筒仓卸料的非局部颗粒流体连续介质模型比较：迈向堵塞预测
Comparing non-local granular fluid continuum models for silo discharge: Toward clogging prediction
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中文总结 AI 辅助
该研究在Basilisk平台上通过二维有限体积法模拟筒仓卸料，系统比较非局部颗粒流体连续介质模型，评估堵塞概率，发现模型间卸料率预测存在定量差异，开源实现计算高效。
中文摘要 AI 辅助
非局部本构理论在颗粒流的连续介质描述中受到越来越多的关注。然而，这些模型尚未在统一的数值框架内针对筒仓卸料进行系统比较。我们通过Basilisk平台开展的二维有限体积法（FVM）筒仓卸料模拟解决了这一空白。首先，我们将动态非局部颗粒流动性（NGF）模型的FVM实现与Dunatunga & Kamrin（《流体力学杂志》，2022年，第940卷，A14）的物质点法结果进行验证，获得了定量一致性。其次，我们将卸料率Q与出口-颗粒尺寸比D/d以及非局部振幅A相关联。随后，我们从模拟得到的Q中，在Janda等人（《欧洲物理快报》第84卷第4期，44002）的概率框架内评估堵塞概率J(D/d, A)。预测的J随D/d呈指数衰减，与Janda等人的实验趋势一致。我们的方法并非直接预测流动停滞，而是捕捉连续的概率转变。最后，在相同的数值框架内并使用相同的A值，我们比较了几种非局部本构模型，包括我们推导的若干线性化变体。几乎所有模型都预测卸料率随A增大而降低，但模型间存在显著的定量差异。结果根据其预测的流动行为进一步分组，揭示了某些公式之间的密切对应关系。值得注意的是，使用文献中报道的非局部振幅[Bouzid等人（《物理评论快报》第111卷，238301）、Henann & Kamrin（《美国国家科学院院刊》第110卷第17期）]会产生接近零的卸料率。我们还讨论了不适定性问题。所有模型的实现均为开源且计算高效。
英文摘要
Non-local constitutive theories have received increasing attention in continuum descriptions of granular flows. However, these models have not been systematically compared for silo discharge within a unified numerical framework. We address this gap with two-dimensional finite-volume method (FVM) simulations of silo discharge using the Basilisk platform. We first validate our FVM implementation of the dynamic non-local granular fluidity (NGF) model against the material point method results of Dunatunga & Kamrin (J. Fluid Mech., 2022, 940, A14), obtaining quantitative agreement. Second, we relate the discharge rate $Q$ to the outlet-to-particle size ratio $D/d$ and the non-local amplitude $A$. From the simulated $Q$, we then evaluate the clogging probability $J(D/d, A)$ within the probabilistic framework of Janda et al. (Europhys. Lett. 84 (4), 44002). The predicted $J$ decays exponentially with $D/d$, consistent with the experimental trend of Janda et al. (Europhys. Lett. 84 (4), 44002). Rather than directly predicting flow arrest, our approach captures the continuous probabilistic transition. Finally, within the same numerical framework and using identical values of $A$, we compare several non-local constitutive models, including several linearised variants that we derive. Almost all models predict a reduction in the discharge rate with increasing $A$, yet significant quantitative differences are observed among the models. The results are further classified into groups according to their predicted flow behaviour, revealing close correspondences among certain formulations. Notably, using the non-local amplitudes reported in the literature [Bouzid et al. (Phys. Rev. Lett. 111, 238301), Henann & Kamrin (Proc. Natl Acad. Sci. USA 110(17))] yields near-zero discharge rates. Ill-posed issues are discussed. The implementation of all models is open-sourced and computationally efficient.
