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A semi-empirical pressure drop model: Part 1--pleated filters.

Article Excerpt
INRODUCTION

Overview of the Research

The demand for improved indoor air quality (IAQ) has created a need for gas phase filtration units capable of removing contaminants such as volatile organic compounds (VOCs), tobacco smoke, carbon monoxide, and formaldehyde. Strategies to remove these harmful contaminants include employing a packed-bed or an adsorbent-entrapped filtration media such as microfibrous sorbent-supported media (MSSM). Through a wet-laid process, MSSM's sinter-locked matrix of micron-sized fibers can entrap sorbent particles with diameters as low as 30 microns, leading to better chemical removal efficiency and higher sorbent utilization than a traditional packed bed. The disadvantages of adsorbent-entrapped media are a high pressure drop created by small, entrapped sorbent particles and a low saturation capacity due to the relatively thin thickness of the media (Harris et al. 2001).

New tactics for building more efficient gas phase filters need to be researched in order to maximize the usefulness of adsorbent-entrapped media. Pleated and V-bank filters are two designs that can improve both pressure drop performance and overall capacity for filtration units made from these materials. By understanding the pressure drop limitations within these filtration systems, additional media and adsorbent material can be packaged into a unit to increase the contaminant removal capacity while maintaining an acceptable resistance.

The following article, Part 1, discusses the creation and utilization of a model that can predict initial flow resistance in a pleated filter with a depth of 89 mm (3.5 in.) or less. The second article, Part 2, will extend the model presented below to include V-banks composed of multiple pleated filters.

Background

The flow resistance of a filter is a critical design and operational parameter. A large pressure drop across the filter can overload the air handler unit and reduce airflow. More importantly, the pressure drop is directly related to the energy consumption of the filtration system. Energy consumption can account for 80% of the total expenses, while labor and procurement costs account for the remaining 20% (Arnold et al. 2005).

Numerous filter designs are commercially available, yet pleated filters are one of the more popular styles due to their unique performance benefits. A pleated filter uses a highly folded media to increase the available filtration area and extend the filter's useful life. The extra area also bestows the additional advantage of reducing the pressure drop and energy consumption of the filter. The resistance across a pleated filter fits a second order polynomial composed of a geometric ([K.sub.G][V.sub.f.sup.2]) and media ([K.sub.M][V.sub.M]) term.

[DELTA]P = [K.sub.G][V.sub.F.sup.2] + [K.sub.M][V.sub.M] (1)

Empirical and computational fluid dynamics (CFD) approaches have been attempted by Chen et al. (1996), Rivers and Murphy (2000), Caesar and Schroth (2002), Del Fabbro et al. (2002), and Tronville and Sala (2003) to determine the constants. Although each method produces accurate results, the models are only applicable to the specific filters studied and lack predictive capabilities due to the heavy reliance on empirical data. The contributions of the pleat tips and filter housing, mentioned by Raber (1982), are often neglected in the models.

The research objective is the development of an accurate model for use as an analytical design tool capable of predicting initial pressure drop performance of pleated filter units based solely on the thickness and permeability of the media utilized. The effects of a filter's geometry and packaging are quantified in a manner that can be universally applied to various pleated filter designs of depths less than 89 mm (3.5 in.). The model is composed entirely of algebraic equations to allow for quick optimization and for prediction calculations to improve the utility.

The approach used to construct the model is similar to Idelchik's (1994) method used to compute pressure drop in an electrostatic filter. In this method, the total pressure drop of a filter is modeled as a summation of smaller, component resistances. The individual components of a pleated filter were deduced from the proposed airflow pathway introduced by Raber (1982). Each component's influence on the total filter resistance was then formulated through the use of Forchheimer-extended Darcy's Law, Bernoulli's equation, and the equation of continuity.

Since the components of a pleat filter interact with one another, the modeling approach could not simply dissect and quantify the exact pressure drop influence of each component. The model is therefore an empirical determination of the relative influence of each term while in the presence of all other terms. This was accomplished by systematically changing design variables, methodically assessing the net increase in the total filter resistance, and then contributing that influence to the appropriate varying term.

THEORY

Forchheimer-Extended Darcy's Law

In a particulate air filter, the high operational velocities (Reynolds number > 20) often result in nonlinear deviations from Darcy's Law for flow through the media (Rivers and Murphy 2000; Chen et al. 1996). Rivers and Murphy concluded that the deviations in filtration media were the product of fiber compression due to the air's inertial force compressing the media's fibers together at higher operational velocities. The compression changes the internal void volume and tortuosity of the media, leading to higher superficial velocities, decreased permeability, and a nonlinear increase in total resistance.

A practical method to account for the nonDarcian behavior is the addition of a second-order term to Darcy's Law (Scheidegger 1974). Equation 2 is known as a Forchheimer-extended Darcy's law. The A is equivalent to the Darcy's Law constant ([mu]L/[kappa]). The B accounts for the nonlinear deviation due to inertial effects.

[DELTA]P = A[V.sub.M] + B[V.sub.M.sup.2] (2)

Various theoretical equations exist that attempt to relate the physical significance of the second media constant, but these theories require extensive knowledge of the media's fiber dimensions and packing densities (Rivers and Murphy 2000). The research presented by Rivers and Murphy demonstrates the complexity and difficulty in accurately modeling media performance with these theories. Since the primary objective of the research is to identify and determine the resistances created by the geometric design parameters, and not the media, it is preferable to model the media constants using a quick, empirical approach that will not introduce as much theoretical error.

Bernoulli's Equation

The mechanical energy balance is a summation of kinetic, potential, mechanical, compressive, and viscous energy terms (Bird et al. 2001). Bernoulli's equation is a reduced version of the mechanical energy balance that assumes incompressible, steady-state flow while maintaining a control volume with stationary, solid boundaries. Bernoulli's equation can be further simplified by eliminating elevation change...

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