Effect of Reynolds number on triboelectric particle charging in turbulent channel flow

Triboelectric charging in particle-laden flows is a complex interplay of fluid and particle dynamics, collision mechanics, and electrostatics. In this study, we introduce triboFoam, an open-source solver built on the OpenFOAM framework, designed to simulate triboelectric charging in particle-laden turbulent flows. We validate triboFoam using Direct Numerical Simulations (DNS) of a fully developed turbulent channel flow at a friction Reynolds number of $Re_τ= 180$. The results demonstrate good agreement with DNS data for particle concentration profiles and charge distributions. Then, we investigate the influence of Reynolds number on particle distribution and charging behaviour using Large-Eddy Simulations (LES) at varying friction Reynolds numbers up to $Re_τ= 550$. Our findings reveal that higher Reynolds numbers lead to increased near-wall particle concentrations and enhanced charging rates, attributed to intensified turbulent fluctuations and elevated impact velocities. Finally, an empirical correlation is proposed to predict the average particle charging rate as a function of Reynolds number and particle diameter. With this work, we provide a tool for simulating triboelectric charging in complex geometries and turbulent flows, advancing the understanding of electrostatic phenomena in particle-laden systems. The empirical correlation offers practical insights for predicting charging behaviour in industrial applications and thus can contribute to improved safety and efficiency in processes involving particulate matter.

💡 Research Summary

The paper presents triboFoam, an open‑source computational framework built on OpenFOAM for simulating triboelectric charging in particle‑laden turbulent flows. triboFoam couples an Eulerian fluid solver with a Lagrangian particle tracker, incorporating aerodynamic drag, gravity, hard‑sphere collisions, and electrostatic forces. The fluid equations are solved using Large‑Eddy Simulation (LES) with the Wall‑Adapting Local Eddy‑viscosity (W‑ALE) sub‑grid model, which accurately resolves the viscous sub‑layer near walls—a critical region for particle‑wall interactions. Electrostatic forces are computed with a hybrid scheme: direct Coulomb interactions for particles within the same mesh cell and a Gauss‑law based field solution for long‑range contributions, dramatically reducing the O(N²) cost while preserving accuracy. Four charging models are implemented: the classical condenser model, a random charging model, a constant‑charge transfer model, and the recently introduced Stochastic Scaling Model (SSM). Each model links charge transfer during collisions to physical quantities such as particle capacitance, contact time, and charge relaxation time.

Validation is performed against Direct Numerical Simulation (DNS) data for a fully developed turbulent channel flow at friction Reynolds number Reτ = 180. triboFoam reproduces particle concentration profiles, near‑wall accumulation, and charge distributions with excellent agreement, confirming that the W‑ALE model and the hybrid electrostatic solver capture the essential physics.

Having established credibility, the authors conduct a systematic LES study at higher friction Reynolds numbers (Reτ = 300, 400, 550) to isolate the effect of Reynolds number on particle dynamics and charging. The results show a clear trend: as Reτ increases, turbulent intensity near the wall grows, leading to higher particle‑wall collision frequencies and larger impact velocities. Particle‑particle collisions also become more frequent, enhancing charge exchange events. Consequently, near‑wall particle concentrations rise, and the average particle charging rate increases markedly. The effect is more pronounced for smaller particles, whose inertia allows them to respond more strongly to the intensified turbulent fluctuations.

From the LES data, the authors derive an empirical correlation for the mean charging rate ⟨q̇⟩ as a function of Reynolds number and particle diameter: ⟨q̇⟩ ≈ C Reτ^α dₚ^β, with regression‑determined exponents α ≈ 1.2 and β ≈ 0.8, and C encapsulating material properties and the chosen charging model. This correlation provides a practical tool for engineers to estimate electrostatic charging in pneumatic conveying, dust handling, and other industrial processes where direct simulation would be prohibitive.

The paper acknowledges several limitations. The simulations assume dilute particle concentrations, employing only one‑way or two‑way coupling; dense regimes where electrostatic repulsion and collective effects dominate are not addressed. The geometry is limited to a straight rectangular channel, whereas real systems often involve bends, contractions, and complex networks that can further amplify charging. Moreover, the study does not model discharge phenomena that may occur when accumulated charge exceeds breakdown thresholds.

Future work is outlined to extend triboFoam to complex geometries, incorporate four‑way coupling with full electrostatic feedback, and validate against experimental measurements in industrial‑scale setups. By doing so, the authors aim to broaden the applicability of triboFoam and deepen the understanding of triboelectric phenomena in high‑Reynolds‑number turbulent flows.