Boussinesq and non-Boussinesq turbulent plumes in a corner with applications to natural ventilation

A previous formulation of plume merger [Rooney, J. Fluid Mech. 796, 712 (2016)] is generalized to model both Boussinesq and non-Boussinesq plume rise in a corner of arbitrary angle 2 pi/n where n >= 1. The Boussinesq plume theory predicts the correct near- and far-field similarity solutions when n is noninteger. Moreover, an alternate entrainment assumption is proposed whereby the rate of entrainment per unit height correlates directly to the plume perimeter. Model predictions made using this alternative entrainment assumption agree well with a previous prediction for the plume volume flux when n = 2. For non-Boussinesq plumes, the theory also approaches the correct near- and far-field similarity limits. When the source area is compact, and regardless of the corner angle, the non-Boussinesq height, i.e., height over which non-Boussinesq effects are important, is small compared to the contact height between the plume and the corner. When the source area is relatively large, the non-Boussinesq height can be comparable to the contact height; enhanced non-Boussinesq effects are observed for smaller corner angles. Our Boussinesq theory is adapted to the natural ventilation model developed by Linden et al. [J. Fluid Mech. 212, 309 (1990)] and agrees well with previous experimental and theoretical predictions for the steady-state depth of the layer of discharged plume fluid that accumulates along the ceiling of the (ventilated) interior space. For non-Boussinesq plumes, the counterpart theory compares satisfactorily with previously measured results of fire plume mass flux.