## 5 Iterative Process to Obtain the Pressure Loss Coefficients per Unit Length
### Reliability of Compact Modeling  
Having presented the correlations, the next step is to observe the results that are obtained through the use of the coefficients that are predicted by the correlations. With this aim, the flow magnitudes (\(\overline{v_{t}}\), \(S\), \(V_{min}\) and \(V_{max}\)) at the outlet cross-section of the domain are compared. On the one hand, the flow magnitudes obtained by the simulations with the pressure loss coefficients from the second iterative process are compared with those obtained by the simulations using the coefficients predicted by the correlations. On the other hand, the magnitudes obtained by the coefficient predictions of the correlations are compared with the magnitudes obtained by the detailed models in [PERSON] et al. (1997) that are used as a reference. It must also be noted that the detailed model was experimentally validated in [PERSON] et al. (1997). The results for the first comparison are shown in Figure 7. From the figure, it can be concluded that using the values for \(\varphi_{p}\) and \(\varphi_{z\;ext}\) obtained by the correlations from the compact model do not produce a big difference in the flow magnitudes with respect to using the coefficients obtained just after the iterative process. There are few samples that escape the \(\pm 20\%\) of difference. Once it was shown that the employed correlations had a reasonable influence on the flow magnitude predictions, these were compared with the flow magnitudes obtained by the detailed models in [PERSON] et al. (1997). This comparison is shown in Figure 8. From this figure, it can be seen that the flow magnitudes obtained by the compact model are satisfactory for \(\overline{v_{t}}\), \(S\) and \(V_{max}\). For these magnitudes, nearly all samples are inside the \(\pm 20\%\) difference. However, for \(V_{min}\), it seems that a considerable error is produced. Nevertheless, this error is not very significant if the velocity contours are analyzed. Figure 6 shows that in spite of there being a great difference between the minimum axial velocity values obtained by the compact model and those obtained by the detailed model, the approach to the velocity fields is excellent. Therefore, the results from the minimum axial velocities values are not significant. Moreover, in order to estimate whether the minimum velocity should be smaller, the reduced model presented in [PERSON] et al. (1997) can be used. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Factor** & \(\beta_{0}\) & \(D\) & \(D_{h}\)/\(D\) & \(S\) & \(V\) & \(a\) & \(t\) \\ \hline
**Value** & \(445.48\) & \(-159.30\) & \(-52.03\) & \(22.94\) & \(-122.42\) & \(-22.02\) & \(257.08\) \\ \hline
**Factor** & \(\varepsilon\) & \(\xi\) & \(D\)-\(V\) & \(D\)-\(t\) & \(D\)-\(\varepsilon\) & \(D\)-\(\xi\) & \(S\)-\(D_{h}\)/\(D\) \\ \hline
**Value** & \(-307.91\) & \(230.03\) & \(84.87\) & \(155.50\) & \(61.81\) & \(53.03\) & \(-56.22\) \\ \hline
**Factor** & \(V\)**-\(t\)** & \(a\)**-\(t\)** & \(\varepsilon\)**-\(t\)** & \(\xi\)**-\(t\)** & \(\varepsilon\)**-\(\xi\)** & & \\ \hline
**Value** & \(107.62\) & \(-60.56\) & \(-175.56\) & \(127.28\) & \(-127.16\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Terms of the correlation for \(\varphi_{p}\).