Akademik Veri Yönetim Sistemi
JOURNAL OF THE FACULTY OF ENGINEERING AND ARCHITECTURE OF GAZI UNIVERSITY, cilt.38, sa.2, ss.1217-1229, 2023 (SCI-Expanded)
In this study, a mathematical model is developed for the determination of the runner moment of a turbine with radial flow from in to out. In this model, the profile of blades is defined mathematically which is used in the formulation of the local velocity and acceleration of the moving particles between blades. The relations obtained for the local velocity enables the establishment of the inlet and outlet velocity triangles and determination of the runner moment via Euler turbine theory. Differently from this, via using the relation obtained for the local acceleration of the fluid particles moving between blades, the inertia forces exerting on annular volume elements positioned on the runner, and the moments generated by these inertia forces are defined. Then a relation is obtained for the total moment of runner. The relation obtained for the total moment enables the calculation of moment of turbine at steady and unsteady working conditions. It is seen that the moment formulae obtained from the current analysis for steady running of turbines is equivalent to the moment formulae given by Euler. By using the developed moment formulae, a Francis turbine runner is designed for a water source with a flow rate of around 10 m3/s and a head in the range of 100-200 m. By assuming the external and internal diameters of runner as 2.5 m and 2 m, the axial dimension of the runner, the inlet and exit angles of blades are determined as 8 cm, 115o and 20o respectively. When the designed runner is working in the range of 100-200 m of head, the optimum flow rate becomes around 8 m3/s and provides 9301 kW maximum power at 45 rad/s runner speed.