Velocity and acceleration statistics in particle-laden turbulent swirling flows (1912.07581v2)

Abstract: We present a comparison of different particles' velocity and acceleration statistics in two paradigmatic turbulent swirling flows: the von K\'arm\'an flow in a laboratory experiment, and the Taylor-Green flow in direct numerical simulations. Tracers, as well as inertial particles, are considered. Results indicate that, in spite of the differences in boundary conditions and forcing mechanisms, scaling properties and statistical quantities reveal similarities between both flows, pointing to new methods to calibrate and compare models for particles dynamics in numerical simulations, as well as to characterize the dynamics of particles in simulations and experiments.

• The paper finds striking statistical similarities in particle velocity and acceleration between experimental von Kármán and simulated Taylor-Green turbulent swirling flows despite different conditions.
• Large-scale mean flow structures significantly influence particle dynamics and contribute to inertial range scaling, suggesting limitations in models that neglect such effects.
• Observed scaling anomalies and the agreement achieved with an empirical model for inertial particles offer insights for refining turbulence models and simulating large particles effectively.

Analysis of Velocity and Acceleration Statistics in Particle-Laden Turbulent Swirling Flows

The paper "Velocity and acceleration statistics in particle-laden turbulent swirling flows" explores the comparative analysis of particle dynamics in two notable turbulent swirling flows: the von Kármán flow, produced experimentally, and the Taylor-Green flow, studied through direct numerical simulation (DNS). Given the inherent differences in boundary conditions and forcing mechanisms between these flows, the paper provides an insightful examination of their scaling properties and statistical similarities, enhancing our understanding of particle dynamics in turbulent environments.

Background and Methodology

Turbulent flows, often characterized by chaotic fluid motion, play a significant role in diverse natural and industrial scenarios, from atmospheric phenomena to water treatment processes. Leveraging this complexity, the authors explore particle behavior within such flows, particularly emphasizing how particles' velocity and acceleration statistics reveal the interplay between flow structures and turbulent mixing.

The paper employs laboratory experiments to generate the von Kármán swirling flow using a setup with counter-rotating disks in a cubic cell and contrasts it with the Taylor-Green flow, a canonical turbulent flow often used in theoretical studies due to its symmetry and periodic boundary conditions.

Key Findings

1. Statistical Similarity: Despite the differences in boundary conditions, both flows exhibit striking similarities in particle velocity and acceleration statistics. The analysis highlights critical parameters, such as Reynolds numbers and Stokes numbers, that bridge the behavior observed in experiments and simulations.
2. Impact of Mean Flow: The paper finds that large-scale flow structures substantially influence particle dynamics, evidenced by the contribution of the mean flow to inertial range scaling. This observation underscores the non-negligible role of coherent flow structures in determining particle paths and velocities.
3. Pinpointing Scaling Anomalies: The paper reports scaling anomalies in statistical quantities, particularly the second-order Lagrangian structure functions. These anomalies manifest as deviations from classical Kolmogorov inertial range predictions and are attributed to the influence of large-scale sweeping effects in the flow.
4. Effective Modeling of Inertial Particles: For inertial particles—those with mass distinct from the surrounding fluid—an empirical model incorporating effective relaxation times yields satisfactory agreement between experiments and DNS results. This approach enables a practical framework for simulating large particles with finite size despite inherent modeling simplifications.

Practical and Theoretical Implications

The agreement between experimental von Kármán flows and numerical Taylor-Green simulations holds promise for calibrating computational models against experimental data. This alignment allows researchers to refine turbulence models across scales, enhancing predictive capabilities for real-world applications like pollutant dispersion and industrial mixing.

Theoretical implications arise from the observed influence of mean flows on statistical properties, suggesting that traditional models, which often neglect such effects, may require revision to accommodate the complex dynamics of swirling flows. Furthermore, the paper highlights the need for comprehensive models that integrate additional forces and effects acting on particles beyond simplified assumptions.

Future Directions

The authors suggest avenues for future research, including:

• Exploration of Diverse Particle Properties: Further studies could investigate particles of varying size and density to fully elucidate their interaction with turbulent flows.
• Refinement of Numerical Models: Enhancements to numerical models incorporating more sophisticated representations of particle dynamics, such as added mass and finite-size effects, could offer deeper insights into complex flow-particle interactions.
• Experimental Variation: Modifications to experimental setups, like adjusting blade geometry in von Kármán flows, could provide experimental conditions more congruent with simulation assumptions, facilitating refined comparative studies.

In conclusion, the paper establishes a foundational analysis of particle-laden turbulent swirling flows, identifying key similarities and disparities between distinct experimental and numerical approaches. This work not only advances the understanding of turbulent particle dynamics but also paves the way for improved predictive models in environmental and industrial contexts.