The Busemann Air Intake for Hypersonic Speeds DOI: http://dx.doi.org/10.5772/intechopen.82736

layer with high shear and attendant losses of intake efficiency. There is then a good reason to expect an improvement in efficiency as a result of eliminating the leading edge surface by foreshortening the intake surface. At the same time one can expect a deterioration of efficiency because the foreshortened intake now has a positive deflection generating a leading edge shock that produces an efficiency loss in the inviscid flow. There is a design trade-off here, between boundary layer and shock losses, which arises from intake foreshortening and it becomes of interest to find an amount of intake foreshortening that minimizes the sum of the boundary layer and the shock losses—maximizes the efficiency. This section describes two representative geometric methods of achieving foreshortening of air intakes, truncation and stunting. Truncation shortens the intake by removing some part of the leading edge surface. The effect of truncation of the Busemann intake was studied in [10, 16, 18]. Stunting is longitudinal contraction of the Busemann intake achieved by multiplying all streamwise intake surface coordinates by a constant factor <1. This is linear stunting or telescoping. When applied to a Busemann intake profile, the intake is foreshortened while the flow areas and the zero leading edge flow deflection and curvature are retained. No shock is produced at the leading edge and the overall design contraction is not changed.

CFD-generated intake performance data is presented for a Mach 8, full Busemann intake, flying at an altitude of 30 km, when foreshortened by various amounts of truncation or stunting. Figure 22 is a plot of intake total pressure recovery against fractional foreshortening of the full Busemann intake calculated by a Navier-Stokes code. The Busemann intake, with applied boundary layer and terminal shock losses lead to a total pressure recovery of 42% for the un-shortened intake.

The effect of truncation on total pressure recovery by various amounts of truncation is shown by the blue curve in Figure 22. Truncation produces a modest increase of total pressure recovery from 42 to 46% at near 30% truncation and it appears that intake efficiency is not very sensitive to the amount of truncation.

The effect of stunting, on total pressure recovery, by various amounts is shown by the red curve in Figure 22. Total pressure recovery peaks at 47% near 15% foreshortening; decreasing noticeably as stunting increases.

Assessment of truncation and stunting. Both truncation and stunting produce only modest, 4 and 5%, improvements in intake efficiency. However, since the methods are geometrically different, they affect intake capability differently as shown by the compression and contraction ratios in Figure 23.

Figure 22. Effects of truncation and stunting on Busemann intake total pressure recovery.

edge, as shown in Figure 21. The surface grid points are easily calculable from r ¼ rð Þ ϕ; θ where 0 ≤ϕ < 2π and θ<sup>2</sup> ≤ θ ≤μ<sup>1</sup> and the Cartesian coordinates of the

Morphing of streamline-traced square (blue) and circular (red) streamlines into composite (purple) yielding cross section transition from large blue square to small red circle: (a) is exit geometry; (b) is entry geometry;

x ¼ r cos θ y ¼ rsin θ cos ϕ z ¼ rsin θ sin ϕ

Morphing can be used also if the axes of the entry and exit flows are offset, but

Although morphing is applied to Busemann flow streamlines, Busemann flow is not preserved in the morphed intake. The morphing process is a purely geometric exercise and its arbitrary nature makes it necessary to verify the morphed intake's flow features and performance, by CFD or experiment. VanWie et al. [7] examined the results of applying various weighting functions and calculated the performance

As discussed in Section 1, full Busemann intakes are inherently long and hence subject to substantial viscous losses and high structural weight. An examination of the Busemann intake flow-field reveals that the surface at the leading edge has no deflection or curvature in the streamwise direction, presenting no compression of the ingested freestream flow. Thus the leading surface makes little contribution to the task of compressing the flow in the intake. Even worse, it supports a boundary

surface are:

Figure 21.

still parallel.

102

of the morphed intakes using CFD.

7.3 Intake foreshortening: truncation and stunting

(c) shows front view of streamlines; and (d) shows side view of streamlines.

Hypersonic Vehicles - Past, Present and Future Developments

an effectively large flow area, on the moving, post-shock side, allowing overboard flow spillage. If the Kantrowitz condition, for the shock at the point of inflection, at the V-notch, is satisfied the shock will continue moving downstream, out through

The entry area of the internal flow, Af, is defined as the conical surface at the angular position where the surface is inflected because the flow is normal to the conical surface at the inflection and a stationary, conical, normal shock is

compatible with the flow there. The size of this area is available from a Busemann intake calculation. This area is needed for application of the Kantrowitz starting

Note that, for given M<sup>2</sup> and δ23, Eq. (9), gives two solutions for θ23, for a weak

The determination of startability for a wavecatcher Busemann intake is as follows. At first we examine the startable weak-shock Busemann flow to show that it

a. At a prescribed weak shock angle, pre-shock Mach number and exit radius y3

b.Halt the integration when reaching the inflection point, (of) in Figure 3, where u = 0. Note the Mach number M<sup>f</sup> = v and θ ¼ θ at this point (u is zero here);

d.Apply the Kantrowitz criterion to Mf, A<sup>f</sup> and A<sup>3</sup> to determine if the internal

e. If a start is indicated the intake is practical and integration can be continued to

Many such calculations, starting from weak shock waves, (os) in Figure 3, were

find the freestream (entry) Mach number, M1, and the other overall performance parameters such as the exit-to-entry area ratio A3/A1, the

performed with the outcomes plotted on a graph of area ratio, A3/A<sup>1</sup> vs. entry Mach number, M1, in Figure 24. Each result is shown as a dot that is colored green if the totally internal flow Busemann intake duct starts, green or yellow if the wavecatcher Busemann intake module starts (as determined in d) above) and red if there is no start. Curves of the "startability index," S = (A<sup>1</sup> – Ai)/(A<sup>K</sup> – Ai), measure the location of a dot on the overall area ratio scale where S = 0 on the isentrope and S = 1 on the Kantrowitz criterion. Intermediate, fractional values, are on curves between these limits. The curve for S = 0.6 seems to well represent the startability limit for wavecatcher Busemann intake designs based on the weak shock condition. As seen from the figure the wavecatcher design lowers the startable area ratio from about 0.6 to 0.4. This is still not good enough. For good engine performance, it is

compression ratio p3/p<sup>1</sup> and the total pressure recovery pt3/pt1.

begin integrating the T-M Eqs. (5) and (6) towards the upstream;

c. Calculate surface area of the conical surface at inflection point, Af;

and a strong shock. This leads to the possibility of generating two different Busemann intakes, the weak shock version would have supersonic and the strong shock would have a subsonic exit flow. Because of its supersonic exit flow the weak shock intake is better suited for scramjet application. However, at contractions to be useful for scramjets, the Busemann intake with a weak shock does not start spontaneously or if it does start then it does so for intakes with an insufficient amount of

the internal flow section, and the intake will start.

The Busemann Air Intake for Hypersonic Speeds DOI: http://dx.doi.org/10.5772/intechopen.82736

8.1 Startability of the weak shock Busemann

does not provide sufficient compression:

passage will start.

105

criterion.

contraction.

Figure 23. Variation of intake compression and contraction as caused by truncation and stunting.

Intake performance, both efficiency and capability, are not affected much by considerable amounts of either truncation or stunting. This is due to the fact that the high-loss leading edge boundary layer flow is not eliminated but merely moved downstream. Also there is some increase in inviscid flow losses from the finite angle leading edge from truncation. However, an estimated 15–30% weight saving is available through wall materials elimination resulting from intake foreshortening. It appears that the significant advantage of truncation and stunting is not to intake performance but to the saving of structural weight. Similar results were found in [10].

#### 7.4 Leading edge blunting

Busemann flow has no deflection at the leading edge so that the leading edge tends to be sharp and thin. Such leading edges are difficult to cool at hypersonic speeds. Transpiration cooling is made possible by a slight rounding of the leading edge. Rounding or blunting affects both the viscous as well as the inviscid flow in the intake [10]. The strong bow shock causes a hot entropy layer to overlay the boundary layer and cause it to thicken. The same shock focuses on the symmetry axis producing a Mach reflection at the center line. It was shown in [10] that a 1 mm diameter leading edge on a 500 mm diameter Busemann intake, flying at Mach 10 and 30 km altitude, is optimal in reducing the viscous and inviscid losses. It seems that the combination of blunting and stunting should be such that the conical shock is kept incident on the Busemann surface corner, so that no reflected shock waves are formed, keeping the exit flow uniform.
