Project Summary Report

PROJECT SUMMARY REPORT

SIMULATION OF FLUID FLOW IN THE SCREEN-BOUNDED CHANNEL IN A FIBER SEPARATOR

Submitted To

The 2013 Academic Year NSF AY-REU Program Part of NSF Type 1 STEP Grant

Sponsored By the National Science Foundation Grant ID No.: DUE-0756921

College of Engineering and Applied Science University of Cincinnati Cincinnati, Ohio

Prepared By

Lana Sneath, Junior, Biomedical Engineering Sandra Hernandez, Junior, Biomedical Engineering

Report Reviewed By:

______

Dr. Urmila Ghia REU Faculty Mentor Professor of Mechanical Engineering Department of Materials and Mechanical Engineering University of Cincinnati

August 26– December 4, 2013 1.1 Goals and Objectives The motivation behind this study is to understand the behavior of the fluid flow within the deep open channel in the BMC apparatus. The goal of the present study is to numerically simulate the three- dimensional flow in the BMC deep open channel of aspect ratio (H/B) 10. During earlier research, the BMC deep open channel was modeled as a channel with both vertical side boundaries as solid walls. This study focuses on replacing a portion of one of the solid walls is replaced by a porous-jump boundary condition, which represents the screen in the BMC apparatus. The focus of the experiment is to analyze the shear stress distribution on the screen, modeled as a porous boundary, understand the porous boundary condition and determine the effectiveness of the BMC for length-based separation of fibers.

The objectives of the study are to: a) Verify boundary conditions and variables of the porous model, using a simplified porous plate model as a verification case b) Simulate and study the flow in the open channel of the BMC apparatus, modeling the screen as a porous boundary c) Determining the orientation of shear stress vector on screen boundary for the porous boundary

1.2 Materials Commercially available Computational Fluid Dynamics (CFD) tools FLUENT and Gambit are used for the simulations in this study.

1.3 Training Received The research group was trained on how to use Gambit and FLUENT to perform Computational Fluid Dynamics (CFD) to multiple fluid flow geometries. In addition, we learned how to post-process the fluid flow solution from FLUENT and interpret the results.

1.4 Methods The goal of this study is to numerically simulate the fluid flow in the screen-bounded channel within the BMC fiber separator. To numerically study the fluid flow, Computational Fluid Dynamic (CFD) software FLUENT and Gambit are used. Computational Fluid Dynamics is the “concepts, procedures, and applications of computational methods in fluids and heat transfer” [9]. CFD tools apply the principles of engineering to the modeling of fluid flow. [10]. Using the CFD tool FLUENT, the 3D, unsteady, incompressible Reynolds-Averaged Navier-Stokes Equations (RANS) are solved to determine the three- dimensional flow in the deep open channel of aspect ratio 10. The Semi-Implicit Pressure-Linked (SIMPLE) algorithm is used to achieve pressure-velocity coupling. The solution is deemed converged, when the residuals of the continuity equation and the conservation of momentum equation reach 10e-6.

2.1 Geometry and Computational Grid The deep open channel geometry is created in Gambit with dimensions of 0.217 x 0.02 x .2 m in the x, z, and y directions, respectively, giving the channel geometry an aspect ratio of 10. A computational grid is created, with grid spacing of 50, 180, and 45 in the x, y, and z directions, respectively. The first step size of the grid is 0.00005 m away from the boundaries in the y direction, and 0.00007 m in the z direction. The small step sizes allow for more computations to be taken along the boundary edges where the fluid flow has greater variation. The grid spacing along the x direction has a successive ratio of 1, meaning that the grid points are evenly spaced. The fluctuations in the fluid flow along the distance of the channel are moderated as compared to the y- and z-directions, hence it was not necessary to cluster the points around the edges.

2.2 Boundary Conditions The boundary conditions used for modeling the wire-mesh wall as a porous boundary is shown in Figure 1. In Fluent, the side of the screen in line with the deep open channel was modeled with a porous- jump boundary condition. After the screen was modeled with a porous-jump boundary condition, a computational domain was extruded from that face. All sides of the computational domain were modeled as walls, with the back face being modeled as a pressure outlet. These boundary conditions were chosen after interpreting the results from the verification case.

Figure 1. Boundary conditions applied on the BMC open channel

In order for FLUENT to solve the Reynolds Stress Equations for the fluid flow in the channel the permeability, pressure-jump coefficient, and the thickness of the porous boundary need to first be determined. The equations and calculations can be found in Section 3.2 of the Verification Case. The final values are as followed: Permeability,K=9.6154e-10m2 Pressure-Jump Coefficient C2 = 7610.739 1m Screen thickness = 0.0009144 m

The turbulence boundary conditions were specified in the form of turbulence intensity and viscosity of 5% and 1, respectively, for the inlet and outlet boundaries. The edges surrounding the porous boundary are modeled as solid no-slip walls with u= v= w=0. The thickness of the porous boundary is equal to 0.0009144 m, which is the set value of the wire diameter for a 16 mesh multiplied by 2, due to the screen being woven.

3.1 Results and Discussion Fluid within the deep open channel will take approximately 0.87 seconds to fully travel the length of the channel, as calculated in the equations below. The Reynolds Stress Time-Averaging equations and continuity equations were unable to run for the appropriate time period.

Time (seconds) for fluid to travel the length of the channel calculations: Time = Length/Velocity Time = 0.217m/0.25s Time = 0.87s

Due to time constraints, FLUENT was only able to calculate up to 0.5s of the fluid flow, which is approximately ½ of the channel. Our results are accurate up to 0.5s, but results for second half of the channel are incomplete. The flow time that was obtained is 0.5 seconds. This means that the fluid has not traveled across the entire channel. This is reflected in figure 15, which shows a certain jump at x position 0.2 m. In addition, the peaks at 0.09m can be attributed to the flow not traveling across the entire channel. The goal of the study was to obtain steady state results, and a flow time of 0.5s does not suffice this goal. Close to the inlet section of the channel, the total shear stress decreases with the axial distance. As expected, the shear stress is maximum at the inlet, and the as the velocity profile develops, the wall shear stress decreases, as seen in Figure 2.

Figure 2. Axial Variation of Shear Stress on the Back Wall at y=0.1 z=0

As discussed previously, the shear stress is also seen to be maximum at the inlet section. The shear stress decreases as the velocity profile develops downstream. At x=0.2m the screen starts, and an increase in area at x=0.2m causes a dip in the shear stress. The end portion of Figure 16 clearly reflects that the flow has not traveled across the channel completely. According to Figure 16, the shear stress around the wire mesh drops down to zero. This can be attributed to the porous boundary condition, or due to the fact that the simulation has not yet reached steady state results. Further analysis is required to understand the implementation of the porous-jump boundary condition by FLUENT.

Figure 3. Axial Variation of Shear Stress on Screen at y=0 z=0.

Velocity contours along the X direction is visualized in Figure 4. In this figure, high velocity corresponds to warmer colors, while lower velocity corresponds to cool colors. The highest velocity is seen in the red portion of the channel, and the lowest velocity of zero is seen at the bottom no-slip wall. At the bottom no-slip wall, boundary layer formation was observed that was in similar to that in the verification case. The higher velocity near the central bottom of the channel could be due to the smaller area at that region, leaving an increase in velocity when using the conservation of mass equation. An increase in centerline velocity before the porous-jump boundary starts is due to the velocity profile development of the axial velocity, giving rise to a higher velocity. At the screen, the area increases due to which it is expected that there will be a corresponding decrease in the overall velocity. Also, some mass escapes the channel through the porous boundary contributing to smaller axial velocity. At the end of the porous-jump boundary condition, area decreases again, thus a resultant increase in axial velocity and further development of the velocity to the end of the channel will likely occur. The yellow velocity contours at the beginning of the channel complement the predictions made, as that slower velocity starts right after the porous-jump boundary condition, where the channel has an increased velocity. Figure 4. Isometric (left) and Front (right) Views of Axial Variation of Velocity on Central Plane

The X-velocity (Axial velocity) components are plotted in Figure 5. The beginning of the inlet and near the free slip wall there is non-zero velocity. The first half of the channel is the region that the fluid flow simulation has covered so far with 0.5s of flow computations completed.

Figure 5. Axial Variation Plot of Velocity at Line y=0.1, z=0.01

3.2 Conclusions The 3D geometry of this case was created in Gambit and run in FLUENT with the appropriate boundary conditions. However, the results from the 3D porous boundary model were incomplete due to time constraints and computationally intensive simulations. The results obtained were obtained for only 0.5 seconds of the fluid flow through the channel. This means that only 57% of the channel was solved computationally. An approximate time required for the flow to travel across the channel was obtained by dividing the length of the channel by the inlet bulk velocity. This time period for the flow to fully travel across the channel was computed to be 0.87 seconds. In order to achieve steady state results, the fluid should completely flow across the channel 4 or 5 times. Hence, it is expected that the results will be significantly different than the results obtained from steady state solution. The current results demonstrate the initial variation of the shear stress and axial magnitude correctly. However, the effect of the porous- jump boundary condition on the shear stress still requires more analysis.

4.1 Future Work In the future, the simulation should run the complex simulations in FLUENT until the fluid flow solution has been calculated for at least 3 minutes. Additionally, further research needs to be conducted to determine the reasoning behind the zero shear stress at the porous boundary. Ultimately, final results need to be compared with literature resources and verified for accuracy. Bibliography 1. Jana, C. (2011), “Numerical Study of Three-Dimensional Flow Through a Deep Open Channel- Including a Wire-Mesh Segment on One Side Wall.” M.S. Mechanical Engineering Thesis, University of Cincinnati. 2. Dodson, R., Atkinson, M., Levin, J. (2003), “Asbestos Fiber Length as Related to Potential Pathogenicity: A Critical Review.” American Journal of Industrial Medicine, Vol. 44, p. 291-297 3. http://www.nlm.nih.gov/medlineplus/asbestos.html 4. Guo, J., Julien, PY. (2005). “Shear stress in smooth rectangular open-channel flows.” American Society of Civil Engineers, 131(1), 30-37. 5. Janna, W. S. (2009) “Introduction to Fluid Mechanics”, CRC press, 4th Edition. 6. White, F. M. (2003) “ Fluid Mechanics”, McGraw-Hill, 5th Edition. 7. Fluent 6.3 User’s Guide. 8. Gambit 2.4 User’s Guide. 9. Chung, T. J. (2010) “Computational Fluid Dynamics”, Cambridge University Press, 2nd Edition. 10. Birchall, D. (2009) “Computational fluid dynamics”, The British Institute of Radiology, 82, S1-S2. 11. “Vorticity.” Def. 1. Meriam Webster Online, Merriam Webster 12. Blake, T., Castranova, V., Baron, P., Schwegler-Berry, D., Deye, G.J., Li, C., and Jones, W., (1998), “Effect of Fiber Length on Glass Microfiber Cytotoxicity,” Journal of Toxicological Environmental Health, Part A, Vol. 54, Issue 4. 13. www.uceindia.com/fiber-classifier-bauer-mcnett-type.htm 14. Paschkewitz, J.S., Dubiel, Y., Shaqfeh, E., (2005), “The dynamic mechanism for turbulent drag reduction using rigid fibers based on Lanrangian conditional statistics”, American Institute of Physics