Mechanical Engineering - Theses
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ItemData-driven large eddy simulation modelling in natural convection( 2022)Natural convection is a commonly occurring heat-transfer problem in many industrial flows and its prediction with conventional large eddy simulations (LES) at higher Rayleigh numbers using progressively coarser grids leads to increasingly inaccurate estimates of important performance indicators, such as Nusselt number (Nu). Thus, to improve the heat transfer predictions, we utilize Gene Expression Programming (GEP) to develop sub-grid scale (SGS) stress and SGS heat-flux models simultaneously for LES. With that as the focus, in the present study, two geometrically distinct natural convection cases are considered to develop and generalize turbulence models. The Rayleigh-Benard Convection (RBC) is used to develop models, while the Concentric Horizontal Annulus (CHA) is used to test the model generalization. An in-house compressible solver, HiPSTAR, for simulating natural convection flows for low Mach number problems is benchmarked against the experiments and Direct Numerical Simulations (DNS) results. Subsequently, HiPSTAR is used to run simulations for the RBC and CHA configurations and the generated DNS database is then used to train and assess LES models. The models’ development starts with RBC, where the fluid is in a cubic box with the bottom wall as the hot wall and the top wall as the cold wall. The alignment between different basis functions and the Gaussian-filtered SGS stress and SGS heat flux is used to determine the most suitable training framework. The trained models in isotropic form, by utilizing the norm of the grid cell as the length scales demonstrate good performance in the bulk region, but less improved performance in the near wall region. It is shown, that for LES of wall-bounded flow, the GEP models in anisotropic form, i.e. using different grid length scales for the different spatial directions, are required to obtain generalized models suitable for different regions. Consequently, the a-priori results demonstrate a significant improvement in the prediction of both instantaneous and mean quantities for a wide range of filter widths. However, developing accurate LES models that generalize well to complex geometries poses a challenge, particularly for data-driven methods. Thus, in the next stage, machine-learned closure models with embedded geometry independence are proposed, where the subgrid-scale (SGS) stress and heat-flux models developed by using Gene Expression Programming (GEP) are built in the computational space. The CHA case is chosen to develop and generalize the models. Subsequently, the formulation between the SGS closures, the total, and the resolved large-scale turbulent stress and heat flux is derived in the compressible LES context. The a-priori results show that the GEP models developed in computational space significantly improve both the SGS stress and SGS heat-flux prediction while being robust to complex flows. Similarly, the a-posteriori results demonstrate that the GEP models perform better than the wall-adapting local eddy-viscosity (WALE) model in the prediction of the mean SGS stress and the SGS heat-flux. The data-driven approach for turbulence model development presented clearly offers promising geometry independence for LES in the prediction of SGS stress and heat flux.
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ItemBoundary layer and bulk dynamics in vertical natural convection( 2017)Results from direct numerical simulations of vertical natural convection at Rayleigh numbers 10^5–10^9 and Prandtl number 0.709 are found to support a generalised applicability of the Grossmann–Lohse (GL) theory, which was originally developed for Rayleigh–Bénard convection. In accordance with the GL theory, we show that the normalised mean boundary- layer thicknesses of the velocity and temperature fields obey the laminar-like Prandtl– Blasius–Pohlhausen scaling, corresponding to the “classical” state. Away from the walls, the dissipation of the turbulent fluctuations, which can be interpreted as the “bulk” or “background” dissipation of the GL theory, is found to obey the Kolmogorov– Obukhov–Corrsin scaling for fully developed turbulence. The present results suggest that, similar to Rayleigh–Bénard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for vertical natural convection and existing empirical relationships should be recalibrated to better reflect the underlying physics. On closer scrutiny of the boundary layers, we find evidence that the boundary layers are undergoing a transition from the classical state to the “ultimate” shear-dominated state. In particular, we observe near-wall higher-shear patches that occupy increasingly larger fractions of the wall-areas. These higher-shear patches exhibit turbulent features, for instance (i) the patches appear streaky, reminiscent of the characteristic near- wall streaks in canonical wall-bounded turbulence, (ii) the local mean temperature profile yields a logarithmic variation, in agreement with the logarithmic law of the wall for mean temperature, and (iii) the local Nusselt number follows an effective Rayleigh number power-law scaling exponent of 0.37, consistent with the logarithmically corrected 1/2 power-law scaling predicted for ultimate thermal convection. We reason that both turbulent and laminar-like boundary layers coexist in the transitional regime of vertical natural convection, consistent with the findings reported for Rayleigh–Bénard convection and Taylor–Couette flows. When the walls are instead removed and boundary layers eliminated, the new setup mimics turbulent bulk-dominated thermal convection. We refer to this new setup as homogeneous vertical natural convection. A direct application of scaling arguments to the governing equations of this new setup yields the asymptotic 1/2 power-law scaling relations for the Nusselt and Reynolds numbers, in accordance to previous theoretical predictions of turbulent bulk-dominated thermal convection. Results from direct numerical simulation of the new setup further supports the predicted 1/2 power- law relations. When employing bulk quantities for the wall-bounded setup, we too find the aforementioned 1/2 power-law scaling. This extended result suggests that the 1/2 power-law scaling relation may even be present at lower Rayleigh numbers provided the appropriate quantities in the turbulent bulk flow are employed for the definitions of the Rayleigh, Reynolds and Nusselt numbers. Lastly, we perform a straightforward assessment of the mixing efficiency in vertical natural convection. The value is predicted and found to be approximately 0.5, which suggests that the dissipation rate of kinetic energy is directly proportional to the rate at which gravitational potential energy is readily available for conversion.