The hydraulic efficiency of impellers has been defined by Brown (MIXING XXII, 2010) as the ratio of the kinetic energy of the mean flow generated to the mechanical energy input by the impeller. This calculation assumes that the velocity of the fluid discharging through the impeller is uniform across the impeller’s swept area (i.e. the mean flow divided by the swept area). In reality the velocity profile across the impeller discharge is highly non-uniform and this should be taken into account when calculating the efficiency.
When the impeller starts rotating in the fluid there is a finite time when the power input is greater than the energy dissipation rate. During this time the power input approaches the dissipation and, once they are equal, the impeller simply maintains the kinetic energy in the system which was delivered during start up.
Lattice-Boltzmann large-eddy simulations are capable of modeling the time dependency of the impeller start up allowing prediction of the power input and energy dissipation during this time. The difference between these two quantities integrated with respect to time is the kinetic energy supplied and maintained once a steady-state has been achieved.
The total energy efficiency of the impellers can be compared using a dimensionless quantity which can be formed by dividing the kinetic energy by the impeller torque.