Entrainment rate predictions of axis-symmetric non-swirling jets using free-jet-theory, Reynolds-averaged Navier-Stokes modelling and large-eddy-simulations resolved up to Kolmogorov scale

Abstract

Jet entrainment - relevant to mixers, sprays and combustion technologies - has been the subject of this work. We limit our considerations to air jets issued from convergent nozzles of diameter smaller than 25.4 mm, the nozzle exit Reynolds number in the range 30,000 to 100,000 and Mach numbers not exceeding 0.4. The emphasis is on jet self-similarity region (60 < x/d₀ < 210) and the key question is with which accuracy can Computational Fluid Dynamics (RANS and LES) and free-jet theory predict jet entrainment. Seven jets have been considered.

The realizable k-є model has outperformed the other models and provides the entrainment predictions within ±6 % margin from the measured data. The standard k-є and the Shear-Stress Transport (SST) k-ω models deliver entrainment figures which are larger than the measured data by 22 % – 24 % whilst predictions of either the Reynolds Stress Model (RSM) or Re-Normalization Group (RNG) k-є models can be off (too large) by as much as 34 % and 40 %, respectively. Such a clarity in classification of turbulence models has been obtained after minimization of numerical related errors to a degree which was not achievable in the past. The Panchapakesan&Lumly's jet has been computed using the Large Eddy Simulations with the filter size of the order of Kolmogorov scale throughout the jet e.g. at the inlet, potential core and the far field. Excellent predictions of the jet spread rate, velocity profiles and the entrainment have been obtained at the expense of huge computational resources.

The well-known engineering correlation ${\dot{m}}_e/\dot{m_0}=0.32\left(x/d_0\right)$ provides entrainment figures that are by 10 % or less larger than the measured values.