激波干扰及超声速湍流边界层的数值模拟研究
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摘要
激波和超声速湍流边界层的研究在流动物理和工程应用中都具有重要意义。本文采用直接数值模拟方法研究了激波-激波干扰和超声速湍流边界层的流动特性。文中着重探讨了激波-激波干扰中的非定常流动现象及反馈机制、超声速湍流边界层内流动拓扑的演化和壁面温度对超声速湍流边界层统计特性的影响。主要工作和研究成果如下：
(1)研究了高超声速IV型激波-激波干扰的非定常流动特性。基于对涡量和胀压输运方程源项的分析,揭示了流动结构与剪切、压缩及热力过程之间的内在联系。详细地分析了流场中存在的非定常流动现象,包括超声速“喷流”冲击壁面、“喷流”激波的非定常运动、激波-边界层相互作用和旋涡-边界层相互作用等。研究表明：“喷流”激波的振荡和变形会产生“热斑”,导致物体表面热流峰值出现瞬时极大值；“喷流”激波和超声速“喷流”所诱导的剪切层相互作用,形成向上游传播的压缩波；压缩波与上游的弓形激波作用产生向物体传播的熵波和涡波。通过对压力场的本征正交分解发现,流场中的压缩波还与激波-边界层相互作用和旋涡-边界层相互作用相关联。基于对流场演化过程的分析,发现流场非定常运动的反馈机制与超声速“喷流”相关,由向上游传播的压缩波和向下游演化的相干涡结构构成反馈回路。基于自激振荡机制,定量地分析了流动的非定常特征,包括非定常运动的频率以及入射激波角度对运动频率的影响。此外,随着雷诺数的减小,流场由非定常状态变为定常状态。
(2)研究了超声速湍流边界层内流体质点的拓扑结构演化。系统地分析了速度梯度不变量空间中不变量变化率的瞬时和平均统计特性。研究表明：不变量发生剧烈变化的可能性呈现明显的-3幂次律衰减特征；在归一化的不变量空间内,边界层外层的条件平均迹向内盘旋至原点,缓冲层的条件平均迹呈现极限环行为。基于不变量动力学演化方程统计分析了相互作用项、压力-Hessian相关项和粘性项对拓扑结构演化的贡献,揭示了压缩性对流动拓扑演化的影响。统计结果表明：拓扑结构的平均演化受压缩性的影响显著；不变量间的相互作用项决定了拓扑结构在不变量Q-R平面按顺时针方向演化；在局部压缩区和局部膨胀区,压力项的贡献起主导作用,但两个区域内的演化趋势是相反的；粘性项主要表现为耗散作用,导致速度梯度衰减,在粘性底层以外可以采用线性衰减模型来模化。
(3)研究了壁面温度对超声速湍流边界层的湍流统计特性的影响。系统地分析了平均量和湍流脉动量的统计特征、拟序涡结构的空间结构以及应变与涡量的相互作用。结果验证了Morkovin假设的合理性,即壁面温度对湍流平均特征的影响主要通过平均密度和粘性的变化所体现。通过分析联合概率密度分布,本文建立了密度脉动和温度脉动之间、流向速度脉动和温度脉动之间的合理关系式。在边界层内层,拟序涡结构与壁面的夹角随着壁面温度的增加而增大；在边界层外层,拟序涡结构与壁面的夹角基本不受壁面温度影响。通过涡拉伸项定量分析了应变与涡量的相互作用；结果表明,在边界层内层第二主应变率相关项占主导,主要来源于不稳定应变占优区域(UN/S/S)和径向收缩、轴向拉伸的涡结构(SF/S),应变占优的UN/S/S的平均涡拉伸强度大于旋转占优的SF/S;在边界层外层第一主应变率相关项占主导,主要来源于SF/S,并且SF/S的平均涡拉伸强度大于UN/S/S。
Investigation of shock-shock interaction and supersonic turbulent boundary layer is of great importance for the development of high-speed vehicles and turbulence model-ing. In this dissertation, the unsteady shock-shock interaction and statistical properties of supersonic turbulent boundary layers are studied by means of direct numerical sim-ulation. The results and conclusions are briefly given as follows:
(1) Characteristics of the unsteady type IV shock interaction of hypersonic blunt body flows are investigated. The intrinsic relations of flow structures to the shearing, compressing and thermal processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous sur-face heating rate peak is caused by the fluid in the "hot spot" generated by an oscillating and deforming jet bow shock just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer in-teraction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the inter-action of the jet bow shock and the shear-layers formed by a supersonic impinging jet, and then the interaction of the free-stream bow shocks and the compression waves results in the entropy waves and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. Moreover, the flow field will become steady for low Reynolds number flow.
(2) Topological evolution of compressible turbulent boundary layers at Mach2is in-vestigated by means of statistical analysis of the invariants of the velocity gradient tensor. The probability density functions of the rate of change of the invariants exhibit the-3power law distribution in the region of large Lagrangian deriva-tive of the invariants in the inner and outer layers.The topological evolution is studied by conditional mean trajectories for the evolution of the invariants. The trajectories illustrate inward spiraling orbits around and converging to the origin of the space of invariants in the outer layer, while they are repelled by the vicinity of the origin and converge towards a limit cycle in the inner layer. The compressibility effect on the mean topological evolution is studied in terms of the'incompressible', compressed and expanding regions. It is found that the mean evolution of flow topologies is altered by the compressibility. The evolution equations of the invariants are derived and the relevant dynamics of the mean topological evolution are analyzed. The compressibility effect is mainly related to the pressure effect. The mutual-interaction terms among the invariants are the root of the clockwise spiral behavior of the local flow topology in the space of invariants.
(3) Turbulent boundary layers at Mach4.9with the ratio of wall temperature to re-covery temperature{Ts,/Tr) from0.5to1.5are investigated. The influence of wall temperature on Morkovin's scaling, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, coherent vortical structure and vor-tex stretching is assessed. The scaling relations proposed for cool and adiabatic cases, such as Morkovin's scaling and the modified strong Reynolds analogy, are also applicable for the hot case. The approximate relations between the densi-ty fluctuations and temperature fluctuations as well as between the streamwise velocity fluctuations and temperature fluctuations are proposed. With the in-crease of wall temperature, the most probable inclination angle (the angle made in the streamwise and wall-normal plane) of coherent vortical structures increases in the inner layer and has little change in the outer layer. Moreover, in the in-ner layer, the enstrophy production is dominated by the intermediate strain-rate term and mainly comes from unstable node/saddle/saddle (UN/S/S) and stable focus/stretching (SF/S), and the vortex stretching of UN/S/S is stronger than SF/S; in the outer layer, the enstrophy production is dominated by the extensive strain-rate term and mainly comes from SF/S, and the vortex stretching of SF/S is stronger than UN/S/S.
(1)研究了高超声速IV型激波-激波干扰的非定常流动特性。基于对涡量和胀压输运方程源项的分析,揭示了流动结构与剪切、压缩及热力过程之间的内在联系。详细地分析了流场中存在的非定常流动现象,包括超声速“喷流”冲击壁面、“喷流”激波的非定常运动、激波-边界层相互作用和旋涡-边界层相互作用等。研究表明：“喷流”激波的振荡和变形会产生“热斑”,导致物体表面热流峰值出现瞬时极大值；“喷流”激波和超声速“喷流”所诱导的剪切层相互作用,形成向上游传播的压缩波；压缩波与上游的弓形激波作用产生向物体传播的熵波和涡波。通过对压力场的本征正交分解发现,流场中的压缩波还与激波-边界层相互作用和旋涡-边界层相互作用相关联。基于对流场演化过程的分析,发现流场非定常运动的反馈机制与超声速“喷流”相关,由向上游传播的压缩波和向下游演化的相干涡结构构成反馈回路。基于自激振荡机制,定量地分析了流动的非定常特征,包括非定常运动的频率以及入射激波角度对运动频率的影响。此外,随着雷诺数的减小,流场由非定常状态变为定常状态。
(2)研究了超声速湍流边界层内流体质点的拓扑结构演化。系统地分析了速度梯度不变量空间中不变量变化率的瞬时和平均统计特性。研究表明：不变量发生剧烈变化的可能性呈现明显的-3幂次律衰减特征；在归一化的不变量空间内,边界层外层的条件平均迹向内盘旋至原点,缓冲层的条件平均迹呈现极限环行为。基于不变量动力学演化方程统计分析了相互作用项、压力-Hessian相关项和粘性项对拓扑结构演化的贡献,揭示了压缩性对流动拓扑演化的影响。统计结果表明：拓扑结构的平均演化受压缩性的影响显著；不变量间的相互作用项决定了拓扑结构在不变量Q-R平面按顺时针方向演化；在局部压缩区和局部膨胀区,压力项的贡献起主导作用,但两个区域内的演化趋势是相反的；粘性项主要表现为耗散作用,导致速度梯度衰减,在粘性底层以外可以采用线性衰减模型来模化。
(3)研究了壁面温度对超声速湍流边界层的湍流统计特性的影响。系统地分析了平均量和湍流脉动量的统计特征、拟序涡结构的空间结构以及应变与涡量的相互作用。结果验证了Morkovin假设的合理性,即壁面温度对湍流平均特征的影响主要通过平均密度和粘性的变化所体现。通过分析联合概率密度分布,本文建立了密度脉动和温度脉动之间、流向速度脉动和温度脉动之间的合理关系式。在边界层内层,拟序涡结构与壁面的夹角随着壁面温度的增加而增大；在边界层外层,拟序涡结构与壁面的夹角基本不受壁面温度影响。通过涡拉伸项定量分析了应变与涡量的相互作用；结果表明,在边界层内层第二主应变率相关项占主导,主要来源于不稳定应变占优区域(UN/S/S)和径向收缩、轴向拉伸的涡结构(SF/S),应变占优的UN/S/S的平均涡拉伸强度大于旋转占优的SF/S;在边界层外层第一主应变率相关项占主导,主要来源于SF/S,并且SF/S的平均涡拉伸强度大于UN/S/S。
Investigation of shock-shock interaction and supersonic turbulent boundary layer is of great importance for the development of high-speed vehicles and turbulence model-ing. In this dissertation, the unsteady shock-shock interaction and statistical properties of supersonic turbulent boundary layers are studied by means of direct numerical sim-ulation. The results and conclusions are briefly given as follows:
(1) Characteristics of the unsteady type IV shock interaction of hypersonic blunt body flows are investigated. The intrinsic relations of flow structures to the shearing, compressing and thermal processes are studied and the physical mechanisms of the unsteady flow evolution are revealed. It is found that the instantaneous sur-face heating rate peak is caused by the fluid in the "hot spot" generated by an oscillating and deforming jet bow shock just ahead of the body surface. The features of local shock/boundary layer interaction and vortex/boundary layer in-teraction are clarified. Based on the analysis of flow evolution, it is identified that the upstream-propagating compression waves are associated with the inter-action of the jet bow shock and the shear-layers formed by a supersonic impinging jet, and then the interaction of the free-stream bow shocks and the compression waves results in the entropy waves and vortical waves propagating to the body surface. Further, the feedback mechanism of the inherent unsteadiness of flow field is revealed to be related to the impinging jet. A feedback model is proposed to reliably predict the dominant frequency of flow evolution. Moreover, the flow field will become steady for low Reynolds number flow.
(2) Topological evolution of compressible turbulent boundary layers at Mach2is in-vestigated by means of statistical analysis of the invariants of the velocity gradient tensor. The probability density functions of the rate of change of the invariants exhibit the-3power law distribution in the region of large Lagrangian deriva-tive of the invariants in the inner and outer layers.The topological evolution is studied by conditional mean trajectories for the evolution of the invariants. The trajectories illustrate inward spiraling orbits around and converging to the origin of the space of invariants in the outer layer, while they are repelled by the vicinity of the origin and converge towards a limit cycle in the inner layer. The compressibility effect on the mean topological evolution is studied in terms of the'incompressible', compressed and expanding regions. It is found that the mean evolution of flow topologies is altered by the compressibility. The evolution equations of the invariants are derived and the relevant dynamics of the mean topological evolution are analyzed. The compressibility effect is mainly related to the pressure effect. The mutual-interaction terms among the invariants are the root of the clockwise spiral behavior of the local flow topology in the space of invariants.
(3) Turbulent boundary layers at Mach4.9with the ratio of wall temperature to re-covery temperature{Ts,/Tr) from0.5to1.5are investigated. The influence of wall temperature on Morkovin's scaling, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, coherent vortical structure and vor-tex stretching is assessed. The scaling relations proposed for cool and adiabatic cases, such as Morkovin's scaling and the modified strong Reynolds analogy, are also applicable for the hot case. The approximate relations between the densi-ty fluctuations and temperature fluctuations as well as between the streamwise velocity fluctuations and temperature fluctuations are proposed. With the in-crease of wall temperature, the most probable inclination angle (the angle made in the streamwise and wall-normal plane) of coherent vortical structures increases in the inner layer and has little change in the outer layer. Moreover, in the in-ner layer, the enstrophy production is dominated by the intermediate strain-rate term and mainly comes from unstable node/saddle/saddle (UN/S/S) and stable focus/stretching (SF/S), and the vortex stretching of UN/S/S is stronger than SF/S; in the outer layer, the enstrophy production is dominated by the extensive strain-rate term and mainly comes from SF/S, and the vortex stretching of SF/S is stronger than UN/S/S.
引文
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