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Project #4: Simulation of Fluid Flow in the Screen-Bounded Channel in a Fiber Separator Lana Sneath and Sandra Hernandez 4 th year - Biomedical Engineering Faculty Mentor: Dr. Urmila Ghia Department of Mechanical and Materials Engineering NSF Type 1 STEP Grant, Grant ID No.: DUE-0756921

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Outline Motivation Introduction to Bauer McNett Classifier (separator) Problem Description Goals & Objectives Methodology Verification Case Porous Boundary Model Future Work 1

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Problem Background Toxicity of asbestos exposure varies with length of asbestos fibers inhaled Further study of this effect requires large batches of fibers classified by length The Bauer McNett Classifier (BMC) provides a technology to length-separate fibers in large batches Figure 1: Bauer McNett Classifier (BMC)Figure 2: Schematic of BMC 2

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Background – Bauer McNett Classifier (BMC) Fiber separation occurs in the deep narrow channel with a wire screen on one side wall Fibers align with local shear stress vectors [1] For successful length-based separation, the fibers must be parallel to the screen Open to atmosphere = deep open channel Figure 3: Top View of One BMC Tank A B C ALAL 1. Civelekogle-Scholey, G., Wayne Orr, A., Novak, I., Meister, J.-J., Schwartz, M. A., Mogilner, A. (2005), “Model of coupled transient changes of Rac, Rho, adhesions and stress fibers alignment in endothelial cells responding to shear stress”, Journal of Theoretical Biology, vol 232, p569-585 3 Wire Screen

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Background – Bauer McNett Classifier (BMC) Fibers length smaller than mesh opening Fibers length larger than mesh opening Figure 4: Fibers parallel to screen Figure 5: Fibers perpendicular to screen Off-plane angle 90° Off-plane angle 0° 4

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Deep Open Channel Dimensions General Dimensions: Length (x) = 0.217 m Height (y) = 0.2 m Width (z) = 0.02 m Aspect ratio = 10; Deep open channel Screen dimensions: Length (x) = 0.1662 m Height (y) = 0.1746 m Thickness (z) = 0.0009144 m screen 5 Figure 6: General Dimensions Figure 7: Porous Model Dimensions

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Goals and Objectives Goal: Numerically study the fluid flow in a deep open channel Objectives: a) Verify boundary conditions and variables of the porous model Simplified porous plate problemas verification case b) Simulate and study the flow in the open channel of the BMC apparatus, modeling the screen as a porous boundary c) Determine the orientation of shear stress vector on the porous boundary 6

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Methodology Computational Grid Figure 8: Porous Model Channel Geometry in FLUENT Table 1: Distribution of grid points and smallest spacing near boundaries Create channel geometry in CFD software Generate grid of discrete points Determine the proper boundary conditions to model the porous boundary –Verification case: Laminar flow over a porous plate Enter boundary conditions into the CFD software Run simulation Determine shear stress from flow solutions Interpret results 7

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Boundary Conditions u, v, w are the x, y, and z components of velocity, respectively Average Inlet Velocity= 0.25m/s Turbulent Flow (Reynolds Number >5000) Reynolds Stress Model Transient Simulation 8 Figure 9: Boundary Conditions Free-Slip Wall, v=0, du/dy=0, dw/dy=0 No-Slip Wall, u = v = w = 0 Inlet, u = u(y,z), v = w =0 Outlet, p stat = 0 Porous-Jump, Permeability(K) = 9.6e- 10, Pressure-Jump Coefficient(C2)=7610.7 1/m, screen thickness = 9e-4 m; Values correspond to a 16 mesh [5] Solid Wall ModelPorous Boundary Model

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Verification Case - Porous Plate Objective Determine proper boundary conditions to use in the Porous Boundary Model case Verify fluid flow behavior Observe how axial flow is inhibited by the plate Methodology: Create 2D geometry in Gambit Calculate Reynolds number for Laminar flow Generate grid points Run simulations in FLUENT Run 4 different cases: changing the mesh boundary condition to determine it’s effect Interpret results 9 Figure 10: Laminar Flow Across Porous Flat Plate

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Case #1: All Solid Walls Case #2: Two Walls, One Pressure Outlet Verification Case - Boundary Conditions (1 of 2) 10

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Verification Case - Boundary Conditions (2 of 2) Case #3: One Wall and Two Pressure Outlets Case #4: All Pressure Outlets 11

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Verification Case - Velocity Magnitude Contours Case #1: Velocity Magnitude Contours for All Walls Case #2: Velocity Magnitude Contours for Two Walls and One Pressure Outlet Case #3: Velocity Magnitude Contours for One Wall and Two Pressure Outlets Case #4: Velocity Magnitude Contours for All Pressure Outlets 12 Conclusion: All cases show a boundary layer and flow crossing the porous plate

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Verification Case - Streamlines for Case #1: All Walls 13

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Verification Case – Darcy’s Law ModelPressure Drop Calculated Using Darcy’s Law Pressure Drop Fluent Percent Error All Walls3.48E-033.51781-031.19% Two Walls and One Pressure Outlet -3.73E-03-3.679068E-031.25% One Wall and Two Pressure Outlets 2.54E-032.53E-030.32% All Pressure Outlet-8.593229E-03-8.68129E-031.01% 13 Table 2: Pressure Drop Verification via Darcy’s Law Conclusion: Hand calculations were equivalent to FLUENT’s values. Better understanding how FLUENT uses the porous-jump condition.

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Porous Boundary Open Channel - Velocity Magnitude Contours Figure 11: Isometric View of Axial Variation of Velocity on Central Plane Figure 12: Front View of Axial Variation of Velocity on Central Plane 14

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Porous Boundary Open Channel - Shear Stress Figure 13: Axial Variation of Shear Stress on the Back Wall at y=0.1 z= 0 Figure 14: Axial Variation of Shear Stress on Screen at y=0.1 z= 0.02 Figure 15: Axial Variation of Velocity at Line y=0.1, z=0.01 15

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Future Work Continue running the porous boundary open channel model until the fluid flow solution has been calculated for at least 3 minutes to achieve a steady state solution Investigate reasoning behind the zero shear stress at the porous boundary Compare verification case results for pressure drop calculations to literature Interpret results further 16

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Acknowledgements Dr. Ghia for being an excellent faculty mentor and taking the time to make sure we fully understood the concepts behind our research. Graduate Students Prahit, Chandrima, Deepak, Nikhil, and Santosh for taking time out of their schedule to teach us the software and help us with any problems we encountered. Funding for this research was provided by the NSF CEAS AY REU Program, Part of NSF Type 1 STEP Grant, Grant ID No.: DUE-0756921 17

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Appendix: Porous Plate Calculation Darcy’s Law pressure drop calculations: 18

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