Project #5: Simulation of Fluid Flow in the Screen-Bounded Channel in a Fiber Separator

1. Project #5: Simulation of Fluid Flow in the Screen-Bounded Channel in a Fiber Separator Lana Sneath and Sandra Hernandez 3rd year - Biomedical Engineering Faculty Mentor: Dr. UrmilaGhia School of Dynamic Systems

2. Outline • Motivation • Introduction to Bauer McNett Classifier (separator) • Problem Description • Goals & Objectives • Methodology • Boundary Conditions • Results • Solid Wall • Porous Wall • Conclusion • Future Work

3. 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 Bauer McNett Classifier (BMC) Schematic of BMC

4. Background – Bauer McNett Classifier (BMC) Open to atmosphere • 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 B A C AL = deep open channel 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 Top View of One BMC Tank

5. Background – Bauer McNett Classifier (BMC) Fibers parallel to side walls Fibers perpendicular to side walls Fibers length larger than mesh opening Fibers length smaller than mesh opening Off-plane angle 90° Off-plane angle 0°

6. Deep Open Channel 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

7. Goals and Objectives Goal: Numerically study the fluid flow in a deep open channel Objectives : a) Learn the fundamentals of fluid dynamics. b) Learn the fundamentals of solving fluid dynamic problems numerically. c) Simulate and study the flow in the open channel of the BMC apparatus, modeling the screen as a solid wall boundary d) Model the screen as a porous boundary e) Determine the orientation of shear stress vector on screen boundary for both the solid wall boundary and porous boundary

8. Methodology Computational Grid • Define channel geometry • Understand differential equations governing fluid flow • Set up channel geometry in CFD software • Generate grid of discrete points • Enter boundary conditions • Solid Wall • Porous Boundary • Obtain flow solutions • Compute shear stress on flow solutions Figure 3: Channel Geometry in Gambit Table 1: Distribution of grid points and smallest spacing near boundaries

9. 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 • Turbulence parameters: • Solid Wall • Intensity = 5% • Viscosity ratio = 10 • Porous Boundary • Intensity = 0.5% • Viscosity ratio = 1 • Characterized by permeability K and pressure-jump coefficient C2

10. Solid Wall Model Results: X-Velocity and Vorticity Contours • Figure 6: x-vorticity contours in top half of; plane at x= 0.2m • Top corners are non-symmetrical about the angle bisector • High vorticity at the free surface • High vorticity is attributed to the free surface being modeled as a free-slip wall • Figure 5: x-velocity contours in top half of channel; plane at x= 0.2 m • Velocity contours bulge towards corners • Symmetric across the center of the channel • Highest velocity is in the center of the channel

11. Shear Stress on Side WallMagnitude and Off-Plane Angle 8∘ Figure 7: Shear Stress (primary y-axis) and off plane angle (secondary y-axis) on z-wall; line at y= 0.1 m (mid-plane), z= 0.02 m

12. Modeling the Porous Boundary • 16 Mesh with a 50% porosity (open area/ total area) • Determine the two unknown coefficients for FLUENT • Permeability (K) • Pressure-Jump Coefficient (C2)

13. Porous Boundary Model Results: X-Velocity and Vorticity Contours Porous Wall Solid Wall Porous Wall Solid Wall • X-velocity contours in top half of channel; plane at x= 0.2 m • Velocity contours bulge towards corners • Not-symmetric across the center of the channel • Highest velocity is in the center of the channel • X-vorticity contours in top half of channel; plane at x= 0.2 m • High vorticity at the free surface and near porous boundary • As previous case, vorticity is low at right side wall • Top corners are much more non-symmetrical about the angle bisector

14. Conclusion • Shear stress angle is greatest at the inlet, and quickly drops down as x-position increases. • In the solid-wall model, the highest out-plane angle where the screen lies in the actual BMC channel is 8 degrees, which is primarily tangential to the wall. • The shear stress off plane angle in the porous boundary model is expected to be slightly greater. • Flow through the screen is expected to be small, therefore the contribution of the porous boundary to the off-plane shear stress angle is expected to be small

15. Future Work • Analyze shear stress distribution along the screen in the porous boundary model • Determine off plane angle • Further understand the behavior of fluid flow in the porous boundary model

16. 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 Chandrima, Deepak, 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. Modeling Porous Boundary Equations 2. Tamayol, A., Wong, K. W., Bahrami, M. (2012), “Effects of microstructure on flow properties of fibrous porous media at moderate Reynolds number”, American Physical Society, vol. 85.