Jets can be classified as submerged if they discharge into an ambient fluid of similar physical properties (e.g., air in air) and unsubmerged if the properties of the two fluids are quite different (e.g., water in air). Several configurations have been tested such as: jets issuing from orifices or round and slot nozzles different types of jet arrays; flat and curved impingement surfaces, normal and inclined impingement, etc. Only the simple geometry of a single jet impinging on a flat surface is treated below. Figure 1 shows the typical fluid-dynamic features of a submerged (top) and an unsubmerged (bottom) jet. For both, three main regions can be identified:
the free jet region, which extends from the nozzle up to a certain distance from the surface and can, in turn, be divided into a potential core, a developing and a fully developed zone;
the stagnation region, where the flow on the wall is accelerated by a streamwise stabilizing pressure gradient (the boundary layer thickness tends to keep constant);
the wall region, where the pressure gradient effect no longer holds and an even steep rise of turbulence can occur.
After issuing from the nozzle, the submerged jet widens linearly with its length due to the exchange of momentum with the ambient fluid over the free boundaries. An outline of the trends of the development of the boundary layer and of the fluid velocity is given in Figure 1a. The unsubmerged jet (liquid in gas) exibits a gas-liquid free boundary which bends close to the solid surface once the liquid starts spreading over the wall. The wall flow is subdivided into four regions as shown in Figure 1b:
a stagnation region with a constant boundary layer;
a zone where the viscous boundary layer enlarges up to the value of the liquid sheet thickness;
a fully viscous region;
the hydraulic jump with the occurrence of a sudden increase in liquid thickness and a slowing down of liquid velocity ( Figure 1b).
The Nusselt Number is most commonly given as a function of Reynolds Number Re and Prandtl Number Pr in the form PrmRen, the dimensionless distance from the stagnation point (line) on the surface, r/D, and the dimensionles nozzie to wall spacing z/D. Roughly speaking, Nu decreases with the increase of r/D and of z/D. Furthermore, the sensitivity of Nu to z/D is more pronounced for submerged jets than for unsubmerged ones. Nevertheless radial peaks, depending on the values of Re and z/D, occur both for submerged and unsubmerged jets and can be ascribed to the thermal boundary layer evolution and to the effect of turbulence. Figure 2 from Lytle and Webb (1991) shows a sketch of this phenomenon. More recently, the influence of splattering [Lienhard et al. (1992)] and of the Froude Number [Di Marco et al. (1993)] have been accounted for. More detailed information on the treated matter and several correlations can be found in Faggiani and Grassi (1990) and Viskanta (1993).
Di Marco, P., Grassi, W., Magrini, A. (1993) Heat transfer between a flat horizontal surface and an unsubmerged liquid jet at low velocity. Eurotherm Seminar. 32. Oxford, UK.
Faggiani, S., Grassi, W. (1990) Impinging liquid jets on heated surfaces. KN16. 9th Int. Heat Transfer Conf. Jerusalem. Israel. 1.
Lienhard, J. H. (V), Liu, X., Gabour, L. A. (1992) Splattering and heat transfer during impingement of a turbulent liquid jet. J. Heat Transfer, Trans. ASME. 114.
Lytle, D., Webb, B. W. (1991) Secondary heat transfer maxima for air jet impingement at low nozzle-to-plate spacing. Experimental Heat Transfer, Fluid Mechanics and Thermodynamics. Elsevier, New York.
Viskanta R. (1993) Heat transfer to impinging gas and flame jets. Experimental Thermal and Fluid Science, vol. 6. DOI: 10.1016/0894-1777(93)90022-B