Quasi-similarity model of synthetic jets

Actuators generating synthetic jets (and related hybrid-synthetic jets) are currently of increasing importance and it is useful to have for their design a simple model evaluating spatial distributions of various quantities of interest in the generated jet. In this paper, such a model – a set o simple ordinary differential equations – is derived and shown to describe synthetic jets remarkably well. It uses the Tollmien hypothesis of the length scale of the vortices proportional to the local jet diameter. The experiments show that for the best fit the proportionality multiplier should vary with the streamwise distance X1* from the nozzle. This variation leads to the new concept of quasi-similarity. The model was tested by application to synthetic jet data obtained at large distances X1* where an interesting change occurs in the character of the dependence.