A general alternate loading technique and its applications in the inverse designs of centrifugal and mixed-flow pump impellers

Rigid vorticity transport equation and its application to vortical structure evolution analysis in hydro-energy machinery

“…To guarantee the prediction accuracy of numerical computation, transient simulations corresponding to the five operating conditions, 0.8Q 0 ∼ 1.2Q 0 , are conducted, and the surface roughness effects are taken into account by using the equivalent sand-grain roughness. The H-Q (head-flowrate) curve, the P-Q (power-flowrate) curve and the peak-to-peak values of pressure fluctuations H/H 0 in the volute casing can be found in the previous studies of the authors (Wang et al, 2021a). Under the design condition, the relative errors are less than 3%, which are kept within reasonable bounds.…”

“…Peakto-peak values of pressure fluctuations H are shown in Figure 14(b). It is found that the peak-to-peak values of pressure fluctuations are suppressed by up to 39.90%, and this improvement in pump stability was also demonstrated by a proof experiment conducted in BIDR (He et al, 2015;Wang et al, 2021a). In summary, the guiding significance and engineering value of the rigid vorticity transport equation for vortical flow analysis and control are preliminarily presented.…”

“…The flow domains are discretized by using the high quality hexahedral grids, and the grids in the near wall region are carefully determined. Moreover, the GCI (grid convergence index) criterion recommended by ASME-FE (Celik et al, 2008;Oberkampf & Roy, 2010) is used for the convergence analyses, and the details of the URANS grids were given in the previous study of the authors (Wang et al, 2021a). The final meshing results are shown in Figure 9.…”

“…The intuitive mechanism of it is as follows. According to the previous studies of the authors (Wang et al, 2021a), the incompressible momentum equation of relative motions in a centrifugal pump impeller can be given by…”

“…As shown in Figure 13(b), the values of δp in the middle part of the S2 streamsurface are appropriately improved to make the maximum PRG move backwards. More details of the modified impeller can be found in the previous study of the authors (Wang et al, 2021a).…”