Unsteady thin film flow on spinning disks at large Ekman numbers using an integral boundary layer method

Spinning disk devices are commonly used in a wide variety of industrial applications. The objective of the present work is to analyze computationally the hydrodynamic and thermal characteristics of thin film flow on rotating disks, which is radially driven by the centrifugal forces. The problem is numerically solved in the boundary layer type limit of thin film approximation using an integral Kármán-Pohlhausen technique in order to avoid the intrinsically high computational costs associated with sufficiently resolved direct numerical simulations. The results obtained from this approximation are compared against experimental data as well as against numerical predictions from an axisymmetric CFD analysis using the Volume-of-Fluid method, where a very good overall agreement is observed. The obtained results also consist that the waviness of the flow occuring at large local Ekman numbers effectively leads to a reduced averaged film height as compared to a corresponding steady-state smooth film solution. At large Ekman numbers the waviness further leads to an increased/decreased liquid film temperature under heating/cooling wall heat flux conditions. The importance of this effect is illustrated by introducing a simplified model for surface etching valid in the limit of reaction controlled chemistry. The predicted etching abrasion is compared against experimental results showing a markedly improved agreement in comparison to a steady-state smooth film solution.