The stagnation-zone characteristics of an impinging liquid jet are of great interest because the maximum heat transfer coefficient occurs in that region. This paper is an analytical study of the fluid flow and heat transfer in the stagnation zone of an unsubmerged liquid jet. The role of surface tension is emphasized. Stagnation-zone transport is strongly dependent on the potential flow above the boundary layer. Only a few studies have examined the potential flow of an unsubmerged jet, each using approximate potential flow theory and neglecting surface tension. In this paper, numerical solutions for a laminar unsubmerged jet are obtained, using a simulation method for steady, inviscid, incompressible flow with surface tension. A series solution that satisfies the boundary conditions in an approximate manner is constructed in terms of Legendre functions. Numerical solution of the momentum equation shows that surface tension has an effect on the stagnation-point flow field when the Weber number is small. Solutions of the associated boundary layer problem are used to obtain predictions of the influence of Weber number on the stagnation-zone heat transfer. The results are validated by comparison to measurements at high Weber number.

Splattering and heat transfer due to impingement of an unsubmerged, fully turbulent liquid jet is investigated experimentally and analytically. Heat transfer measurements were made along a uniformly heated surface onto which a jet impacted, and a Phase Doppler Particle Analyzer was used to measure the size, velocity, and concentration of the droplets splattered after impingement. Splattering is found to occur in proportion to the magnitude of surface disturbances to the incoming jet, and it is observed to occur only within a certain radial range, rather than along the entire film surface. A nondimensional group developed from inviscid capillary disturbance analysis of the circular jet successfully scales the splattering data, yielding predictive results for the onset of splattering and for the mass splattered. A momentum integral analysis incorporating the splattering results is used to formulate a prediction of local Nusselt number. Both the prediction and the experimental data reveal that the Nusselt number is enhanced for radial locations immediately following splattering, but falls below the nonsplattering Nusselt number at larger radii. The turbulent heat transfer enhancement upstream of splattering is also characterized.

Jet impingement cooling applications often involve rough surfaces, yet few studies have examined the role of wall roughness. Surface protrusions can pierce the thermal sublayer in the stagnation region and increase the heat transfer. In this paper, the effect of surface roughness on the stagnation-point heat transfer of an impinging unsubmerged liquid jet is investigated. Experiments were performed in which a fully developed turbulent water jet struck a uniformly heated rough surface. Heat transfer measurements were made for jets of diameters 4.4–9.0 mm over a Reynolds number range of 20,000–84,000. The Prandtl number was held nearly constant at 8.2–9.1. Results are presented for nine well-characterized rough surfaces with root-mean-square average roughness heights ranging from 4.7 to 28.2 μm. Measured values of the local Nusselt number for the rough plates are compared with those for a smooth wall, and increases of as much as 50 percent are observed. Heat transfer in the stagnation zone is scaled with Reynolds number and a roughness parameter. For a given roughness height and jet diameter, the minimum Reynolds number required to increase heat transfer above that of a smooth plate is established. A correlation for smooth wall heat transfer is also given.