Filter Media Modeling

This presentation reviews our past and current studies on modeling dust particles filtration via fibrous filters. This includes ways to create a realistic three-dimensional structure to virtually reproduce the internal geometry of a filter, and the list of equations that need to be solved to obtain the pressure drop and collection efficiency of the filter. Both microscale (fiber-level) and macroscale (pleat-level) approaches will be discussed and their predictions will be compared with one another, and with experimental data whenever possible. Effects of microstructural properties of a fibrous filter (e.g., fiber orientation or size distribution) on its particle collection efficiency and pressure drop will be discussed in detail. This presentation will also report on our most recent experimental–computational studies on multiphase droplet detachment from fibers and fibrous structures. This information is important in designing new products for droplet removal from gases, droplet removal from liquids, protective textiles, and membranes among many others. 

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CFD based development of coalescence filters requires accurate evaluation of the several underlying processes such as mist capture, coalescence, fluid redistribution, and equilibrium state of fluid saturation with balanced collection and drainage or re-entrainment.

This work firstly identifies deficiencies in modeling mist as akin to dust particles in the initial capture regime, and discusses the necessity for extending the SFE theory to account for fluid-filter wetting properties.

Secondly, pore-scale simulation of coalescence and re-entrainment processes requires the development of efficient virtual media generation methodologies that are not only independent of imagery inputs, but also accommodate isolated variations in micro-structural properties, for media optimization. An open-source technique for the generation of nonwoven (single/ multimodal fibres), open-cell foam and knitted geometries are presented. The microstructural properties and CFD predictions for pressure drop and saturation are validated using experimental measurements, and the uncertainties due to the influence of computational domain size are quantified.

Further, the resource requirements due substantial variations in the length scales among mist, fibres and coalesced fluid that need to be resolved for CFD of the entire mist/ coalescence filtration process can be overwhelming and thus necessitates multi-scale CFD strategies. The results from such novel Lagrangian-VOF or Euler-Euler-VOF simulations of gas-liquid and liquid-liquid filtration are discussed with examples.

Finally, considering that the largest length scales of the fluid structures are expected during steady state, and that equilibrium conditions are weakly related to mist loading at low loading rates, a pore-network approach is proposed for evaluating steady state saturation and pressure drop, and validated.

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Major challenges in predicting fibrous filter loading curves (the pressure drop versus mass collected) are that (1) filters load heterogeneously and (2) dust “cake” forms both within filters and on top of filters.  Even in instances where the pressure drop across the filter and filter collection efficiency curve are initially predictable, combined, asymmetric loading and cake formation complicate prediction of filter performance over time.  Modeling approaches that make use of individual particle trajectory and deposition calculations are typically utilized to predict filter performance over time.  However, they are computationally expensive, and additionally require detailed microstructural filter models for implementation.  In our work, we have made efforts to develop computationally less expensive Eulerian approaches to model the evolution of particle solidity and cake formation across a heterogeneous filter domain.  A filter is described initially by the fiber size distribution function and fiber solidity, both as functions of position.  Model predictions hinge upon a recently developed pressure drop model for mixed fiber-particulate media, single fiber collection efficiency correlations, and an input maximum particle solidity for cake formation, which can be a function of particle size.  They key advantage of the Eulerian approach is its significantly reduced computational cost in comparison to particle tracking approaches.  This enables its implementation in whole filter models, and implementation in conjunction with computational fluid dynamics models (e.g. for pleated filters). Example calculations are provided for polydisperse particle loading of heterogeneous filter media.  

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The focus of this presentation is the design of filtration devices for two applications in extreme environments that are hostile to human habitation. The applications are (1) air particulate filtration in a closed living environment and (2) capture of carbon particles that are a byproduct of plasma pyrolysis assembly (PPA) that recovers hydrogen, that would otherwise be lost, in the system for producing oxygen and water from carbon dioxide. The authors have developed analytical solutions for the mathematical model governing cross flow filtration in both tubular and narrow rectangular geometries. Under appropriate conditions, cross flow filtration is known to reach a state of dynamic equilibrium. This result, that is well known for solid-liquid cross flow filter separations is also possible (or nearly so) for solid/gas separations. A cross flow filter can be designed to operate in cross flow or closed (dead-end) mode.

The mathematical model yields bounding values of filter length, inlet flow rate and pressure drop that arise in the clean filter (no-fouling) case, providing a safe and reasonable operating envelope for the transient case with fouling. Analytical solutions for pressure, flow rate, and permeate flux in the transient case provide insight to both fouling on the filter surface (as a cake) and in the filter media (depth plugging). A generalization of the Darcy equation introduces terms governing a static, incompressible cake layer which grows in time, under laminar flow conditions and time-dependent depth plugging. A distribution function controls the balance between cake deposition and depth plugging in the filter. Modeling provides insight into the relationships between geometry and process parameters and filter performance. Analytical solutions also serve as valuable benchmarks for numerical solutions for more complex mathematical models that cannot be solved analytically.

The models are being developed for use both as predictive tools (given input parameters determine the output) and also in design mode, i.e. determine filter characteristics that will produce optimal results under specified process conditions. The latter capability enables the consideration of econometric criteria such as frequency of regeneration, launch mass and volume. An overview of the applications will be presented, along with the models, results to date and a discussion of continuing work including planned experiments for determining permeability of carbon cakes that form from the particles associated with the PPA reactor.

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Nonwoven filter media performance depends on spatial distribution, orientation, length, curvature, and center line of individual fibers and volume- or weight-percentage and spatial distribution of binder. Fibers and binder which often appear with the same gray values in μCT scans can be separated based on shape by a deep artificial neural network (ANN) trained to distinguish them using modelled artificial 3-D scans of nonwoven with known distribution of binder.

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Spinning processes for fibers, filaments and nonwovens differ in their mechanism to draw the melt or solution to generate the resulting fiber diameter. On the one hand there are processes like spunbond or staple fibers where spinning speed in relation to hole throughput determines the diameter – typically above 10 microns. On the other hand there are processes like electrospinning or meltblown where additional acceleration steps during spinning lead to much finer diameters down to submicron or nano fibers. Their productivity in fine fiber generation enables a wide spectrum of nonwoven-based filtration applications.

We present the physical modeling and simulation of meltblown concerning the fila-ment dynamics in this turbulence-driven process. The modeling is embedded in the so-called Cosserat-rod framework which describes the dynamical change of cross-sectional properties along the center line of the filament. These partial differential equations are based on the balance laws for mass, momentum and energy includ-ing visco-elastic effects for stretching and bending. The fiber dynamics are coupled with the surrounding air flow concerning heat and momentum exchange. The turbu-lence of transonic air is causing highly fluctuating velocities which are responsible for the effectiveness of meltblown.

The meltblown process is shown to be a combination of spunbond like uniaxial-stretching near to the nozzle with high air speed and further acceleration by sto-chastic forces caused from turbulent air fluctuations. These interactions between filament dynamics and turbulent air flow are highly complex due to local stretching and cool down together with the visco-elastic behavior of the fibers. The fundamen-tal understanding of its dependency on the material and process parameters togeth-er with the process design enables further optimization concerning higher productiv-ity and/or finer fibers.

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