8/12/2019 CFD for a Newtonian Oil in Pipe

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A Newtonian oil of density 850 kg/m3and a viscosity of 0.05 Pa.s flows into a section of a pipe that expands

into a larger pipe as sketched below. The angle of expansion is 45o. For simplicity, assume that the inlet

velocity is uniform at 0.3m/s and ignore the effects of gravity and pressure. You may pick any reasonable

lengths of the pipe before and after the expansion, mainly for the flow to be fully developed before and after

the expansion i.e. the artificial edge effects of inflow and outflow boundaries are minimized.

2.5 cm 10 cm

10 cm

5 cm 10 cm

In Elmer, axisymmetric shapes such as a pipe can be handled (Model Setup).

a) Generally in CFD, using a sufficiently fine mesh is critical to ensure that the results are trustworthy.Solve for the velocity profile using increasingly finer mesh. Show evidence that the solution changes

a lot, but eventually it does not change much, i.e. the solution becomes mesh-independent.

It is assumed that the pipe is vertical and inflow is from upwards. Using mesh size of 0.025, 0.020, 0.010,

0.008, 0.005 and 0.001; the following graph and figures are obtained.

Graph 1: Velocity against radius of different mesh size. Figure 1: ElmerPost graphical results.

Figure 2: Gmsh diagram after 2D meshing.

It is found that the maximum velocity at the outflow increases from -0.20 m/s to -0.38 m/s before reaching a

constant value of -0.35 m/s when the mesh size increasingly getting finer. This figure is expected because

for increasingly finer mesh, more fluid actually flowing in at the inflow boundary condition. For mesh sizeof 0.025, there is only 2 points at the inflow. Since one of it falls on the no slip boundary condition, the fluid

enters only at the top left corner or the tube. However at mesh size of 0.001, much more fluids enter the

inflow boundary condition that eventually changes the velocity of the outflow. (SHOWN)

-0.45

-0.40

-0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.00 0.10 0.20 0.30 0.40 0.50 0.60

8/12/2019 CFD for a Newtonian Oil in Pipe

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b) (Bonus) Use the post-processing graphics capability of Elmer to show the region of recirculation, i.e.where the liquid has a velocity component that is opposite to the direction of the main flow.

Figure 3: Magnified ElmerPost graphical results with vector

It is found that there is recirculation of the fluid near the boundary of the tube after expansion. With

increasingly finer mesh, more fluid is actually being re-circulated and the velocity increases from 0 m/s at

0.025 mesh size to 0.54 m/s at 0.001 mesh size.