Effect of Particle Size Distribution on Collapse of Immersed Polydisperse Granular Columns
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摘要:
基于典型的颗粒柱坍塌试验，采用计算流体力学与离散单元法耦合的数值方法，系统探讨了以分形维数表征的粒径分布特征在不同流态下对颗粒柱坍塌过程的流动能力和能量演化的影响机制.结果表明：随着环境流体由空气逐步过渡至低粘度流体和高粘度流体，颗粒柱的运动距离相比干燥条件降低约40%，流动能力显著减弱；在自由下落态和惯性态中，不同分形维数系统的流动性差异仅约1%，而在粘性态中，较高分形维数的系统表现出明显的运动延迟且运动能力降低幅度达11%；并且这种差异被认为是细颗粒含量更多的系统更容易在高粘度流体中耗散能量引起的；利用渗透性测试方法发现，水下颗粒系统的运动能力主要受初始渗透性影响，渗透性越差运动能力越弱.
Abstract:In this study, a typical granular column collapse scenario is investigated using a numerical approach that couples computational fluid dynamics (CFD) with the discrete element method (DEM). Granular columns with varying fractal dimensions—used to characterize PSD—are simulated in different fluids to examine the influence of PSD on flow behavior and energy evolution across distinct flow regimes. The results show that as the ambient fluid gradually changes from air to low-viscosity fluid and then to high-viscosity fluid, the runout distance of the granular systems decreases by about 40% compared to dry conditions, and the mobility is significantly weakened. In free-fall and inertial regimes, the mobility difference between systems with different fractal dimensions is only about 1%, whereas in viscous regimes, the system with a higher fractal dimension shows a significant movement delay and the mobility is reduced by 11%. This reduced mobility can be attributed to the increased presence of fine particles, which enhance energy dissipation under low Stokes number conditions. Permeability tests further reveal that mobility is primarily governed by the initial permeability of the immersed granular system-lower permeability corresponds to reduced mobility.
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Key words:
- granular material /
- fractal dimension /
- submarine landslide /
- column collapse /
- permeability /
- engineering geology
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图 2 水下多分散颗粒柱坍塌计算模型
Fig. 2. Numerical model of immersed polydisperse granular column collapse
图 4 水下颗粒柱坍塌模拟与经典实验(Polanía et al., 2024)在3个典型时刻(T = tf/3, 2tf/3, tf)的沉积物轮廓对比
Fig. 4. Comparison of the height profiles of final deposit from immersed column collapse simulation with those in typical experiment (Polanía et al., 2024) at three typical times (T = tf /3, 2 tf /3, tf)
图 5 多分散颗粒柱在自由下落态(干燥)的坍塌过程对比
a.分形维数D=1.0；b.分形维数D=3.5
Fig. 5. Comparison of the collapse sequence of polydisperse granular columns in regime FF (dry)
图 6 多分散颗粒柱在惯性态的坍塌过程对比
a.分形维数D=1.0；b.分形维数D=3.5
Fig. 6. Comparison of the collapse sequence of polydisperse granular columns in regime I
图 7 多分散颗粒柱在粘性-惯性过渡态的坍塌过程对比
a.分形维数D=1.0；b.分形维数D=3.5
Fig. 7. Comparison of the collapse sequence of polydisperse granular columns in regime VI
图 8 多分散颗粒柱在粘性态的坍塌过程对比
a.分形维数D=1.0；b.分形维数D=3.5
Fig. 8. Comparison of the collapse sequence of polydisperse granular columns in regime V
图 9 多分散颗粒柱在不同流态内的流动前端随时间的变化曲线
Fig. 9. Normalized flow front position over time for the collapse of polydisperse granular column under various flow regimes
图 10 多分散颗粒柱的最终运动距离与斯托克斯数的关系
Fig. 10. Normalized runout distance as a function of St of polydisperse granular columns
图 11 不同流态下多分散颗粒柱坍塌过程的能量演化曲线(a); 不同分形维数试样在各流态下的能量耗散比例(b)
Fig. 11. Evolution of normalized energy for polydisperse granular column collapse in different flow regimes (a); energy dissipation ratio of samples with different fractal dimensions under different flow regimes (b)
图 12 不同流态内多分散颗粒系统在不同流速下的压降
Fig. 12. Pressure drop of a polydisperse granular system at various flow velocity in different flow regimes
图 13 多分散颗粒系统在不同流态内的渗透特性
Fig. 13. Permeability characteristics of polydisperse particle systems in different flow regimes
图 14 无量纲运动距离与修正斯托克斯数的关系
Fig. 14. Relationship between normalized runout distance and modified Stokes number
表 1 水下颗粒柱坍塌模拟的参数设置
Table 1. Physical parameters used in immersed granular column collapse
参数 值 流体密度ρf($ \mathrm{k}\mathrm{g}/{\mathrm{m}}^{3} $) 1 000 流体动力粘度μf$ (\mathrm{P}\mathrm{a}\cdot \mathrm{s}) $ 10-3, 10-2 分形维数D 1.0, 3.5 平均粒径dp(mm/mm) 4.9, 2.3 初始体积分数φ 0.667 颗粒密度ρp$ (\mathrm{k}\mathrm{g}/{\mathrm{m}}^{3}) $
颗粒杨氏模量$ (\mathrm{M}\mathrm{P}\mathrm{a} $)2 650
50颗粒泊松比υ 0.24 颗粒摩擦系数μp 0.4 颗粒恢复系数e 0.65 
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表 2 不同流态对应的颗粒粒径与流体动力粘度
Table 2. Particle size and fluid dynamic viscosity for different flow regimes
分形维数D 平均粒径dp
(mm)流体动力粘度
$ {\mu }_{\mathrm{f}} $ (Pa·s)斯托克斯数St 1.0 4.90 10-5 6 213.000 (FF) 3.5 2.30 10-5 1 998.000 (FF) 1.0 4.90 10-3 88.260 (I) 3.5 2.30 10-3 28.380 (I) 1.0 0.49 10-3 2.880 (VI) 3.5 0.23 10-3 0.730 (VI) 1.0 0.49 10-2 0.287 (V) 3.5 0.23 10-2 0.073 (V)
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