PROJECT SUMMARY REPORT
SIMULATION OF FLUID FLOW IN THE SCREENBOUNDED CHANNEL IN A FIBER SEPERATOR
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, Pre-Junior, Biomedical Engineering
Sandra Hernandez, Pre-Junior, Biomedical Engineering
Report Reviewed By:
___________________________
Dr. Urmila Ghia
REU Faculty Mentor
Professor of Mechanical Engineering
School of Dynamic Systems
University of Cincinnati
January 7 – April 26, 2013
1
Chapter 1
1.1 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. The
BMC deep open channel is first modeled as a channel with both vertical side boundaries as solid
walls. Next, 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) 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 (i)
d) Model the screen as a porous boundary (ii)
1.2 Materials
Commercially available Computational Fluid Dynamics (CFD) tools FLUENT and Gambit
are used for the simulations in this study.
1.3 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 pressurevelocity 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 – Solid Side Walls
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.
The boundary conditions used for modeling the wire-mesh wall as a solid boundary are
shown in Figure 1. 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. The fluid flow is
computed in FLUENT at every discrete grid point, and the Reynolds-stress model includes the
effects of turbulence. 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.
2
Free-Slip Wall, v=0, du/dy=0, dw/dy=0
No-Slip Wall, u = v = w = 0
Inlet, u = U, v = w =0
Outlet, pstat = 0
Figure 1. Boundary conditions applied on the BMC open channel
2.3 Results and Discussion
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. Figures 2 shows the x-velocity contours on the cross plane of the open channel
near the free surface, respectively. Velocity is lowest at the edges of the channel due to friction of
the stationary wall. The velocity contours are bulged towards the corners near the free surface at
the top of the channels, while elsewhere along the vertical wall boundaries, the contours
gradually shift towards the center of the plane. The free surface at the top of the channel is
modeled by a zero-shear stress wall, which attracts the high-momentum fluid from the center of
the open channel. In order to preserve the channel continuity, low momentum fluid from the
corner regions flows towards the center of the channel. This motion of fluid flow creates a
circulatory effect near the corners, which causes the bulge in velocity contours near the free
surface.
Figure 2. X- Velocity Contours on Top
Half of channel
Figure 3. X-Vorticity Contours on Top
Half of channel
Figure 3 shows the x-vorticity on the cross plane of the BMC open channel. Vorticity is
defined as the tendency of a fluid to rotate [11]. In the corners near the free surface, the vortex
pair is not symmetrical about the angle bisector. The variation in vorticity along the top of the
channel is due to the different boundary conditions, which changes the behavior of the fluid flow.
Shear stress, as shown in Figure 4 in blue, was computed along the x-direction of the
channel. Total shear stress, including 𝜏𝑧𝑥 , 𝜏𝑧𝑦 , and 𝜏𝑧𝑧 , was calculated along the z=0.02 m
sidewall at x = 0 to 0.217 m, y = 0.1 m (mid-plane). The computations from FLUENT for each
partial derivative in respect to z were written out as a text file, and uploaded into Microsoft Excel
in order to calculate 𝜏 for each shear stress component on the sidewall. Each of the three
components was squared and added together. The square root of the summation is taken to
obtain the total shear stress along the x- direction acting on the sidewall at y = 0.1m.
3
2
14
12
1.5
10
8
1
6
4
0.5
2
0
0
0
0.1
X-Position (m)
Off Plane Shear Stress
Angle (degrees)
Total X-Wall Shear Stress
(Pascals)
Total Shear Stress
Total
Stress
Off
Plane
Shear
Stress
Angle
0.2
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
The off-plane angle, shown in red, is the angle between resultant shear stress vectors
and the xy plane. These results show the shear stress angle between the free surface and the
wall in the BMC channel with respect to the x-position in the channel geometry. It is shown that
the shear stress angle is greatest at the inlet, and quickly drops down to around 8 degrees as the
x-position increases. The highest off-plane angle occurs at the inlet, x= 0m, and quickly drops
down to 8.36 degrees around x = 0.0116 m.
Chapter 3
Flow in the BMC Open Channel with a Screen on a Side Wall
3.1 Geometry and Computational Grid
As a second step, portion of the sidewall of the channel containing the screen was
replaced with a porous boundary. The porous boundary represents the screen in the BMC
apparatus. The porous boundary is modeled with 1 inch (0.0254 m) margins lengthwise and a 1
inch margin from the bottom of the channel. The dimensions of the boundary are x= 0.1662 m, y=
0.1746 m, and a wire diameter 0.0004572 m. The grid spacing for the channel with a porous
boundary maintains the same grid spacing and ratio of points per inch as the previous mesh.
3.2 Boundary Conditions
The boundary conditions for all parameters except a portion of a side wall are the same
as the previous case with solid side walls, as seen in figure 5. In Fluent, one side of the screen
was specified as a porous-jump boundary condition, and the other as a pressure-outlet. In order
for FLUENT to solve the Reynolds Stress Equations for the fluid flow in the channel with a porous
boundary, the permeability, pressure-jump coefficient, and the thickness of the porous boundary
need to first be determined.
Calculating Permeability (K) and Pressure-Jump Coefficient (𝐶2 ):
The standard screen thickness for a 16 Mesh is 0.0009144 m (0.036 Inch) and the wire
diameter is 0.0004572m (0.0180 Inch). When evaluating through-plane flow through a 2D planar
𝐾
structure, the 2 value is given to be 0.0056 with F=0.118. The equation used to calculate the
𝑑
permeability (K) and the pressure-jump coefficient are:
2𝐹
𝐾
𝐾
𝐶2 =
and 2 = 2
√𝐾
𝑑
𝑑
4
To first solve for K, the given wire diameter (d) and the
a planar 2D structure are imputed into the equation
𝐾
0.0046 =
2
𝐾
𝑑2
value for a through-plance flow through
(0.0004572)
𝐾 = 9.6154𝑒 −10 𝑚2
This means the face permeability (K) of the screen mesh is 9.6154𝑒 −10 𝑚2
The pressure-jump coefficient (𝐶2 ) is calculated by replacing F with the given 0.118 value and
using the calculated K
2(0.118)
1
𝐶2 =
= 7610.739
−10 2
√(9.6154𝑒
𝑚 )
𝑚
These values are then entered into FLUENT along with the overall screen thickness of 0.0009144
m to analyze the flow in the 3D open channel with the screen modeled as a porous-jump
boundary.
Free-Slip Wall, u= v = w = 0
No-Slip Wall, u = v = w = 0
Inlet, u = U, v = w =0
Outlet, pstat = 0
Porous-Jump, K = 9.6e-10, C2=7610.7 1/m, thickness = 9e-4 m
𝐾 = 9.6154𝑒 −10 𝑚2
Figure 5. Boundary Conditions of Channel with Porous Boundary
The turbulence boundary conditions were specified in the form of turbulence intensity and
viscosity of 0.5% 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.
3.3 Results and Discussion
Figures 6 shows the x-velocity contours on the cross plane of the open channel near the
free surface and the channel base, respectively. The velocity is similar to the two wall case with
the velocity being highest towards the center and lowest at the edges of the walls. The velocity
contours are bulged towards the corners near the free surface at the top of the channels, while
elsewhere along the vertical wall boundaries, the contours gradually shift towards the center of
the plane. However, unlike the previous case, the velocity contours along each wall are not
symmetric. This can be attributed to the addition of the porous boundary.
Figure 6. X- Velocity Contours on Top
Half of channel
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Figure 7. X-Vorticity Contours on Top
Half of channel
Figure 7 shows the x-vorticity on the cross plane of the BMC open channel. The porous
boundary is modeled from x= 0.0254 m to 0.1916 m. The vorticity contours were taken at a plane
at x= 0.20m in line with the outlet, right after the porous boundary ends. The addition of the
porous boundary greatly increased the vorticity along the sidewall of the channel.
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 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. As a second step, the BMC channel geometry is
modified to have one of the sidewalls contain a porous boundary condition.
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, nonporous sidewalls. In the second porous wall model, it was found that the x-velocity contours
followed the same behavior as the previous case. However, once the flow reaches the porous
boundary, the x-velocity of the flow begins to fluctuate. In both of the x-velocity contour plots,
bulges are observed near the free surface.
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-vorticiy
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.
Future Work
The future work of this study is to further analyze the off-plane and shear stress
distribution of the channel modeled with a porous boundary. We hope to further understand the
effects of the porous boundary on fluid flow behavior and compare the porous boundary results to
those of a 3x3 array of square apertures.
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