利用三維、混合非結構性網格、平行化之直接蒙地卡羅法進行多超音速噴流流場之模擬。分別計算一個、二個、三個及四個噴口，將氬氣噴向低壓環境的模擬。利用流續流體的假設計算出喉管口的出口流場，並帶入直接蒙地卡羅法來模擬。在這個模擬中，上游的停滯壓力跟下游腔體的壓力比值固定為50。以喉管為基礎的Knudsen number 範圍為0.001~0.1，其流場特徵為近流續流到過渡流。結果顯示流場Knudsen number為0.001時可以清楚的描述出barrel shock及Mach disk shock，隨著Knudsen number的增加而消失而成為可壓縮的膨脹流。而具有多噴管流場的流場也會被詳細的討論。在不同稀薄程度的流場也會因不同的理由產生不平衡現象。

Flow fields of multiple underexpanded supersonic jets are simulated using the three-dimensional, parallel direct simulation Monte Carlo (DSMC) method employing an unstructured mesh incorporating static domain decomposition. One, two, three and four jets of argon gas issuing from the orifice(s) into a lower-pressure environment are considered, respectively. Inflow conditions at the orifice outlet (throat) required for the DSMC computation are calculated using the continuum approach. Ratio of upstream stagnation pressure to downstream chamber pressure remains fixed at 50 in the current study. Rarefaction parameter characterized by Knudsen numbers (based on throat conditions) is varied in the range of 0.001~0.1, which corresponds to the flow from near-continuum to transitional regimes. Results show that a distinct barrel shock and Mach disk structure is clearly captured for a single jet flow at Knudsen number of 0.001, while it is diminished to a purely compressible, expanding flow with increasing Knudsen number. Interaction between multiple jets is discussed in detail. Strong thermal non-equilibrium in translational degree of freedoms appears for both high and low Knudsen-number flows due to different reasons.

摘要……………………………………………………….……………….I
ABSTRACT …………………………………………………...………..II
TALBE OF CONTENTS III
LIST OF TABLE IV
LIST OF FIGURE V
NOMENCLATURE XIV
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 NUMERICAL METHOD 5
2.1 The Conventional DSMC Method 5
2.2 Parallel DSMC Method 6
2.3 Hybrid Grid 9
CHAPTER 3 RESULTS AND DISCUSSIONS 11
3.1 Application of the Hybrid DSMC 11
3.2 Single/Multiple Jets Simulation 12
3.2.1 Pre-computation 13
3.2.2 Simulation results and discussions 14
CHAPTER 4 CONCLUSIONS 20
REFERENCES 22

1. Abbett, M., "The Mach Disk in Underexpanded Exhaust Plumes, "AIAA Journal, Vol.9, 1971, pp. 512-514.
2. Bailey, A.B., "Flow-Angle Measurements in a Rarefied Nozzle Plume," AIAA Journal, Vol. 25, pp. 1301-1304, 1987.
3. Bergers, D., "The Interaction of Plane and Axisymmetric Jets with a Rarefied Background Gas," Physics of Fluids, Vol. 28, pp. 489-497, 1985.
4. Bird, G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, New York, 1994.
5. Boyd, I. D., "Monte Carlo Simulation of Nonequilibrium Flow in a Low-power Hydrogen Arcjet," Physics of Fluids, Vol. 9, pp. 3086-3095, 1997.
6. Boyd, I.D., Penko, P.F, Meissner, D.L. and Kennetch, J.D., "Experimental and Numerical Investigations of Low-Density Nozzle and Plume Flows of Nitrogen," AIAA Journal, Vol. 30, pp. 2453-2461, 1992.
7. Crist, S., Sherman, P.M. and Glass, D.R., "Study of the Highly Underexpanded Sonic Jet," AIAA Journal, Vol.4, 1966, pp.68-71.
8. Dagum, L. and Zhu, S.K., "Direct Simulation Monte Carlo Simulation of the Interaction Between Rarefied Free Jets," Journal of Spacecraft and Rockets, Vol. 31, pp. 960-964, 1994.
9. Eastman, D.W. and Radtke, C.P., "Location of the Normal Shock Wave in the Exhaust Plume of a Jet," AIAA Journal, Vol. 1, 1963, pp. 918-919.
10. Engstrom, J.R., Hansen, D.A., Furjanic, M. J., and Xia, L.Q., Journal Chemical Physics, Vol. 99, 1993, pp. 4051.-4058.
11. Eres, D., Lowdes, D.H. and Tishler, J.Z., Applied Phys. Letter, Vol. 55, 1989, pp. 1008-1010.
12. Gribeen, B.J., Badcock, K.J. and Richard, B.E., "Numerical Study of Shock-Reflection Hysteresis in an Underexpanded Jet, " AIAA Journal, Vol. 38, 2000, pp. 275-283.
13. Jones, M.E., Xia, L.Q., Maity, N. and Engstrom, Chemical Phyics Letter, Vol. 229, 1994, pp. 401-403.
14. Moustafa, G.H., "Interaction of Axisymmetric Supersonic Twin Jets," AIAA Journal, Vol. 33, pp.871-875, 1995.
15. Niimi, Tomohide, Fujimoto, T. and Taoi, N., "Flow Fields of Interacting Parallel Supersonic Free Jets," JSME International Journal, Series B, Vol. 39, pp. 95-100, 1996.
16. Penko, P.F., Boyd, I.D., Meissner, D.L. and DeWitt, J.D., "Measurement and Analysis of a Small Nozzle Plume in Vacuum," Journal of Propulsion, Vol. 9, pp. 646-648, 1993.
17. Raghynathan, S. and Reid, I.M., "A Study of Multiple Jets," AIAA Journal, Vol. 19, pp. 124-127, 1981.
18. Rothe, D.E., "Electron-Beam Studies of Viscous Flow in a Supersonic Nozzle," AIAA Journal, Vol. 9, pp. 804-811, 1971.
19. Teshima, K. and Nakatasuji, H., "Visualization of Rarefied Gas Flows by a Laser Induced Flurescence Method," 14th Int. Symp. on Rarefied Gas Dynamics, ed. Ouguchi, H., University of Tokyo, Tokyo, Japan, 1984, pp. 447-454.
20. Teshima, K. and Usami, M., "An Experimental Study and DSMC Simulation of Rarefied Supersonic Jets," 20th Int. Symposium on Rarefied Gas Dynamics, Ed. C. Shen, Bejing University Press, Bejing, China, 1997, pp. 567-572.
21. Teshima, K. and Usami, M., "DSMC Calculation of Supersonic Expansion at a Very Large Pressure Ratio," 22nd International Symposium on Rarefied Gas Dynamics, Sydney, Australia, 2000.
22. Usami, M. and Teshima, K., "DSMC Calculation of Supersonic Free Jets from an Orifice with Convex and Concave Corners," 22nd International Symposium on Rarefied Gas Dynamics, Sydney, Australia, 2000.
23. Usami, M. and Teshima, K., "Molecular Simulation of Rarefied Supersonic Free Jets by DSMC Method," JSME International Journal, Series B, Vol. 42, pp. 369-376, 1999.
24. Usami, M. and Teshima, K., "Three Dimensional DSMC Calculation of Interacting Flowfield in Two Parallel Underexpanded Jetsm 21st Int. Symp. on Rarefied Gas Dynamics, Ed. Brun, R. et al., Spadues-editions, Toulouse, France, 1999, pp. 569-576.
25. Wlezien, R.W., "Nozzle Geometry Effects on Supersonic Jet Interaction," AIAA Journal, Vol. 27, pp. 1361-1367, 1989.
26. Wu, J.-S. and Lian, Y.-Y., "Parallel Three-Dimensional Direct Simulation Monte Carlo Method and Its Applications," Computers & Fluids (Submitted).