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Starting with FEBio 2.7, a fluid solver is available for performing computational fluid dynamics analyses. In this example, we examine flow in an expanding pipe, which is characterized by flow reversal in the expanded pipe domain.
The FEBio model file is FlowExpandingPipe.feb.zip. It was created in PreView 2.0.0, using two cylinders (diam=1, height=3 and diam=2, height=3) and a cone (bottom diam=1, top diam=2, height=1), meshed and merged together. A biased mesh was created near the no-slip boundary using the PostBL tool in PreView, with bias=2 and segments=5).
The fluid is Newtonian with density=1, bulk modulus=1e9, shear viscosity=0.01, bulk viscosity=0.
Zero fluid velocity was prescribed on the lateral surfaces (pipe wall) to enforce the no-slip condition. A normal velocity was prescribed on the upstream face (vn=-1 for inflow, with parabolic profile) with a load curve that increased from 0 to 1 from time t=0 to t=1. Zero fluid dilatation was prescribed on the downstream face (equivalent to zero fluid pressure). Back flow stabilization (beta=1) and tangential stabilization (beta=1) were also prescribed on the downstream face, to enhance the stability of the analysis in the presence of flow reversal.
A fluid analysis step was selected, of type dynamic, with 140 times steps of 0.1 (total time of 14). The solver used Broyden's method 50 max updates, turning off "Reform on diverge" and "Reform each time step" to increase computation efficiency.
Results are plotted with PostView 2.3.1. A plane cut is used which is normal to the X-direction. An animation of the fluid velocity magnitude shows that a central stream travels from the inlet to the outlet.
An animation of the streamlines clearly demonstrates that flow reversal develops in the pipe expansion.
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It is also possible to plot the motion of particles that are released at the inlet face and trace their paths.
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This fluid solver expands the set of features available in FEBio.
The FEBio model file is FlowExpandingPipe.feb.zip. It was created in PreView 2.0.0, using two cylinders (diam=1, height=3 and diam=2, height=3) and a cone (bottom diam=1, top diam=2, height=1), meshed and merged together. A biased mesh was created near the no-slip boundary using the PostBL tool in PreView, with bias=2 and segments=5).
The fluid is Newtonian with density=1, bulk modulus=1e9, shear viscosity=0.01, bulk viscosity=0.
Zero fluid velocity was prescribed on the lateral surfaces (pipe wall) to enforce the no-slip condition. A normal velocity was prescribed on the upstream face (vn=-1 for inflow, with parabolic profile) with a load curve that increased from 0 to 1 from time t=0 to t=1. Zero fluid dilatation was prescribed on the downstream face (equivalent to zero fluid pressure). Back flow stabilization (beta=1) and tangential stabilization (beta=1) were also prescribed on the downstream face, to enhance the stability of the analysis in the presence of flow reversal.
A fluid analysis step was selected, of type dynamic, with 140 times steps of 0.1 (total time of 14). The solver used Broyden's method 50 max updates, turning off "Reform on diverge" and "Reform each time step" to increase computation efficiency.
Results are plotted with PostView 2.3.1. A plane cut is used which is normal to the X-direction. An animation of the fluid velocity magnitude shows that a central stream travels from the inlet to the outlet.
An animation of the streamlines clearly demonstrates that flow reversal develops in the pipe expansion.
.It is also possible to plot the motion of particles that are released at the inlet face and trace their paths.
.This fluid solver expands the set of features available in FEBio.
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