Add support for hexagonal ducts with filleted corners

[dlangewisch]

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ARMI currently supports Hexagonal ducts with sharp corners, but in many practical cases the hex ducts have rounded (filleted) corners with a specified corner radius, which reduces both the flow area and wetted perimeter of these ducts and increases the hydraulic diameter by as much as ~2.4% (neglecting pins). Capability should be added to support either specifying a corner radius when defining a component of shape Hexagon, or perhaps a new FilletedHexagon shape should be added with that capability.

If $D$ denotes the flat-to-flat inner duct diameter (i.e., the value returned by duct.getDimension('ip')) and $r$ denotes the corner radius ($0 \le r \le D/2$), then the perimeter, $P$, of the inner duct surface and the cross-sectional area $A$ inside the duct are given, respectively, by:

$$P(D,r) = \underbrace{2\sqrt{3}D}_{P(D,r=0)} \left[1 - \left(1 - \frac{\pi}{2\sqrt{3}}\right)\left(\frac{2r}{D}\right)\right]$$

and

$$A(D,r) = \underbrace{\frac{\sqrt{3}}{2}D^2}_{A(D,r=0)} \left[1 - \left(1 - \frac{\pi}{2\sqrt{3}}\right)\left(\frac{2r}{D}\right)^2 \right]$$

where $P(D, r=0)$ and $A(D, r=0)$ denote the perimeter and cross-sectional area assuming unrounded corners. Note that in the limiting case where $r = D/2$, the hexagon reduces to a circle and we have $A(D, D/2) = \pi D^2 /4$ and $P(D, D/2) = \pi D$ as expected.

The hydraulic diameter of a filleted duct is given by

$$D_{hyd} = D \left[ \frac{1 - \left(1 - \frac{\pi}{2\sqrt{3}} \right) \left( \frac{2r}{D} \right)^2}{ 1 - \left(1 - \frac{\pi}{2\sqrt{3}} \right) \left( \frac{2r}{D} \right) } \right]$$

The quantity in brackets is maximum when $r \approx 0.256 D$, in which case $D_{hyd} \approx 1.0224 D$