Non-Boussinesq turbulent buoyant jet resulting from hydrogen leakage in air

This paper is devoted to introduce a numerical investigation of a vertical axisymmetric non-Boussinesq buoyant jet resulting from hydrogen leakage in air as an example of injecting a low-density gas jet into high-density ambient. As the domain temperature is assumed to be constant and therefore the density of the mixture is a function of the concentration only, the binary gas mixture is assumed to be of a linear mixing type. Also, it is assumed that the rate of entrainment to be a function of the plume centerline velocity and the ratio of the mean plume and ambient densities. On the other hand, the local rate of entrainment may be considered to be consisted from two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. Firstly, the integral models of the mass, momentum and concentration fluxes are obtained and transformed to a set of ordinary differential equations using some non-dimensional transformations known as similarity transformations. The given ordinary differential system is integrated numerically and the mean centerline mass fraction, jet width and mean centerline velocity are obtained. In the second step, the mean axial velocity, mean concentration and mean density of the jet are obtained. Finally in the third step of this article, several quantities of interest, including the cross-stream velocity, Reynolds stress, velocity-concentration correlation (radial flux), turbulent eddy viscosity and turbulent eddy diffusivity, are obtained. In addition, the turbulent Schmidt number is estimated and the normalized jet-feed material density and the normalized momentum flux density are correlated.