Non-deterministic simulation for CFD-Based Design methodologies
Analysis and design methods in aeronautical industry, particularly the aerodynamic simulation tools based on Computational Fluid Dynamics (CFD) and their multidisciplinary extensions (such as fluid-structure; fluid-thermal; aero-acoustics applications), are based on simulations with a unique set of input data and model variables. However, realistic operating conditions are a superposition of numerous uncertainties under which the industrial products operate (uncertainties on boundary and initial conditions, on geometries resulting from manufacturing tolerances, numerical error sources and uncertain physical model parameters. The presence of these uncertainties is the major source of risk in the design decision process and increases therefore the level of risks of failure of a given component.
The NODESIM-CFD project addressed the EU objectives of reduction of aircraft development costs and increase of safety, through the introduction of a new paradigm for computational fluid dynamics (CFD)-based virtual prototyping, aimed at the incorporation of operational and other uncertainties in the simulation process. The project pursued the following scientific and technological objectives:
- identification and quantification of the uncertainty parameters associated to a wide variety of aeronautical applications; the domains of application cover: engine aerodynamics, wing aerodynamics, conjugate heat transfer and fluid-structure interactions;
- development of several non-deterministic methodologies focusing on the most promising methods, such as perturbation techniques and adjoint-based methods, efficient Monte Carlo (MC) methods and polynomial chaos methods;
- applications to subsystems and systems: the general methodologies and software tools developed under the previous actions will be applied, tested and validated for the various applications for which the uncertainty variables have been identified and analysed;
- introduction of non-deterministic simulations into the design and decision process, focusing on the development of aerodynamic optimisation algorithms that provide designs, which are robust with respect to uncertainties in geometry, operating conditions, and code simulation uncertainties, and to control and reduce risks by providing designs with aerodynamic performances insensitive to intrinsically uncertain quantities;
- stimulate the scientific cooperation and transfer of knowledge within the NODESIM-CFD consortium, through a specific task of support from the developers to the implementation of the developed new methodologies in the in-house codes of the industrial partners.
The NODESIM-CFD project was composed of the following action lines:
- the identification and probabilistic quantification of the most significant uncertainty sources, related to CFD and multidisciplinary based simulations, of aeronautical components (wings, aircraft and engines);
- the development and incorporation of efficient non-deterministic methodologies into the CFD simulation systems to produce reliability bounds of the predictions in a rational way;
- application and evaluation of the developed methodologies to the non-deterministic analysis of aeronautical components by the industrial manufacturers;
- the development and application of robust CFD-based design methodologies incorporating the non-deterministic based simulations, enabling rational estimates of probabilities of failure.
The first objective has been accomplished by an intensive and thorough analysis of the potential uncertainties to be accounted for. Three classes of uncertainties were identified: operational, geometrical and numerical uncertainties. The identified uncertainties are statistically described through a probability distribution functions (PDF). In order to prescribe the input parameters of a selected PDF based on expert opinion or to identify the type of PDF from experimental data two software tools have been developed: a beta PDF defining tool and a distribution fitting tool.
The second objective, namely the development of the non-deterministic methodologies for uncertainty propagation represented the core of the NODESIM-CFD project. Three categories of non-deterministic methodologies were developed and applied:
- perturbation techniques with adjoint methods;
- MC methods with surrogate methods;
- polynomial chaos methods (PCMs).
The third listed objective aimed at validating the non-deterministic methodologies on representative test cases and for various uncertainties sources. Therefore, a database of test cases has been built up with different levels of complexity. Academic test cases and industrial ones coexisted and have been classified following the range of applications: external flows around wings, propulsion flows and multi-physics. As applications to external flows around the wings, the transonic flows around the RAE 2822 airfoil and ONERA M6 wing have been selected as compulsory tests.
With respect to applications to propulsion flows the transonic flow in NASA Rotor 37 configuration has been selected as compulsory test case. As applications to multi-physics the flutter of AGARD 445.6 wing, an aero-elastic of wing model and a planar combustor test rig have been considered.
The last two objectives have foreseen actions for the transfer of knowledge among the developers' teams and the end-user partners. This was a two way process: a direct action was dedicated to the actual transfer of the non-deterministic software modules, coupling with end-users' in-house codes and training. An important feed-back arrived from the end-users towards the developers on the appropriateness of a specific uncertainty propagation method with respect with a range of applications and suggestions of improvement.
For the first category of techniques, actions were directed towards the automatic differentiation for the management of uncertainties, studies on the influence of the computational mesh on the drag and lift output functionals and an adjoint-based error estimator have been developed. Inria succeeded in identifying and implementing strategies for computing second derivatives of CFD codes, while the German Aerospace Centre (DLR) developed an error-based adaptation technique.
The second category of developed non-deterministic methodologies aimed at circumventing the high computational cost and consequently the MC analysis systems were combined with surrogate models based on various response surface methods or design of experiments.
CIMNE has achieved the adaptation and integration in its Monte-Carlo analysis system stochastic analysis computation (STAC) of new capabilities related to the needs of multidisciplinary codes. Among these capabilities, one can underline the generation of random variables from given marginal distribution as well as a joint distribution of all the variables and STAC's usage for robust design.
ONERA focused on the following surrogate models in combination with their developed MC method: eight order polynomial approximation, radial basis function neuronal network and simple Kriging. SIGMA focused in turn to surrogate model construction tools based on polynomial regression, simplified 'weighted' approximation and radial basis function neuronal networks. UNITS developed DACE technologies with the classical and adaptive versions particularly.
The third category of non-deterministic methodologies accounts for two main types of PCMs: intrusive and non-intrusive. For both types of PCM, the principal interest was concentrated on the assessment of the effects due to the nonlinear character of the flow governing system and to improve the computational efficiency. VUB developed an intrusive PCM, tested by NUMECA, and non-intrusive probabilistic collocation methods were developed by QQ and WSA. In addition TUD developed also the probabilistic radial basis function approach.