Data-driven turbulence modelling for fluid topology optimisation
File(s)
Author(s)
Hammond, James
Type
Thesis
Abstract
Fluid Topology Optimisation (FTO) is becoming a popular approach in the development of designs for additive manufacturing in aero-thermal applications. However, one of the main limitations of current approaches considering turbulent flow is the fidelity of the Reynolds-averaged Navier-Stokes (RANS) models employed. This thesis develops techniques to improve the fidelity of turbulence modelling in FTO through the incorporation of data-driven methods. First, the framework for including data-driven turbulence models in FTO is developed by deriving the continuous adjoint form of the generalised Explicit Algebraic Stress Model, of which most data-driven turbulence models are specific forms. Following this, methods are formulated to generate robust data-driven turbulence models and bound their expected performance. The upper bound is obtained by inserting high fidelity data directly into the RANS equations to discern the performance available from the dataset. The lower bound comes from models that are linear with respect to the chosen input features. Results suggest that the lower bound often provides significant, robust improvement over baseline models, without the need to resort to more complex data-driven techniques.
Next, techniques for uncertainty quantification and reliability analysis are established for systems where acquisition of sample data is expensive. Specifically, characterisation of multivariate data exhibiting non-trivial parameter dependencies is proposed by defining a probability box (p-box) of Sliced-Normal (SN) distributions. The p-box spans maximum likelihood and moment-bounded maximum entropy estimations which converge to a single distribution as more data is collected. Conservative estimation of the failure probability is obtained by finding the worst-case distribution in the p-box. This p-box is complimented by a bounding range, provided by the Sliced-Normals leading to the maximal and the minimal failure probability.
Finally, the data-driven FTO method is tested on a selection of two- and three-dimensional cases including a U-bend, representative of a single bend in a gas turbine internal cooling duct. Results highlight the reduction in the objective function that can be obtained from the data-driven FTO method over standard turbulence models, when designs are tested using high fidelity solvers.
Next, techniques for uncertainty quantification and reliability analysis are established for systems where acquisition of sample data is expensive. Specifically, characterisation of multivariate data exhibiting non-trivial parameter dependencies is proposed by defining a probability box (p-box) of Sliced-Normal (SN) distributions. The p-box spans maximum likelihood and moment-bounded maximum entropy estimations which converge to a single distribution as more data is collected. Conservative estimation of the failure probability is obtained by finding the worst-case distribution in the p-box. This p-box is complimented by a bounding range, provided by the Sliced-Normals leading to the maximal and the minimal failure probability.
Finally, the data-driven FTO method is tested on a selection of two- and three-dimensional cases including a U-bend, representative of a single bend in a gas turbine internal cooling duct. Results highlight the reduction in the objective function that can be obtained from the data-driven FTO method over standard turbulence models, when designs are tested using high fidelity solvers.
Version
Open Access
Date Issued
2023-01-12
Date Awarded
2023-08-01
License URL
Advisor
Montomoli, Francesco
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/L016230/1
Publisher Department
Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)