Project #4: Simulation of Fluid Flow in the Screen- Bounded Channel in a Fiber Separator
By
Lana Sneath and Sandra Hernandez
4th Year, Biomedical Engineering
University of Cincinnati
Faculty Mentor: Dr. Urmila Ghia
Department of Mechanical and Materials Engineering
University of Cincinnati
Sponsored By the National Science Foundation
Grant ID No.: DUE-0756921
Abstract
The goal of this project was to verify the ability of the Bauer McNett Classifier (BMC) to classify asbestos fibers in large batches for use in toxicology studies. Previous studies have shown that fiber toxicity varies with changes in fiber length. In the present study, the Bauer McNett Classifier was modeled using CFD (Computational Fluid Dynamics) to analyze its potential use to classify fibers based on their length. The focus of this study was to simulate the flow in the deep open channel of the BMC, with focus on the screen. The channel geometry was first modeled in Gambit, and then the computational grid was imported into FLUENT to solve the three-dimensional Navier-Stokes equations governing the fluid flow. Turbulence in the channel was found using the Reynolds Stress Model (RSM). Initial work was completed by modeling the screen with a solid wall boundary to facilitate the computations. The results from this case concluded that the out-plane angle of shear stress on the XY plane was around 8 degrees for the solid wall model, inferring that the shear stress distribution of the flow was parallel to the screen. Upon completion of the solid wall simulation, a verification study with a 2D porous plate using the porous-jump boundary condition was conducted to see if this boundary condition simulates flow through the screen correctly. The 2D results show that FLUENT implements a pressure drop across the porous-jump surface using Darcy's law. Once the correct boundary conditions were determined from the verification case, a portion of the sidewall in the channel was replaced by a porous boundary to represent the screen openings. The results showed that the shear stress on the screen approaches zero. The next step in this study will be to obtain steady state results and further investigate the shear stress on the screen.
Contents
Abstract
Contents
Nomenclature
Chapter 1
Introduction
1.1 Bauer McNett Fiber Classifier
1.2 Objectives
1.3 Materials
1.4 Methods
Chapter 2
Flow in the BMC Open Channel with Two Solid Walls
2.1 Geometry and Computational Grid
2.2 Boundary Conditions
2.3 Results and Discussion
Chapter 3
Verification Case: Flow Across a Porous Plate
3.1 Geometry and Computational Grid
3.2 Boundary Conditions.
Two Wall Model
One Wall and One Pressure Outlet Model
Two Pressure Outlets Model
3.3 Results and Discussion
All Wall Model
Two Wall Model
One Wall and One Pressure Outlet Model
All Outlets Model
3.4 Conclusion
Chapter 4
Flow in the BMC Open Channel with a Screen on a Side Wall
4.1 Geometry and Computational Grid
4.2 Boundary Conditions
4.3 Results and Discussion
4.4 Conclusions
Future Work
Acknowledgements
Bibliography
Nomenclature
The following symbols have been used in this document:
μ: Viscosity of the fluid
Re: Reynolds number.
Fr: Froude number.
d: Wire diameter.
K: Permeability
: Pressure-jump coefficient
Ui: Velocity.
Elent: Entrance length number.
lentrance: Length to fully developed velocity profile.
: density
: Shear stress
Chapter 1
Introduction
Asbestos fibers are naturally found in the environment and have been used in many commercial products such as insulation, flooring, plaster, and cloth materials. Asbestos is a known carcinogen that can lead to one or more disorders if fibers in the air are inhaled [3]. It has been proposed that alveolar macrophages (AM) are unable to completely engulf longer asbestos fibers, leading to oxidants and enzymes leakage from the AM, in turn causing cell damage [12]. The effect of asbestos can be determined by various factors including fiber length, concentration, and duration of exposure. Previous experiments conducted by the National Institute of Occupational Safety and Health (NIOSH) have shown that asbestos toxicity varies with fiber length; longer fibers have a greater chance of it being toxic compared to shorter fibers [1]. The current fiber classifier being used is only able to separate small batches of fibers based on their length at a time, making it difficult to conduct a large-scale toxicology study. In order to be able to conduct large-scale studies, technologies that will be able to classify large batches of fibers are being explored. The objective of this study is to determine the efficiency of the Bauer McNett Fiber Classifier (BMC) as a fiber length-based classifier.
1.1 Bauer McNett Fiber Classifier
The Bauer McNett Fiber Classifier is a device commonly used for paper fiber classification based on length. The BMC is a system with 5 elliptical tanks arranged in a cascade, as shown in Figure 1. An agitator slowly circulates the water flow within each of the elliptical tanks. The water then flows past a screen in the channel within the tank, causing separation of fibers based on their length, as shown in Figure 2. This fiber separation occurs due to the cross flow through the screen which allows fluid to escape through the square apertures of the mesh, leaving behind the fibers that are too long to fit lengthwise through the aperture. Fiber orientation upon passing through the screen is governed by the shear stress distribution on the wire mesh screen. It is assumed that the fibers flowing in the fluid align themselves in the direction of the shear stress on the boundary, and any change in the direction of the shear stress vectors will result in a change in the fiber orientation [1]. For successful length-based separation, the fibers must be oriented parallel to the screen. If the fiber orientation is parallel to the screen and the diameter is greater than the opening, it is expected that fibers larger in length than the aperture size of the particular screen size will be filtered.
Figure 1: Bauer McNett Classifier
The flow across the cascading tanks is governed by gravity. This study concentrates on modeling a portion of the deep, open channel within the BMC as a porous boundary to replicate the wire mesh. The previous study on length-based fiber orientation in the BMC apparatus found that the Reynolds number of the deep open channel was greater than 4000, classifying the flow as turbulent. The Reynolds number is a dimensionless number, which correlates the viscous behavior of Newtonian fluids [6]. The flow was also found to be subcritical as determined from the value of Froude number, which was about 0.18 [1].
1.2 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. In previous studies, the channel was modeled with both vertical side boundaries as solid walls. In this study, 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, and determine the effectiveness of the BMC for length-based separation of fibers.
The objectives of the study are to:
a)Determine proper boundary conditions, inputs, and geometry
b)Conduct a verification case
c)Simulate and study the flow in the open channel of the BMC apparatus, modeling the screen as a porous boundary
d)Interpret results and form conclusions
1.3 Materials
Commercially available Computational Fluid Dynamics (CFD) tools FLUENT and Gambit are used for the simulations in this study.
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. In order to numerically study the fluid flow, Computational Fluid Dynamic (CFD) software FLUENT and Gambit are used. Computational Fluid Dynamics is defined as “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.
Chapter 2
Flow in the BMC Open Channel with Two Solid Walls
2.1 Geometry and Computational Grid
The deep open channel geometry, within the BMC apparatus, is created and meshed in Gambit and the mesh is later imported into FLUENT where the RANS equations are solved to simulate fluid flow.
The 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. Figure 3 shows the computational grid used for this study.
Figure 2. Computational Grid [1]
Total Size / X / Y / Z / ∆Y / ∆X405000 / 50 / 180 / 45 / 0.00005 / 0.0007
Table 1. Computational Grid Spacing
2.2 Boundary Conditions
The boundary conditions used for modeling the wire-mesh wall as a solid boundary are shown in Figure 4. The two sidewalls and the bottom wall are specified as no-slip stationary walls, where the values of the u, v, and w components of velocity are zero. The average velocity at the inlet is specified to be 0.25 m/s. The Reynolds number for the BMC apparatus is equal to 9982, classifying it as a turbulent flow. Turbulent flows contain fluctuations, whereas laminar fluid flows are smooth without many irregularities. The fluid flow is computed in FLUENT at every discrete grid point, and the Reynolds-stress model includes the effects of turbulence. The Reynolds-stress model takes into account the fluid rotation, curvature, and rapid changes in strain rate more rigorously than one or two-equation models and, therefore, is an ideal model to use when analyzing the complex flow within the BMC apparatus [7]. The turbulence boundary conditions were specified in the form of turbulence intensity and viscosity of 5% and 10, respectively, for the inlet and outlet boundaries.
Figure 3. Boundary Conditions for Solid Wall Model
The non-dimensional entrance length, , for turbulent flow is expressed as
(3)
For a Re of 9844, the non-dimensional entrance length is:
(4)
(5)
Therefore the entrance length for the flow is:
(6)
Entrance length is defined as the length of the inlet to the point where the flow becomes fully developed. It is assumed that the fluid does not undergo any further changes in velocity along x, after the entrance length. The velocity and vorticity results are analyzed in cross planes at x= 0.2 m, y = 0 to 20 m, and z= 0.02 m.
2.3 Results and Discussion
The objective of this study was to numerically study the flow through the deep open channel of the BMC with an aspect ratio of 10. The BMC channel geometry is initially modeled as two sidewalls and the bottom wall that are no-slip stationary walls, where the u, v, and w components of velocity are equal to zero.
Initially it was found in the first model with solid sidewalls that the x-velocity contours were highest in magnitude towards the center of the channel and lowest at the stationary, non-porous sidewalls.
The bulges in the x-velocity contour plots can be attributed to the presence of a free surface attracting higher momentum fluid, pushing the lower momentum fluid towards the center of the channel [1]. The shear stress distribution on the vertical sidewalls near the free surface is affected by this circulatory effect. Furthermore, the circulation of fluid is observed in the x-vorticity contour plots, which show the highest vorticity in the corners near the free surface.
In the solid side walls channel geometry, the off-plane angle is greatest at the inlet and drops down and remains around 8 degrees as the x-position increases. These results indicate that the shear stress is mainly aligned tangential to the fluid flow.
Figure 4. Total Shear Stress along (left y-axis) and off plane shear stress angle (right y-axis); line at y= 0.1 m (mid-plane), z= 0.02 m
2.4 Conclusion
The objective of this study was to numerically study the flow through the deep open channel of the BMC with an aspect ratio of 10. The BMC channel geometry was modeled as two sidewalls and the bottom wall that are no-slip stationary walls, where the u, v, and w components of velocity are equal to zero.
The results indicated that the x-velocity contours were highest in magnitude towards the center of the channel and lowest at the stationary, non-porous sidewalls. In the solid side walls channel geometry, the off-plane angle was greatest at the inlet and drops down and remained around 8 degrees as the x-position increases. These results indicated that the shear stress was mainly aligned tangential to the fluid flow.
Chapter 3
Verification Case: Flow Across a Porous Plate
The objective of this verification study was to determine the proper boundary conditions to model in the model with a portion of the wall replaced by a screen. The case was also used to determine how the porous plate affected axial flow and the laminar fluid flow behavior. The verification case was modeled as a laminar flow to simulate the ideal case and to facilitate computations.
3.1 Geometry and Computational Grid
Reynolds number was calculated in the beginning of the verification case to classify the proper fluid flow to be laminar or turbulent. The original inlet velocity was divided by 10 to ensure that the flow would be laminar. The Reynolds Number, , was calculated to be 5500 with a velocity of 0.025 m/s, classifying the verification case as a laminar flow.
Calculating Reynolds Number ():
(7)
(8)
(9)
With signifying the density of the water, V for the velocity, and being the viscosity of fluid.
ANSYS Gambit was used to create a 2D geometry of a porous plate and a computational domain. The geometry in the 2D case was modeled to reflect the actual BMC apparatus dimensions with a decreased velocity by 10 to simulate a laminar flow. Figure 5. labels the dimensions accordingly. The computational grid spacing can be seen in Table 2. Grid points were clustered at the inlet using a First Length distance in Gambit to better capture the fluid flow fluctuations.
Three different cases were simulated to determine the effect of the various boundary conditions on the fluid flow behavior. The three cases change the boundary conditions on the sides and bottom of the computational domain after the porous-jump.
Figure 5. Verification Case Geometry
Total Size / X / Y / ∆X / ∆Y20000 / 100 / 200 / 0.01 / 0.01
Table 2. Computational Grid Spacing
3.2 Boundary Conditions.
In order to model a face or line with a porous-jump boundary condition, FLUENT requires the Permeability (K), thickness, and Pressure-Jump Coefficient () to be entered. In the actual BMC apparatus, the screen portion is a 16 Mesh with wire diameter (d) of 0.0004572m. All calculations for permeability, thickness, and Pressure-Jump Coefficient were done using the corresponding values for a 16 mesh found in literature.
Calculating Permeability (K) and Pressure-Jump Coefficient ():
The standard wire diameter (d) for a 16 Mesh is 0.0004572m. The screen being modeled is woven, making the thickness of the screen 2*d, which is equivalent to 0.0009144 m. When evaluating through-plane flow through a 2D planar structure, the value is given in Table 3 to equal 0.0046 with F=0.118. The equation used to calculate the permeability (K) and the pressure-jump coefficient are:
and (10)
To first solve for K, the given wire diameter (d) and the value for a through-plane flow through a planar 2D structure are imputed into the equation
(11)