Inertial filters

The design of a cross-flow filter system employs an inertial filter principle that allows the permeate or filtrate to flow radially through the porous media at a relatively low face velocity compared to that of the mainstream slurry flow in the axial direction, as shown schematically in Figure 15.1.9 Particles entrained in the high-velocity axial flow field are prevented from entering the porous media by the ballistic effect of particle inertia. It has been suggested that submicron particles penetrate the filter medium and form a dynamic membrane or submicron layer, as shown in... 

FIG. A-71 Inertial filters showing severe corrosion. (Source Altair RIters International Limited.)... 

Mechanisms of Filter Retention. In general, filtrative processes operate via three mechanisms inertial impaction, diffusional interception, and direct interception (2). Whereas these mechanisms operate concomitantly, the relative importance and role of each may vary. 

Inertial impaction involves the removal of contaminants smaller than the pore size. Particles are impacted on the filter through inertia. In practice, because the differential densities of the particles and the fluids are very small, inertial impaction plays a relatively small role in Hquid filtration, but can play a major role in gas filtration. 

Deep Bed Filters. Deep bed filtration is fundamentally different from cake filtration both in principle and appHcation. The filter medium (Fig. 4) is a deep bed with pore size much greater than the particles it is meant to remove. No cake should form on the face of the medium. Particles penetrate into the medium where they separate due to gravity settling, diffusion, and inertial forces attachment to the medium is due to molecular and electrostatic forces. Sand is the most common medium and multimedia filters also use garnet and anthracite. The filtration process is cycHc, ie, when the bed is full of sohds and the pressure drop across the bed is excessive, the flow is intermpted and solids are backwashed from the bed, sometimes aided by air scouring or wash jets. 

Fibrous or particulate filters are not important anymore because membrane filters are relatively compac t and perform veiy well. For filtration by straining, there is an intermediate air velocity at which filtration efficiency is a minimum because different collec tion mechanisms predominate at different ranges of velocity. At low velocities, diffusional and elec trostatic forces on the particle are important, and increased velocity shortens the time for them to operate. At high velocities, inertial forces that increase with air velocity come into play below a certain air velocity, their effect on collection is zero. Surges or brief power failures could change velocity and collection efficiency. 

The collection technique involves the removal of particles from the air stream. The two principal methods are filtration and impaction. Filtrahon consists of collecting particles on a filter surface by three processes—direct interception, inertial impaction, and diffusion (5). Filtration attempts to remove a very high percentage of the mass and number of particles by these three processes. Any size classification is done by a preclassifier, such as an impactor, before the particle stream reaches the surface of the filter. 

Dry aerosols, or particulate matter, differ so much from the carrying gas stream that their removal should present no major difficulties. The aerosol is different physically, chemically, and electrically. It has vastly different inertial properties than the carrying gas stream and can be subjected to an electric charge. It may be soluble in a specific liquid. With such a variety of removal mechanisms that can be applied, it is not surprising that particulate matter, such as mineral dust, can be removed by a filter, wet scrubber, or electrostatic precipitator with equally satisfactory results. 

Direct interception occurs when the fluid streamline carrying the particle passes within one-half of a particle diameter of the filter element. Regardless of the particle s size, mass, or inertia, it will be collected if the streamline passes sufficiently close. Inertial impaction occurs when the particle would miss the filter element if it followed the streamline, but its inertia resists the change in direction taken by the gas molecules and it continues in a... 

Filters for mists and droplets have more open area than those used for dry parhcles. If a filter is made of many fine, closely spaced fibers, it will become wet due to the collected liquid. Such wethng will lead to mathng of the fibers, retenhon of more liquid, and eventual blocking of the fiter. Therefore, instead of fine, closely spaced fibers, the usual wet filtrahon system is composed of either knitted wire or wire mesh packed into a pad. A looser filtrahon medium results in a filter with a lower pressure drop than that of the filters used for dry parhculates. The reported pressure drop across wire mesh mist eliminators is 1-2 cm of water at face velocihes of 5 m sec T The essenhal collechon mechanisms employed for filtrahon of droplets and mists are inertial impachon and, to a lesser extent, direct intercephon. 

The trajectory followed by water in a filter mass it is not linear. Water is forced to follow the outlines of the grains that delineate the interstices. These changes in direction are also imposed on particles in suspension being transported by the water. This effect leads to the evacuation of particles in the dead flow zones. Centrifugal action is obtained by inertial force during flow, so the particles with the highest volumetric mass are rejected preferentially. 

Figure 4-56. Inertial centrifugal dust separator. Courtesy of American Air Filter Co.

For the separation of gas-solid mixtures, preliminary design of inertial separators, cyclones, electrostatic precipitators, scrubbers and some types of filters can be carried out on the basis of collection efficiency curves derived from experimental performance. 

To continuously separate FT wax products from ultrafine iron catalyst particles in an SBCR employed for FTS, a modified cross-flow filtration technique can be developed using the cross-flow filter element placed in a down-comer slurry recirculation line of the SBCR. Counter to the traditional cross-flow filtration technique described earlier, this system would use a bulk slurry flow rate below the critical velocity, thereby forcing a filter cake of solids to form between the filter media and the bulk slurry flow, as depicted in Figure 15.2b. In this mode, multiple layers of catalyst particles that deposit upon the filter medium would act as a prefilter layer.10 Both the inertial and filter cake mechanisms can be effective however, the latter can be unstable if the filter cake depth is allowed to grow indefinitely. In the context of the SBCR operation, the filter cake could potentially occlude the slurry recirculation flow path if allowed to grow uncontrollably. 

Therefore, when operating in the filter cake mode, the axial velocity should be maintained at a level such that an adequate shear force exists along the filter media to prevent excessive caking of the catalyst that could cause a blockage in the down-comer circuit. For the separation of ultrafine catalyst particles from FT catalyst/wax slurry, the filter medium can easily become plugged using the dynamic membrane mode filtration. Also, small iron carbide particles (less than 3 nm) near the filter wall are easily taken into the pores of the medium due to their low mass and high surface area. Therefore, pure inertial filtration near the filter media surface is practically ineffective. 

This type of technology is a part of the group of air pollution controls collectively referred to as wet scrubbers. Fiber-bed scrubbers are also known as wetted-filter scrubbers and mist eliminators. The technology is based on the removal of air pollutants by inertial and diffusional interception. 

A detailed description of LES filtering is beyond the scope of this book (see, for example, Meneveau and Katz (2000) or Pope (2000)). However, the basic idea can be understood by considering a so-called sharp-spectral filter in wavenumber space. For this filter, a cut-off frequency kc in the inertial range of the turbulent energy spectrum is chosen (see Fig. 4.1), and a low-pass filter is applied to the Navier-Stokes equation to separate the... 

The calculations were performed for a Reynolds number based on the channel hydraulic diameter (Ri ) of 1,800. This high Reynolds number was chosen since a more accurate determination of ( can be obtained at these flow conditions (either experimental or computational) keeping in mind that inertial effects are more pronounced at high Reh. The permeabilities of the filter wall... 

The data clearly can be only approximately correlated in terms of the open area fraction as shown in Fig. 27. Subsequently we studied the effect of the plug length on the inertial losses coefficient for a clean filter at the three different... 

Konstandopoulos, A. G., Skaperdas, E., and Masoudi, M. Inertial contributions to the pressure drop of diesel particulate filters. SAE Technical Paper No. 2001-01-0909 (SP-1582) (2001). 

In addition, the simple phenomenological relation (6.1.4), with a constant electro-osmotic coefficient lc, was replaced by a more elaborate one, accounting for the w dependence on the flow rate and the concentrations Ci, C2 via a stationary electro-osmotic calculation. This approach was further adopted by Meares and Page [7] [9] who undertook an accurate experimental study of the electro-osmotic oscillations at a Nuclepore filter with a well-defined pore structure. They compared their experimental findings with the numerically found predictions of a theoretical model essentially identical to that of [5], [6]. It was observed that the actual numerical magnitude of the inertial terms practically did not affect the observable features of the system concerned. 

The mechanism of particle capture by depth filtration is more complex than for screen filtration. Simple capture of particles by sieving at pore constructions in the interior of the membrane occurs, but adsorption of particles on the interior surface of the membrane is usually at least as important. Figure 2.34 shows four mechanisms that contribute to particle capture in depth membrane filters. The most obvious mechanism, simple sieving and capture of particles at constrictions in the membrane, is often a minor contributor to the total separation. The three other mechanisms, which capture particles by adsorption, are inertial capture, Brownian diffusion and electrostatic adsorption [53,54], In all cases, particles smaller than the diameter of the pore are captured by adsorption onto the internal surface of the membrane. 

Filtration is a physical separation whereby particles are removed from the fluid and retained by the filters. Three basic collection mechanisms involving fibers are inertial impaction, interception, and diffusion. In collection by inertial impaction, the particles with large inertia deviate from the gas streamlines around the fiber collector and collide with the fiber collector. In collection by interception, the particles with small inertia nearly follow the streamline around the fiber collector and are partially or completely immersed in the boundary layer region. Subsequently, the particle velocity decreases and the particles graze the barrier and stop on the surface of the collector. Collection by diffusion is very important for fine particles. In this collection mechanism, particles with a zig-zag Brownian motion in the immediate vicinity of the collector are collected on the surface of the collector. The efficiency of collection by diffusion increases with decreasing size of particles and suspension flow rate. There are also several other collection mechanisms such as gravitational sedimentation, induced electrostatic precipitation, and van der Waals deposition their contributions in filtration may also be important in some processes. 

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