Figure 19.

Computational Fluid Dynamics (CFD) test studies fall into two categories; 2-D

the premise of reducing numerical and modeling errors. As such, the IDS

Both Euler and viscous studies were conducted on the scramjet forebody, inlet, and isolator sections. 2-D Euler flow studies were conducted using the air vehicles unstructured solver (AVUS) [11]. AVUS is a three-dimensional finite volume unstructured-grid Euler/Navier-Stokes flow solver. 2-D isolator viscous simulations were conducted using an in-house computational scheme, the integral differential scheme (IDS) [12]. The following contour plots (Figures 17–19 and 24–29) represent the solution of the AVUS software, whose units are in the SI. Whereas the contour plots shown in Figure 20 depict the solution of the IDS. The IDS is built on

simulations and 3-D simulations.

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

Hypersonic Vehicles - Past, Present and Future Developments

5.1 2-D simulations

Figure 16.

Figure 17.

64

AVUS Euler results velocity distribution.

AVUS Euler results pressure contours.

#### Figure 20.

Results from isolator 2-D IDS simulation.

Figure 21. 3-D stream tube in computational domain.

Figure 24.

Figure 25.

Figure 26.

67

Centerline 2-D pressure contours.

Centerline 2-D Mach number contours.

Forebody-inlet-isolator validation study with 2-D slices.

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

#### Figure 22.

<sup>3-</sup>D stream tube cross-section (isolator exit) with clustering unstructured grids.

Figure 23. 3-D stream tube centerline with clustering unstructured grids.

Figure 24. Forebody-inlet-isolator validation study with 2-D slices.

Figure 25. Centerline 2-D Mach number contours.

Figure 26. Centerline 2-D pressure contours.

Figure 21.

Figure 22.

Figure 23.

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3-D stream tube in computational domain.

Hypersonic Vehicles - Past, Present and Future Developments

3-D stream tube cross-section (isolator exit) with clustering unstructured grids.

3-D stream tube centerline with clustering unstructured grids.

Figure 27. Centerline z-component velocity contours.

distributions. Once more we observe the organized nature of the 2-D flow, which is supported by the constant property in the respective zones. The development of the

A 2-D viscous simulation was conducted on the isolator section using the integral differential scheme (IDS), currently under development at North Carolina Agricultural & Technical State University. At the heart of the IDS numerical scheme is the unique combination of both the differential and integral forms of the Navier-Stokes

3-D computational simulations were also conducted on the scramjet forebody, inlet, and isolator sections. Computational tools used were Fluent and AVUS. In the case of the 3-D Euler computational simulation, a single 3-D stream tube, Figure 13, was exposed to a Mach 6 flow-field. The simulation was first conducted using Fluent, where the process is summarized by Figures 21–23. Examining Figures 22 and 23 demonstrates the use of unstructured grids with clustering in key areas for the analysis. The 3-D simulation required 6.7 million elements, 1,165,267 nodes, and 14.75 GB memory. To aid with visualization, 2-D slices, such as those seen in

shock train within the isolator duct is also captured in these figures.

equations (NSE). The differential form of the NSE is used for explicit time marching, whereas integral form of the NSE is used to evaluate the spatial fluxes. The IDS scheme has the ability to capture the complex physics associated with fluid flows. It does this by using a 'method of consistent averages' (MCA) procedure which ensures the continuity of the numerical flux quantities. The objective of this initial simulation was to observe the flow behavior. Further details on the physics and computational numerical scheme associated with the IDS can be found in [12]. Figure 20 presents the flow-field distribution. Flow-field properties presented in Figure 20 include Mach number distribution, pressure distribution, density distribution, and temperature distribution. Examination of theses flow-field properties supports the fact that the flow-field is behaving in a manner as it was designed to.

5.1.2 2-D isolator viscous simulations

Pressure contours at the isolator exit.

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

Figure 29.

5.2 3-D simulations

69

Figure 24, were extracted for analysis.

Figure 28. Mach contours at the isolator exit.

implements the dimensionless form of the Navier Stokes equations, and therefore it reduces the round-off error.
