Representation of a smooth helix with winding radius $R$ and winding distance $h$ covering a total height $l$. Both, pressure loss coefficient and Nusselt-number are computed based on the correlations provided in VDI: $$\zeta_{lam}=\frac{64}{\text{Re}}\cdot\left(1+0.33\cdot\left[\log\left(\text{Re}\cdot\sqrt{\frac{D_2}{D_1}}\right)\right]^4\right)$$ $$\zeta_{turb}=\frac{0.3164}{\text{Re}^{0.25}}\cdot\left[1+0.095\cdot\left(\frac{D_2}{D_1}\right)^{0.5}\cdot\text{Re}^{0.25}\right]$$ $$\text{Nu}_{lam}=3.66+0.08\cdot\left[1+0.8\cdot\left(\frac{D_2}{D_1}\right)^{0.9}\right]\cdot\text{Re}^m\cdot\text{Pr}^{1/3}$$ $$\text{Nu}_{turb}=\frac{\left(\xi/8\right)\cdot\text{Re}\cdot\text{Pr}}{1+12.7\cdot\sqrt{\xi/8}\cdot\left(\text{Pr}^{2/3}-1\right)}$$ where $\displaystyle m=0.5+0.2903\cdot\left(D_2/D_1\right)^{0.194}$ and $\xi=0.3164/\text{Re}^{0.25}+0.03\cdot\left(D_2/D_1\right)^{0.5}$.
Parameter | Symbol | Unit | Description |
Radius | \(R\) | m | Radius of the coil |
Height | \(l\) | m | Total height of the coil |
Distance | \(h\) | m | Winding distance of the coil |