Week 12 - Symmetry vs Wedge vs HP equation

Objective: To create blockMeshDict file by using MATLAB for three wedges of 10,25,45 degrees and comparing the difference in the results when ‘symmetry’ and ‘wedge’ boundary conditions were given.

Theory:

The two different boundry conditions used here are:

1.Symmetry- This boundry condition enforces a symmetric constraint.

2.Wedge- This boundry condition enforces a cyclic condition between a pair of boundries , however it is used in 2D geometries.

The Hagen-Poisuille equation is used as a standard for comparison of both results.

It applies to smooth fully developed laminar flow and gives a relationship between pressure drop , inlet velocity , pipe length , volumetric flow rate , pipe radius ,area and absolute coefficent of viscousity.

`Deltap=(8*pi*mu*L*Q)/(A^2)`

Results and conclusion

Here is a comparison of the maximum velocity obtained at 0.9m from the inlet , the Hagen-Posiuille equation gives it a 0.8034

Angle	Symmetry condition	Wedge Condition	Time of simulation -Symmetry	Time of simulation -Wedge
10	0.7937	0.7989	1203	925
25	0.7937	0.7980	1093	1243
45	0.7937	0.7989	787	1761

Here is a comparison of the velocity distribution over the radial direction of the wedge and symmetric boundry condition for each angle.

Here is a comparison of the three angles for each of the wedge and symmetric condition.

1. There is no significant difference in the two boundry conditions.

2.The sumulation run time increased with increasing angle for the symmetry case . This variation was not consistant in the wedge case.

3.The courant number showed an increase in the case for the symmetry boundry condition this necessitated a change in the time step value.

4.The parabolic velocity profiles of the three angle are different . The 45 degree case showed significant deviation.