4.1 Free-standing conical shock

In a parallel, uniform, freestream a conical axisymmetric shock is produced by a conical body and the shock strength is proportional to the cone angle. In Busemann flow there is no solid cone, yet a conical shock is produced. This "free-standing" shock is possible because the flow in front of the shock is converging towards the center line and the center line behind the shock is acting as a zero-angle cone to force the flow into a parallel and uniform downstream direction. Such a freestanding conical shock, with uniform post-shock flow, is unique to Busemann flow.

Experiments were conducted, in a Mach 3 wind tunnel, at the Defence Research and Development Canada (Valcartier) laboratories to demonstrate the existence of the free-standing conical shock [40]. Since a full Busemann intake would not start spontaneously in the steady wind tunnel flow and, also, since the shock would be hidden from tunnel optics by a full Busemann duct, only an annular, leading edge portion of the Busemann duct was constructed and tested (Figure 7b). The tip of the conical shock, produced by the annulus, is in the region of influence of the annulus and that was sufficient to produce a freestanding conical shock at the center line that was in the field of view of the tunnel optics (Figure 8). Compression waves, from the annulus, converge to the center line and reflect as a conical shock as calculated by CFD in Figure 7a. No incident shock or Mach reflection is apparent. Calculated post-shock Mach number is 1.48, and pressure is 10.1 and temperature is 1.94 times their freestream values.

the required Busemann annulus calculated so as to create a local high pressure hot

Freestanding conical shock in Busemann flow at Mach 3 (DRDC). Blue arrow points to apex of conical shock.

Characteristics are two sets of intersecting lines in supersonic flow. The characteristics carry a physical significance in that they delineate the region of space that influences flow conditions at a particular point as well as the region of space that depends on the flow conditions at a point. The characteristic lines are selected such that, along these lines, the governing partial differential equations become total differential, finite difference equations, allowing numerical solutions of the

Alternatively, once a supersonic flow-field has been calculated by some noncharacteristic methods, the characteristic lines can be calculated and superimposed and inferences about influences, causes and effects can be drawn. The α and β or C+ and C� characteristics are inclined at �μ to the local streamlines where

(1/M) (Figure 9). In polar coordinates the α and β characteristics'shapes

where the plus sign is for the α characteristic and minus is for the β characteris-

ð Þ dx=dθ <sup>α</sup> ¼ r cosð Þ δ þ μ = cosð Þ π=2 � δ � μ ð Þ dy=dθ <sup>α</sup> ¼ rsin ð Þ δ þ μ = cosð Þ π=2 � δ � μ

¼ r cotð Þ δ � θ � μ (15)

(16)

spot for igniting a supersonic fuel/air mixture at a precise location.

dr dθ 

α, β

tic. For x-y plotting one can integrate the α-characteristics directly:

4.2 Characteristics

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

Figure 8.

flow-field [42, 46].

are determined by integrating,

μ = sin�<sup>1</sup>

89

The yellow arrow points to the focal point where the converging compression fan and the free-standing conical shock meet. The analytically predicted Busemann flow and its features have been confirmed by both CFD and experiment. The approach presented here is the only method for establishing a centered axial compression followed by a conical shock at the center line in a steady flow. Flow properties inside the apex of the conical shock can be precisely set and the shape of

#### Figure 7.

(a) Freestanding conical shock at center line, produced by axisymmetric Busemann leading edge annulus in a Mach 3 freestream. CFD calculation by E.V. Timofeev. (b) Busemann leading edge annulus in Mach 3 wind tunnel at DRDC [40].

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

Another very important feature is the fact that all solutions of the T-M equations, starting from an acute angled, conical shock, always end up at a straight and parallel freestream flow. Busemann flow would be useless, as the basis for an air intake, if this were not so. This fortuitous feature must be inherent in the T-M Eqs. (5) and (6). This property of the T-M equations holds whether the downstream

The downstream end of the Busemann flow has an inflection point where the surface turns away from the axis, towards being parallel with the exit flow. This lessens the flow deflection required from the terminal shock and also lessens the strength and loss produced by the terminal shock. This feature contributes directly

In a parallel, uniform, freestream a conical axisymmetric shock is produced by a conical body and the shock strength is proportional to the cone angle. In Busemann flow there is no solid cone, yet a conical shock is produced. This "free-standing" shock is possible because the flow in front of the shock is converging towards the center line and the center line behind the shock is acting as a zero-angle cone to force the flow into a parallel and uniform downstream direction. Such a freestanding conical shock, with uniform post-shock flow, is unique to Busemann flow. Experiments were conducted, in a Mach 3 wind tunnel, at the Defence Research and Development Canada (Valcartier) laboratories to demonstrate the existence of the free-standing conical shock [40]. Since a full Busemann intake would not start spontaneously in the steady wind tunnel flow and, also, since the shock would be hidden from tunnel optics by a full Busemann duct, only an annular, leading edge portion of the Busemann duct was constructed and tested (Figure 7b). The tip of the conical shock, produced by the annulus, is in the region of influence of the annulus and that was sufficient to produce a freestanding conical shock at the center line that was in the field of view of the tunnel optics (Figure 8). Compression waves, from the annulus, converge to the center line and reflect as a conical shock as calculated by CFD in Figure 7a. No incident shock or Mach reflection is apparent. Calculated post-shock Mach number is 1.48, and pressure is 10.1 and temperature is

The yellow arrow points to the focal point where the converging compression fan and the free-standing conical shock meet. The analytically predicted Busemann flow and its features have been confirmed by both CFD and experiment. The approach presented here is the only method for establishing a centered axial compression followed by a conical shock at the center line in a steady flow. Flow properties inside the apex of the conical shock can be precisely set and the shape of

(a) Freestanding conical shock at center line, produced by axisymmetric Busemann leading edge annulus in a Mach 3 freestream. CFD calculation by E.V. Timofeev. (b) Busemann leading edge annulus in Mach 3 wind

flow is set to be uniform or not, as long as it is conical.

Hypersonic Vehicles - Past, Present and Future Developments

to the high efficiency of the Busemann intake flow.

4.1 Free-standing conical shock

1.94 times their freestream values.

Figure 7.

88

tunnel at DRDC [40].

Figure 8. Freestanding conical shock in Busemann flow at Mach 3 (DRDC). Blue arrow points to apex of conical shock.

the required Busemann annulus calculated so as to create a local high pressure hot spot for igniting a supersonic fuel/air mixture at a precise location.
