超声速小攻角钝锥边界层稳定性分析及转捩预测研究
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摘要
本文以来流马赫数为6的小钝度小攻角圆锥边界层为对象，采用直接数值模拟的方法，利用流动稳定性理论分析了相同来流条件下多种钝度、多个攻角的圆锥边界层的稳定性问题；并用直接数值模拟的方法研究了小攻角钝锥边界层中小扰动的演化过程，验证了线性稳定性理论的结果；最后，用直接数值模拟的方法对扰动的非线性演化过程进行研究并对转捩位置的预测进行了初步探讨。
在计算定常基本流时，对计算方案进行了改进，大大缩短了基本流场的计算时间。
通过计算和分析，得到如下结论：
1.对圆锥头部钝度的研究结果：圆锥钝头使流场变得稳定，不稳定区域向后推移。钝头的影响范围在300倍头部半径之内，之后流场的稳定性特性与尖锥的一致。
2.对小攻角圆锥边界层的流动稳定性分析结果：攻角使边界层厚度在迎风面减小，在背风面增加，从而改变了各子午面上不稳定波的频率范围。零攻角时边界层开始失稳的位置最靠下游，随着攻角增加，开始失稳位置在迎风面和背风面均向上游移动，在背风面前移的较多。利用eN方法计算扰动沿流向的增长，结果表明在流向相同位置，背风面的扰动增长更大。
3.对小扰动演化的数值模拟的研究结果：单个频率的小扰动的演化过程与流动稳定性理论分析的结果基本相符，这表明流动稳定性理论在超声速小攻角小钝度圆锥绕流的三维边界层中是适用的。当扰动幅值超过0.07后，非线性的作用开始明显。几个频率的扰动共存时，各频率扰动的演化发展与加单个频率时的相同，相互作用不明显。
4.对转捩位置预测的数值模拟研究结果：在计算域入口加较大幅值扰动，计算域内可以出现转捩现象。根据扰动的增长速度和壁面摩擦系数曲线都可以判断转捩开始的位置，这两中方法判断出的转捩开始位置基本一致。计算结果表明，转捩位置的周向分布与计算域入口扰动有密切的关系，改变入口处的扰动，可以得到完全不同的分布形式。在开始转捩的位置附近，各频率的扰动幅值为来流速度的1.0~3.2%，比较分散，迎风面和背风面的差别也较大。但是，总的扰动速度幅值在转捩开始的位置附近基本都是来流速度的5%。因此，在预测转捩位置时，以流场中总扰动的幅值作为转捩开始的判据可能更为合理。
In this paper, the supersonic boundary layer over blunt cone at angle of attack(AOA) and Mach 6 is studied. DNS is done to get the base flow over various bluntcones and at several of AOA in the same incoming flow condition. Linear stabilitytheory (LST) is used to analyze the stability of the base flows. The LST results areverified by DNS of the small amplitude disturbance evolvement. The evolvementsof large amplitude disturbance are also computed by DNS for the elementary study ofthe transition estimation.
When base flow is got by DNS, the computation time is markedly saved byrefining the computation scheme.
The following conclusions are got by LST or DNS:
1. The study of blunt effect of cone shows the following results: The blunteffect stabilizes flow field and moves the unstable region aftward. Theblunt nose can affect as long as 300 times of nose radius distance and theflow field agrees with the sharp cone case at the further location.
2. The linear stability analysis of the boundary layer over the cone at AOAshows the following results: When the cone at AOA, the boundary becomesthinner on the windward and thicker on the leeward so that the frequency ofunstable wave changes on different meridian. The boundary layer becomesunstable the most downstream at zero AOA, such that the unstable regionmoves forward at AOA, and it moves faster on the leeward. Thedisturbance amplitude is computed by eNmethod, and the result shows that,at the same location, the disturbance growth greater on the leeward.
3. The DNS of small disturbance evolvement shows the following results: Theevolvement of single wave is the same as the result of LST estimate, whichindicates LST can be applied to the 3D supersonic flow over blunt cone atsmall AOA. When the amplitude of single wave exceeds 0.07, thenonlinear effect becomes strong so that the LST fails. When multiplewaves exist in the same field, the evolvement of each wave agrees with thesingle case, which indicates that there is no remarkable interaction.
4. The numerical study of transition estimation shows the following results: Transition occurs when the large disturbances are introduced at the inlet.Both the disturbance amplification and Cf curve can reflect the spot wheretransition begins, and the both can give the same location. The DNS resultsshow that the transition locations are seriously affected by the disturbancesat the inlet, so that the change of disturbance at the inlet can result indifferent transition location. On the transition beginning spot, theamplitudes of each wave are different, which are the 1.0~3.2% of thefreestream velocity, while the total amplitude is all about 5% of thefreestream velocity. Consequently, when we estimate the transitionlocation, it is more acceptable to use the total amplitude to fix the spot wheretransition begins.
在计算定常基本流时，对计算方案进行了改进，大大缩短了基本流场的计算时间。
通过计算和分析，得到如下结论：
1.对圆锥头部钝度的研究结果：圆锥钝头使流场变得稳定，不稳定区域向后推移。钝头的影响范围在300倍头部半径之内，之后流场的稳定性特性与尖锥的一致。
2.对小攻角圆锥边界层的流动稳定性分析结果：攻角使边界层厚度在迎风面减小，在背风面增加，从而改变了各子午面上不稳定波的频率范围。零攻角时边界层开始失稳的位置最靠下游，随着攻角增加，开始失稳位置在迎风面和背风面均向上游移动，在背风面前移的较多。利用eN方法计算扰动沿流向的增长，结果表明在流向相同位置，背风面的扰动增长更大。
3.对小扰动演化的数值模拟的研究结果：单个频率的小扰动的演化过程与流动稳定性理论分析的结果基本相符，这表明流动稳定性理论在超声速小攻角小钝度圆锥绕流的三维边界层中是适用的。当扰动幅值超过0.07后，非线性的作用开始明显。几个频率的扰动共存时，各频率扰动的演化发展与加单个频率时的相同，相互作用不明显。
4.对转捩位置预测的数值模拟研究结果：在计算域入口加较大幅值扰动，计算域内可以出现转捩现象。根据扰动的增长速度和壁面摩擦系数曲线都可以判断转捩开始的位置，这两中方法判断出的转捩开始位置基本一致。计算结果表明，转捩位置的周向分布与计算域入口扰动有密切的关系，改变入口处的扰动，可以得到完全不同的分布形式。在开始转捩的位置附近，各频率的扰动幅值为来流速度的1.0~3.2%，比较分散，迎风面和背风面的差别也较大。但是，总的扰动速度幅值在转捩开始的位置附近基本都是来流速度的5%。因此，在预测转捩位置时，以流场中总扰动的幅值作为转捩开始的判据可能更为合理。
In this paper, the supersonic boundary layer over blunt cone at angle of attack(AOA) and Mach 6 is studied. DNS is done to get the base flow over various bluntcones and at several of AOA in the same incoming flow condition. Linear stabilitytheory (LST) is used to analyze the stability of the base flows. The LST results areverified by DNS of the small amplitude disturbance evolvement. The evolvementsof large amplitude disturbance are also computed by DNS for the elementary study ofthe transition estimation.
When base flow is got by DNS, the computation time is markedly saved byrefining the computation scheme.
The following conclusions are got by LST or DNS:
1. The study of blunt effect of cone shows the following results: The blunteffect stabilizes flow field and moves the unstable region aftward. Theblunt nose can affect as long as 300 times of nose radius distance and theflow field agrees with the sharp cone case at the further location.
2. The linear stability analysis of the boundary layer over the cone at AOAshows the following results: When the cone at AOA, the boundary becomesthinner on the windward and thicker on the leeward so that the frequency ofunstable wave changes on different meridian. The boundary layer becomesunstable the most downstream at zero AOA, such that the unstable regionmoves forward at AOA, and it moves faster on the leeward. Thedisturbance amplitude is computed by eNmethod, and the result shows that,at the same location, the disturbance growth greater on the leeward.
3. The DNS of small disturbance evolvement shows the following results: Theevolvement of single wave is the same as the result of LST estimate, whichindicates LST can be applied to the 3D supersonic flow over blunt cone atsmall AOA. When the amplitude of single wave exceeds 0.07, thenonlinear effect becomes strong so that the LST fails. When multiplewaves exist in the same field, the evolvement of each wave agrees with thesingle case, which indicates that there is no remarkable interaction.
4. The numerical study of transition estimation shows the following results: Transition occurs when the large disturbances are introduced at the inlet.Both the disturbance amplification and Cf curve can reflect the spot wheretransition begins, and the both can give the same location. The DNS resultsshow that the transition locations are seriously affected by the disturbancesat the inlet, so that the change of disturbance at the inlet can result indifferent transition location. On the transition beginning spot, theamplitudes of each wave are different, which are the 1.0~3.2% of thefreestream velocity, while the total amplitude is all about 5% of thefreestream velocity. Consequently, when we estimate the transitionlocation, it is more acceptable to use the total amplitude to fix the spot wheretransition begins.
引文
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[2]是勋刚，湍流.天津：天津大学出版社，1994，213~230
[3] Mack L.M., Linear stability theory and the problem of supersonic boundarylayer transition, AIAA Journal, 1975, 13(3): 278289
[4] Mack L.M. Boundarylayerlinear stability theory. AGARD Report, 1984, No.709
[5] Mack L.M., Boundary layer stability analysis for sharp cones at zero angle ofattack, AFWAL TR873022,1986
[6] Mack L.M., Stability of axisymmetric boundary layers on sharp cones athypersonic mach numbers, AIAA Paper, 1987, No. 871413
[7] Helen L.R, William S.S. Stability of threedimensionalboundary layers. Ann.Rev. Fluid Mech. , 1989, 21: 235~284
[8] Stetson K.F., Rushton G.H., A Shock Tunnel Investigation of the Effects ofNose Bluntness,Angle of Attack and Boundary Layer Cooling on BoundaryLayer Transition at a Mach Number of 5.5, AIAA Journal, 1967, 5(5):899~906
[9] Stetson K.F., Hypersonic boundary layer transition experiments,AFWALTR803062,1980
[10] Stetson K.F., Mach 6 experiments of transition on a cone at angle of attack,Journal of Spacecraft, 1982, 19(5): 397~403
[11] Stetson K.F., Thompson E.R/, Donaldson J.C. and Siler L.G., Laminarboundary layer stability experiments on a cone at Mach 8. Part 1. sharp cone,AIAA Paper 831761,1983
[12] Stetson K.F., Thompson E.R/, Donaldson J.C. and Siler L.G., Laminarboundary layer stability experiments on a cone at Mach 8. Part 2. blunt cone,AIAA Paper 840006,1984
[13] Stetson K.F., Thompson E.R/, Donaldson J.C. and Siler L.G., Laminarboundary layer stability experiments on a cone at Mach 8. Part 3. sharp cone atangle of attack, AIAA Paper 850492,1985
[14] Stetson K.F., Thompson E.R/, Donaldson J.C. and Siler L.G., Laminarboundary layer stability experiments on a cone at Mach 8. Part 4. on unitReynolds number and environmental effects, AIAA Paper 861087,1986
[15] Stetson K.F., Thompson E.R/, Donaldson J.C. and Siler L.G., Laminarboundary layer stability experiments on a cone at Mach 8. Part 5. tests with acooled model, AIAA Paper 891895,1989
[16] K.F. Stetson, E.R. Thompson, J.C. Donaldson and L.G. Siler, on hypersonictransition testing and prediction, AIAA Paper 882007,1988
[17] Stetson K.F. and Kimmel T.L., on hypersonic boundarylayerstability, AIAAPaper 920737,1992
[18] Lees L. and Lin C.C, Investigation of the stability of the laminar boundarylayer in a compressible fluid, NACA TN1115,1946
[19] Lees L., The stability of the laminar boundary layer in a compressible fluid,NACA TR876,1947
[20] Demetriades A., Laminar boundary layer stability measurements at Mach 7including wall temperature effects, AFOSRTR771311,1977
[21] Demetriades A., New experiments on hypersonic boundary layer stabilityincluding wall temperature effects, Proceedings of the heat transfer and fluidmechanics institutes, 1978, 39~54
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