Influence of source conditions and heat losses on the upwind back-layering flow in a longitudinally ventilated tunnel

We study experimentally the dynamics of a back-layering flow developing below the ceiling of a longitudinally ventilated tunnel, and induced by the presence of a steady source of buoyancy at the tunnel floor. Our aim is to identify the dependence of the longitudinal extent of the back-layering flow upwind of the source (and therefore against the tunnel ventilation velocity) as a function of the parameters characterising the buoyant release at the source and of those characterising the thermal losses at the tunnel ceiling. To this end purpose we performed experiments in two different reduced scale models, using helium and hot air as buoyant fluids. Based on the experimental results, we develop a semi-empirical model for the prediction of the (non-dimensional) extent of the back-layering flow. This can be expressed as a function of three non-dimensional parameters. The first one is the tunnel Richardson number Ri, expressing the ratio between the buoyancy effects induced by the source and the inertia effects of the tunnel ventilation. The second is its critical value Ric, obtained by imposing the so-called critical ventilation velocity, preventing the formation of a back-layer flow upstream of the source. The third parameter, referred to as λT∗, characterises the heat losses at the tunnel walls. The variability of the conditions imposed at the source, namely the momentum flux related to the injection of buoyant fluid, have negligible influence on the critical condition and therefore on the extent of the back-layering flow (which depends therefore on the buoyancy flux at the source, only). In contrast, the heat losses play instead a major role, which results in a relevant reduction of the back-layering flow that can be five times shorter than in the adiabatic case.