edge-sizing

Edge Sizing in ANSYS Meshing

This is a general edge sizing app where smallest cell size is calculated for given $y^+$ in a turbulent pipe flow with input properties and velocity and mesh parameters and recommend a closer bias factor for the given $y^+$.

This contains two different options.

1. Water
2. Other Fluids

Water

This can calculate the thermophysical properties for Water from IAPWS module from initial temperature and properties and calculate the smallest cell size and a recommended bias factor accordingly.

Other Fluids

This contains general edge sizing app where y+ is calculated for a turbulent pipe flow with input properties and velocity and geometry parameters.

Calculation module:

Skin Friction Coefficient

The Skin-friction coefficient is calculated by Schlichting Skin-Friction Coefficient that is Valid for $Re_x < 10^9$ as follows.

$$ c_f = (2 log_{10}(Re_D) - 0.65)^{-2.3} $$

Smallest Cell Size for given $y^+$

$$ \Delta x_{min} = \frac{2 y^+ \mu}{\rho u^*} $$

where $u^*$ is calcualted as,

$$ u^* = \sqrt{\frac{\tau_w}{\rho}} = \sqrt{0.5 c_f U^2} $$

Smallest Cell Size in the mesh

The Edge Sizing method in ANSYS Meshing works by a simple geometric progression where the bias factor (bf) is the ratio of the G.P, and L is the length of the edge divided into N divisions.

$$ \Delta x_{min} = \frac{L}{\Sigma_{i = 0}^{N} (bf^{(1/N-1)})^i} $$

Recommended Bias factor

This runs the Small cell utility for multiple bias factors from 1 to 31 with a step of 0.01 and find the closest value to the Small cell size given by $y^+$ and recommend that bias factor to be used for the given $y^+$.