(178g) Probabilistic CFD Modeling of Fibrous Filters Using Single Fiber Filtration Efficiency and Monte-Carlo Simulation

Fibrous filters are widely employed for the removal of particulate matter from air and impurities from liquid streams. Due to their broad application, accurate prediction of particle capture efficiency and transport behavior within filters is essential for their design and performance evaluation. In computational fluid dynamics (CFD), particle capture in fibrous filters is typically simulated using either micro-scale or macro-scale modeling approaches. Micro-scale modeling [1] explicitly resolves each individual fiber, allowing detailed simulation of particle-fiber interactions with high accuracy, but at a substantial computational cost. In contrast, macro-scale modeling [2] is a method of simulating particle collection using an internal function assuming the porous media characteristics of the filter, which is less accurate than micro-scale modeling, but has an advantage in computational cost. Conventional macro-scale models typically assume unconditional capture of particles when specific conditions are satisfied within the filter cell zone. However, this kind of model has a limitation in that it is difficult to reflect the complex flow and particle behavior inside the filter. Since actual filters have a complex shape and various variables (e.g., particle size, particle velocity, particle-fiber interaction), a modeling approach that reflects more realistic conditions is required. To address this limitation, we propose a novel Probabilistic Filtration (PF) model that integrates Single Fiber Filtration Efficiency (SFFE) with a Monte Carlo (MC) simulation framework.

SFFE quantifies the capture efficiency of individual fibers and is fundamental to micro-scale understanding of filtration performance. SFFE has three main particle collection mechanisms (Diffusion, Interception, and Inertial impaction) depending on the particle size, and calculates the efficiency corresponding to each mechanism [3]. In this study, we focus only on the interception mechanism, assuming specific particle properties and operating conditions. Monte Carlo simulation, which approximates solutions to complex problems through stochastic sampling, is employed to model particle capture probabilistically.

The proposed PF model calculates the capture efficiency of each cell in the porous media based on SFFE, and each cell is treated as a representative single fiber. As particles traverse the domain, their probability of capture in each cell is determined using a Bernoulli trial, with the capture probability derived from the SFFE. During this kind of operation, particle tracking includes unique cell identifiers to ensure non-redundant probabilistic calculation to prevent duplicate calculation within the same cell across different time steps. Model validation was conducted by comparing simulation results with experimental data on pressure drop and captured particle mass over time. A modified form of Darcy’s law, assuming permeability is proportional to filter porosity, was employed to model the evolving pressure drop due to particle loading. Empirical coefficients were obtained through experimental calibration. The PF model closely matched the linear trend of pressure drop observed in experiments, and predicted a capture mass accuracy of 99.05%, indicating strong agreement.

Furthermore, the model was applied to evaluate filtration performance in complex industrial filter geometries. In the simulation on the U-shaped filter, the thinner the U-shaped thickness, the lower the performance in the mass of the collected particles, but the better the performance in other values such as collection efficiency, pressure drop, and collection standard deviation.

In conclusion, the proposed PF model is a new simulation framework that reflects the realistic conditions of the fiber filtering process while maintaining computational efficiency and is a model with both industrial applicability and academic contribution as well. By incorporating probabilistic modeling into conventional CFD frameworks, the proposed approach enables more accurate and quantitative predictions of filtration efficiency and internal particle behavior in complex filter geometries that are difficult to model with traditional deterministic methods. Additionally, it enhances the reliability of particle capture simulations in fibrous filter and can ultimately be used to support safe operation and preventive maintenance of related processes, thereby minimizing the risk of failures or malfunctions.

This research was financially supported by the Ministry of Small and Medium-sized Enterprises(SMEs) and Startups(MSS), Korea, under the “Supporting Project for boosting a Local Innovation Leading Company(R&D), (S3453150)” supervised by the Korea Technology and Information Promotion Agency for SMEs(TIPA).

[1] Liu, X., Ding, X., Chen, C., An, R., Guo, W., Zhang, W., 2019. Investigating the filtration behavior of metal fiber felt using CFD-DEM simulation. Eng. Applications of Computational Fluid Mechanics 13 (1), 426-437.

[2] Cheng, K., Zhu, J., Qian, F., Cao, B., Lu, J., Han, Y., 2023. CFD-DEM simulation of particle deposition characteristics of pleated air filter media based on porous media model. Particuology 72, 37-48.

[3] Hinds, W. C., 1999. Aerosol technology: properties, behavior, and measurement of airborne particles. John Wiley & Sons