An analysis on Pigford model for a liquid film developing over a rotating disk

The present study aims to analyze and improve the empirical parameters of the 1-D Pigford model to predict the liquid film flows developing over a rotating disk. The empirical parameters reflect the physical effects such as the near-wall velocity profiles, which may affect the predicted results significantly. To evaluate the results of the Pigford model, a set of highly resolved 3-D simulations is performed by changing a few operational parameters and material properties. A revised inner boundary condition of the Pigford model for the impinging jet case is derived considering the gravity effect between the jet nozzle and disk, which improves the prediction accuracy. From a similarity in the viscous terms between the Pigford model and Navier-Stokes equation, two approximate relationships for the empirical parameters are derived. Using these, a few models for the empirical parameters are developed, which can improve the prediction accuracy significantly compared to the constant empirical parameters used in the previous studies. Also, a few existing assumptions on the empirical parameters are analyzed using the relationships and simulation data, which presents the characteristics of the empirical parameters that can be useful for a future modeling effort.