Swirling flow in a conical diffuser generated with rotor-stator interaction

Application Challenge AC6-14 © copyright ERCOFTAC 2024

Comparison of Test Data and CFD

The mean velocity field is determined by time averaging over five complete runner revolutions for the hybrid models and eight complete runner revolutions for the URANS models to filter out all unsteadiness. The survey axes, \textit{S*}, at sections W0-W2 (see Fig. \ref{Test_rig}), are normalized by the throat radius, $R_{throat}$=0.05m, and the velocity is normalized by the bulk velocity at the throat, $W_{throat}$. The axial axis is downward and the runner rotates in the positive direction according to the right-hand rule.

Figure \ref{fig6} compares the axial and tangential velocity distributions of the high-Reynolds number turbulence models, standard $k-\epsilon$, SST $k-\omega$, realizable $k-\epsilon$ and RNG $k-\epsilon$, with the experimental results at W1 and W2. It is shown that the turbulence models predict the mean velocity very similarly. It is known that a high level of swirl leads to an on-axis recirculation region due to the high centrifugal force~\cite{Javadi2015}. The models overestimate the size of that region, although the RNG $k-\epsilon$ and standard $k-\epsilon$ models predict the recirculation region more realistically than the other models. Javadi et al.~\cite{Javadietal2014} used the RNG $k-\epsilon$ model in the swirl generator over a wide range of runner rotational speeds, from part load to full load. They concluded that the applicability of the RNG $k-\epsilon$ model is restricted to a range close to the best efficiency point. As mentioned before, the current flow field resembles the Francis turbine at 70\% load, which is far from the best efficiency point. The disintegration process of the vortex rope is highly unsteady and needs to be resolved to capture its realistic representation. The turbulence models reproduce the width of the central stagnant region reasonably well at W2.

Figure \ref{fig7} compares the axial and tangential velocity distributions of the low-Reynolds number turbulence models, Launder-Sharma and Lien-cubic $k-\epsilon$, with the experimental results at W1. The results show that Lien-cubic $k-\epsilon$ underestimates the main character of the flow, the on-axis recirculation region, considerably. It can be seen that Launder-Sharma $k-\epsilon$ model, on the other hand, overestimates the recirculation region. The LS model was initially proposed for predicting swirling flows. The model, as a modified version of the standard $k-\epsilon$ model, is one of the earliest and most widely used models for resolving the near-wall flow behavior. Although some damping functions are added in the LS model to account for the viscous and wall effects, the improved near-wall behavior does not significantly increase the quality of the mean velocity profiles in the draft tube.

Figure \ref{fig8} compares the axial and tangential velocity distributions of the hybrid models DDES-SA, IDDES-SA and DDES-SST, with the experimental results at sections W0-W2. Figure \ref{fig8}a shows that the velocity increases linearly from the hub to the shroud downstream of the runner, at W0. The blade wakes are responsible for the change in the slope of velocity components at $0.25<S^*<0.4$. The wakes travel closer to the hub, i.e. the velocity components decrease in the inner half of the annular cross-section. The hybrid models realistically predict the inner half of the flow, close to the hub. The axial velocity in the outer part, close to the shroud, is overestimated and the tangential velocity is underestimated, i.e. the predicted flow is too axial in the outer part, at W0. The effects of the wakes on the averaged velocity is overestimated by DDES-SA and IDDES-SA. Nevertheless, the wakes predicted by these two models are remarkably in spite of while a different wall treatment being used by IDDES-SA. DDES-SST presents weaker wakes compared with the other models while the results agree with the experimental results. Figure 8b shows the axial and tangential velocity components at W1, close to the throat. As mentioned before, the vortex breakdown leads to a disintegration of the helical vortex. The vortex rope forms slightly downstream the nozzle and immediately deflects outwards, see Figs. \ref{fig11} and \ref{fig13}. The on-axis axial velocity is almost zero and the tangential velocity increases linearly with the radius. In the outer part of the draft tube, both the axial and tangential velocity magnitudes increase at W1. The central recirculation region thus ends at the throat, yielding an on-axis stagnation region at W1. The experimental results show $W/W_{throat}$=0.08 on-axis at W1 while numerical results predict $W/W_{throat}$=-0.010, -0.041 and -0.187 with DDES-SA, DDES-SST and IDDES-SA, respectively. Figure \ref{fig8}c shows the axial and tangential velocity components at W2. The central cone-shaped stagnant region in the draft tube occupies 60\% of the cross-section and is thus much wider than at W1. The velocity profiles at W2 follow the same patterns as at W1 but with a lower magnitude.