In this study, a modified partially averaged Navier–Stokes (MPANS) model is applied to investigate the flow instability characteristics in a low specific centrifugal pump. In MPANS model, the unresolved-to-total ratio of kinetic energy fk is determined according to the local grid size and turbulence length scale. The numerical results by MPANS model are compared with that simulated by SST k-ω model and the available experimental data. It is noted that MPANS model shows better performance for investigating the unstable flow in the current pump under part-load operation conditions. The time-averaged internal flow and flow incidence in the pump impeller depicts that with the decreasing flow coefficient, flow separation develops in the impeller. Owing to the strong separation flow as well as vortex evolution, incidence angle is large and varies remarkably at the entrance of blade-to-blade passage in the pump impeller. The evolution dynamics of rotating stall is further discussed in detail based on vorticity transport equation. During the evolution of rotating stall, the vortex stretching term has an important effect on vorticity transport under the part-load conditions. The analysis of the pressure fluctuations excited by periodic evolution of rotating stall shows that the rotating stall cell propagates along the rotational direction, and identifies the rotating stall frequency ( fstall), which is much lower than the rotational frequency of the impeller, fn ( fstall = 8.76% fn). Finally, two-dimensional Lagrangian coherent structure (LCS) is used to reveal the separation flow in blade-to-blade passages of the pump by monitoring the trajectory of the particles. Both LCS and vortex structure by λ2 can clearly demonstrates the passage blockage and flow separation under the part-load operation conditions, depicting that the separation flow occurs at blade suction side and develops from the leading edge to the main passage in the impeller.
The current study numerically investigates the flow instability under several part-load conditions in a centrifugal pump with a straight inlet pipe to explore the underlying relationship between a positive slope phenomenon and internal flow using a partially averaged Navier–Stokes model. The model was validated by comparing the hydraulic performance and averaged flow in the impeller between the numerical results and experimental data of a tested pump. The internal flows in pumps have been intensively investigated based on Batchelor vortex family, Rayleigh–Taylor criterion, entropy generation rate, and energy equation to analyze the flow instability from different aspects. The simulation results using partially averaged Navier–Stokes model are acceptable due to the good agreement with the experimental data for the tested pump. No matter the geometry of the inlet pipe, the pre-swirling flows in the inlet pipe are in the convective instability region. Under the part-load condition of φ = 0.5 φbep, the axial vorticity coefficient is affected by the geometry of the inlet pipe. However, under the part-load condition with rotating stall, e.g. φ = 0.78 φbep, the flow in the inlet pipe is affected by the unstable flow in the pump impeller. For the pump with a straight inlet pipe, the vortex inside the blade-to-blade passage is in a stable state according to Rayleigh–Taylor criterion under the condition of φ = 0.5 φbep. However, the vortex in the blade-to-blade passage is in an unstable state due to centrifugal instability under those operation conditions with rotating stall cells in the impeller, and the dominant oscillations are dependent on the propagation of rotating stall cells. Finally, head loss analysis based on energy equations elucidates that turbulent kinetic energy production term is predominant in the head loss in pump impeller. The present results are helpful for better understanding of the unstable flows and positive slope phenomenon for centrifugal pumps.
This study presents a partially averaged Navier–Stokes model, MSST PANS, based on a modified SST [Formula: see text] turbulence model to predict turbulent flows with large streamline curvature. The model was validated for turbulent flow in a [Formula: see text] curved rectangular duct (Re = 224,000) to assess the MSST PANS capabilities. The predictions are compared against flow simulations for the same curved rectangular duct using four turbulence models including the standard [Formula: see text] model, SST [Formula: see text] model, [Formula: see text] PANS model and SST [Formula: see text] PANS model. Comparisons among those numerical results and available experimental data show that the MSST PANS model more accurately predicts the velocity components in all three directions, especially in the wall-bounded region than the other models. The study also shows the advantages of the MSST PANS model for predicting the Reynolds stresses, vorticity, and smaller scale turbulent structures in the wall-bounded region not only qualitatively but quantitatively. Furthermore, the MSST PANS model requires fewer computations than the SST PANS model, indicating that this turbulence model, which takes large streamlines curvature effects into consideration, is an effective alternative for capturing the small-scale turbulence flow structures. This turbulence model is expected to be very useful for engineering applications, especially for flows in turbomachinery.
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