A Multidimensional Anisotropic Two-Phase Flow Model to Predict Total Dissolved Gas in Wanapum Dam

A two phase model based on mechanistic principles capable of predicting water entrainment, gas volume fraction, bubble size and total dissolved gas (TDG) concentration in hydropower installations is presented. The model uses a Reynolds stress model accounting for the attenuation of the normal fluctuations at the free surface to capture the anisotropic turbulence structure and water entrainment observed in the spillway surface jets. A modified bubble-induced turbulence term is extended for the Reynolds stress components to account for suppression and production of turbulence by the bubbles. A bubble number density transport equation is used to predict the bubble size, which can change due to mass transfer and pressure. The TDG is calculated with a two-phase transport equation in which the source is the bubble/liquid mass transfer, function of the gas volume fraction and bubble size. Quantitative agreement between predictions and field data for the TDG and velocities in the stilling basin of Wanapum Dam is obtained. Numerical results of the hydrodynamics and TDG for two different operational conditions are presented discussed.