Numerical simulation of freezing shear driven rivulets using an enthalpy method formulation

A numerical simulation of freezing shear driven rivulets is presented herein. The physics of the freezing process is captured in the simulation through application of the “enthalpy method”; a formulation well suited for the Stefan class of problems. The associated system of fully implicit finite difference equations was solved using the Gauss-Seidel iterative technique. The enthalpy method formulation is first applied to the case of a “stationary” freezing rivulet, but with a convective boundary at the free surface. The “stationary” simulation is utilized as a subset of the more complex “traveling”, or shear driven, simulation. The freezing process of shear driven rivulets was divided into three distinct modes based upon macro-scale observations of freezing rivulet flow on a NACA 0012 airfoil. From such observations, a non-dimensional empirical parameter was developed which establishes the bulk rivulet halt criterion for a freezing rivulet during runback.