Technical Evaluation Report for Symposium AVT-147: Computational Uncertainty in Military Vehicle Design

The complexity of modern military systems, as well as the cost and difficulty associated with experimentally verifying system and subsystem design makes the use of high-fidelity based simulation a future alternative for design and development. The predictive ability of such simulations such as computational fluid dynamics (CFD) and computational structural mechanics (CSM) have matured significantly. However, for numerical simulations to be used with confidence in design and development, quantitative measures of uncertainty must be available. The AVT 147 Symposium has been established to compile state-of-the art methods of assessing computational uncertainty, to identify future research and development needs associated with these methods, and to present examples of how these needs are being addressed and how the methods are being applied. Papers were solicited that address uncertainty estimation associated with high fidelity, physics-based simulations. The solicitation included papers that identify sources of error and uncertainty in numerical simulation from either the industry perspective or from the disciplinary or cross-disciplinary research perspective. Examples of the industry perspective were to include how computational uncertainty methods are used to reduce system risk in various stages of design or development

Uncertainty quantification for wind energy applications

Uncertainties are omni-present in wind energy applications, both in external conditions (such as wind and waves) as well as in the models that are used to predict key quantities such as costs, energy yield, and fatigue loads. This report summarizes and reviews the application of uncertainty quantification techniques to wind energy problems. In th

On the influence of uncertainty in computational simulations of a high-speed jet flow from an aircraft exhaust

A classic approach to Computational Fluid Dynamics (CFD) is to perform simulations with a fixed set of variables in order to account for parameters and boundary conditions. However, experiments and real-life performance are subject to variability in their conditions. In recent years, the interest of performing simulations under uncertainty is increasing, but this is not yet a common rule, and simulations with lack of information are still taking place. This procedure could be missing details such as whether sources of uncertainty affect dramatic parts in the simulation of the flow. One of the reasons of avoiding to quantify uncertainties is that they usually require to run an unaffordable number of CFD simulations to develop the study. To face this problem, Non-Intrusive Uncertainty Quantification (UQ) has been applied to 3D Reynolds-Averaged Navier-Stokes simulations of an under-expanded jet from an aircraft exhaust with the Spalart-Allmaras turbulent model, in order to assess the impact of inaccuracies and quality in the simulation. To save a large number of computations, sparse grids are used to compute the integrals and built surrogates for UQ. Results show that some regions of the jet plume can be more sensitive than others to variance in both physical and turbulence model parameters. The Spalart-Allmaras turbulent model is demonstrated to have an accurate performance with respect to other turbulent models in RANS, LES and experimental data, and the contribution of a large variance in its parameter is analysed. This investigation explicitly outlines, exhibits and proves the details of the relationship between diverse sources of input uncertainty, the sensitivity of different quantities of interest to said uncertainties and the spatial distribution arising due to their propagation in the simulation of the high-speed jet flow. This analysis represents first numerical study that provides evidence for this heuristic observation

Inherent and model-form uncertainty analysis for CFD simulation of synthetic jet actuators

A mixed aleatory (inherent) and epistemic (model-form) uncertainty quantification (UQ) analysis method was applied to a computational fluid dynamics (CFD) modeling problem of synthetic jet actuators. A test case, (Case 3, flow over a hump model with synthetic jet actuator control) from the CFDVAL2004 workshop was selected to apply the Second-Order Probability framework implemented with a stochastic response surface obtained from Quadrature-Based Non-Intrusive Polynomial Chaos (NIPC). Three uncertainty sources were considered: (1) epistemic uncertainty in turbulence model, (2) aleatory uncertainty in free stream velocity and (3) aleatory uncertainty in actuation frequency. Uncertainties in both long-time averaged and phase averaged quantities were quantified using a fourth order polynomial chaos expansion (PCE). Results were compared with experimental data available. A global sensitivity analysis with Sobol indices was utilized to rank the importance of each uncertainty source to the overall output uncertainty. The results indicated that for the long-time averaged separation bubble size, the uncertainty in turbulence model had a dominant contribution, which was also observed in the long-time averaged skin friction coefficients at three selected locations. For long-time averaged pressure coefficient, the contributions from free stream velocity and turbulence model are depending on the locations. The mixed UQ results for phase averaged x-velocity distributions at three selected locations showed that the 95% confidence intervals (CI) could generally envelope the experimental data. The Sobol indices showed that near the wall, the turbulence model had a main influence on the x-velocity, while approaching the main stream, the uncertainty in free stream velocity became a larger contributor. The uncertainty in frequency was found to have a very small contribution to both long-time averaged and phase averaged quantities with the range of variance considered --Abstract, page iii

Conception aérodynamique robuste

Les études aérodynamiques s'appuient en grande partie sur quelques grandeurs d'intérêt comme la traînée ou la portance. Il est donc primordial d'avoir divers outils et stratégies adaptés au calcul efficace de telles observations scalaires. Cette thèse est dédiée au développement de méthodologies efficaces et innovantes destinées à renforcer la maîtrise d'une grandeur d'intérêt. Trois types de stratégie ont été étudiés. L'évaluation consiste à estimer à faible coût de calcul l'évolution de la fonction lorsqu'un paramètre d'entrée varie. En ce sens, les dérivées premières et surtout secondes, obtenues par différentiation automatique des codes industriels, renseignent sur le comportement local de l'observation (tangentes et courbures). La méthode des perturbations singulières est une alternative innovante pour estimer une évolution non linéaire sans faire appel aux dérivées secondes. La fiabilité est destinée à renforcer le niveau de confiance qu'il est possible d'accorder à la valeur d'observation calculée. La prise en compte des incertitudes affectant certains paramètres d'entrée va rendre le calcul d'observation robuste et donc plus fiable. Enfin, l'optimisation permet de trouver des valeurs particulières de l'observation répondant à un certain nombre de contraintes. L'optimisation sous incertitude permet de déterminer les solutions robustes à l'aléa impactant notre fonctionnelle, en s'appuyant pour cela sur des grandeurs statistiques (moment ou probabilité de défaillance).Aerodynamic studies are often based on some numerical observations like the drag or lift coefficients. Consequently, it is fundamental to define tools and methodologies devoted to the reliable evaluation of these scalar observations. This master thesis will describe some strategies and methods in order to better control the computation of a scalar aerodynamic observation. Three classes of strategies have been considered. The evaluation strategy consists in determining the kind of evolution of the observation depending on parameters. In this context, the estimation of the first and especially second order sensibilities, obtained by automatic differentiation of industrial codes, allows us to know the local evolution (tangents and curvatures). The singular perturbation method is another and innovant method to determine the non-linear evolution of an aerodynamic observation without using the second order derivatives. The fiability strategy will try to increase the level of confidence in the numerical evaluation of the scalar aerodynamic observation. The uncertainty affecting some parameters that influence the scalar observation is taken into account in order to make the numerical evaluation more robust and reliable. Finally, the optimisation strategy consists in finding particular values of the aerodynamic observation which respects some constraints. The optimisation under uncertainty means that optimisation parameters are uncertain, that is to say constraints are statistical variables, like statistical moments or failure probabilities

Reduced order methods for laminar and turbulent flows in a finite volume setting: projection-based methods and data-driven techniques

This dissertation presents a family of Reduced Order Models (ROMs) which is specifically designed to deal with both laminar and turbulent flows in a finite volume full order setting. Several aspects associated with the reduction of the incompressible Navier\u2013Stokes equations have been investigated. The first of them is related to the need of an accurate reduced pressure reconstruction. This issue has been studied with the help of two main approaches which consist in the use of the Pressure Poisson Equation (PPE) at the reduced order level and also the employment of the supremizer stabilization method. A second aspect is connected with the enforcement of non-homogeneous Dirichlet boundary conditions at the inlet boundary at the reduced order level. The solutions to address this aspect include two methods, namely, the lifting function method and the penalty method. Different solutions for the treatment of turbulence at the reduced order level have been proposed. We have developed a unified reduction approach which is capable of dealing with turbulent flows based on the Reynolds Averaged Navier\u2013Stokes (RANS) equations complemented by any Eddy Viscosity Model (EVM). The turbulent ROM developed is versatile in the sense that it may be applied on the FOM solutions obtained by different turbulent closure models or EVMs. This is made possible thanks to the formulation of the ROM which merges projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields. The newly proposed turbulent ROM has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to Re 10 to 5

Uncertainty quantification of turbulence model closure coefficients for transonic wall-bounded flows

The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-ω Model, and the Menter Shear-Stress Transport Model. The FUN3D code developed by NASA Langley Research Center and the BCFD code developed by The Boeing Company were used as the flow solvers. The uncertainty quantification analysis employed stochastic expansions based on non-intrusive polynomial chaos as an efficient means of uncertainty propagation. Several integrated and point-quantities are considered as uncertain outputs for both CFD problems. All closure coefficients were treated as epistemic uncertain variables represented with intervals. Sobol indices were used to rank the relative contributions of each closure coefficient to the total uncertainty in the output quantities of interest. Two studies were performed in this work. The main study identified a number of closure coefficients for each turbulence model for which more information will reduce the amount of uncertainty in the output significantly for transonic, wall-bounded flows. A case study demonstrated that the RAE 2822 sensitivity results of the main study are independent of the flow solver and of the computational grid topology and resolution --Abstract, page iii