Toward Modular Prediction of Free-Surface Jet Array Cooling: The Hydraulic Jump Location and Non-Monotonous Heat Transfer

The present study develops the ground work for modular prediction of free-surface jet arrays. Jet arrays generate one of the highest single-phase heat transfer rates, while covering reasonably large areas with good thermal uniformity, relevant to electronics cooling. However, due to liquid evacuation problems, free-jet arrays suffer from flooding, cross-flow and jet interaction, together with the large amount of influencing geometrical parameters, this makes them very difficult to predict. For the modular prediction approach to be applied, key issues are here addressed: experiments were conducted employing de-ionized water in both single and basic multiple-jet array (2×2, with local liquid extraction in the jet interaction zones) configurations. Modular conditions, wherein all jets are similar to each other, were created experimentally in a consistent fashion, by use of liquid extraction in the jet-interaction zones. Based on present and previous experimental data the influencing parameters on the pre-jump depth were identified. This description was then used to predict the location of the hydraulic jump (as dependant on the measured post-jump depth). The model combines elements of two previous approaches the shallow-water vs. jump conservation model, and obtains good agreement with available data. In addition conditions were shown for maximizing the distance at which the hydraulic jump occurs — to the point that the supercritical flows of adjacent jets touch (standing fountain type jump). This not only permits prediction of the supercritical flow heat transfer distribution over almost the entire array area, but also reduces the low heat transfer post-jump regions to a minimum. Finally, a more universal single-jet heat transfer model was developed incorporating inherent self-similarities recently identified by the authors and considering all relevant parameters: jet velocity profiles, nozzle-plate spacing, and inclination relative to gravity, to predict stagnation heat transfer as well as its radial decay. It is further identified that the influence of inclination is also of vital importance to free-surface jets (breakage of symmetry) and must be examined in future studies. By addressing these three key issues the foundation for a modular prediction of heat transfer under a free jet array is laid.