The present investigation of aerofoil self-noise generation and propagation concerns the effects of mean flow and quadrupole sources on the broadband noise that arises from the interaction of turbulent boundary layers with the aerofoil trailing edge and the tonal noise that arises from vortex shedding generated by laminar boundary layers and trailing-edge bluntness. Compressible large-eddy simulations (LES) are conducted for a NACA0012 aerofoil with rounded trailing edge for four flow configurations with different angles of incidence, boundary layer tripping configurations and free-stream Mach numbers. The Reynolds number based on the aerofoil chord is fixed at ${\mathit{Re}}_{c} = 408\hspace{0.167em} 000$. The acoustic predictions are performed by the Ffowcs Williams & Hawkings (FWH) acoustic analogy formulation and incorporate convective effects. Surface and volume integrations of dipole and quadrupole source terms appearing in the FWH equation are performed using a three-dimensional wideband multi-level adaptive fast multipole method (FMM) in order to accelerate the calculations of aeroacoustic integrals. In order to validate the numerical solutions, flow simulation and acoustic prediction results are compared to experimental data available in the literature and good agreement is observed in terms of both aerodynamic and aeroacoustic results. For low-Mach-number flows, quadrupole sources can be neglected in the FWH equation and mean flow effects appear only for high frequencies. However, for higher speeds, convection effects are relevant for all frequencies and quadrupole sources have a more pronounced effect for medium and high frequencies. The convective effects are most readily observed in the upstream direction.

SUMMARYThis work describes the implementation and analysis of high-order accurate schemes applied to highspeed flows on unstructured grids. The class of essentially non-oscillatory schemes (ENO), that includes weighted ENO schemes (WENO), is discussed in the paper with regard to the implementation of thirdand fourth-order accurate methods. The entire reconstruction process of ENO and WENO schemes is described with emphasis on the stencil selection algorithms. The stencils can be composed by control volumes with any number of edges, e.g. triangles, quadrilaterals and hybrid meshes. In the paper, ENO and WENO schemes are implemented for the solution of the dimensionless, 2-D Euler equations in a cell centred finite volume context. High-order flux integration is achieved using Gaussian quadratures. An approximate Riemann solver is used to evaluate the fluxes on the interfaces of the control volumes and a TVD Runge-Kutta scheme provides the time integration of the equations. Such a coupling of all these numerical tools, together with the high-order interpolation of primitive variables provided by ENO and WENO schemes, leads to the desired order of accuracy expected in the solutions. An adaptive mesh refinement technique provides better resolution in regions with strong flowfield gradients. Results for high-speed flow simulations are presented with the objective of assessing the implemented capability.

No abstract

In many complex aerospace applications, it is common to use numerical tools to evaluate the unsteady aerodynamic behavior. The present work presents an alternate formulation for the state-space representation of aeroelastic systems based on digital control theory that is shown to be more effective and accurate for the coupling of numerical solutions with such systems. The application of the z transform allows for direct frequency domain representations of the aerodynamic solutions without the need for approximating models, as generally occurs in other state-space formulations. This fact also makes this new methodology a more straightforward procedure for aeroelastic analyses. A typical section model of a NACA 0012 airfoil at transonic flow conditions is used as a test case to assess the correctness and accuracy of the proposed formulation. The present results are compared with data obtained from continuous-time state-space formulations and through the direct integration of the aerodynamic and structural dynamic equations.

A practical high resolution upwind differencing scheme for the numerical solution of convection-dominated transport problems is presented. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite difference methodology. The performance of the scheme is investigated by solving the 1D/2D scalar advection equations, 1D inviscid Burgers’ equation, 1D scalar convection–diffusion equation, 1D/2D compressible Euler’s equations, and 2D incompressible Navier–Stokes equations. The numerical results displayed good agreement with other existing numerical and experimental data