Submerged jet's profile-specific heat transfer: Stagnation zone and beyond

• Analysis of a new free-surface jet regime, in which centerline velocity remains constant over long distances, is explained and generalized for all issuing profiles. • The deceleration during wall-approach is successfully captured over a wide range of conditions, as an interpolation between far- and near-wall analytical solutions. • Flow aspects, such as the boundary layer thickness are quite well predicted in the stagnation zone and a foundation is laid for more detailed radial distributions. • An explicit heat transfer prediction within the stagnation zone is provided, which is shown to be dependent only on arrival jet profile for a multitude of conditions: horizontal jets, vertical jets with gravity, high surface tension, highly viscous flows, etc. A general analytical description for the heat transfer distribution (HTD) under an impinging submerged jet is derived, from the jet velocity profile arriving at the wall. First, the cause-and-effect chain is broken down: i) the streamline-bending projection of the arriving profile's dynamic pressure gives the wall pressure distribution; ii) the pressure gradient drives the radial acceleration; iii) the acceleration unlocks the entire flow field: boundary layer, wall-shear and vorticity distributions; iv) ultimately also the HTD is recovered from similarity; iv) this extends up to deceleration, approaching the known wall-jet solution. This new theory is validated against simulations and experiments over a wide range of conditions: from uniform to fully developed issuing profiles, over a range of flights. Thus, confirming that the arriving profile contains everything needed for the subsequent wall-flow description, and demonstrating that the HTD diversity corresponds to that of the arrival profiles. This permits the prediction of the HTD in a universal way, from stagnation point to wall-jet. Specifically, relating the well-known off-center peak (boundary layer thinning) to an incoming profile shape with strong velocity gradients, as encountered in profiles with a potential core. Two different pathways for the generation of this off-center peak are studied and compared.