Letteratura scientifica selezionata sul tema "Time-Harmonic convected acoustics"

The NPE (nonlinear progressive wave equation) and associated computer program is a time-domain representation of acoustic propagation in waveguides that includes the effect of nonlinearity. In that approach a spatial window is initialized with the original waveform and then convected in the primary propagation direction as time evolves. Previous work modified NPE by using cylindrical coordinates to describe a paraxial approximation suitable for axisymmetric sound beams. The present development further modifies NPE by using spherical coordinates. The matter of interfacing it with the cylindrical coordinate version, in order to describe the far field of a sound beam, is described. This simulation technique is used to evaluate the long range propagation of the signal radiating from a piston in an infinite baffle that is subjected to harmonic excitation. It is also applied to a focussed sound beam generated by transient excitation of a concave projector. Comparison of the results with experimental data shows good overall agreement, with the main source of error apparently being due to dissipation, which is not addressed in the present models.

A mathematical model is formulated to describe the initiation and evolution of intense unsteady vorticity in a low Mach number (M), weakly viscous internal flow sustained by mass addition through the sidewall of a long, narrow cylinder. An O(M) axial acoustic velocity disturbance, generated by a prescribed harmonic transient endwall velocity, interacts with the basically inviscid rotational steady injected flow to generate time-dependent vorticity at the sidewall. The steady radial velocity component convects the vorticity into the flow. The axial velocity associated with the vorticity field varies across the cylinder radius and in particular has an instantaneous oscillatory spatial distribution with a characteristic wavelength O(M) smaller than the radius. Weak viscous effects cause the vorticity to diffuse on the small radial length scale as it is convected from the wall toward the axis. The magnitude of the transient vorticity field is larger by O(M−1) than that in the steady flow.An initial-boundary-value formulation is employed to find nonlinear unsteady solutions when a pressure node exists at the downstream exit of the cylinder. The complete velocity consists of a superposition of the steady flow, an acoustic (irrotational) field and the rotational component, all of the same magnitude.

Abstract We analyse the convergence of finite element discretizations of time-harmonic wave propagation problems. We propose a general methodology to derive stability conditions and error estimates that are explicit with respect to the wavenumber $k$. This methodology is formally based on an expansion of the solution in powers of $k$, which permits to split the solution into a regular, but oscillating part, and another component that is rough, but behaves nicely when the wavenumber increases. The method is developed in its full generality and is illustrated by three particular cases: the elastodynamic system, the convected Helmholtz equation and the acoustic Helmholtz equation in homogeneous and heterogeneous media. Numerical experiments are provided, which confirm that the stability conditions and error estimates are sharp.

Gas turbine combustors are often susceptible to self-excited oscillations, which lead to unacceptable levels of pressure, velocity, and heat release fluctuations. Although instabilities can occur in systems with locally constant equivalence ratio, it is very important to take into account the influence of equivalence ratio fluctuations, which are generated in the fuel air mixer in the unstable case. These fluctuations are convected into the flame and lead to an additional mechanism for the generation of heat release fluctuations. Moreover, entropy waves are produced in the flame, which travel through the combustor and generate additional pressure waves during the acceleration of the flow at the combustor exit. To date, available theories use the physically unrealistic assumption that the equivalence ratio waves as well as the entropy waves are convected downstream without any spatial dispersion due to the combustor aerodynamics. An analytical approach is presented, which allows us to take the spatial dispersion into consideration. For that purpose, the response of the burner and the combustor to an equivalence ratio impulse or an entropy impulse is calculated using the Laplace transformation and a more general transfer function for harmonic waves is derived. The obtained expression has three parameters, which represent the influence of the burner or the combustor aerodynamics, respectively. This equation can be used in numerical codes, which represent the combustion system through a network of acoustic multiports, if the equivalence ratio and the entropy are added to the vector of variables considered. The parameters required for the dynamic combustor model can be deduced from a detailed CFD analysis of the combustor flow in case of the application of the theory to a particular combustor design. As an example, a simple model combustor is used to demonstrate the application of the theory. It is highlighted how the spatial dispersion of the equivalence ratio and entropy fluctuations can be included in the stability analysis. The calculated examples reveal that the influence of both variables on the generation of instabilities is highly overpredicted if the spatial dispersion is not taken into account. Furthermore, it can be deduced from the study that burner and combustor designs with a wide range of convective time scales have advantages with respect to the stability of the combustor.

The generation of a viscous–inviscid instability through scattering of an acoustic wave by localised and distributed roughness on the upper surface of a NACA 0012 aerofoil is studied with a time-harmonic compressible adjoint linearised Navier–Stokes approach. This extends previous work by the authors dedicated to flat plate geometries. The key advancement lies in the modelling of the inviscid acoustic field external to the aerofoil boundary layer, requiring a numerical solution of the convected Helmholtz equation in a non-uniform inviscid field to determine the unsteady pressure field on the curved aerofoil surface. This externally imposed acoustic pressure field subsequently drives the acoustic boundary layer, which fundamentally determines the amplitudes of acoustic-roughness receptivity. A study of receptivity in the presence of Gaussian-shaped roughness and sinusoidally distributed roughness at Mach number $M_\infty =0.4$ and Strouhal numbers $\mathcal {S} \approx \{46,69,115\}$ shows the effects of various parameters, most notably angle of attack, angle of incidence of the externally imposed plane acoustic wave and geometry of surface roughness; the latter is varied from viewpoint of its placement on the aerofoil surface and its wavelength. The parametric study suggests that non-parallel effects are quite substantial and that considerable differences arise when using parallel flow theory to estimate the optimal width of Gaussian-shaped roughness elements to provoke the greatest response. Furthermore, receptivity amplitudes for distributed roughness are observed to be generally higher for lower angles of attack, i.e. for less adverse pressure gradients. It is also shown that the boundary layer is more receptive to upstream-travelling acoustic waves.

An approximate analytical method is described for determining the sound produced by a class of complex fluid-structure interactions in low Mach number flows. This can be used to model noise sources in practical systems, and to check the accuracy of predictions based on time accurate numerical solutions of the Navier-Stokes equations. The dominant acoustic sources are dipoles whose strengths are dependent on the unsteady surface forces, and are expressed in terms of fluid velocity and vorticity, and a set of harmonic functions determined by the shapes of the structural elements interacting with the flow. (The theory of surface forces for arbitrary motion of a rigid body in viscous, incompressible flow in the presence of a fixed system of boundaries is discussed in an appendix.) These elements can influence both the generation and propagation of sound, and are frequently sources of new vorticity shed into wakes. The procedure is illustrated by application to a model problem in which sound is generated by a vortex interacting with a shrouded rotor in a duct. High-frequency sound is generated when the vortex is draw n into the rotor disc and ‘chopped’ by the blades. Sound is also produced through indirect blade-vortex interactions which, in this case, occur as a result of unsteady blade loadings produced when the core of the vortex is close to the leading edge of the shroud. This is relatively low-frequency sound and is the only component of blade-vortex interaction noise when the vortex is convected through the gap between the shroud and wall of the duct.

Ce travail de thèse est consacré aux méthodes de décomposition de domaine de Schwarz sans recouvrement pour la résolution de problèmes industriels hautes fréquences d'acoustique en écoulement. Les méthodes de résolution en régime harmonique sont difficiles à paralléliser en raison de leur caractère oscillatoire, si bien que les méthodes actuelles sont limitées par une fréquence maximale, imposée par la mémoire disponible de l'ordinateur. Les méthodes de Schwarz sans recouvrement divisent le domaine en sous-domaines d'un point de vue continu et fournissent un cadre approprié en vue d'une parallélisation à mémoire distribuée. Le problème est résolu de manière itérative sur les inconnues d'interface, où la convergence rapide repose sur des conditions de transmission appropriées. La première partie de cette thèse est consacrée à la conception d'opérateurs de transmission adaptés à la propagation d'ondes harmoniques en milieu convecté et hétérogène. Dans ce cadre nous étudions deux catégories de conditions aux limites non-réfléchissantes qui fournissent des approximations locales de l'opérateur Dirichlet-to-Neumann. Dans un premier temps, des conditions aux limites absorbantes sont conçues basées sur l'analyse microlocale et le calcul pseudodifférentiel. Dans un second temps, la problématique de la stabilité acoustique en écoulement des couches parfaitement adaptées est abordée pour des domaines convexes par la transformation de Lorentz. La deuxième partie de cette thèse étend une méthode générique de décomposition de domaine à des problèmes d'acoustique en écoulement, et applique les conditions de transmission préalablement étudiées à des problèmes académiques simples. Nous expliquons le lien entre la méthode de Schwarz sans recouvrement et une factorisation algébrique LU par blocs du problème. Enfin, nous proposons une mise en œuvre parallèle et montrons l'intérêt de l'approche au rayonnement acoustique tridimensionnel de l'avant d'un turboréacteur d'avion
This PhD project is devoted to non-overlapping Schwarz domain decomposition methods for the resolution of high frequency flow acoustics problems of industrial relevance. Time-harmonic solvers are difficult to parallelize due to their high-oscillatory behaviour, and current solvers quickly reach an upper frequency limit dictated by the available computer memory. Non-overlapping Schwarz methods split the domain into subdomains at the continuous level and provide a suitable setting for distributed memory parallelization. The problem is solved iteratively on the interface unknowns, where the keystone for quick convergence relies on appropriate transmission conditions. The first part of this thesis is devoted to the design of transmission operators tailored to convected and heterogeneous time-harmonic wave propagation. To this end we study two non-reflecting boundary techniques that provide local approximations to the Dirichlet-to-Neumann operator. On the one hand, Absorbing Boundary Conditions are designed based on microlocal analysis and pseudodifferential calculus. On the other hand, the convected acoustic stability issue is addressed for Perfectly Matched Layers in convex domains with Lorentz transformation. The second part of this thesis describes how to adapt a generic domain decomposition framework to flow acoustics, and applies the newly designed transmission conditions to simple academic problems. We explain the relation between the non-overlapping Schwarz formulation and an algebraic block LU factorization of the problem. Finally we propose a parallel implementation of the method and show the benefit of the approach for the three-dimensional noise radiation of a high by-pass ratio turbofan engine intake

Gas turbine combustors are often susceptible to self excited oscillations, which lead to unacceptable levels of pressure, velocity and heat release fluctuations. Although instabilities can occur in systems with locally constant equivalence ratio, it is very important to take into account the influence of equivalence ratio fluctuations, which are generated in the fuel air mixer in the unstable case. These fluctuations are convected into the flame and lead to an additional mechanism for the generation of heat release fluctuations. Moreover, entropy waves are produced in the flame, which travel through the combustor and generate additional pressure waves during the acceleration of the flow at the combustor exit. To date, available theories use the physically unrealistic assumption that the equivalence ratio waves as well as the entropy waves are convected downstream without any spatial dispersion due to the combustor aerodynamics. An analytical approach is presented, which allows to take the spatial dispersion into consideration. For that purpose, the response of the burner and the combustor to an equivalence ratio impulse or an entropy impulse is calculated using the Laplace transformation and a more general transfer function for harmonic waves is derived. The obtained expression has three parameters, which represent the influence of the burner or the combustor aerodynamics, respectively. This equation can be used in numerical codes, which represent the combustion system through a network of acoustic multiports, if the equivalence ratio and the entropy are added to the vector of variables considered. The parameters required for the dynamic combustor model can be deduced from a detailed CFD analysis of the combustor flow in case of the application of the theory to a particular combustor design. As an example, a simple model combustor is used to demonstrate the application of the theory. It is highlighted how the spatial dispersion of the equivalence ratio and entropy fluctuations can be included in the stability analysis. The calculated examples reveal that the influence of both variables on the generation of instabilities is highly overpredicted if the spatial dispersion is not taken into account. Furthermore, it can be deduced from the study, that burner and combustor designs with a wide range of convective time scales have advantages with respect to the stability of the combustor.