Abstract For the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupling occur through a smoothed-kernel averaging procedure). Laboratory-scale tests display grid-independence problems due to bubble diameter being larger than voxel size, thereby breaking the pointwise Euler-Lagrange assumption of negligible particle size. To tackle this problem and thereby have grid-independent results, a novel data-scaling approach to pointwise Euler-Lagrange grid independence evaluation, based on an application of the Buckingham π theorem, is proposed. Evaluation of laboratory-scale flow patterns and comparison to experimental data show only marginal differences in between the models, and between numerical modelling and experimental data. Pilot-scale simulations show that all the models produce grid-independent, coherent data if the Euler-Lagrange assumption of negligible (or at least, small) particle size is recovered. In both cases, a second-order convergence was achieved. A discussion follows on the opportunity of applying the proposed data-scaling approach rather than the smoothing-kernel model.

中文翻译：

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Buckingham π 定理在污水污泥消化的 Lattice-Boltzmann 模型中的应用

摘要 首次将一组Lattice-Boltzmann双向耦合逐点Euler-Lagrange模型应用于厌氧消化污泥的气体混合。该集合包括一个局部模型、一个“第一邻居”（即，粒子所在的体素以及它的第一个邻居发生反向耦合）和一个“平滑内核”（前向和反向耦合通过平滑核平均过程）。由于气泡直径大于体素尺寸，实验室规模的测试显示网格无关问题，从而打破了可忽略颗粒尺寸的逐点欧拉-拉格朗日假设。为了解决这个问题，从而获得与网格无关的结果，基于白金汉 π 定理的应用，提出了一种用于逐点欧拉-拉格朗日网格独立性评估的新数据缩放方法。实验室规模的流动模式的评估和与实验数据的比较表明模型之间以及数值建模和实验数据之间的差异很小。中试规模的模拟表明，如果恢复了可忽略的（或至少是小）颗粒尺寸的欧拉-拉格朗日假设，则所有模型都会产生与网格无关的相干数据。在这两种情况下，都实现了二阶收敛。接下来讨论应用所提出的数据缩放方法而不是平滑核模型的机会。如果 Euler-Lagrange 假设可忽略不计（或至少很小）颗粒尺寸被恢复，则相干数据。在这两种情况下，都实现了二阶收敛。接下来讨论应用所提出的数据缩放方法而不是平滑核模型的机会。如果 Euler-Lagrange 假设可忽略不计（或至少很小）颗粒尺寸被恢复，则相干数据。在这两种情况下，都实现了二阶收敛。接下来讨论应用所提出的数据缩放方法而不是平滑核模型的机会。