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

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. • Flow and heat transfer characteristics shown to be predictable within stagnation, and transition zones. Agreement found with detailed, validated simulations of wall-pressure, free-stream velocity, boundary layer thickness, wall-shear and heat transfer distributions. • Streamline bending analysis employed to predict wall-pressure distribution for all relevant arrival profiles (various issuing profiles and relaxation during flights). • Velocity profile's dynamic pressure converts into the static wall-pressure which dictates local radial acceleration, explaining the source of local boundary layer thinning and associated off-center heat transfer peak, for the first time. • An approximate, continuous description of Homann's and Glauert's basic solutions, enables analysis of advanced flow characteristics – even the vorticity field. • Interpolation to previous wall-jet analysis covers the entire wall-domain under a submerged impinging jet in terms of flow field (vorticity field) and heat transfer.