RANS model predictions for desalination discharges implemented with a dynamic turbulent Schmidt number approach

Abstract Desalination discharges are commonly in the form of inclined negatively buoyant jets (INBJs). Numerical predictions of INBJs remain a challenge. While accurate large eddy simulations (LES) of INBJs have become available very recently, they are substantially more resource intensive. Reynolds-averaged Navier–Stokes (RANS) modelling is potentially more efficient and can be more readily applied in practice. However, existing RANS simulations show substantial error when compared with experimental measurements. In this study, RANS simulations of 45° INBJs are performed with a dynamic turbulent Schmidt number (DTSN) approach. This new approach involves extracting turbulent Schmidt number ( $$S{c}_{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> </mml:math> ) profiles in the INBJs from recently published LES data that have been validated by experiments. Detailed cross-sectional $$S{c}_{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> </mml:math> profiles in INBJs are reported here for the first time. The relationship between $$S{c}_{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> </mml:math> and a local mean flow parameter is also determined from the LES data. RANS simulations are then performed—with $$S{c}_{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> </mml:math> being allowed to change dynamically during the simulation according to the pre-determined relationship. The results show that the DTSN approach improved the overall predictive capabilities of the RANS model to a limited extent. However, significant issues remain in terms of the models’ ability to predict dilutions in the descending portion of the flow. Importantly, the DTSN simulations demonstrate that the model predictions are sensitive to the determination of the relationship between $$S{c}_{t}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:mrow> </mml:math> and the local flow parameter. Further improvements in the DTSN approach are therefore possible with refinement to the characterisation of this relationship. Based on a discussion of the present and recent literature describing RANS simulations of INBJs, the authors encourage a more cautious interpretation of the current predictive capabilities of RANS simulations in the context of INBJs.