Effect of rectangular nozzle exit aspect ratioon flow field and acoustic field
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摘要: 为探究矩形喷管出口宽高比对喷流流场和声场的影响规律，采用DES/FW–H混合算法对出口宽高比为3和1.5的矩形喷管超声速完全膨胀喷流开展研究，分析出口宽高比对喷流流动与噪声的影响。针对多个流场变量进行对比分析，以验证数值模拟方法的可行性，发现喷管出口宽高比不同，靠近出口内壁面上的压力变化也有所不同：喷管出口宽高比越大，压力变化越快。结合已有噪声实验数据和计算数据，验证了噪声模拟的准确性。对不同出口宽高比下剪切层厚度的变化进行了分析，研究了这种变化对喷流噪声的影响，发现随着宽高比增大，剪切层厚度增大，且剪切层快速扩张位置和高频噪声源位置向上游方向移动。对比了不同宽高比下出口唇线上特定频率噪声的相速度，研究发现：喷管宽高比不同，同样频率的近场噪声有着不同的相速度，这决定了近场噪声向下游传播的最大角度；相速度对应的马赫角越大，近场噪声向下游传播的最大角度越大；宽高比增大，长轴唇线上的相速度显著降低，近场噪声向下游的辐射角度减小。Abstract: To investigate the influence of the aspect ratio on the flow field and acoustic field of a rectangular nozzle, study has been conducted using DES/FW–H hybrid algorithm on two different aspect ratios of rectangular supersonic fully expanded jet nozzles. The influence of the aspect ratio on flow dynamics and noise of the jet has been analyzed. Firstly, multiple flow field variables were compared and analyzed to verify the feasibility of numerical simulation methods. Differences were observed in the pressure changes on the inner wall surface near the outlet for different aspect ratios, with the larger aspect ratio exhibiting faster pressure changes. Also, it was found that the velocity decreases more rapidly with distance from the outlet on the short axis of the lip, while on the long axis of the lip, the velocity decreases slowly. Next, relating the aspect ratio of the nozzle exit to the jet noise field, and comparing existing noise experimental data with computed data, it was found that in all angles, the maximum difference between the experimental and computed total sound pressure level was 2.6 dB (AR = 3) and 4 dB (AR = 1.5). Increasing the aspect ratio could reduce the total sound pressure level upstream. Furthermore, changes in the shear layer thickness under different aspect ratios were analyzed, and the impact of these changes on the jet noise was studied. The results reveal that increasing the aspect ratio would increase the shear layer thickness and shift the rapid expansion location of the shear layer and high-frequency noise sources upstream. Finally, the phase velocities of specific frequency noise at the lip of the exit were compared for different aspect ratios, revealing a significant reduction in the phase velocity along the long axis of the exit lip with increasing aspect ratio, which affects the angle of the near-field noise radiation.
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图 1 不同宽高比的矩形喷管模型
Figure 1. Different aspect ratio rectangular nozzles corresponding to models
图 3 宽高比为1.5的喷管垂直于y轴截面上的网格及垂直于x轴截面上的网格
Figure 3. Grids on the section perpendicular to the y-axis and the section perpendicular to the x-axis of the nozzle with aspect ratio of 1.5
图 4 沿中心轴的时均流向速度变化
Figure 4. Time-averaged flow velocity variation along the center axis
图 5 喷管内壁短轴平面与壁面交线上的压力分布
Figure 5. Pressure distribution on the intersection between the short-axis plane and the nozzle inner wall surface
图 6 垂直于流向的截面上沿短轴和长轴分布的时均流向速度
Figure 6. Time-averaged flow velocity variation along the short and long axes on the cross-section perpendicular to the flow direction
图 7 喷管出口唇线上的时均流向速度变化曲线
Figure 7. The time-averaged flow velocity variation curve on the nozzle exit lip line
图 8 喷管出口附近长短轴平面上的湍动能云图
Figure 8. Turbulence kinetic energy contour map on the plane of the short and long axes near the nozzle exit
图 9 喷管长短轴唇线上的湍动能变化曲线
Figure 9. The turbulence kinetic energy variation curve on the nozzle lip line along the short and long axes
图 10 速度散度云图（灰色）与密度梯度云图（彩色）的叠加
Figure 10. Overlay of velocity divergence contour map (in gray) and density gradient contour map (in color)
图 11 不同监测角的声压级频谱对比（对相邻声压级频谱附加20 dB）
Figure 11. Comparison of sound pressure level spectra at different viewing angles (with an additional 20 dB added to adjacent sound pressure level spectra)
图 12 喷流噪声总声压级随监测点角度的变化曲线对比
Figure 12. Comparison of the total sound pressure level versus angle for jet noise
图 13 剪切层涡厚度沿流向的变化曲线
Figure 13. The variation curve of shear layer vortex thickness along the flow direction
图 14 长轴和短轴平面上的总声压云图
Figure 14. Total sound pressure contour maps on the plane of the long and short axes
图 15 长轴和短轴唇线上的的近场噪声频谱
Figure 15. Near-field noise spectrum on the lip line of the long and short axes
图 16 长轴和短轴唇线上不同频率噪声的相位随距离的变化
Figure 16. Phase variation of noise at different frequencies along the distance on the lip line of the long and short axes
图 17 长轴和短轴平面上的压力梯度云图
Figure 17. Pressure gradient map on the long and short axis plane
表 1 两种矩形喷管的几何参数（单位：mm）
Table 1. Two geometric parameters of rectangular nozzles (unit: mm)
出口
宽高比入口
半径喉道宽/高 出口宽/高 收缩段
长度扩张段
长度3 101 82.98/21.26 82.98/27.66 200 35 1.5 101 58.68/31.62 58.68/39.12 200 35 
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表 2 喷管出口下游4个外部块的网格参数
Table 2. Grid parameters of the four external blocks downstream of the nozzle outlet
外部块 网格参数 网格数目（x向, r向, Φ向） （357, 173, 91/61） 网格点数量 24 × 106 喷管出口处的$ \Delta x/D $ 0.0148 剪切层中最小的$ \Delta r/D $ 0.001 最高Sr数 4
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表 3 完全膨胀喷流的工况设置
Table 3. Configuration settings for fully expanded jet flows
编号 RA RNP RTT Maj Case 1 3 4.65 1 1.66 Case 2 1.5 4.65 1 1.66
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表 4 长轴和短轴唇线上不同频率噪声的统计数据
Table 4. Statistical data of noise at different frequencies on the lip line of the long and short axes
Sr RA 长轴/短轴 $ \omega $ k up/c0 0.318 3 L 3.32 2.65 1.25 0.318 3 S 3.32 1.78 1.87 0.318 1.5 L 3.32 1.95 1.69 0.318 1.5 S 3.32 1.84 1.80 0.636 3 L 6.64 5.18 1.28 0.636 3 S 6.64 4.12 1.61 0.636 1.5 L 6.64 4.19 1.58 0.636 1.5 S 6.64 3.52 1.89
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