Modelling laminar flow in V-shaped filters integrated with catalyst technologies for atmospheric pollutant removal

Abstract

Atmospheric pollution from particulate matter, volatile organic compounds and greenhouse gases is a critical environmental and public health issue, leading to respiratory diseases and climate change. A potential mitigation strategy involves utilising ventilation systems, which process large volumes of indoor and outdoor air and remove particulate pollutants through filtration. However, the integration of catalytic technologies with filters in ventilation systems remains underexplored, despite their potential to simultaneously remove particulate matter and gases, as seen in flue gas treatment and automotive exhaust systems. In this study, we develop a predictive, long-wave model for V-shaped filters, with and without separators. The model, validated against experimental and numerical data, provides a framework for enhancing flow rates by increasing fibre diameter and porosity while reducing aspect ratio and filter thickness. These changes lead to increased permeability, which lowers energy requirements. However, they also reduce the pollutant removal efficiency, highlighting the trade-off between flow, filtration performance and operational costs. Leveraging the long-wave model alongside experimental results, we estimate the maximum potential removal rate ($4.5\times10^{-3}$ GtPM$_{2.5}$, $6.4\times10^{-3}$ GtNO$_{\text{x}}$, $2.0\times10^{-2}$ GtCH$_{4}$ per year; $1.6\times10^{0}$ GtCO$_{2}$e per year, 20-year GWP for CH$_4$) and minimum cost (\$$3.4\times10^{3}$ per tNO$_{\text{x}}$, \$$1.1\times10^{3}$ per tCH$_{4}$; \$$1.3\times10^{1}$ per tCO$_{2}$e) if a billion V-shaped filters integrated with catalytic enhancements were deployed in operation. These findings highlight the feasibility of catalytic filters as a scalable, high-efficiency solution for improving air quality and mitigating atmospheric pollution.

Figures (8)

• Figure 1: A pressure-driven airflow through a (a) duct containing a V-shaped filter, (b) a single half period of the V-shaped filter, (c) duct containing a separated V-shaped filter and (d) a single half period of the separated V-shaped filter. In (b, d), we position the origin of the coordinate system, $(\hat{x}, \, \hat{y}, \, \hat{z})$, at the start of the V-shaped filter, midway between the filter sheets and transverse width. Each period of the V-shaped filter has length $\hat{L}$, height 2$\hat{H}$ and width $\hat{W}$. The location of the filter sheet is given by $\hat{y} = \hat{s}(\hat{x})$; the area below and above the filter sheet defines subdomains $\hat{D}_1$ and $\hat{D}_2$, respectively. (e) Photograph of a $\phi = 80$% porosity fibre sheet and SEM image of the microstructure with fibres of around $\hat{d} = 100 \mu$m thickness, reproduced from Huang et al.huang2021effective, licensed under CC BY 4.0.
• Figure 2: (a) Comparison of the pressure field in pereira2021optimising (symbols) with the long-wave model \ref{['eq:bvp_1']} (lines) for a V-shaped filter without separators. (b) The pressure field in the long-wave model \ref{['eq:bvp_3']} for a V-shaped filter with separators. In (a--b), the location of the filter sheet is prescribed by $s(x) = a + \beta(1/2 - x)$, with $\beta = 0.05$ and $a = 0.5$ as illustrated in the inset, such that the non-dimensional half-period length and height are unity and the permeance $\kappa = 1$.
• Figure 3: Comparison of the pressure drop ($\Delta \hat{p}$) with the filtration velocity ($\hat{v}_f$) predicted using the long-wave model \ref{['eq:bvp_1']} (solid lines) and experiments (symbols) in (a) del2002air for $\epsilon = 0.065$, 0.037, 0.026, (b) mrad2021local for $\epsilon = 0.45$, (c) zhang2022operating for $\epsilon = 0.11$ and (d) al2011effect for $\epsilon = 0.0089$, 0.0083, 0.0078, 0.0074. (e) Comparison of $\Delta \hat{p}$ with $\hat{v}_f$ predicted using the long-wave model \ref{['eq:bvp_1']} (solid lines) and del2002airmrad2021localzhang2022operatingal2011effect (symbols), where porosity $\phi$ and fibre diameter $\hat{d}$ are listed for each dataset. The superscript$^\dagger$ implies either that these values have been assumed or they have been calculated based on available data and \ref{['eq:kc']}--\ref{['eq:exp']}.
• Figure 4: Comparison of the normalised permeability (a) $\hat{k} / (\phi^3/(1-\phi^2))$ and (b) $\hat{k} / \hat{d}^2$ with the average fibre diameter ($\hat{d}$) and porosity ($\phi$) using the Kozeny--Carman model \ref{['eq:kc']} (solid lines) and experiments del2002airmrad2021localzhang2022operatingal2011effect (symbols).
• Figure 5: Comparison of the removal efficiency $\eta$ with the permeability $\hat{k}$ using the exponential model \ref{['eq:exp']} (solid line) and experiments del2002airmrad2021localzhang2022operatingteng2022research (symbols). Note that as $\hat{d}$ varies from $1\times10^{-6}$ in Fabbro et al.del2002air to $6\times10^{-6}$ m in Fig. \ref{['fig:flux']}(a), $Q$ increases but $\eta$ decreases from 99.97 to 29%.