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ABSTRACT
A study of the tangential velocity field in a strong free-surface vortex is presented. Experiments were conducted on an open channel scroll type vortex chamber by investigating the tangential velocity for three approach flow conditions. The tangential velocity and circulation fields were ascertained at various sub-surface depths using particle tracking techniques. The results revealed that the experimental tangential velocity distribution is dependent on the initial circulation but is largely independent of the vertical axis. The theoretical tangential velocity profile was found to diverge from the experimental data in the near-field close to the core. It was concluded that the tangential velocity field in this region is strongly dependent on the axial flow conditions. Consequently, an alternative tangential velocity model was developed which models the near-field axial flow effects using the inverse circulation number and an empirical coefficient. Application of a nonlinear least squares multiple regression analysis identified values for the empirical coefficient to obtain a good solution.
Notation
| = | circulation (m2 s−1) | |
| = | bulk circulation (m2 s−1) | |
| = | local circulation (m2 s−1) | |
| = | discharge (m3 s−1) | |
| = | tangential velocity (m s−1) | |
| = | axial velocity (m s−1) | |
| = | axial velocity at the orifice (m s−1) | |
| = | radial velocity (m s−1) | |
| = | pressure (N m−2) | |
| d | = | orifice diameter (m) |
| dp | = | particle diameter (m) |
| ds | = | drop shaft width (m) |
| h | = | approach flow depth (m) |
| hcr | = | critical depth (m) |
| r | = | radius (m) |
| rin | = | inlet radius (m) |
| B | = | inlet channel width (m) |
| b | = | =inlet width (m) |
| Deff | = | effective scroll diameter (m) |
| ac | = | air-core diameter (m) |
| = | Subsurface depth (m) | |
| = | density (kg m−3) | |
| = | angle of conical coordinates (°) | |
| H | = | chamber height (m) |
| rl | = | radius on left side (m) |
| rr | = | radius on right side (m) |
| xp | = | particle streak length (m) |
| = | coordinates (–) | |
| t | = | time (s) |
| Ld | = | dropshaft length (m) |
| = | surface tension coefficient (N m−1) | |
| g | = | gravitational coefficient (m s−2) |
| = | kinematic viscosity (m2 s−1) | |
| = | effective viscosity (kg m−1 s−1) | |
| = | eddy viscosity (m2 s−1) | |
| = | approach flow factor (–) | |
| = | dimensionless exponent (–) | |
| = | image magnification (–) | |
| Fi | = | inlet Froude number (–) |
| F | = | outlet Froude number (–) |
| Rr | = | radial Reynolds number (–) |
| = | correction factor (–) | |
| We | = | Weber number (–) |
| NΓ | = | circulation number (–) |
| NQ | = | discharge number (–) |