# Laboratory Modeling of an Axial Flow Micro Hydraulic Turbine
## 3 Results and Discussion  
The measured velocity distributions in the conical section and their downstream evolution are presented in Figures 3-8. Profiles of the averaged velocities and fluctuations for the part load regime are shown in Figures 3 and 4. Figure 2: Experimental conditions: (**a**) Axial velocity profile (left axis—mean; right axis—RMS of velocity fluctuations) measured by LDA upstream of the bend and (**b**) \(M\) (left axis) and \(Q_{i}Q_{n}\) (right axis) conservation as function of \(z/D\). This case is characterized by high tangential velocity, which coincides in direction with the rotation of the runner (Figure 3b). Due to intense swirling, the flow is shifted to the side walls of the conical channel with a corresponding reduction of the velocity along the axis, and axial reverse flow occurs. The most intense reverse flow is observed in the immediate  
Figure 3: Time-averaged velocity profiles at different distances from the runner at a constant runner speed \(\omega_{n}\): (**a**) Axial component; (**b**) Tangential component. Part load regime with \(Q=0.6Q_{n}\). The legend indicates the distances of the measuring section from the tip of the runner cowl. In the section \(z/D=1.30\) the swirl number is \(S=0.6\). vicinity of the runner cowl, where it is further enhanced by the formation of a wake behind the cowl. Further downstream, the reverse flow decreases and practically disappears in cross-sections distant from the runner, where the axial velocity profile becomes much smoother. In this case, the swirl decays downstream, which is reflected in a decrease in the tangential velocity (Figure 3b). At small \(z\), the swirling of the flow by the runner cowl near the axis leads to a pronounced peak of the tangential velocity, which flattens out downstream and shifts toward the side wall. At larger \(z\), the tangential velocity profiles assume a smooth shape with the tangential velocity increasing monotonically from the center to the side wall. The swirling flow structure with a central recirculation zone that occurs in the part load regime usually leads to flow instability in the form of a precessing vortex core (PVC) [35; 36]. The PVC generates increased flow pulsations, as can be seen from the distributions of Root Mean Square (RMS) fluctuations of the axial and tangential velocity components (Figure 4). It is evident that the peaks of the RMS axial velocity are located at the boundary of the reverse flow zone which is always close to the point of maximum radial gradient of the axial velocity (Figure 4a), whereas the peaks of the RMS tangential velocity profiles are near the center (Figure 4b); this unambiguously indicates the precessional motion of the vortex core [22]. It should be noted that RMS distributions contain not only the stochastic turbulence fluctuations, but also the coherent pulsations due to the PVC motion, which may produce the major contribution to the RMS. It will be shown later that the tangential velocity spectra at the monitor point labeled in the figure have a distinct peak at the same frequency of 14.5 Hz, which corresponds to the precession frequency of the coherent vortex structure \(f_{\text{PVC}}\). Increasing the flow rate to the level \(Q=Q_{n}\) corresponding to the design case close to the BEP leads to a more uniform distribution of the axial velocity along the cross-section (Figure 5a). The central dip due to the wake behind the cowl is quite pronounced at small \(z\), but is rapidly filled downstream. The swirl level decreases significantly, although the tangential velocity remains nonzero and coincides in direction with the rotation of the runner at all cross-sections (Figure 5b). As in the previous case, there is a region of higher swirl close to the turbine formed by the rotation of the cowl. This localized region is completely smoothed only after \(z/D=0.30\). In the design case, the velocity fluctuations are generally significantly reduced. The RMS distributions of the axial component become uniform in both the radial and axial directions (Figure 6a).