Similar to the element DefinedValues, this element type uses pre-set values for the pressure loss coefficient and the heat transfer coefficient. But within this model, these values are flow rate dependent. This is realized by three vectors of length $M$: $$\vec Q=[Q_1, \,\ldots,Q_M]^\text{T}$$ $$\vec\zeta=[\zeta_1, \,\ldots,\zeta_M]^\text{T}$$ $$\vec\alpha=[\alpha_1, \,\ldots,\alpha_M]^\text{T}$$ Given a flow rate $\dot V$, the values $\zeta$ and $\alpha$ are interpolated based on the provided vectors: $$\zeta = \zeta_i+\left(\dot{V}-Q_i\right)\cdot\frac{\zeta_{i+1}-\zeta_i}{Q_{i+1}-Q_i}$$ $$\alpha = \alpha_i+\left(\dot{V}-Q_i\right)\cdot\frac{\alpha_{i+1}-\alpha_i}{Q_{i+1}-Q_i}$$ Where the interpolation point $i$ is selected as follows: $$i=\left\lbrace\begin{matrix}1&\text{if } \dot{V}\lt Q_1\\ M-1 & \text{if }>Q_M\\ i \text{ s.t. } Q_i\leq\dot{V}\lt Q_{i+1} & \text{otherwise}\end{matrix}\right.$$
Please be aware, that the geometric properties $l$, $V$ and $S$ are used as they are configured, without checking any conflicts. Hence, the parameters could be set s.t $S\neq l\cdot U$ and $V\neq l\cdot A$, where $U$ and $A$ are the circumference and cross sectrion area acording to the configured profile.
Parameter | Symbol | Unit | Description |
HeatTransferCoefficients | \(\vec\alpha\) | m2 kg s-3 K-1 | Vector of heat transfer coefficient samples (same size as flow rate samples) |
Length | \(l\) | m | Length of the element |
Volume | \(V\) | m3 | Volume of the element |
FlowRateSamples | \(\vec Q\) | l/min | Vector of flow rate samples |
PressureLossCoefficients | \(\vec\zeta\) | - | Vector of pressure loss coefficient samples (same size as flow rate samples) |
Surface | \(S\) | m2 | Surface area |