ISOSURFACE-BASED POPULATION AND SHAPE ANALYSIS OF 3 D VORTICES
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摘要: 涡旋是紊流的基本结构, 被誉为流体运动的肌腱, 涡旋研究对自然探索和工程应用有重要的意义. 基于直接数值模拟的槽道紊流数据与旋转强度涡旋识别方法, 以涡旋三维结构等值面体(以三角网格为单位)为研究对象, 通过设置三角形切面, 利用两三角形相交快速检测算法提取涡旋多边形, 研究不同等值面体阈值及壁面距离条件下, 涡旋数量与形状特征(圆度、半径、凸状及纵横比因子)的变化规律. 以对数区内涡旋为例: 随着阈值的增加, 涡旋密度呈对数律快速递减, 圆度与半径因子PDF变高耸, 圆度均值快速递增后保持不变而半径均值不断递减, 纵横比因子PDF未显著改变且均值基本不变, 凸状因子PDF向脉冲函数靠近, 说明阈值增大导致涡旋逐渐变少、变圆、变小并更饱满. 在同一阈值下, 随着壁面距离的增加, 涡旋密度在外区(除靠近水面区域外)也呈对数律递减, 圆度、纵横比及凸状因子先快速增加随后不变或缓慢增长, 半径因子快速递减后保持不变, 说明涡旋在远离壁面的过程中在不断破灭但形态却较为稳定.Abstract: Vortex is the elementary structure in turbulence and is known as the 'sinews' of fluid motion. Vortex research is of great significance for natural exploration and engineering applications. The swirling strength method is used to extract vortices embedded inside the direct numerical simulation flow field, and the isosurface of 3D vortices was constructed at a certain isovalue. Based on the fast triangle-triangle intersection method, lines of intersection between the triangular mesh of the isosurface of 3D vortex structures and a triangular cutting plane were extracted, and among which vortices were identified as polygons by the property of closed cutting edge. Under the condition of different isovalues in the plane of the log layer and different wall distances from the cutting plane to the bed, variation trends of population and shape factors (circularity, radius, convexity and aspect ratio) of vortices in the cutting plane were studied. Results show that in the cutting plane of the log layer as the isovalue increases, the extracted vortices gradually become fewer, more circular, smaller, and rounder: the vortex population rapidly decreases in a logarithmic law; PDF curves of circularity and radius become taller and thinner, and the mean value of circularity rapidly increases to a stable stage while that of radius decreases monotonously; PDF curves of aspect ratio do not have significant change and its mean value remains essentially unchanged; PDF curves of convexity approximate the impulse function. As the wall distance increases vortices at certain swirling strength threshold continuously vanish while their shapes are relatively stable: vortex population in the outer region except the region near the water surface decreases in a logarithmic law; mean values of shape factors (circularity, aspect ratio, and convexity) first rapidly increase and then remain constant or increase slowly; mean value of radius rapidly decreases and then remains constant.
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Key words:
- isosurface /
- vortex /
- population /
- shape factor /
- isovalue /
- wall distance
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图 1 涡旋等值面体与三角形切面
Figure 1. 3D vortex structure indicated by isosurface of swirling strength and a triangular cutting plane
图 3 本文结果与前人结果涡旋半径PDF对比图(y + = 110平面, 样本数量9423250)
Figure 3. Comparison on PDF of vortex radius between this study and previous study (y + = 110)
图 4 阈值对涡旋提取密度的影响(y + = 110平面)
Figure 4. Influence of threshold on the number of extracted vortices (y + = 110)
图 5 阈值对涡旋形状因子概率函数PDF及CDF的影响(y + = 110平面)
Figure 5. Influence of threshold on PDFs and CDFs of vortex shape factors (y + = 110)
图 6 阈值对涡旋形状因子均值的影响(y + = 110平面)
Figure 6. Influence of threshold on mean values of vortex shape factors (y + = 110)
图 7 固定阈值($ \lambda _{ci}^ + = 0.04 $)与各zx平面内旋转强度最大值($ \lambda _{ci}^{\max}\left( y \right) $)的比值
Figure 7. ratio of fixed threshold ($ \lambda _{ci}^ + = 0.04 $) to the maximum swirling strength in each zx-plane ($ \lambda _{ci}^{\max}\left( y \right) $)
图 8 壁面距离对涡旋提取密度的影响
Figure 8. Influence of wall distance on the number of extracted vortices
图 9 壁面距离对涡旋形状因子概率函数PDF及CDF的影响
Figure 9. Influence of wall distance on PDFs and CDFs of vortex shape factors
图 10 壁面距离对涡旋形状因子均值的影响
Figure 10. Influence of wall distance on mean values of vortex shape factors
表 1 DNS槽道紊流计算参数
Table 1. Parameters of the DNS channel flow dataset
Mesh spacing Grid points Sample
numberΔx + Δz + Δyc + Nx Nz Ny Ns 3.8* 3.8 7.6 6144* 2304 385 48 *注: 为避免网格分辨率不均匀性对涡旋识别产生影响, 将原x方向分辨率从7.6 + 插值到3.8 + . 
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