International Journal of Multiphase Flow最新文献_第4页

On the particle clustering in the wake of a normal flat plate: Influence of inflow boundary conditions 普通平板尾迹中的颗粒聚集：流入边界条件的影响

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-20 DOI: 10.1016/j.ijmultiphaseflow.2026.105623

Peddi Harishteja , Deekshith I. Poojary , Cristian Marchioli , Vagesh D. Narasimhamurthy

In this study, we examine the effect produced by different inflow conditions on the behavior of inertial particles within the wake produced by a normal flat plate. To this aim, we perform Euler–Lagrangian simulations of the particle-laden wake, using the in-house solver MGLET-LaParT. An unsteady wake with a Reynolds number of 60 is considered, and four inflow conditions are examined: uniform inflow, planar shear inflow, and addition of inflow turbulence to both uniform and planar shear. Particles with different Stokes numbers (

S t = 0.1, 1, 5

, and 10) are analyzed. Particle dispersion, voids, and connected clusters are quantified using Voronoï tessellations and Minkowski functionals, along with statistics of concentration, particle velocity, and slip velocity. The results reveal a distinct influence of both inertia and inflow conditions. Uniform inflow produces symmetric lateral accumulation, whereas planar shear induces asymmetry and enhances wake centerline concentration. With the addition of inflow turbulence to planar shear, the particles at the periphery of the voids created by vortices become more dispersed and irregular, particularly at the highest Stokes number (

S t = 10

). Cluster formation is analyzed by backtracking the particles that eventually form clusters. Further analysis indicates that cluster morphology depends on particle inertia: Elongated clusters are found at

S t = 1

, the largest compact clusters at

S t = 5

, and diffuse clusters at

S t = 10

. Inflow conditions modulate cluster coherence, particularly at higher Stokes numbers. The probability distributions of normalized cluster areas exhibit power-law decay, highlighting fractal, scale-free organization dominated by intermediate-sized clusters. We believe these findings provide a quantitative framework linking inflow, inertia, and wake dynamics, offering benchmarks for predictive multiphase flow models.

在这项研究中，我们研究了不同的流入条件对普通平板产生的尾迹内惯性粒子行为的影响。为此，我们使用内部求解器MGLET-LaParT对粒子负载尾迹进行欧拉-拉格朗日模拟。考虑雷诺数为60的非定常尾迹，研究了四种入流条件：均匀入流、平面剪切入流以及在均匀和平面剪切基础上加入入流湍流。对不同Stokes数（St=0.1,1,5和10）的粒子进行了分析。使用Voronoï镶嵌和Minkowski泛函，以及浓度、粒子速度和滑移速度的统计数据，对粒子弥散、空隙和连接簇进行量化。结果表明，惯性和入流条件都有明显的影响。均匀入流产生对称侧向积聚，而平面剪切引起不对称积聚，增强尾流中心线集中。在平面剪切的基础上加入入流湍流，涡流形成的空洞外围的颗粒变得更加分散和不规则，特别是在Stokes数最高时（St=10）。通过回溯最终形成星团的粒子来分析星团的形成。进一步的分析表明，团簇的形态取决于粒子的惯性：在St=1时发现了细长团簇，在St=5时发现了最大的致密团簇，在St=10时发现了弥散团簇。流入条件会调节集群的相干性，特别是在斯托克斯数较高的情况下。归一化集群区域的概率分布呈现幂律衰减，突出分形，以中等规模集群为主的无标度组织。我们相信这些发现提供了一个定量框架，将流入、惯性和尾流动力学联系起来，为预测多相流模型提供了基准。

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引用次数: 0

A filter-dependent granular temperature model from large-scale CFD-DEM data 基于大尺度CFD-DEM数据的滤波相关颗粒温度模型

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-29 DOI: 10.1016/j.ijmultiphaseflow.2026.105625

L. Rosenberg , W.D. Fullmer , S. Beetham

The computational study of strongly-coupled, gas–solid flows at scales relevant to most environmental and engineering applications requires the use of ‘coarse-grained’ methodologies such as the two-fluid model, particle-in-cell approach or the multiphase Reynolds Averaged Navier–Stokes equations. While these strategies enable computations at desirable length- and time-scales, they rely heavily on models to capture important flow physics that occur at scales smaller than the mesh. To date, the models that do exist are based on a limited set of flow conditions, such as very dilute particle phase. To this end, we leverage a large-scale repository of CFD-DEM data to develop filter-size dependent models for the mean variance in particle volume fraction, a quantity commonly used to assess the degree of clustering, and the granular temperature, a key quantity for accurately predicting gas–solid flows. Because of its filter-size dependence, the granular temperature model can be directly translated to coarse-grained approaches and tied directly to grid size.

在与大多数环境和工程应用相关的尺度上，强耦合气固流动的计算研究需要使用“粗粒度”方法，如双流体模型、细胞内颗粒方法或多相Reynolds平均Navier-Stokes方程。虽然这些策略能够在理想的长度和时间尺度上进行计算，但它们严重依赖于模型来捕捉比网格小尺度上发生的重要流动物理。到目前为止，现有的模型都是基于一组有限的流动条件，比如非常稀的颗粒相。为此，我们利用大规模的CFD-DEM数据库，开发了颗粒体积分数（通常用于评估聚类程度的数量）和颗粒温度（准确预测气固流动的关键数量）的平均方差的过滤器大小依赖模型。由于其过滤器大小的依赖性，颗粒温度模型可以直接转换为粗粒度方法，并直接绑定到网格大小。

引用次数: 0

Multiphase flow impressions: Selected poster contributions from ICMF 2025 多相流印象：ICMF 2025的精选海报贡献

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2025-12-26 DOI: 10.1016/j.ijmultiphaseflow.2025.105594

Manuel Moriche, S. Balachandar, Alfredo Soldati

引用次数: 0

On the modelling of the wall-void layer in high-pressure, subcooled flow boiling 高压过冷流动沸腾中壁面空洞层的模拟

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-08 DOI: 10.1016/j.ijmultiphaseflow.2026.105609

Silvia Nauer, Joel-Steven Singh, Djamel Lakehal

In the context of the wall heat flux partitioning approach, we propose a new modelling route for high-pressure, subcooled flow boiling, which we simplify by removing the quenching part. Examining the experimental data used for comparison showed that bubble nucleation at the wall disrupts the boundary layer structure in the same way as wall roughness. We demonstrate that redefining wall friction by linking the roughness length to the bubble departure diameter produces unexpectedly good results. Only when this new model is activated can the boundary layer be correctly recovered. In addition, this work reveals that the lift force should be activated based on fundamental operating conditions such as system pressure, power, mass flux and subcooling, rather than on bubble diameter alone. The aim of this work is not to introduce a universal boiling model, but rather to highlight a few research directions that may provide greater insight into the fundamental mechanisms governing highly convective boiling flows, including the validity of lift forces in this context.

在壁面热流密度划分方法的背景下，我们提出了一种新的高压过冷流动沸腾的建模路线，我们通过去除淬火部分来简化该路线。对比实验数据表明，壁面气泡成核破坏边界层结构的方式与壁面粗糙度破坏边界层结构的方式相同。我们证明，通过将粗糙度长度与气泡离开直径联系起来重新定义壁面摩擦会产生意想不到的好结果。只有激活这个新模型，才能正确地恢复边界层。此外，这项工作还揭示了升力的激活应基于系统压力、功率、质量通量和过冷度等基本运行条件，而不仅仅是气泡直径。这项工作的目的不是介绍一个通用的沸腾模型，而是强调一些研究方向，这些研究方向可以提供对控制高对流沸腾流的基本机制的更深入的了解，包括升力在这种情况下的有效性。

引用次数: 0

Relative contributions of drag and non-drag forces governing particle motion in pressurized gas-solid jets 在加压气固射流中控制粒子运动的阻力和非阻力的相对贡献

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-09 DOI: 10.1016/j.ijmultiphaseflow.2026.105612

Donald E. Peterson, Bradley R. Adams

This study numerically evaluated the relative contributions of drag (F_D), fluid stress (F_SF), added mass (F_AM), and Basset history (F_H) forces on particle motion as a function of particle size and gas pressure in a one-dimensional gas-solid jet. The analysis used particle and CO₂ gas properties representative of a pilot-scale pressurized oxy-coal combustor inlet at 300 K. Particle diameters of 20-125 μm and gas pressures of 5-40 bar were considered with an inlet velocity of 5 m/s. Force contributions were assessed through force-to-gravity ratios and cumulative force fractions. Results showed that drag was the dominant force beyond the velocity core. However, for larger particles at elevated pressures, F_SF and F_H locally exceeded F_D in regions where gas-particle velocity differences were small. F_SF and F_AM peaked at the gas velocity gradient discontinuity at the jet core exit, while F_H peak lagged this location due to its history effects. F_SF and F_H were consistently greater than F_AM at all conditions. Cumulative force contribution results confirmed that non-drag forces influenced early particle motion for 125 μm particles at 20–40 bar, though their relative importance diminished with distance. Particle velocity responsiveness to changing gas velocity increased with both size and pressure, with non-drag forces most relevant when drag was weak. Findings demonstrate that under high-pressure conditions, forces often considered negligible in atmospheric gas-solid flows may contribute significantly to local particle dynamics.

在一维气固射流中，阻力（FD）、流体应力（FSF）、附加质量（FAM）和巴塞特历史力（FH）对颗粒运动的相对贡献以粒径和气体压力为函数进行了数值计算。该分析使用了代表中试加压氧煤燃烧室进口在300 K时的颗粒和CO2气体特性。考虑颗粒直径为20 ~ 125 μm，气体压力为5 ~ 40 bar，入口速度为5 m/s。通过力与重力比和累积力分数来评估力的贡献。结果表明，在速度核心之外，阻力是主导力。然而，对于高压下较大的颗粒，在气粒速度差较小的区域，FSF和FH局部超过FD。FSF和FAM峰值出现在射流核心出口处的气体速度梯度不连续处，而FH峰值由于其历史影响而滞后于该位置。在所有条件下，FSF和FH均大于FAM。累积力贡献结果证实，在20-40 bar条件下，非阻力力影响125 μm颗粒的早期运动，但其相对重要性随着距离的增加而降低。颗粒速度对气体速度变化的响应性随尺寸和压力的增加而增加，当阻力较弱时，非阻力最相关。研究结果表明，在高压条件下，在大气气固流动中通常被认为可以忽略不计的力可能对局部粒子动力学有重大贡献。

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引用次数: 0

Large eddy simulation of fiber flocculation in a diffuser: Effects of fiber inertia and reinjection kinematics 扩散器中纤维絮凝的大涡模拟：纤维惯性和回喷运动学的影响

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-20 DOI: 10.1016/j.ijmultiphaseflow.2026.105627

MohammadJavad Norouzi , Jelena Andrić , Anton Vernet , Jordi Pallares , Håkan Nilsson

This study investigates flocculation in dilute suspensions of rigid fibers flowing through an asymmetric diffuser using an Eulerian–Lagrangian approach. The analysis focuses on flow-induced ballistic flocculation under varying fiber inertia and inlet (reinjection) kinematics. The fiber length exceeds the Kolmogorov length scale of the carrier flow, and finite inertia leads to a non-negligible slip velocity relative to the fluid. Large eddy simulation (LES) is applied with a dynamic subgrid-scale model to resolve the flow field and turbulence. One-way coupling between the fibers and the flow is assumed, while fiber–fiber interactions are modeled using short-range attractive forces that promote floc formation. The results show that ballistic deflection significantly accelerates flocculation in the diffuser region, establishing ballistic deflection as the dominant mechanism. In addition, inlet fiber kinematics and inertia strongly influence flocculation within the straight inflow channel.

本研究利用欧拉-拉格朗日方法研究了刚性纤维稀悬浮液流过不对称扩散器时的絮凝作用。重点分析了不同纤维惯量和进（回）喷运动条件下的流致弹道絮凝。光纤长度超过载流子流动的柯尔莫哥洛夫长度尺度，有限的惯性导致相对于流体的不可忽略的滑移速度。采用动态亚网格尺度模型，采用大涡模拟方法求解流场和湍流。假设纤维与流体之间存在单向耦合，而纤维与纤维之间的相互作用则使用促进絮团形成的短程吸引力来建模。结果表明，弹道偏转显著加速了扩散区的絮凝，表明弹道偏转是主要机理。此外，进口纤维的运动学和惯性对直流通道内的絮凝有很大的影响。

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引用次数: 0

Experimental investigation of secondary atomization in high-speed gas flow 高速气流中二次雾化的实验研究

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-08 DOI: 10.1016/j.ijmultiphaseflow.2026.105611

Dajun Xin , Jinhong Liu , Kun Xue

This study develops empirical correlations for the secondary atomization dynamics of water droplets exposed to high-speed flows spanning three orders of Weber number magnitude (We ∼ O(10¹)–O(10³)). It achieves this by employing shock-tube experiments coupled with time-resolved shadowgraph imaging. Over 100 trials resolve the deformation and breakup processes across subsonic to supersonic regimes. Thereby, the cross-stream deformation rates, maximum flattening ratios, and dimensionless breakup initiation times (τ_b,i) were quantified as functions of We. The results reveal that a two-stage trend in τ_b,i emerges: a rapid decay below We ∼ 500 transitions to a gradual saturation above We ∼ 1500. This is consistent with a shift in breakup regime dominance from bag-type breakup to shear-induced entrainment. A novel grayscale intensity analysis method isolates the core droplet morphology from the surrounding satellite mist. This enables a precise tracking of the transient mass shedding. Core flattening persists until perimeter shear stripping initiates an exponential mass decay that follows a We-independent scaling law in the shear/ Catastrophic regime. Spatial satellite distributions (resolved via high-resolution digital in-line holography (DIH)) reveal We-dependent shedding mechanisms governed by the transition from bag-type (We ∼ O(10¹))to transition from bag-type to shear-driven (We ∼ O(10²)) and shear-driven breakup (We ∼ O(10³)). The transient drag coefficient for the core droplet depends on its aspect ratio, which evolves dynamically with shape deformation and mass shedding. Integrating these correlations for secondary atomization and time-varying drag yields trajectory predictions for core droplet that exhibit deviations less than 7% from experimental data across the tested conditions. This demonstrates the enhanced predictive accuracy of the proposed models over a broad We range.

该研究开发了暴露在高速流动中的水滴的二次雾化动力学的经验相关性，跨越三个韦伯数量级(We ~ O（101) -O(103)）。它通过使用激波管实验和时间分辨阴影成像来实现这一目标。超过100次试验解决了亚音速到超音速的变形和破裂过程。因此，横流变形速率、最大扁化比和无因次破碎起始时间（τb,i）被量化为We的函数。结果表明，τb，i出现了两个阶段的趋势：在We ~ 500以下快速衰减，在We ~ 1500以上逐渐饱和。这与破碎机制主导地位的转变是一致的，从袋状破碎到剪切诱导的夹带。一种新的灰度强度分析方法将核心液滴形态从周围的卫星雾中分离出来。这样可以精确地跟踪瞬态质量脱落。岩心扁化一直持续到周长剪切剥离引发指数质量衰减，该衰减遵循剪切/灾难性状态下与we无关的标度定律。空间卫星分布（通过高分辨率数字直线全息（DIH）解析）揭示了We依赖的脱落机制，由从袋型（We ~ O(101)）到从袋型到剪切驱动（We ~ O(102)）和剪切驱动的破裂（We ~ O(103)）的转变所控制。岩心液滴的瞬态阻力系数取决于其长径比，长径比随形状变形和质量脱落而动态变化。将二次雾化和随时间变化的阻力的这些相关性整合在一起，得出了在测试条件下，岩心液滴的轨迹预测与实验数据的偏差小于7%。这证明了所提出的模型在广泛的We范围内具有更高的预测精度。

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引用次数: 0

Study of hydrodynamic forces on a finite particle attached to a wall in a confined Couette flow 受限库埃特流中附着在壁上的有限颗粒的水动力研究

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-23 DOI: 10.1016/j.ijmultiphaseflow.2026.105629

Kun Meng , Binbin Shan , Yan Cui , Peng Gao , Chengjun Zhang , Xuyao Mao , Jure Ravnik , Matjaž Hriberšek , Yinshui Liu

Contaminant particles adhering to walls within narrow fluid clearances significantly degrade the performance and service life of precision systems such as hydraulic components and microsensors. This study investigates the effects of wall confinement on hydrodynamics and particle detachment in a Couette flow, where a spherical particle is attached to the bottom wall and subject to the influence of the top wall. Results demonstrate that confinement deflects streamlines downward and shifts stagnation points upward, thereby reducing flow velocity beneath the particle while accelerating it above. The enhanced particle blockage effect increases both the drag and torque coefficients, while the suppression of vertical velocity markedly reduces the lift coefficient. Phase diagrams identify the critical particle Reynolds numbers for three initial detachment modes (rolling, sliding, and lifting), revealing that rolling detachment is the most readily initiated. Empirical correlations for the force and torque coefficients in confined Couette flow are proposed, along with an algorithm for determining the critical particle Reynolds numbers. These tools can be integrated into Eulerian–Lagrangian computational frameworks to improve the efficiency and accuracy of predicting contaminant particle detachment in precision fluid systems.

在狭窄的流体间隙内，污染物颗粒粘附在壁上，会显著降低液压元件和微传感器等精密系统的性能和使用寿命。在Couette流中，球形颗粒附着在底壁上并受到顶壁上的影响，本文研究了壁面约束对流体动力学和颗粒分离的影响。结果表明，约束使流线向下偏转，使停滞点向上移动，从而降低了粒子下方的流速，同时加速了粒子上方的流速。颗粒堵塞效应的增强增加了阻力系数和扭矩系数，而垂直速度的抑制显著降低了升力系数。相图确定了三种初始分离模式（滚动、滑动和提升）的临界粒子雷诺数，揭示了滚动分离是最容易开始的。提出了密闭库埃特流中力和扭矩系数的经验关联，以及确定临界粒子雷诺数的算法。这些工具可以集成到欧拉-拉格朗日计算框架中，以提高预测精密流体系统中污染物颗粒脱离的效率和准确性。

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引用次数: 0

The broken link between space and time in elastic turbulence 弹性湍流中空间和时间之间断裂的联系

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2026-01-27 DOI: 10.1016/j.ijmultiphaseflow.2026.105630

Giulio Foggi Rota , Rahul K. Singh , Alessandro Chiarini , Christian Amor , Giovanni Soligo , Dhrubaditya Mitra , Marco Edoardo Rosti

Elastic turbulence (ET), observed in flows of sufficiently elastic polymer solution at small inertia, is characterized by chaotic motions and power-law scaling of energy spectrum (

E

) in both wavenumber (

k

) and frequency (

ω

):

E (k) \sim k^{- α}

and

E (ω) \sim ω^{- β}

. Experiments of ET have obtained a vast range of values for the exponent

β

. In inertial turbulence, Taylor’s frozen-flow hypothesis implies

α = β

, i.e., spatial and temporal scales are linearly related to each other. In contrast, from high-resolution simulation in three different setups, a tri-periodic box, a channel, and a planar jet, we show that in ET

α \approx 4

while

β

varies significantly. Our analysis shows that in general Taylor’s hypothesis does not hold in ET as there is no universal relation, linear or otherwise, between space and time. We thus clear the confusion of the different scaling exponents found in ET, and focus the attention of future research on understanding

α

. Our analysis also implies that waves-like dynamics with a linear dispersion relation (e.g., Alfvén waves) cannot play a role in determining the scaling behavior of ET. The techniques introduced here can be useful for studying smooth chaotic flows in general, e.g., active turbulence.

弹性湍流（ET），在足够弹性的聚合物溶液以小惯性流动中观察到，其特征是波数(k)和频率（ω）的能谱(E)的混沌运动和幂律缩放：E(k) ~ k−α和E(ω) ~ ω−β。ET实验已经获得了β指数的大范围值。在惯性湍流中，Taylor的冻结流假设意味着α=β，即空间尺度和时间尺度彼此线性相关。相比之下，在三周期盒子、通道和平面射流三种不同设置下的高分辨率模拟中，我们发现在ET中α≈4而β变化显著。我们的分析表明，一般来说，泰勒的假设在ET中不成立，因为空间和时间之间没有普遍的关系，无论是线性的还是其他的。因此，我们澄清了在ET中发现的不同标度指数的混淆，并将未来的研究重点放在理解α上。我们的分析还表明，具有线性色散关系的类波动力学（例如，alfv诈骗波）不能在确定ET的标度行为中发挥作用。这里介绍的技术可用于研究一般的光滑混沌流动，例如主动湍流。

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引用次数: 0

Adaptively reconstructed spectral eddy-viscosity in large eddy simulations of particle-laden isotropic turbulence, Part I: Particle statistics at low Reynolds number 大涡模拟中自适应重建谱涡黏度的粒子负载各向同性湍流，第一部分：低雷诺数下的粒子统计

IF 3.8 2区工程技术 Q1 MECHANICS

International Journal of Multiphase Flow

Pub Date : 2026-03-01 Epub Date: 2025-12-29 DOI: 10.1016/j.ijmultiphaseflow.2025.105584

Michał Rajek , Jacek Pozorski

Large eddy simulations (LES) of isotropic turbulence coupled with the Lagrangian particle tracking have consistently been disregarded as a means of exploring the physics underlying turbulent dispersed two-phase flows, specifically at Reynolds numbers beyond the reach of direct numerical simulations (DNS). In the current two-part study we focus on evaluating the impact of our recently developed adaptively reconstructed spectral eddy-viscosity on the dynamics of inertial particles in LES of isotropic turbulence. To confirm the robustness of our computational framework, in the present work we first concentrate on the settling speed enhancement, clustering, and relative velocities at low Reynolds numbers. These particle statistics are of importance to determining the collision rates, influencing various environmental phenomena and industrial processes. We also indicate that the LES enriched with a well-established spectral eddy-viscosity which assumes the existence of an infinite

k^{- 5 / 3}

energy spectrum is unable to reliably predict the radial distribution function and the radial relative velocities at contact. We show that the adaptively reconstructed eddy-viscosity significantly improves the predictive capabilities of LES, thus providing a tool to explore the physics underlying dispersed two-phase flows. We particularly demonstrate that under conditions relevant to cloud turbulence, certain phenomena related to particle motion can be accurately predicted without the subgrid-scale contribution to the fluid velocity at the particle location. In the companion paper we assess the ability of the proposed LES to accurately quantify particle clustering at length scales relevant to the inertial subrange at high Reynolds numbers.

各向同性湍流的大涡模拟（LES）与拉格朗日粒子跟踪相结合，一直被忽视为探索湍流分散两相流的物理基础的手段，特别是在直接数值模拟（DNS）无法达到的雷诺数下。在目前的两部分研究中，我们重点评估了我们最近开发的自适应重建光谱涡流粘度对各向同性湍流LES中惯性粒子动力学的影响。为了证实我们的计算框架的鲁棒性，在目前的工作中，我们首先关注低雷诺数下的沉降速度增强、聚类和相对速度。这些粒子统计对于确定碰撞率、影响各种环境现象和工业过程具有重要意义。我们还指出，假设存在无限k−5/3能谱，且具有完善的谱涡黏度的LES不能可靠地预测接触时的径向分布函数和径向相对速度。我们发现自适应重建的涡流粘度显著提高了LES的预测能力，从而为探索分散两相流的物理基础提供了工具。我们特别证明，在与云湍流有关的条件下，某些与粒子运动有关的现象可以准确地预测，而不需要亚网格尺度对粒子位置流体速度的贡献。在配套论文中，我们评估了所提出的LES在高雷诺数下与惯性子范围相关的长度尺度上精确量化粒子聚类的能力。

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引用次数: 0