6. Boundary layer effects

High performance intakes have to have a very weak leading edge shock. Such a weak shock is inclined at near the Mach angle. This leads to the length-to-height ratio of the intake to be approximately M, the freestream Mach number. So that high performance intakes, including the Busemann intake, tend to become long and slender with large surface areas that have high shear near the leading edge, causing disproportionately high viscous losses. Surface length also leads to thick boundary layers at the exit with losses and the potential for major flow disruptions by boundary layer separation.

A comparison of inviscid and viscous flow in the Busemann intake is shown in Figure 15 by Mach number contours. The blue, low Mach number boundary layer, appears in the viscous flow. The effect of the boundary layer has led directly to the presence of a shock from the leading edge and a noticeable change in the flow at the center line, a change of exit Mach number from 5.3 to 4.8 and a reduction in total pressure recovery from 0.97 to 0.43. The boundary layer has a significant effect on the inviscid flow even when it appears to stay attached.

Flow displacement by the boundary layer causes a conical shock to appear and focus to a point on the center line ahead of the Busemann flow focal point and a reflected, conical shock appears downstream that impinges on the surface ahead of the corner, Figure 16. To restore the inviscid flow topology and pressure distribution of the Busemann flow it is necessary to correct the surface shape of the intake

Figure 17 where the bottom half of the figure shows the inviscid and viscous flow on a surface that has been obtained by enlarging the inviscid surface by the boundary layer displacement thickness. There is close resemblance between the inviscid and the boundary layer corrected inviscid flows in this figure. Both Figures 16 and 17

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 circu-

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

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].

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

lar. 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

7. Geometric modifications to Busemann flow: wavecatching,

morphing, truncation, leading-edge blunting

were calculated by H. Ogawa.

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

morphing [5, 7, 22, 23].

99

achieved from decreased boundary layer losses.

7.1 Wavecatching (streamline tracing)

Figure 15.

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

#### Figure 16.

Mach 8 Busemann intake flows, upper half without and lower half with boundary layer showing the effect of boundary layer on the wave structure of the inviscid flow in the unmodified Busemann intake.

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

#### Figure 17.

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 be similar to inviscid flow.

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

Figure 17 where the bottom half of the figure shows the inviscid and viscous flow on a surface that has been obtained by enlarging the inviscid surface by the boundary layer displacement thickness. There is close resemblance between the inviscid and the boundary layer corrected inviscid flows in this figure. Both Figures 16 and 17 were calculated by H. Ogawa.
