Drilling


Model description

This model implements the same correlations as the Pipe model. How ever, the wall roughness $R_a$ is estimated based on the expected process capabilities of drilling: $$\zeta_{lam}=\frac{64}{\text{Re}}$$ $$\frac{1}{\sqrt{\zeta_{turb}}}=-2 \log\left(\frac{2.51}{\text{Re}\cdot\sqrt{\zeta_{turb}}}+\frac{R_a}{3.71\cdot D}\right)$$ The surface roughness is automatically determined based on an assumed manufacturing technology dependent on the profile type:

As for the pressure loss coefficient, the Nusselt correlation is provided for the laminar and turbulent region: $$\text{Nu}_{lam}=\begin{cases}3.66&\text{for constant wall temperature}\\4.364&\text{for constant wall heat flux}\end{cases}$$ $$\text{Nu}_{turb}=\frac{\left(\xi/8\right)\cdot\text{Re}\cdot\text{Pr}}{1+12.7\cdot\sqrt{\xi/8}\cdot\left(\text{Pr}^{2/3}-1\right)}\cdot\left[1+\frac{1}{3}\left(\frac{D}{l}\right)^{2/3}\right]$$ where $\displaystyle\xi=\left(1.8\log_{10}\text{Re}-1.5\right)^{-2}$

  1. Züst S (2017) Model Based Optimization of Internal Heat Sources in Machine Tools. ETH Diss-Nr. 24482.
  2. VDI Wärmeatlas

Parameters

ParameterSymbolUnitDescription
Length\(l\)mLength of the drilling
Count\(N\)noneNumber of parallel drillings