An experimental study of impulsively started turbulent axisymmetric jets

Abstract.

An impulsively started turbulent jet injected into quiescent surroundings with a constant inlet velocity has been studied experimentally. Results show that the jet length increases linearly with the square-root of time, over a wide range of Reynolds number calculated with respect to the jet diameter. The celerity factor, x_f/t U, has been found to be nearly constant at 2.47 throughout with a 5% variance. Here, x_f is the jet length, t is the time and U is the jet exit velocity. These results compare favourably with earlier results reported at lower Reynolds numbers. Finally, we present a simple model based on the integral energy balance of the turbulent boundary layer equation for an impulsively started turbulent axisymmetric jet. The model predicts a jet length that scales as, $(x_f/d) = \sqrt{(9B/10) (t U /d) }$ where d is the nozzle diameter and B(≈6.0) is the velocity-decay constant. This gives a celerity factor, $\alpha\equiv \sqrt{9B/10}=2.32$ in close agreement with the experiments.