Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

OBJECTIVE:

Compare the results with higher wedge angle:

• 10
• 25
• 45

Simulate for both wedge and symmetry boundary conditions for each of the above angles and validate the results with analytical result:

1. Validate Hydro-dynamic length with the numerical result
2. Validate the fully developed flow velocity profile with its analytical profile
3. Validate maximum velocity and pressured drop for fully developed flow
4. Post-process Shear stress and validate wall shear stress for fully developed flow
5. Highligh the differences in both boundary conditions in terms of their usage and aplication

THEORY:

Hagen-Poiseuille Equation:

It is a physical law which gives the value of the pressure drop as a fluid in laminar flow, flows along a long cylindrical pipe of constant cross-section. It has the following assumptions:

• The fluid is compressible and newtonian.
• The flow is laminar
• The pipe length of pipe is substabntially greater than its constant cross-section
• There is no acceleration of fluid in pipe

Mathematically,

CASES:

Wedge Boundary

10 Degrees:

25 Degrees:

45 Degrees:

RESULTS:

The results are similar for the three cases:

Pressure Drop:

Velocity Profile:

Shear Stress at fully developed flow:

Symmetry Boundary Condition:

10 Degrees:

25 Degrees:

45 degrees:

RESULTS:

The results are similar for the three cases:

Pressure Drop:

Velocity Profile:

Shear Stress at fully developed flow:

SYMMETRY VS WEDGE BOUNDARY CONDITION:

A symmetry boundary condition presents a mirroring plane effect on the boundary while the wedge condition acts like an axial or spherical mirror instead of a plane mirror.

Thus for this case if the results were post-processed to a complete 360 degree pipe, the symmetry boundary condition would produce inaccurate results.

Comparison with Analytical Results:

The end results are same as the 3 degree case simulated previously hence the difference b/w analytical and simulated results remains same.

CONCLUSION:

Symmetry and Wedge Boundary conditions have been studied and differentiated successfully.