超声速流中反向和横向射流及静止流中射流的数值研究
摘要
逆向流和横向流中的超声速喷射问题十分复杂,这类问题中存在射流与来流的相互作用及其复杂的激波振荡结构等。超声速射流在其逆向超声速来流或高超声速来流作用下,会形成弓形激波结构且具有振荡特性,因而被用于高超声速返回式飞行器的减阻。在超声速横向流作用下的声速射流可用于在低密度大气层中快速运行运载器的姿态控制,而在静止流中的射流还可用于推力矢量控制、火箭燃烧和流动混合的非设计工况下的不稳定侧向载荷的估算。
本文数值模拟了在逆向流、横向流和静止流中的超声速、声速射流问题,文中着重研究了激波诱导的分离流动,探讨了射流干扰流场的机制。数值计算是采用PAK-3D的CFD程序实现,通过求解雷诺平均N-S方程(RANS),并采用合适的湍流模型,可以合理地模拟超声速和高超声速下的二维和三维的射流问题。通过对压比、流线、马赫数和入射角等参量的影响特性分析,给出了力和力矩综合效应的简化模型。同时,还详细分析探讨了逆向流、横向流和静止流中射流问题的激波结构和流动机理。
首先,研究了半球柱体高超声速绕流中头部的逆向超声速射流问题。采用两方程湍流模型求解非定常雷诺平均方程,模拟了四种不同压比下高超声速来流问题。研究工作主要关注两种不同的典型流动形态,即SPM(短穿透模式)和LPM(长穿透模式),以及达到最大减阻效果的LPM。对于半球柱体结构外形,振荡流动形态SPM→LPM在所研究的压比流动中占主导。对常压比下的较高马赫数流动,获得了明显的减阻效果,可能是由于喷射的相对质量流量的增大所致。研究表明,倘若采用不同自由来流作用下的逆向喷射方式,其阻力降低规律可表示成质量流量的函数。进而,文中给出了不同自由来流下基于相对质量流量所描述的阻力减少量的简化数学模型。
其次,研究了超声速横向流中的声速射流问题。通过一系列数值模拟,估算出随压比PR及攻角α增大时的喷射效率。运用半圆锥角10.4。钝锥体作为模型问题,在超声速流动中可以提供方向控制的效果。对马赫数4的自由来流,喷射与横向流的相互作用导致了净力的增加,通过改变喷射近前端和近尾端的压力分布,可以获得有利的俯仰力矩。进而,文中还提出了描述静态气动力系数随压比和攻角变化的数学模型。同时,基于激波结构、压力和马赫数的流场分布,对流动特性进行了分析。
最后,研究了收缩-扩喷(CD)喷管的超声速射流问题。针对不同的面积收缩-扩张比,研究了“设计”和“非设计”两种工况下CD喷管的射流特性。对在设计工况下运行的CD喷管,发现研究结果与已公开发表的试验结果相符良好。此外,喷气舵置于CD喷管的超声速喷口,研究了喷气舵在0度偏转和20度偏转下的二种极端试验状态。对非设计工况,研究了不同的喷管压比NPR以及喷管面积比Ae／At,从1.2变化到1.6的流动特性。在较小的面积比和喷管压力比的条件下,喷管内的激波结构可视为正激波。在较小的面积比和中等的喷管压比条件下,可以观察到清晰的对称λ-激波结构。对于Ae／At=1.3和NPR≥1.70,可以观察到清晰的反对称λ-激波结构。反对称的λ-激波结构表明可运用射流的羽流来加强流动的混合效果。
The supersonic jet exhausting in counterflow and crossflow is very complex problem owing to the nature of the jet interacting with the oncoming flow field and complex oscillatory shock structure. The supersonic jet exhausting in supersonic/hypersonic flows in counterflow direction has the oscillatory nature of the bow shock and is used for drag reduction of hypersonic vehicle. The sonic jet exhausting in the supersonic crossflow has the application in the attitude control for the fast moving vehicle in low density atmosphere whereas the jet exhausting in the quiescent flow has the application in thrust vector control, the estimation of unsteady side loads for off design conditions of rocket firing and flow mixing. The present study is aimed to apply the computational methodology for the shock induced separated turbulent flows and explore the mechanics in the jet interaction flow field. Specifically, the supersonic/sonic jet exhausting in the counterflow, crossflow and quiescent flow are investigated. The computational investigations are carried using a CFD code PAK-3D. The CFD code PAK-3D solve the Reynolds averaged Navier-Stokes (RANS) equations with a practical turbulence model to properly simulate the physics of supersonic and hypersonic two and three-dimensional jet interaction flowfield. The parametric study was performed to investigate the effect of pressure ratio, freestream Mach number and incidence. The mathematical models based on the calculations performed, were proposed defining the integrated effect in the form of force and moment. Further, the shock structures and flow physics for the three cases is discussed in detail.
Firstly, a counterflow supersonic jet emanating from the nose of a hemispherical cylinder is investigated. Four different hypersonic oncoming freestream flows at various pressure ratios were solved using unsteady RANS equations with the two-equation k-εturbulence model. The investigations were mainly focused on two different flow regimes, SPM (short penetration mode)→LPM (long penetration mode) and LPM to ensure that the maximum drag reduction is achieved. For the present configuration being the hemispherical cylinder, the oscillatory flow regime SPM→LPM remains dominant over the most of the pressure ratios investigated. The obvious drag reduction is obtained for the higher Mach number flows at a constant pressure ratio, which can be attributed to the increase in relative mass flow rate of jet. The physical mechanism suggests that the drag reduction using a counterflow jet with different oncoming freestream flows can be expressed as a function of mass flow ratio. A model for the various freestream flows describing the drag reduction as a function of relative mass flow rate is proposed.
Secondly, a sonic jet exhausting in the supersonic crossflow is investigated and series of numerical simulations were performed to evaluate the effectiveness of the jet with increase in pressure ratio and the angle of attack. The jet emanating from a blunted cone with a half-cone angle of 10.4°was used that provide possible directional control in supersonic flows. For an oncoming freestream flow of Mach number 4, the jet interaction in the crossflow causes an increase in net force and consequently a useful pitching moment is obtained through altering pressure distribution in its near forward and aft vicinity of the jet. A model describing the computed static aerodynamic coefficients variation with pressure ratios and angle of attack are presented to demonstrate this jet interaction effect. The shock structures, pressure and Mach number contours with streamline patterns gave a qualitative insight.
For jet exhausting in the quiescent flow, the supersonic flow through various area ratio convergent-divergent, CD nozzles was investigated for both "designed "and "off designed" conditions. For CD nozzle operating at designed conditions, a reasonable agreement was found with the published experimental results. Further a jet vane was placed at supersonic exhaust of the CD nozzle. Two extreme test cases were studied with zero and 20°of jet vane deflection. For the off designed conditions, the nozzle area ratio Ae/At ranges from 1.2 to 1.6 with various nozzle pressure ratios NPR. At lower end of Ae/At and NPR, the shock structure inside the nozzle may be regarded as a normal shock. At lower Ae/At and moderate NPR, a well defined symmetricλ-shock was observed. For Ae/At = 1.3 with NPR≥1.70, a well defined asymmetricλ-shock structure was observed. The asymmetricλ-shock structure suggests that jet plume can be used for the mixing enhancement.
本文数值模拟了在逆向流、横向流和静止流中的超声速、声速射流问题,文中着重研究了激波诱导的分离流动,探讨了射流干扰流场的机制。数值计算是采用PAK-3D的CFD程序实现,通过求解雷诺平均N-S方程(RANS),并采用合适的湍流模型,可以合理地模拟超声速和高超声速下的二维和三维的射流问题。通过对压比、流线、马赫数和入射角等参量的影响特性分析,给出了力和力矩综合效应的简化模型。同时,还详细分析探讨了逆向流、横向流和静止流中射流问题的激波结构和流动机理。
首先,研究了半球柱体高超声速绕流中头部的逆向超声速射流问题。采用两方程湍流模型求解非定常雷诺平均方程,模拟了四种不同压比下高超声速来流问题。研究工作主要关注两种不同的典型流动形态,即SPM(短穿透模式)和LPM(长穿透模式),以及达到最大减阻效果的LPM。对于半球柱体结构外形,振荡流动形态SPM→LPM在所研究的压比流动中占主导。对常压比下的较高马赫数流动,获得了明显的减阻效果,可能是由于喷射的相对质量流量的增大所致。研究表明,倘若采用不同自由来流作用下的逆向喷射方式,其阻力降低规律可表示成质量流量的函数。进而,文中给出了不同自由来流下基于相对质量流量所描述的阻力减少量的简化数学模型。
其次,研究了超声速横向流中的声速射流问题。通过一系列数值模拟,估算出随压比PR及攻角α增大时的喷射效率。运用半圆锥角10.4。钝锥体作为模型问题,在超声速流动中可以提供方向控制的效果。对马赫数4的自由来流,喷射与横向流的相互作用导致了净力的增加,通过改变喷射近前端和近尾端的压力分布,可以获得有利的俯仰力矩。进而,文中还提出了描述静态气动力系数随压比和攻角变化的数学模型。同时,基于激波结构、压力和马赫数的流场分布,对流动特性进行了分析。
最后,研究了收缩-扩喷(CD)喷管的超声速射流问题。针对不同的面积收缩-扩张比,研究了“设计”和“非设计”两种工况下CD喷管的射流特性。对在设计工况下运行的CD喷管,发现研究结果与已公开发表的试验结果相符良好。此外,喷气舵置于CD喷管的超声速喷口,研究了喷气舵在0度偏转和20度偏转下的二种极端试验状态。对非设计工况,研究了不同的喷管压比NPR以及喷管面积比Ae／At,从1.2变化到1.6的流动特性。在较小的面积比和喷管压力比的条件下,喷管内的激波结构可视为正激波。在较小的面积比和中等的喷管压比条件下,可以观察到清晰的对称λ-激波结构。对于Ae／At=1.3和NPR≥1.70,可以观察到清晰的反对称λ-激波结构。反对称的λ-激波结构表明可运用射流的羽流来加强流动的混合效果。
The supersonic jet exhausting in counterflow and crossflow is very complex problem owing to the nature of the jet interacting with the oncoming flow field and complex oscillatory shock structure. The supersonic jet exhausting in supersonic/hypersonic flows in counterflow direction has the oscillatory nature of the bow shock and is used for drag reduction of hypersonic vehicle. The sonic jet exhausting in the supersonic crossflow has the application in the attitude control for the fast moving vehicle in low density atmosphere whereas the jet exhausting in the quiescent flow has the application in thrust vector control, the estimation of unsteady side loads for off design conditions of rocket firing and flow mixing. The present study is aimed to apply the computational methodology for the shock induced separated turbulent flows and explore the mechanics in the jet interaction flow field. Specifically, the supersonic/sonic jet exhausting in the counterflow, crossflow and quiescent flow are investigated. The computational investigations are carried using a CFD code PAK-3D. The CFD code PAK-3D solve the Reynolds averaged Navier-Stokes (RANS) equations with a practical turbulence model to properly simulate the physics of supersonic and hypersonic two and three-dimensional jet interaction flowfield. The parametric study was performed to investigate the effect of pressure ratio, freestream Mach number and incidence. The mathematical models based on the calculations performed, were proposed defining the integrated effect in the form of force and moment. Further, the shock structures and flow physics for the three cases is discussed in detail.
Firstly, a counterflow supersonic jet emanating from the nose of a hemispherical cylinder is investigated. Four different hypersonic oncoming freestream flows at various pressure ratios were solved using unsteady RANS equations with the two-equation k-εturbulence model. The investigations were mainly focused on two different flow regimes, SPM (short penetration mode)→LPM (long penetration mode) and LPM to ensure that the maximum drag reduction is achieved. For the present configuration being the hemispherical cylinder, the oscillatory flow regime SPM→LPM remains dominant over the most of the pressure ratios investigated. The obvious drag reduction is obtained for the higher Mach number flows at a constant pressure ratio, which can be attributed to the increase in relative mass flow rate of jet. The physical mechanism suggests that the drag reduction using a counterflow jet with different oncoming freestream flows can be expressed as a function of mass flow ratio. A model for the various freestream flows describing the drag reduction as a function of relative mass flow rate is proposed.
Secondly, a sonic jet exhausting in the supersonic crossflow is investigated and series of numerical simulations were performed to evaluate the effectiveness of the jet with increase in pressure ratio and the angle of attack. The jet emanating from a blunted cone with a half-cone angle of 10.4°was used that provide possible directional control in supersonic flows. For an oncoming freestream flow of Mach number 4, the jet interaction in the crossflow causes an increase in net force and consequently a useful pitching moment is obtained through altering pressure distribution in its near forward and aft vicinity of the jet. A model describing the computed static aerodynamic coefficients variation with pressure ratios and angle of attack are presented to demonstrate this jet interaction effect. The shock structures, pressure and Mach number contours with streamline patterns gave a qualitative insight.
For jet exhausting in the quiescent flow, the supersonic flow through various area ratio convergent-divergent, CD nozzles was investigated for both "designed "and "off designed" conditions. For CD nozzle operating at designed conditions, a reasonable agreement was found with the published experimental results. Further a jet vane was placed at supersonic exhaust of the CD nozzle. Two extreme test cases were studied with zero and 20°of jet vane deflection. For the off designed conditions, the nozzle area ratio Ae/At ranges from 1.2 to 1.6 with various nozzle pressure ratios NPR. At lower end of Ae/At and NPR, the shock structure inside the nozzle may be regarded as a normal shock. At lower Ae/At and moderate NPR, a well defined symmetricλ-shock was observed. For Ae/At = 1.3 with NPR≥1.70, a well defined asymmetricλ-shock structure was observed. The asymmetricλ-shock structure suggests that jet plume can be used for the mixing enhancement.
引文
AGARD "Computational and experimental assessment of jets in crossflow," AGARD Conference Proceedings, No.534, Winchester, United Kingdom,1993.
Agarwal, R.K., Halt, D.W. "Compact higher order characteristic-based Euler method for unstructured grids," AIAA Journal, Vol.30, pp.1993-99,1992.
Agui, J.H., Briassulis, P., and Andreopoulos, Y., " Studies of interactions of a propagating shock wave with decaying grid turbulence:velocity and vorticity fields," Journal of Fluid Mechanics,524:143-195.,1992.
Ajmal, B., Zahir, S., Ali, A. "Numerical Study of Effects of injection pressure and location of secondary injection inside a low thrust Satellites nozzle," 25th Congress of the International Council of the Aeronautical Sciences, ICAS, Germany,2006.
Andreopoulos, J. "On the structure of jets in a crossflow," Journal of Fluid Mechanics, No. 157, pp.163-197,1985.
Baldwin, B.S., and Lomax, H. "Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA Paper, pp.78-257,1978.
Barber, E.A. Jr. "An Experimental Investigation of Stagnation-Point Injection," Journal of Spacecraft and Rockets, Vol.2, No.5, pp.770-774,1965.
Barre, S., Alem, D., and Bonnet, J.P., "Experimental study of a normal shock/homogeneous turbulence interaction," AIAA Journal, vol.34(5), pp.968-974,1996.
Bergelson V.I., Medvedyuk S.A., Nemchinov I.V., Orlova T.I. and Hazins V.M., "Aerodynamic characteristics of a body at various localization of a thermal needle," Matematicheskoe modelirovanie.Vol.8, No.1, pp.3-10 (in Russian),1996.
Bogdonoff, S. M., and Vas, I. E. "Preliminary Investigations of Spiked Bodies at Hypersonic Speeds," Journal of the Aerospace Science, Vol.26, No.1, pp.65-74,1959.
Borzov, V.Yu., Rybka, I.V. and Yurev, A.S., "Influence of the local energy input in a hypersonic flow on drag of bodies with various bluntness," IFZh, Vol.67, No.5, pp.355-361 (in Russian),1994.
Bosanquet, C.H. and Pearson, J.L. "The spread of smoke and gases from chimneys," Trans. Faraday Soc.32:1249,1936.
Charles Hirsch, "Numerical Computations of internal and external flows," Vol., I and II, Published by John Wiley & Sons, Ltd Second edition,2007.
Chang, H. C, "The Roll-up of a Cylindrical Jet in a Cross Flow," translated by Nagaraja, USAF-ARL73-0131,1942.
Chenault, C.F., Beran, P.S., "k-ε and Reynolds stress turbulence model comparisons for two-dimensional injection flows," AIAA Journal, Vol.36, No.8, pp.1401-1412,1998.
Chenault, C.F., Beran, P.S., and Bowersox, R.D.W., "Numerical Investigation of Supersonic Injection Using a Reynolds-Stress Turbulence Model," AIAA Journal, Vol.37, No.10,1999.
Clark, S.W., Chan, S.C., "Numerical investigation of a transverse jet for supersonic aerodynamic control," AIAA Paper,92-0639,1992.
Cohen, J., "Statistical power analysis for the behavioral sciences," (2nd ed.),1988.
Curran, E. and Murthy, S.B. "Scramjet propulsion," Progress in Astronautics and Aeronautics,189:20-21,2000.
Deck, S,, Hollard, R. and Guillen, P. "Numerical Simulation of Steady and Unsteady Separated Nozzle Flows," AIAA-0406,2002.
Dennis, M., Bushnell "Annual Review of Fluid Mechanics," NASA Langley Research Center, Hampton, Virginia, Vol.36, pp.81-96,2004.
Finley, P.J., "The Flow of a Jet from a Body Opposing a Supersonic Freestream," Journal of Fluid Mechanics, Vol.26. Pt.2, pp.337-368,1966.
Fomin, V.M., Maslov, A.A., Shashkin, A.P., Korotaeva, T.A., and Malmuth N.D., "Flow regimes formed by a counterflow jet in supersonic flow," Journal of Applied Mechanics and Technical Physics, Vol.42, No.5, pp.757-764,2001.
Foster C, Summer_eld M, Swan W.,"Flow separation in overexpanded supersonic exhaust nozzles," Jet Propulsion; Vol.24, No.9, pp.319-320,1954.
Ganiev, Y.G., Gordeev, V.P., Krasilnikov, A.V., Lagutin, V.I., and Otmennikov, V.N., "Experimental Study of the Possibility of Reducing Supersonic Drag by Employing Plasma Technology," Fluid Dynamics, Vol.31, No.2, Consultants Bureau, New York,translated from Izvestia Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gasa, No.2, pp.177-182,1996.
Ganiev, Y., Gordeev, V., Krasilnikov, A., Lagutin, V., and Otmennikov, V., "Experimental Study of the Possibility of Reducing Aerodynamic Drag by Employing Plasma Injection," Proceedings of the Third International Conference on Experimental Fluid Mechanics, Korolev, Moscow Region, Russia,1997.
Ganiev, Y.G., Gordeev, V.P., Krasilnikov, A.V., Lagutin, V.I., Otmennikov, V.N., and Panasenko, A.V., "Experimental and Theoretical Study of the Possibility of Reducing Aerodynamic Drag by Employing Plasma Injection," Proceedings of the 2nd Workshop of Weakly Ionized Gases, Norfolk, VA,1998.
Ganiev, Y.G., Gordeev, V.P., Krasilnikov, A.V., Lagutin, V.I., Otmennikov, V.N., and Panasenko, A.V., "Theoretical and Experimental Study of the Possibility of Reducing Aerodynamic Drag by Employing Plasma Injection," AIAA Paper 99-0603,1999.
Ganiev, Y.C., "Aerodynamic drag reduction by plasma and hot gas injection," Journal of Thermophysics and heat transfer, Vol.14, No.1,2000.
Hameed, A., and Vogiatzis, C, "Overexpanded two dimensional convergent Divergent Nozzle flow simulation, Assement of Turbulence Models," Journal of Propulsion and Power, Vol.13, No.3, pp.444-445,1997.
Hannappel, R., and Friedrich, R., "Direct numerical simulation of a Mach 2 shock interacting with isotropic turbulence." Applied Scientific Research, vol.54, pp.205-221,146,1995.
Hameed, A., and Vogiatzis, C, "Overexpanded two dimensional convergent Divergent Nozzle performance, Effect of three dimensional flow interaction," Journal of Propulsion and Power, Vol.14, No.2, pp.234-240,1998.
Honkan, A., and Andreopoulos, J., "Rapid compression of grid-generated turbulence by a moving shock wave," Physics of Fluids, vol.4, pp.2562-2572,1992.
Hunter, C.A., "Experimental, Theoretical, and Computational Investigation of Separated Nozzle Flows," AIAA paper, pp.98-3107,1998.
Hussaini, M.Y., Zang, T.A., "Spectral methods in fluid dynamics," Annual Review of. Fluid Mechanics, Vol.19, pp.339-67,1987.
Hutt, C.R., and Howe, A.J., "Forward Facing Spike Effects of Bodies of Different Cross Sections in Supersonic Flow," Aeronautical Journal of the Royal Aeronautical Society, Vol.93, No.926, pp.229-234,1989.
Jacquin, L., Cambon, C, and Blin E., "Turbulence amplification by a shock wave and rapid distortion theory," Physics of Fluids A,5:2539-2550,1993.
Jameson, A, "Iterative solution of transonic flows over airfoil and wings, including flows at Mach 1," Commun. Pure Appl. Math., vol.27,pp.283,1974.
Jameson, A., Schmidt, W. and Turkel, E. "Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes," AIAA Paper, pp.81-1259,1981.
Jiang Zonglin, Yunfeng Liu, Guilai Han and Wei Zhao., "Experimental demonstration of a new concept of drag reduction and thermal protection for hypersonic vehicles," Acta Mechanica Sinica, Vol.25, No.3,2009.
Launder, B.E. and Spalding, D.B., "The numerical computation of turbulent flows," Computer Methods in Applied Mechanics and Engineering, Vol.3, No.2, pp.269-289, 1974.
Lefrancois, E., "Numerical validation of a stability model for a flexible over-expanded rocket nozzle," International Journal for Numerical Methods in Fluids, Vol.49, No.4, pp. 349-369,2005.
Lee, S., Lele, S.K., and Moin, P., "Direct numerical simulation of isotropic turbulence interacting with a weak shock wave," Journal of Fluid Mechanics, No.251, pp.533-562, 1993.
Lee, S., Lele, S.K., and Moin, P., "Interaction of isotropic turbulence with shock waves: Effect of shock strength," Journal of Fluid Mechanics,No,340, pp.225-247,1997.
Lele, S. "Compact finite difference schemes with spectral like resolution," Rep. CTR107, Stanford Univ., CA,1990.
Liang, S.M., Huang, K.L., and Chen, K.C., "Numerical Study of Low-Thrust Nozzles for Satellites," Journal of Spacecraft and Rockets, AIAA, Vol.33, No.5, pp.693-699,1996.
Mahapatra, D., Sriram, R. and Jagadesh, G., "Effect of counterflow argon plasma jet on aerodynamic drag of a blunt body at hypersonic mach numbers," The aeronautical Journal, 112(1137),2008.
Mahesh, k., Lele, S.K., and Moin, P., "The influence of entropy fluctuations on the interaction of turbulence with a shock wave," Journal of Fluid Mechanics, No.334, pp. 353-379,1997.
Margason, R.J., "Analysis of the Flow Field of a Jet in a Subsonic Crosswind," NASA SP-228,pp.683-702,1969.
Margason, R.J "Fifty years of jet in crossow research, AGARD Symp. On a jet in Cross Flow, Winchester, UK, AGARD CP-534,1993.
McDaniel, J., Glass, G., Staack, D. and Miller, C., "Experimental and computational comparison of an under-expanded jet flowfield," AIAA Paper-0305,2002.
Morrisette, E.L., Goldberg, T.J., "Turbulent Flow Separation Criteria for Over-Expanded Supersonic Nozzles," NASA, TP-1207,1978.
Mouronval, A.S., and Hadjadj, A., "Numerical study of the starting process in a supersonic nozzle," CIMNE, West East High Speed Flow Fields, Barcelona,2002.
Murakami, E., and Papamoschou, D., "Experiments on Mixing Enhancement in Dual-Stream Jets," AIAA Paper-0668,2001.
Murman, E., and Cole, J., "Calculation of plane steady transonic flows," AIAA Journal, Vol.9, pp.114-21,1971.
Osher, S., "Riemann solvers, the entropy condition, and difference approximations," SIAM Journal of. Numerical Analysis, No.121, pp.217-35,1984.
Ostlund, J., Damgaard, M., Frey, M.,"Side load phenomenon in highly overe-expanded rocket nozzles," AIAA paper-3684,2001.
Papamoschou, D. "Mixing Enhancement Using Axial Flow," AIAA Paper-0093,2000.
Papamoschou, D., Zill, A., "Fundamental Investigation of Supersonic Nozzle Flow Separation," AIAA Paper-1111,2004.
Papamoschou, Dixon, D., and Nishi, K., "Mean Flow of Multi-Stream Rectangular Jets under Normal and Mixing-Enhancement Conditions," AIAA Paper-0919,2004.
Reshotko, E., and Tucker, M., "Effect of a Discontinuity on Turbulent Boundary Layer Thickness Parameters with Application to Shock-Induced Separation," NACA TN-3454, 1955.
Roe, P.L. "Approximate Riemann solvers, parameter vectors, and difference schemes," Journal of Computational Physics, Vol.43, pp.357-372,1981.
Romine, G.L. "Nozzle Flow Separation," AIAA Journal, Vol.36, No.9, pp.1618-1625, 1998.
Rosenhead, L. "The Formation of Vortices from a Surface of Discontinuity," Proc. Roy. Soc. A 134, pp.170-192,1932.
Santiago, J., Dutton J., "Crossflow vortices of a jet injected into a supersonic crossflow." AIAA Journal, Volume.35, No.5, pp.915-917,1997.
Sesterhenn, J., Dohogne, J.F., and Friedrich, R., "Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting", Comptes Rendus de Mecanique,No.333, pp.87-94,2005.
Shang J.S. "Jet-Spike Bifurcation in High-Speed Flows," AIAA Journal, Vol.39, No.6, 2001.
Shang, J.S., Hankey, W.L., and Smith, R.E., "Flow Oscillations of Spike-Tipped Bodies," AIAA Journal, Vol.20, No.1, pp.25-26,1982.
Spaid, F.W., Zukoski, E.E., Rosen R., "A study of secondary injection of gases into a supersonic flow," NACA Technical Report No.32-834, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA,1966.
Steger, J., Warming, R., "Flux vector splitting of the inviscid gas dynamic equations with applications to finite difference methods," J. Comput. Phys. Vol.40, pp.263-93,1981.
Sterrett, J.R., and Romeo, D.J., "Exploratory investigation of the effect of a forward-facing jet on the bow shock of a blunt body in a Mach number 6," NASA TND-1605, 1963.
Strike, W.T., Schueler, C.J., "Investigation of interference effects produced by lateral jets on surfaces in a supersonic stream," AIAA Paper 63-184,1963.
Sutton, O.G. "A theory of Eddy di_usion in the atmosphere," Proc. Roy. Soc. A 135, pp. 143-165,1932.
Tannehill, J.C., Anderson, D.A., and Pletcher, R. H. "Computational Fluid and Heat Transfer," 2nd Ed., Taylor & Francis.,1997.
Thompson, D.S. "Numerical solution of a two-dimensional jet in a supersonic crossflow using an upwind relaxation scheme," AIAA Paper 89-1869,1989.
User Manual PAK-3D Aerodynamics Directorate, Aerodynamics and Structural Analysis Centre, Islamabad, Pakistan,2006.
Vaivads R.H., Gauthier J.E. D., Farinaccio R., "CFD Simulation of a Jet Vane Thrust Vector Control System," CFD Conference of the Computational Fluid Dynamic society of Canada 1998.
Valerio V., PhD Thesis "Numerical Studies of the Jet Interaction Flowfield with a Main Jet and an Array of Smaller Jets," Virginia Polytechnic Institute and State University, Blacksburg, VA,2002.
Valerio, V., Reece, N., and Schetz, J.A., (2009), "Detailed flow physics of the supersonic jet interaction flow field", Physics of Fluids,21,046101.
Van Leer, B., (1982), "Flux vector splitting for Euler equations," Proceedings of International Conference on Numerical Methods, Aachen, ed., E Krause, pp.507-12.
Venkatkrishnan, V., "A perspective on unstructured grid flow solvers," AIAA Journal Vol. 34, pp:533-47,1996.
Venukumar, B., Jagadeesh, G., and Reddy, K.P.J., "Counterflow drag reduction by supersonic jet for a blunt body in hypersonic flow," Physics of Fluids,18(118104),2006.
Vinayak Kulkarni and Reddy, K.P.J., "Enhancement in counterflow drag reduction by supersonic jet in High enthalpy flows," Physics of Fluids,20(016103),2008.
Walker, R.E., Stone A.R., and Shandor, M., "Secondary gas injection in a conical rocket nozzle-I, Effect of Orifice diameter and molecular weight of injectant," AIAA Journal, Vol.1, pp.334-338,1963.
Wallis, S. "Innovative transverse jet interaction arrangements in supersonic crossflow," Master Thesis, Department of Aerospace and Ocean Engineering, Virginia Tech,2001.
Wallis, S., Schetz J.A., (2002), "Experimental studies of jet interaction with a main jet and an array of smaller jets", AIAA paper-3148.
Watt, G.A., "An experimental investigation of a sonic jet directed upstream against a uniform supersonic flow", Institute of Aero physics, Univ. of Toronto TN 7,1956.
Westwater, F.L. "Rolling Up of the Surface of Discontinuity Behind an Aerofoil of Finite Span," Aerosp. Res. Comm. Rep. Memo.1692m,1935.
Wilcox, D.C., "Comparison of Two-Equation turbulence models for boundary layers with pressure gradient," AIAA Journal, Vol.38, No.8, pp.1414-1421,1993.
Wilcox, D.C. "Turbulence Modeling for CFD," ISBN 1-928729-10-X,2nd Ed., DCW Industries, Inc,1998.
Williams, S., Hartfield, R., Jr., "An analytical investigation of angled injection into a compressible flow," AIAA Paper 96-3142,1996.
Wilmoth, R.G., and Leavitt L.D., "Navier Stokes prediction of multifunction Nozzle flows", Society of Auomotive Engineers Transcations, Vol.96, Sec.6, paper 871753,pp. 6.685-6.879,1987.
Woodmansee, M.A., and Dutton, J.C., "Experimental measurements of pressure, temperature, and density in an under-expanded sonic jet flowfield," AIAA Paper,.99-3600,1999.
Woodmansee, M.A., Kuenher, J.P., Lucht, L.P., and Dutton, J.C. "Pressure, temperature, and density measurements using high-resolution N2 CARS," AIAA Paper No.98-3456, 1998.
Xiao, Q., Tsai, H.M., and Papamoschou, D., "Numerical Investigation of Supersonic Nozzle Flow Separation," AIAA Paper-4640,2005.
Zahir, S. "Computational Aerodynamic Simulations for Pin-Protuberances in Supersonic Flow", EUCASS-292,2009.
Zahir, S., Asif, M., Kamran. N., and Khan, M.A., "Computational Investigations of aerodynamics forces at supersonic/Hypersonic Flows past a blunt body with various forward facing spikes", AIAA-2004-5189,2001.
Agarwal, R.K., Halt, D.W. "Compact higher order characteristic-based Euler method for unstructured grids," AIAA Journal, Vol.30, pp.1993-99,1992.
Agui, J.H., Briassulis, P., and Andreopoulos, Y., " Studies of interactions of a propagating shock wave with decaying grid turbulence:velocity and vorticity fields," Journal of Fluid Mechanics,524:143-195.,1992.
Ajmal, B., Zahir, S., Ali, A. "Numerical Study of Effects of injection pressure and location of secondary injection inside a low thrust Satellites nozzle," 25th Congress of the International Council of the Aeronautical Sciences, ICAS, Germany,2006.
Andreopoulos, J. "On the structure of jets in a crossflow," Journal of Fluid Mechanics, No. 157, pp.163-197,1985.
Baldwin, B.S., and Lomax, H. "Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows," AIAA Paper, pp.78-257,1978.
Barber, E.A. Jr. "An Experimental Investigation of Stagnation-Point Injection," Journal of Spacecraft and Rockets, Vol.2, No.5, pp.770-774,1965.
Barre, S., Alem, D., and Bonnet, J.P., "Experimental study of a normal shock/homogeneous turbulence interaction," AIAA Journal, vol.34(5), pp.968-974,1996.
Bergelson V.I., Medvedyuk S.A., Nemchinov I.V., Orlova T.I. and Hazins V.M., "Aerodynamic characteristics of a body at various localization of a thermal needle," Matematicheskoe modelirovanie.Vol.8, No.1, pp.3-10 (in Russian),1996.
Bogdonoff, S. M., and Vas, I. E. "Preliminary Investigations of Spiked Bodies at Hypersonic Speeds," Journal of the Aerospace Science, Vol.26, No.1, pp.65-74,1959.
Borzov, V.Yu., Rybka, I.V. and Yurev, A.S., "Influence of the local energy input in a hypersonic flow on drag of bodies with various bluntness," IFZh, Vol.67, No.5, pp.355-361 (in Russian),1994.
Bosanquet, C.H. and Pearson, J.L. "The spread of smoke and gases from chimneys," Trans. Faraday Soc.32:1249,1936.
Charles Hirsch, "Numerical Computations of internal and external flows," Vol., I and II, Published by John Wiley & Sons, Ltd Second edition,2007.
Chang, H. C, "The Roll-up of a Cylindrical Jet in a Cross Flow," translated by Nagaraja, USAF-ARL73-0131,1942.
Chenault, C.F., Beran, P.S., "k-ε and Reynolds stress turbulence model comparisons for two-dimensional injection flows," AIAA Journal, Vol.36, No.8, pp.1401-1412,1998.
Chenault, C.F., Beran, P.S., and Bowersox, R.D.W., "Numerical Investigation of Supersonic Injection Using a Reynolds-Stress Turbulence Model," AIAA Journal, Vol.37, No.10,1999.
Clark, S.W., Chan, S.C., "Numerical investigation of a transverse jet for supersonic aerodynamic control," AIAA Paper,92-0639,1992.
Cohen, J., "Statistical power analysis for the behavioral sciences," (2nd ed.),1988.
Curran, E. and Murthy, S.B. "Scramjet propulsion," Progress in Astronautics and Aeronautics,189:20-21,2000.
Deck, S,, Hollard, R. and Guillen, P. "Numerical Simulation of Steady and Unsteady Separated Nozzle Flows," AIAA-0406,2002.
Dennis, M., Bushnell "Annual Review of Fluid Mechanics," NASA Langley Research Center, Hampton, Virginia, Vol.36, pp.81-96,2004.
Finley, P.J., "The Flow of a Jet from a Body Opposing a Supersonic Freestream," Journal of Fluid Mechanics, Vol.26. Pt.2, pp.337-368,1966.
Fomin, V.M., Maslov, A.A., Shashkin, A.P., Korotaeva, T.A., and Malmuth N.D., "Flow regimes formed by a counterflow jet in supersonic flow," Journal of Applied Mechanics and Technical Physics, Vol.42, No.5, pp.757-764,2001.
Foster C, Summer_eld M, Swan W.,"Flow separation in overexpanded supersonic exhaust nozzles," Jet Propulsion; Vol.24, No.9, pp.319-320,1954.
Ganiev, Y.G., Gordeev, V.P., Krasilnikov, A.V., Lagutin, V.I., and Otmennikov, V.N., "Experimental Study of the Possibility of Reducing Supersonic Drag by Employing Plasma Technology," Fluid Dynamics, Vol.31, No.2, Consultants Bureau, New York,translated from Izvestia Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gasa, No.2, pp.177-182,1996.
Ganiev, Y., Gordeev, V., Krasilnikov, A., Lagutin, V., and Otmennikov, V., "Experimental Study of the Possibility of Reducing Aerodynamic Drag by Employing Plasma Injection," Proceedings of the Third International Conference on Experimental Fluid Mechanics, Korolev, Moscow Region, Russia,1997.
Ganiev, Y.G., Gordeev, V.P., Krasilnikov, A.V., Lagutin, V.I., Otmennikov, V.N., and Panasenko, A.V., "Experimental and Theoretical Study of the Possibility of Reducing Aerodynamic Drag by Employing Plasma Injection," Proceedings of the 2nd Workshop of Weakly Ionized Gases, Norfolk, VA,1998.
Ganiev, Y.G., Gordeev, V.P., Krasilnikov, A.V., Lagutin, V.I., Otmennikov, V.N., and Panasenko, A.V., "Theoretical and Experimental Study of the Possibility of Reducing Aerodynamic Drag by Employing Plasma Injection," AIAA Paper 99-0603,1999.
Ganiev, Y.C., "Aerodynamic drag reduction by plasma and hot gas injection," Journal of Thermophysics and heat transfer, Vol.14, No.1,2000.
Hameed, A., and Vogiatzis, C, "Overexpanded two dimensional convergent Divergent Nozzle flow simulation, Assement of Turbulence Models," Journal of Propulsion and Power, Vol.13, No.3, pp.444-445,1997.
Hannappel, R., and Friedrich, R., "Direct numerical simulation of a Mach 2 shock interacting with isotropic turbulence." Applied Scientific Research, vol.54, pp.205-221,146,1995.
Hameed, A., and Vogiatzis, C, "Overexpanded two dimensional convergent Divergent Nozzle performance, Effect of three dimensional flow interaction," Journal of Propulsion and Power, Vol.14, No.2, pp.234-240,1998.
Honkan, A., and Andreopoulos, J., "Rapid compression of grid-generated turbulence by a moving shock wave," Physics of Fluids, vol.4, pp.2562-2572,1992.
Hunter, C.A., "Experimental, Theoretical, and Computational Investigation of Separated Nozzle Flows," AIAA paper, pp.98-3107,1998.
Hussaini, M.Y., Zang, T.A., "Spectral methods in fluid dynamics," Annual Review of. Fluid Mechanics, Vol.19, pp.339-67,1987.
Hutt, C.R., and Howe, A.J., "Forward Facing Spike Effects of Bodies of Different Cross Sections in Supersonic Flow," Aeronautical Journal of the Royal Aeronautical Society, Vol.93, No.926, pp.229-234,1989.
Jacquin, L., Cambon, C, and Blin E., "Turbulence amplification by a shock wave and rapid distortion theory," Physics of Fluids A,5:2539-2550,1993.
Jameson, A, "Iterative solution of transonic flows over airfoil and wings, including flows at Mach 1," Commun. Pure Appl. Math., vol.27,pp.283,1974.
Jameson, A., Schmidt, W. and Turkel, E. "Numerical solution of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes," AIAA Paper, pp.81-1259,1981.
Jiang Zonglin, Yunfeng Liu, Guilai Han and Wei Zhao., "Experimental demonstration of a new concept of drag reduction and thermal protection for hypersonic vehicles," Acta Mechanica Sinica, Vol.25, No.3,2009.
Launder, B.E. and Spalding, D.B., "The numerical computation of turbulent flows," Computer Methods in Applied Mechanics and Engineering, Vol.3, No.2, pp.269-289, 1974.
Lefrancois, E., "Numerical validation of a stability model for a flexible over-expanded rocket nozzle," International Journal for Numerical Methods in Fluids, Vol.49, No.4, pp. 349-369,2005.
Lee, S., Lele, S.K., and Moin, P., "Direct numerical simulation of isotropic turbulence interacting with a weak shock wave," Journal of Fluid Mechanics, No.251, pp.533-562, 1993.
Lee, S., Lele, S.K., and Moin, P., "Interaction of isotropic turbulence with shock waves: Effect of shock strength," Journal of Fluid Mechanics,No,340, pp.225-247,1997.
Lele, S. "Compact finite difference schemes with spectral like resolution," Rep. CTR107, Stanford Univ., CA,1990.
Liang, S.M., Huang, K.L., and Chen, K.C., "Numerical Study of Low-Thrust Nozzles for Satellites," Journal of Spacecraft and Rockets, AIAA, Vol.33, No.5, pp.693-699,1996.
Mahapatra, D., Sriram, R. and Jagadesh, G., "Effect of counterflow argon plasma jet on aerodynamic drag of a blunt body at hypersonic mach numbers," The aeronautical Journal, 112(1137),2008.
Mahesh, k., Lele, S.K., and Moin, P., "The influence of entropy fluctuations on the interaction of turbulence with a shock wave," Journal of Fluid Mechanics, No.334, pp. 353-379,1997.
Margason, R.J., "Analysis of the Flow Field of a Jet in a Subsonic Crosswind," NASA SP-228,pp.683-702,1969.
Margason, R.J "Fifty years of jet in crossow research, AGARD Symp. On a jet in Cross Flow, Winchester, UK, AGARD CP-534,1993.
McDaniel, J., Glass, G., Staack, D. and Miller, C., "Experimental and computational comparison of an under-expanded jet flowfield," AIAA Paper-0305,2002.
Morrisette, E.L., Goldberg, T.J., "Turbulent Flow Separation Criteria for Over-Expanded Supersonic Nozzles," NASA, TP-1207,1978.
Mouronval, A.S., and Hadjadj, A., "Numerical study of the starting process in a supersonic nozzle," CIMNE, West East High Speed Flow Fields, Barcelona,2002.
Murakami, E., and Papamoschou, D., "Experiments on Mixing Enhancement in Dual-Stream Jets," AIAA Paper-0668,2001.
Murman, E., and Cole, J., "Calculation of plane steady transonic flows," AIAA Journal, Vol.9, pp.114-21,1971.
Osher, S., "Riemann solvers, the entropy condition, and difference approximations," SIAM Journal of. Numerical Analysis, No.121, pp.217-35,1984.
Ostlund, J., Damgaard, M., Frey, M.,"Side load phenomenon in highly overe-expanded rocket nozzles," AIAA paper-3684,2001.
Papamoschou, D. "Mixing Enhancement Using Axial Flow," AIAA Paper-0093,2000.
Papamoschou, D., Zill, A., "Fundamental Investigation of Supersonic Nozzle Flow Separation," AIAA Paper-1111,2004.
Papamoschou, Dixon, D., and Nishi, K., "Mean Flow of Multi-Stream Rectangular Jets under Normal and Mixing-Enhancement Conditions," AIAA Paper-0919,2004.
Reshotko, E., and Tucker, M., "Effect of a Discontinuity on Turbulent Boundary Layer Thickness Parameters with Application to Shock-Induced Separation," NACA TN-3454, 1955.
Roe, P.L. "Approximate Riemann solvers, parameter vectors, and difference schemes," Journal of Computational Physics, Vol.43, pp.357-372,1981.
Romine, G.L. "Nozzle Flow Separation," AIAA Journal, Vol.36, No.9, pp.1618-1625, 1998.
Rosenhead, L. "The Formation of Vortices from a Surface of Discontinuity," Proc. Roy. Soc. A 134, pp.170-192,1932.
Santiago, J., Dutton J., "Crossflow vortices of a jet injected into a supersonic crossflow." AIAA Journal, Volume.35, No.5, pp.915-917,1997.
Sesterhenn, J., Dohogne, J.F., and Friedrich, R., "Direct numerical simulation of the interaction of isotropic turbulence with a shock wave using shock-fitting", Comptes Rendus de Mecanique,No.333, pp.87-94,2005.
Shang J.S. "Jet-Spike Bifurcation in High-Speed Flows," AIAA Journal, Vol.39, No.6, 2001.
Shang, J.S., Hankey, W.L., and Smith, R.E., "Flow Oscillations of Spike-Tipped Bodies," AIAA Journal, Vol.20, No.1, pp.25-26,1982.
Spaid, F.W., Zukoski, E.E., Rosen R., "A study of secondary injection of gases into a supersonic flow," NACA Technical Report No.32-834, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA,1966.
Steger, J., Warming, R., "Flux vector splitting of the inviscid gas dynamic equations with applications to finite difference methods," J. Comput. Phys. Vol.40, pp.263-93,1981.
Sterrett, J.R., and Romeo, D.J., "Exploratory investigation of the effect of a forward-facing jet on the bow shock of a blunt body in a Mach number 6," NASA TND-1605, 1963.
Strike, W.T., Schueler, C.J., "Investigation of interference effects produced by lateral jets on surfaces in a supersonic stream," AIAA Paper 63-184,1963.
Sutton, O.G. "A theory of Eddy di_usion in the atmosphere," Proc. Roy. Soc. A 135, pp. 143-165,1932.
Tannehill, J.C., Anderson, D.A., and Pletcher, R. H. "Computational Fluid and Heat Transfer," 2nd Ed., Taylor & Francis.,1997.
Thompson, D.S. "Numerical solution of a two-dimensional jet in a supersonic crossflow using an upwind relaxation scheme," AIAA Paper 89-1869,1989.
User Manual PAK-3D Aerodynamics Directorate, Aerodynamics and Structural Analysis Centre, Islamabad, Pakistan,2006.
Vaivads R.H., Gauthier J.E. D., Farinaccio R., "CFD Simulation of a Jet Vane Thrust Vector Control System," CFD Conference of the Computational Fluid Dynamic society of Canada 1998.
Valerio V., PhD Thesis "Numerical Studies of the Jet Interaction Flowfield with a Main Jet and an Array of Smaller Jets," Virginia Polytechnic Institute and State University, Blacksburg, VA,2002.
Valerio, V., Reece, N., and Schetz, J.A., (2009), "Detailed flow physics of the supersonic jet interaction flow field", Physics of Fluids,21,046101.
Van Leer, B., (1982), "Flux vector splitting for Euler equations," Proceedings of International Conference on Numerical Methods, Aachen, ed., E Krause, pp.507-12.
Venkatkrishnan, V., "A perspective on unstructured grid flow solvers," AIAA Journal Vol. 34, pp:533-47,1996.
Venukumar, B., Jagadeesh, G., and Reddy, K.P.J., "Counterflow drag reduction by supersonic jet for a blunt body in hypersonic flow," Physics of Fluids,18(118104),2006.
Vinayak Kulkarni and Reddy, K.P.J., "Enhancement in counterflow drag reduction by supersonic jet in High enthalpy flows," Physics of Fluids,20(016103),2008.
Walker, R.E., Stone A.R., and Shandor, M., "Secondary gas injection in a conical rocket nozzle-I, Effect of Orifice diameter and molecular weight of injectant," AIAA Journal, Vol.1, pp.334-338,1963.
Wallis, S. "Innovative transverse jet interaction arrangements in supersonic crossflow," Master Thesis, Department of Aerospace and Ocean Engineering, Virginia Tech,2001.
Wallis, S., Schetz J.A., (2002), "Experimental studies of jet interaction with a main jet and an array of smaller jets", AIAA paper-3148.
Watt, G.A., "An experimental investigation of a sonic jet directed upstream against a uniform supersonic flow", Institute of Aero physics, Univ. of Toronto TN 7,1956.
Westwater, F.L. "Rolling Up of the Surface of Discontinuity Behind an Aerofoil of Finite Span," Aerosp. Res. Comm. Rep. Memo.1692m,1935.
Wilcox, D.C., "Comparison of Two-Equation turbulence models for boundary layers with pressure gradient," AIAA Journal, Vol.38, No.8, pp.1414-1421,1993.
Wilcox, D.C. "Turbulence Modeling for CFD," ISBN 1-928729-10-X,2nd Ed., DCW Industries, Inc,1998.
Williams, S., Hartfield, R., Jr., "An analytical investigation of angled injection into a compressible flow," AIAA Paper 96-3142,1996.
Wilmoth, R.G., and Leavitt L.D., "Navier Stokes prediction of multifunction Nozzle flows", Society of Auomotive Engineers Transcations, Vol.96, Sec.6, paper 871753,pp. 6.685-6.879,1987.
Woodmansee, M.A., and Dutton, J.C., "Experimental measurements of pressure, temperature, and density in an under-expanded sonic jet flowfield," AIAA Paper,.99-3600,1999.
Woodmansee, M.A., Kuenher, J.P., Lucht, L.P., and Dutton, J.C. "Pressure, temperature, and density measurements using high-resolution N2 CARS," AIAA Paper No.98-3456, 1998.
Xiao, Q., Tsai, H.M., and Papamoschou, D., "Numerical Investigation of Supersonic Nozzle Flow Separation," AIAA Paper-4640,2005.
Zahir, S. "Computational Aerodynamic Simulations for Pin-Protuberances in Supersonic Flow", EUCASS-292,2009.
Zahir, S., Asif, M., Kamran. N., and Khan, M.A., "Computational Investigations of aerodynamics forces at supersonic/Hypersonic Flows past a blunt body with various forward facing spikes", AIAA-2004-5189,2001.