Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations

Tiltrotor CFD part II: aerodynamic optimisation of tiltrotor blades

This paper presents aerodynamic optimisation of tiltrotor blades with high-fidelity computational fluid dynamics. The employed optimisation framework is based on a quasi-Newton method, and the required high-fidelity flow gradients were computed using a discrete adjoint solver. Single-point optimisations were first performed, to highlight the contrasting requirements of the helicopter and aeroplane flight regimes. It is then shown how a trade-off blade design can be obtained using a multi-point optimisation strategy. The parametrisation of the blade shape allowed to modify the twist and chord distributions, and to introduce a swept tip. The work shows how these main blade shape parameters influence the optimal performance of the tiltrotor in helicopter and aeroplane modes, and how a compromise blade shape can increase the overall tiltrotor performance. Moreover, in all the presented cases, the accuracy of the adjoint gradients resulted in a small number of flow evaluations for finding the optimal solution, thus indicating gradient-based optimisation as a viable tool for modern tiltrotor design

Contributions to Jet Noise Prediction and Characterisation by Means of Hybrid Acoustic Analogy Techniques

In Computational aeroacoustics, hybrid approaches first resolve the source and nearfield regions of the flow field by employing Reynolds Averaged Navier-Stokes (RANS) equations, Large Eddy Simulations (LES) or Direct Numerical Simulations (DNS).The source region data is used to form source terms, which are, in turn, applied to either empirical models or equations linearized around a mean flow. An acoustic analogy type of model is used to propagate the acoustics to the farfield regions. The aim of this research is twoold: to introduce and test a hybrid acoustic analogy, based on a coupling between the Navier-Stokes equations, applied in the source region, and the Non-linear Euler (NLE) equations applied in the acoustic propagation region; and to test and validate a recently derived generalized acoustic analogy theory in the framework of jet noise with acoustic source information obtained from RANS or LES. In the first part, the coupling between the Navier-Stokes and the NLE equations is accomplished via a buffer region, which is used to interpolate and penalize the flow variables of interest from the source region. The penalized flow variables are then applied as source terms in the NLE equations, to calculate the acoustic propagation. The non-linear Euler equations, discretized using highurate dispersion-relation preserving schemes constitute a very efficient approach for jet noise predictions in complex environments, especially for supersonic and hypersonic jets, where nonlinearities may propagate over long distances. In the second part, a RANS- or LES-informed model, which is used to provide data for Goldstein\u27s generalized acoustic analogy, is presented. The generalized acoustic analogy of Goldstein is considered, wherein the effects of non-parallelism are taken into account and an asymptotic expansion is utilized to simplify the adjoint Green function equations. The use of the adjoint Green\u27s function leads to a simple model for jet noise predictions for low frequencies and small observation angles, in the linear regime. Both approaches are extensively tested and validated against numerous benchmark problems and applications

Shape Optimization of Turbomachinery Blades Using an Adjoint Harmonic Balance Method

The high-dimensional harmonic balance (HDHB) method has recently become popular in the field of periodic unsteady flow prediction due to its accuracy and high efficiency. In the present dissertation research, two and three-dimensional parallelized computational fluid dynamic (CFD) codes based on the HDHB method are developed and validated for unsteady turbulent flows. It is found that the stability condition for an explicit solver is highly dependent on the reduced grid frequency, a non-dimensional parameter that depends on the grid size, characteristic wave speed, and the highest frequency retained in the harmonic balance solver. Furthermore, for certain moderately and highly nonlinear problems, the pseudo-spectral operator used in the HDHB method is found to introduce aliasing errors, which may lead to nonlinear instabilites or non-physical solutions. As a remedy, a temporal spectral viscosity operator is proposed for de-aliasing purpose so as to stabilize HDHB solver. The proposed method is validated for a simple nonlinear Duffing oscillator case and laminar vortex shedding over an oscillating circular cylinder at Re=500. Another focus of this research is the design optimization of the turbomachinery blades for unsteady flows. The \u27\u27steady state\u27\u27 nature of the HDHB technique makes it very-well suited for an adjoint sensitivity analysis mainly due to the fact that the storage requirements are greatly reduced. To date, the investigators have used the adjoint technique mainly for steady shape optimization. To the author\u27s best knowledge, the technique has not been applied for unsteady design optimization of turbomachinery blades. In this dissertation, a discrete adjoint HDHB method is employed for unsteady turbomachinery shape optimization. With the help of the automatic differentiation (AD) tool, TAPENADE, the development time for an optimization solver can be reduced substantially. Both inverse design and optimization problems are considered to validate the optimization solver