Weighted proper orthogonal decomposition of the swirling flow exiting the hydraulic turbine runner

• We focus on application of Proper Orthogonal Decomposition to hydraulic turbines.
• Two flow quantities with vanishing integrals on the computational domain are found.
• POD is applied on these flow quantities instead on the velocity field directly.
• The property of vanishing integral is conserved for each individual mode.
• The leading modes are identified within reduced order models of the velocities.

In this paper we propose a framework for orthogonal decomposition of swirling flows applied to problems originating from turbomachines, where dynamics of the swirling flow in the draft cone is strongly influenced by the turbine discharge coefficient. A weighted proper orthogonal decomposition method (wPOD) is proposed for analyzing the evolution of the swirling flow exiting the hydraulic turbine runner as the turbine discharge is modified. The chief idea is that through orthogonal decomposition one can better identify the leading modes of the axial and circumferential velocity profiles perturbation with respect to a simple base flow. Moreover, it is expected that only one mode is actually responsible for the stability loss. The key innovation introduced in this paper resides in identification of two perturbation quantities having vanishing integrals on the computational domain. By applying the weighted POD on these perturbation quantities, the property of vanishing integral is conserved for each individual mode. As a result, the POD representation of the velocity field is achieved with a number of modes significantly lower compared with other classic techniques. The efficiency of the reduced order model developed in this paper is tested by comparing the computed solution with the experimentally measured profiles. In addition, a qualitative analysis of the reduced order model by its correlation coefficient and root mean squared error (RMSE) is performed.