Symmetry breaking of flow and heat transfer in multiple impinging jets

This paper focuses on the effect of nozzle arrangement on the heat transfer of multiple impinging jets. Two different geometrical arrangements with an equal number of nozzles are studied, a square set-up (3 × 3 regularly spaced jets) and a circular set-up (eight jets surrounding a central jet). The predictions with two turbulence models are compared, the standard k–ε model with wall functions and Durbin’s v2–f model [Theor. Comput. Fluid Dyn. 3 (1991) 1] with integration to the wall. Quite surprisingly we find for one of the arrangements––the square set-up––an asymmetric flow field, even though the geometry, as well as the initial and boundary conditions are perfectly symmetric. Both turbulence models predict this peculiar broken symmetry. The other arrangement––the circular set-up––behaves more in line of expectation: both turbulence models predict a flow field that reflects all the symmetries of the physical situation. Interestingly, the differences between the two arrangements are quite small, but the corresponding flow fields clearly exhibit marked differences. Although both turbulence models agree qualitatively quite well on the mean features of the flow field for the two different set-ups, there are significant quantitative differences between the models regarding the turbulent kinetic energy and heat transfer. In particular the peak values of both the kinetic energy and the Nusselt number are quite different. Finally, we make a detailed comparison between the resulting heat transfer of the different arrangements. In the circular set-up the individual jets have a similar heat transfer, except for the central jet which is stabilized by the outer jets. In the square set-up, the difference between the jets is much more pronounced: due to the aforementioned asymmetry, some jets impinge vigorously, with a high heat transfer at the expense of the other, deflected, jets.