# Modeling and Tools

Major issues regarding the prediction of TDG are related to the gas distribution and the effect of spillway surface jets on the flow field. The most important source of TDG is the gas transferred from the bubbles to the liquid; therefore a proper model for TDG prediction must account for the two-phase flow in the stilling basin and the mass transfer between bubbles and water.

**TDG-MP3** is a multidimensional anisotropic multiphase flow model, which includes:

- A VOF model to predict the spillway flow regime and free-surface characteristics near the dam;
- A mixture model with space-time averaged quantities accounting for the effect of bubbles on the flow field;
- A two-phase transport equation to compute the TDG concentration. TDG production is due to bubble/liquid mass transfer, function of the gas volume fraction, and bubble size.
- Two-phase transport equations to compute bubble size, which can change due to mass transfer and pressure;
- An algebraic equation to calculate bubble velocities considering buoyancy, pressure, drag, and turbulent dispersion forces; and
- An anisotropic turbulence model that accounts for the attenuation of the normal fluctuations at the free surface and suppression and production of turbulence by the bubbles to capture the turbulence field and water entrainment.

The model is implemented into the IIHR code CFDShip-Iowa and into the commercial CFD code FLUENT using User Defined Functions.