Modelling of a planar impinging jet at unity, moderate and low Prandtl number: Assessment of advanced RANS closures

The numerical simulation of turbulent heat transfer in complex industrial flows represents a major challenge for RANS models. The impinging jet configuration is a popular test case for turbulence models, due to both the challenging nature of the flow field for the RANS approach and its widespread use in industrial applications. As a consequence, a large number of studies in the literature is dedicated to the assessment of a broad variety of turbulence models in this configuration. In particular, a significant effort has been put into the assessment of different closures for the turbulent momentum flux. In contrast, relatively little attention has been paid to the modelling of the turbulent heat flux term, and the classical Reynolds analogy is almost universally employed for this purpose despite its well-known limitations. Nevertheless, recently there has been a growing interest towards the development and assessment of more advanced closures for the turbulent heat flux. In this context, in the present work six turbulence models relying on different closures for both the turbulent momentum and heat fluxes have been used to simulate a planar impinging jet at unity, moderate and low Prandtl number and thoroughly assessed against a recently published reference DNS database. It is shown that the use of an advanced differential closure for the Reynolds stresses can result in an improvement in the prediction of the flow field. This, in turn, directly results in a more accurate prediction of the mean temperature at unity Prandtl number when the Reynolds analogy is employed for the closure of the turbulent heat flux. On the other hand, the inadequacy of the latter approach appears evident at low Prandtl values, and the necessity to account at least for the variability of the turbulent Prandtl number is demonstrated. It is then inferred that the most promising approach for such complex cases is represented by the combined use of anisotropic models for both the turbulent flow and the thermal fields.