## 3 Analysis and Discussion of the Results
### Validation of the CFD Simulation and Analysis of the Loss Behaviour  
The head determined by the CFD simulation (CFD) is illustrated in Figure 9, accompanied by the corresponding measurements (Exp). The left-hand side diagrams depict the head, while the right-hand side diagrams illustrate the power consumption for the three prewhirl body angles under analysis. The head was identified as being located at the boundary outlet, as well as between the prewhirl body and inlet housing. For \(\Delta\alpha_{\rm pb}=0^{\circ}\), there are slight deviations for flow rates \(Q<100\frac{\rm m^{3}}{\rm h}\). Furthermore, deviations are observable in the remaining prewhirl body angles. For \(\Delta\alpha_{\rm pb}=+30^{\circ}\), larger deviations occur at \(Q>120\frac{\rm m^{3}}{\rm h}\). The maximum relative deviation between the simulation and the measurements is less than 4%. Only the operating point at \(Q=140\frac{\rm m^{3}}{\rm h}\) of \(\Delta\alpha_{\rm pb}=+30^{\circ}\) is an exception and exhibits a deviation greater than 10%. In conclusion, the observed deviations are significantly below those reported by [PERSON] et al. [19], rendering them suitable for the analysis of the flow fields and losses. Figure 9 also shows the characteristic curves of the power consumption (\(P_{2}\)) for the measurements (Exp) and the simulations (CFD) with variation of the prewhirl body angle \(\Delta\alpha_{\rm pb}\in\{-30^{\circ};0^{\circ};+30^{\circ}\}\). It is important to note that the power consumption in the measurements is larger than that in the simulation due to mechanical losses (\(P_{\rm mech}\)). Nevertheless, there is a high degree of concordance between experimental and simulated results. In particular, the simulation is expected to accurately model secondary losses, such as friction in the impeller side gaps. As previously outlined in the introduction, the entropy production method is commonly employed to examine the causes of losses in centrifugal pumps. According to the URANS, the entropy production (\(S_{\rm pro}\)) is decomposed into an averaged (\(\overline{S}_{\rm pro}\)) and a turbulent (\(S_{\rm pro}\)) part, as shown in Equation (9) [22; 31]. Equation (10) [22; 31] illustrates the averaged entropy production, whereas Equation (11) [22; 31] depicts the turbulent entropy production. The equations of [22; 31] were multiplied by the temperature. \[S_{\rm pro}=\overline{S}_{\rm pro}+{S_{\rm pro}}^{\prime} \tag{9}\]  
\[ \begin{array}{c}\overline{S}_{\rm pro}=\mu\bigg{(}2\bigg{(}\Big{(}\frac{ \overline{\partial\
u}}{\partial x}\Big{)}^{2}+\Big{(}\frac{\partial\overline{ \
u}}{\partial y}\Big{)}^{2}+\Big{(}\frac{\partial\overline{\
u}}{\partial z} \Big{)}^{2}\bigg{)}+\Big{(}\frac{\partial\overline{u}}{\partial y}+\frac{ \partial\overline{v}}{\partial x}\Big{)}^{2}+\Big{(}\frac{\partial\overline{ u}}{\partial z}+\frac{\partial\overline{w}}{\partial x}\Big{)}^{2}\\ \hskip 56.905512 pt+\Big{(}\frac{\partial\overline{v}}{\partial z}+\frac{ \partial\overline{w}}{\partial y}\Big{)}^{2}\bigg{)}\end{array}  \tag{10}\]  
\[ \begin{array}{c}S_{\rm pro}^{\prime}=\mu\bigg{(}2\bigg{(}\Big{(}\frac{ \partial u^{\prime}}{\partial x}\Big{)}^{2}+\Big{(}\frac{\partial v^{\prime}}{ \partial y}\Big{)}^{2}+\Big{(}\frac{\partial u^{\prime}}{\partial z}\Big{)}^{2 }\bigg{)}+\Big{(}\frac{\partial u^{\prime}}{\partial y}+\frac{\partial v^{ \prime}}{\partial x}\Big{)}^{2}+\Big{(}\frac{\partial u^{\prime}}{\partial z}+ \frac{\partial u^{\prime}}{\partial x}\Big{)}^{2}\\ \hskip 56.905512 pt+\Big{(}\frac{\partial v^{\prime}}{\partial z}+\frac{ \partial w^{\prime}}{\partial y}\Big{)}^{2}\bigg{)}\end{array}  \tag{11}\]  
The velocity components in the three spatial directions, designated \(x,y,z\), are labelled \(u,v,w\), respectively. The bar above the velocity components indicates the averaged components, while the vertical line represents the fluctuating components. The dynamic viscosity of the pumped medium is designated by \(\mu\).