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Large eddy simulations of wall jets with coflow for the study of turbulent Prandtl number variations and data-driven modeling

Ali Haghiri* and Richard D. Sandberg

  • Department of Mechanical Engineering University of Melbourne Parkville, Victoria 3010, Australia

  • *haghiri.a@unimelb.edu.au
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Phys. Rev. Fluids 5, 064501 – Published 18 June, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.064501

Abstract

There is a continuing effort by turbulence researchers to provide improved turbulent heat flux predictions for Reynolds-averaged Navier-Stokes (RANS) calculations of heat transfer applications. In this paper, data-driven models are developed for the turbulent heat flux prediction in wall jets with coflow using a gene expression programming (GEP)–based machine-learning technique. The training data used as input to the optimization algorithm are obtained by performing highly resolved large eddy simulations (LES) of nine cases covering various flow and geometry conditions. The study examines whether predictive RANS-based heat transfer closures can be trained that are robust to these physically very different nine LES cases. The GEP heat flux closures were developed by adopting the gradient-diffusion hypothesis with the optimization target being a nondimensional parameter representing the inverse of a nonconstant turbulent Prandtl number (Prt), with a functional dependence on the velocity and temperature gradients. First, examination of the turbulent Prandtl number calculated from time-averaged LES data showed a significant deviation from the commonly assumed constant value of 0.9, with a more significant dependence on the lip wall thickness than the blowing ratio. Second, a posteriori testing of the developed closures by solving the RANS-based scalar transport equation using as input the LES time-averaged velocity and turbulent viscosity showed a significant improvement in the prediction of adiabatic wall effectiveness not only for the cases they were trained on, but also for the entire matrix of LES cases. Finally, our best-performing model (trained on the thickest lip wall case) was also evaluated in a full RANS context and a significant improvement for the prediction of the adiabatic wall effectiveness was achieved, in particular for the medium and the thin lip thickness cases. The lack of improvement when testing the thickest lip wall case in a full RANS context indicates that for cases with strong vortex shedding the effect of organized unsteadiness on the turbulent flow field is important. In such cases, only modifying the heat flux model without improving the RANS velocity field is not sufficient and other methodologies like deriving a model for the Reynolds stress are necessary. Collectively, the current study demonstrates the ability of the presented model-development framework in creating bespoke models that can provide accurate predictions for a wide range of operating conditions.

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Outline

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Phys. Rev. Fluids 5, 064501– Published 18 June, 2020
  • Received 28 August 2019
  • Accepted 28 May 2020
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