Yann Druon

Nonlinear waves and shocks in a rigid acoustical guide

A model is developed for the propagation of finite amplitude acoustical waves and weak shocks in a straight duct of arbitrary cross section. It generalizes the linear modal solution, assuming mode amplitudes slowly vary along the guide axis under the influence of nonlinearities. Using orthogonality properties, the model finally reduces to a set of ordinary differential equations for each mode at each of the harmonics of the input frequency. The theory is then applied to a two-dimensional waveguide. Dispersion relations indicate that there can be two types of nonlinear interactions either called resonant or non-resonant. Resonant interactions occur dominantly for modes propagating at a rather large angle with respect to the axis and involve mostly modes propagating with the same phase velocity. In this case, guided propagation is similar to nonlinear plane wave propagation, with the progressive steepening up to shock formation of the two waves that constitute the mode and reflect onto the guide walls. Non-resonant interactions can be observed as the input modes propagate at a small angle, in which case, nonlinear interactions involve many adjacent modes having close phase velocities. Grazing propagation can also lead to more complex phenomena such as wavefront curvature and irregular reflection.

A Nonlinear Computational Method for the Propagation of Shock Waves in Aero-engine Inlets Towards a new Model for Buzz-saw Noise Prediction

The nonlinear propagation of finite amplitude acoustic waves in hard-walled guides is treated in the following paper. A convected nonlinear wave equation is derived, and a quasianalytical solution based on axially varying modal amplitudes is presented for a no-flow case. Plane and non-planar finite amplitude wave propagation is investigated, and nonlinear interactions of higher order modes are studied in two-dimensional and three-dimensional cylindrical configurations.

Computational AeroAcoustics of Realistic Co‐Axial Engines

This study, that is relevant from the turbofan engines noise prediction/reduction, aims at CAA‐computing the aft fan noise propagation/radiation of a realistic full‐3D exhaust (with pylon and internal bifurcations), the latter being affected of (i) typical in‐flight (take‐off) thermodynamic conditions and of (ii) a representative fan noise modal content. As for previous studies conducted over baseline geometries, this CAA computation is conducted following the usual hybrid process, where a preliminary aerodynamic calculation provides a heterogeneous steady mean flow on which an acoustic calculation is then conducted A RANS computation is first performed, delivering the stationary jet mean flow characterizing the 3D exhaust in its typical take‐off flight (M∞ = 0.25). A CAA grid (22 blocks, 28 millions cells) is then derived from the CFD one, before the RANS steady jet mean‐flow is interpolated on it. After what the CAA computation is computed, a fan noise mode (26, 1) being emitted at a reduced frequency...

A nonlinear computational method for the propagation of shock waves in ducts: Application to buzz‐saw noise.

A numerical method to compute shock wave propagation in uniform waveguides in 2‐D and 3‐D is presented. The solution is searched under the form of a modal solution of the Kuznetsov equation for which the modal amplitudes of the analytical linear modes are supposed to vary along the duct axis due to nonlinear interactions between the different modes and frequencies. This finally yields to a differential system on the mode amplitudes, which is solved numerically using a standard Runge‐Kutta algorithm for ordinary differential equations after numerical truncation of the modal series. Examples are presented of the nonlinear evolution of the pressure field for a 2‐D waveguide. One important 3‐D application is the so‐called “buzz‐saw” noise occurring for high‐bypass‐ratio turbofan engines, when fan blade tip relative flows exceed the sound velocity. First results on 3‐D simulations for nonlinear propagation of a saw‐tooth waveform spiraling inside a hard‐walled cylindrical will be presented. Extensions of the m...

Buzz‐saw noise : propagation of shock waves in aero‐engine inlet ducts

When high bypass ratio aircraft engines run at takeoff operating conditions, blade relative flow velocities can exceed sonic speed, thus generating forward propagating shock waves that spiral inside the intake before being radiated. “Buzz‐saw” or “multiple pure tone” noise then occurs, and measured acoustic spectra close to the fan display tones at the blade passing frequency and its harmonics, along with those of the engine shaft rotation frequency. This work first attempts to reformulate McAlpine and Fishers frequency domain model for the propagation of a sawtooth waveform spiralling inside a hard‐walled and lined cylindrical duct with uniform flow. The nondissipative Burgers equation is solved, and modal attenuation and dispersion are added using a split‐step computational method. In practice, shocks do not only occur at blade tips, but on a significant portion of the blade span. The plane wave hypothesis being no longer valid, a new three‐dimensional model is presented for a no‐flow case. This model ...