RESEARCH ON HETEROGENEOUS SOLID STRESS MODEL BASED ON ARTIFICIAL NEURAL NETWORK
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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.
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关键词:
- 两相流 /
- 多相质点网格法 (MP-PIC) /
- 非均匀固相应力 /
- 机器学习 /
- 流态化
Abstract: The Energy-Minimization Multi-Scale (EMMS) theory has been introduced into the multiphase particle-in-cell (MP-PIC) method to establish the heterogeneous EMMS solid stress model to account for the effect of non-uniform solid distribution. However, the calculation process is very complex and also very time consuming for this heterogeneous solid stress model. The expression of the heterogeneous EMMS solid stress can be obtained by manual fitting method. However, the fitting variable describes heterogeneous solid distribution as well as the fitting function describe the shape of solid stress are required for manually fitting. Since the heterogeneous solid stress function is highly nonlinear in nature, the fitting precision is not high enough for the manually fitting model. And there is an obvious deviation between the fitting correlation and the original EMMS solid stress, because it is hard to find out an appropriate parameter to characterize the heterogeneous solid concentration distribution as well as to find out an appropriate fitting function. In order to solve the above problems, an artificial neutral network (ANN) based machine learning method was proposed to avoid the characterization of the local distribution of solid volume fraction. Subsequently an ANN solid stress model which accounts for the detailed distribution of particle concentration was proposed to improve the fitting accuracy. Firstly, a two-marker based ANN solid stress model was established based on local particle concentration and particle non-uniform distribution index. Further, particle concentrations in the current cell and its neighboring cells were arrayed to represent the particle concentration distribution, thus to establish the ANN solid stress model based on particle concentration distribution. Then, the two models are compared with the EMMS solid stress model, and the effects of grid resolution and coarse-graining ratio on the model are also tested. The simulation results predicted with ANN model agreed well with that of the EMMS solid stress model, and the dependence of simulation results on grid resolution and coarse-graining ratio was also reduced. -
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
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
Description Equation 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 $f\left({\varepsilon }_{s},{\delta }_{s}\right) = -3.273{\varepsilon }_{s}^{0.7115} + 1.370-{\delta }_{s}$
${ {p}_{s,Fit} }\left( { {\varepsilon }_{s} },{ {\delta }_{s} } \right)\text{=}\left\{\begin{aligned} & 1.164\varepsilon _{s}^{0.9862}\Biggr/\left[ { {\left( \frac{ { {\varepsilon }_{s} }+1}{0.2721} \right)}^{-0.7787} }-{ {\varepsilon }_{s} } \right],f\left( { {\varepsilon }_{s} },{ {\delta }_{s} } \right)\leqslant 0 \\ & { {{\rm{e}}}^{\left( -9.373\delta _{s}^{3}-0.4545{ {\delta }_{s} }-7.014 \right)\text{ } \cdot \text{ }{ {\left( { {\delta }_{s} }+3.319{ {\varepsilon }_{s} } \right)}^{-3.61} }+9.459} },f\left( { {\varepsilon }_{s} },{ {\delta }_{s} } \right) > 0 \\ \end{aligned} \right.$表 2 算例参数
Table 2. Simulation parameters
Schematic drawing Parameters Value Diameter, D/m 0.09 Height, H/m 10.50 Operating temperature, Top/K 298 Operating pressure, Pop/Pa 1.01 × 105 Particle diameter, dp/μm 54 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, εs00.058 Solid volume fraction at close pack, εs,cp 0.60 Solid stress parameter, ps*/Pa 100 Solid stress parameter, α 2 Particle–wall restitution coefficient, ew 0.90 Coarse-grained ratio, np 100,200,500,1000 Number of grids, I × J 20 × 200,20 × 400,30 × 500,40 × 600 Time step, Δt/s 5 × 10-4 Simulation time, t/s 25 -
[1] 李洪钟, 郭慕孙. 回眸与展望流态化科学与技术. 化工学报, 2013, 64(1): 52-62 [2] Zhao X, Jiang Y, Li F, et al. A scaled MP-PIC method for bubbling fluidized beds. Powder Technol, 2022, 404: 117501 doi: 10.1016/j.powtec.2022.117501 [3] Chen XZ, Wang JW. A comparison of two-fluid model, dense discrete particle model and CFD-DEM method for modeling impinging gas-solid flows. Powder Technol, 2014, 254: 94-102 doi: 10.1016/j.powtec.2013.12.056 [4] Cai W, Kong X, Ye Q, et al. Numerical modelling of hydrodynamics of molten salt fluid-particles fluidized beds using CFD-DEM and TFM approaches. Powder Technol, 2022: 117882 [5] Leckner B. Hundred years of fluidization for the conversion of solid fuels. Powder Technol, 2022: 117935 [6] Wang J, Ku X, Lin J. Numerical investigation of biomass pyrolysis performance in a fluidized-bed reactor by a TFM-DEM hybrid model. Chemical Engineering Science, 2022, 260: 117922 doi: 10.1016/j.ces.2022.117922 [7] Chu KW, Chen YX, Ji L, et al. Coarse-grained CFD-DEM study of Gas-solid flow in gas cyclone. Chemical Engineering Science, 2022, 260: 117906 doi: 10.1016/j.ces.2022.117906 [8] Gao X, Li TW, Sarkar A, et al. Development and validation of an enhanced filtered drag model for simulating gas-solid fluidization of Geldart A particles in all flow regimes. Chemical Engineering Science, 2018, 184: 33-51 doi: 10.1016/j.ces.2018.03.038 [9] Sarkar A, Sun X, Sundaresan S. Verification of sub-grid filtered drag models for gas-particle fluidized beds with immersed cylinder arrays. Chemical Engineering Science, 2014, 114: 144-154 doi: 10.1016/j.ces.2014.04.018 [10] Ebrahimi M, Crapper M, Ooi JY. Numerical and experimental study of horizontal pneumatic transportation of spherical and low-aspect-ratio cylindrical particles. Powder Technol, 2016, 293: 48-59 doi: 10.1016/j.powtec.2015.12.019 [11] Miao Z, Kuang SB, Zughbi H, et al. CFD simulation of dilute-phase pneumatic conveying of powders. Powder Technol, 2019, 349: 70-83 doi: 10.1016/j.powtec.2019.03.031 [12] Radl S, Sundaresan S. A drag model for filtered Euler-Lagrange simulations of clustered gas-particle suspensions. Chemical Engineering Science, 2014, 117: 416-425 doi: 10.1016/j.ces.2014.07.011 [13] Yuan ZH, Wang SY, Shao BL, et al. Investigation on effect of drag models on flow behavior of power-law fluid-solid two-phase flow in fluidized bed. Particuology, 2022, 70: 43-54 doi: 10.1016/j.partic.2022.01.008 [14] Yang N, Chen JH, Ge W, et al. A conceptual model for analyzing the stability condition and regime transition in bubble columns. Chemical Engineering Science, 2010, 65(1): 517-526 doi: 10.1016/j.ces.2009.06.014 [15] Kadyrov T, Li F, Wang W. Impacts of solid stress model on MP-PIC simulation of a CFB riser with EMMS drag. Powder Technol, 2019, 354: 517-528 doi: 10.1016/j.powtec.2019.06.018 [16] 姜勇. 基于MP-PIC方法的流态化反应器快速模拟研究. [博士论文]. 北京: 中国科学院大学, 2020Jiang Yong. Rapid simulation of fluidized reactor based on MP-PIC method. [PhD Thesis]. Beijing: University of Chinese Academy of Sciences, 2020 (in chinese)). [17] Jiang Y, Li F, Ge W, et al. EMMS-based solid stress model for the multiphase particle-in-cell method. Powder Technol, 2020, 360: 1377-1387 doi: 10.1016/j.powtec.2019.09.031 [18] Harris A, Davidson J, Thorpe R. The prediction of particle cluster properties in the near wall region of a vertical riser (200157). Powder Technol, 2002, 127(2): 128-143 doi: 10.1016/S0032-5910(02)00114-6 [19] Wang J, Ge W, Li J. Eulerian simulation of heterogeneous gas–solid flows in CFB risers: EMMS-based sub-grid scale model with a revised cluster description. Chemical Engineering Science, 2008, 63(6): 1553-1571 doi: 10.1016/j.ces.2007.11.023 [20] Zou B, Li H, Xia Y, et al. Cluster structure in a circulating fluidized bed. Powder Technol, 1994, 78(2): 173-178 doi: 10.1016/0032-5910(93)02786-A [21] Aguila-Leon J, Vargas-Salgado C, Chiñas-Palacios C, et al. Energy management model for a standalone hybrid microgrid through a particle Swarm optimization and artificial neural networks approach. Energy Conversion and Management, 2022, 267: 115920 doi: 10.1016/j.enconman.2022.115920 [22] Calisir T, Çolak AB, Aydin D, et al. Artificial neural network approach for investigating the impact of convector design parameters on the heat transfer and total weight of panel radiators. International Journal of Thermal Sciences, 2023, 183: 107845 doi: 10.1016/j.ijthermalsci.2022.107845 [23] Skrypnik A, Shchelchkov A, Gortyshov YF, et al. Artificial neural networks application on friction factor and heat transfer coefficients prediction in tubes with inner helical-finning. Applied Thermal Engineering, 2022, 206: 118049 doi: 10.1016/j.applthermaleng.2022.118049 [24] Kalay E, Boğoçlu ME, Bolat B. Mass flow rate prediction of screw conveyor using artificial neural network method. Powder Technol, 2022, 408: 117757 doi: 10.1016/j.powtec.2022.117757 [25] Zhang K, Zhang Z, Han Y, et al. Artificial neural network modeling for steam ejector design. Applied Thermal Engineering, 2022, 204: 117939 doi: 10.1016/j.applthermaleng.2021.117939 [26] Afandi A, Lusi N, Catrawedarma I, et al. Prediction of temperature in 2 meters temperature probe survey in Blawan geothermal field using artificial neural network (ANN) method. Case Studies in Thermal Engineering, 2022, 38: 102309 doi: 10.1016/j.csite.2022.102309 [27] Pappachan BK, Tjahjowidodo T. Parameter Prediction Using Machine Learning in Robot-Assisted Finishing Process. International Journal of Mechanical Engineering and Robotics Research, 2020, 9(3): 435-440 [28] Gao G, Li Y, Li J, et al. A hybrid model for short-term rainstorm forecasting based on a back-propagation neural network and synoptic diagnosis. Atmospheric and Oceanic Science Letters, 2021, 14(5): 100053 doi: 10.1016/j.aosl.2021.100053 [29] Chen H, Wang Y, Zuo MS, et al. A new prediction model of CO2 diffusion coefficient in crude oil under reservoir conditions based on BP neural network. Energy, 2022, 239: 122286 doi: 10.1016/j.energy.2021.122286 [30] Snider DM. An incompressible three-dimensional multiphase particle-in-cell model for dense particle flows. J Comput Phys, 2001, 170(2): 523-549 doi: 10.1006/jcph.2001.6747 [31] Li F, Song FF, Benyahia S, et al. MP-PIC simulation of CFB riser with EMMS-based drag model. Chemical Engineering Science, 2012, 82: 104-113 doi: 10.1016/j.ces.2012.07.020 [32] Ariyaratne WKH, Ratnayake C, Melaaen MC. Application of the MP-PIC method for predicting pneumatic conveying characteristics of dilute phase flows. Powder Technol, 2017, 310: 318-328 doi: 10.1016/j.powtec.2017.01.048 [33] Kadyrov T, Li F, Wang W. Bubble-based EMMS/DP drag model for MP-PIC simulation. Powder Technol, 2020, 372: 611-624 doi: 10.1016/j.powtec.2020.06.023 [34] Dymala T, Wytrwat T, Heinrich S. MP-PIC simulation of circulating fluidized beds using an EMMS based drag model for Geldart B particles. Particuology, 2021, 59: 76-90 doi: 10.1016/j.partic.2021.07.002 [35] Li J, Kwauk M. Particle-fluid Two-phase Flow: The Energy-minimization Multi-scale Method. Beijing: Metallurgical Industry Press, 1994. [36] 鲁波娜. 基于EMMS的介尺度模型及其在气固两相流模拟中的应用. [博士论文]. 北京: 中国科学院过程工程研究所, 2009Lu Bona. EMMS-based Meso-Scale Model and Its Application in Simulating Gas-Solid Two-Phase Flows. [PhD Thesis]. Beijing: Institute of Process Engineering, Chinese Academy of Sciences, 2009 (in Chinese) [37] Lu B, Wang W, Li J. Eulerian simulation of gas–solid flows with particles of Geldart groups A, B and D using EMMS-based meso-scale model. Chemical Engineering Science, 2011, 66(20): 4624-4635 doi: 10.1016/j.ces.2011.06.026 [38] Wang W, Li J. Simulation of gas–solid two-phase flow by a multi-scale CFD approach—of the EMMS model to the sub-grid level. Chemical Engineering Science, 2007, 62(1-2): 208-231 doi: 10.1016/j.ces.2006.08.017 -