Marco Fossati

Evaluation of Aerodynamic Loads via Reduced-Order Methodology

Centroidal Voronoi tessellation, leave-one-out cross validation, proper orthogonal decomposition, and multidimensional interpolation are integrated to define a reduced-order modeling approach for the parametric evaluation of steady aerodynamic loads. The proper orthogonal decomposition-based methodology allows reducing the number of degrees of freedom of the problem while maintaining good accuracy for the solution of complex three-dimensional viscous turbulent flows. As a result, it yields fairly accurate solutions at a fraction of the time required by standard computational fluid dynamics approaches. Three-dimensional examples for fixed- and rotary-wing cases of industrial relevance are used to assess the method in the cases of subsonic and transonic flow conditions.

Local Reduced-Order Modeling and Iterative Sampling for Parametric Analyses of Aero-Icing Problems

A framework of local reduced-order modeling using machine learning algorithms is presented together with an approach to optimally select the snapshots for strongly nonlinear problems. By using an unsupervised learning algorithm, solutions are grouped into clusters of similar features. The input parameter space is divided into subregions by decision boundaries based on a supervised learning algorithm. Local reduced-order bases are extracted on each cluster, for which the solutions are represented as a linear combination of the basis vectors from their corresponding subregion. The proposed methodology is employed to conduct a comprehensive, exploration of the in-flight icing certification envelopes.

Kinetic Node-Pair Formulation for Two-Dimensional Flows from Continuum to Transitional Regime

A hybrid finite-element/finite-volume node-pair discretization of conservation laws is reformulated in terms of a Bhatnagar–Gross–Krook kinetic scheme to address flows from the continuum up to the transitional regime in a seamless fashion. Integrals of the particle distribution function from the kinetic theory of gases are adopted to compute the numerical fluxes along the boundary of each control volume. Flow features typical of the transitional regime like velocity and temperature slip condition at solid walls are automatically assured by the kinetic formulation of the node-pair boundary conditions. Exemplary two-dimensional numerical experiments ranging from continuum flows up to the transitional regime are presented.

Simulation of Supercooled Large Droplet Impingement via Reduced Order Technology

A IRCRAFT flying through clouds of supercooled liquid droplets (SLD) can be subjected to in-flight ice accretion. Surface tension prevents the expansion of the droplets that would occur with phase change, forcing them to remain in liquid form even though their temperature is below the freezing point. When the droplets hit an aircraft’s surfaces, the surface tension decreases at the contact point, and theymay freeze completely on impact if the temperature is very low or freeze partially at higher temperatures, whereas the remaining liquid portion runs back on the surface, transported by the pressure gradient and the shear stress of the airflow. If no ice protection is provided, the aerodynamic characteristics of the aircraft and its handling can be severely degraded when ice accretes. The increased drag generated by the roughness of the ice can lead to flow separation, reduction of the stall margins, control reversals, and engine blockages [1]. Airworthiness of transport airplanes in icing conditions is demonstrated by compliance with certification standards (Appendix C of the FAA Federal Aviation Regulations, part 25) set by agencies, such as the Federal Aviation Administration, European Air Safety Association, Transport Canada, etc. These standards, frozen for 50 years, will soon undergo significant revisions with the adoption of Appendix O to address the icing threat posed by SLD conditions. Unlike smaller droplets, SLD can distort, break into smaller droplets, splash, bounce off surfaces, get carried downstream by the flow, and reimpinge, increasing the potential for ice contamination on unprotected surfaces [2–4]. Nowadays, wind tunnel tests, icing tunnel tests, and computer simulations play major complementary roles in the process of certifying a new aircraft [5,6]. Advances in modeling capabilities have created the conditions to accurately simulate the ice accretion process in a realistic three-dimensional (3-D) context [7,8]. Unfortunately, the computational cost associated with performing a multitude of 3-D simulations of various aeroicing conditions somewhat limits the widespread use of computational fluid dynamics (CFD), even if advanced computational resources are available [9,10]. To overcome this difficulty, mostly low-cost and, consequently, low-fidelity tools are usually employed. These may be based on empirical correlations, two-dimensional (2-D) approximations, inviscid or incompressible flow assumptions, and/or other simplifications that result in limited accuracy and realism. A viable alternative is the reduced-order modeling (ROM) approach [11,12], which dramatically reduces the cost of highfidelity simulations while providing solutions of superior accuracy to low-fidelity methods because it preserves the detailed physical modeling of the problem under consideration [13–16]. Although the use of this approach in the aeroicing environment is in its pioneering phase, recent results support the effectiveness of this methodology as a valuable tool in the context of a multicondition, multiparameter certification process [17–20]. In a framework of ice accretion simulation as the succession of airflow, water concentration, and heat transfer calculations, the most time-consuming part is obtaining the water impact patterns. The common practice is to assume a distribution of discrete droplet diameters, compute the impingement distribution of each diameter class, andweight-average thesemonodispersed solutions. In the case of the droplet sizes of Appendix C, seven distinct monodispersed sizes (Langmuir-D distribution) are used to compute the overall impingement distribution. In the SLD regime, however, due to the complex phenomena of droplet breakup, splashing, and bouncing, distributions containing up to 27 diameters of monodispersed droplets are needed to obtain realistic impingement predictions [5–7]. The computational cost of an SLD simulation is hence four times that of a Langmuir-D distribution. In the presentwork, it will be shown that the ROM approach can dramatically reduce cost with only a very modest degradation of the overall accuracy of the simulation. The essentials of the ROM approach used to extract the solution eigenfunctions (or modes) and compute solutions at unknown states are introduced in sections II and III of this paper, whereas section IV illustrates the interpolation technique used to compute the surrogate solutions. Finally, 2and 3-D results and comparison with experiments and other methods are presented to validate the present methodology. Received 29 July 2011; revision received 14 September 2011; accepted for publication 15 September 2011. Copyright

Real-Time Regional Jet Comprehensive Aeroicing Analysis via Reduced-Order Modeling

This paper presents a reduced-order modeling framework based on proper orthogonal decomposition, multidimensional interpolation, and machine learning algorithms, along with an error-driven iterative sampling method, to adaptively select an optimal set of snapshots in the context of in-flight icing certification. The methodology is applied, to the best of our knowledge for the first time, to a complete aircraft and to the entire icing certification envelope, providing invaluable additional data to those from icing tunnels or natural flight testing. This systematic methodology is applied to the shape/mass of ice and to the aerodynamics penalties in terms of lift, drag, and pitching moments. The level of accuracy achieved strongly supports the drive to incorporate more computational fluid dynamics information into in-flight icing certification and pilot training programs, leading to increased aviation safety.

Quasi-molecular modeling of supercooled large droplets dynamics for in-flight icing simulations

A fine-scale model of Supercooled Large Droplets dynamics is proposed based on a quasi-molecular approach, a meso-scale method that mimics the interaction between quasimolecules within a single liquid droplet. Each quasi-molecule is a combination of a large number of real molecules which are considered to be an ensemble. The goal is to simulate the deformation and the splashing processes of a droplet to obtain a better understanding of the dynamics of large droplets collisions with aircraft at realistic flight conditions in order to refine the macroscopic Eulerian description of the process.

An Eulerian re-impingement model of splashing and bouncing supercooled large droplets

A purely Eulerian numerical approach to track secondary droplets resulting from the bouncing and splashing of supercooled large droplets is proposed. Different models have been analyzed on the basis of their ability to provide initial conditions for the re-injected mass. The numerical method is evaluated for clean and iced NACA 23012 geometries in SLD conditions. Tests are performed to compare the accuracy of the proposed method with other numerical methods and icing tunnel experiments. Improvement is observed in the accuracy of the impingement limits, as well as the local collection efficiency, compared to other models. No improvement is seen in the prediction of local collection efficiency for severely contaminated geometries, and an analysis of potential influencing factors is reported.

Numerical modeling and simulation of supersonic flows in propulsion systems by open-source solvers

Two open-source solvers, Eilmer and hyFoam, are here considered for their performance in simulating high-speed flows in different flow conditions and geometric configurations typical of propulsive systems at supersonic speeds. The goal is to identify the open-source platform providing the best compromise between accuracy, flexibility and computational cost to eventually simulate the flow fields inside ramjet and scramjet engines. The differences in terms of discretization and solution methods of the selected solvers are discussed in terms of their impact on solution accuracy and computational efficiency and in view of the aerothermodynamic analysis and design of future trans-atmospheric propulsive systems. In this work steady state problems are considered. Numerical results of two scramjet type engines demonstrated a similar predictive capability of both codes in non-reacting conditions. These results highlight their potential to be considered for further characterization of overall engine performance.

Development of a Jacobian-free finite element solver for aerothermodynamic design

Within the context of hypersonic flight, a finite element solver is introduced on the basis of a Jacobian-free implementation with the aim to address an arbitrary number of species with complex non-equilibrium thermodynamics in a computationally efficient and flexible manner. An adaptive edge-based formulation is proposed to define a general framework for the accurate solution of the conservation laws. Numerical and physical difficulties specific to high-speed flows are addressed for 2D and 3D cases.

Finite-Element Formulation of a Jacobian-free Solver for Supersonic Viscous Flows on Hybrid Grids

A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.