在21世紀的今天飛行器減阻的課題越來越重要，在軍事用途上，它可以使戰鬥機或飛彈變得更省油，飛的更快；民用方面則可發展出更省油更環保的飛行器。在此我們試圖使用噴流方法達到減阻效果，我們於超音速彈體的前後方，分別加上逆向噴流及順向噴流，並分析其物理現象，利用逆向噴流衝擊相對氣流來改變外部流場並達到減阻效果；利用順向噴流補足彈體後方因分離流或膨脹波所形成的低壓區塊，以減少壓差阻力。
　　我們利用Gambit產生網格，並使用CFD求解軟體Fluent中內建的LES及κ-ε 模組求解驗證案例及新案例，新的案例中包含半球形及喇叭狀的機鼻外型之局部逆向噴流、數個局部順向噴流、以及細長比為14.5的全彈體於飛行速度2.5馬赫時兩種噴流的搭配結果。另外我們還嘗試計算噴流所需的耗能量及其效率的基本推算：逆向噴流因為動量損失而使減阻效果變差，順向噴流則可製造出一個淨推力的效果，且似乎不需花費太多能量，所以整體效果優於逆向噴流。就結果而言，噴流概念將來也許可以實際應用於真實的超音速飛行器或彈體設計上。

Drag reduction is an important objective for aircraft operation, and become even more vital in the twenty-first century. In military usage, fighters or missiles can therefore save fuel consumption and attain higher flying speed; and in civil practice, the goal of more efficient and environmental concerned flights can be achieved. Here we try some approaches to accomplish the purpose of drag reduction. The physical phenomenon of supersonic projectile aerodynamics with counter-flow and rear end jets are analyzed in current effort. Using counter-flow jet to impinge upon the opposite free stream flow in order to change the flow field and thus in the hope of reducing drag force. On the other hand, we could also employ rear end jets to fill the domain which is after the projectile rear end so as to decrease the base drag and the drag from supersonic expansion waves.
     In addition to the grid construction and flow solver routine, LES model and k-epsilon model of CFD Fluent code are also employed in our studies for verification and case studies. Investigated problems include local counter-flow jet situations with hemispherical nose and trumpet-like nose configurations, several local rear end jet cases, and the combination of both nose counter-flow and rear end jets for a real missile-like projectile with a fineness ratio of 14.5 and Mach number of 2.5. With the newly defined drag reduction efficiency parameter; the drag reduction of counter-flow jet is not so good because of loss momentum of the reverse thrust. The rear end jet flow can be considered a big thrust there, and comparisons are also made. After the simulations of the energy consumption of the jets and efficiency of all different cases, it appears that we do not need to spend too much energy to transform the total drag to become net thrust, and it is believed that the jet conception considered in this work can found their practical application in future supersonic projectile operation.

Abstract	II
Contents	IV
List of Tables	V
List of Fighures	VI
Nomenclatures	XII
Chapter 1 Introduction	1
Chapter 2 Research Background	4
Chapter 3 Numerical Modeling	12
3.1 The Cases of Verification	12
3.2 Geometry Configuration and Mesh Generation for Verification	14
3.3 Governing Equations	18
3.4 Solver	19
3.5 The Cases in Real Atmosphere	21
Chapter 4 Result and Discussion	28
4.1 Verification	28
4.2 Local Counter-flow Jet Cases	39
4.3 Local Rear End Jet Cases	48
4.4 Projectile Drag Reduction	58
Chapter 5 Conclusions	70
References	72
Appendix A	76
Appendix B	79
Table 2-1. Counterflowing nozzle jet flow conditions..	5
Table 4-1.The comparison of the nose cases for verification	31
Table 4-2. The comparison of hemispherical nose of counter-flow jet cases	40
Table 4-3. The comparison of trumpet-like nose of counter-flow jet cases	43
Table 4-4. The comparison of 3-D rear end jet cases of static pressure ratio equals 3	50
Table 4-5. (a) The comparison of 3-D rear end jet cases of static pressure ratio equals 10	51
Table 4-5. (b) The comparison of 3-D rear end jet cases of static pressure ratio equals 10	51
Table 4-6. (a) The comparison of 3-D rear end jet cases of total pressure ratio equals 1	52
Table 4-6. (b) The comparison of 3-D rear end jet cases of total pressure ratio equals 1	53
Table 4-7. The comparison of a projectile with only counter-flow jet	60
Table 4-8. The comparison of a projectile with only rear end jet	65
Table 4-9. The comparison of a projectile with both two jets	69


Figure 2-1. Percentage of drag reduction measured for different values of the ratio of jet pressure to the pitot pressure of the Mach 8 test flow.	5
Figure 2-2. Effects of angle of attack and flow rate on the interaction of the counter-flowing jet with Mach 4	6
Figure 2-3.(a-e) Pressure counter of two flow mode with the variation of P, (a) P=4.5, (b) P=8.9, (c) P=22.3, (d) P=31.2, and (e) P=44.6	7
Figure 2-4. The variation of drag coefficient to jet total pressure ratio P	7
Figure 2-5. Numerical schlieren-like visualizations by contours of the norm of the gradient of mean density in the meridian plane for P=0.816 at two instants in (a) and (b) and the corresponding enlarged jet structure in (c) and (d)	8
Figure 2-6. Numerical schilweren-like visualizations by contours the norm of the gradient of mean density in the meridian plane for P=1.633 at two instants in (a) and (b) and the corresponding enlarged jet structures in (c) and (d)	9
Figure 2-7. Distributions of the mean local Mach number M for (a) P=0.816 and (b) P=1.633. Here, solid lines denote M>1 and dashed lines M<1 with a contour increment 0.1	9
Figure 2-8. The results of different jet diameter by Meyer cases	11
Figure 3-1. The geometry configuration of counter-flow jet cases drew by Pro-E	15
Figure 3-2.(a) Side view of sturcture type meshes with no jet case drew by Gambit	15
Figure 3-2.(b) Slanting view of sturcture type meshes with no jet case drew by Gambit	16
Figure 3-3.(a) Side view of the case for verification with counter-flow jet	16
Figure 3-3.(b) Slanting view of the case for verification with counter-flow jet	17
Figure 3-4.(a) 2-D rear end case with 32160 cells mesh	17
Figure 3-4.(b) 2-D rear end case with 86160 cells mesh	18
Figure 3-5.(a) Overall side view of trumpet-like nose with 2274432 cells mesh	23
Figure 3-5.(b) Overall slanting view of trumpet-like nose with 2274432 cells mesh	23
Figure 3-5.(c) Local side view of trumpet-like nose with 2274432 cells mesh	23
Figure 3-5.(d) Local slanting view of trumpet-like nose with 2274432 cells mesh	24
Figure 3-6.(a) Side view of rear end case with 451040 cells mesh	24
Figure 3-6.(b) Slanting view of rear end case with 451040 cells mesh	25
Figure 3-7.(a) Side view of hemispherical nose projectile with 3360624 cells mesh	25
Figure 3-7.(b) Slanting view of hemispherical nose projectile with 3360624 cells mesh	26
Figure 3-7.(c) Side view of hemisphical nose projectile with 466624 cells mesh	26
Figure 3-7.(d) Slanting view of hemispherical nose projectile with 466624 cells mesh	26
Figure 3-7.(e) Side view of trumpet-like nose projectile with 4101204 cells mesh	27
Figure 3-7.(f) Slanting view of trumpet-like nose projectile with 4101201 cells mesh	27
Figure 4-1. The pressure data of the cases for verification of head with and without jet	28
Figure 4-2.(a) Y-plus of the case for verification of head case with no jet	29
Figure 4-2.(b) Counters of Mach number of the head case with no jet	29
Figure 4-2.(c) Contours of static pressure of the head case with no jet	30
Figure 4-3.(a) Y-plus of the case for verification of head with counter-flow jet	31
Figure 4-3.(b) Contours of Mach number of the head case with counter-flow jet	32
Figure 4-3.(c) Contours of static pressure of the head case with counter-flow jet	32
Figure 4-4. 2-D rear end cases by steady and unsteady state	33
Figure 4-5. There is a wall or a symmetry line behide the step	34
Figure 4-6.(a) Test different meshes for 2-D cases for verification	35
Figure 4-6.(b) Y-plus of 32160 cells mesh of 2-D rear end case	36
Figure 4-6.(c) Y-plus of 86160 cells mesh of 2-D rear end case	36
Figure 4-6.(d) Contours of Mach number of 32160 cells mesh of 2-D rear end case	37
Figure 4-6.(e) Contours of Mach number of 86160 cells mesh of 2-D rear end case	37
Figure 4-6.(f) Counters of static pressure of 32160 cells mesh of 2-D rear end case	38
Figure 4-6.(g) Contours of static pressure of 86160 cells mesh of 2-D rear end case	38
Figure 4-6.(h) The 2-D rear end case whichhas 154560 cells mesh	39
Figure 4-7.The pressure data of hemispherical nose of counter-flow jet cases	41
Figure 4-8.(a) Mach contour of Case 7 of local counter-flow jet case	44
Figure 4-8.(b) Mach contour of Case 8 of local counter-flow jet case	44
Figure 4-8.(c) Mach contour of Case 9 of local counter-flow jet case	45
Figure 4-8.(d) Pressure contour of Case 7 of local counter-flow jet case	45
Figure 4-8.(e) Pressure contour of Case 8 of local counter-flow jet case	46
Figure 4-8.(f) Pressure contour of Case 9 of local counter-flow jet case	46
Figure 4-8.(g) The pessure data of trumpet-like nose cases	47
Figure 4-8.(h) Y-plus of outer surface of trumpet-like nose case	47
Figure 4-8.(i) Y-plus of inner surface of trumpet-like nose case	48
Figure 4-9.(a) Contours of Mach number of rear end case with no jet	48
Figure 4-9.(b) Contours of static pressure of rear end case with no jet	49
Figure 4-9.(c) The pressure data pressure of rear end case with no jet	49
Figure 4-10. The pressure data of rear end jet cases with total pressure ratio equals to 1	54
Figure 4-11.(a) Contours of Mach number when M=0.65 of local rear end jet case	55
Figure 4-11.(b) Contours of Mach number when M=1 of local rear end jet case	55
Figure 4-11.(c) Contours of Mach number when M=1.8 of local rear end jet case	56
Figure 4-11.(d) Contours of static pressure when M=0.65 of local rear end jet case	56
Figure 4-11.(e) Contours of static pressure when M=1 of local rear end jet case	57
Figure 4-11.(f) Contours of static pressure when M=1.8 of local rear end jet case	57
Figure 4-12.(a) Contours of static pressure without jet of a projectile case	58
Figure 4-12.(b) Contours of Mach number without jet of a projectile case	58
Figure 4-12.(c) The pressure data of without jet case of a projectile	59
Figure 4-13.(a) Mach contour of Case 1 of the projectile case	61
Figure 4-13.(b) Mach contour of Case 2 of the projectile case	61
Figure 4-13.(c) Mach contour of Case 3 of the projectile case	61
Figure 4-13.(d) Mach contour of Case 4 of the projecile case	62
Figure 4-13.(e) Pressure contour of Case 1 of the projectile case	62
Figure 4-13.(f) Pressure contour of Case 2 of the projectile case	62
Figure 4-13.(g) Pressure contour of Case 3 of the projectile case	63
Figure 4-13.(h) Pressure contour of Case 4 of the projecile case	63
Figure 4-13.(i) Density contour of Case 1 of the projectile case	63
Figure 4-13.(j) Density contour of Case 2 of the projectile case	64
Figure 4-13.(k) Density contour of Case 3 of the projectile case	64
Figure 4-13.(l) Density contour of Case 4 of the projecile case	64
Figure 4-14.(a) Mach contour of only rear end jet case of a projectile	66
Figure 4-14.(b) Pressure contour of only rear end jet case of a projectile	66
Figure 4-14.(c) Density contour of only rear end jet case of a projectile	66
Figure 4-15.(a) Mach contour for Case 1 of both jets case of a projectile	67
Figure 4-15.(b) Mach contour for Case 2 of both jets case of a projectile	67
Figure 4-15.(c) Pressure contour for Case 1 of both jets case of a projectile	67
Figure 4-15.(d) Pressure contour for Case 2 of both jets case of a projectile	68
Figure 4-15.(e) Density contour for Case 1 of both jets case of a projectile	68
Figure 4-15.(f) Density contour for Case 2 of both jets case of a projectile	68

[1]	Love, E.S., “The Effects of a Small Jet of Air Exhausting from the Nose of a Body of Revolution in Supersonic Flow,” National Advisory Committee for Aeronautics, November 1952.
[2]	Finley, P.J., “The Flow of a Jet from a Body Opposing a Supersonic Free Stream,” Journal of Fluid Mechanics, Vol. 26, 1966, pp. 337-368.
[3]	Shang, J.S., “Plasma Injection for Hypersonic Blunt-Body Drag Reduction,” AIAA Journal, Vol. 40, No. 6, June 2002, pp. 1178-1186.
[4]	Shang, J.S., “Plasma Injection for Hypersonic Blunt-Body Drag Reduction,” AIAA Journal, Vol. 40, No. 6, June 2002, pp. 1178-1186.
[5]	Gauer, M. and A. Paull, “Numerical Investigation of a Spiked Blunt Nose Cone at Hypersonic Speeds,” Journal of Spacecraft and Rockets, Vol. 45, No. 3, May-June 2008.
[6]	Ahmed, M.Y.M. and N. Qin, “Drag Reduction Using Aerodisks for Hypersonic Hemispherical Bodies,” Journal of Spacecraft and Rockets, Vol. 47, No. 1, January-February 2010, pp. 62-80.
[7]	Kalimuthu, R., R.C. Mehta, and E. Rathakrishnan, “Drag Reduction for Spike Attached to Blunt-Nosed Body at Mach 6,” Journal of Spacecraft and Rockets, Vol. 47, No. 1, January-February 2010, pp. 219-222.
[8]	Zhou, C.Y., W.Y. Ji, and P. Xie, “Numerical Investigation on the Drag and Heat Flux Reduction of a Supersonic Reentry Capsule with a Counter-flow Jet,” Information Technology Journal, Vol. 11, 2012, pp. 1705-1713.
[9]	Forrester, A.I.J., A. Sobester, and A.J. Keane, Engineering Design via Surrogate Modelling: A Practical Guide, John Wiley & Sons, Inc., 2008.
[10]	Josyula, E., M. Pinney, and W.B. Blake, “Applications of a Counterflow Drag Reduction Technique in High-Speed Systems,” Journal of Spacecraft and Rockets, Vol. 39, No. 4, July-August 2002.
[11]	Venukumar, B., G. Jagadeesh, and K.P.J. Reddy, “Counterflow Drag Reduction by Supersonic Jet for a Blunt Body in Hypersonic Flow,” Physics of Fluids, Vol. 18, 2006.
[12]	Daso, E.O., V.E. Pritchett, T.S. Wang, D.K. Ota, I.M. Blankson, and A.H. Auslender, “Dynamics of Shock Dispersion and Interactions in Supersonic Freestreams with Counterflowing Jets,” AIAA Journal, Vol. 47, No. 6, 2009, pp. 1313-1326.
[13]	Venukumar, B. and K.P.J. Reddy, “Experiments Investigation of Drag Reduction by Forward Facing High Speed Gas Jet for a Large Angle Blunt Cone at Mach 8,” Sadhana, Vol. 32, Parts 1 & 2, February-April 2007, pp. 123-131.
[14]	Meyer, B., H.F. Nelson, and D.W. Riggins, “Hypersonic Drag and Heat-Transfer Reduction Using a Forward-Facing Jet,” Journal of Aircraft, Vol. 38, No. 4, July-August 2011, pp. 680-686.
[15]	Khamooshi, A., T. Taylor, and D.W. Riggins, “Drag and Heat Transfer Reductions in High-Speed Flows,” AIAA Journal, Vol. 45, No. 10, October 2007, pp. 2401-2413.
[16]	Daso, E.O., W. Beaulieu, and J.O. Hager, “Prediction of Drag Reduction in Supersonic and Hypersonic Flows with Counterflow Jets,” AIAA 2002-5115, October 2002.
[17]	Chen, L.W., C.T. Xu, and X.Y. Lu, “Large-Eddy Simulation of Opposing-Jet-Perturbed Supersonic Flows Past a Hemispherical Nose,” Modern Physics Letters B, Vol. 24, No. 13, 2010, pp. 1287-1290.
[18]	Chen, L.W., G.L. Wang, and X.Y. Lu, “Numerical Investigation of a Jet from a Blunt Body Opposing a Supersonic Flow,” Journal of Fluid Mechanics, Vol. 684, October 2011, pp. 85-110.
[19]	Khan, O.U. and K.A. Hoffmann, “Flow Control over a Backward-Facing Step with Application of a Magnetic Field,” Journal of Spacecraft and Rockets, Vol. 45, No. 2, March-April 2008, pp. 255-263.
[20]	Fujita, M., “Axisymmetric Oscillations of an Opposing Jet from a Hemispherical Nose,” AIAA Journal, Vol. 33, 1995, pp. 1850-1856.
[21]	Fluent User’s Guide.
[22]	Venkatachari, B.S., Y. Ito, and G. Cheng, “Numerical Investigation of the Interaction of Counterflowing Jets and Supersonic Capsule Flows,” AIAA Journal, June 2011.
[23]	Shah, S.B.H., S. Zahir, and I. Ahmed, “Numerical Investigation on the Effect of Shock Standoff Distance due to Counterflow Jets Injection from a Hemispherical Cylinder,” Proceedings of International Bhurban Conference on Applied Sciences & Technology, January 2011.
[24]	Finley, P.J., “The Flow of a Jet from a Body Opposing a Supersonic Free Stream,” Journal of Fluid Mechanics, Vol. 26, part 2, December 1965, pp. 337-368.
[25]	Emami-Naeini, A., S.A. McCabe, D. de Roover, J. L. Ebert, and R. Le Kosut, “Active Control of Flow over a Backward-Facing Step,” Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, December 2005.
[26]	Mehrez, Z., M. Bouterra, A.E. Cafsi, A. Belghith, and P.L. Quere, “Active Control of Flow Behind a Backward Facing Step by Using a Periodic Perturbation,” ARPN Journal of Engineering and Applied Sciences, Vol. 5, No. 2, February 2010.
[27]	Behrens, A.A., J.M. Lutz, and P.J. Strykowski, “Instantaneous Flame Anchor Measurements Behind a Rearward-Facing Step,” AIAA Journal, Vol. 47, No. 6, June 2009, pp. 1350-1357
[28]	Mehrez, Z., M. Bouterra, A.E. Cafsi, A. Belgith, and P.L. Quere, “Mass Transfer Control of a Backward-Facing Step Flow by Local Forcing-Effect of Reynolds Number,” Thermal Science, Vol. 15, No. 2, 2011, pp. 367-378.
[29]	Henning, L. and R. King, “Robust Multivariable Closed-Loop Control of a Turbulent Backward-Facing Step Flow,” Journal of Aircraft, Vol. 44, No. 1, January-February 2007, pp. 201-208.