Pipe


Model description

Given is a pipe of length $l$ and sourface roughness $R_a$. For laminar flow, the pressure loss coefficient is calculated based on the Reynolds-number: $$\zeta_{lam}=\frac{64}{\text{Re}}$$ For turbulent flow, the explicit characterization by VDI is used: $$\frac{1}{\sqrt{\zeta_{turb}}}=-2 \log\left(\frac{2.51}{\text{Re}\cdot\sqrt{\zeta_{turb}}}+\frac{R_a}{3.71\cdot D}\right)$$ The implicit correlation for $\zeta_{turb}$ is solved numerically.

For laminar flow, the Nusselt-number is computed based on the applied boundary condition: $$\text{Nu}_{lam}=\begin{cases}3.66&\text{for constant wall temperature}\\4.364&\text{for constant wall heat flux}\end{cases}$$ For laminar flow the correlation by VDI is used: $$\text{Nu}_{turb}=\frac{\left(\xi/8\right)\cdot\text{Re}\cdot\text{Pr}}{1+12.7\cdot\sqrt{\xi/8}\cdot\left(\text{Pr}^{2/3}-1\right)}\cdot\left[1+\frac{1}{3}\left(\frac{D}{l}\right)^{2/3}\right]$$ where $\displaystyle\xi=\left(1.8\log_{10}\text{Re}-1.5\right)^{-2}$

The element type Drilling implements the same models, but $R_a$ is set based on manufacturing technologies.

  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 pipe
Wall Roughness\(R_a\)mMean roughness of the wall