IMECH-IR
携带颗粒各向同性湍流的大涡模拟与亚格子模型
Alternative TitleLarge-eddy simulation of particle-laden isotropic turbulent flows and sub-grid scale models
周志登
Thesis Advisor何国威 研究员 ; 晋国栋 研究员
2019-11-16
Degree Grantor中国科学院大学
Place of Conferral北京
Subtype博士
Degree Discipline流体力学
Keyword颗粒拉格朗日弥散 大涡模拟 湍流亚格子模型 颗粒亚格子模型 人工神经网络 有限颗粒雷诺数
Abstract

    携带颗粒的湍流二相流在环境流动和工业应用中广泛存在。与直接数值模拟 (DNS) 相比,大涡模拟 (LES) 作为湍流二相流工程预测的下一代主要工具,大大降低了计算支出,能够应用于更高雷诺数的湍流。然而,降低计算量的同时,LES 由于小尺度湍流的缺失,无法准确地模拟颗粒与湍流的相互作用。而将 LES 应用于湍流混合与输运过程的研究,需要其准确地预测湍流中的颗粒相对弥散,或者至少准确预测流场的拉格朗日统计量。因此,本文针对 LES 的小尺度运动缺失问题,分别研究滤波和亚格子模型误差对流体颗粒弥散的影响;构造运动学-反卷积混合颗粒亚格子模型,同时恢复 LES 的解析尺度和亚格子尺度对颗粒运动的贡献;根据大量湍流 DNS 数据,采用人工神经网络 (ANN) 建立数据驱动的亚格子模型。此外,对于球形颗粒在静止流体中靠近壁面运动的受力和力矩,本文基于传统模型,发展适用于有限颗粒雷诺数情况的亚格子尺度模型。

    本文的主要创新性工作包括以下四个部分:

(一). 研究滤波和亚格子模型误差对流体颗粒弥散的影响

    该部分通过开展各向同性湍流的 DNS、滤波的 DNS (FDNS) 和 LES,比较单颗粒、颗粒对和四颗粒弥散,分别研究滤波和谱涡粘模型误差对流体颗粒弥散的影响。对于单颗粒弥散,LES 略微高估了一点两时间速度关联函数,但准确预测了单颗粒位移。对于颗粒对弥散,当初始分离距离较小时,与 DNS 相比,LES 低估了分离距离的平均值和方差以及相对扩散、高估了速度关联函数,FDNS 的结果处于二者之间。当初始分离距离较大时,速度关联函数曲线在初始阶段短暂抬升,我们理论推导出关联函数随时间变化的表达式,证明了这一抬升现象。对于四颗粒弥散,与 DNS 相比,LES 低估了四面体平均表面积和体积,且表征形状变化的无量纲系数曲线出现了明显滞后,FDNS 结果仍处于二者之间。此外,LES 和 FDNS 的颗粒对速度关联函数相对误差随着雷诺数的增大而减小。

(二). 构造运动学-反卷积混合颗粒亚格子模型

    该部分通过构造运动学-反卷积 (KSAD) 混合颗粒亚格子模型,提升 LES 对颗粒弥散的预测精度。对各向同性湍流的 LES,采用近似反卷积模型 (ADM) 恢复解析尺度流场;基于 LES+ADM 速度场,采用运动学模型 (KS) 构造亚格子尺度流场。通过参数研究,发现可采用较少数目的波数模态和矢量构造 KS,减少计算支出。随后详细评估 KSAD 模型对流体颗粒弥散的作用。对于颗粒对统计量,包括分离距离的平均值与方差、相对扩散以及两点一时间拉格朗日速度关联函数,模型几乎完全补偿了 LES 和 DNS 的偏差;对于四颗粒统计量,模型显著提升了 LES 对四面体的平均表面积、体积以及无量纲系数的预测。最后,将 KSAD 模型应用于 LES 预测惯性颗粒聚团,定量准确地补偿了所有 St 下 LES 与 DNS 的径向相对速度误差和 St≥2.0 的径向分布函数误差。

(三). 人工神经网络建立数据驱动的湍流亚格子模型

    该部分基于大量的湍流 DNS 数据,采用 ANN 建立数据驱动的亚格子模型。对各向同性湍流 DNS 进行高斯滤波,获得不同雷诺数和滤波宽度的解析尺度流场与亚格子应力张量数据。随后选取速度梯度张量和滤波宽度作为输入特征、亚格子应力张量作为输出标签,采用单隐层前馈 ANN 进行训练,并讨论了隐层神经元数目的影响。训练成功后,对 ANN 模型进行先验评估和后验验证。在先验评估中,ANN 模型预测的关联系数基本都大于 0.9,与梯度模型结果相近,远高于 Smagorinsky 模型;ANN 模型预测的能量传输率相比梯度模型结果有显著的提升。在后验验证中,采用修正的 ANN 模型进行各向同性湍流 LES,其预测的能谱满足惯性区的 k-5/3 标度律,预测的流体颗粒对统计量接近于 FDNS 结果。

(四). 发展球形颗粒在流体中靠近壁面运动的受力和力矩模型

    对球形颗粒在静止流体中靠近壁面的运动,该部分基于 Stokes 流动假设下的传统模型,发展有限颗粒雷诺数下的颗粒受力和力矩模型。将颗粒靠近壁面的一般运动划分为四种基本运动,采用格子 Boltzmann 方法进行解析颗粒的直接数值模拟。在确定合适的计算区域尺寸并进行网格无关性检验后,设置不同的颗粒与壁面的间距以及颗粒雷诺数,计算颗粒受力和力矩的无量纲系数。随后对数据进行拟合处理,提出颗粒受力和力矩的有限颗粒雷诺数模型。接下来,我们对模型的正确性与适用性进行验证。验证包括两部分,其一为颗粒不同基本运动组合成的复合运动模拟,数值结果与提出的模型基本吻合;其二为引入不同文献中的相似算例,发现文献结果与提出的模型也有很好的一致性。

Other Abstract

    Particle-laden turbulent flows are ubiquitous in environmental applications and industrial processes. As a potential method in the engineering prediction of particle-laden turbulent flows, large-eddy simulation (LES) significantly reduces the computational cost compared to direct numerical simulation (DNS), and can be applied to practical turbulent flow simulations at high Reynolds numbers. However, accompanying with the low computational cost, the LES cannot accurately predict the interaction between the particle and turbulence due to the lack of small-scale turbulence. The application of LES to investigate the turbulent transport processes raises a requirement of accurately predicting the particle motion in turbulence, or at least the Lagrangian statistics of the flow field. Therefore, this paper focuses on the problem of missing small-scale turbulence in LES, investigating the effects of filtering and subgrid-scale (SGS) model error on the Lagrangian dispersion of fluid particles. Based on the LES flow field, a particle subgrid-scale model coupling kinematic simulation with approximate deconvolution method is proposed to recover the contribution of turbulence at both resolved scales and subgrid scales on particle motion. Then, an artificial neural network (ANN) is used to establish the data-driven SGS model for the LES of isotropic turbulent flows. Besides, we propose the hydrodynamic force and torque models for a particle moving near a plane wall at finite particle Reynolds numbers.

    The main innovative works of this paper are listed as follows:

1. The effects of filtering and SGS model error on the fluid particle dispersion

    The effects of filtering and SGS model error on the fluid particle dispersion are investigated by comparing the Lagrangian statistics of single-, two- and four-particle dispersion in the DNS, filtered DNS (FDNS) and LES of isotropic turbulent flows. For the single-particle dispersion, LES slightly overestimates the one-point two-time Lagrangian velocity correlation function, but accurately predicts the single-particle displacement. For the particle-pair dispersion, the LES underestimates the mean and variance of separation distances and the relative dispersion, and overestimates the one-time two-point Lagrangian velocity correlation function compared to DNS when the initial separation distance is small. The results of FDNS are always in between the former two. When the initial separation distance is large, the curve of one-time two-point Lagrangian velocity correlation function slightly increases at the initial stage. To explain this phenomenon, the expression of velocity correlation function varying with time is derived from the separation vector based on the Taylor expansion and Kolmogorov similarity theory. For the four-particle dispersion, LES underestimates the mean surface area and volume of the tetrahedrons, and the temporal variations of dimensionless coefficients characterizing the shape of tetrahedron in LES are slower than DNS. Also, the results of FDNS are in between the DNS and LES. In addition, the relative error of one-time two-point Lagrangian velocity correlation function between the LES and FDNS decreases with the increasing Reynolds numbers.

2. A particle subgrid-scale model coupling kinematic simulation with approximate deconvolution method

    A kinematic simulation with an approximate deconvolution (KSAD) hybrid model is proposed to predict the Lagrangian relative dispersion of fluid particles and clustering of inertial particles in the LES of isotropic turbulent flows. Based on the flow field of LES, we use an approximate deconvolution model (ADM) to improve the resolved scales near the filter width and a kinematic simulation (KS) to recover the missing velocity fluctuations beneath the subgrid scales. Then, a parametric study regarding the wavenumbers and orientation wavevectors of KS is conducted to reduce the computational cost. To assess the performance of KSAD model, we compare the Lagrangian statistics of fluid particles obtained from the DNS, LES and LES+KSAD. For the particle-pair dispersion, the KSAD model accurately recover the errors of the mean and variance of separation distances, the relative dispersion and the one-time two-point Lagrangian velocity correlation function between the LES and DNS. For the four-particle dispersion, the KSAD model significantly improves the predictions of mean surface area and volume of the tetrahedrons and their dimensionless coefficients in LES. Finally, the KSAD model is applied to predict the statistics of inertial particle clustering in LES. It is found that the KSAD model quantificationally compensates the errors of radial relative velocity at all St and the radial distribution function at St≥2.0 between the LES and DNS.

3. Subgrid-scale model for large-eddy simulation of isotropic turbulent flows using an artificial neural network

    An artificial neural network is used to establish the relation between the resolved-scale flow field and the SGS stress tensor, to develop a new SGS model for LES of isotropic turbulent flows. The data required for training and testing of the ANN are the resolved-scale flow fields with different filter widths, which can be obtained by performing Gaussian filtering on the DNS of isotropic turbulent flows. Then, the velocity gradient tensor and filter width are used as input features, and the SGS stress tensor is used as output label to train a single-hidden-layer feedforward ANN. And the effects of the number of neurons in the hidden layer is discussed by three comparative cases. After training, the a priori test and a posteriori validation are carried out to assess the ANN model. In the a priori test, the correlation coefficients predicted by the ANN model are mostly larger than 0.9, close to those by the gradient model and obviously better than the Smagorinsky model. The relative errors of the energy transfer rate predicted by the ANN model show significant improvement compared to the gradient model. In the a posteriori validation, the improved ANN model is coupled with a real LES. The energy spectrum computed by the improved ANN model nearly obeys the inertial range scaling law of k-5/3. The Lagrangian statistics obtained from the improved ANN model almost approach those from the FDNS, better than the results from the spectral eddy viscosity model and dynamic Smagorinsky model.

4. Hydrodynamic force and torque models for a particle moving near a wall at finite particle Reynolds numbers

    For a spherical particle moving near a plane wall in the quiescent fluid, the conventional lubrication theory was developed in the Stokes flow limit. This research work is aimed at proposing models for the hydrodynamic force and torque acting on the particle at finite particle Reynolds numbers. The general motion of the particle near a plane wall can be decomposed into four simple types of particle motion, and the lattice Boltzmann method is used to fully resolve the interaction between the particle and fluid flow. After the discussion of computational domain size and grid-size convergence, the hydrodynamic forces and torques on the particle are computed at different particle Reynolds number and dimensionless gap between the particle and the wall. Through the data fitting on the dimensionless coefficients, we obtain the hydrodynamic force and torque models as functions of particle Reynolds number and the dimensionless gap size. Subsequently, it is necessary for us to assess the predicting accuracy and applicability of the models. First, the general motions of the particle composed by different simple motions are simulated, and the numerical results basically agree with the proposed models. Second, the similar cases of particle motion in several literatures are introduced, and the corresponding results coincide well with the proposed models.

Language中文
Document Type学位论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/80685
Collection中国科学院力学研究所
非线性力学国家重点实验室
Recommended Citation
GB/T 7714
周志登. 携带颗粒各向同性湍流的大涡模拟与亚格子模型[D]. 北京. 中国科学院大学,2019.
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