8. Startability

The Kantrowitz criterion for intake starting [26] says that the normal shock, in front of an intake duct, will move downstream and out of the duct if the flow at the exit of the duct is not choked—the duct flow will start. This criterion applies to the normal shock at the entry of the duct as well as at any other position in the duct. On a wavecatcher intake, Figures 18 and 19, overboard flow spillage will allow the shock to move downstream, over the external/open portion of the intake, until it reaches the V-notch at the beginning of the internal flow. This is made possible by

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

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 internal flow section, and the intake will start.

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 criterion.

## 8.1 Startability of the weak shock Busemann

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

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 does not provide sufficient compression:


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

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 fore-

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

Hypersonic Vehicles - Past, Present and Future Developments

were found in [10].

Figure 23.

8. Startability

104

7.4 Leading edge blunting

are formed, keeping the exit flow uniform.

shortening. It appears that the significant advantage of truncation and stunting is not to intake performance but to the saving of structural weight. Similar results

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

The Kantrowitz criterion for intake starting [26] says that the normal shock, in front of an intake duct, will move downstream and out of the duct if the flow at the exit of the duct is not choked—the duct flow will start. This criterion applies to the normal shock at the entry of the duct as well as at any other position in the duct. On a wavecatcher intake, Figures 18 and 19, overboard flow spillage will allow the shock to move downstream, over the external/open portion of the intake, until it reaches the V-notch at the beginning of the internal flow. This is made possible by

back-pressure is lowered to be replaced by a weak shock structure. This now opens a possibility. We calculate a Busemann intake module, with a strong shock, such that it starts spontaneously, at a high overall contraction ratio, and then reduce the back-pressure to remove the strong shock and obtain a supersonic exit flow, with a weak shock. This yields an exit flow which is suitable for scramjet operation. In doing this, we note that the flow, from the freestream to the location of the strong shock has not changed as we switch to the weak shock, so that the intake remains on the strong-shock design flow up to the corner while being started. Also, the amount of internal contraction remains the same and we could really start the intake with the weak shock structure in the first place. The strong Busemann shape is really a design tool which leads to a modified Busemann flow but with a started intake of high compression and efficiency having a supersonic exit Mach number-an intake with a high overall contraction but with a low internal, startable contraction. The supersonic exit flow is no longer conical although its axial symmetry is preserved. In comparison to the weak shock case (Figure 24) there is a considerable enhancement of startability in the enlarged yellow domain so that starting can be expected near the S = 0.1 curve, which is acceptable for scramjet applications.

The reason for this improvement in startability stems from the fact that, for the strong shock option, the angular distance between the strong shock (at the corner) and the inflection cone is small so that A<sup>f</sup> and A<sup>3</sup> areas are close in size, i.e., there is not much internal contraction. This makes it easy for the conical normal shock, at the inflection location, to be swallowed. The strong shock design's aim is to produce a wavecatcher Busemann intake with a high overall contraction ratio and a low internal contraction that starts spontaneously. The calculated shape is compatible with a normal conical shock positioned at the inflection location (angle) and we select the intakes, with internal contractions, that permit the shock to be swallowed. Flow downstream of the inflection shock is subsonic. The strong shock is present only fleetingly during flow starting. After swallowing a weak shock system appears in the exit with supersonic flow downstream. This flow is suitable for a scramjet combustor. Within the calculated strong shock contour the supersonic weak shock flow is no longer conically symmetric and has to be examined via CFD and experiment. The end result is a wavecatcher Busemann intake with a high overall contraction (S 0.1) but with a low internal, self-starting contraction and hence a

Figure 26 is a schlieren picture of four quarter-circle Busemann intake modules each with flows started by the unsteady gun tunnel starting flow [4]. Arrow points

Impulsively started 4-module Busemann intake in the gun tunnel at Mach 8.33 (model is similar to

startable intake and supersonic exit flow.

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

Figure 26.

Figure 19).

107

#### Figure 24.

Busemann intake startability based on weak shock design: green—full Busemann start; green and yellow wavecatcher start with spillage; and red—no start.

desirable to operate intakes near the curve S = 0.1 in Figure 24. Startable weak shock Busemann designs do not produce this amount of contraction—the prospect of obtaining startable full or wavecatcher intakes, with sufficient compression, from weak shock Busemann flows is disappointing.

#### 8.2 Startability of the strong shock Busemann

Startability calculations for the full and wavecatcher Busemann intakes were done also by starting the integration of Eqs. (5) and (6) from strong shock waves, following the (a–e) steps above.

The outcomes are plotted in Figure 25. Each result is shown as a dot that is coloured 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.

The strong shock version has high overall contraction but low internal contraction so that it will self-start at overall contractions useful to the scramjet as a wavecatcher, but the strong shock and subsonic exit flow are not useful to the scramjet engine. In a wavecatcher module the about-to-start strong shock will be held in place by the appropriate back-pressure. It will move downstream if the

#### Figure 25.

Busemann intake startability regimes based on strong shock design. green—full Busemann start; green and yellow—module start with spillage; and red—no start.
