This study conducts a comprehensive analysis of the Fourier spectra characteristics of particle preferential concentration in turbulent flows obtained by Eulerian and Lagrangian modelling approaches for different Stokes numbers. Particle preferential concentration is characterized by clusters and voids in the spatial particle distributions formed in turbulent flows and can significantly influence processes such as droplet coalescence, evaporation, and gas-particle reactions. The research primarily focuses on comparing the performance of two Eulerian models—one with and one without second-order velocity moments—and one Lagrangian model, which are used to predict particle dispersion. Key findings include the impact of artificial diffusion in Eulerian methods, the superiority of methods incorporating second-order velocity moments contributions at higher Stokes numbers, and the sensitivity of the Lagrangian method to Poisson statistics. Notably, the study reveals minimal variation in mean velocity spectra across different Stokes numbers, as opposed to the marked variations in particle concentration, momentum, and energy spectra. Grid resolution emerges as a crucial factor in enhancing spectral energy predictions in Eulerian methods. The research underscores the nuanced distinctions between Eulerian and Lagrangian methods in modelling preferential concentration, providing a detailed spectral comparison of particle concentration, velocity, momentum, and energy, highlighting the importance of method selection based on specific modelling needs.

中文翻译：

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欧拉法和拉格朗日法计算湍流中粒子择优浓度的光谱特征

本研究对不同斯托克斯数的欧拉和拉格朗日建模方法获得的湍流中颗粒优先浓度的傅里叶谱特征进行了全面分析。颗粒优先浓度的特征是在湍流中形成的空间颗粒分布中的簇和空隙，并且可以显着影响液滴聚结、蒸发和气体颗粒反应等过程。该研究主要集中于比较两种欧拉模型（一种具有二阶速度矩和一种不具有二阶速度矩）以及一种用于预测粒子分散的拉格朗日模型的性能。主要发现包括欧拉方法中人工扩散的影响、在较高斯托克斯数下结合二阶速度矩贡献的方法的优越性，以及拉格朗日方法对泊松统计的敏感性。值得注意的是，该研究揭示了不同斯托克斯数的平均速度谱变化最小，而粒子浓度、动量和能谱的显着变化相反。网格分辨率成为增强欧拉方法光谱能量预测的关键因素。该研究强调了欧拉方法和拉格朗日方法在优先浓度建模方面的细微差别，提供了粒子浓度、速度、动量和能量的详细光谱比较，强调了根据特定建模需求选择方法的重要性。