The Optimum Meridian Profile of Various Annular Surface Roughness and Impeller Blade Number

In the previous study, the optimum meridian profile of impeller and guidevane in two kinds of typical specific speed (very high and very low). The two kinds of optimum meridian profile were obtained by one initial meridian profile obtained by no restriction optimum process. As a result, the design parameters of almost all kinds of specific speed were obtained in above optimum process. In no restriction optimum process, the all of design parameters and specification are variable optimum parameters. In the optimum process, loss calculation consists of blade-to-blade diffusion loss and axial-symmetrical annular wall friction loss. In the calculation of axial-symmetrical annular wall friction loss, the wall friction factor is the function of Reynolds number because tip and hub annular walls were smooth surfaces. One of important merit of this optimum method is to obtain the best flow condition in inlet and outlet of impeller and guidevane without detailed impeller and guidevane shape design. This optimum method is executed on the assumption that the impeller and guidevane was designed to satisfy inlet and outlet flow conditions from hub to tip. In the present case study, the influence of the annular rough surface friction loss was studied in above two kinds of specific speed. In large Reynolds number, the relative roughness influences the wall friction factor but Reynolds number does not influence the wall friction factor. It is assumed that the annular surface is rough and Reynolds number is sufficiently high. Then, the annular wall friction factor is constant value decided by surface roughness. In the result, the optimum meridian profile was obtained in case of the rough annular surfaces. In the next case study, the impeller blade number of the previous optimum meridian profile is small. So, the restriction of impeller blade number was calculated to obtain the large blade number impeller. When one design parameter was changed gradually as restriction for goal value, the other design parameters were variable optimum design parameters or constant design parameters. In case study, the specific speed N_S, mixed flow angle of impeller inlet N₁ or impeller blade number N_imp were three design parameters as restriction. It is important that the only one parameter of three design parameters was changed gradually as restriction at the same time. In the optimum process, the restriction parameter was changed gradually as restriction. In the result, the optimum meridian profile of the large impeller blade number was obtained. It was difficult to obtain the initial design parameters of traditional impeller and guidevane using in this method up to now. In the future, the traditional impeller and guidevane will be able to modify by means of the design parameters restriction of this optimum method to agree with the primary design parameters of traditional impeller and guidevane.