Improved Parabolization of the Euler Equations

Inflow/Outflow conditions are formulated for time-harmonic waves in a duct governed by the Euler equations. These conditions are used to compute the propagation of acoustic and vortical disturbances and the scattering of vortical waves into acoustic waves by an annular cascade. The outflow condition is expressed in terms of the pressure, thus avoiding the velocity discontinuity across any vortex sheets. The numerical solutions are compared with the analytical solutions for acoustic and vortical wave propagation with and without the presence of vortex sheets. Grid resolution studies are also carried out to discern the truncation error of the numerical scheme from the error associated with numerical reflections at the boundary. It is observed that even with the use of exponentially accurate boundary conditions, the dispersive characteristics of the numerical scheme may result in small reflections from the boundary that slow convergence. Finally, the three-dimensional interaction of a wake with a flat plate cascade is computed and the aerodynamic and aeroacoustic results are compared with those of lifting surface methods.

Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or random and described by a Gaussian correlation function. [Work supported by RSF-17-72-10277 and by the Labex CeLyA of Universite de Lyon, operated by the French National Research Agency (ANR-10-LABX-0060/ ANR-11-IDEX-0007).]Irregular reflection of weak acoustic shock waves occurs under the framework of the von Neumann paradox. In this study, the influence of the surface roughness on the reflection pattern was studied experimentally using spark-generated spherically divergent N-waves of 1.4 cm length reflecting from rigid rough surfaces in air. Dimensions of the roughness were varied from 20 up to 500 μm for different surfaces. A Mach-Zehnder interferometry method was used to reconstruct the pressure waveforms near the surface. The reconstruction was performed by applying the inverse Abel transform to the phase of the signal measured by the interferometer. It was shown that the height of the Mach stem became shorter for surfaces with larger dimensions of the roughness and disappeared when the surface roughness was large enough. Such tendency was also observed in simulations based on the Euler equations where the acoustic source was introduced as a Gaussian-envelope energy injection and the roughness was either sinusoidal or r...

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

There is a one academic year theoretical acoustics course for postgraduate students in the Department of Acoustic Science and Engineering of Nanjing University. The course introduces the physical principles and mathematical methods for acoustics in fluids, and the main objective is to deepen understanding of acoustical principle for postgraduate students in the field of acoustics following their undergraduate fundamental acoustics course. The contents include acoustic waves in ideal fluids, acoustic radiation in infinite space, acoustic scattering and diffractions, propagation and radiation of acoustic waves in dust, acoustic fields in enclosed space, acoustic waves in dissipative fluids, acoustic waves in layered fluid, acoustic waves in moving fluids, propagation of acoustic waves with finite amplitude, and effects generated by acoustic waves with finite amplitude. More details can be found in the book title “Principle of Acoustics in Fluids” published by Science Press in China in 2012.

We simulate the generation of acoustic and tsunami waves generated by submarine landslides using the linear model developed in [1]. The model is able to reproduce both acoustic and surface gravity waves generated by a moving source (e.g. earthquake, landslide) in a vertically stratified ocean.There are only a few studies that focus on the generation of acoustic waves by submarine landslides. In [2], the combined analysis of field data and simulations underline the presence of an interference pattern in the acoustic waves' spectrogram. The interference pattern has a time-varying bandwidth, which is a signature of the submarine landslide dynamics. In a previous work [3], we used the model developed in [1] to reproduce the interference pattern for a static source. Here we use the same model to simulate a submarine landslide in the 2D case. The simulations reproduce the time-varying bandwidth. They are then used to study the influence of two parameters on the acoustic spectrograms, namely landslide velocity and topography. Different velocity profiles available in the literature [4] are tested. For the topography, we use as reference the 2D case simulated in [1]. We also provide illustrations for the tsunami generation by the landslide. [1] Dubois J, Imperiale S, Mangeney A, Bouchut F, Sainte-Marie J. Acoustic and gravity waves in the ocean: a new derivation of a linear model from the compressible Euler equation. Journal of Fluid Mechanics. 2023;970:A28. doi:10.1017/jfm.2023.595[2] Caplan-Auerbach, J., Dziak, R. P., Bohnenstiehl, D. R., Chadwick, W. W., and Lau, T.-K. (2014), Hydroacoustic investigation of submarine landslides at West Mata volcano, Lau Basin, Geophys. Res. Lett.,  41,  5927– 5934, doi:10.1002/2014GL060964.[3] Dubois, J., Imperiale, S., Mangeney, A., and Sainte-Marie, J.: Simulation of the hydro-acoustic and gravity waves generated by a landslide, EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-15937, https://doi.org/10.5194/egusphere-egu23-15937, 2023. [4] Farin, M., Mangeney, A., de Rosny, J., Toussaint, R., & Trinh, P.-T. (2019). Relations between the characteristics of granular column collapses and resultant high-frequency seismic signals. Journal of Geophysical Research: Earth Surface, 124, 2987–3021. https://doi.org/10.1029/2019JF005258

This paper demonstrates a real-time hybrid substructuring (RTHS) shake table test to evaluate the seismic performance of a base isolated building. Since RTHS involves a feedback loop in the test implementation, the frequency dependent magnitude and inherent time delay of the actuator dynamics can introduce inaccuracy and instability. The paper presents a robust stability and performance analysis method for the RTHS test. The robust stability method involves casting the actuator dynamics as a multiplicative uncertainty and applying the small gain theorem to derive the sufficient conditions for robust stability and performance. The attractive feature of this robust stability and performance analysis method is that it accommodates linearized modeled or measured frequency response functions for both the physical substructure and actuator dynamics. Significant experimental research has been conducted on base isolators and dampers toward developing high fidelity numerical models. Shake table testing, where the building superstructure is tested while the isolation layer is numerically modeled, can allow for a range of isolation strategies to be examined for a single shake table experiment. Further, recent concerns in base isolation for long period, long duration earthquakes necessitate adding damping at the isolation layer, which can allow higher frequency energy to be transmitted into the superstructure and can result in damage to structural and nonstructural components that can be difficult to numerically model and accurately predict. As such, physical testing of the superstructure while numerically modeling the isolation layer may be desired. The RTHS approach has been previously proposed for base isolated buildings, however, to date it has not been conducted on a base isolated structure isolated at the ground level and where the isolation layer itself is numerically simulated. This configuration provides multiple challenges in the RTHS stability associated with higher physical substructure frequencies and a low numerical to physical mass ratio. This paper demonstrates a base isolated RTHS test and the robust stability and performance analysis necessary to ensure the stability and accuracy. The tests consist of a scaled idealized 4-story superstructure building model placed directly onto a shake table and the isolation layer simulated in MATLAB/Simulink using a dSpace real-time controller.

The two-dimensional problem of hypersonic flow past a cylindrical body with a plane magnetic dipole in the presence of an external magnetic field is considered. The magnetic moment of the dipole is parallel to the free-stream velocity. The flow parameters correspond to a velocity of 7000 m/s at an altitude of approximately 65 km in the Earth’s atmosphere. The system of MHD equations (the Euler equations with volume MHD momentumand energy sources and the magnetic induction equation) was solved using the stabilization method. The calculations were carried out for two magnetic Reynolds numbers: (Rem)1 = 0.18 (corresponds to the parameters of the equilibrium ionized plasma in the shock layer) and (Rem)2 = 1.8 (the plasma conductivity increases by a factor of 10). The solutions obtained are analyzed, the effect of Rem on the flow characteristics, namely, the shock wave stand-off from the body, the configuration of the vortex structures, and the aerodynamic and ponderomotive components of the body drag, is determined.

In this paper, the effect of Lorentz force on the stability of attitude orientation of a charged spacecraft moving in an elliptic orbit in the geomagnetic field is considered. Euler equations are used to derive the equations of attitude motion of a charged spacecraft. The equilibrium positions and its stability are investigated separately in the pitch, roll and yaw directions. In each direction, we use the Lorentz force to identify an attitude stabilization parameter. The analytical methods confirm that we can use the Lorentz force as a stabilization method. The charge-to-mass ratio is the main key of control, in addition to the components of the radius vector of the charged center of the spacecraft, relative to the center of mass of the spacecraft. The numerical results determine stable and unstable equilibrium positions. Therefore, in order to generate optimum charge, which may stabilize the attitude motion of a spacecraft, the amount of charge on the surface of spacecraft will need to be monitored for passive control.

Foldable, origami-inspired transducer arrays have recently been found to offer a straightforward approach of topological transformations on a single tessellated array, rather than signal controls on many transducers, to enable orders of magnitude tuning of acoustic wave guiding capability. Although optimization approaches exist to develop tessellations that serve simple mechanical functions, there are not yet established methods to design tessellated acoustic arrays for targeted acoustic wave guiding properties. This research presents a first approach to design, evaluate, and iteratively refine the tessellations that make up origami-inspired acoustic transducer arrays for desired wave guiding abilities. To exemplify the procedure, two folding patterns are investigated using this process. The approach aims to integrate computational tools to create the tessellation, modify the design based on intuition or prior knowledge, evaluate the acoustic wave radiation characteristics, and iterate on the design according to the outcomes of the evaluations. The two examples exemplify the efficacy of this new process and identify means for improvement and automation. The approach will enable ongoing efforts to devise origami-inspired acoustic transducers and arrays that may serve diverse applications demanding adaptable acoustic wave energy guiding, from biomedical imaging and diagnostics to portable communication and alert devices.

This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this frequency. Such conditions are generally met in the case of weakly non-parallel open flows exhibiting a convectively unstable mean flow. The spatial structure of the singular mode may in these cases be approximated by a local spatial stability analysis based on parabolised stability equations (PSE). We have also shown that the frequency spectrum of the flow field at any arbitrary location of the domain may be predicted from the frequency evolution of the dominant optimal response mode and the knowledge of the frequency spectrum at one or more points. Results are illustrated in the case of a high Reynolds number turbulent backward facing step flow.

Acoustic gravity waves: a computational approach

The radiation of high-order spinning modes from a semi-infinite exhaust duct is studied numerically. The issues involved have applications to noise radiation from the exhaust duct of an aircraft engine. The numerical method is based on solutions of linearised Euler equations (LEE) for propagation in the duct and near field, and the acoustic analogy for far field radiation. A 2.5D formulation of a linearised Euler equation model is employed to accommodate a single spinning mode propagating over an axisymmetric mean flow field. In the solution process, acoustic waves are admitted into the propagation area surrounding the exit of an axisymmetric duct and its immediate downstream area. The wave admission is realised through an absorbing non-reflecting boundary treatment, which admits incoming waves and damps spurious waves generated by the numerical solutions. The wave propagation is calculated through solutions of linearised Euler equations, using an optimised prefactored compact scheme for spatial discretisation. Far field directivity is estimated by solving the Ffowcs Williams-Hawkings equations. The far field prediction is compared with analytic solutions with good agreement.

Verification and application of a mean flow perturbation method for jet noise

An analytical study is presented for vibration and acoustic radiation of a finite thin orthotropic composite cylindrical shell excited by a harmonic concentrated force in a hygroscopic environment. The modal analysis method is used to solve the governing equations. Theoretical results are presented in natural vibration, radial quadratic velocity, sound power and radiation efficiency, with uniform incremental moisture content. Furthermore, different stiffness, length and thickness are set respectively to research the effects of the material and structure parameters variation of the orthotropic cylindrical shell on the vibration and acoustic radiation characteristics. It is found that the natural frequencies decrease with an increase of moisture content. The modal indices associated with the lowest frequency mode reaches the modal indices corresponding to the lowest buckling mode near the critical buckling moisture content with moisture content. The radial quadratic velocity and sound radiation power decrease with the incremental moisture content in the lower frequency band. The vibration and acoustic response decrease with the enhanced stiffness. The increasing length has little impact on the sound radiation and the thickened cylindrical shell weakens the sound radiation response.

Guided acoustic waves at periodically structured edges: Linear modes and nonlinear generation of Lamb and surface waves