the inletdiameter ratio (ratio of inlet diameter to maximum diameter) is of secondary im-portance. The latter quantity, however, in conjunction with the temperatureratio due to heat addition, determines the inlet velocity ratio (entry air velo-city to flight speed) upon which the ex- ternal drag largely depends. An inlet velocity ratio smaller thanunity results in a divergence of the streamlines in front of the entry, and thesmaller this ratio, the more careful should be the design of the external fairing. Ithas to be remembered that the flow con- ditions in the combustion chamber andthe propelling nozzle will considerably affect external flow. It has been found that inlet velocityratios equal to, or greater than, 0.3 result in total head pressures at inlet practic-ally equal to that of the free airstream. Supersonic Requirements For supersonic velocities, a somewhatdifferent configuration should be adopted. The use of a reversed de Laval nozzleto convert the kinetic energy of the free stream into pressure was found to be un-stable and finally'led to a normal shock wave at the entry; this resulted in highexternal drag and low pressure recovery. Furthermore, the use of a straight pitottube at high flight Mach numbers was found to be inefficient because of theappearance of a normal shock wave at the entry. Means must thus be found toovercome these difficulties. One such method embodies a centralcore placed coaxially within the entry duct. The function of this conical noseis to induce a series of weak oblique shock waves and finally to end in anormal shock wave that will bring the flow into the subsonic region. This willresult in a high pressure recovery that otherwise could, not be achieved by asingle normal shock wave. After a theo- retical analysis, it was found that, foroptimum conditions, the strength of the B 35 oblique shock waves should be the same,which means that the total head pressure ratio across the oblique shock wavesshould be identical. It was also found that, in order to keep the pressure re-covery at a certain level, the number of oblique shock waves should be increasedwith increasing forward Mach number. From the experimental work done, itwas found that the two requirements of high pressure recovery and low externaldrag were in conflict, but from the meagre experimental results available to-day, it may be inferred that the skin friction coefficient decreases with theMach number. Boundary Layer Effects The boundary layer on the conicalnose has a great influence on shock wave formation. Tests in a large wind tunnelshowed that the effect of the boundary layer on a short nose with one re-entrantangle was small, but the influence on a long nose was, however, important; anadditional weak shock wave was observed in front of the transition point due tothe thickening of the boundary layer. Photographs have shown that the boun-dary layer grows rapidly in front of each re-entrant angle. The sensitivity of theconical nose boundary layer effects de- pends, therefore, both uppji its lengthand the number of re-entrant angles. There is evidence to show that boundarylayer processes in the presence of rising pressure completely change the struc-ture of the flow. The shock wave pat- tern is very sensitive to the nature ofthe boundary layer and depends entirely on whether the flow in the layer ahead ofthe shock wave is laminar or turbulent. When the Mach number is just aboveunity, and the boundary layer is laminar, • multiple shock waves occur, decreasingin number with an increase in Mach number, until finally a simple branchedshock wave appears. This results in a large thickening of the boundary layerbehind the shock wave and in high losses. The increase in thickness of a laminarboundary layer passing through a shock wave is higher than that correspondingto a turbulent layer. The latter gives only non-branched shock waves and itis immaterial whether the turbulence is made naturally or artificially. Internal Losses The author of the report analyses in-ternal losses as being made up of (i) entry losses, (ii) diffuser losses, (iii) com-bustion chamber losses, and (iv) expan- sion losses. The first quantity has beensurveyed in conjunction with the external losses already dealt with. From tests on subsonic diffusers, it hasbeen found that the main design para- meter is the iniet velocity ratio times thetangent of the diffuser angle, i.e., ent . tan 0. This implies that larger Vambdiffuser angles may be used if the inlet velocity ratio is kept low, e.g., if theairflow has already begun to diverge out- side the diffuser. In a given diffuser itwas found that the loss was neligible up to^5^ . tan 0=0.16. » amV The flow conditions before and alterthe diffuser have a great influence on the losses. In a ramjet entry diffuser thereis always a velocity ratio smaller than unity, and thus the divergence of the ex-ternal streamlines assists the flow to follow the diverging walls of the entry. In diffusers with high Mach number -subsonic flow, two counteracting effects are present; a higher pressure recoveryper unit length, and a greater breakaway tendency. Experimental evidence hafshown that a sudden drop in efficiency occurs in the neighbourhood of M = o.g2.The optimum diffuser angle found was 0 = 3.5 deg.Boundary layer effects play an im- portant r61e in a diffuser. In a largeangle diffuser, a higher pressure efficiency may be achieved by use of a boundarylayer by-pass or a system of vanes. In the case of a subsonic diffuser after asupersonic entry, a thick boundary layer results from the shock wave system andthis, combined with the high Mach number after the normal shock wave, re-duces considerably the optimum diffuser angle. Experimental evidence with adiffuser of 0 = 6 deg has shown that for M = o.67 and M = o.98, the respectivepressure efficiencies were 99.5 and 93 per cent. Here the necessity of boundarylayer control is clearly indicated. Losses occurring in the combustor aredivisible into two principle groups, namely, pressure losses and combustionlosses. The former are due mostly to aerodynamic and thermodynamic effects,whilst the latter are due to chemical and physical conditions. It has been foundthat these losses are interchangeable, i.e., for a given weight or bulk of thecombustor, a high combustion efficiency is achieved at the expense of a highpressure loss and vice versa. Expansion Losses On the subject of expansion losses, thereport states that at subsonic flight speeds the expansion ratio in the pro-pelling nozzle is always sub-critical; at supersonic speeds, however, dependingon the magnitude of the internal losses, it may become super-critical. In a conver-gent nozzle when the critical pressure ratio is exceeded, critical conditions atthe throat are established and stationary shock waves are initiated at the edgesof the nozzle throat. For expansion pressure ratios up to the order of 4:1,the losses due to these shock waves are comparatively low. However, athigher expansion ratios the pressure distributions and shock wa-ves have apeculiar form. The pressure losses due to these shock waves and from reflections atthe jet boundaries, give rise to additional losses which increase with the expansionpressure ratio. The mixing of the hot jet with the freestream has not, as yet, been thoroughly investigated. Tests on the V-2 rocket haveshown that for mixing of the hot jet with a subsonic free stream, an increase indrag results as compared with that of the body -without jet, although a smallimprovement at supersonic flight speeds may be realized. End of Part I.
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