Numerical Modeling and Analysis of Entrainment in Turbulent Jets After the End of Injection

Previous velocity and scalar measurements in both single-phase jets and two-phase diesel fuel sprays indicate that after the flow at the nozzle decelerates, ambient-gas entrainment increases compared to a steady jet. Previous studies using simplified analytical models and computational fluid dynamics (CFD) simulations using a one-dimensional (1D) inviscid, incompressible momentum equation have predicted that an “entrainment wave” propagates downstream along the jet axis during and after the deceleration, increasing entrainment by up to a factor of 3. In this study, entrainment is analyzed using the full compressible, unsteady Navier–Stokes momentum equations in axisymmetric two-dimensional (2D) CFD simulations of single-pulsed transient round gas jets. The 2D simulations confirm the existence of the entrainment wave, although the region of increased entrainment is distributed over a wider axial region of the jet than predicted by the simplified 1D model, so that the peak entrainment rate increases by only 50% rather than by a factor of 3. In the long time limit, both models show that the rate of mixing relative to the local injected fluid concentration increases significantly, approaching a factor of 3 or more increase in the wake of the entrainment wave (relative to a steady jet). Analysis of the terms in the momentum equation shows that the entrainment wave in the full 2D CFD predictions occurs in two phases. The entrainment first increases slightly due to a radial pressure gradient induced by a relatively fast acoustic wave, which the simple 1D model does not account for. The acoustic wave is followed by a slower momentum wave of decreased axial velocity initiated at the nozzle, which is convected downstream at the local flow velocities. The largest increase in entrainment accompanies the momentum wave, which is captured by the 1D momentum-equation model.