Case Study of Impeller Profile Considering Additional Parameters

In the previous paper, the optimum meridian profile of impeller was obtained for various specific speed by means of five shape factors. In this paper, the optimum meridian profile of impeller is obtained by means of eight shape factors. The basic five shape factors are inlet relative flow angle β₁, turning angle Δβ, axial velocity ratio k_c = C_m2/C_m1 impeller diameter ratio k_d = D_1c/D_2c and outlet hub-tip ratio ν₂ (β₁ and Δβ are in mid span stream surface). The additional three parameters are three stream lines solidity (tip solidity σ_t, mid span solidity σ_c, and hub solidity σ_h). The blade length of impeller meridian profile is able to obtain by additional three parameters. The method of optimization is the calculation of hydraulic efficiency and suction specific speed in all combinations of eight shape parameters. The number of five shape factors are expressed by N_β1, N_Δβ, N_kc, N_kd, N_ν2. The number of calculations is expressed by N_β1 × N_Δβ × N_kc × N_kd × N_ν2. For example, N_β1 = N_Δβ = N_kc = N_kd = N_ν2 = 40, the number of calculations is about 100000000. The calculation time is about 2 hours. The best parameters are selected in 100000000 cases. In case of eight shape factors, the number of calculation is N_β1 × N_Δβ × N_kc × N_kd × N_ν2 × N_σt × N_σc × N_σh. N_β1 = N_Δβ = N_kc = N_kd = N_ν2 = N_σt = N_σc = N_σh = 10, the number of calculation is 100000000. In this case, the calculation time of eight shape factors is as same as that of five shape factors. By means of this method, the more detailed optimum mixed flow impeller meridian shape is obtained. In case study, the best 1000 optimum meridian profiles and the best design parameter are selected for few kinds of specific speed using eight dimensional optimum method. In the previous paper, the mixed flow angle on tip meridian stream line isn’t able to be decided by this optimization using diffusion factor. But, in this paper, the mixed flow angle is able to be decided by the number of blade and optimum solidity. As the best solidity of three stream lines is obtained, the axial coordinates of impeller inlet and outlet are obtained. The more detailed optimum mixed flow impeller meridian shape is drawn.