利用三維非結構性調適網格、平行化之直接蒙地卡羅法進行單噴流及雙噴留再稀薄氣體流場模擬。在不同的 Knudsen number 及不同壓力比下觀察噴流的結構變化的超音速噴流流場之模擬。分別計算一個及二個噴口，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自50變化至真空。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。而隨著壓力比的增加，Mach disk shock 的位置也向下游推移。

Supersonic jets issuing from a sonic orifice over a wide range of the stagnation
knudsen numbers，from a continuum to a near free molecular condition，and over a wide range of the pressure ratio are simulated by the DSMC method. single and twin jets of argon gas from the orifice(s) into a lower-pressure chamber are considered,
in order to minimize the computational time and reduce CPU load. An adaptive mesh-embedding (h-refinement) scheme using unstructured grid and variable time step scheme in three-dimensional Direct Simulation Monte Carlo method is used. The result reproduces very well the jet structure including the Mach disk and the barrel shock for a near continuum flow condition as well as the jets in the transition regime.

CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 LITERATURE SURVEY 2
1.3 OBJECTIVES AND ORGANIZATION OF THE THESIS 10
1.3.1 objectives 10
1.3.2 organization of the thesis 10
CHAPTER 2 NUMERICAL METHOD 11
2.1 DSMC METHOD 11
2.2 PARALLEL DSMC METHOD 12
2.3 MESH ADAPTATION 13
2.4 VARIABLE TIME STEP SCHEME 17
Chapter 3 Results and Discussion 22
3.1 FLOW AND SIMULATION CONDITIONS 22
3.2 SIMULATION RESULTS AND DISCUSSIONS 23
CHAPTER 4 CONCLUSIONS AND FUTURE WORK 39
4.1 CONCLUSIONS 39
4.2 FUTURE WORK 39
RERERENCES 41

[1] Nabu, R.P., “Monte Carlo Simulation of Three-dimensional Hypersonic Flows on Parallel Architectures,” Master Thesis, North Carlolina State University, 1995
[2] Gang Chen, “Direct Simulation Monte Carlo Modeling of Silicon Thin Film Deposition Using Supersonic Beams” Ph.D. Thesis, Cornell University, 1998
[3] Engstrom , J.R., Xia, L. Q., Furjanic, M.J. and Hansen. D.A. Dissociative Adsorption of Si2H6 on Silicon at Hyperthermal Energies: The Influence of Surface Structure. Apply. Phys. Lett.,63(13):1821,1993.
[4] Adamson, T. C., Jr., “The structure of the rocket exhaust plume without reaction at various altitudes,” Supersonic Flow, Chemical Processes and Radiation Transfer (Pergamon Press, New York, 1964).
[5] Abbett, M., "The Mach Disk in Underexpanded Exhaust Plumes, "AIAA Journal, Vol.9, 1971, pp. 512-514.
[6] Bailey, A.B., "Flow-Angle Measurements in a Rarefied Nozzle Plume," AIAA Journal, Vol. 25, pp. 1301-1304, 1987.
[7] Bergers, D., "The Interaction of Plane and Axisymmetric Jets with a Rarefied Background Gas," Physics of Fluids, Vol. 28, pp. 489-497, 1985.
[8] Bird, G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, New York, 1994.
[9] Boyd, I. D., "Monte Carlo Simulation of Nonequilibrium Flow in a Low-power Hydrogen Arcjet," Physics of Fluids, Vol. 9, pp. 3086-3095, 1997.
[10] 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.
[11] Crist, S., Sherman, P.M. and Glass, D.R., "Study of the Highly Underexpanded Sonic Jet," AIAA Journal, Vol.4, 1966, pp.68-71.
[12] 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.
[13] 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.
[14] Engstrom, J.R., Hansen, D.A., Furjanic, M. J., and Xia, L.Q., Journal Chemical Physics, Vol. 99, 1993, pp. 4051.-4058.
[15] Eres, D., Lowdes, D.H. and Tishler, J.Z., Applied Phys. Letter, Vol. 55, 1989, pp. 1008-1010.
[16] 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.
[17] Jones, M.E., Xia, L.Q., Maity, N. and Engstrom, Chemical Phyics Letter, Vol. 229, 1994, pp. 401-403.
[18] Moustafa, G.H., "Interaction of Axisymmetric Supersonic Twin Jets," AIAA Journal, Vol. 33, pp.871-875, 1995.
[19] 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.
[20] 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.
[21] Raghynathan, S. and Reid, I.M., "A Study of Multiple Jets," AIAA Journal, Vol. 19, pp. 124-127, 1981.
[22] Rothe, D.E., "Electron-Beam Studies of Viscous Flow in a Supersonic Nozzle," AIAA Journal, Vol. 9, pp. 804-811, 1971.
[23] 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.
[24] 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.
[25] 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.
[26] 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.
[27] 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.
[28] 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.
[29] Wlezien, R.W., "Nozzle Geometry Effects on Supersonic Jet Interaction," AIAA Journal, Vol. 27, pp. 1361-1367, 1989.
[30] Wu, J.-S. and Lian, Y.-Y., "Parallel Three-Dimensional Direct Simulation Monte Carlo Method and Its Applications," Computers & Fluids (Submitted).
[31] Wu, J.-S., Tseng, K.-C. and Kuo, C.-H., “The direct simulation Monte Carlo method using unstructured adaptive mesh and its application,” International Journal of Numerical Methods in Fluids, Volume 38, Issue 4, pp, 351-375, 2002.
[32] Wu, J.-S., Tseng, K.-C. and Yang, T.-J., “Parallel implementation of the direct simulation Monte Carlo using unstructured mesh and its application,” International Journal of Computational Fluid Dynamics, 2003 (in press).
[33] Wu, J.-S and Tseng, K.-C., “Parallel Particle Simulation of the near-continuum hypersonic flows over compression ramps,” ASME-Journal of Fluids Engineering, 2003 (in press).
[34] Wu, J.-S. and Lian, Y.-Y., “Development of parallel three-dimensional DSMC method and its applications,” Computer & Fluids, 2003 (in press).
[35] Wu, J.-S. and Tseng, K.-C., “Parallel DSMC method using dynamic domain decomposition,” 23rd Internal Symposium on Rarefied Gas Dynamics, British Columbia, Canada, July, 2002.
[38] Wu, J.-S., Tseng, K.-C. and Wu, F.-Y. "Three-Dimensional DSMC Method Using Unstructured Adaptive Mesh and Variable Time-Step", International Journal for Numerical Methods in Fluids, 2003 (submitted).