Impact of fiber sizes on multi-fiber filter performance using coupled Eulerian-Lagrangian and Immersed Boundary in OpenFOAM

Author: Sajad Khodadadi

Supervisor: Dr. Reza Maddahian

Abstract

This research investigates two-dimensional flow dynamics of the transport and deposition of particles in the fibrous filter using the developed Eulerian-Lagrangian solver coupled with the Immersed Boundary (IB) method in OpenFOAM. This research focuses on providing an improved model for the wall boundary condition in the Immersed Boundary method and the effect of filter geometry on the performance of the fibrous filter.

1. Introduction

A fibrous filter is one of the most effective methods for controlling solid particles, and it is used in various industries due to its low cost and simple operation. The capability of the developed solver is examined by simulating a single square fiber. Also, the potential of changing the size and number of fiber rows in the staggered structure is addressed by analyzing the collection efficiency and the quality factor of the multi-fiber filter.

2. Methodology

2.1 Geometry and Computational Domain

The validation test case involves a single square fiber in a channel with a length of L = 1 mm. The channel has dimensions of 30L × 4L, with the center of the obstacle located 10L from the inlet.

The second test case involves a multi-fiber filter structure with a staggered arrangement in two, four, and six rows, with two columns of fibers simulated in each row. The fibers in this test case are all equal with a dimension of L = 333 µm. The spacing between the fibers in both the horizontal and vertical directions is equal to L. The fibers do not overlap in the vertical direction, so the domain width is 4L. The distance of the first row of fibers from the inlet is the same as in the validation test case.

The third test case is similar to the second one, featuring a multi-fiber filter structure with a staggered arrangement. However, the size of the fibers in the odd-numbered rows increases by different growth factors (A) of 1.2, 1.4, and 1.6. The size of the fibers in the even-numbered rows is reduced to prevent overlap and changes in the domain width. The horizontal spacing between the fibers is equal to L = 333 µm, as in the second test case.

2.2 Boundary Conditions

The simulation required careful definition of boundary conditions to reflect realistic physical scenarios. A fixed velocity corresponding to Re = 20 was assigned at the inlet, while a zero-gradient condition for pressure was applied at the outlet. No-slip boundary conditions were imposed on the fiber surfaces to ensure accurate interaction between the fluid and solid boundaries.

3. Mesh Independence Study

A crucial step in the simulation process was to ensure mesh independence. The simulations were executed on three different mesh densities: coarse (11,644 cells), medium (30,996 cells), and fine (97,608 cells). Pressure drop and collection efficiency parameters at Stokes number 5×10-1 were investigated for grid independency. Results indicated that the medium mesh density provided an optimal balance between computational efficiency and numerical accuracy, allowing for reliable data collection.

4. Validation of Results

A single fiber collection efficiency at different Stokes numbers was compared to other studies to ensure the credibility of the simulation results. The simulation results indicate that the developed solver with the modified boundary condition (corrected face) shows good accuracy with other studies, particularly at higher Stokes numbers, where the default boundary condition shows significant deviations.

5. Flow Simulation Results

5.1 Staggered structure of equal fibers

Collection efficiency diagram of the two-row array of equal fibers can be classified into three regions: Constant Minimum Efficiency (CMNE), Transient Region (TR), and Constant Maximum Efficiency (CMXE). In the CMNE region, unlike the other regions, collection efficiency is independent of the Stokes number. The results show that the collection efficiency in even rows is significantly higher than in odd rows. This behavior is related to the increased local Stokes number of particles between the odd-row fibers, which enhances the drag force on the particles. Consequently, the even rows play a more significant role in mid-range Stokes numbers. The collection efficiency was obtained using the formula:

\[ \eta = \frac{\text{number of collected particles}}{\text{number of injected particles}} \]

5.2 Staggered structure of unequal fibers

Using unequal fibers increases the collection efficiency in both the TR and CMNE regions, which is related to the increase in the local Stokes number between the fibers. The increase in the fiber growth rate results in a smaller range for the TR region. However, as the fiber growth rate increases, the filter's quality factor decreases due to a higher pressure drop. Therefore, a filter structure with a specific growth rate can be utilized depending on the specific objective. The quality factor efficiency was obtained using the formula:

\[ QF = \frac{\ln(1 - \eta)}{\frac{\Delta p}{0.5 \rho_f U_0^2}} \]

5.3 The impact of the number of rows in filter with unequal fibers

The increase in the number of rows in the CMNE region does not affect the collection efficiency, but it is effective in the TR and CMXE regions. Increasing the number of rows up to a certain Stokes number increases the quality factor. However, beyond that point, it decreases. The results indicate that an unequal structure with a higher growth rate can achieve the collection efficiency of a lower growth rate fiber while using fewer rows. As long as the growth factor does not increase excessively, this behavior is also associated with an increase in the quality factor. For instance, a two-row structure with a fiber growth rate of 1.2 has a collection efficiency equivalent to that of a six-row equal structure but with a lower pressure drop.

6. Conclusion

In this research, a developed Eulerian-Lagrangian solver coupled with the Immersed Boundary (IB) method was used to simulate particle deposition in the fibrous filter. Solver capabilities were evaluated by examining the collection efficiency. Additionally, a geometric parameter analysis revealed that using unequal fibers is more effective than increasing the number of rows for enhancing the collection efficiency. Therefore, unequal fibers with smaller thicknesses can be utilized in various industries.