Turbulent Prandtl number and characteristic length scales in stably stratified flows: steady-state analytical solutions

In this study, the stability dependence of turbulent Prandtl number ($$Pr_t$$ P r t ) is quantified via a novel and simple analytical approach. Based on the variance and flux budget equations, a hybrid length scale formulation is first proposed and its functional relationships to well-known length scales are established. Next, the ratios of these length scales are utilized to derive an explicit relationship between $$Pr_t$$ P r t and gradient Richardson number. In addition, theoretical predictions are made for several key turbulence variables (e.g., dissipation rates, normalized fluxes). The results from our proposed approach are compared against other competing formulations as well as published datasets. Overall, the agreement between the different approaches is rather good despite their different theoretical foundations and assumptions.

Evaluation of a Machine Learning Turbulence Model in a Square Transverse Jet in Crossflow

Film cooling is an important technique to ensure safe operation and performance fulfillment of turbines. Its ultimate goal is to protect the axial turbine blades from high gas temperatures. An appropriate study is necessary in order to obtain a reliable representation of the flow characteristics involved in such phenomena. Because of the high computational cost of high-fidelity simulations, the low-fidelity simulation method Reynolds Averaged Navier Stokes (RANS) is commonly used in practical configurations. However, the majority of the current turbulent heat flux models fail to accurately predict heat transfer in film cooling flows. Recent work suggests the use of machine learning models to improve turbulent closure in these flows. In the present work, a machine learning model for spatially varying turbulent Prandtl number previously described in the literature is applied to a transverse film cooling flow consisting of a jet square channel. The results obtained in the present work were compared to adiabatic effectiveness experimental data available in the literature to assess the performance of the machine learning model. The results shown that for low blowing ratios (BR = 0.2 and BR = 0.4) the proposed machine learning model has poor performance. However, for the case with the highest blowing ratio (BR = 0.8), the proposed model presented better results. These results are then explained in terms of the resulting turbulent Prandtl number field and suggest that the training set is not appropriate for capturing the turbulent heat flux in fully attached jets in crossflow.

Numerical Investigation on Heat Transfer of Supercritical Water With a Variable Turbulent Prandtl Number Model

Turbulent Prandtl number (Prt) has a great impact on the performance of turbulence models in predicting heat transfer of supercritical fluids. Unrealistic treatment of Prt may lead to large deviations of the prediction results from experimental data under supercritical conditions. In this study, the effect of Prt on heat transfer of supercritical water was extensively studied by using shear stress transport (SST) k–ω turbulence model, and the results suggested that using the existing Prt models would lead to failures in predicting the heat transfer characteristics of supercritical water under deteriorated heat transfer (dht) conditions. A new variable Prt model was proposed with the Prt varied with pressure, turbulent viscosity ratio, and molecular Prandtl number. The new model was validated by comparing the numerical results with the corresponding experimental data, and it was found that the new variable Prt model exhibited better performance on reproducing the dht of supercritical water in vertical tubes than those of the existing Prt models.