Buoyancy Driven Effects in Formation of Mixing Zones

Abstract

The release of a mass of hydrogen fuel (gas) into the ambient atmosphere results in the transient formation of flammable mixture zones that represent potential fire, explosion and toxic hazards. The formation of mixing zones of air and hydrogen for this simple geometry follows the classical Rayleigh Taylor (R-T) instability, which is induced when a heavy fluid is placed over a light fluid in a gravitational field. Buoyancy driven mixing in such flow configurations is studied by using the Boussinesq approximation and considering the flow to be laminar. However, this approximation is valid only at low Atwood numbers (non-dimensional density differences). As Atwood number increases (>0.1, i.e. large density differences) the Boussinesq approximation is no longer valid and a distinct bubble and spike geometry of Rayleigh-Taylor buoyant plumes is formed. Aside from asymmetry in the flow the Atwood number also affects key parameters such as the growth constants and molecular mix. The effect of initial conditions on the growth rate of turbulent Rayleigh-Taylor (RT) mixing has been studied using carefully formulated numerical simulations. A monotone integrated large-eddy simulation (MILES) using a finite-volume technique was employed to solve the three-dimensional incompressible Euler equations with numerical dissipation for air and hydrogen mixing at Atwood number 0.875. The study also provides preliminary guidelines for reducing the fire and explosion hazards in enclosures where such situations are present.