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ABSTRACT
A numerical model, based on the open source code OpenFOAM, was developed to predict jet regimes and total dissolved gas downstream of spillways. The model utilizes the volume of fluid method to track the interface between air and water. A detached eddy simulation model is used for turbulence closure. Transport and dissolution of bubbles are predicted using an Eulerian approach. A bubble number density equation was implemented to predict bubble size changes caused by dissolution and compression. Total dissolved gas was computed using a transport equation that includes the mass transfer between bubbles and water. The model simultaneously captured spillway jet regimes and distribution of total dissolved gas in a spillway sectional model of McNary Dam. Model parameters, gas volume fraction and bubble size at the entrainment region, were calibrated to match total dissolved gas measured in the field under different dam operations.
Supplemental data
Supplemental data for this article can be accessed doi:10.1080/00221686.2018.1428231
Notation
| C | = | TDG concentration (–) |
| Db | = | bubble diameter (m) |
| g | = | gravitational field (m s−2) |
| kh | = | Henry’s constant (N m−2) |
| kl | = | mass transfer coefficient due to turbulence (–) |
| M | = | average molar mass of air (g mol−1) |
| N | = | bubble number density (–) |
| p | = | pressure (Pa) |
| Q | = | flowrate at the gate (m3 s−1) |
| R | = | universal gas constant (J mol−1 k−1) |
| = | bubble Reynolds number (–) | |
| = | Schmidt number (–) | |
| t | = | time (s) |
| T | = | temperature (k) |
| U | = | liquid velocity vector (m s−1) |
| Ub | = | bubble velocity vector (m s−1) |
| Ur | = | relative velocity vector of the bubble with respect to the liquid phase (m s−1) |
| α | = | gas volume fraction of bubbles (–) |
| γ | = | liquid volume fraction for the interface water/air (–) |
| µl | = | liquid dynamic viscosity (kg m−1 s−1) |
| ν | = | liquid kinematic molecular viscosity (m2 s−1) |
| νt | = | liquid kinematic turbulent viscosity (m2 s−1) |
| ρl | = | liquid density (kg m−3) |
| ρb | = | bubble density (kg m−3) |
| σ | = | interfacial tension (N m−1) |