Development of turbulent heat flux model for unsteady forced convective heat transfer of small-to-medium Prandtl-number fluids based on deep learning

• Development of turbulent heat flux models suitable for low-to-medium Pr fluids using deep neural network. • Establishment of turbulent heat flux models suitable for complex conditions with flow separations. • Adopting proper orthogonal decomposition method to carry out the triple decomposition for unsteady flow. Turbulent heat flux (THF) models are used for the closure of the THF term when solving the steady/unsteady Reynolds-averaged scalar transport equation to simulate the turbulent heat transfer in industry. It is known that the simple gradient diffusion hypothesis (SGDH) has deficiencies under complex conditions with flow separations. To develop a more general THF model, this paper firstly establishes a high-fidelity database of forced convective heat transfer passing a circular cylinder under different Prandtl number ( Pr ) conditions at the Reynolds number ( Re ) of 500 via the direct numerical simulations. Proper orthogonal decomposition method is then employed for the triple decomposition on unsteady turbulent flow with the first two orders of eigenmodes reconstructing the large-scale field and the remaining reconstructing the turbulent field. Then, architectures using different neural network structures based on tensor basis neural network (TBNN), including MLP-TBNN-THF which adopts the multilayer perceptron (MLP) and ResNet-TBNN-THF that uses the residual network (ResNet), are constructed to predict normalized THF from large-scale flow features and Pr . Posterior tests are carried out on different Pr s and three different Re s: 500, 5000 and 16900 using the well-trained TBNN-THF models to evaluate their performance and generalization capability. Most models proposed in this paper predict the heat transfer more accurately than the SGDH model, even when extended to conditions out of the range trained. The failure of the isotropic assumption of SGDH model is observed in most regions. In that case, it is vitally necessary to use a model like proposed in this paper to simulate the THF term more accurately. In conclusion, the THF model, which is appropriate for complex working conditions and fluids with small-to-medium range of Pr , obtained by deep learning method in this paper, is helpful to improve the prediction accuracy of temperature field or concentration field by steady or unsteady Reynolds-averaged Naiver-Stokes approach in engineering. Besides, the current framework can be generalized to scalar-flux modeling under other conditions with the supplement of more databases in the future.