Open Channel Helium Flow during Rupture Event

Open channel fluid flow principles are applied to understand how helium might behave in the event of a release or spill in a long tunnel enclosure. An example would be helium flowing along the Tevatron accelerator tunnel as a result of some rupture of a header system. Buoyant forces would drive the helium along the ceiling until a vent to atmosphere is reached. An analogy is water flowing up to and over the crest of a dam. The momentum and continuity equations will be used to calculate the depth of helium from the ceiling as a function of length down the tunnel, for rectangular and semicircular cross sections. Testing was conducted on a scale model of the Tevatron tunnel, which generally indicated agreement between the simplified predictions and observations. VARIABLE DEFINITIONS R radius of channel m h thickness of helium from the ceiling m Fr Froude Number = V/ √(gh) -Re Reynolds number = ρVRh/μ -w width of helium for semicircle m b width of helium for rectangle m Pa wetted perimeter of helium to air surface m Pw wetted perimeter of helium to wall surface m τa air interface viscous shear stress N τw wall interface viscous shear stress N x distance along tunnel floor from the leak m Q volumetric flow rate m/s A cross sectional area m g acceleration due to gravity m/s ρ density kg/m θ the angle, starting at the origin of the tunnel radius, that defines the interface of the tunnel wall and the helium rad Rh hydraulic radius = 4A/Pw m μ viscosity of fluid Pa-s c f,L friction coefficient over length -FERMILAB-PUB-02-424-AD