Fig 12 - uploaded by Christophe Bailly
Content may be subject to copyright.
Jet at M = 2:0 and T j /T o = 2:8, acoustic directivity in decibels as a function of the outlet angle µ: ——, Mach-wave model (17); – – – , Goldstein–Howes model (16); and – -– , Ribner's model (10): ¦ , Seiner et al. 33 data.
Source publication
Subsonicandsupersonicjetnoiseisdeterminednumerically from statisticalsourcemodels.Thegoalistodevelop prediction methods for high-speed jet noise for application to aeronautical and space transportation systems. In this framework, a combination of a k-≤ turbulence closure with an acoustic analogy provides an interesting way to compute such radiated...
Similar publications
The scattering of harmonic sound waves by a single vortex is studied to provide some insight into the more complex problem of sound scattering by a turbulent layer. Two different methods are used to model the scattering by a steady vortex or by a vortex convected in a uniform mean flow. The first method is based on the linearized Euler equations in...
Citations
... In the past, most of the efforts of improvements have focused in finding a proper description of the source correlation term by modelling the sound stemming from fluid dilatation [3,4], from the quadrupole correlations arising in isotropic turbulence [5][6][7] or those from more complex shell models of turbulence [8][9][10]. The definition of the source term and its associated wave equation is also a critical step [11][12][13]. ...
... where the source term presented in Eq. (6) has been reduced to its main contribution provided by Reynolds stress tensor. A drastic simplification of the source term is considered in Tam and Auriault [4] by contracting the instantaneous Reynolds stress tensor 0 ⊗ ≈ , where is linked to the turbulent kinetic energy and is the identity matrix. ...
... Choosing a self-adjoint operator such as Pierce's wave equation (6) to compute the radiation of sound has two major advantages. Along with ensuring the conservation of the acoustic energy, and thus preventing the development of instability waves, this feature enables the computation of adjoint solutions to Pierce's wave equation (9) by making use of the flow reversal theorem (FRT). ...
... Acoustic spectra are now commonly inferred from a RANS solution of the jet flow, and involve the subtle combination of many ingredients. Among these are the choice of an acoustic analogy such as Lighthill's [2], Lilley's [3], LEE [4], GAA [5], or based on Pierce's equation [6]; the calibration [7] [8] and the modelling of the sound source intercorrelation with for instance a Gaussian function [9] [10], an exponential function [7] or a hyperbolic cosine function [11]. The choice of a fixed [5] or moving [7] reference frame for the source modelling; the account of the source convection [1] [12]; the taking into account of the source compactness [13] as well as the choice of a turbulence model for the source [14] [3] [15] [16] are other parameters to be set. ...
... In the developed region, that is for ≳ 8 the slope of the computed characteristic length matches with the reference solution inferred from the LES solution. The characteristic time scale of Tam and Auriault's mixing noise model is rebuilt subsequently using equation (11). ...
Tam and Auriault's statistical mixing noise model has been reformulated by the authors so to be able to compute propagation effects with help of Pierce's wave equation, that is fairly accurate and acoustic preserving. This study presents predictions computed with this model for the sound emitted by two Mach 0.9 round jets. One is isolated, the other one is installed beneath a flat plate. Tailored adjoint Green's functions are computed using the finite element solver Actran TM. The methodology is able to retrieve acoustic measurements within 2 dB for a range of Strouhal numbers of more than two orders of magnitude. For an observer located close to the jet axis, at polar angle smaller than = 50°, poorer predictions are obtained however. It is found that Tam and Auriault's mixing noise model designed for the radiation of the turbulence fine scales does not radiate isotropically but peaks instead around = 45°. Tailored adjoint Green's functions computed for the isolated and installed configuration demonstrate the ability of the proposed methodology to account for propagation effects due to the flow and the presence of surfaces.
... However, these simulations are computationally very expensive. An alternative approach involves a steady-state RANS solution to predict the TBL parameters [27,28]. Researchers have shown an increased interest in using RANS. ...
A hybrid uncorrelated wall plane wave (UWPW) and finite element method (FEM) technique is introduced to the predict vibroacoustic response of a panel under turbulent boundary layer (TBL) excitation. The spectrum of the wall pressure fluctuations is evaluated from the TBL parameters and by using semi-empirical models from literature. TBL parameters can be estimated by different means, using theoretical formula, Reynolds-averaged Navier Stokes (RANS) simulations or experimental data. The wall pressure field (WPF) underneath the TBL is then synthesized by realisations of uncorrelated wall plane waves. The FEM is employed to compute the structural and acoustic responses of the panel for each realisation of uncorrelated wall plane waves. The responses are then obtained from an ensemble average of the different realisations. Selection criteria for cut-off wavenumber, mesh size and number of realisation are discussed. Two simply-supported baffled panels under TBL excitation are examined. Numerical results are compared with analytical results using the sensitivity functions of the panels, showing excellent agreement.
... 3 (Béchara et al., 1995), (Bailly et al., 1996), (Bailly et al., 1997), (Bodard et al., 2009), (Henry et al., 2012), (Martelet et al., 2019). ...
La question de dissocier le champ acoustique du champ aérodynamique, étroitement liée à celle de la définition adéquate des sources de bruit, reste une question ouverte d'une grande importance pratique en aéroacoustique. En proposant une analogie acoustique construite sur le potentiel acoustique, cette étude veut contribuer à la construction d'un modèle de prédiction du bruit de jet, qui soit robuste et pragmatique pour des applications de l'industrie aéronautique. Le formalisme de l'adjoint utilisé dans le calcul de la propagation du son, recours au principe de réciprocité, et est réalisé indépendamment des sources de bruit. Ce formalisme est le seul capable de modéliser le rayonnement acoustique de l'air éjecté par un turboréacteur, lorsque cet écoulement est calculé par les équations de Navier-Stokes moyennés et n'est connu que de manière statistique.Le modèle statistique du bruit de mélange turbulent de Tam et Auriault (1999) est le premier à recourir à une approche adjointe de ce type. Ce travail reformule pour le potentiel acoustique ce modèle emblématique, et compare le modèle de propagation proposé, basée sur l'équation de Pierce (1990), au modèle original utilisé par Tam et Auriault (1998). Un accord satisfaisant est trouvé entre les deux approches.Contrairement à la formulation de Tam et Auriault, l'équation d'onde pour l'acoustique potentielle conserve l'énergie acoustique et ainsi ne présente pas de couplage avec le mode hydrodynamique généralement instable. La formulation proposée prend de plus en compte l'effet de la présence des surfaces dans le calcul de la propagation acoustique. Le calcul de la solution réciproque par retournement d'écoulement représente une alternative plus intuitive et plus simple à mettre en œuvre que la méthode de l'adjoint. Ce travail montre que cette approche simplifiée ne s'applique que pour des opérateurs auto-adjoints comme l'équation de Pierce retenue. Pour démontrer la viabilité opérationnelle de la méthode, la solution adjointe à l'équation de Pierce pour une configuration réaliste de turboréacteur a été calculée à l'aide du code commercial Actran TM. Des champ adjoints correspondant à une propagation en champ proche et en champ lointain sont présentés.Dans le modèle considéré, le champ acoustique est linéaire, dérive d'un potentiel et se propage autour d'un écoulement moyen quelconque. La théorie peut être réécrite à l'aide du formalisme des rayons exacts (Foreman, 1989), et coïncide ainsi avec les cas limites de l'acoustique potentielle et de l'acoustique géométrique; soit avec les deux seuls cas pour lesquels l'acoustique peut être définie sans ambivalence. De surcroît, ce travail réécrit les équations d'Euler sous une forme originale et fournit une équation d'onde très générale sur la seule variable de la vitesse.
... 3 (Béchara et al., 1995), (Bailly et al., 1996), (Bailly et al., 1997), (Bodard et al., 2009), (Henry et al., 2012), (Martelet et al., 2019). ...
The issue of properly distinguishing the acoustic field from the aerodynamic field, which is in close relation with that of the adequate definition of noise sources, remains an open question of great practical importance in aeroacoustics. By proposing an acoustic analogy built on the acoustic potential, this study intends to contribute to the construction of a prediction model for jet noise, that is robust and pragmatic with respect to the context of the aeronautical industry. The adjoint formalism used in the calculation of the sound propagation is based on the reciprocity principle, and is carried out independently of noise sources. This formalism is the only one capable of modelling the acoustic radiation of the air ejected by an aircraft engine, at a reasonable computational cost, when this flow is obtained by Reynolds averaged Navier-Stokes (RANS) equations and is only known statistically.
The statistical model of turbulent mixing noise of Tam and Auriault (1999) is the first to use an adjoint approach of this kind. This work reformulates this emblematic model for the acoustic potential, and compares the proposed model, based on the equation of Pierce (1990), with the original propagation model that Tam and Auriault (1998) used. A satisfactory agreement is found between the two approaches. Unlike in Tam and Auriault’s formulation, the wave equation for the acoustic potential conserves the acoustic energy and therefore does not present any coupling with the entropic mode nor with the hydrodynamic mode, that is possibly unstable. The proposed formulation also takes into account the effect of the presence of surfaces in the calculation of acoustic propagation. The calculation of the reciprocal solution by flow reversal represents a more intuitive and easier to implement alternative to the adjoint method. This work shows that this simplified approach is applicable only for self-adjoint operators such as Pierce’s wave equation that has been selected. To demonstrate the operational viability of the method, the adjoint solution to Pierce’s equation for a realistic turbofan engine configuration is calculated using the commercial code Actran TM. Adjoint fields corresponding to near-field and far-field propagation are presented.
In the model considered, the linear acoustic field is obtained from a potential scalar function and propagates around an arbitrary mean flow. The theory can be rewritten using the exact ray formalism (Foreman, 1989), and thus coincides with the two limiting cases of potential acoustics and geometric acoustics, the only cases in which acoustics can be defined without ambivalence. Furthermore, Euler’s equations are recast in an original form in this study and provides a very general wave equation based solely on the velocity variable.
... Acoustical characteristics of a similar free jet were discussed by Freund [29] under cold conditions. The directional dependence of such an acoustic source was described by Bailly et al. [30]. Combustion acoustics and its modeling was excellently reviewed by Candel et al. [31]. ...
Swirl burners are widely used in numerous practical applications since they are characterized by low pollutant emission and a wide operating range. Besides reliable operation, a burner must fulfill noise emission regulations, which is often a sound pressure level in dB(A) when people are affected. Therefore, the present paper evaluates the overall sound pressure level (OASPL) variation of a 15-kW liquid-fueled turbulent atmospheric swirl burner at various setups. Firstly, the combustion air flow rate was adjusted, which induced a swirl number modification due to the fixed swirl vanes. Secondly, the atomizing pressure of the plain-jet airblast atomizer was modified, which also affected the swirl number. High atomizing air jets notably increased combustion noise by intensifying the shear layer. Thirdly, a geometrical modification was performed; 0°–60° half cone angle quarls in 15° steps were installed on the lip of the baseline burner for extended flame stability. By filtering the OASPL to the V-shaped flames, a linearly decreasing trend was observed as a function of swirl number. Their derivative also has a linearly decreasing characteristic as a function of the atomizing pressure.
... However, the applications of noise prediction from correlation quantities have been widely attempted. Based on Ribner's model, Bailly et al. 6 proposed a prediction method ...
In a turbulent jet, the numerical investigation of space-time correlations $C(r,\tau)$ at two-point and two-time of streamwise fluctuating velocities is presented along the nozzle lipline. Large-eddy simulation (LES) is performed for a Mach $0.9$ turbulent jet issuing from a round nozzle. The turbulent boundary layer is well developed at the nozzle outlet, upon the inner wall, by adopting synthetic turbulent inlet boundary conditions. We study the cross-correlations of streamwise fluctuating velocities at three particular streamwise positions, i.e. $x=0.71,7.03$ and $34.47r_0$, corresponding to different stages of jet development, where $r_0$ is the radius of the nozzle. Present results show that the classical Taylor's frozen-flow model is unable to predict $C(r,\tau)$ accurately in this strongly spatially developing shear flow since the distortion of flow pattern is missing. The isocorrelation contours of the $C(r,\tau)$ show a clearly elliptical feature, which is found to be well predicted by the elliptic approximation (EA) model [He \& Zhang, PRE, 73, 055303 (2006)]. According to the EA model, the $C(r,\tau)$ has a scaling form of $C(r_E,0)$ with two characteristic velocities $U$ and $V$, i.e. $r_E = (r-U\tau)^2+V^2\tau^2$. By examining LES data, it is found that the characteristic velocity $U$ determined in LES is in general consistent with the theoretical $U_t$ in EA model, while the trend of $V$ in LES also matches with that of theoretical $V_t$. Additionally, it is interesting that the ratio of $V$ and $V_t$ is approximately a constant $V/V_t\simeq1.3$ in the turbulent jet.
... Ribner's work [43] on separating the two-point space-time correlation function forms the basis of many statistical jet noise models. A combination of such a model with a CFD mean-flow field has been used by Mani et al. [44], Bechara [45], Bailly [46,47], Khavaran [48,49,50,51], Frendi [52] etc. Some of these works assumed isotropic flow where the use of a single characteristic length-scale and time-scale is justified to describe the spatial and temporal decay rate of the velocity correlation, respectively. ...
Hybrid tools based on Reynolds Averaged Navier-Stokes (RANS) and Computational Aero-Acoustics (CAA) methods have been the current focus of industries to aid the design and development of quieter nozzles with novel configurations for future aircraft. In the current work, improvements to a RANS-based jet noise prediction method are proposed. The source model is based on Lighthill’s acoustic analogy and ray theory (geometric acoustics) is used to compute the propagation effects. The method is named, Lighthill Ray Tracing, ‘LRT’. In this thesis, improvements within the RANS informed source and propagation model are proposed. These improvements are applied to a wide range of nozzle geometries, both single stream and coaxial stream, with varying flow conditions. The LRT predictions are validated against experimental data. All RANS-based jet noise methods include model coefficients associated with eddy length-scales and time-scales. Computation of these model coefficients are dependent on measured acoustic spectrum at the 90o polar angle, thus making it difficult to predict noise from new conceptual nozzles. The current work focuses on arriving at a formalism to determine the RANS-associated length-scale and time-scale coefficients with reduced dependency on experimental data. This procedure is used to perform a parametric study on isothermal single stream and coaxial stream nozzles with varying geometry and flow parameters. Effect of velocity ratio, area ratio, bypass ratio and the effect of the primary nozzle in different noise producing regions of the nozzle are investigated. Along with the LRT method, the 4-source semi empirical ESDU noise prediction program has been extensively used to perform a characterisation study of far-field noise from ultra high bypass ratio (UHBR) nozzles. The study showed that noise from nozzles with higher area ratios can be modelled using a single equivalent jet. RANS-based prediction methods coupled with ray theory have been proven to be computationally fast and capable of providing good jet noise predictions. While the use of real rays to calculate propagation effects is not new, the calculation of so-called complex rays - that allow for the modelling of mevanescent waves - is typically not accounted fornin generic ray programmes. This presents serious shortcomings when dealing with highspeed jets, where high-frequency waves refract away from the downstream axis giving rise to a region exclusive to complex rays commonly referred to as the cone of silence (CoS). In the current work, two methods are proposed to model the field in the CoS. The first method is based on modelling the exponential decay using an approximate WKB solution for a parallel shear flow; the second method exploits the canonical nature of the cone of silence boundary to continue solutions inside the CoS via a complex ray embedded inside the Airy function and its derivative. To demonstrate both methods, the results are compared against Lilley’s Green’s function solution for a parallel shear flow using a variety of parametric studies. The first method is applied to an isothermal single stream jet and the noise predictions at the CoS angles are compared with experimental data.
... The upper limit of integration is chosen to minimise the low-correlation noise. The proportionality coefficients that relate the models to the integral scales are assumed to be fixed for a range of jet conditions [12,24,32]. ...
This paper investigates the broadband shock-associated noise (BBSAN) radiated from supersonic jets at the rootsource level. The sources are modeled according to an acoustic analogy. The acoustic-analogy model is informed byhigh-spatial-resolution two-dimensional two-component particle image velocimetry (PIV) data and solutions to theReynolds-averaged Navier–Stokes (RANS) equations for the reconstruction of the equivalent BBSAN sources. Themeasurements are of screeching underexpanded jets issuing from a purely converging nozzle at ideally expandedMach numbers of 1.45 and 1.59. The jet conditions are simulated using a RANS solver with a k − ω shear-stress-transport turbulence model. The RANS scales are modeled using formulations of a two-timescale model based on theturbulence dissipation and large-eddy-convection time. The large-eddy-convection-based scale is recommended as areplacement for the standard turbulence-dissipation scale in low-order BBSAN models. The equivalent BBSANsources are reconstructed from the PIV measurements and RANS solutions at the peak Strouhal number. Theequivalent BBSAN sources extracted from the PIV and RANS data are shown to have a favorable agreement.
... Several theories based on acoustic analogies derived by Lighthill [5] directly relate the pressure fluctuations and the noise intensity to fourth-order velocity correlations and the eddy convective velocity. Bailly et al. [6] summarize the relevant aspects with regards to the convective amplification factor for models by Ribner, Goldstein-Howes and Ffowcs Williams and Maidanik [7]. In all models the convective Mach number, based on the eddy convective velocity, can be identified as a driver of the produced noise intensity and, similarly, the radiation efficiency [1]. ...
The noise generated by supersonic plumes is of growing concern given the enormous peak noise intensity radiated by tactical aircraft engines. A key component of this noise is the enhanced radiation of mixing noise caused by large scale eddies convecting supersonically relative to the surrounding quiescent medium. As very little data exist for eddy convection in high Reynolds number, supersonic plumes, our current ability to develop concepts that alter compressible eddy convection is limited. Herein we present new experimental data of eddy convective wavespeeds in the developing shear layer of supersonic heated jets. A new scaling of the wavespeed in radial similarity coordinates is proposed which takes into account the influence of the ratio of static densities between the jet and ambient streams. In particular, we observe a structural change in wavespeed spectra at the end of the potential core—in addition to high turbulence levels, the potential core breakdown region can have enhanced eddy wavespeeds, increasing noise radiation efficiency. The results provide a first examination of the interplay of density ratio effects and the dynamic breakdown process of the potential core in supersonic jets—physics integral to the noise generation process.
