Stability and transition prediction of the hypersonic plate boundary layers for wall temperature distribution
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摘要: 针对来流马赫数为4.5、6.0和7.0的高超声速平板边界层，取30km高空处的气体参数，壁面为等温、绝热和温度分布等3种不同条件，采用eN方法进行转捩预测。其中，壁面温度分布条件下，在等温壁（冷壁）和绝热壁之间，给出4种流向分布进行分析。取扰动的初始幅值为0.3‰，以幅值达到1.5%作为转捩判断依据。结果表明：当温度为来流温度时，等温壁面条件的转捩位置最靠前，并随马赫数增大更加靠前；绝热壁面条件的转捩位置随马赫数增大而推后；壁面温度分布条件下，在相同时刻，马赫数越大，转捩位置越靠前。相同马赫数下，壁面温度较高者转捩位置较靠后（马赫数为7.0时，不完全满足此规律）。在马赫数为4.5和6.0时，绝热壁面条件转捩由第一模态主导，其余情况主导转捩的都是第二模态。Abstract: The transition prediction of the hypersonic boundary layer on a flat plate is investigated by using the eN method under three different wall conditions including the isothermal, adiabatic and wall temperature distribution conditions. The gas parameters are taken as the corresponding air parameters at the height of 30km with the incoming flow Mach numbers 4.5, 6.0 and 7.0. The calculation results are given and analyzed for four different cases of the wall temperature distribution. The initial disturbance amplitude is estimated to be 0.3‰. The transition is assumed to begin when the disturbance amplitude grows up to 1.5%. It can be seen that the transition location is most close to the leading edge in the case of the isothermal wall condition, and the transition location would move forward as the incoming flow Mach number increases. However, it would move backward as the incoming flow Mach number increases under the adiabatic wall condition. In the case of the wall temperature distribution condition, the transition location moves forward as the incoming flow Mach number increases. It is also found that the higher the wall temperature is, the further backward the transition location is (whereas, at Mach number 7.0, the result is different). In the adiabatic wall cases at the incoming flow Mach numbers 4.5 and 6.0, the transition locations are determined by the first mode waves, whereas the transition locations for the other cases are determined by the second mode waves.
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Key words:
- hypersonic /
- plate boundary layer /
- wall temperature distribution /
- eN method /
- transition
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图 1 两种计算方法得到的基本流比较
Figure 1. Comparison of the base flow computed by two different calculation methods
图 2 不同壁面温度条件下的温度分布曲线
Figure 2. Temperature profiles under different wall temperature conditions
图 3 不同壁面温度条件下的速度剖面
Figure 3. Velocity profiles under different wall temperature conditions
图 4 不同壁面温度条件下的温度剖面
Figure 4. Temperature profiles under different wall temperature conditions
图 5 不同壁面温度条件下的中性曲线
Figure 5. Neutral curves under different wall temperature conditions
图 6 壁面温度分布条件下不同时刻的中性曲线
Figure 6. Neutral curves at different times under different wall temperature conditions
图 7 不同壁面温度条件下增长率随频率的变化曲线
Figure 7. Variation of growth rate with frequency under different wall temperature conditions
图 8 不同壁面温度条件下的N值曲线
Figure 8. Envelope curves of N values under different wall temperature conditions
图 9 壁面温度分布条件下不同时刻的N值曲线
Figure 9. Envelope curves of N values at different times under different wall temperature conditions
图 10 两种基本流的N值曲线比较
Figure 10. Comparison of envelope curves of N values for two base flows
表 1 转捩位置预测(单位：m)
Table 1. Prediction results of transition locations (unit:m)
Isothermal 120s 300s 400s 600s Adiabatic Ma=4.5 1.4 2.9 － － － 2.5(1st) Ma=6.0 1.3 2.5 2.9 3.2 3.6 2.7(1st) Ma=7.0 1.2 2.4 3.1 3.0 2.9 2.9 注：“1st”表示由第一模态主导转捩，未加说明的皆由第二模态主导转捩；“－”表示在计算域内N值达不到4。 
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