Mechanical Engineering - Theses
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ItemData-driven Reynolds-averaged turbulence closures for buoyancy-affected flow( 2021)Turbulent flow subjected to buoyancy force is ubiquitous in daily life, e.g. in building ventilation, nuclear reactor containment, and geophysical flows. To improve the prediction accuracy of existing turbulence models, this thesis presents the results of the application of an in-house symbolic regression tool, i.e. gene expression programming (GEP), on buoyancy-extended Reynolds-averaged closure models for buoyant flows in a differentially heated vertical planar channel. In the first part of this study, attention is paid to understanding the turbulent Prandtl number's behaviour and improve the predictability of the linear eddy diffusivity models. By comparing the location of mean velocity maxima, there is an infinity anomaly for the eddy viscosity and the turbulent Prandtl number, as both terms are divided by the mean velocity gradient according to the standard definition, in vertical buoyant flow. To predict the quantities of interest, e.g. the Nusselt number, GEP is used with various cost functions, e.g. the mean velocity gradient, with the aid of the latest direct numerical simulation (DNS) dataset for vertical natural and mixed convection. It is found that the new machine-learnt algebraic models, as the reciprocal of $Pr_t$, successfully handle the infinity issue for both vertical natural and mixed convection. Moreover, the proposed models with embedded coordinate frame invariance can be conveniently implemented in the Reynolds-averaged scalar equation and are proven to be robust and accurate in the current parameter space, where the Rayleigh number spans from $10^5$ to $10^9 $ for vertical natural convection and the bulk Richardson number $Ri_b $ is in the range of $ 0$ and $ 0.1$ for vertical mixed convection. However, there are notable errors between the prediction and DNS data when incorporating the algebraic model of turbulent Prandtl number into full Reynolds--averaged Navier--Stokes (RANS) equations. As a result, the turbulence closure is upgraded with buoyancy-extended terms. The second part of this study re-examines the buoyancy-accounting algebraic scalar-flux model proposed by Kenjeres et al., Int. J. Heat Fluid Flow, Vol. 26, pp. 569-586 (2005). Based on a term-by-term analysis on the model with the aid of high-fidelity datasets, it is demonstrated that there are significant discrepancies in the predicted turbulent heat fluxes once the model is combined with the existing algebraic Reynolds stress models. Consequently, it is suggested that the quadratic terms in buoyancy-extended explicit algebraic Reynolds stress models should be included, and such non-linear Reynolds-stress and heat-flux closure models are then developed via GEP. The evaluation of these GEP-based models shows significant improvements in the prediction of mean quantities and second moments in an a-priori stage and in an a-posteriori stage, with the latter being realised by embedding the new models into the elliptic relaxation v^2-f equations, across different Rayleigh number cases. In comparison to passive scalar flow, the complexity of turbulence modelling for natural convection problems is increased as the velocity and scalar fields are strongly coupled by the buoyancy force. The above data-driven turbulence modelling approaches have treated the unclosed terms of the velocity and thermal fields separately, which has lead to inaccurate predictions when handling natural convection problems. Hence, the appropriate Reynolds-averaged closure models for natural convection ought to capture this interaction within the second-moment terms. In the last part of this study, we therefore develop fully coupled buoyancy-extended models by using a novel multi-objective and multi-expression machine-learning framework that is based on CFD-driven training (Zhao et al., J. Comput. Phys., 411, 109413, (2020)).The model candidates obtained from a Gene-Expression Programming approach, and thus available in symbolic form, are evaluated by running RANS solvers for different Rayleigh number cases during the model training process. This novel framework is applied to vertical natural convection, with the emphasis on the importance of coupling the explicit closure model formulations, the choice of cost functions, and the appropriate input flow features (i.e. a generalised flux Richardson number) for developing accurate models. It is shown that the resulting machine-learnt models improve the predictions of quantities of interests, e.g. mean velocity and temperature profiles, for vertical natural convection with Rayleigh numbers in the range of $10^5$ to $10^9$.