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

from a circular capture tube shape, where the exit shape is also circular. Such a module was tested in a wind tunnel at Mach 4 [25].

The swept leading edges of modular wavecatcher surfaces permit flow spillage at design and below-design conditions thus promoting intake flow starting. Once started, the apparent three-dimensional intake flowpath contains a started, steady flow with the original Busemann flow properties. These are the two significant virtues of wavecatcher intake modules.

## 7.2 Morphing (modification of intake flow cross section)

The technique of generating wavecatcher intakes, described in Section 7.1, produces exit flow cross-section shapes that are geometrically similar to the freestream capture streamtube shapes. The purpose of morphing is to produce cross-sectional shapes of the intake flow path that gradually transform the intake's entry shape to a geometrically different exit shape while, as much as possible, preserving the crosssectional areas as well as the flow characteristics. For example, the flow from a quarter-circle entry is to be morphed to feed a circular combustor.

Figure 20 shows three orthogonal views of a wavecatcher intake and its cross sections when morphed from a quarter-circle to a full-circle. A detailed morphing method, as applied to the Busemann intake streamline r ¼ fð Þθ , is pictured in Figure 21.

We illustrate by morphing a large, square (blue) inflow cross section into a (red), small circular exit section. A typical morphed Busemann intake design starts from specifying the initial conditions at the Busemann shock. A Busemann streamline r ¼ fð Þθ , Figure 3, is then calculated from the shock to the freestream, as in Section 3. For each value of ϕ, ranging from 0 to 360°, in a meridional plane, two streamlines are calculated, r<sup>1</sup> ¼ y1ð Þ ϕ fð Þθ and r<sup>3</sup> ¼ y3ð Þ ϕ fð Þθ where y1ð Þ ϕ is the distance from the axis to the freestream capture cross section (blue) and y3ð Þ ϕ is the distance from the axis to the exit flow cross section (red). All the r<sup>1</sup> streamlines project downstream from the leading edge and all the r<sup>3</sup> streamlines project upstream from the trailing edge. The morphed streamline shape, r ¼ rð Þ ϕ; θ , is then composed of the weighted average of the two streamlines, r ¼ r<sup>1</sup> þ gð Þθ ½ � r<sup>3</sup> � r<sup>1</sup> where gð Þθ is some assigned morphing function that varies from 0 to 1 as θ varies from the freestream Mach angle to the shock inclination. r ¼ rð Þ ϕ; θ , then, represents a streamtube surface that joins the square leading edge to the circular trailing

#### Figure 20.

Three (blue) orthogonal views of a wavecatcher module and cross sections of the modular intake (black) when morphed from a quarter circle to a full circle.

of the Busemann streamline. The scaling factor measures how far the streamline is from the axis of symmetry; its parameter ϕ is unique to each streamline, being the circumferential location of the streamline, the azimuthal angle, measured around the axis. It defines the cross-sectional shape yð Þ ϕ of the freestream capture tube. Note that, on the resulting surface, the variable θ uniquely determines all property values including surface inclination—this being a characteristic of conical symmetry.

Wavecatcher intake modules traced from full Busemann flows.

Hypersonic Vehicles - Past, Present and Future Developments

Four-module Mach 5 scramjet intake based on Busemann flow.

Figure 18.

Figure 19.

100

Two streamline traced intake modules are shown in Figure 18. Both are based on Busemann flow. In Figure 18a, the freestream capture tube shape is a quarter circle. The exit is also a quarter circle. Four such modules were placed back-to-back to construct the intake in Figure 19. Such four-module intakes were tested in a gun tunnel at Mach 8.33 [4] and this intake, on a scramjet, was launched from a ballistic gun at Mach 5 [41]. Figure 18b shows an intake, also traced from Busemann flow,

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

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

The effect of truncation on total pressure recovery by various amounts of trun-

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

cation 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.

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

compression and contraction ratios in Figure 23.

design contraction is not changed.

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

intake.

Figure 22.

103

#### Figure 21.

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

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 surface are:

$$\infty = \overline{r}\cos\theta \qquad \jmath = \overline{r}\sin\theta\cos\phi \qquad z = \overline{r}\sin\theta\sin\phi$$

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

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 of the morphed intakes using CFD.

#### 7.3 Intake foreshortening: truncation and stunting

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
