Characterization of Showerhead Performance At Low Pressure
The overall objective of this work is to characterize the flow to rough showerheads by deriving pressure drop versus velocity correlations to at can be then used in reactor scale simulations where the showerhead is approximated as a porous medium. At relatively low Reynolds numbers (less than 1-10 based on the hole length scale) and in the absence of slip flow, Darcy's Law, grad P = mu U/k, can be used to express the relation between the pressure drop and velocity where @mu@ is the fluid viscosity and it is the permeability that can be theoretically predicted as k= e R^2 /8, where e is the porosity. However, at sufficiently small hole diameters and decreased pressures (less than 5 Torr), the Knudsen number based on showerhead tube radius increases, and the flow may be in a transition regime. Different expressions have been proposed to account for this effect in the permeability by expressing k as a function of either pressure or Knudsen number. But at even higher Knudsen numbers, the pressure drop - velocity dependence is non-linear, and Darcy's Law no longer holds such that a permeability cannot be defined. The direct simulation Monte Carlo method is used along side conventional CFD techniques to determine the extent to which the CFD technique is appropriate and helps to derive correlations for the more rarefied cases of interest in these showerhead flows.