Time-adaptive Adomian decomposition-based numerical scheme for Euler equations

Time efficiency is one of the more critical concerns in computational fluid dynamics simulations of industrial applications. Extensive research has been conducted to improve the underlying numerical schemes to achieve time process reduction. Within this context, this paper presents a new time discretization method based on the Adomian decomposition technique for Euler equations. The obtained scheme is time-order adaptive; the order is automatically adjusted at each time step and over the space domain, leading to significant processing time reduction. The scheme is formulated in an appropriate recursive formula, and its efficiency is demonstrated through numerical tests by comparison to exact solutions and the popular Runge–Kutta-discontinuous Galerkin method.     

On the governing equations for the compressing process and its coupling with other processes

As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decompos...     

Investigation of high frequency noise generation in the near-nozzle region of a jet using large eddy simulation

This paper reports on the simulation of the near-nozzle region of an isothermal Mach 0.6 jet at a Reynolds number of 100,000 exhausting from a round nozzle geometry. The flow inside the nozzle and the free jet outside the nozzle are computed simultaneously by a high-order accurate, multi-block, large eddy simulation (LES) code with overset grid capability. The total number of grid points at which the governing equations are solved is about 50 million. The main emphasis of the simulation is to capture the high frequency noise generation that takes place in the shear layers of the jet within the first few diameters downstream of the nozzle exit. Although we have attempted to generate fully turbulent boundary layers inside the nozzle by means of a special turbulent inflow generation procedure, an analysis of the simulation results supports the fact that the state of the nozzle exit boundary layer should be characterized as transitional rather than fully turbulent. This is believed to be most likely due to imperfections in the inflow generation method. Details of the computational methodology are presented together with an analysis of the simulation results. A comparison of the far field noise spectrum in the sideline direction with experimental data at similar flow conditions is also carried out. Additional noise generation due to vortex pairing in the region immediately downstream of the nozzle exit is also observed. In a second simulation, the effect of the nozzle exit boundary layer thickness on the vortex pairing Strouhal frequency (based on nozzle diameter) and its harmonics is demonstrated. The limitations and deficiencies of the present study are identified and discussed. We hope that the lessons learned in this study will help guide future research activities towards resolving the pending issues identified in this work.

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Presented as AIAA Paper 2006-2499 at 12th AIAA/CEAS Aeroacoustics Conference, 8–10 May 2006, Cambridge, MA, USA.     

Réduction semi-active du battement de volume généré par une cavité profonde soumise à un écoulement aérodynamiqueSemi-active reduction of the sound generated by a deep cavity under an airflow

We present experimental results obtained with a deep cavity, such as a Helmholtz resonator, excited by an airflow. The resonance under the action of the vortices generated in the shear layer is well described and quantified. The mounting of actuators, based on a few piezo-electric elements, allows us to generate a series of two-dimensional vortices forced at a frequency which is different than the natural resonance frequency. The sound level in the cavity is strongly decreased and only the broadband noise of the turbulence remains. To cite this article: X. Amandolese et al., C. R. Mecanique 330 (2002) 101–106.     

Noise radiated by a non-isothermal,temporal mixing layer. Part I: Direct computation and prediction using compressible DNS

Direct numerical simulations (DNSs) are performed in order to study acoustic emissions generated during the transition of isothermal and non-isothermal mixing layers. The sound from temporally evolving mixing layers is computed directly using DNS for a computational domain, which includes both aerodynamic and acoustic fields. Good precision of the computed acoustic field is ensured by using a numerical code based on high-order finite difference schemes of quasi-spectral accuracy. Two- and three-dimensional simulations of mixing layers are performed for various Mach numbers and temperature ratios. For each case, the acoustic radiation of the mixing layer transition is investigated. Comparisons illustrate the importance of the combined effects of temperature and Mach number on the acoustic intensity. Qualitative agreement with existing experimental observations for hot jet flows is observed. It is also found that the appearance of three-dimensional motion leads to a substantial reduction of sound emissions. In the second part of this study, DNS data are used to perform acoustic analogy predictions. Excellent agreement between direct computations and predictions is obtained in all cases. Analysis of the source terms yields a new interpretation of temperature and Mach number effects, based on the predominance of one term over the other.     

Verification of higher-order discontinuous Galerkin method for hexahedral elements

A high-order implementation of the Discontinuous Galerkin (dg) method is presented for solving the three-dimensional Linearized Euler Equations on an unstructured hexahedral grid. The method is based on a quadrature free implementation and the high-order accuracy is obtained by employing higher-degree polynomials as basis functions. The present implementation is up to fourth-order accurate in space. For the time discretization a four-stage Runge–Kutta scheme is used which is fourth-order accurate. Non-reflecting boundary conditions are implemented at the boundaries of the computational domain.The method is verified for the case of the convection of a 1D compact acoustic disturbance. The numerical results show that the rate of convergence of the method is of order $p+1$ in the mesh size, with p the order of the basis functions. This observation is in agreement with analysis presented in the literature. To cite this article: H. Özdemir et al., C. R. Mecanique 333 (2005).     

Stream function–potential function coordinates for aeroacoustics and unsteady aerodynamics

‘Stream function as a coordinate approach’ (SFC) combined with compact high-order finite difference schemes has been developed and applied to aeroacoustics and unsteady aerodynamics problems. Straightforward implementation of SFC creates coarse grids at the vicinity of stagnation points that smears high-order numerical computations. Grid clustering is employed to resolve coarse grid near stagnations points. The agreement between numerical results and particle image velocimetry (PIV) measurements for flapping airfoil shows the robustness of the current approach for performing high-order computations.     

Cavity Tones by Computational Aeroacoustics

The flow past open cavities is a problem that is encountered in many engineering applications and can result in intense acoustic tones. The flow physics and acoustics of cavity configurations are complex and computational simulation techniques provide an opportunity to gain further understanding and provide a tool to predict not only cavity tone frequencies but their amplitude. In this paper, we describe the available techniques for performing computational aeroacoustic simulations of cavity flows, and review recent applications for the prediction and control of cavity tones in subsonic, transonic and supersonic regimes.     

Development of Computational Aeroacoustics Tools for Airframe Noise Calculations

This paper discusses the development of computational aeroacoustics (CAA) tools for airframe noise analysis and prediction. We review recent progress in this topic, but emphasize our vision for the future development of such tools. Our intention is for this vision to drive future CAA research in directions that will accelerate widespread use of CAA for airframe noise applications. We discuss the needs for accuracy, efficiency, and easy interface with other design tools and illustrate how CAA tools may help future aircraft design. We explain what appears to be achievable in a 20-year time frame, and what goals will probably take longer.

Important barrier issues include the effects of numerical dispersion and dissipation, the treatment of highly curved, irregular boundary surfaces, and grid generation. Beyond these largely numerical issues, we discuss the role of physics-based modeling, including turbulence modeling in unsteady flow computations and the importance of developing sophisticated techniques for analyzing results of computations. Numerical simulations combined with the acoustic analogy methodology to predict noise are also reviewed. Finally, we discuss how to use recent advances in measurement techniques for CAA tool validation, which is an integral part of future development.     

Inflow broadband noise from an isolated symmetric airfoil interacting with incident turbulence

Inflow noise from a symmetric airfoil interacting with homogeneous and isotropic turbulence is investigated focusing on the effects of airfoil geometry. The numerical method employed is based on computational aeroacoustic techniques using the high-order dispersion-relation-preserving finite-difference schemes for solving two-dimensional linearized Euler equations. Effects on inflow noise of the airfoil thickness, leading-edge radius, and freestream Mach number are examined by comparing the acoustic power spectrum of the airfoils and their flow field characteristics. Acoustic power levels of airfoils are found to exponentially decrease in the high-frequency range as airfoil thickness increases because incident turbulent velocities are more distorted in the larger stagnation region near the leading edge. This distortion is shown to be related to the slope angle of the streamline of steady mean flow near the leading edge. However, this high-frequency reduction weakens as the Mach number increases due to the decreasing slope angle. In addition, the chordwise velocity component in the incident turbulence contributes more to the radiating acoustic pressure level as the freestream Mach number increases, which also results in less high-frequency reduction at higher freestream Mach number. At fixed airfoil thickness, increasing the leading-edge radius leads to decreases in the acoustic power level, which may also be explained by size variation of the stagnation region around the leading edge. An approximate algebraic formula for acoustic power spectra is derived on the basis of these observations. Acoustic power spectra predicted using this formula are shown to closely follow the numerical results. Finally, the applicability of the algebraic formula and the current numerical methods to more realistic problems are confirmed by comparing their predictions with the measured data.