Mixing of inclined dense jets in stationary ambient

Abstract

This paper reports results of a comprehensive experimental investigation of inclined round dense jets in an otherwise stagnant fluid. The tracer concentration field is measured for six jet discharge angles ${\theta }_0=({15}^o,{30}^o,{38}^o,{45}^o,{52}^o,\mathrm{\&}{60}^o)$ and jet densimetric Froude number of $F_r$ = 10 – 40 using the planar laser-induced fluorescence (LIF) technique; selected jet velocity measurements are made using Particle Image Velocimetry (PIV). The detailed jet mixing characteristics and turbulence properties are presented. The direct velocity measurement reveals that the mixing is jet-like until the maximum rise. Empirical correlations for the maximum jet rise height, jet dilution at maximum rise, and impact dilution are presented. Both the time-mean concentration and intermittency show that the upper jet edge spreading is similar to a positively buoyant jet; at the lower edge the buoyant instability induces significant detrainment and mass outflux for ${\theta }_0>{15}^o$. The dimensionless maximum rise height $Z_{max}/(F_{r}D)$ is independent of source conditions for $F_r\ge 25$, and varies from 0.44 for ${\theta }_0={15}^o$ to 2.08 for ${\theta }_0={60}^o$. Dilution measurements at terminal rise show the difference in dilution is small for ${\theta }_0={38}^o–{60}^o$ and the asymptotic dilution constant is $S_i/F_r$ = 0.45. The impact dilution $S_i$ is also not sensitive to jet angle for ${\theta }_0={38}^o–{60}^o$ and can be expressed as $S_i/F_r$ = 1.06 for $F_r\ge 20$. The Lagrangian jet model VISJET is used to interpret the experimental results. A detailed derivation for a general formulation of the entrainment coefficient is presented. Despite the observed detrainment, the trajectory and dilution are reasonably predicted; the maximum jet rise is generally under-predicted by $10–15\mathrm{\%}$ and associated dilution by $30\mathrm{\%}$. However, the predicted variation of jet behavior with discharge angle is in good agreement with measurements. The experimental data is also compared with predictions of alternative models that employ an ad hoc entrainment hypothesis.