Inexpensive uncertainty analysis for CFD applications - Ghate, D (2014)
The work presented in this thesis aims to provide various tools to be used during design process to make maximum use of the increasing availability of accurate engine blade measurement data for high fidelity fluid mechanic simulations at a reasonable computational expense. A new method for uncertainty propagation for geometric error has been proposed for fluid mechanics codes using adjoint error correction. Inexpensive Monte Carlo (IMC) method targets small uncertainties and provides complete probability distribution for the objective function at a significantly reduced computational cost. A brief literature survey of the existing methods is followed by the formulation of IMC. An example algebraic model is used to demonstrate the IMC method. The IMC method is extended to fluid mechanic applications using Principal Component Analysis (PCA) for reduced order modelling. Implementation details for the IMC method are discussed using an example airfoil code. Finally, the IMC method has been implemented and validated for an industrial fluid mechanic code HYDRA. A consistent methodology has been developed for the automatic generation of the linear and adjoint codes by selective use of automatic differentiation (AD) technique. The method has the advantage of keeping the linear and the adjoint codes in-sync with the changes in the underlying nonlinear fluid mechanic solver. The use of various consistency checks have been demonstrated to ease the development and maintenance process of the linear and the adjoint codes. The use of AD has been extended for the calculation of the complete Hessian using forward-on-forward approach. The complete mathematical formulation for Hessian calculation using the linear and the adjoint solutions has been outlined for fluid mechanic solvers. An efficient implementation for the Hessian calculation is demonstrated using the airfoil code. A new application of the Independent Component Analysis (ICA) is proposed for manufacturing uncertainty source identification. The mathematical formulation is outlined followed by an example application of ICA for artificially generated uncertainty for the NACA0012 airfoil.