A coupled time-reversal/complex differentiation method for aeroacoustic sensitivity analysis: towards a source detection procedure

The one- and two-dimensional inviscid Euler equations are formulated in an integro-differential form for shape design sensitivity analysis and optimization. The principal tool employed to derive the performance derivative sensitivity equations is the variational method, which is a continuous alternative to the discrete sensitivity analysis. Along with the sensitivity equations, the co-state equations and their boundary conditions are derived. Thereafter, based on the modal analysis of Von Neumann theory, the stability limits of the co-state equations are investigated. The stability characteristics of the co-state equations are compared with those of the Euler equations. Finally, using the criteria from the stability analysis of the state and co-state equations, some results of shape design optimization and sensitivity analysis for both quasi one- and two-dimensional Euler equations are presented. Copyright © 1999 John Wiley & Sons, Ltd.

The growth that aviation has seen in the last decades has drawn the attention on the environmental impact of aircraft. An important part of this environmental impact is the noise emitted by air vehicles, which is considered rather significant for community annoyance. The generation and propagation of air vehicle noise are two different areas of interest, which require accurate prediction in order to control the emitted noise levels. The present thesis employs numerical methods in order to investigate various air vehicle noise propagation effects. It is divided in two parts: the far field and the near field study. Each of these studies is concentrated on the sound propagation mechanisms that are dominant for each case and uses a numerical method that is best suited for it in terms of mechanisms incorporated and cost effectiveness. The far-field study of this thesis focuses on the nonlinear propagation of helicopter rotor noise using the Burgers equation, a well known one direction propagation method. The Burgers equation incorporates geometrical spreading, atmospheric absorption and nonlinear distortion effects. Towards this study, the HELISHAPE descent case experimental database is used. Blade Vortex Interaction (BVI) noise, the dominant noise contributor during descent, is mainly examined. It is shown that advancing side BVI noise is affected by nonlinear distortion, while retreating side BVI noise is not. For some frequency bands the difference between linear and nonlinear calculations can be as high as 7 dB. Based on signal characteristics at source, two quantities are derived. The first quantity (termed polarity) is based on the pressure gradient of the source signal and can be used to determine whether a BVI signal will evolve as an advancing or a retreating side signal. The second quantity (termed weighted rise time) is a measure of the impulsiveness of the BVI signal and can be used to determine at which frequency nonlinear effects start to appear. Finally, polarity and weighted rise time are shown to be applicable in cases of BVI noise generated from different blade tips, as well as, in cases of non-BVI noise. However, employment of the Burgers equation can be time consuming to be included in routine calculations. It also requires knowledge of the initial pressure time signal. The power spectrum alone, which is usually known, is not sufficient. In order to ii overcome these difficulties, three prediction methods are presented that are based on the Burgers equation. These are: i) a numerically generated database, ii) correlation equations and iii) the phase assignment method. Near field propagation of air vehicle noise requires different treatment than far field. The effects which are mainly affecting the propagation are geometrical spreading, convection and refraction effects due to the flow field, as well as reflections and diffraction on the air vehicle surfaces. Towards these objectives, a new low-order flow/acoustics interaction method for the prediction of sound propagation and diffraction in unsteady compressible flow using adaptive 3-D hybrid grids is investigated. The total field is decomposed into the flow field described by the Euler equations, and the acoustics field described by the Nonlinear Perturbation equations. The method is shown capable of predicting monopole sound propagation, while employment of acoustics-guided adapted grid refinement improves the accuracy of capturing the acoustic field. Interaction of sound with solid boundaries is also examined in terms of reflection and diffraction. Sound propagation through an unsteady flow field is examined using static and dynamic flow/acoustics coupling demonstrating the importance of the latter. Proof of concept for the new method is provided by its application to the case of a conventional jet transport airplane, examining the effect of flow field and wing shielding on the near field noise levels. During the aforementioned noise investigation and analysis, results on Blade Wake Interaction (BWI) noise were also reached. Presently, the mechanism of BWI noise generation, as well as the corresponding prediction model, are still under consideration. Helicopter rotor BWI noise is known to be significant during take-off and level flight, while less attention has been given to descent flight conditions, where BVI noise is dominant. Through signal analysis of the HELISHAPE descent case acoustic database, the rotor azimuthal region responsible for BWI noise is localized and the dominance of BVI noise in the BWI frequency region is shown. Coherence analysis of the blade pressure data indicate significant chordwise coherence in the 3 to 4 Struhal number range and absence of acoustic dipoles in the BWI frequency range. The findings of this study support BWI prediction models based on Amiet’s theory and suggest that BWI noise can be ignored for predictions of rotor noise in descent flight conditions.

There are many approaches to determine the sound propagated from turbulent flows. In hybrid methods, the turbulent noise source field is computed or modeled separately from the far-field calculations. To have an initial and quick estimation of the sound propagation, less computationally intensive methods can be developed using stochastic models of the turbulent fluctuations. In this paper, turbulent mean flow of a two dimensional, compressible, cold-jet at Mach 0.56 is computed using RANS with 2 equation k-e RNG model. The above mean-flow quantities are then used in a stochastic model to generate the details of the turbulent velocity fluctuations. This method is based on the use of classical Langevin equation to model the details of fluctuating flow field superimposed on the averaged computed quantities. The resulting sound field due to the generated unsteady flow is then evaluated using Lighthill's acoustic analogy. Our results are validated by comparing the directivity and the overall sound pressure level (OASPL) magnitudes with the available experimental data. Numerical results show reasonable agreement with the experiments, both in maximum directivity and the magnitude of the OASPL.

The Cauchy–Lagrangian method for numerical analysis of Euler flow

Long range sound propagation is largely affected by the vertical wind and temperature gradients. These gradients are more complicated in areas where the meteorology can be complex, such as: coastal areas, islands, and lake districts. Furthermore, the gradients usually vary as a function of the horizontal distance, for instance at water-land crossings near a coast or a lake. As a result the sound propagation in these areas cannot be calculated with "standard" acoustic models, such as the ISO 9613 or Harmonoise engineering model. By using an advanced meso-scale meteorological model, which is using large-scale weather forecast data, and an acoustical model, that incorporates horizontal and vertical meteorological variations, long range sound propagation in such complex areas is calculated. In this paper we present two applications of this hybrid meteorological-acoustical calculation scheme: i) propagation of impulse noise in a coastal area, and ii) propagation of industrial noise in a rural area with a lake. For the coastal area sound level contours have been calculated as a function of the meteorology for a complete year. For the lake area the effect of the lake on the sound propagation is demonstrated.

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

A self-adaptive Euler equation solver with moving boundary conditions was developed to simulate the aerodynamic effects induced by a high speed train passing through a tunnel. First, a mesh generation method was developed based on the omni-tree grid structure, and a hybrid mesh generation strategy was established based on a structured grid and a Cartesian grid. Then, a three-dimensional numerical solver was constructed based on the Euler equations, and moving boundary conditions were developed in the numerical solver. Taking the absolute value of the pressure gradient as the control parameter, the grid size can be automatically adjusted under the moving boundary condition. The developed numerical solver was used to simulate a train passing through a tunnel, and the pressure time histories at the probes on the tunnel wall were analysed. In addition, moving model rig experiments were performed under the same conditions, and the numerical results and experimental results were compared. The results agreed well, indicating that both the mesh generation strategy and the numerical solver are highly accurate and could be a good choice for simulating tunnel aerodynamic problems in moving boundary conditions.

A low order flow/acoustics interaction method for the prediction of sound propagation using 3D adaptive hybrid grids

The two-dimensional Euler equations have been solved by a finite volume method (FVM). The computational domain is divided into either quadrilateral or triangular cells. Spatial discretization of the Euler equations on each cell yields a system of ordinary differential equations (ODEs) in time. A rational Runge-Kutta (RRK) scheme is used to integrate the system of ODEs. The implicit residual averaging (IRA) and local time step have been employed to accelerate the convergence to a steady state. Numerical solutions are presented for flows past a circular cylinder at Mach 0.38, the NACA 0012 airfoil at Mach 0.8 and an angle of attack of 1.25°, and a channel flow at Mach 0.675. The effects of the shape of control volume and convegence acceleration techniques are investigated by comparing the results with those of the conventional finite difference discretization method (FDM). It is concluded that accuracy and efficiency of the FVM are comparable to those of the FDM.

This article is concerned with research on parallel pro cessing for chemically reactive supersonic flows. Effi ciency of autotasking and microtasking is examined for the problems of linear algebra and two-dimensional Euler equations with the finite element method. For microtasking, satisfactory improvements in speedup (2.63 for 4 CPUs and 1.67 for 2 CPUs) are achieved, with the load balance and the amount of parallelism being the dominant factors for the speedup. Autotask ing has advantages in providing automatic paralleliza tion, but it has been shown that in the solution of finite element Euler equations based on conventional algo rithms, parallelization by means of user's intervention is required for significant speedups (3.35 for 4 CPUs and 1.79 for 2 CPUs). A much better performance may be achieved with a combination of autotasking and microtasking. These results are verified from various example problems of linear algebra and supersonic diffuser flow field calculations with hydrogen-oxygen chemical reactions.

In this article, we prove nonlinear orbital stability for steadily translating vortex pairs, a family of nonlinear waves that are exact solutions of the incompressible, two-dimensional Euler equations. We use an adaptation of Kelvin’s variational principle, maximizing kinetic energy penalised by a multiple of momentum among mirror-symmetric isovortical rearrangements. This formulation has the advantage that the functional to be maximized and the constraint set are both invariant under the flow of the time-dependent Euler equations, and this observation is used strongly in the analysis. Previous work on existence yields a wide class of examples to which our result applies.

A numerical algorithm is presented for solving the two-dimensional flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for an NACA 0012 airfoil in a freestream with Mach numbers of 0.95 and 1.054. Excellent resolution of the shock structures is obtained with the adaptive grid embedding method with significantly fewer grid points than the comparable structured grid.

The propagation of sound in the atmosphere is influenced by meteorological conditions. During computation a detailed description of meteorological conditions takes a lot of time but principally the needed meteorological data are not available in most cases. That is why the sound propagation calculation of common tools, like the German AzB or the Integrated Noise Model, is based on standardised meteorological conditions. The main objective of this study is to quantify the noise level differences between common propagation and propagation considering real weather conditions. Therefore the two important sound propagation effects for free sound propagation (atmospheric attenuation and geometrical spreading) are investigated for sources in higher altitudes. A ray-tracing algorithm is used to model the refractions of sound due to wind, wind gradients, and temperature gradients. The atmospheric attenuation is calculated by ISO 9613-1. The used meteorological conditions based on the parameters, i.e. temperature, wind, and relative humidity, from one year radiosonde measurements taken at the meteorological observatory Lindenberg in Germany. All in all, for long-term periods all these calculated average sound pressure levels and the levels calculated for standardised atmospheric conditions are similar in size. Furthermore, common noise calculations overestimate the meteorological influence on sound propagation slightly.

Chapter 10 - Companion Computer Programs

The present paper reviews and discusses the physical mechanisms of noise generation and reduction in turbulent flows with their applications towards aircraft noise reduction at takeoff and on the approach. This work began in 1948 when Lilley undertook an experimental investigation into the source of jet noise as a necessary precursor to finding methods for the reduction of high speed jet engine noise on civil jet airliners. Westley and Lilley completed this experimental programme in 1951, which included the design of a range of devices for high speed jet noise reduction. It was about this time that similar studies on jet noise were being started elsewhere and in particular by Lassiter and Hubbard in USA. The major contribution to the subject of turbulence as a source of noise came from Sir James Lighthill’s remarkable theory in 1952. In spite of the difficulties attached to theoretical and experimental studies on noise from turbulence, it is shown that with the accumulated knowledge on aerodynamic noise over the past 50 years, together with an optimisation of aircraft operations including flight trajectories, we are today on the threshold of approaching the design of commercial aircraft with turbofan propulsion engines that will not be heard above the background noise of the airport at takeoff and landing beyond 1-2km, from the airport boundary fence.It is evident that in the application of this work, which centres on the physical mechanisms relating to the generation of noise from turbulence and turbulent shear flows, to jet noise, there is not one unique mechanism of jet noise generation for all jet Mach numbers. This author in this publication has concentrated on what appears to be the dominant mechanism of noise generation from turbulence, where the mean convection speeds of the turbulence are subsonic. The noise generated at transonic and supersonic jet speeds invariably involves extra mechanisms, which are only briefly referred to here.