A multidimensional two-phase flow model for the total dissolved gas downstream of spillways

Abstract

Elevated levels of dissolved gas in the spillway stilling basin, which are responsible for gas bubble disease in fish, constitute an important negative environmental effect of dams. Bubbles, entrained when a plunging jet impacts the tailwater pool, plunge beneath the surface and transfer mass to the liquid, causing an increase in the total dissolved gas (TDG) concentration. Most of the numerical studies onTDG downstream of spillways found in the literature are based on experimental correlations for the gas volume fraction.Abetter approach involves the use of a two-phase flowmodel. In this paper, a two-fluid model is used to calculate the gas volume fraction and velocity of the bubbles. A polydisperse model is used in which a Boltzmann transport equation predicts the bubble size distribution, to account for the different bubble sizes found in the flow downstream of spillways. The bubble mass is discretized considering groups of bubbles of variable mass, with the mass of the bubbles changing due to bubble/liquid mass transfer and pressure. A two-phase transport equation for the TDG is presented, whose source is the bubble/liquid mass transfer, which is a function of the gas volume fraction and bubble size distribution. Two-dimensional numerical results of TDG, gas volume fraction, bubble number density, and velocities are presented and discussed. The predictions of TDG downstream of a spillway are compared against field data in the stilling basin ofWanapum Dam, on the Columbia River.