A PRIOR INVESTIGATION ON HEAVY PARTICLES’ MOVEMENT IN COMPRESSIBLE HOMOGENOUS ISOTROPIC TURBULENCE
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摘要:本研究以高精度可压缩均匀各向同性湍流直接数值模拟数据为基础, 通过点粒子模型和单向耦合方式模拟了100万个重粒子在湍流中的运动. 着重进行了两方面的研究, 首先, 通过使用不同滤波宽度的谱截断滤波器来获得大尺度流场, 并研究了不同滤波尺度对粒子运动的影响; 其次, 设置了5种不同的粒子初速度, 以研究粒子聚集性和运动学性质的演化. 在研究粒子聚集性方面, 使用了香农熵来描述粒子的瞬时聚集性, 而稳态时的统计结果则通过概率密度分布函数来描述. 研究结果表明, 滤波尺度对不同Stokes数的粒子聚集效应产生不同的影响. 具体而言, 小尺度流动结构对低Stokes数的粒子聚集性有促进作用, 而对高 Stokes数的粒子聚集性则有抑制作用. 此外, 随着Stokes数的增加和截断波数的减小, 粒子的速度和加速度的概率密度分布变得更为集中. 另外, 还发现颗粒的初始速度差异会在演化的初期产生明显影响, 最终会趋于相同的统计定常状态. 这一发现强调了湍流中粒子运动的复杂性和统计特性的重要性.Abstract:The main objective of this study is to simulate the motion of one million heavy particles in turbulence using a point particle model and one-way coupling, based on high-precision compressible homogenous isotropic turbulence direct numerical simulation data. This work focuses on two aspects. Firstly, it uses spectral truncation filters with different filter widths to obtain large-scale flow fields and investigates the influence of different filter scales on particle motion. Secondly, this study sets five different initial particle velocities to investigate the evolution of particle clustering and kinematic properties. In the study of particle clustering, Shannon entropy is used to describe the instantaneous clustering of particles, while statistical results in the steady state are described using probability density distribution functions. The results show that the filter scale has different effects on particle clustering for different Stokes numbers. Specifically, small-scale flow structures promote particle clustering for low Stokes numbers, while they inhibit clustering for high Stokes numbers. Additionally, with increasing Stokes numbers and decreasing truncation wavenumbers, the probability density distribution of particle velocity and acceleration becomes more concentrated. Furthermore, this work also finds that differences in initial particle velocities have a significant impact in the early stages of evolution but eventually converge to the same statistical steady state. This discovery emphasizes the complexity of particle motion in turbulence and the importance of statistical characteristics.
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Key words:
- turbulence/
- heavy particles/
- turbulent scale
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图 1图中的黑点表示粒子位置
Figure 1.Contour of (a) and (b) nondimensional vorticity. Here, the back points indicate the location of the particles
图 2一个随机选择的粒子在流动中的路径. 初始速度采用I.C.4
Figure 2.Path of a randomly selected particle. Here, the initial velocity is I.C.4
图 3流动能量谱$ E\left(k\right) $(实线), 和5个不同的截断波数(虚线). 从左到右分别是${k_{{\rm{max}}}}/{k_c} = 2,4,8,16,32$
Figure 3.Flow energy spectrum $ E\left(k\right) $(solid line) and five different cut-off wavenumbers (dashed line). From left to right, they are ${k_{{\rm{max}}}}/{k_c} = 2,4,8,16,32$, respectively
图 4$S(t)$随着时间的演化. 初始速度采用I.C.2
Figure 4.$S(t)$ as a function of time. Initial velocity is I.C.2
图 8粒子数平均速度随时间的演化. 驱动流场采用${k_{{\rm{max}}}}/{k_c} = 4$
Figure 8.Averaged particle velocity as a function of time. Flow field is filtered by ${k_{{\rm{max}}}}/{k_c} = 4$
图 9$S(t)$随时间的演化. 驱动流场采用${k_{{\rm{max}}}}/{k_c} = 4$
Figure 9.$S(t)$ as a function of time. Flow field is filtered by ${k_{{\rm{max}}}}/{k_c} = 4$
图 10与图 9相同, 但驱动流场采用${k_{{\rm{max}}}}/{k_c} = 16$
Figure 10.Same as Fig. 9, but the flow field is filtered by ${k_{{\rm{max}}}}/{k_c} = 16$
表 1粒子的初始速度条件.
Table 1.Initial velocity of particles.
Names Initial velocity/${v_{p,i}} $ I.C.1 $0.0$ I.C.2 $0.1{u_{{\rm{rms}}} }$ I.C.3 $0.5{u_{{\rm{rms}}} }$ I.C.4 $1.0{u_{{\rm{rms}}} }$ I.C.5 $u\left( { {x_{p,i} } } \right)$ 
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