# Hypersonic Interaction Flows

## Objective

The main objective of this research is to develop a hybrid particle/continuum numerical method for simulating hypersonic interaction flows. This method is expected to be physically more accurate and numerically more efficient than a conventional method that simply employs either particle or continuum approach, but not both.The particle approach in the hybrid method employs the direct simulation Monte Carlo-Information Preservation (DSMC-IP), a special version of the DSMC by Graeme Bird. The continuum approach employs a Computational Fluid Dynamics (CFD) method that solves the Navier-Stokes equations using a finite-volume, second order accurate scheme. More specific, this scheme employs an explicit Gauss-Seidel line relaxation technique and a modified Steger-Warming flux vector splitting.

## Background

The interactions of the bow shock of a hypersonic vehicle and the shock waves from a wing or control surface are of great interest in space vehicle design because of the potentially high localized temperature and the associated extremely high heating rates in the interaction region. Also, the shock waves impinging on the vehicle control surface may cause boundary layer separation and, as a result, may reduce the control surface effectiveness. Space Shuttle and X-43 are two examples that have to take the effects of hypersonic interaction flows into account during design stage.

Future hypersonic vehicles will very likely have leading edges made from a material similar to the Ultra-High Temperature Ceramics (UHTC's) being developed at the NASA Ames Research Center. The use of UHTC's makes it possible to design a new generation of vehicles with very sharp leading edges and smooth surfaces, resulting in a much smaller, lighter, and more efficient space vehicle than ever. For a vehicle flying at Mach 12 and altitude 40 km, for instance, the leading edge made from UHTC's could have radius as small as 0.23 cm, compared with 81.5 cm for the leading edge made from the traditional carbon-carbon material. Therefore, non-actively cooled leading edges of the order of 1 mm in radius are feasible.

### Rarefied Effects

The fact that future hypersonic vehicles will have very small leading edge radii does not solve the problems of localized high heat transfer from shock interactions. It instead puts these interactions into the regime where the continuum approach is not necessarily valid. Let us consider the Knudsen number with 0.23 cm of leading edge radius as the characteristic length. At altitude 30 km it is 0.016 and at altitude 40 km 0.074. It is clear that the flow in the region of the shock interaction is likely to be non-continuum at 30 km and will certainly be rarefied at 40 km. Therefore, the new UHTC's materials will result in leading-edge shock interactions at conditions where the flow field is poorly understood and where little research has been performed.

## Geometry and Code Validation

Two simple geometric configurations have been tested to validate our code, MONACO. The flow conditions were carefully selected to ensure that the entire flow fields were stable and laminar.

### Hollow Cylinder/Flare

Fig. 1. Schematic of the hollow |

The first configuration consists of a hollow cylinder followed by a 30° flare. The leading edge of the hollow cylinder is sharp and aligned in the free stream direction. Flow through the hollow cylinder is designed to pass through the model without influencing the external flow.

The working fluid in this validation is pure nitrogen. The free stream
conditions are U_{∞} = 2609 m/sec, T_{∞} = 128.9 K,
P_{∞} = 19.4 Pa and ρ_{∞} = 5.066×10^{-4}
Kg/m^{3}. The corresponding Mach number is 11.1 and the Reynolds number
based on the length of hollow cylinder is 4.74×10^{4}. The wall
temperature remains constant at 297.2 K.

The computation was performed in a 1000x200 structured grid with more than 3.5 million simulation particles. It took about a total of 88 hours to get the solutions at 4 msec in a parallel job with 32 processors on the IBM-SP at University of Minnesota. The translational temperature is displayed in Fig. 2. The temperature is increased in the region above the cylinder due to viscous interaction with a peak value less than 1,000 K. The strong compression caused by the flare leads to further heating with peak values of about 1,500 K reached above the flare.

Fig. 2. Translational temperature for the cylinder/flare flow

The comparisons of pressure and heat transfer coefficients between the numerical and experimental results along the body surface are made in Figs. 3 and 4. It is clear that results of DSMC agree very well with the measurements. The size of separation zone and the position of the shock are correctly predicted by DSMC.

Fig. 3. Pressure coefficient along the cylinder/flare |
Fig. 4. Stanton number along the cylinder/flare |

### Sharp Double Cone

Fig. 5. Schematic of the 25-55° |

The second model in our investigation is a 25°/55° cone/cone
configuration with a sharp leading edge. The free stream conditions of this
computation are U_{∞} = 2072.6 m/s, T_{∞} = 42.6 K,
P_{∞} = 2.2 Pa and ρ_{∞} = 1.757×10^{-4}
Kg/m^{3}. The corresponding Mach number is 15.6 and the Reynolds number
based on the length of the first cone is 4.19×10^{4}. The wall
temperature also remains constant at 297.2 K.

This configuration usually creates more complex flow structures. At this high Mach number, the first cone produces an attached oblique shock wave, and the second, larger angle cone produces a detached bow shock. These two shocks interact to form a transmitted shock that strikes the second cone surface near the cone-cone juncture. The adverse pressure gradient due to the cone juncture and the transmitted shock generates a large region of separated flow that produces its own separation shock. This shock interacts with the attached oblique shock from the first cone, altering the interaction with the detached shock from the second cone. This in turn affects the size of the separation region.

The computational grid employed in this study consists of 2000 cells along the body by 256 cells normal to the body. The translational temperature at t = 1.8 msec is shown in Fig. 6.

Fig. 6. Translational temperature for the 25-55° sharp double cone flow

The comparisons of computational and experimental results are demonstrated in Figs. 7 and 8. On the forecone ahead of separation, it is shown that numerical methods estimate the heat transfer rate and pressure very well. The size of the separation zone is under-predicted by both numerical method. It is likely that a longer computational time is necessary.

Fig. 7. Pressure coefficient along the 25-55° |
Fig. 8. Stanton number along the 25-55° |

## Domain Coupling

To implement the coupling between the particle method and the NS solver, buffer and reservoir DSMC-IP cells are introduced in the continuum domain adjacent to the domain interface, as depicted in Fig. 9.

Fig. 9. Interface cell types

The buffer DSMC-IP cells work as an extension of the particle domain. Simulation particles that end their movement phase within the pure particle domain or in the buffer cells are retained. Those that leave these two regions are removed. For each time step, all simulation particles in the reservoir cells are first deleted and then re-generated based on the cell-centered values. The number of new particles is evaluated from the cell density value and the particle velocities and temperature are initialized to the Chapman-Enskog distribution based on the corresponding cell values. The newly generated particles are randomly distributed within the reservoir cells.

## Hybrid Results

### 25° blunted cone

Fig. 10. Temperature contours |
Fig. 11. Density contours |

Fig. 12. Temperature profiles along the stagnation line |
Fig. 13. Density profiles along the stagnation line |

### 25° Hollow Cylinder/Flare

Fig. 14. Temperature contours |
Fig. 15. Density contours |

Fig. 16. Temperature profiles along the line normal to |
Fig. 17. Density profiles along the line normal to |

## Acknowledgments

Great acknowledgments go to Professor Graham Candler of University of Minnesota for providing the CFD code and Ioannis Nompelis for providing the CFD solution of the hollow cylinder-flare example. This work was supported by the Air Force Office of Scientific Research under grant F49620-01-1-0003.## Investigation Members

- Iain D. Boyd, Professor
- Wen-Lan Wang, Graduate Student

## Recent Publications

Wang, W.-L. and Boyd, I. D.,

**A New Energy Flux Model in the DSMC-IP Method for Nonequilibrium Flows**, AIAA-03-3774,*Presented at the 36th AIAA Thermophysics Conference*, June 2003, Orlando, FL.Wang, W.-L. and Boyd, I. D.,

**Hybrid DSMC-CFD Simulations of Hypersonic Flow over Sharp and Blunted Bodies**, AIAA-03-3644,*Presented at the 36th AIAA Thermophysics Conference*, June 2003, Orlando, FL.Wang, W.-L. and Boyd, I. D.,

**Predicting Continuum Breakdown in Hypersonic Viscous Flows**,*Physics of Fluids*, January 2003, Vol. 15, pp91-100.