Abstract
The flow in a decelerating turbulent round jet is investigated using direct numerical simulation. The simulations are initialised with a flow field from a statistically stationary turbulent jet. Upon stopping the inflow, a deceleration wave passes through the jet, behind which the velocity field evolves towards a new statistically unsteady self-similar state. Assumption of unsteady self-similar behaviour leads to analytical relations concerning the evolution of the centreline mean axial velocity and the shapes of the radial profiles of the velocity statistics. Consistency between these predictions and the simulation data supports the use of the assumption of self-similarity. The mean radial velocity is predicted to reverse in direction near to the jet centreline as the deceleration wave passes, contributing to an approximately threefold increase in the normalised mass entrainment rate. The shape of the mean axial velocity profile undergoes a relatively small change across the deceleration transient, and this observation provides direct evidence in support of previous models that have assumed that the mean axial velocity profile, and in some cases also the jet spreading angle, remain approximately constant within unsteady jets.
Highlights
Mixing processes in statistically unsteady jets are relevant to a wide range of environmental, biological and technical systems
Validation of the various self-similarity-based statistically unsteady turbulent jet and plume models in Scase, Caulfield & Dalziel (2008), Musculus (2009), Scase, Aspden & Caulfield (2009) and Craske & van Reeuwijk (2015b) indicates that assumption of self-similar mean axial velocity profiles provides a useful basis for development of models in statistically unsteady jets; the underlying assumption that self-similarity persists as the jet decelerates has not been examined directly
Self-similarity leads to analytical relations concerning the evolution of the centreline mean axial velocity and the shapes of the radial profiles of the velocity statistics
Summary
Mixing processes in statistically unsteady jets are relevant to a wide range of environmental, biological and technical systems. Validation of the various self-similarity-based statistically unsteady turbulent jet and plume models in Scase, Caulfield & Dalziel (2008), Musculus (2009), Scase, Aspden & Caulfield (2009) and Craske & van Reeuwijk (2015b) indicates that assumption of self-similar mean axial velocity profiles provides a useful basis for development of models in statistically unsteady jets; the underlying assumption that self-similarity persists as the jet decelerates has not been examined directly. The measurements by Borée et al (1996) indicate that the radial profiles of phase-averaged axial velocity and other velocity moments deviate from the self-similar profiles of a statistically steady jet as the jet decelerates, and that the profiles vary axially through the confined deceleration region (Borée et al 1996, 1997). We investigate self-similarity in decelerating jets through theoretical analysis and statistical analysis of a stopping jet using new DNS data where the inflow stops abruptly
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