超音速尖锥/钝锥边界层稳定性、转捩及湍流的研究
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摘要
近年来,随着航空航天技术的发展,超音速、高超音速边界层的转捩与湍流问题越来越受到人们的关注。为了更贴近工程需要,本文以超音速、高超音速锥体边界层为研究对象,用直接数值模拟(DNS)的方法研究了其稳定性、转捩及湍流,并对用BL湍流模式计算锥体湍流边界层进行了研究,主要得到以下结论:
1.用摄动法对小攻角尖锥边界层的层流基本流进行了简化计算,并通过扰动演化的DNS与线性稳定性理论结果的比较,证实了所用方法的可靠性。
2.通过对马赫数为6的高超音速零攻角尖锥边界层转捩机理的数值研究,得到与平板情况相似的结论,即平均流剖面稳定性的迅速变化是breakdown过程的内在机理,并且第一模态不稳定波在此过程中起主导作用。
3.通过超音速钝锥湍流边界层的DNS,发现经过Van Driest变换后的平均速度壁面律与平均流剖面的相似性不受锥体效应的影响;而与平板相比,钝锥湍流边界层内的平均温度较高,压缩性较弱;钝锥湍流边界层内雷诺应力的分布规律,脉动量的相关函数,以及湍动能方程中各项的贡献与平板趋势相同,锥体效应的影响只表现在定量上。
4.通过BL湍流模式与DNS计算结果的对比,发现二者给出的湍流区壁面摩擦系数基本吻合,但它们给出的热力学量相差较大;BL模式计算的速度经过Van Driest变换后,能很好地满足不可压缩湍流的壁面律,但是平均流剖面在有些地方与DNS结果有一定的差别;另外,BL模式所给出的转捩判定准则可能是针对某一风洞实验提出的,由于风洞的背景湍流度比较大,它不适用于预测高空飞行器的转捩。
5.分析表明,BL模式不能准确给出壁面处的热力学量的原因是它对湍流普朗特数为常数的假设不正确。本文提出了修正方法,使计算结果有了很大改进。
With the development of the aeronautics and aerospace technology in recent years, the problems of transition and turbulence in supersonic and hypersonic boundary layers attract more and more attention. In order to be closer to real situation in the engineering problems, boundary layers on supersonic and hypersonic cones are selected as prototypes for our research. Direct numerical simulation (DNS) method is used to study the stability, transition and turbulence of the boundary layers, and the BL turbulence model has also been used to compute the turbulent boundary layers. The main conclusions obtained are as follows:
1. The laminar basic flow of the boundary layer of a sharp cone with small angle of attack is calculated by a simplified perturbation method. Through the comparison of the evolution of disturbances obtained by DNS with that obtained by linear stability theory (LST), the reliability of the method is confirmed.
2. Through the numerical study and the subsequent analysis of the transition process in the boundary layer of a hypersonic sharp cone with zero angle of attack and oncoming Mach number 6, similar conclusions, in regard with the mechanism of transition, has been found as for the transition in boundary layers on flat plates, i.e., the rapid change of the stability characteristics of the mean flow profile is the inherent mechanism for the breakdown in the transition, and in which the first mode unstable waves play the key role.
3. Through the DNS of supersonic turbulent boundary layers on a blunt cone, it is found that, the near-wall law of the mean velocity, under Van Driest transformation, and the similarity of the mean profiles are not influenced by the cone effect, while the mean temperature of the turbulent boundary layers is higher and the compressibility effect is weaker than those for flat plates. The distribution of the Reynolds stresses, the correlation of the fluctuations of turbulent quantities and the budget of turbulent kinetic energy in the turbulent boundary layers of a blunt cone are similar, in tendency, with those for boundary layers on flat plates, and the influence of cone effect is only of quantitative nature.
4. Through the comparison between the results obtained by BL turbulence model and the DNS, it is found that the wall friction coefficient obtained by both methods agree well with each other, while the thermodynamic variables do not. The near wall Van Driest transformed velocity profile agrees well with the near-wall law in incompressible turbulent boundary layers, while for other places, there are certain differences between the mean flow profiles obtained by DNS and BL model. In addition, the method proposed in the BL model for predicting the transition is found to be inapplicable for vehicles flying at high altitude, because its parameters seem to be determined by conventional wind tunnel experiments, for which the background disturbances is relatively high.
5. By analyzing the result of DNS, it is found that the assumption of a constant turbulent Prandl number in the BL model is the main cause for its incorrect prediction of the thermodynamic variables. Modification is accordingly proposed, and the result is satisfactory.
1.用摄动法对小攻角尖锥边界层的层流基本流进行了简化计算,并通过扰动演化的DNS与线性稳定性理论结果的比较,证实了所用方法的可靠性。
2.通过对马赫数为6的高超音速零攻角尖锥边界层转捩机理的数值研究,得到与平板情况相似的结论,即平均流剖面稳定性的迅速变化是breakdown过程的内在机理,并且第一模态不稳定波在此过程中起主导作用。
3.通过超音速钝锥湍流边界层的DNS,发现经过Van Driest变换后的平均速度壁面律与平均流剖面的相似性不受锥体效应的影响;而与平板相比,钝锥湍流边界层内的平均温度较高,压缩性较弱;钝锥湍流边界层内雷诺应力的分布规律,脉动量的相关函数,以及湍动能方程中各项的贡献与平板趋势相同,锥体效应的影响只表现在定量上。
4.通过BL湍流模式与DNS计算结果的对比,发现二者给出的湍流区壁面摩擦系数基本吻合,但它们给出的热力学量相差较大;BL模式计算的速度经过Van Driest变换后,能很好地满足不可压缩湍流的壁面律,但是平均流剖面在有些地方与DNS结果有一定的差别;另外,BL模式所给出的转捩判定准则可能是针对某一风洞实验提出的,由于风洞的背景湍流度比较大,它不适用于预测高空飞行器的转捩。
5.分析表明,BL模式不能准确给出壁面处的热力学量的原因是它对湍流普朗特数为常数的假设不正确。本文提出了修正方法,使计算结果有了很大改进。
With the development of the aeronautics and aerospace technology in recent years, the problems of transition and turbulence in supersonic and hypersonic boundary layers attract more and more attention. In order to be closer to real situation in the engineering problems, boundary layers on supersonic and hypersonic cones are selected as prototypes for our research. Direct numerical simulation (DNS) method is used to study the stability, transition and turbulence of the boundary layers, and the BL turbulence model has also been used to compute the turbulent boundary layers. The main conclusions obtained are as follows:
1. The laminar basic flow of the boundary layer of a sharp cone with small angle of attack is calculated by a simplified perturbation method. Through the comparison of the evolution of disturbances obtained by DNS with that obtained by linear stability theory (LST), the reliability of the method is confirmed.
2. Through the numerical study and the subsequent analysis of the transition process in the boundary layer of a hypersonic sharp cone with zero angle of attack and oncoming Mach number 6, similar conclusions, in regard with the mechanism of transition, has been found as for the transition in boundary layers on flat plates, i.e., the rapid change of the stability characteristics of the mean flow profile is the inherent mechanism for the breakdown in the transition, and in which the first mode unstable waves play the key role.
3. Through the DNS of supersonic turbulent boundary layers on a blunt cone, it is found that, the near-wall law of the mean velocity, under Van Driest transformation, and the similarity of the mean profiles are not influenced by the cone effect, while the mean temperature of the turbulent boundary layers is higher and the compressibility effect is weaker than those for flat plates. The distribution of the Reynolds stresses, the correlation of the fluctuations of turbulent quantities and the budget of turbulent kinetic energy in the turbulent boundary layers of a blunt cone are similar, in tendency, with those for boundary layers on flat plates, and the influence of cone effect is only of quantitative nature.
4. Through the comparison between the results obtained by BL turbulence model and the DNS, it is found that the wall friction coefficient obtained by both methods agree well with each other, while the thermodynamic variables do not. The near wall Van Driest transformed velocity profile agrees well with the near-wall law in incompressible turbulent boundary layers, while for other places, there are certain differences between the mean flow profiles obtained by DNS and BL model. In addition, the method proposed in the BL model for predicting the transition is found to be inapplicable for vehicles flying at high altitude, because its parameters seem to be determined by conventional wind tunnel experiments, for which the background disturbances is relatively high.
5. By analyzing the result of DNS, it is found that the assumption of a constant turbulent Prandl number in the BL model is the main cause for its incorrect prediction of the thermodynamic variables. Modification is accordingly proposed, and the result is satisfactory.
引文
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