4.1.2 The 2-D inlet construction (side view)

The inlet construction is an extension of the 2-D forebody construction. The oblique shock AB hits the cowl lip at point B and is reflected as shown in Figure 6.

Figure 5. Nonweiller caret wing waverider configuration.

Inversely Designed Scramjet Flow-Path DOI: http://dx.doi.org/10.5772/intechopen.85697

In reality, the caret waverider is carved from an inverse design approach that relies on the inviscid streamline principle. This principle states that any inviscid streamline can be replaced by a solid wall. The principle also states that replacing the inviscid streamline with a solid wall has no effect on the external flow. Planar inviscid stream surfaces are formed from these inviscid streamlines. These inviscid stream surfaces are then brought together to construct 3-D inviscid waverider geometries and stream tubes. An examination of Figure 5 demonstrates how the streamlines form planar stream surfaces, such as, upper inviscid surfaces, ABB3 and

This approach is further explained the next sub-section and is demonstrated by the construction of a supersonic 3-D wedge followed by a 3-D supersonic caretshaped geometry. This caret-shaped geometry will then be used to generate super-

The review of begins with the construction of the supersonic wedge. Established ideal oblique 2-D shockwave relationships are used to construct the supersonic 2-D forebody. There are two ideal oblique shock relationships which can be used, the Theta-Beta Mach relationship, or the Beta-Theta Mach relationship. In this review, the Theta-Beta Mach [3–5] relationship, described in Section 3.2 above is used in the construction of the supersonic 2-D forebody. For a prescribed Mach number, shock angle, Beta, at a given altitude, a wedge angle, Theta, is extracted. The next step is to set a forebody length. Having all the geometric data the 2-D forebody with the

The inlet construction is an extension of the 2-D forebody construction. The oblique shock AB hits the cowl lip at point B and is reflected as shown in Figure 6.

ABB4, or lower stream surfaces, such as, AB1B3 and AB1B4.

Hypersonic Vehicles - Past, Present and Future Developments

sonic star-shaped geometries of interest.

4.1.1 The 2-D forebody construction (side view)

attached shock is constructed as presented in Figure 6.

4.1.2 The 2-D inlet construction (side view)

Figure 5.

58

Nonweiller caret wing waverider configuration.

Figure 6. Preparation for extracting information for 2-D base view.

Line BC represents the reflected shock from the interaction of the oblique shock and the cowl lip. Ideal oblique shock relationships are used to determine the reflected shock angle, Beta reflected. Note that the line AB1 which represents the lower surface of the forebody continues to point C where it intersects with line BC. At this point in the design process the 2-D forebody and the inlet are constructed.

### 4.1.3 Streamline preparation of flow-field

A 2-D base view of the forebody-inlet components are constructed from geometric information obtained from the 2-D side view. The streamline cross-marching method used preserves both the geometric information and the 2-D flow-field information. The oblique shockwave, line AB, is first divided up into N number of equal parts, in this case six, as seen in Figure 6. Streamlines are then constructed emanating from the oblique shockwave. Each streamline has a starting point on the oblique shockwave, and ends on the reflected shockwave, line BC as presented in Figure 6. The longest streamline is represented by line AC and is the lower surface of the forebody-inlet. The shortest streamline is represented by point 6; here the streamline starts and stops at the same point. The streamlines emanating from the oblique shockwave and ending on the reflected shockwave travel parallel with respect to the lower surface of the forebody-inlet as presented in Figure 6. All streamlines are now processed by the reflected shockwave, BC, and travel parallel to the surfaces beginning at points C and B as shown in Figure 6. The 2-D base view can be extracted from the flow field.

#### 4.1.4 Wedge geometry extraction from flow-field

The base view for the 2-D wedge is now extracted for the 2-D forebody-inlet and the associated 2-D flow-field. A zy-coordinate system is set up and a wedge width is prescribed. Streamlines emanating from the reflected shockwave, BC, are now mapped onto the zy-coordinate system as presented in Figure 7. Having completed the construction of the 2-D side view and the 2-D base view, the designer now has

Figure 7. Generation of 2-D base view for a wedge.

the 3-D coordinates that can be used to generate the 3-D forebody-inlet geometry for a 3-D wedge.

#### 4.2 The caret geometry

The caret geometry forms the basis of the design of the star shaped geometries in this study. A similar process is used to obtain the caret-shaped 2-D base view. Now instead of providing a wedge width, a star angle, Phi, is provided as presented in Figure 8. For the four-point-star, Phi is 45 degrees. Reflecting points ABPointC, about the z-axis will generate the 2-D base view for the caret-shaped waverider geometry. As before, all data required for the 3-D construction of the 3-D caretshaped forebody-inlet have been extracted from the flow-field. Figures 9–12 present the 3-D caret-shaped geometry obtained by using the design process described above and programmed using FORTRAN90/95.

#### 4.3 3-D stream tube construction using the waverider approach

The scramjet forebody-inlet-isolator design concept as being proposed suggests a new use for waverider geometries. Here, the focus is not only of the waverider

shape, but also on the external flow-field supporting the waverider configuration. As seen in Figure 5, attention is on the external 2-D flow on the waverider lower surfaces, that is, AB1B3 and AB1B4, and the flow entering and exiting the planes, AB3B4 and B1B3B4. With this alternative perspective, the innovation lies in the fact that the flow moving across the lower surface of the waverider is treated as the flow

Figure 9. Caret 2-D side view.

Inversely Designed Scramjet Flow-Path DOI: http://dx.doi.org/10.5772/intechopen.85697

Figure 10. Caret 2-D base view.

Figure 11. Caret 2-D plan view.

Figure 12.

61

Caret 2-D isometric view.

Figure 8. Generation of 2-D caret-shaped geometry, base view. Inversely Designed Scramjet Flow-Path DOI: http://dx.doi.org/10.5772/intechopen.85697

Figure 10. Caret 2-D base view.

Figure 9.

the 3-D coordinates that can be used to generate the 3-D forebody-inlet geometry

The caret geometry forms the basis of the design of the star shaped geometries in this study. A similar process is used to obtain the caret-shaped 2-D base view. Now instead of providing a wedge width, a star angle, Phi, is provided as presented in Figure 8. For the four-point-star, Phi is 45 degrees. Reflecting points ABPointC, about the z-axis will generate the 2-D base view for the caret-shaped waverider geometry. As before, all data required for the 3-D construction of the 3-D caretshaped forebody-inlet have been extracted from the flow-field. Figures 9–12 present the 3-D caret-shaped geometry obtained by using the design process described

The scramjet forebody-inlet-isolator design concept as being proposed suggests a

new use for waverider geometries. Here, the focus is not only of the waverider

for a 3-D wedge.

Figure 7.

Figure 8.

60

4.2 The caret geometry

Generation of 2-D base view for a wedge.

Hypersonic Vehicles - Past, Present and Future Developments

above and programmed using FORTRAN90/95.

Generation of 2-D caret-shaped geometry, base view.

4.3 3-D stream tube construction using the waverider approach

shape, but also on the external flow-field supporting the waverider configuration. As seen in Figure 5, attention is on the external 2-D flow on the waverider lower surfaces, that is, AB1B3 and AB1B4, and the flow entering and exiting the planes, AB3B4 and B1B3B4. With this alternative perspective, the innovation lies in the fact that the flow moving across the lower surface of the waverider is treated as the flow

Figure 13. Waverider derived stream tube.

entering a stream tube through surface, AB3B4 and leaving through the plane, B1B3B4. Recall at this point that the flow-field is two dimensional, confined to the xy-plane and can be treated as a collection of 2-D slices that are parallel to each other. The flow within the stream tube is bounded by the lower inviscid surfaces, AB1B3 and AB1B4 and an imaginary line surface, B3B4.

A completed stream tube consisting of the forebody-inlet-isolator sections is presented in Figure 13. This stream tube is carved/extracted from a supersonic flow-field travelling parallel to the x-axis, which is compressed by two oblique shock waves; resulting in the flow once again traveling in a direction parallel to the x-axis. Further examination of Figure 13 identifies the primary shock wave plane as AB3B4, which supports two compression surfaces, ACB3 and ACB4. At this stage the flow field is no longer parallel to the x-axis. A reflected shock wave is constructed to form the plane, CB3B4. This specially designed plane, CB3B4, now straightens the flow leaving the shock surface, CB3B4, so that it once again travels parallel to the x-axis. The reflected flow now forms the stream tube comprising of the following planar surfaces, CDD3B3, CDD4B4, and B3B4D4B3.

### 4.4 Transforming stream tubes to 'star' shaped geometries

The preceding section saw the design of a single stream tube. These single stream tubes can now be used to create star-shaped geometries of interest, an example of which is presented in Figure 14. Presented in Figure 14 is a four point star geometry, so termed because it is a collection of four stream tubes that is assembled in a manner to create a 'closed form' geometry of interest.

seen in Figure 13. In generating the four point star configuration the angle α is set to

This section focuses on the validation of the forebody-inlet-isolator sections

associated with the proposed scramjet engine concept. The independent

90 degrees.

63

Figure 15.

Figure 14.

A 4-points star-shaped scramjet forebody-inlet-isolator [1].

Inversely Designed Scramjet Flow-Path DOI: http://dx.doi.org/10.5772/intechopen.85697

5. Validation section

Five-points scramjet forebody-inlet-isolator [1].

The fundamental concept in moving from a 2-D geometry, Figure 4, to the 3-D geometries, Figures 13–16, lies mainly on identifying the coordinates along the z-axis. Determination of the location of points, B3, B4, D3 and D4, is of significant importance. These points are responsible for the development of a closed form geometry/closed tube with the ability of preserving the aerodynamics associated with the inviscid flow-field behavior. Additionally, the 'y' and 'z' coordinates of these points rely of the choice of angle α, an example of which is the angle D3DD4 as Inversely Designed Scramjet Flow-Path DOI: http://dx.doi.org/10.5772/intechopen.85697

Figure 14. A 4-points star-shaped scramjet forebody-inlet-isolator [1].

Figure 15. Five-points scramjet forebody-inlet-isolator [1].

seen in Figure 13. In generating the four point star configuration the angle α is set to 90 degrees.
