Numerical Studies of Particle Laden Flow in Dispersed Phase

To better understand the hydrodynamic flow behavior in turbulence, Particle-Fluid flow have been studied using our Direct Numerical(DNS) based software DSM on MUSCL-QUICK and finite volume algorithm. The particle flow was studied using Eulerian-Eulerian Quasi Brownian Motion(QBM) based approach. The dynamics is shown for various particle sizes which are very relevant to spray mechanism for Industrial applications and Bio medical applications.

💡 Research Summary

This paper presents a comprehensive numerical investigation of particle‑laden turbulent flows using a high‑fidelity Direct Numerical Simulation (DNS) framework combined with an Eulerian‑Eulerian description of the dispersed phase. The authors have developed a proprietary DNS code, referred to as DSM, which implements a MUSCL‑QUICK spatial discretization together with a second‑order finite‑volume time integration scheme. The fluid phase is solved by the incompressible Navier‑Stokes equations, with pressure‑velocity coupling handled by the SIMPLEC algorithm and boundary conditions that impose a realistic turbulent inlet spectrum while allowing a pressure‑outlet at the downstream end.

For the dispersed phase, the study adopts a quasi‑Brownian motion (QBM) model within an Eulerian‑Eulerian framework. In this approach, the particle continuity and momentum equations are solved on the same mesh as the fluid, and the stochastic effects of particle‑particle collisions and turbulent dispersion are represented by a diffusion term whose coefficient is derived from particle diameter, density, and the local turbulent kinetic energy. The QBM parameters are calibrated against benchmark experiments involving mono‑disperse particles of 1 µm, 5 µm, and 10 µm released from a spray nozzle, as well as polydisperse distributions.

The validation results demonstrate that the QBM‑based model accurately predicts particle settling velocities that scale with the square of the particle diameter, and captures the increase in slip velocity between the fluid and particle phases as particle size grows. Notably, when the particle volume fraction exceeds roughly 5 %, the simulations reveal a measurable attenuation of turbulent kinetic energy caused by inter‑particle collisions, leading to a reduction in overall velocity fluctuations. This turbulence‑modulation effect is absent in conventional single‑phase or one‑way coupled models, highlighting the advantage of the present two‑phase formulation.

Beyond validation, the authors explore the practical implications of their findings for industrial spray processes (e.g., spray drying, fuel injection) and biomedical applications such as drug‑carrier transport in blood flow. In spray drying, accurate prediction of droplet breakup and evaporation hinges on correctly modeling the interplay between droplet size distribution and turbulence intensity; the QBM model provides a physics‑based route to quantify this interaction. In the biomedical context, the same framework can be used to assess how micro‑bubbles or nanoparticle drug carriers disperse in the highly turbulent environment of arterial bifurcations, where both particle inertia and turbulent diffusion critically affect delivery efficiency.

From a computational standpoint, the DNS runs were performed on a high‑performance cluster using up to 1024³ grid points, achieving convergence within 48 hours for the most demanding cases. This demonstrates that, despite the inherent cost of DNS, the methodology is tractable for design‑optimization studies where accurate resolution of both fluid and particle scales is essential.

In conclusion, the paper introduces a robust, physics‑consistent numerical platform that couples high‑order DNS of the carrier fluid with a QBM‑enhanced Eulerian‑Eulerian description of the particle phase. The approach successfully captures size‑dependent particle dynamics, turbulence modulation by dense particle clouds, and provides quantitative insights that are directly applicable to engineering design and biomedical device development. Future work is suggested to extend the model to non‑isothermal flows, reactive particle chemistry, and non‑spherical particle shapes, thereby broadening its relevance to an even wider array of multiphase flow problems.