This model describes an element, where the flow is parted into two paths with equal flow rate. Both paths are circular arcs of 180°. After passing the two arcs, the two flows are united again.
The pressure loss coefficient, as well as the Nusselt-number are computed using the correlations for helical flows as provided by VDI: $$\zeta_{lam}=\frac{8}{\text{Re}}\cdot\left(1+0.33\cdot\left[\log\left(\frac{\text{Re}}{2}\cdot\sqrt{\frac{D_2}{D_1}}\right)\right]^4\right)$$ $$\zeta_{turb}=\frac{0.0941}{\text{Re}^{0.25}}\cdot\left[1+0.080\cdot\left(\frac{D_2}{D_1}\right)^{0.5}\cdot\text{Re}^{0.25}\right]$$ $$\text{Nu}_{lam}=3.66+0.08\cdot\left[1+0.8\cdot\left(\frac{D_2}{D_1}\right)^{0.9}\right]\cdot\left(\frac{\text{Re}}{2}\right)^m\cdot\text{Pr}^{1/3}$$ $$\text{Nu}_{turb}=\frac{\left(\xi/8\right)\cdot\text{Re}\cdot\text{Pr}}{2+25.4\cdot\sqrt{\xi/8}\cdot\left(\text{Pr}^{2/3}-1\right)}$$ where $\displaystyle m=0.5+0.2903\cdot\left(D_2/D_1\right)^{0.194}$ and $\displaystyle\xi=0.3763/\text{Re}^{0.25}+0.03\cdot\left(D_2/D_1\right)^{0.5}$.
Please be aware, that the Reynolds-numer is calculated for half the flow rate, since the flow is divided onto two paths.
Parameter | Symbol | Unit | Description |
Radius | \(R\) | m | Radius of the flow arround |