Horizontal H2–air turbulent buoyant jet resulting from hydrogen leakage

The current article is devoted to introducing mathematical and physical analyses with numerical investigation of a buoyant jet resulting from hydrogen leakage in air from a horizontal round source. H2–air jet is an example of the non-Boussinesq buoyant jet in which a low-density gas jet is injected/leak into a high-density ambient. 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 and the rate of entrainment is assumed 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 consists of two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. The top-hat profile assumption is used to obtain the mean centerline velocity, width, density and concentration of the H2–air horizontal jet in addition to kinematic relations which govern the jet trajectories. A set of ordinary differential equations is obtained and solved numerically using Runge-Kutta method. In the second step, the mean axial velocity, mean concentration and mean density of the jet are obtained based on Gaussian model. Finally, 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 by solving the governing partial differential equations. Additionally, the turbulent Schmidt number is estimated and the normalized jet-feed material density and the normalized momentum flux density are correlated.