Numerical Simulation on the Scalar Transport in Rotating Channel Turbulence
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摘要: 展向旋转槽道湍流中的标量场输运过程是与众多工程流动直接相关的模型问题。基于直接数值模拟工作对该问题开展系统性的研究。由壁面摩擦速度定义的流动Reynolds数固定在180, 重点考察Schmidt数和旋转数的影响。结果表明, 较弱旋转强度即可对主导流动结构形态产生明显的影响: 此时槽道不稳定侧产生流向大尺度结构, 由此导致标量场出现条带状结构。强旋转时不稳定侧出现被湍流充分混合的区域, 而在稳定侧流动层流化并出现近似传导区。平均标量剖面在湍流区和层流区呈现斜率不同的线性分布。Schmidt数小于1时, 湍流区标量场脉动和湍流输运随旋转数出现非单调变化, 而Schmidt数大于等于1时两者都随旋转数单调下降。由此导致总标量传输率在Schmidt数小于1时随旋转数先上升后下降, 而当Schmidt数大于1时单调下降且在弱旋转区域下降趋势最快。Abstract: Passive scalar transport in channel turbulence with spanwise rotation is of relevance to many engineering applications. A systematical study on this problem was conducted based on direct numerical simulations. The Reynolds number defined by wall-friction velocity was fixed at 180, and the influences of the Schmidt and rotation numbers were investigated. Results reveal that even a weak rotation can have strong effects on the dominant flow structures: streamwise long streaks appear in scalar field at the unstable side due to the development of large scale streamwise rolls in the momentum field. With strong rotation, there exists a well mixed turbulent region at the unstable side, and a conductive region with near laminar flow at the stable side. The mean scalar profiles are linear in both the turbulent and conductive regions with different slopes. When the Schmidt number is smaller than unity, both the scalar fluctuation and convective transport in the turbulent region show nonmonotonic variations with rotation number, while they monotonically decrease for Schmidt number equal to or larger than unity. Therefore, for Schmidt number smaller than unity, the total flux first increases and then decreases as the rotation becomes faster. But the total flux decreases with the rotation speed when the Schmidt number is equal to or larger than unity, and it decreases fastest at small rotation speeds.
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图 2 不同Schmidt数和旋转数流场z-y截面上瞬时标量场分布云图
Figure 2. Contour of instantaneous scalar fields for different Schmidt and rotation numbers on an arbitrary z-y cross-section
图 3 不同Schmidt数和旋转数流场中y=-0.5水平截面上瞬时标量场云图
Figure 3. Contour of instantaneous scalar fields at the horizontal plane y=-0.5 for different Schmidt and rotation numbers
图 4 不同旋转数时平均流向速度和平均标量场剖面(曲线颜色从蓝到红代表旋转数的增加)
Figure 4. Mean profiles of streamwise velocity and scalar for different rotation numbers (curve color from blue to red represents an increase in rotation number)
图 5 不同旋转数时标量场标准差剖面(曲线颜色从蓝到红代表旋转数的增加)
Figure 5. Profiles of standard deviation of scalar for different rotation numbers (curve color from blue to red represents an increase in rotation number)
图 6 不同旋转数时＜u′c′＞剖面(曲线颜色从蓝到红代表旋转数的增加)
Figure 6. Profiles of < u′c′ > for different rotation numbers (curve color from blue to red represents an increase in rotation number)
图 7 不同旋转数时＜v′c′＞剖面(曲线颜色从蓝到红代表旋转数的增加)
Figure 7. Profiles of < v′c′ > for different rotation numbers (curve color from blue to red represents an increase in rotation number)
表 1 数值模拟设置
Table 1. Setting of numerical simulations
Sc Roτ Lx Nx Ny mx my 0.1 0~80 16 240~288 240~288 1 1 1 0~100 16 320~384 160~288 1 1 4 0~60 8 240~288 240~288 2 2 10 0~60 8 240~288 240~288 4 2 
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