DIRECT NUMERICAL SIMULATION OF DRAG REDUCTION IN TURBULENT BOUNDARY LAYERS CONTROLLED BY INCLINED BLOWING AND SUCKING
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摘要: 雷诺切应力是壁湍流高摩擦阻力的重要来源, 有理论认为可以通过壁面生成负雷诺应力(数值上为正)的方式来削弱湍流流场中雷诺应力的分布, 以此获得流动减阻. 而通过对雷诺平均运动方程的法向二次积分, 可以发现壁面生成正雷诺应力(数值上为负)对壁面摩擦阻力系数才有负贡献. 文中在湍流边界层流动的控制区域下边界设置一系列倾斜狭缝, 利用该装置通过周期性吹吸的方法产生壁面生成正(负)雷诺应力, 并采用直接数值模拟方法考察和验证上文提到的减阻理论. 文中采用的湍流边界层流动模型, 其流动雷诺数(基于外流速度及动量损失厚度)从300 发展到860. 文中通过多组数值模拟算例, 考察了射流强度和频率对壁面摩擦阻力系数的影响, 并对比了壁面生成正或负雷诺应力对流动的影响. 研究表明, 壁面生成正雷诺应力控制的减阻率能达到3.26, 而壁面生成负雷诺应力控制的减阻效果较壁面生成正雷诺应力控制的要差; 壁面生成的正雷诺应力对壁面摩擦阻力有负贡献, 而壁面生成的负雷诺应力对壁面摩擦阻力有正贡献; 通过考察控制的收支比, 发现控制方案不能获得能量净收益.Abstract: Reynolds shear stress (RSS) is an important source of high frictional resistance in wall turbulence. A theory suggests that the distribution of Reynolds shear stress in turbulent flow fields can be weakened through negative Reynolds stress (net positive) on walls in order to achieve drag reduction. However, integrals of the Reynolds−averaged Navier−Stokes equations indicate that the positive Reynolds stress (net negative) generated on a wall has a negative contribution to the skin friction coefficient of the wall. In this study, a series of inclined slits are being set up at the bottom of the control region for the turbulent boundary layer flow. Positive or negative wall Reynolds stress is generated by periodic blowing and sucking achieved by this device. Direct numerical simulation method is used to validate and explore the drag reduction theory described above. The turbulent boundary flow model used here has a Reynolds number (based on the outer flow velocity and momentum loss thickness) from 300 to 860. Through multiple sets of numerical simulations, the influences of jet strength and frequency on skin friction coefficient have been explored and the effects of positive and negative wall-generated Reynolds stress on the flow have been compared. Results show that the drag reduction rate associated with positive wall-generated Reynolds stress can reach 3.26, which is higher than that associated with negative Reynolds stress. It is concluded that the positive wall-generated Reynolds stress has a negative contribution to the skin friction, while the negative Reynolds stress has a positive contribution to the skin friction. Based on the gain-loss ratio, this control strategy is not able to obtain a net energy gain.
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图 4 摩擦阻力系数(
$C_{\rm{f}}$ )在壁面生成正雷诺应力控制下沿流向的分布Figure 4. Evolution of the skin friction coefficient in wall-generated positive RSS cases,
$C_{\rm{f}}$ 
图 5 壁面生成正雷诺应力的各算例在不同流向位置的平均雷诺应力分布对比
Figure 5. Profiles of the RSS at different streamwise locations
图 6 壁面生成正雷诺应力的各算例在流向不同位置的平均速度剖面的对比
Figure 6. Mean velocity profiles at different streamwise direction locations
图 7 壁面生成正雷诺应力的各算例在不同流向位置脉动量均方根
Figure 7. Profiles of the root mean square of
$u^\prime$ and$v^\prime$ at different streamwise locations
图 8
$ y^+ $ = 15平面的流向速度脉动云图Figure 8. Instantaneous of the streamwise velocity fluctuation
$ u^\prime $ at$ y^+ $ = 15
图 9
$C_{\rm{f}}$ 在壁面生成负雷诺应力控制下的沿程发展Figure 9. Evolution of the
$C_{\rm{f}}$ in wall-generated negative RSS cases
图 10 壁面生成负雷诺应力控制各算例在流向不同位置的平均速度(U)剖面对比
Figure 10. Profiles of mean streamwise velocity (U) in wall-generated negative RSS cases at different streamwise locations
图 11 壁面生成负雷诺应力的各算例在不同流向位置处的平均雷诺应力分布对比
Figure 11. Profiles of the mean RSS at different streamwise locations
图 12
$C_{\rm{f}}$ 及$C_{\rm{w}}$ 沿流向发展情况Figure 12. Evolution of
$C_{\rm{f}}$ and$C_{\rm{w}}$ in streamwise direction
图 13
$C_{\rm{f}}$ 各贡献项在流向的发展情况Figure 13. Streamwise evolution of the different terms on the right hand side of Eq. (3) for the no-control case and the control cases with same amplitude (
$ A_3$ ) and frequency ($\omega_3$ )
图 14 各算例边界层厚度沿流向的发展
Figure 14. Evolution of the boundary layer thickness (99% velocity thickness)
图 16 各算例控制算例沿程减阻率的变化
Figure 16. Evolution of the drag reduction rate in streamwise direction
图 17 各控制算例获得能量收支比的沿程发展情况
Figure 17. Evolution of the cost-effectiveness ratio (gain) in streamwise direction
表 1 算例参数表
Table 1. Setup of the input parameters
Case A & $\omega$ A $\omega$ $\alpha$ $\mid \left\langle { {u_{\rm{w}}} {v_{\rm{w}}} } \right\rangle \mid$$(\times 10^3)$ C13N (P) A1ω3 0.009 0.235 π/4 (3π/4) 0.02 C23N (P) A2ω3 0.025 0.235 π/4 (3π/4) 0.15 C31N (P) A3ω1 0.044 0.057 π/4 (3π/4) 0.48 C32N (P) A3ω2 0.044 0.094 π/4 (3π/4) 0.48 C33N (P) A3ω3 0.044 0.235 π/4 (3π/4) 0.48 C43N (P) A4ω3 0.058 0.235 π/4 (3π/4) 0.84 C53N (P) A5ω3 0.065 0.235 π/4 (3π/4) 1.06 uc A3ω3 0.044 0.235 ${\text{π}}$/2 0.00 vc A3ω3 0.044 0.235 0 0.00 NC − 0 0 − 0.00 
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