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基于人工神经网络的非均匀固相应力模型

吴雪岩 李煜 谢妍妍 李飞 陈昇

吴雪岩, 李煜, 谢妍妍, 李飞, 陈昇. 基于人工神经网络的非均匀固相应力模型. 力学学报, 待出版 doi: 10.6052/0459-1879-22-511
引用本文: 吴雪岩, 李煜, 谢妍妍, 李飞, 陈昇. 基于人工神经网络的非均匀固相应力模型. 力学学报, 待出版 doi: 10.6052/0459-1879-22-511
Wu Xueyan, Li Yu, Xie Yanyan, Li Fei, Chen Sheng. Research on heterogeneous solid stress model based on artificial neural network. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-22-511
Citation: Wu Xueyan, Li Yu, Xie Yanyan, Li Fei, Chen Sheng. Research on heterogeneous solid stress model based on artificial neural network. Chinese Journal of Theoretical and Applied Mechanics, in press doi: 10.6052/0459-1879-22-511

基于人工神经网络的非均匀固相应力模型

doi: 10.6052/0459-1879-22-511
基金项目: 国家自然科学基金(22161142006, 51876212, 22208379), 中国科学院多相复杂系统国家重点实验室(MPCS-2021-A-06)和中国特种设备检测研究院二级学科建设(2021XKTD004)资助项目
详细信息
    通讯作者:

    李飞, 副研究员, 主要研究方向: 多相流数值模拟. E-mail:lifei@ipe.ac.cn

  • 中图分类号: TQ021.1

RESEARCH ON HETEROGENEOUS SOLID STRESS MODEL BASED ON ARTIFICIAL NEURAL NETWORK

  • 摘要: 最小多尺度理论(Energy-Minimization Multi-Scale, EMMS)已经被引入多相质点网格法(multiphase particle-in-cell, MP-PIC)中, 建立了非均匀EMMS固相应力模型. 但现有的非均匀固相应力模型计算中, 中间步骤繁琐且花费时间长. 采用人工拟合的方式能获得非均匀固相应力表达式, 但需要人为确定拟合变量和拟合函数, 且针对于非均匀固相应力这种高度非线性函数所得到的拟合精度不高、用于MP-PIC模拟的结果相比原EMMS固相应力模型结果存在偏差. 针对上述问题, 本文提出通过机器学习的方法, 规避对固相体积分数的局部分布情况的表征, 并提出和建立能考虑颗粒浓度详细分布的人工神经网络(artificial neutral network, ANN)固相应力模型. 首先, 基于局部颗粒浓度和颗粒非均匀分布指数建立了双变量的ANN固相应力模型; 进一步将当前网格及其周边网格颗粒浓度组成的序列来详细表征颗粒浓度分布, 并建立相应的ANN固相应力模型. 然后, 将两种模型与EMMS固相应力模型进行了对比并测试了网格分辨率和粗化率对模型的影响. 研究表明: 基于ANN固相应力模型的模拟结果对EMMS固相应力模型结果有较高的还原度, 同时具有一定的网格分辨率无关性和粗化率无关性.

     

  • 图  1  反距离权重法计算网格颗粒非均匀分布指数的示意图(iji + iij + jj均为网格格点的编号, 其中ii, jj为−1或1)

    Figure  1.  Demonstration for predicting the heterogeneity index of particle concentration distribution of a cell (iji + ii and j + jj are the numbers of grid points, where ii, jj = −1 or 1)

    图  2  隐藏层神经元数对R2决定系数和MAE损失函数的影响(横坐标神经元的个数代表两层隐藏层所包含的全部神经元个数)

    Figure  2.  The effect of cell number for hidden layer on R2 coefficient of determination and MAE loss function (The number of neurons on the horizontal axis represents the total number of neurons contained in the two hidden layers)

    图  3  人工神经网络模型结构图

    Figure  3.  Structure diagram of artificial neural network model

    图  4  (a)人工拟合模型与EMMS固相应力模型的对比; (b) ANN model 1与EMMS固相应力模型的对比; (c) ANN model 2与EMMS固相应力模型的对比; (d)模型误差

    Figure  4.  (a) Comparison between the manually fitted model and EMMS solid stress model; (b) Comparison between the ANN model 1 and EMMS solid stress model; (c) Comparison between the ANN model 2 and model EMMS solid stress model;(d) Model errors

    图  5  不同非均匀固相应力模型预测的时均轴向空隙率分布与瞬时固相流率

    Figure  5.  Time-average axial void distribution and instantaneous solid flow rate predicted by stress models with different heterogeneous solids

    图  6  网格分辨率对时均轴向孔隙率分布的影响

    Figure  6.  Effect of grid resolution on time-average axial void distribution

    图  7  网格分辨率对径向时均孔隙率分布的影响

    Figure  7.  Effect of grid resolution on time-average radial voidage distribution

    图  8  粗化率对时均轴向孔隙率分布的影响(Grid: 20 × 200)

    Figure  8.  Effect of coarse-graining ratio on time-average axial voidage distribution (Grid: 20 × 200)

    图  9  粗化率对径向孔隙率分布的影响

    Figure  9.  Effect of coarse-graining ratio on time-average radial voidage distribution

    表  1  MP-PIC方法的控制方程和本构模型

    Table  1.   Governing equations and constitutive models of MP-PIC method

    DescriptionEquation
    Governing equations for gas phase$\begin{gathered}\dfrac{\partial }{\partial t}\left({\varepsilon }_{g}{\rho }_{g}\right) + \nabla \cdot \left({\varepsilon }_{g}{\rho }_{g}{u}_{g}\right) = 0\\ \dfrac{\partial }{\partial t}\left({\varepsilon }_{g}{\rho }_{g}{u}_{g}\right) + \nabla \cdot \left({\varepsilon }_{g}{\rho }_{g}{u}_{g}{u}_{g}\right) = -{\varepsilon }_{g}\nabla {p}_{g} + \nabla \cdot \left({\varepsilon }_{g}{\tau }_{g}\right) + {\varepsilon }_{g}{\rho }_{g}g-F\\ {\tau }_{g} = {\mu }_{g}\left[\nabla {u}_{g} + {\left(\nabla {u}_{g}\right)}^{{\rm{T}}}\right]-\dfrac{2}{3}{\mu }_{g}\left(\nabla \cdot {u}_{g}\right)I\end{gathered}$
    Particle distribution function$\dfrac{\partial \phi }{\partial t} + \nabla \cdot \left({u}_{p}\varphi \right) + {\nabla }_{ {u}_{p} }\cdot \left({a}_{p}\phi \right) = 0$
    Particle speed${u}_{p} = \dfrac{{\rm{d}}{x}_{p} }{{\rm{d}}t}$
    Particle acceleration${a}_{p} = {\beta }_{p}\left({u}_{g,p}-{u}_{p}\right)-\dfrac{\nabla {p}_{gp} }{ {\rho }_{s} } + g-\dfrac{\nabla {p}_{s,p} }{ {\varepsilon }_{s}{\rho }_{s} }$
    Gas-solid inter-phase momentum exchange rate$F = \displaystyle\sum _{k = 1}^{ {n}_{T} } \frac{ {n}_{p}^{k}{V}_{p}^{k} }{ {V}_{c} }{\beta }_{p}^{k}\left({u}_{g}^{k}-{u}_{p}^{k}\right)$
    Homogeneous drag model${\beta }_{0} = \dfrac{3}{4}{C}_{d0}\dfrac{ {\varepsilon }_{g}{\rho }_{g}\left|{u}_{gp}-{u}_{p}\right|}{ {d}_{p} }{\varepsilon }_{g}^{-2.7}$
    Heterogeneous drag model[36]$\begin{gathered}{H}_{D} = a{\left(R{e}_{p} + b\right)}^{c}\\ {\beta }_{p} = {\beta }_{p0}{H}_{D}\end{gathered}$
    Homogeneous solid force model${p}_{s0} = \dfrac{ {p}_{s}^{*}{\varepsilon }_{s}^{\alpha } }{{\rm{max}}\left[{\varepsilon }_{s,cp}-{\varepsilon }_{s},\delta \left(1-{\varepsilon }_{s}\right)\right]}$
    EMMS solid stress model${p}_{s,EMMS} = \displaystyle\sum _{k = 1}^{ {n}_{T} } \left(\frac{ {f}_{k}{p}_{s}^{*}{\left({\varepsilon }_{sc}^{k}\right)}^{\alpha } }{{\rm{max}}\left[{\varepsilon }_{s,cp}-{\varepsilon }_{sc}^{k},\delta \left(1-{\varepsilon }_{sc}^{k}\right)\right]}\right)$
    Artificial fitting model of EMMS solid stress$f\left({\varepsilon }_{s},{\delta }_{s}\right) = -3.273{\varepsilon }_{s}^{0.7115} + 1.370-{\delta }_{s}$

    ${ {p}_{s,Fit} }\left( { {\varepsilon }_{s} },{ {\delta }_{s} } \right)\text{=}\left\{\begin{aligned} & 1.164\varepsilon _{s}^{0.9862}\Biggr/\left[ { {\left( \frac{ { {\varepsilon }_{s} }+1}{0.2721} \right)}^{-0.7787} }-{ {\varepsilon }_{s} } \right],f\left( { {\varepsilon }_{s} },{ {\delta }_{s} } \right)\leqslant 0 \\ & { {{\rm{e}}}^{\left( -9.373\delta _{s}^{3}-0.4545{ {\delta }_{s} }-7.014 \right)\text{ } \cdot \text{ }{ {\left( { {\delta }_{s} }+3.319{ {\varepsilon }_{s} } \right)}^{-3.61} }+9.459} },f\left( { {\varepsilon }_{s} },{ {\delta }_{s} } \right) > 0 \\ \end{aligned} \right.$
    下载: 导出CSV

    表  2  算例参数

    Table  2.   Simulation parameters

    Schematic drawingParametersValue
    Diameter, D/m0.09
    Height, H/m10.50
    Operating temperature, Top/K298
    Operating pressure, Pop/Pa1.01 × 105
    Particle diameter, dp/μm54
    Particle density, ρs/(kg·m−3)970
    Gas density, ρg/(kg·m−3)1.185
    Gas viscosity, μg/(Pa·s)1.90 × 10-5
    Superficial gas velocity, Ugo/(m·s−1)1.52
    Incipient average solid volume
    fractions, εs0
    0.058
    Solid volume fraction at close pack, εs,cp0.60
    Solid stress parameter, ps*/Pa100
    Solid stress parameter, α2
    Particle–wall restitution coefficient, ew0.90
    Coarse-grained ratio, np100,200,500,1000
    Number of grids, I × J20 × 200,20 × 400,30 × 500,40 × 600
    Time step, Δt/s5 × 10-4
    Simulation time, t/s25
    下载: 导出CSV
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  • 收稿日期:  2022-10-27
  • 录用日期:  2023-01-10
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