Three-Dimensional Simulation of Highly Unsteady and Isothermal Flow in Centrifugal Pumps for the Local Loss Analysis Including a Wall Function for Entropy Production

A local loss analysis (LLA) based on entropy production is presented for the numerical three-dimensional (3D) simulation of isothermal centrifugal pump flow. A finite volume method and a statistical turbulence model are employed. Wall functions for direct and turbulent entropy production in isothermal flow are derived, implemented in a node-centered finite volume scheme as a postprocessing procedure, and validated on an attached channel flow as well as on separated flow in an asymmetric diffuser. The integrity of the entropy wall function is demonstrated by a loss balance for a wide range of boundary layer resolution in terms of nondimensional wall distance y + approximate to 1 to approximate to 200. Remaining differences to the total pressure loss are traced back to the particular turbulent wall function for the flow solution within the finite volume solver and vanish toward a wall resolution of the viscous sublayer, i.e., y + approximate to 1. LLA together with the new entropy wall function is applied to highly unsteady isothermal flow in a single-blade pump as well as to part-load operation of a conventional multiblade pump which reveals distinctive flow structures that are associated with entropy production. By these examples, it is demonstrated how efficiency characteristics of centrifugal pumps can be attributed to local loss production in particular flow regions.