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LES和DNS在平坡异重流数值模拟中的比较研究
Comparative Study of LES and DNS on Numerical Simulation of Gravity Current over a Flat Bed
DOI: 10.12677/IJFD.2021.92003, PDF, HTML, XML, 下载: 137  浏览: 214  国家科技经费支持

Abstract: In this paper, the FLUENT software was used to simulate the evolution characteristics of the lock-exchange gravity currents over a flat bed. Two-dimensional large eddy simulation (LES) and direct numerical simulation (DNS) were utilized to compare the morphological change, instantane-ous mixing coefficient, potential energy transformation, and kinetic energy at the characteristic section. The results show that both LES and DNS have good accuracy in predicting the head position of the gravity currents, but the results of DNS are slightly more accurate with more computational grids required. For simulating the development process of gravity currents, the DNS results show less K-H instability occurring at the interface of current and ambient fluid than the LES simulations do. For DNS simulations, heavy fluid basically concentrates on the current head. In addition, the DNS results are closer to the gravity current morphology from experimental observations. The mixing degree of density flow with ambient fluid estimated by LES and DNS simulations is similar, but the result of DNS shows smoother current-ambient fluid interface. LES and DNS results obtain similar potential energy changes along the course of density flow, but the results of DNS have smaller background potential energy. For the temporal variations of kinetic energy at characteristic cross-sections, compared with LES, DNS performs fewer oscillating peaks. The results of this paper can provide a reference for the selection of numerical models on gravity current simulations in the future.

1. 引言

2. 数值模型

Figure 1. Schematic diagram of physical model

2.1. 数值模型

2.1.1. 网格及求解方法

2.1.2. 边界条件

2.2. 模型验证

Figure 2. Comparison of temporal head position of gravity current between numerical and experimental results

$X=\frac{{x}_{f}-{x}_{0}}{H}$ (1)

$T=\frac{t\sqrt{{g}^{\prime }H}}{H}$ (2)

2.3. 特征参数及组别

Table 1. Parameters of numerical cases

3. 结果分析

3.1. 流态分析

Figure 3. Development processes of gravity current in the case N3: (a) LES; (b) DNS; (c) Experimental results

3.2. 卷吸和掺混

${E}_{i}=\frac{2\left({M}_{i}-{M}_{i-1}\right)}{\left({x}_{f,i}+{x}_{f,i-1}\right)\left({U}_{b,i}+{U}_{b,i-1}\right)\left({t}_{i}-{t}_{i-1}\right)}$ (3)

Figure 4. The variation of entrainment parameter with front position of gravity current: (a) N1; (b) N2; (c) N3

3.3. 势能转换

${E}_{p}\left(t\right)=g\underset{V}{\int }〈\rho \left(x,z,t\right)〉z\text{d}V$ (4)

${E}_{b}\left(t\right)=g\underset{V}{\int }〈\stackrel{˜}{\rho }\left(x,z,t\right)〉z\text{d}V$ (5)

${E}_{a}\left(t\right)={E}_{p}\left(t\right)-{E}_{b}\left(t\right)$ (6)

Figure 5. The variation of the dimensionless total potential energy, background potential energy, and available potential energy with head position of gravity current in N1: (a) LES; (b) DNS

3.4. 动能峰值

$K=\frac{1}{2}\underset{\Omega }{\int }{\stackrel{¯}{u}}^{2}+{\stackrel{¯}{w}}^{2}\text{d}\Omega$ (7)

Figure 6. Kinetic energy profile at the characteristic section of density currents of the case N3: (a) LES; (b) DNS

4. 结语

1) LES和DNS对于异重流头部位置的预测都具有较好的准确性，DNS的结果略微精确，但所需网格数较多；

2) 在异重流与环境流体的交界面发展过程中，相比于LES模拟的结果，DNS的结果具有较少的K-H不稳定性产生，而DNS模拟的结果与实验异重流的形态较为接近；

3) LES和DNS模拟计算得出的异重流与环境流体的掺混程度相近，但DNS的交界面较为光滑；

4) LES和DNS对于异重流沿途势能变化的计算结果相近，但DNS的结果具有较小的背景势能；

5) 对于特征断面处动能逐时变化，相较于LES，DNS模拟较少出现多次波峰的震荡现象。

NOTES

*通讯作者。

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