A. Velazquez

Generation of Aerodynamics Databases Using High-Order Singular Value Decomposition

The fast generation of aerodynamic databases is important in the aeronautic industry because of its implication on both the cost and time needed to complete design cycles. This paper presents a method of generating those databases that uses a limited number of computational fluid dynamics computations, thereby saving CPU time. The method is based on a high-order singular value decomposition approach and is able to deal efficiently with complex airfoil flowfields that contain, simultaneously, two shock waves and a large separation region. This feature is critical because methods based on the singular value decomposition approach tend to encounter difficulties when dealing with shock wavelike structures. To illustrate the methodology, the flow around a two-dimensional airfoil is considered at a Reynolds number of 20 ×10 6 with three free parameters, namely, the Mach number, angle of attack, and flap deflection angle in the ranges of 0.4-0.8, -3- + 3 deg, and -5- + 5 deg, respectively. The method is robust in the sense that it is able to deal with very different flow topologies. Also, it is expected that it will contribute to significant savings in CPU time in aerodynamic database generation activities.

VISCOUS–INVISCID METHOD FOR THE SIMULATION OF TURBULENT UNSTEADY WIND TURBINE AIRFOIL FLOW

Abstract A Viscous–inviscid interaction method is presented that allows for the simulation of unsteady airfoil flow in the context of wind turbine applications. The method couples a 2-D external unsteady potential flow to a 2-D unsteady turbulent boundary layer. The separation point on the airfoil leeward side is determined in a self-consistent way from the boundary-layer equations, and the separated flow region is modelled independently. Wake shape and motion are also determined in a self-consistent way, while an unsteady Kutta condition is implemented. The method is able to deal with attached flow and light stall situations characterised by unsteady turbulent boundary-layer separation size up to 50% of the airfoil chord length. The results of the validation campaign show that the method could be used for industrial design purposes because of its numerical robustness, reasonable accuracy, and limited computational time demands.

Reduced-Order Model for Viscous Aerodynamic Flow Past an Airfoil

A method is presented to obtain reduced-order models of multiparametric, steady, transonic aerodynamic flows around two-dimensional airfoils. The method is based on proper orthogonal decomposition and appropriate projection on the proper orthogonal decomposition manifold of the governing equations and boundary conditions, and it includes various ingredients that are new in this field. Proper orthogonal decomposition modes are obtained from a set of snapshots calculated by computational fluid dynamics based on the compressible Navier―Stokes equations and a turbulence model, but projection on the proper orthogonal decomposition manifold is made using the inviscid Euler equations, which makes the method independent of the computational fluid dynamics scheme; projection is made using only a limited number of mesh points, obtaining quite good results. Shock waves are treated specifically in the proper orthogonal decomposition description, to avoid the need of using a too-large number of snapshots. The method is checked and discussed on a specific aerodynamic problem.

Numerical simulation of unsteady aerodynamics effects in horizontal-axis wind turbines

Abstract This paper deals with the numerical simulation of unsteady aerodynamics effects in horizontal-axis wind turbines. In particular, an unsteady three-dimensional potential method is presented whose aim is to predict time-dependent forces and moments on wind turbines operating in a field environment. The algorithm structure is such that the wake is not prescribed; instead, its shape and motion are obtained self-consistently from the solution of the problem. Flow separation effects are not considered. Once the mathematical formulation is discussed, the results of the solver validation campaign, including a parametric sensitivity study of the solutions, are presented. Then, the solver is applied to a practical case involving a wind turbine specifically constructed to collect unsteady aerodynamics data. It is found that the comparison between experimental data and computed results shows a good agreement. Finally, conclusions are drawn.

Reduced-Order Modeling of Three-Dimensional External Aerodynamic Flows

AbstractA method is presented to construct computationally efficient reduced-order models (ROMs) of three-dimensional aerodynamic flows around commercial aircraft components. The method is based on the proper orthogonal decomposition (POD) of a set of steady snapshots, which are calculated using an industrial solver based on some Reynolds averaged Navier-Stokes (RANS) equations. The POD-mode amplitudes are calculated by minimizing a residual defined from the Euler equations, even though the snapshots themselves are calculated from viscous equations. This makes the ROM independent of the peculiarities of the solver used to calculate the snapshots. Also, both the POD modes and the residual are calculated using points in the computational mesh that are concentrated in a close vicinity of the aircraft, which constitute a much smaller number than the total number of mesh points. Despite these simplifications, the method provides quite good approximations of the flow variables distributions in the whole computa...

Vortex-induced vibration of a prism in internal flow

In this article, we study the influence of solid-to-fluid density ratio m on the type of vortex-induced oscillation of a square section prism placed inside a two-dimensional channel. We assume that the solid body has neither structural damping nor spring restoring force. Accordingly, the prism equation of motion contains only inertia and aerodynamics forces. The problem is considered in the range of Reynolds numbers Re ∈ [50 200] (based on the prism cross-section height h ) and channel widths H = H ′/ h ∈ [2.5 10]. We found that, for each Re and H , there is a critical mass ratio m c that separates two different oscillation regimes. For m > m c , the prism oscillation is periodical and contains a single harmonic. For m m c , the prism oscillation changes completely and assumes an irregular pattern that is characterized by multiple harmonics that appear to belong to a uniform spectrum. The change from one regime to the other is abrupt and we were not able to observe a transitional regime in which the number of response harmonics grew by finite steps. The value of the critical mass ratio grows along with the Reynolds number and the channel width.

Numerically robust 3-D finite element Reynolds Averaged Navier-Stokes solver for the study of turbulent supersonic external flows

Abstract A 3-D finite element Reynolds Averaged Navier-Stokes solver for supersonic flows is presented and described. The solver has been developed to target industrial aerodynamics applications in the field of reusable launcher design and, therefore, specific emphasis has been put on maximizing numerical robustness. To achieve this goal, the turbulence model can be chosen beforehand between two options: a k -e formulation or a combined algebraic/ k -e scheme that gets the best characteristics out of both formulations. In addition, to ensure quick convergence in the early stages of the time-marching procedure, a theoretical analysis is performed to gather and implement into the algorithm the limiting behavior of k and e wherever turbulent production is dominant. Results of the validation campaign are presented, a practical application case is shown, and finally, conclusions are drawn.

Finite point based numerical study on the unsteady laminar wake behind square cylinders

Purpose – The purpose of this paper is to present numerical study on the behaviour of 2D unsteady incompressible laminar wakes behind square cylinders.Design/methodology/approach – The numerical method that has been developed is based on a finite point formulation characterised by its weak connectivity requirements. This formulation allows for a patched unstructured approach to computational domain modelling that is of interest for industrial applications. Time evolution of pressure is computed by using a pseudo‐compressibility relaxation model that is based on physical considerations.Findings – This model is characterised by the fact that no sub‐iterations on a numerical pseudo‐time are required so that computational efficiency is increased. Algorithm stability requires the use of second and fourth order artificial viscosity operators that effectively change the order of the equations. A discussion is included regarding the boundary conditions for these operators that do not influence vortex shedding beh...

Aeronautic Conceptual Design Optimization Method Based on High-Order Singular Value Decomposition

Anoptimizationmethod for conceptual design in aeronautics is presented that is based on a genetic algorithm. The various ingredients in the target function are calculated for each individual using surrogates of the associated technical disciplines that are constructed via high-order singular value decomposition and one-dimensional interpolation. These surrogates result from a limited number of computational fluid dynamics calculated snapshots. The resulting method is both flexible and much more computationally efficient than the conventional method based on direct calculation of the target function, especially if a large number of free design parameters and/or tunable modeling parameters are present. Themethod is illustrated considering a simplified version of the conceptual design of an aircraft empennage.

EARSM finite element solver for the study of turbulent 3-D compressible separated flows

A 3-D finite element solver, based on a semi-implicit formulation, that uses an algebraic Reynolds stress turbulence closure is presented. This solver aims to predict separated flow field behavior that typically appears in aerospace applications. In particular, analysis of control device efficiency and base flow/plume interaction of rocket-like configurations are the driving subjects behind this work. Concerning the organization of the paper, a limited review of Reynolds stress models is carried out in the introduction. Then, the numerical algorithm is described and details of the validation campaign are provided. Finally, an application case is presented that deals with the numerical re-building of some of the base flow/plume interaction experiments that have been carried out in the context of the ESA program: FESTIP technology developments in aerothermodynamics for reusable launch vehicles.