2.3 Filtration efficiency and its optimization
2.3.1 Comparison of filtration performance between parallel and staggered designs
The pressure drop and filtration efficiency are two important filtration performance indicators.A good filtration performance is characterized by a low pressure drop and high filtration efficiency.The filtration performance of the parallel and staggered designs with different face velocities (from 0.1 m/s to 1.0 m/s) are compared in Fig.2-5 and Fig.2-6,respectively.Here,the fiber diameter is 20μm and the SVF is 19.63%.A particle diameter (dp) of 1.0μm was chosen.
Fig.2-5 shows that pressure drops of two designs are linearly proportional to the face velocity,which is consistent with the results of Darcy equation [20,37].Moreover,the pressure drop of the staggered design is always higher than that of the parallel design,and the difference of the pressure drop between them increases with increasing face velocity.
Fig.2-5 Effect of face velocity on the pressure drops for different fibrous designs
Fig.2-6 Effect of face velocity on the filtration efficiencies for different fibrous designs
Fig.2-6 shows filtration efficiencies of two designs.The filtration efficiency of the staggered design is higher and its value changes significantly with face velocity,while the filtration efficiency of the parallel design remains below 10%.
Because of the large particle diameter (1.0μm) used in this simulation,inertial impaction is expected to be the principal mechanism of particle trapping [14,27,37].The staggered pattern of the fibrous media has better obstructive effects for the incoming particles,but the parallel pattern of the fibrous media provides many channels through which particles can escape,resulting in lower filtration efficiency.Moreover,the particles with a higher velocity are more easily deviated from the streamline of the flow field and collide with the fiber wall then captured by fibers.Whereas the particles with a lower velocity tend to follow the streamline of the flow field and are more likely to escape with the airflow from the filter.
2.3.2 Filtration efficiency at different face velocities and particle diameters
The staggered design with a fiber diameter of 20 μm and SVF of 19.63%is further investigated.Fig.2-7 shows effects of face velocity on the filtration efficiency for various particle sizes.The filter is found to have higher filtration efficiency for larger particles (dp=0.5μm,0.8μm and 1.0μm),and this value increases significantly as face velocity increases.However,the filtration efficiency for the small particles (dp=0.1 μm and 0.2 μm) is less sensitive to the face velocity.And the filtration efficiency decreases when face velocity increases.This can be accounted for the dominating mechanism of particle trapping.Inertial impaction is the dominating mechanism for the trapping of large particles [45],which is sensitive to the face velocity.At lower fluid flow velocity,as shown in Fig.2-7,the smallest particle (dp=0.1μm) indeed has the highest filtration efficiency.It indicates that Brownian diffusion plays an important role.The Brownian diffusion is the principal mechanism for small particles trapping [46],which is insensitive to face velocity.With increasing face velocity,the Brownian diffusion is weakened and particles are more likely to escape by following the streamline of the flow field.
Fig.2-7 Effect of face velocity on the filtration efficiency for different particle sizes
Particle trajectories at a diameter of 1.0μm are shown in Fig.2-8(a).The face velocity is 1.0 m/s.There are 1600 particles to be injected from the inlet and every single streamline represents the track of one particle.Inertial impaction is known to be the dominating mechanism of trapping for this size of particle (as shown above).So this filter gets higher filtration efficiency for relatively bigger particles in a larger face velocity.It is also found that more particles are trapped on front-row fibers.Fig.2-8(b) lists the number of trapped particles in each row of fibers.The fibers in the first row trap fewest of the particles.And rows with even index (2,4,6 and 8) always trap more particles than the rows with odd index (3,5,7 and 9).In general,front-row fibers except the first row trap most particles.And the back-row fibers make small contribution to the filtration.
Fig.2-8 Trapping process of particles:(a) particle trajectories in X-Y profile and (b) trapped particles of each row
2.3.3 Filtration performance of layered filters with the same total SVF
To improve the filtration performance,the staggered design with the even structure (as shown in Fig.2-8(a)) was divided into three layers.The layered filter designs were classified as the dense-sparse and sparse-dense structure,as shown in Fig.2-9(a) and Fig.2-9(b).Detailed parameters are shown in Table 2-1.Although these layered structures have the same total SVF of 19.63%,each layer has a different SVF value (α1,α2 andα3).The fiber diameter (20μm) was consistent across three designs.
Fig.2-9 Arrangements of fibers of different structures in X-Y profile:
(a) dense-sparse structure (Structure-A),(b) sparse-dense structure,
(c) Structure-C,(d) Structure-D,(e) Structure-E and (f) Structure-F
Table 2-1 Parameters of different structures
a df iis the fiber diameter of each layer of the filter.
Pressure drops of layered filters are listed in Table 2-2.The even structure has a pressure drop of 205.54 Pa,which is lower than those of other two structures.Fig.2-10 shows the filtration efficiencies of three structures.The dense-sparse structure has the highest filtration efficiency for all the simulated particle sizes.That is because the large SVF of the dense-sparse structure's front layer has a higher resistance effect for the particles.Moreover,the filtration efficiency of the sparse-dense structure is only marginally lower than that of the even structure for large particles (dp=0.8μm and 1.0μm),while results are opposite for the small particles (dp=0.1μm and 0.2μm).
It is concluded that the dense-sparse structure has high filtration efficiency for all particle sizes.However,it is associated with an increase of the pressure drop.Therefore,there appears to be a trade-off between the pressure drop and the filtration efficiency.
Table 2-2 Pressure drops of the layered filters (V=1.0 m/s)
Fig.2-10 Filtration efficiencies of layered filters for different particle sizes
2.3.4 Optimization of pressure drop and filtration efficiency
1) Decreasing the fiber diameter in the first layer
To achieve a low pressure drop while maintaining high filtration efficiency,the dense-sparse structure in Fig.2-9(a) (Structure-A) was further optimized by replacing fibers of the first layer with either 18 μm or 15 μm diameter fibers,giving the Structure-C and Structure-D,as shown in Fig.2-9(c) and Fig.2-9(d),respectively.Detailed parameters of these structures are shown in Table 2-1.
As listed in Table 2-3,the pressure drops of Structure-C and Structure-D are significantly reduced by more than 34%and 15%compared to Structure-A.Although Structure-C and Structure-D have the same SVF,their different fiber diameters in the first layer result in different pressure drops.
Fig.2-11 compares filtration efficiencies of five structures for various particle sizes.The results show that filtration efficiencies of Structure-C and Structure-D are higher than that of Structure-A for all particle sizes.These data suggest that simultaneously decreasing the SVF and the fiber diameter appropriately are effective ways to improve the filtration performance of filters.Moreover,it is found that the Structure-D with smaller fibers in the front-row has better filtration efficiency than the Structure-C,although its pressure drop is relatively higher.These findings indicate that using large numbers of thin fibers is beneficial to improve the filtration efficiency for all particle sizes but also results in a higher pressure drop.
Table 2-3 Pressure drops of the optimized filters (V=1.0 m/s)
Fig.2-11 Filtration efficiencies of optimized filters for different particle sizes
2) Removing partial filter fibers
The Structure-D has higher filtration efficiency but a relatively higher pressure drop (Fig.2-11 and Table 2-3).Therefore,the Structure-D was selected for further optimization.A reduced number of fibers results in less resistance.To reduce the pressure drop,we removed the first two rows of fibers in Structure-D to obtain Structure-E.Since the contribution of the fibers in the back-row is small,as shown in Fig.2-8.We also removed the relatively useless fibers in the back-row of the Structure-E to obtain the Structure-F (Fig.2-9).
Pressure drops of the above structures are listed in Table 2-3 and their filtration efficiencies are compared in Fig.2-11.Table 2-3 shows that the pressure drops of Structure-E and Structure-F are reduced by nearly 25%and 34%compared to the Structure-D.Whereas filtration efficiencies of the Structure-E and Structure-F have only a small reduction compared to the Structure-D as shown in Fig.2-11.
Moreover,since the Structure-F is formed by removing fibers from the back-row of the Structure-E,Structure-F is expected to have smaller filtration efficiency.Interestingly,results in Fig.2-11 show that the Structure-F outperforms the Structure-E,having a lower pressure drop and higher filtration efficiency for most particle sizes (from 0.1μm to 0.8μm).This is probably owing to the fact that the flow field is altered after removing fibers from the back-row,with particles being now more likely to strike on the fibers.These findings indicate that partially removing sections of fibers may also improve the filtration performance of the filters.