Surface waves in transitional liquid film flow on a rotating disk

Liquid film flow over a rotating disk is applied in many engineering fields by virtue of its rapid spreading and excellent heat transfer performance. Large-scale surface waves in the film flow are critical to determine heat transfer rate and spreading pattern in most of practical flow conditions. In this work, the film flow formed by impinging a circular liquid jet on a rotating disk is numerically investigated. The modeling of the film flow using the integral boundary layer (IBL) approach has been limited to axisymmetric waves initiated in downstream where centrifugal force is dominant. However, according to experimental visualization, while axisymmetric waves are formed only in low flow rate conditions, concentric waves in upstream followed by solitary waves in downstream are observed in a more practical range of the flow rate. We suggest an extended IBL model for the transitional film flow covering both turbulent and laminar regimes, which is coupled with the shallow-water turbulence model. The formation of concentric waves and their transition to solitary waves are successfully captured by the proposed transitional film flow model. The effects of time-averaged velocity and upstream turbulent structures on downstream solitary waves are then analyzed.