Uncertainty Quantification for Airfoil Icing using Polynomial Chaos Expansions

The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a large amount of uncertainty in aerodynamic performance metrics (e.g., stall angle of attack). The main focus of this work concerns using the techniques of Polynomial Chaos Expansions (PCE) to quantify icing uncertainty much more quickly than traditional methods (e.g., Monte Carlo). First, we present a brief survey of the literature concerning the physics of wing icing, with the intention of giving a certain amount of intuition for the physical process. Next, we give a brief overview of the background theory of PCE. Finally, we compare the results of Monte Carlo simulations to PCE-based uncertainty quantification for several different airfoil icing scenarios. The results are in good agreement and confirm that PCE methods are much more efficient for the canonical airfoil icing uncertainty quantification problem than Monte Carlo methods.Comment: Submitted and under review for the AIAA Journal of Aircraft and 2015 AIAA Conferenc

Multigrid solution of the Navier-Stokes equations on triangular meshes

A Navier-Stokes algorithm for use on unstructured triangular meshes is presented. Spatial discretization of the governing equations is achieved using a finite element Galerkin approximation, which can be shown to be equivalent to a finite volume approximation for regular equilateral triangular meshes. Integration steady-state is performed using a multistage time-stepping scheme, and convergence is accelerated by means of implicit residual smoothing and an unstructured multigrid algorithm. Directional scaling of the artificial dissipation and the implicit residual smoothing operator is achieved for unstructured meshes by considering local mesh stretching vectors at each point. The accuracy of the scheme for highly stretched triangular meshes is validated by comparing computed flat-plate laminar boundary layer results with the well known similarity solution, and by comparing laminar airfoil results with those obtained from various well-established structured quadrilateral-mesh codes. The convergence efficiency of the present method is also shown to be competitive with those demonstrated by structured quadrilateral-mesh algorithms

Towards full molecular gas dynamics simulations of complex flows via the Boltzmann equation

This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation has generally limited its application to simpler, two-dimensional flow problems. Utilizing a combination of high-order spatial discretizations and discretely-conservative velocity models along with their highly-efficient implementation on massively-parallel GPU computing architectures, we demonstrate the current ability of directly solving the Boltzmann equation augmented with the BGK collision model for complex, three-dimensional flows. Numerical results are presented for a variety of these problems including rarefied microchannels, transitional and turbulent flows, and high-speed atmospheric re-entry vehicles, showcasing the ability of the approach in accurately predicting complex nonlinear flow phenomena and non-equilibrium effects.Comment: 14 pages, 9 figures, Cambridge Unsteady Flow Symposiu

Outcomes in the emergency endovascular repair of blunt thoracic aortic injuries

Abstract Thoracic aorta blunt injury (BAI) is a highly lethal lesion. A large number of victims die before obtaining emergency care. Thoracic endovascular aneurysm repair (TEVAR) is a less invasive method compared with open surgery and may change protocols for BAI treatment. This retrospective study was developed to evaluate the potential issues about thoracic endografting in the management of these patients. Twenty-seven patients with a BAI underwent aortic stent grafting. Intervention was preceded by the treatment of more urgent associated lesions in nine cases. In-hospital mortality was 7.4%. No paraplegia or ischemic complications developed because of the coverage of the left subclavian artery. In one case (3.2%), a type I endoleak was detected, proximal endograft infolding in two cases (7.4%) and endograft distal migration in further two cases were detected during follow-up (6-110 months). Thoracic endovascular aneurysm repair of BAI showed encouraging results in terms of perioperative mortality and morbidity. Concerns still remain about the potential mid- and long-term complications in younger patients

Endoscopic vein harvesting Impact of learning curve on results and rehabilitation

Background: The tendency of modern surgery is towards the reduction of invasiveness. The aim of this study is to evaluate the impact of the learning curve, the reliability, the short term results and the advantages in terms of rapid rehabilitation of endoscopic vein harvesting (EVH) in a consecutive series of 20 patients operated on of aorto-coronary bypass surgery. Methods: Between February and June 2005, 20 patients between 61 e 82 years of age underwent EVH with the use of Vasoview® 5 (Guidant Corporation, Indianapolis, USA). To evaluate the impact of learning curve on the total operative time, patients were divided in 4 chronologically consecutive groups (G1, G2, G3, G4). Intraoperative characteristics and short term results were evaluated. Results: The mean velocity and the mean time of harvesting in G4 were 0,68 cm/min and 45 min. respectively, similar to the time required for a scheletonized left internal mammary artery harvesting. In the first 5 patients 2 conversions were required, one of them related to the EVH technique. No bleeding, functional impairment or infective complications are reported. Active mobilization was possible in every case in the first post-operative day. Conclusions: EVH is a reliable technique and the learning curve can be limited to the first 5 cases. The foreseeble reduction of infectious complications, the absence of pain and the immediate mobilization of the leg allow a rapid and effective rehabilitation

A positivity-preserving and conservative high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation

In this work, we present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation augmented with a discrete velocity model that ensures the scheme is discretely conservative. Through modeling the internal degrees of freedom, the approach is further extended to polyatomic molecules and can encompass arbitrary constitutive laws. The approach is validated on a series of large-scale complex numerical experiments, ranging from shock-dominated flows computed on unstructured grids to direct numerical simulation of three-dimensional compressible turbulent flows, the latter of which is the first instance of such a flow computed by directly solving the Boltzmann equation. The results show the ability of the scheme to directly resolve shock structures without any ad hoc numerical shock capturing method and correctly approximate turbulent flow phenomena in a consistent manner with the hydrodynamic equations.Comment: 31 pages, 20 figure

The Second Moment of the Pion Light Cone Wave Function

We present a preliminary result for second moment of the light cone wave function of the pion. This parameter is the subject of a discrepancy between theoretical predictions (coming from lattice and sum rules) and a recent experimental result (that remarkably agrees with purely perturbative predictions). In this work we exploit lattice hypercubic symmetries to remove power divergences and, moreover, implement a full 1-loop matching for all the contributing operators.Comment: 3 pages, proceedings of the Lattice 2002 conferenc

Validation of wall boundary conditions for simulating complex fluid flows via the Boltzmann equation: Momentum transport and skin friction

The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational cost of directly solving the Boltzmann equation has limited the extent of numerical validation studies to simple, often two-dimensional, flow problems. Recent algorithmic advancements for the Boltzmann--BGK equation introduced by the authors, consisting of a high-order spatial discretization augmented with a discretely-conservative velocity model, have made it feasible to accurately simulate unsteady three-dimensional flow problems across both the rarefied and continuum regimes. This work presents a comprehensive evaluation and validation of wall boundary conditions across a variety of flow regimes, primarily for the purpose of exploring their effects on momentum transfer in the low Mach limit. Results are presented for a range of steady and unsteady wall-bounded flow problems across both the rarefied and continuum regimes, from canonical two-dimensional laminar flows to unsteady three-dimensional transitional and turbulent flows, the latter of which are the first instances of wall-bounded turbulent flows computed by directly solving the Boltzmann equation. We show that approximations of the molecular gas dynamics equations can accurately predict both non-equilibrium phenomena and complex hydrodynamic flow instabilities and show how spatial and velocity domain resolution affect the accuracy. The results indicate that an accurate approximation of particle transport (i.e. high spatial resolution) is significantly more important than particle collision (i.e. high velocity domain resolution) for predicting flow instabilities and momentum transfer consistent with that predicted by the hydrodynamic equations and that these effects can be computed accurately even with very few degrees of freedom in the velocity domain.Comment: 34 pages, 36 figure