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To propose an integrated algorithm for aerodynamic shape optimization of aircraft wings under the effect of aeroelastic deformations at supersonic regime.

A methodology is proposed in which a high‐fidelity aeroelastic analyser and an aerodynamic optimizer are loosely coupled. The shape optimizer is based on a “CAD‐free” approach and an exact gradient method with a single adjoint state. The global iterative process yields optimal shapes in the at‐rest condition (i.e. with the aeroelastic deformations substracted).

The methodology was tested under different conditions, taking into account a combined optimization goal: to reduce the sonic boom production, while preserving the aerodynamic performances of flexible wings. The objective function model contains both aerodynamic parameters and an acoustic term based on the sonic boom downwards emission.

This paper proposes a shape optimization methodology developed by researchers but aiming at the final strategic goal of creating tools that can be really integrated in design processes.

The paper presents an original loosely coupled method for the shape optimization of flexible wings in which recent and modern techniques are used at different levels of the global algorithm: the aerodynamic optimizer, the aeroelastic analyser, the shape parametrization and the objective function model.

The geometric conservation law (GCL) is an important concept for moving grid techniques because it directly regulates the treatments of the fluid flow and grid movement. With the grid movement at every time instant, the Jacobian, associated with the volume of each element in curvilinear co‐ordinates, needs to be updated in a conservative manner. In this study, alternative GCL schemes for evaluating the Jacobian have been investigated in the context of a pressure‐based Navier‐Stokes solver, utilizing moving grid and the first‐order implicit time stepping procedure as well as the PISO scheme. GCL‐based on first and second‐order, implicit as well as time‐averaged, time integration schemes were considered. Accuracy and conservative properties were tested on steady‐state, laminar flow inside a 2D channel and time dependent, turbulent flow around a 3D elastic wing; both treated with moving grid techniques. It seems that the formal order of accuracy is not a decisive indicator. Instead, the speed of grid movement and the interplay between the flow solver and the GCL treatments make a more noticeable impact.

This study aims to feature the application of the artificial compressibility method (ACM) for the numerical prediction of two-dimensional (2D) axisymmetric swirling flows.

The respective academic numerical solver, named IGal2D, is based on the axisymmetric Reynolds-averaged Navier–Stokes (RANS) equations, arranged in a pseudo-Cartesian form, enhanced by the addition of the circumferential momentum equation. Discretization of spatial derivative terms within the governing equations is performed via unstructured 2D grid layouts, with a node-centered finite-volume scheme. For the evaluation of inviscid fluxes, the upwind Roe’s approximate Riemann solver is applied, coupled with a higher-order accurate spatial reconstruction, whereas an element-based approach is used for the calculation of gradients required for the viscous ones. Time integration is succeeded through a second-order accurate four-stage Runge-Kutta method, adopting additionally a local time-stepping technique. Further acceleration, in terms of computational time, is achieved by using an agglomeration multigrid scheme, incorporating the full approximation scheme in a V-cycle process, within an efficient edge-based data structure.

A detailed validation of the proposed numerical methodology is performed by encountering both inviscid and viscous (laminar and turbulent) swirling flows with axial symmetry. IGal2D is compared against the commercial software ANSYS fluent – by using appropriate metrics and characteristic flow quantities – but also against experimental measurements, confirming the proposed methodology’s potential to predict such flows in terms of accuracy.

This study provides a robust methodology for the accurate prediction of swirling flows by combining the axisymmetric RANS equations with ACM. In addition, a detailed description of the convective flux Jacobian is provided, filling a respective gap in research literature.

The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated.

The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion.

Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state.

A complete investigation of the stabilized formulation of the compressible problem is addressed.

To improve flow solutions on meshes with cells/elements which are distorted/ non‐orthogonal.

The cell‐centred finite volume (FV) discretisation method is well established in computational fluid dynamics analysis for modelling physical processes and is typically employed in most commercial tools. This method is computationally efficient, but its accuracy and convergence behaviour may be compromised on meshes which feature cells with non‐orthogonal shapes, as can occur when modelling very complex geometries. A co‐located vertex‐based (VB) discretisation and partially staggered, VB/cell‐centred (CC), discretisation of the hydrodynamic variables are investigated and compared with purely CC solutions on a number of increasingly distorted meshes.

The co‐located CC method fails to produce solutions on all the distorted meshes investigated. Although more expensive computationally, the co‐located VB simulation results always converge whilst its accuracy appears to grace‐fully degrade on all meshes, no matter how extreme the element distortion. Although the hybrid, partially staggered, formulations also allow solutions on all the meshes, the results have larger errors than the co‐located vertex based method and are as expensive computationally; thus, offering no obvious advantage.

Employing the ability of the VB technique to resolve the flow field on a distorted mesh may well enable solutions to be obtained on complex meshes where established CC approaches fail

This paper investigates a range of cell centred, vertex based and hybrid approaches to FV discretisation of the NS hydrodynamic variables, in an effort characterize their capability at generating solutions on meshes with distorted or non‐orthogonal cells/elements.

To outline a transonic wing design problem by applying real coded genetic algorithm (GA) and dynamic mesh technique to reduce the optimization time and cost.

Dynamic mesh technique was used in the design of a transonic wing by matching it with heuristic algorithms.

It is observed that the drag coefficient can be reduced by 25 percent. While this has been done, the lift coefficient is tried to be close to the design value determined at the beginning as a design constraint.

It is the first time that the dynamic mesh technique is used for regenerating the mesh structures of the new population members in the GA.

This paper presents preliminary results of the modeling of a large autonomous quad-rotor airship, with flying wing shape. This airship is supposed to be a flexible body. This study promotes an entirely analytical methodology with some assumptions. In this study and as first assumption, the shape of the careen is supposed to be an elliptic cone. To retrieve the velocity potential shapes, this paper solved the Laplace’s equation by using the sphero-conal coordinates. This leads to the Lamé’s equations. The whole system equations governing the interaction of air–structure, including the boundary conditions, is solved in an analytical setting.

This paper opted for a modeling and determination of the added masses of a flexible airship by an analytical method illustrated by a comparison with a geometric method. This analytical method includes the study of complex functions which are the Lamé functions.

This paper provides an analytical way to estimate an aerodynamic phenomenon which acts on the airship and in particular on its envelope and known as the phenomenon of added masses or virtual masses, as well as the means of defining it and the calculation analytically for the case of the flexible airship.

Considering that the calculation of the added masses is very difficult and the numerical methods increase the number of degrees of freedom, the analytical method established in this paper has become a solution of calculations of these virtual masses.

This paper includes an application for determining the added masses of a new generation MC500 airship.

This paper allows defining an analytical method which determines the added masses of an airship, which helps the automation engineer to develop a control strategy to stabilize this airship.

The purpose of this paper is to investigate a large‐eddy simulation, using low order numerical discretization and upwinding schemes on unstructured grids, for a turbulent free jet at Mach number 0.95. The accuracy and stability performance is discussed for the finite element/volume upwinding numerical code used.

This code is equipped with a self‐adaptive upwinding method which has been previously developed to reduce the numerical dissipation of applied low order flux calculation on unstructured elements using Roe's scheme. Herein, this method is used to numerically investigate a high Reynolds, compressible turbulent free jet and compare the results with a recently published set of experimental data. The effect of grid size is also investigated. A reasonable good agreement with the experimental measurements is obtained.

Based on the results, it is concluded that the developed self‐adaptive upwinding scheme provides a considerably better emulation of the flow regime in comparison to the full‐upwinding scheme. Different case studies have been carried out to assess the performance of self‐adaptive upwinding method and the effect of the subgrid model.

This paper presents an original research on self‐adaptive upwinding scheme and the effect of the subgrid model on a compressible turbulent free jet.

This paper presents a shape optimization problem under acoustic, aerodynamic and geometric constraints. The acoustic specification concerns the generated sonic boom. The aim is to see the validity of incomplete sensitivities when a nonlinear CFD model is coupled with a nonlinear wave transport model to define pressure rise on the ground.

This paper's purpose is to deal with single point and multipoint optimization of an airfoil. The aim of the paper is to discuss optimization in several design points (multipoint optimization) and compare the results with those of optimization at a specified design point.

A gradient‐based method is adopted for optimization and the flow is governed by two dimensional, compressible Euler equations. A finite volume code based on unstructured grid is developed to solve the equations.

Two test cases are studied for an airfoil with initial profile of NACA0012, with two types of design variables. And at the end a multi‐point case is presented.

The advantage of this technique over the other gradient‐based methods is its high‐convergence rate.