Unsteady load on an oscillating Kaplan turbine runner

A Kaplan turbine runner oscillating in turbine waterways is subjected to a varying hydrodynamic load. Numerical simulation of the related unsteady flow is time-consuming and research is very limited. In this study, a simplified method based on unsteady airfoil theory is presented for evaluation of the unsteady load for vibration analyses of the turbine shaft line. The runner is assumed to oscillate as a rigid body in spin and axial heave, and the reaction force is resolved into added masses and dampings. The method is applied on three Kaplan runners at nominal operating conditions. Estimates for added masses and dampings are considered to be of a magnitude significant for shaft line vibration. Moderate variation in the added masses and minor variation in the added dampings is found in the frequency range of interest. Reference results for added masses are derived by solving the boundary value problem for small motions of inviscid fluid using the finite element method. Good correspondence is found in the added mass estimates of the two methods. The unsteady airfoil method is considered accurate enough for design purposes. Experimental results are needed for validation of unsteady load analyses.