Supplementary Number 1, Supplementary Number 2, Supplementary Number 3, Supplementary Number 4, Supplementary Number 5, Supplementary Number 6

Fig. S1. Research study of a submersible drainage pump, Fig. S2. Meshing quality of the submersible pump, Fig. S3. Boundary conditions setting for the computational analysis, Fig. S4. First step optimization plan for casing shape change models (a) original model (b) Model 1 (c) Model 2, Fig. S5. First step performance comparison of casing shape change model (a) Head vs. flow rate and (b) Effi-ciency vs. flow rate, S6. Details of mathematical models: 1. Continuous phase, 2. Discrete phase, 3. Turbulence model, 4. Erosion model, 5. Cavitation model.