Large eddy simulations of isolated and installed jet noise using the high-order discontinuous Galerkin method

A recently developed computational framework for jet noise is used to compute the noise generated by an isolated and installed jet. The framework consists of two parts. In the first part, the spectral/hp element framework Nektar++ is used to compute the near-field flow. Nektar++ solves the unfiltered Navier-Stokes equations on unstructured grids using the high-order discontinuous Galerkin method. The discrete equations are integrated in time using an implicit scheme based on the matrix-free Newton-GMRES method. In the second part, the Antares library is used to compute the far-field noise. Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time domain using a source-time dominant algorithm. The simulations are validated against experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton. For the isolated jet, good agreement is achieved, both in terms of the flow statistics and the far-field noise. The discrepancies observed for the isolated jet are believed to be caused by an under-resolved boundary layer in the simulations. For the installed jet, the flow statistics are also well predicted. In the far-field, very good agreement is achieved for downstream observers. For upstream observers, some discrepancies are observed for very high and very low frequencies

Aeroacoustic analysis of a closely installed chevron nozzle jet using the high-order discontinuous Galerkin method

In this paper, we use Large Eddy Simulations (LES) in combination with the Ffowcs Williams - Hawkings method to study the influence of chevrons on the flow field as well as the noise produced by a closely installed M = 0.6 jet. The LES simulations are performed with the spectral/hp element framework Nektar++. Nektar++ uses the high-order discontinuous Galerkin method and an implicit scheme based on the matrix-free Newton-GMRES method to discretize the unfiltered Navier-Stokes equations in space and time, respectively. The far-field noise is computed using Antares. Antares solves the Ffowcs Williams - Hawkings equation for a permeable integration surface in the time-domain using a source-time dominant algorithm. The aerodynamic results show good agreement with experimental data obtained in the Doak Laboratory Flight Jet Rig, located at the University of Southampton. Some discrepancies are observed in terms of the far-field noise levels, especially for higher polar observer angles relative to the downstream jet axis. In terms of noise reduction potential, the simulations predict that the chevrons reduce the OASPL by 1dB compared to an installed round nozzle for all observers located on the unshielded side of the wing. This should be compared to the experiments, which predict a 1.5dB noise reduction for the same chevron nozzle

Variational multiscale stabilization and local preconditioning for compressible flow

This thesis is about the stabilization of the numerical solution of the Euler and Navier- Stokes equations of compressible flow. When simulating numerically the flow equations, if no stabilization is added, the solution presents non-physical (but numerical) oscillations. For this reason the stabilization of partial differential equations and of the fluid dynamics equations is of great importance. In the framework of the so-called variational multiscale stabilization, we present here a stabilization method for compressible flow. The method assessment is done first of all on a batch of academical examples for different Mach numbers, for viscous and inviscid, steady and transient flow. Afterwards the method is applied to atmospheric flow simulations. To this end we solve the Euler equations for dry and moist atmospheric flow. In the presence of moisture a set of transport equations for water species should be solved as well. This domain of application is a real challenge from the stabilization point of view because the correct amount of stabilization must be added in order to preserve the physical properties of the atmospheric flow. At this point, in order to even improve our method, we turn towards local preconditioning. Local preconditiong permits to reduce the stiffness problems that present the flow equations and cause a bad and slow convergence to the solution. With this purpose in mind we combine our stabilization method with local preconditioning and present a stabilization method for the preconditioned Navier-Stokes equations of compressible flow, that we call P-VMS. This method is tested over several examples at different Mach numbers and proves a significant improvement not only in the convergence to the solution but also in the accuracy and robustness of the method. Finally, the benefits of P-VMS are theoretically assessed using Fourier stability analysis. As a result of this analysis a modification on the computation of the time step is done even improving the convergence of the method.Aquesta tesi tracta sobre l'estabilització de la solució numèrica de les equacions d'Euler i Navier-Stokes de flux compressible. Quan es simulen numèricament les equacions que governen els fluids, si no s'afegeix cap estabilització, la solució presenta oscil·lacions no físiques sinó numèriques. Per aquest motiu l'estabilització de les equacions en derivades parcials i de les equacions de la mecànica de fluids és de gran importància. Dins del marc de l'anomenada estabilització de multiescales variacionals, presentem aquí un mètode d'estabilització per flux compressible. L'evaluació del mètode es realitza primer en varis exemples acadèmics per diferents nombres de Mach, per flux viscós, inviscid, estacionari i transitori. Després el mètode s'aplica a simulacions de flux atmosfèric. Per això, resolem les equacions d'Euler per flux atmosfèric sec i humit. En presència d'humitat, també s'ha de resoldre un grup d'equacions de transport d'espècies d'aigua. Aquest domini d'aplicació representa un desafiament des del punt de vista de l'estabilització, donat que s'ha d'afegir la quantitat adequada d'estabilització per tal de preservar les propietats físiques del flux atmosfèric. Arribat aquest punt, per tal de millorar el nostre mètode, ens interessem pels precondicionadors locals. Els precondicionadors locals permeten reduir els problemes de rigidesa que presenten les equacions dels fluids i que són causa d'una pitjor i més lenta convergència cap a la solució. Amb aquest propòsit en ment, combinem el nostre mètode d'estabilització amb els precondicionadors locals i presentem un mètode d'estabilització per les equacions de Navier-Stokes de flux compressible, anomenem aquest màtode P-VMS. Aquest mètode es evaluat per mitjà de varis exemples per diferents nombres de Mach i demostra una millora sustancial no només pel que fa la convergència cap a la solució, sinó també en la precisió i robusteza del mètode. Finalment els beneficis del P-VMS es demostren teòricament a través de l'anàlisi d'estabilitat de Fourier. Com a resultat d'aquest anàlisi, sorgeix una modificació en el càlcul del pas de temps que millora un cop més la convergència del mètodePostprint (published version

Fourier stability analysis and local Courant number of the preconditioned variational multiscale stabilization (P-VMS) for Euler compressible flow

The results of a Fourier stability analysis of the preconditioned variational multiscale stabilization (P-VMS) method introduced in Moragues et al. (2015) are presented in this paper. P-VMS combines a variational multiscale stabilized finite elements discretization together with local preconditioning. In this work, we deal with the P-VMS method using van Leer-Lee-Roe's (vanLeer et al., 1991) and Choi-Merkle's (Choi and Merkle, 1993) local preconditioners. We solve the Euler equations of compressible flow for steady problems. We concentrate on explicit time integration schemes. The stability analysis is performed on a two dimensional simplified problem with a structured mesh and its conclusions are applied to two and three dimensional general problems with unstructured meshes. As a result of this analysis a local Courant-Friedrichs-Lewy number is defined for the computation of the time step. The convergence rate is evaluated, and compared with the traditional constant Courant-Friedrichs-Lewy number for various test cases spanning a large range of Mach numbers. © 2015 Elsevier B.V.Peer Reviewe