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 $10^9$.
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ItemTurbulence Model Development and Implementation for Low Pressure Turbines using a Machine Learning Approach( 2019)The design of the gas turbine, which is the work horse of the aviation industry, has reached a high degree of maturity; given that the first gas turbine flew in the late 1930s. Despite this, the industrial sector is looking towards harnessing even incremental points of efficiency with novel methods, which can translate to millions of dollars of savings and large reductions in carbon emissions. Current gas turbine design is primarily carried out using low-fidelity simulations due to their low cost and user-friendliness. However, these simulations lack the accuracy of high-fidelity simulations, largely due to the use of a linear stress-strain relation – the Boussinesq approximation. With the increase in the power of computing, high-fidelity simulations are becoming increasingly commonplace but are still not feasible as an iterative industrial design tool. In order to bridge the gap between high and low-fidelity simulations, certain high-fidelity data sets can be harvested to extract meaningful physics-based insights with machine learning processes to improve the accuracy of iterative low-fidelity calculations. This thesis focuses on improving low-fidelity modelling strategies (Reynolds–Averaged Navier–Stokes (RANS)) for low pressure turbine (LPT) flows, by harnessing meaningful physics-based information from high-fidelity data using a machine learning approach – gene expression programming (GEP). Improvement in the accuracy of the existing linear stress-strain closure relations is sought by developing machine-learnt explicit algebraic Reynolds stress models (EARSM). Of the many physical phenomena that occur in an LPT, designers are very interested in being able to accurately model the wake mixing using RANS, as this phenomenon governs the stagnation pressure loss in a turbine and also because existing RANS-based turbulence models fail to accurately predict this phenomenon. Therefore, the goal of this thesis is to develop and implement non-linear EARSMs to enhance the wake mixing in LPTs using GEP and high-fidelity data sets at realistic engine operating conditions. Firstly, an extensive analysis of the existing RANS-based turbulence models for LPTs with steady inflow conditions was conducted. None of these RANS models were able to accurately reproduce wake loss profiles based on high-fidelity data. However, the recently proposed k-v2-omega transition model was found to produce the best agreement with high-fidelity data in terms of blade loading and boundary layer behaviour and was thus selected as the baseline model for turbulence closure development. Using different training regions for model development, the resulting closures were extensively analysed in an a priori sense (without running any CFD) and also while running CFD calculations. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e. previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, TKE production, wake loss profiles and wake maturity across all cases. The existing GEP framework was extended to include RANS feedback during the model development process. It was found that the models generated via this method allow greater flexibility to the user in terms of selecting metrics of direct interest. The models returned offer a higher degree of numerical stability and robustness across different flow conditions and even geometries. Models developed on the LPT were tested on a high pressure turbine case and vice-versa and some of the models were able to reduce the peak wake loss error by up to 90% over the Boussinesq approximation in this cross-validation study. A zonal based model development approach was proposed with an aim to enhance the wake mixing prediction of unsteady RANS calculations for LPTs with unsteady inflow conditions. High-fidelity time-averaged and phase-lock averaged data at a realistic isentropic Reynolds number and two reduced frequencies, i.e. with discrete incoming wakes and with wake ‘fogging’, were used as reference data. This is the first known study to develop machine learning based turbulence models for unsteady flows, and also the first study to use phase-lock averaged data for the same. Models developed via phase-lock averaged data were able to capture the effect of certain prominent physical phenomena in LPTs such as wake-wake interactions, whereas models based on the time-averaged data could not. Correlations with the flow physics led to a set of models that can effectively enhance the wake mixing prediction across the entire LPT domain for both cases. Based on a newly developed error metric, the developed models have reduced the a priori error over the Boussinesq approximation on average by 45%. Based on the analysis conducted in this work, a few best practice guidelines have been proposed which can offer future designers an insight into the GEP-based model development process. Overall, this study showcases that GEP is a promising avenue for future RANS-based turbulence model development.