Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines

This chapter highlights the impact of manufacturing errors on performances of aircraft engines and gas turbines in general. The reader should use this chapter to identify the regions where uncertainty quantification (UQ) should be used to improve the reliability of a gas turbine design and define where this matters.

The main difference between an experimental study and the corresponding numerical simulation is that the latter is usually considered a deterministic exercise, while the experiments are inherently affected by uncertainty. Despite this, the usage of numerical simulations is gaining more and more importance in aero-engine research thanks to their growing accuracy and accessibility. It must be underlined that even the most sophisticated numerical simulation cannot consider by default the impact of the uncertainties. Therefore, uncertainty quantification (UQ) techniques are increasingly coupled with deterministic calculations to include the most relevant variabilities. The overall goal of UQ is to investigate the impact of aleatory and epistemic uncertainties on a system response quantity of interest. The lesson learnt after applying UQ techniques to the numerical study of several aero-engine components is that to fully understand simulation results, it is imperative to incorporate uncertainty from the very beginning of the numerical procedure. To demonstrate that outcome, this chapter presents a discussion about the concepts of code verification and calculation validation, with a special interest in the analysis of the observed order of accuracy. A discussion about the definitions of aleatory and epistemic uncertainty follows, aiming at defining a common ground to start with the definition of what is called “uncertainty quantification” in engineering problems. A detailed list of limitations in deterministic computational fluid dynamics is also included in the chapter.

The overall goal of this chapter is to highlight the mathematical framework useful to carry out an uncertainty quantification study. The chapter starts with some basic definition of probability, explains non-intrusive Polynomial Chaos methods and, at the end, shows some more advanced techniques used today.

The chapter shows an overview of all the most common techniques that have been used in UQ for CFD and there is the presentation of new ideas that will become more common in the coming years. There is a clear trend from bespoke solution towards more automatic UQ methods.

The previous chapters analyzed the level of uncertainty in different gas turbine components, how this affects the performance such as life and fuel consumption, and the numerical uncertainty introduced by the CFD modeling itself. This chapter shows how uncertainty quantification techniques are used nowadays in CFD to study the impact of such manufacturing errors, pointing out, for each component, what has been learned and/or discovered using UQ, and which methodology has been used.

This chapter suggests future development in Uncertainty Quantification for Aircraft Engines.