流动矢量主动控制的微射流技术研究
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摘要
以微电子机械系统(MEMS)、混沌论及非线性复杂大系统不稳定理论为基础，一种全新的流场主动控制技术——微射流技术应运而生。作为一种全新的流场主动控制手段，微射流是通过其微尺度扰动同宏观大尺度流动的整体耦合作用达到控制宏观流动的目的。微射流控制系统简单、轻便、能耗极小且不需要工质源，初步显示出了常规射流控制方法所不具备的优势，具有非常广阔的应用前景。本文对微射流及其与主射流的合成流场进行数值模拟和机理分析，为微射流技术的工程应用研究打下基础。
本文的主要研究成果如下：
1．通过对微射流与主射流合成流场的深入分析，分别建立了微射流作动器二维、三维可压外流场控制方程以及二维微射流与主流合成流场的控制方程。采用快速求解的近似隐式因式分解法(AF方法)并内置似牛顿子迭代，有效地抑制了数值振荡、提高了稳定性并恢复了非线性方程在线化过程中所丢失的一些重要特性，同时还消除了因使用显式边界条件、人工粘性及隐式一边使用低阶空间差分近似所带来的误差。显式一边的空间导数采用具有较高精度和良好数值稳定性的隐式高阶紧致差分格式，同时采用适于低马赫数流动计算的隐式高阶数值过滤方法。
2．分别采用层流、湍流模型对单微射流流场进行了数值模拟。模拟结果显示了微射流的产生、形成、发展与耗散过程以及微射流的卷吸特征等。分析了双微射流作动器在不同频率、相位下协调工作时所形成的合成流场的特征。“低压回流区”的细观分析诠释了微射流的作用机制。
3．三维微射流流场的数值模拟再现了实验所观察到的旋涡对的生成、发展及其相干性的消失过程；揭示了旋涡对沿展向的不稳定性是旋涡对相干性消失的主要原因。在三维数值模拟中还捕捉到了二次涡，这为以后进一步研究微射流旋涡对的细微结构打下了良好的基础。
4．微射流与主射流合成流场的数值模拟再现了实验所观察到的主射流流动方向发生偏转的情形；分析了在“拉”模型单、双微作动器模式下，微射流控制宏观流动的现象及内在机理；揭示了微射流与主流之间“低压回流区”所引起的主流通道内的压力分布不平衡是主射流宏观流动方向发生偏转的
西北工业大学博士学位论文
Ph.D.Dissertation ofNorthwesternPolyteehnieal University
内在原因。分析了“拉”模型单作动器模式下，微射流作动器的入射角度、
驱动频率、速度幅值及与主射流间的距离对主射流偏转程度的影响，并确定
了作动器工作参数的最佳范围;分析了“拉”模型双作动器模式下，不同的
相位差对主流偏转程度的影响。
5.数值模拟再现了微射流改变绕流圆柱气动性能的情形。相邻微作动器同相工
作时部分分离流重新附面、尾流区减小。相邻微作动器存在相位差时，圆柱
上下表面压力系数的差值发生改变，进而使绕流圆柱的气动性能发生变化。
微作动器放置的位置不同，对圆柱气动性能的影响亦不同。微作动器放置在
分离点附近时对圆柱的气动性能影响较大。
A new method for active control of flow field appears. It is the so-called microjet technology. Its fundamental principle is based on the MEMS, the chaotic theory and non-linear complicated system theory. The mechanism of active flow direction control is the microjet's microscale disturbance coupling with the macroscale's flow through collective interaction. The microjet is a zero net mass-flux and doesn't require internal source of jet fluid. Its control system is simple, light and little energy consumed. Microjet is superior to conventional jet. So this dissertation studies the microjet flow field and the synthetic flow field of the microjet and the mean flow by numerical simulation. The main research results in the dissertation are as follows:
1. According to the characteristics of the microjet and the synthetic flow field, the unsteady, two/three dimensional, compressible N-S equations were used for the flow field simulation. Time-accurate solutions to N-S equations were obtained by the implicit approximately-factored(AF) finite-difference algorithm. Newton-like subiterations were used within a time step to reduce errors due to factorization, linerization and explicit application of boundary conditions. Numerical fluxes considered in the explicit portion of the algorithm were evaluated by an implicit high-order compact scheme to augment stability. Meanwhile, an implicit high-order compact numerical filter was used.
2. The laminar/turbulence models were used to simulate the single microjet flow field. The result shows the periodic characteristics of microjet flow field including vortex pair evolution, immigration and dissipation process. The synthetic flow field of two adjacent microjet actuators and its evolvement with time, as well as different working frequencies and relative phase angles were numerically simulated. The "low pressure closed recircular flow region" was analyzed to explain the characteristics of the synthetic flow field.
3. The 3D simulation result shows characteristics as well as creating, developing and dissipation process of the microjet. The results show good agreement with
experimental results. The numerical study reveals the spanwise instability of vortex pairs, resulting in the breakdown of the coherent vortex structure. Especially the secondary vortex is also captured.
4. Vectoring of a primary jet with a single or two adjacent microjets in a pull mode was numerically investigated. The result shows the primary jet can be vectored and trends towards the microjet actuators. Analysis indicates the "low pressure closed reticular flow region" results in the non-equilibrium of pressure along the primary jet's orifice. To obtain as large vectoring angle as possible, the optimal ranges of angles, frequencies, velocity amplitudes, and distances from the microjet actuator to the primary jet exit were discussed. The relationship between the vectoring angle of the primary jet and the phase-difference of two adjacent actuators was analyzed.
5. The modification of the aerodynamic force performance on a 2D cylinder by use of microjet was numerically simulated. The result shows that the pressure distribution on the cylinder and the wake are modified, and the separate flow partially is attached to the surface again.
本文的主要研究成果如下：
1．通过对微射流与主射流合成流场的深入分析，分别建立了微射流作动器二维、三维可压外流场控制方程以及二维微射流与主流合成流场的控制方程。采用快速求解的近似隐式因式分解法(AF方法)并内置似牛顿子迭代，有效地抑制了数值振荡、提高了稳定性并恢复了非线性方程在线化过程中所丢失的一些重要特性，同时还消除了因使用显式边界条件、人工粘性及隐式一边使用低阶空间差分近似所带来的误差。显式一边的空间导数采用具有较高精度和良好数值稳定性的隐式高阶紧致差分格式，同时采用适于低马赫数流动计算的隐式高阶数值过滤方法。
2．分别采用层流、湍流模型对单微射流流场进行了数值模拟。模拟结果显示了微射流的产生、形成、发展与耗散过程以及微射流的卷吸特征等。分析了双微射流作动器在不同频率、相位下协调工作时所形成的合成流场的特征。“低压回流区”的细观分析诠释了微射流的作用机制。
3．三维微射流流场的数值模拟再现了实验所观察到的旋涡对的生成、发展及其相干性的消失过程；揭示了旋涡对沿展向的不稳定性是旋涡对相干性消失的主要原因。在三维数值模拟中还捕捉到了二次涡，这为以后进一步研究微射流旋涡对的细微结构打下了良好的基础。
4．微射流与主射流合成流场的数值模拟再现了实验所观察到的主射流流动方向发生偏转的情形；分析了在“拉”模型单、双微作动器模式下，微射流控制宏观流动的现象及内在机理；揭示了微射流与主流之间“低压回流区”所引起的主流通道内的压力分布不平衡是主射流宏观流动方向发生偏转的
西北工业大学博士学位论文
Ph.D.Dissertation ofNorthwesternPolyteehnieal University
内在原因。分析了“拉”模型单作动器模式下，微射流作动器的入射角度、
驱动频率、速度幅值及与主射流间的距离对主射流偏转程度的影响，并确定
了作动器工作参数的最佳范围;分析了“拉”模型双作动器模式下，不同的
相位差对主流偏转程度的影响。
5.数值模拟再现了微射流改变绕流圆柱气动性能的情形。相邻微作动器同相工
作时部分分离流重新附面、尾流区减小。相邻微作动器存在相位差时，圆柱
上下表面压力系数的差值发生改变，进而使绕流圆柱的气动性能发生变化。
微作动器放置的位置不同，对圆柱气动性能的影响亦不同。微作动器放置在
分离点附近时对圆柱的气动性能影响较大。
A new method for active control of flow field appears. It is the so-called microjet technology. Its fundamental principle is based on the MEMS, the chaotic theory and non-linear complicated system theory. The mechanism of active flow direction control is the microjet's microscale disturbance coupling with the macroscale's flow through collective interaction. The microjet is a zero net mass-flux and doesn't require internal source of jet fluid. Its control system is simple, light and little energy consumed. Microjet is superior to conventional jet. So this dissertation studies the microjet flow field and the synthetic flow field of the microjet and the mean flow by numerical simulation. The main research results in the dissertation are as follows:
1. According to the characteristics of the microjet and the synthetic flow field, the unsteady, two/three dimensional, compressible N-S equations were used for the flow field simulation. Time-accurate solutions to N-S equations were obtained by the implicit approximately-factored(AF) finite-difference algorithm. Newton-like subiterations were used within a time step to reduce errors due to factorization, linerization and explicit application of boundary conditions. Numerical fluxes considered in the explicit portion of the algorithm were evaluated by an implicit high-order compact scheme to augment stability. Meanwhile, an implicit high-order compact numerical filter was used.
2. The laminar/turbulence models were used to simulate the single microjet flow field. The result shows the periodic characteristics of microjet flow field including vortex pair evolution, immigration and dissipation process. The synthetic flow field of two adjacent microjet actuators and its evolvement with time, as well as different working frequencies and relative phase angles were numerically simulated. The "low pressure closed recircular flow region" was analyzed to explain the characteristics of the synthetic flow field.
3. The 3D simulation result shows characteristics as well as creating, developing and dissipation process of the microjet. The results show good agreement with
experimental results. The numerical study reveals the spanwise instability of vortex pairs, resulting in the breakdown of the coherent vortex structure. Especially the secondary vortex is also captured.
4. Vectoring of a primary jet with a single or two adjacent microjets in a pull mode was numerically investigated. The result shows the primary jet can be vectored and trends towards the microjet actuators. Analysis indicates the "low pressure closed reticular flow region" results in the non-equilibrium of pressure along the primary jet's orifice. To obtain as large vectoring angle as possible, the optimal ranges of angles, frequencies, velocity amplitudes, and distances from the microjet actuator to the primary jet exit were discussed. The relationship between the vectoring angle of the primary jet and the phase-difference of two adjacent actuators was analyzed.
5. The modification of the aerodynamic force performance on a 2D cylinder by use of microjet was numerically simulated. The result shows that the pressure distribution on the cylinder and the wake are modified, and the separate flow partially is attached to the surface again.
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84. S.G. Millinson, G. Hon, J. A. Reizes, Some characteristics of syntheti.c jets, AIAA 99-3651.
85. B. L. Smith and Ari Glezer, Vectoring of a high aspect ratio rectangular air jet using a zero mass flux control jet, Bull. Am. Phys. Soc.39 (1994).
86. A. Leonard, Vortex Methods for Flow Simulation, Journal of computational physics 37,(1980).
87. A. Nase and J. C. S. Lai, Comparison of flow characteristics in the near field of tow Parallel plane jets and an offset plane jet, Phys. Fluids 9 (10), may 1997.
88. Ari Glezer, the formation of vortex rings, Phys. Fluids 31 (12), December 1998.
89. D. J. Coe, M. G. Allen, B. L. Smith, A. Glezer, Addressable Micro-machined Jet Arrays,TRANSDUCERS' 95/EUROSENSORS IX, Stockhom, Sweden, 1995.
90. E F. Grinstein and C. R. Devore, Dynamics of coherent structures and transition to turbulence in free square jets, Phys. Fluids 8 (5), May 1996.
91. P.D. Thomas, Boundary Condition for Implicit Solutions to the Compressible Navier-Stokes Equations in Finite Computational Domains, AIAA 79-1447.
92. W. R. Briley and H. MC. Donald, Analysis and Computation of Viscous Subsonic Primary and Secondary Flows, AIAA 79-1453.
93. R.G. Hindman, E Kutler, D. Anderson, A Tow-Dimensional Unsteady Euler-equations Solver for Flow Regions with Arbitrary Boundary, AIAA 79-1465.
94. R. Gordnier, M. R. Vibal, Numerical Simulation of DeltaoWing Roll, AIAA 93-0554.
95. F. Nasuti and M. Onofri, Viscous and Inviscid Vortex Generation During Nozzle Flow Transients, AIAA 96-0076.
96. R. Melville, R. W. MacCormack, Free Vortex Burst Simulations with Compressible Flow,AIAA 96-0805.
97. M. R. Visbal, Computed Unsteady Structure of Spiral Vortex Breakdown on Delta Wing,AIAA 96-2074.
98. Xiaogang Deng, Hiroshi Maekawa, A Uniform Fourth-order Compact Schemes for Discontinuities Capturing, AIAA 96-1974.
99. S. Wernz, H. F. Fasel, Numerical Investigation of unsteady Phenomena in Wall Jets, AIAA 96-0076.
100. D.P. Hwang, A Proof of Concept Experiments for Reducing Skin Friction Using a Micro Blowing Technique, AIAA 97-0546.
101. T. Tefy, Pénécope Leylanu, Complete Matrix Implicit Method for Multi-Block Navier-Stokes Compressible Solvers, AIAA 97-2104.
102. D. Gaitonde, J. S. Shang, J. L. Young, Practical Aspects of High-order Accurate Finite-Volume Schemes for Electromagnetics, AIAA 97-0306.
103. A. A. Hassan, Numerical Simulations and Potential Application of Zero-mass Jets for Enhanced Rotoreraft Aerodynamics Performance, AIAA 98-0211.
104. M. R. Visbal, D. V. Gaitonde, Direct Numerical Simulation of a Forced Transitional Plane Wall Jet, AIAA 98-2643.
105. E. Gutmark and Chin-Ming Ho, Preferred Modes and the Spreading rates of Jets, Phys. Fluid 26 (10), October 1983.
106. E. Villermaux and E. J. Hoppinger, Periodically arranged Co-Flowing Jets, J. Fluid Mech. (1994), Vol. 263.
107. H. Aref, "Integrable, Chaoic, and Turbulent Vortex Motion in Tow-Dimensional Flows", Ann. Rev. Fluid Mech. 1983.15.
108. H. Rehab, E. Villermaux and E. J. Hoppinger, "Flow regimes of large-velocity-ratio coaxial jets", J. Fluid Mech. (1997), Vol. 345.
109. K.J. Nygaad, J. M. Wiltse and A. Glezer, Method and Apparatus for controlled Modification of Fluid Flow, U.S. Patent NO. 5.040.560.
110. K.H. Ahuja, R. H. Burrin, Control of flow separation by sound, AIAA 84-2998.
111. L.S. Huang, L. Maestrello and T. D. Bryant, Separation control over an airfoil at high angles of attach by sound emanating from the surface, AIAA 87-1261.
112. D. Neuberger, I. Wygnanski, The use of a vibrating ribbon to delay separation on tow dimensional airfoil, Tr-88-0004, U. S. Air Force Academy, 1987.
113. D. Pal, K. Sinha, Controlling an unsteady separating boundary layer on a cylinder with an active compliant wall, AIAA 97-0212.
114. L. S. Sigurdson, A. Roshko, Controlled unsteady excitation of a reattaching flow, AIAA 85-00552.
115. Williams, Acharya, Bernhardt and Yang, The mechanism of flow control on a cylinder with the unsteady bleed technique, AIAA Paper, 29th Aerospace Science meeting, NV, 1991.
116. A. Seifert, T. Bachar, I. Wygnanski, D. Koss and M. Shepshelovich, "Oscillatory blowing, a tool to delay boundary layer separation", AIAA Paper 973-0440, 31st Aerospace Sciences meeting, Reno, NV, 1993..
117. E J. Strykoski, K. R. Sreenivasan, On the formation and suppression of vortex 'shedding' at low Reynolds numbers, J. Fluid Mech., 218, pp 71-107,1990.
118. A. Krothapalli, C. Shih and L. M. Lourence, Drag reduction of a circular cylinder at high Reynolds numbers, AIAA 97-0211.
119. Y.L. Conrad, B. G. David, Tow-Dimensional Synthetic Jet Simulation, AIAA Journal, Vol.40,NO.3, MARCH 2002.
120. A. L. Duncan, R W. Carpenter, Numerical Simulation of the Interaction of Microactuators and Boundary Layers, AIAA Journal, Vol.40, NO. 1, JANUARY 2002.
121. D.R. Smith, Interaction of a Synthetic Jet with a Crossflow Boundary Layer, AIAA Journal, Vol.40, NO. 11, NOVEMBER 2002.
122. M.K. Ibrhim, R. Kunimura, and Y. Nakamura, Mixing Enhancement of Compressible Jets by Using Unsteady Microiets Actuators, AIAA Journal, Vol.40, NO.4, APRIL 2002.
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2. Lumley J L, Strange Attactors, Coherent Structures and Statistical Approaches, In: Theoretical Approaches to turbulence, Applied Mathematical Sciences 58, pp359-363, 1985.
3. Smith B L and Glezer A, Jet vectoring by Synthetic Jet Actuators, Bull.Am.Phys.Soc.40,pp.2025.
4. Michael Amitay, Andrew Honohan, Mark Trautman and Ari Glezer, Modification of the Aerodynamics Characteristics of Bluff Bodies Using Fluidic Actuators, AIAA 97-2004.
5. Michael Amitay, Barton L. Smith and Ari Glezer, Aerodynamics Using Synthetic Jet Technology, AIAA 98-0208.
6. D. Smith, M. Amitay, etc., Modification of Lifting Body Aerodynamics Using Synthetic Jet Actuators, AIAA 98-0209.
7. M. Amitay, V. Kibens, D. Parekh, and A. Glezer, The Dynamics of Flow Reattachment over a Thick Airfoil Controlled by Synthetic Jet Actuators, AIAA 99-1001.
8. J.L. Gilarranz and O. K. Rediniotis, Compact High-Power Synthetic Jet Actuators for Flow Separation Control, AIAA 2001-0737.
9. B.D. Ritchie and J. M. Seitaman, Acetone Mixing Control of Fuel Jets using Synthetic Jet technology: Scalar Field Measurements, AIAA 99-0448.
10. Y. Chen, S. Liang, K. Aung, A. Glezer, and J. Jagoda, Enhanced Mixing in a Simulated Combustor Using Synthetic Jet Actuators, AIAA 99-0449.
11. Smith B L and Glezer A, Vectoring and Small-Scale Motions Effected in Free Shear Flows Using Synthetic Jet Actuators, AIAA 97-0213.
12. Smith B L and Glezer A, The formation and evolution of Synthetic Jet, Phys. Fluids Vol.10, NO.9, September 1998.
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15. Catalin Nae, SYNTHETIC JETS INFLUENCE ON NACA-0012 AIRFOIL AT HIGH ANGLES OF ATTACK, AIAA 98-4523.
16. A.B. Cain, L. D. Kral J. F. Donovan and T. D. Smith, Numerical Simulation of Compressible Synthetic Jet Flowfields, AIAA 98-0084.
17. Ahmed A. Hassan and Ram D. Janakiram, EFFECTS OF ZERO-MASS "SYNTHETIC" JETS ON THE NACA-0012 AIRFOIL, AIAA 97-2326.
18. D.P. Rizztta, M. R. Visbal, and M. J. Stanek, Numerical investigation of Synthetic Jet Flow fields, AIAA 98-2910.
19. G.N. Markelov and M. S. Ivanov, A Comparative Analysis of 2D/3D Micronozzle Flows by the DSMC Method, AIAA 2002-1009.
20. Norad Y. Lee and David B. Goldstein, DNS of Microjets for Turbulent Boundary Layer Control, AIAA 2001-1-13.
21. Avi Seifert and La Tunia G. Pack, Oscillatory Excitation of Unsteady Compressible Flows over Airfoils at Flight Reynolds Numbers, AIAA 2000-0925.
22. Alison M. Lamp and Ndaona Chokani, Control of Cavity Resonance using Steady and Oscillatory Blowing, AIAA 99-0999.
23. Frederick W.Roos, Synthetic-jet Microblowing For Forebody Flow-Asymmetry Management, AIAA 98-0212.
24. A. Naguib, C. Christophoron, E. Alnajjar, H. Naguib, C. C. Huang and K. Najati, Arrays of MEMS-Based Actuators for control of Supersonic Jet screech, AIAA 97-1963.
25. Dahai Guo and Linda D. Kral, Andrew W. Cary, Numerical Simulation of the Interaction Adjacent Synthetic Jet Actuators, AIAA 2000-2565.
26. Michael O. Müller, Luis P. Bernal, Paul K. Miska, Peter D. Washabaugh, Tsung-Kuan Allen Chou, Babak Amir Parviz, Chunbo Zhang, Khalil Najafi, FLOW STRUCTURE AND PERFORMANCE OF AXISYMMETRIC SYNTHIC JETS, AIAA 2001-1008.
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28. K.T. Ma, F. G Tseng, C. C. Chieng, Numerical Simulation of Micro-channel Flow over a wall of Hydrophilic and Hydrophobic surface, A IAA 2001-1014.
29. E. Chatlynne, N. Rumigny, M. Amitay, Virtual Aero-shaping of Clark -Y Airfoil using Synthetic Jet Actuators, AIAA 2001-0732.
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37. John A. Ekaterinaris, Implicit High-Order Accurate in Space Algorithms for the Navier-Stokes Equations, AIAA 99-3257.
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41. Xiaogang Deng, Hiroshi Maekawa, An Uniform fourth-Order Compact Schemes for Discontinuities Capturing, AIAA 96-1972.
42. M. M. Rai, S. R. Chakravarthy, An Implicit Form for the Osher Upwind Scheme, AIAA Journal, Vol. 24, NO. 5, MAY 1986.
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45. B.L. Smith, M. A. Tyautman, A. Glezer, Controlled Interaction of Adjacent Synthetic Jets,AIAA 99-0669.
46. D. Guo and A. W. Cary, Vectoring Control of a Primary Jet with Synthetic Jets, AIAA 2001-0738.
47. Jain-Ming Wu, Xi-Yun Lu, A. G. Denny, Meng Fan, and Jie-Zhi Wu, Post-Stall Flow on An Airfoil by Local Unsteady Forcing, Part Ⅰ. Lift, Drag, and Pressure Characteristics, AIAA 97-2063.
48. Jie-Zhi Wu, Xi-Yun Lu, Jain-Ming Wu, Post-Stall Flow on An Airfoil by Local Unsteady
Forcing, Part Ⅱ. Mode Competition and Vortex Dynamics, AIAA 97-2064.
49. Staci A.Davis and Ari Glezer, Mixing control of Fuel Jets Using Synthetic Jet Technology:Velocity Field Measurements, AIAA 99-0447.
50. Herng Lin and Ching-Chang Chiang, Computations of Compressible Synthetic Jet Flows Using Multigrid/Dual Time Stepping Algorithm, AIAA 99-3114.
51. K. G. Powell, G. Toth, D. L. De Zeeuw, P. L. Roe, T. I. Gombosi and Q. F. Stout, Development and Validation of Solution-Adaptive Parallel Schemes for Compressible Plasmas, AIAA 2001-2525.
52. Yao Zhang and Meng-Sing Liou, Progress in the Three-dimensional DRAGON Grid Scheme,AIAA 2001-2540.
53. A. Povitsky, High-order Compact Simulation of Wave Propagation in Non-uniform Flow,AIAA 2001-2628.
54. Chun-ho Sung, Soo-Hyung Park, J. H. Kown, Multigrid Diagonalized-ADl Method for Compressible Flows, AIAA 2001-2556.
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57. J. C. Tarmehill, J. H. Miller, S. L. Lawrence, Development of an Iterative PNS Code for Separated Flows, AIAA 99-3361.
58. J. J. Hoffman, T. L. Doligalski, Initial Development of a Low-Speed Jet in A Cross-Flow,AIAA 85-1619.
59. W. Bao-Guo, New Iterative Algorithm Between Stream Function and Density for Transonic Cascade Flow, AIAA 85-1594.
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77. L. D. Kral, D. Guo, Characterization of jet Actuators for Active Flow Control, AIAA99-3575.
78. O.K. Rediniotis, J. Jo, X. Yue, A. J. Kurdile, Synthetic Jets, Their Reduced Order Modeling and Applications to Flow Control, AIAA 99-1000.
79. C. Christophorou, H. Nagib, A. Nagib, D. Fabris, Array of MEMS -Based Actuators for the Excitation of a High-speed Axisymmetic Jet, AIAA 2000-2559.
80. B.D. Ritchie, J. M. Seitzman, Controlled Fuel-Air Mixing Using a Synthetic Jet Array, AIAA 2000-3465.
81. G.L. Lee, D. B. Goldstein, Tow-Dimensional Synthetic Jet Simulation, AIAA 2000-0406.
82. A. A. Alexeenko, S. F. Gimelshein, D. A. Levin, R. J. Collins, Numerical modeling of Axisymmetic and Three-Dimensional Flows in MEMS Nozzles, AIAA 2000-3668.
83. G.Y. Lee, D. B. Goldstein, D. Guo, A. W. Cary, DNS of Microjets for Turbulent Boundary Layer Control, AIAA 2001-1013.
84. S.G. Millinson, G. Hon, J. A. Reizes, Some characteristics of syntheti.c jets, AIAA 99-3651.
85. B. L. Smith and Ari Glezer, Vectoring of a high aspect ratio rectangular air jet using a zero mass flux control jet, Bull. Am. Phys. Soc.39 (1994).
86. A. Leonard, Vortex Methods for Flow Simulation, Journal of computational physics 37,(1980).
87. A. Nase and J. C. S. Lai, Comparison of flow characteristics in the near field of tow Parallel plane jets and an offset plane jet, Phys. Fluids 9 (10), may 1997.
88. Ari Glezer, the formation of vortex rings, Phys. Fluids 31 (12), December 1998.
89. D. J. Coe, M. G. Allen, B. L. Smith, A. Glezer, Addressable Micro-machined Jet Arrays,TRANSDUCERS' 95/EUROSENSORS IX, Stockhom, Sweden, 1995.
90. E F. Grinstein and C. R. Devore, Dynamics of coherent structures and transition to turbulence in free square jets, Phys. Fluids 8 (5), May 1996.
91. P.D. Thomas, Boundary Condition for Implicit Solutions to the Compressible Navier-Stokes Equations in Finite Computational Domains, AIAA 79-1447.
92. W. R. Briley and H. MC. Donald, Analysis and Computation of Viscous Subsonic Primary and Secondary Flows, AIAA 79-1453.
93. R.G. Hindman, E Kutler, D. Anderson, A Tow-Dimensional Unsteady Euler-equations Solver for Flow Regions with Arbitrary Boundary, AIAA 79-1465.
94. R. Gordnier, M. R. Vibal, Numerical Simulation of DeltaoWing Roll, AIAA 93-0554.
95. F. Nasuti and M. Onofri, Viscous and Inviscid Vortex Generation During Nozzle Flow Transients, AIAA 96-0076.
96. R. Melville, R. W. MacCormack, Free Vortex Burst Simulations with Compressible Flow,AIAA 96-0805.
97. M. R. Visbal, Computed Unsteady Structure of Spiral Vortex Breakdown on Delta Wing,AIAA 96-2074.
98. Xiaogang Deng, Hiroshi Maekawa, A Uniform Fourth-order Compact Schemes for Discontinuities Capturing, AIAA 96-1974.
99. S. Wernz, H. F. Fasel, Numerical Investigation of unsteady Phenomena in Wall Jets, AIAA 96-0076.
100. D.P. Hwang, A Proof of Concept Experiments for Reducing Skin Friction Using a Micro Blowing Technique, AIAA 97-0546.
101. T. Tefy, Pénécope Leylanu, Complete Matrix Implicit Method for Multi-Block Navier-Stokes Compressible Solvers, AIAA 97-2104.
102. D. Gaitonde, J. S. Shang, J. L. Young, Practical Aspects of High-order Accurate Finite-Volume Schemes for Electromagnetics, AIAA 97-0306.
103. A. A. Hassan, Numerical Simulations and Potential Application of Zero-mass Jets for Enhanced Rotoreraft Aerodynamics Performance, AIAA 98-0211.
104. M. R. Visbal, D. V. Gaitonde, Direct Numerical Simulation of a Forced Transitional Plane Wall Jet, AIAA 98-2643.
105. E. Gutmark and Chin-Ming Ho, Preferred Modes and the Spreading rates of Jets, Phys. Fluid 26 (10), October 1983.
106. E. Villermaux and E. J. Hoppinger, Periodically arranged Co-Flowing Jets, J. Fluid Mech. (1994), Vol. 263.
107. H. Aref, "Integrable, Chaoic, and Turbulent Vortex Motion in Tow-Dimensional Flows", Ann. Rev. Fluid Mech. 1983.15.
108. H. Rehab, E. Villermaux and E. J. Hoppinger, "Flow regimes of large-velocity-ratio coaxial jets", J. Fluid Mech. (1997), Vol. 345.
109. K.J. Nygaad, J. M. Wiltse and A. Glezer, Method and Apparatus for controlled Modification of Fluid Flow, U.S. Patent NO. 5.040.560.
110. K.H. Ahuja, R. H. Burrin, Control of flow separation by sound, AIAA 84-2998.
111. L.S. Huang, L. Maestrello and T. D. Bryant, Separation control over an airfoil at high angles of attach by sound emanating from the surface, AIAA 87-1261.
112. D. Neuberger, I. Wygnanski, The use of a vibrating ribbon to delay separation on tow dimensional airfoil, Tr-88-0004, U. S. Air Force Academy, 1987.
113. D. Pal, K. Sinha, Controlling an unsteady separating boundary layer on a cylinder with an active compliant wall, AIAA 97-0212.
114. L. S. Sigurdson, A. Roshko, Controlled unsteady excitation of a reattaching flow, AIAA 85-00552.
115. Williams, Acharya, Bernhardt and Yang, The mechanism of flow control on a cylinder with the unsteady bleed technique, AIAA Paper, 29th Aerospace Science meeting, NV, 1991.
116. A. Seifert, T. Bachar, I. Wygnanski, D. Koss and M. Shepshelovich, "Oscillatory blowing, a tool to delay boundary layer separation", AIAA Paper 973-0440, 31st Aerospace Sciences meeting, Reno, NV, 1993..
117. E J. Strykoski, K. R. Sreenivasan, On the formation and suppression of vortex 'shedding' at low Reynolds numbers, J. Fluid Mech., 218, pp 71-107,1990.
118. A. Krothapalli, C. Shih and L. M. Lourence, Drag reduction of a circular cylinder at high Reynolds numbers, AIAA 97-0211.
119. Y.L. Conrad, B. G. David, Tow-Dimensional Synthetic Jet Simulation, AIAA Journal, Vol.40,NO.3, MARCH 2002.
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