New insight into frost growth under turbulent flow conditions using direct numerical simulations*

We developed a new model to predict frost growth over a flat plate maintained at sub-freezing temperatures and subjected to a relatively hot and moist turbulent air flow. The model consists of a dynamically coupled air-frost system. The air phase is resolved using direct numerical simulations, and the frost phase is modeled from first principles using the conservation equations of mass and energy. The two phases are coupled using either the immersed boundary method or by deforming the bottom boundary and using a body-fitted grid. Due to the vastly different time scales between the fast turbulent flow and the slow frost phase, a slow-time acceleration technique is implemented to make the simulations feasible by accelerating the frost growth. The model is validated against laboratory experiments and then used to predict frost growth under a variety of free-stream and plate conditions. We observe that the Nusselt and Sherwood numbers can be properly scaled so as to become primarily dependent only on the Reynolds, Prandtl, and Schmidt numbers. A series of simulations covering a range of shear Reynolds numbers between 100 and 2000 are then used to extract the Nusselt and Sherwood number dependence on Reynolds number after the frost reaches a finite thickness.