Frequency-Domain Linearized Euler Model for Turbomachinery Noise Radiation Through Engine Exhaust

Iob, Andrea; Arina, Renzo; Schipani, Claudia

doi:10.2514/1.j050084

Cited by 26 publications

(10 citation statements)

References 21 publications

(43 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Applying the aforementioned space-time transformations, the Linearised Euler Equations in the PML read [15]:…”

Section: Perfectly Matched Layermentioning

confidence: 99%

See 1 more Smart Citation

A High-Order Finite Element Method for the Linearised Euler Equations

Hamiche¹,

Gabard²,

Bériot³

2016

Acta Acustica united with Acustica

View full text Add to dashboard Cite

SummarySound propagation in complex non-uniform mean flows is an important feature of turbofan exhaust noise radiation. The Linearised Euler Equations are able to represent the strong shear layer refraction effects on the sound field, as well as multiple length scales. Frequency domain solvers are suitable for tonal noise and considered a way to avoid linear instabilities, which may occur with time domain solvers. However, the classical Finite Element Method suffers from dispersion error and high memory requirements. These shortcomings are particularly critical for high frequencies and for the Linearised Euler Equations, which involve up to five unknowns. In this paper, a high-order Finite Element Method is used to solve the Linearised Euler Equations in the frequency domain in order to overcome those issues. The model involves high-order polynomial shape functions, unstructured triangular meshes, numerical stabilisation and Perfectly Matched Layers. The acoustic radiation from a straight circular semi-infinite hard-wall duct with several mean flow configurations is computed. Comparisons with analytic solutions demonstrate the method accuracy. The acoustic and vorticity waves are well represented, as well as the refraction of the sound field across the jet shear layer. The high-order approach allows to use coarse meshes, while maintaining a sufficient accuracy. The benefits in terms of memory requirements are significant when compared to standard low-order Finite Element Method.

show abstract

“…Applying the aforementioned space-time transformations, the Linearised Euler Equations in the PML read [15]:…”

Section: Perfectly Matched Layermentioning

confidence: 99%

“…The PML can also be used to impose the incident wave. In practice, the PML equations are applied to the reflected field only [13,15]: q re = q − q in , where q in is the incident field and q re is the reflected field. The Linearised Euler Equations for incident wave injection in the PML are: 4.…”

Section: Perfectly Matched Layermentioning

confidence: 99%

A High-Order Finite Element Method for the Linearised Euler Equations

Hamiche¹,

Gabard²,

Bériot³

2016

Acta Acustica united with Acustica

View full text Add to dashboard Cite

show abstract

“…In this way it is ensured that the control surface, treated as a permeable closed surface, contains in its interior all the noise sources. For a uniform mean flow of Mach number M and aligned with the z axis, the FW‐H integral can be written, in the frequency domain, for a Cartesian coordinate system as

H ((), f) c_{0} 2 \overset{ρ}{true} ((), bold-italicy MathClass-punc, ω) MathClass-rel= MathClass-bin- {MathClass-op\int}_{σ} normalI ω \overset{Q}{true} ((), bold-italicξ MathClass-punc, ω) G ((), bold-italicy MathClass-punc; bold-italicξ) normald σ MathClass-bin- {MathClass-op\int}_{σ} {\overset{F}{true}}_{i} ((), bold-italicξ MathClass-punc, ω) \frac{∂G ((), bold-italicy MathClass-punc; bold-italicξ)}{\partial y_{i}} normald σ MathClass-punc,

where σ defines the integration surface, ξ are the surface coordinates and y are the listener coordinates. Moreover, considering that the present FW‐H formulation will be applied only to problems where there is no noise contribution because of turbulence, the quadrupole term in Equation is omitted.…”

Section: Ffowcs Williams and Hawkings Formulation Couplingmentioning

confidence: 99%

An efficient discontinuous Galerkin method for aeroacoustic propagation

Rinaldi

Iob

Arina

2011

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARY An efficient discontinuous Galerkin formulation is applied to the solution of the linearized Euler equations and the acoustic perturbation equations for the simulation of aeroacoustic propagation in two‐dimensional and axisymmetric problems, with triangular and quadrilateral elements. To improve computational efficiency, a new strategy of variable interpolation order is proposed in addition to a quadrature‐free approach and parallel implementation. Moreover, an accurate wall boundary condition is formulated on the basis of the solution of the Riemann problem for a reflective wall. Time discretization is based on a low dissipation formulation of a fourth‐order, low storage Runge–Kutta scheme. Along the far‐field boundaries a perfectly matched layer boundary condition is used. For the far‐field computations, the integral formulation of Ffowcs Williams and Hawkings is coupled with the near‐field solver. The efficiency and accuracy of the proposed variable order formulation is assessed for realistic geometries, namely sound propagation around a high‐lift airfoil and the Munt problem. Copyright © 2011 John Wiley & Sons, Ltd.

show abstract

“…Since the analytical solution is available only for points at great distance from the cylinder exit, it is not possible to compare directly the solution of LEE obtained using the DGM with the analytical one. Instead LEE are solved only in a small computational domain, the near-field domain, and then the far-field solution is evaluated for the near-field one using the three-dimensional integral formulation of the wave equation proposed by Ffowcs Williams and Hawkings [Iob et al (2010)]. The far-field results are then compared with the analytical solution.…”

Section: Circular Duct Propagation and Radiationmentioning

confidence: 99%