任意解流流固耦合数值方法及在砂土渗流分析中应用

王胤; 陶奕辰; 程旷; 杨庆

doi:10.11779/CJGE202111015

任意解流流固耦合数值方法及在砂土渗流分析中应用 English Version

王胤^1,,
陶奕辰¹,
程旷¹,
杨庆¹

大连理工大学海岸和近海工程国家重点实验室,辽宁　大连　116024

基金项目:

国家自然科学基金项目 51879035

国家自然科学基金项目 51890912

详细信息

作者简介:
王胤(1982— ),男,教授,博士生导师,主要从事海洋土力学、海洋结构基础及相关岩土数值方法方面的教学和科研工作。E-mail：y.wang@dlut.edu.cn

中图分类号: TU43
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出版历程
- 收稿日期: 2020-12-24
- 网络出版日期: 2022-12-01
- 刊出日期: 2021-10-31

Arbitrary resolved-unresolved CFD-DEM coupling method and its application to seepage flow analysis in sandy soil

State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China

摘要

摘要: 基于欧拉-拉格朗日连续体与非连续体耦合理论进行岩土工程流固耦合问题分析是一种较新颖和盛行的方法。针对该理论下的全解流（Fully-resolved）耦合与非解流（Un-resolved）耦合方法各自的缺陷,在已有的半解流（Semi-resolved）流固耦合数值方法（将全解流与非解流联合）基础上,通过引入修正的高斯权函数,建立了新的任意解流流固耦合方法（Arbitrary Resolved-Unresolved CFD-DEM coupling method）。该任意解流流固耦合方法能够较好地解决全解流方法中由于对粗颗粒周围流场精细化所带来的计算量过大问题；同时,成功地解决了流体网格内细颗粒较大时无法获得局部平均化变量问题；因此,该方法能够对具有一定粒径级配砂土土体的流固耦合问题开展模拟分析。通过室内砂土向上渗流试验,对所建立的任意解流流固耦合方法的准确性和有效性进行了验证；进一步地,采用该任意解流流固耦合模型,从细观层面上分析和研究了砂土渗流过程中水力梯度、土体变形随渗流速度变化规律。建立的任意解流流固耦合方法能够为岩土工程土体渗流问题的研究提供新的方法和手段。
- 流固耦合 /
- 砂土渗流 /
- 土颗粒 /
- 拖曳力 /
- 孔隙率
Abstract: The Euler-Lagrange coupling scheme based on the continuous and discrete theories has been becoming increasingly popular in numerical analysis of fluid-particle interaction. In this study, by introducing the modified Gaussian weighting function, a new arbitrary resolved-unresolved CFD-DEM coupling method (ARU CFD-DEM) is proposed based on the authors’ previous developed semi-resolved coupling approach by combing the fully-resolved and un-resolved coupling methods. This ARU CFD-DEM method is powerful to relieve the overload in computation due to refining the flow field around the coarse particles in the fully-resolving method. At the same time, it is also able to solve the difficulty in computing the local averaging variables when fine particles with large diameter exist in fluid grids. By doing so, the ARU CFD-DEM is able to simulate the fluid-particle interaction in sand mass which contains a wide range of particle diameters. By comparing with the results of upward seepage flow tests in sand, the accuracy and effectiveness of ARU CFD-DEM model is verified. Furthermore, the hydraulic gradient-flow velocity relationship and soil deformation-flow velocity relationship in the upward seepage flow are analyzed on the particle-scale by the ARU CFD-DEM. The proposed ARU CFD-DEM model can provide a new tool for investigating the fluid-particle interaction in the seepage flow in geotechnical engineering.
- CFD-DEM coupling /
- seepage flow /
- sand particles /
- drag force /
- void fraction

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图 1 高斯权函数支撑域示意图

Figure 1. Diagram of supporting domain of Gaussian-based weighting function

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图 2 任意解流耦合数值求解流程图

Figure 2. Flow chart of numerical solution of ARU CFD-DEM coupling

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图 3 基准渗流模型及边界条件

Figure 3. CFD-DEM model for benchmark of seepage flow

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图 4 全解流与任意解流用时对比

Figure 4. Comparison in CPU time between full resolved and ARU method

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图 5 向上渗流试验布置图

Figure 5. Set-up of upward seepage tests

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图 6 向上渗流数值模型及边界条件

Figure 6. CFD-DEM model of seepage tests

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图 7 水力梯度、滤层变形随表观渗流速度变化关系

Figure 7. Relationship between hydraulic gradient and coarse-particle layer deformation with superficial flow velocity

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图 8 不同阶段粗颗粒滤层变形随表观渗流速度变化情况

Figure 8. Evolution of coarse-particle layer deformation with superficial flow velocity

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图 9 土层孔隙率分布随表观渗流速度变化情况（粗细颗粒粒径比α_s=6.7）

Figure 9. Evolution of porosity profile with superficial flow velocity (diameter ratio, α_s=6.7)

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图 10 土基颗粒力链分布随表观渗流速度变化情况（粗细颗粒_.粒径比α_s=6.7）

Figure 10. Evolution of force chain in fine-particle layer with superficial flow velocity (diameter ratio, α_s=6.7)

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表 1 基准渗流模拟所采用材料属性

Table 1 Material properties in the benchmark of seepage flow

颗粒属性						流体属性
颗粒密度ρ_s/(kg·m^-3)	滑动摩擦系数μ_r	杨氏模量E/Pa	回弹系数e	泊松比 $ν$ $ν$	滚动摩擦系数μ_f	密度ρ_f/(kg·m^-3)	动力黏度μ_f/(kg·m^-1·s^-1)
2650	0.84	2×10⁷	0.9	0.2	0.26	1000	1×10^-3

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表 2 基准渗流模拟相关设置

Table 2 Computational settings in the benchmark of seepage flow

计算设置		任意解流设置		全解流设置
DEM时间步长Δt_DEM/s	CFD时间步长Δt_CFD/s	流体网格尺寸L_m/mm	高斯权函数带宽b_w/mm	流体网格尺寸L_m/mm
2×10^-5	2×10^-4	1.32, 0.8, 0.5	8.0	0.5

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表 3 滤层-土基数值模型中的颗粒属性

Table 3 Material properties in numerical simulations of seepage test

参数	数值	参数	数值
砂颗粒密度ρ_s/(kg·m^-3)	2650	玻璃-玻璃滑动摩擦μ_{s_gg}	0.1545
玻璃珠密度ρ_g/(kg·m^-3)	2450	砂-玻璃滑动摩擦μ_{s_sg}	0.3
砂颗粒杨氏模量E_s/Pa	2×10¹⁰	砂-砂滚动摩擦μ_{r_ss}	0.26
玻璃珠杨氏模量E_g/Pa	5×10¹⁰	玻璃-玻璃滚动摩擦μ_{r_gg}	0.045
砂颗粒泊松比 $ν_{s}$ $ν_{s}$	0.2	砂-玻璃滚动摩擦μ_{r_sg}	0.1
玻璃珠泊松比 $ν_{g}$ $ν_{g}$	0.25	砂颗粒回弹系数e_s	0.9
砂-砂滑动摩擦μ_{s_ss}	0.84	玻璃珠回弹系数e_g	0.9

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表 4 滤层-土基数值模型中的流体属性

Table 4 Computational settings in numerical simulations of seepage test

密度ρ_f/(kg·m^-3)	动力黏度μ_f/(kg·m^-1·s^-1)	DEM时间步长Δt_DEM/s
1000	1×10^-3	2×10^-5

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表 5 滤层-土基数值模型中的计算设置

Table 5 Computational settings in numerical simulations of seepage test

CFD时间步长Δt_CFD/s	流体网格尺寸L_m/mm	高斯权函数带宽b_w/mm
2×10^-4	1, 0.5	3.0

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