关艺璞　周益娴　陈相　张家博

摘要：研究颗粒流的运动规律对核安全学科有重要意义。目前颗粒流的数值模拟方法主要是离散元法。该方法的弊端是计算速度慢。近年来，通过对大量实验和离散元模拟结果进行无量纲分析后，科学家得出了颗粒物质的本构理论，本质上是将颗粒物质看成带有摩擦性质的非牛顿流体。该方法与离散元方法相比能够大大降低运算时间，本文主要研究基于上述本构理论的三维计算在筒仓卸载构型中的适用性。结果表明，出口为矩形情况下，类似二维筒仓（quasi 2D）和二维（2D）筒仓卸载出口流量完全吻合，该三维计算模型得到了验证。且流量满足二维Beverloo关系式。另外，出口为圆形的情况下，流量满足三维Beverloo关系式。证明了该局部本构理论在筒仓卸载三维构型中仍适用。

关键词：颗粒物质 本构理论 流量 筒仓卸载

Study of the Discharge Flow of Granular Media from a Three Dimensional Silo Based on the Local Constitutive Law

GUAN Yipu1 ZHOU Yixian1* CHEN Xiang1 ZHANG Jiabo1

（1. Beijing Key Laboratory of Passive Safety Technology for Nuclear Energy， North China Electric Power University， Beijing， 102206 China）

Abstract： The study of the motion of granular flow is important for nuclear safety. The current simulation method to study granular flow is mainly discrete element simulation. The computational cost of this discrete element method simulation is high. In recent years， by conducting a dimensionless analysis of a large number of experiments and discrete element simulation results， scientists have derived the constitutive law of granular matter， which essentially treats the granular matter as a non-Newtonian fluid with frictional properties. Comparing with the discrete element method， this constitutive law can greatly reduce the calculation time. This work studies the applicability of the three-dimensional simulation based on the constitutive law in the configuration of the discharge of silo. The results show that when the outlet is rectangular， the discharge flow rate of a quasi two-dimensional silo and a real two-dimensional silo are completely consistent. Thus， the three-dimensional simulation model has been verified. And the two-dimensional Beverloo law has been recovered. In addition， when the outlet is circular， the three-dimensional Beverloo law has also been recovered. This demonstrates the applicability of the local constitutive law in the three-dimensional configuration of silo discharge.

Key Words： Granular media; Constitutive law; Flow rate; Discharge of silo

0 引言

反應性事故发生后，核燃料棒可能会在侧面产生破口，并且核燃料物发生破损后形成颗粒状碎片，它们将从容器内泄漏出来与冷却水发生剧烈反应。这些颗粒物质的动量将对其与冷却剂碰撞后果产生影响，因此研究颗粒流的运动规律对核安全有重要意义。颗粒物在筒仓中的流动是与核事故发生后颗粒物质流动最为接近的场景。实验证明，当筒仓高度和宽度足够大时，与普通流体不同，颗粒物卸载的流量总是保持恒定。沙漏流这一特性至今还没有准确的物理解释。目前颗粒流的数值模拟方法主要是离散元法。……