7. Geometric modifications to Busemann flow: wavecatching, morphing, truncation, leading-edge blunting

The basic Busemann flow is contained in an axisymmetric streamtube of high contraction. As an intake, such a shape will not start at steady flow conditions. Also the axisymmetric shape may not conform well to the shape of the rest of the airplane surface nor the desired combustor entry and a need arises to modify its cross-sectional shape. Such modifications can be done while still retaining the basic Busemann flow characteristics by tracing the streamlines of the Busemann flow. This process depends on scaling and assembling adjacent, scaled streamlines into streamline sheets that form the wall surfaces of the intake module. The technique produces a wavecatcher intake module. In such constructions a chosen freestream capture cross-section shape becomes mirrored in a smaller, but geometrically similar, intake exit cross-section shape. If done properly, a wavecatcher module has a swept leading edge that captures the leading shock wave and mass flow at design conditions but permits flow spillage and promotes intake flow starting at design and off-design conditions. So a wavecatcher design gets away from an axisymmetric flowpath shape and it also leads to a startable intake as a separate outcome.

The wavecatcher intake shape, that integrates well with the airplane, may have an exit shape that is not necessarily the best shape for the combustor. The combustor shape is very likely wanted to be circular because it is to join to the contiguous combustor duct which is strongest and least aerodynamically lossy when it is circular. There is thus a need to deform the intake flow path gradually from the freestream entry to the exit; typically, from a segment of a circle to that of a full circle or possibly to an ellipse, (Figure 18). The method of doing this is called morphing [5, 7, 22, 23].

The Busemann intake has a large amount of surface immediately behind the leading edge. This surface carries a thin boundary layer and a high shear stress, contributing disproportionately to boundary layer losses. The question arises: Can boundary layer losses be decreased by foreshortening some of the surface aft of the leading edge? Realizing that truncation of the leading edge or stunting the intake will result in leading edge flow deflection and shock losses which counter gains achieved from decreased boundary layer losses.

Difficulties of cooling sharp leading edges lead to the adoption of leading edge blunting. Even a small amount of leading edge blunting can have a significant effect on the Busemann flow both in the boundary layer and in the inviscid stream [10].

#### 7.1 Wavecatching (streamline tracing)

The objective of wavecatching is to generate intake flowpath surfaces different from the basic axisymmetric surface of the Busemann flow. The design starts with selecting the desired Busemann flow and calculating its streamline shape, r ¼ fð Þθ , as in Figure 3. Wavecatcher intake surfaces are then generated from adjacent Busemann streamlines, r ¼ yð Þ ϕ fð Þθ where r is a radial coordinate on the streamline, yð Þ ϕ is a scaling factor that varies smoothly from streamline to streamline and fð Þθ is the shape

by the boundary layer displacement thickness. The importance of viscous correction methodologies has attracted considerable attention and research efforts as accurate calculation of the boundary layer displacement thickness plays a pivotal role in intake performance assessment. Complex interactions of the shock waves and boundary layers developed on the curved surface of the Busemann intakes pose a challenge to accurate detection of the boundary layer edge. A viscous correction was applied [39, 49] to the full and truncated Busemann intakes by using the displacement thickness obtained through numerical integration of the CFDgenerated boundary layer properties. Reasonable detection of the boundary layer edge was attained by examining the total enthalpy profile [50, 51]. Viscous correction is applied typically once only to produce the final geometry. However, the importance of repeating the process, with subsequent iterations, has been highlighted in [52] with the application of an updating procedure of the displacement thickness. The results of correcting for the boundary layer effect are shown in

Upper half contains inviscid Busemann flow. Lower half of flow is contained in a Busemann surface that has been corrected (enlarged) for boundary layer presence [17]. Note successful restoration of BL-corrected flow to

boundary layer on the wave structure of the inviscid flow in the unmodified Busemann intake.

Mach 8 Busemann intake flows, upper half without and lower half with boundary layer showing the effect of

Inviscid and viscous flow in the Mach 8 Busemann intake at 30 km flight altitude [20].

Hypersonic Vehicles - Past, Present and Future Developments

Figure 15.

Figure 16.

Figure 17.

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be similar to inviscid flow.

from a circular capture tube shape, where the exit shape is also circular. Such a

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

The swept leading edges of modular wavecatcher surfaces permit flow spillage at

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

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

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

Three (blue) orthogonal views of a wavecatcher module and cross sections of the modular intake (black) when

module was tested in a wind tunnel at Mach 4 [25].

7.2 Morphing (modification of intake flow cross section)

quarter-circle entry is to be morphed to feed a circular combustor.

virtues of wavecatcher intake modules.

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

Figure 21.

Figure 20.

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morphed from a quarter circle to a full circle.

Figure 18. Wavecatcher intake modules traced from full Busemann flows.

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.

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,

Figure 19. Four-module Mach 5 scramjet intake based on Busemann flow.
