Numerical Simulation Of An Over-Expanded Supersonic Nozzle Flow

Flaring in oil and gas production is the controlled burning of unwanted exhaust gases to enhance safety. Obtaining complete combustion and thus eliminating or reducing smoke is critical to meet increasingly strict environmental regulations. To improve flare combustion, gas flares are equipped with air nozzles that introduce extra oxygen and improve mixing in the combustion zone. These nozzles are operated in the subsonic, sonic, or supersonic regimes. In this paper we are concerned with turbulence modeling of the jet flow exiting from a particular convergent-divergent nozzle used in flare systems. The Realizable 𝑘−𝜀 and SST 𝑘−𝜔 models are used to study the compressible flow within that specific nozzle, which has an exit diameter of 3.38 mm and has convergent and divergent sections that are connected via a throat section with a finite length and constant diameter. The velocity profiles and turbulent kinetic energy predicted by both turbulence models, in the vicinity of the nozzle outlet and along the symmetry axis of the nozzle, are compared for nozzle pressure ratios in the range 1.18≤NPR ≤1.78 . It is shown that for 𝑀𝑎≤1, both turbulence models predict nearly identical flow evolution along the nozzle. When the flow becomes supersonic, the shock surface, and consequently nozzle outlet velocity profiles, predicted by the SST 𝑘−𝜔 model deviates slightly from the other model. The differences, however, become negligible a couple of diameters downstream of the nozzle outlet. Computed entrainment rate coefficients vary slightly when changing the turbulence model, and this difference remains insignificant with increasing downstream distance.