توسعه و اعتبار تغییر فاز و کاهش فیلترینگ آزاد برای بهره برداری از داده های CFD

A causal filtering method is developed to perform decimation and storage of aerodynamic data without signal distortion. When done without precaution, decimation of instantaneous computed flow fields for storage and subsequent exploitation generates aliasing. Use of a low-pass filter limits the creation of spurious noise but attenuates signal amplitudes and shifts phases. The proposed filtering method combines the application of a low-pass filter before decimation, during the aerodynamic simulation, with that of a corrective filter, applied in the frequency domain after the full storage. This corrective filter is designed to correct attenuation and phase distortion caused by the low-pass filter. The method is validated on analytical signals and successfully applied to turbulent shear layer and noise radiation problems.

The increase of the computational power observed during the last decades currently allow people to use numerical simulations as an efficient prediction and optimisation tool for aircraft design and conception in many topics such as combustion, turbine blade cooling, aerodynamic performances and noise emission, for instance. For noise reduction, a commonly used approach consists in simulating the flow field using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) to compute the noise sources generated by the flow and its turbulence, as done by Freund [1] and Bogey and Bailly [2]. Such simulations nevertheless require dense computational grids to properly resolve turbulence and flow gradients, and a direct computation of the noise from generation zones to the far field in the same calculation is out of consideration. It is preferred, outside of the source zones and in the uniform medium, to perform either noise radiation using integral formulations such as Lighthill [3], Kirchhoff [4] or Ffowcs Williams and Hawkings [5], or sound propagation based on isentropic linearised Euler equations [6], which can provide the time signatures in the far field with a limited computational cost compared to the resolution of the Navier–Stokes equations. This one-way coupling is often performed using files for data exchange, leading to an important amount of stored data. Frequency ranges of interest in aerodynamics and acoustics are different. In the acoustics, the low frequency part of the spectrum contains most of the energy and is especially investigated. Thus, storing every time step from the aerodynamics for noise radiation may not be relevant and can lead to highly over-resolved acoustic waves in the time domain, resulting in too long computations and a too large amount of data to store. This is especially visible when considering Lighthill integral formulation, where the five aerodynamic variables ρ, p, ux, uy, uz are to be stored over the whole integration volume. Based on this consideration, the acoustic radiation step in usually performed using 1 every n time steps of the aerodynamic simulation. This decimation of the aerodynamic signals for their acoustic post-processing reduces the amount of stored data and numerical operations by a factor n, but without applying any filter before this operation aliasing occurs and frequencies above the cut off contaminate the resolved ones. Such an approach is nevertheless successfully applied daily for aeroacoustics simulations using a surface integral method, where the flow variables are stored on surfaces surrounding the noise sources and on which turbulence is limited and low frequency acoustic fluctuations predominate (see simulations of Vuillot et al. [7] and [8] for instance). In that case, the grid used for the simulation is dense in the noise generation volume and progressively coarsened towards the storage surfaces; numerical dissipation hence plays the role of a low-pass filter that makes aliasing negligible during the decimation of the signal on the storage surface. This approach can however not always be used when data are required to be stored in the volume. Indeed, inside the generation domain the grid is dense to ensure a correct resolution of the turbulence and corresponding noise sources. Even not predominant, levels above the cut-off frequency thus contaminate lower frequency levels during the decimation process and lead to erroneous time signals, as observed by Perez et al. [9]. In this latter case, it becomes necessary to apply a low-pass filter to the aerodynamic fields, in the time domain, before their decimation and storage to limit aliasing. This filter being causal, it introduces attenuation and phase shift that modify the time signature of the considered signals. Considering for instance noise radiation using Lighthill analogy, attenuation can cause an underprediction of the radiated noise and phase shift a wrong evaluations of the non linear term ρuiuj, which can finally lead to fully erroneous results. Application of an inverse filtering, also referred as deconvolution or inverse convolution in the literature, is then required to restore the altered frequencies of interest, in terms of amplitude and phase. Such inverse convolutions of filtered signals have theoretically been successfully performed in the frame of geophysical data, without considering decimation. Depending on the signal to be treated, this deconvolution can be performed using either analog or digital techniques. The first technique is used for analog signals and requires the design of an analog inverse filter, as discussed by Burch et al. [10], which does not correspond to the case considered here. The digital technique, described for instance by George et al. [11], is well-suited for discrete signals and is based on the division of the altered signal by the low-pass filter in the frequency domain. The objective of the work presented here is to apply a full filtering procedure to data representative of those to be stored during CFD simulations. This procedure is composed of a low-pass causal filtering and a decimation of the time signals followed by a digital deconvolution in the frequency domain. Influence of aliasing on signal distortion, which was not discussed by previous authors [10] and [11], will especially be investigated. The paper is organised as follows. The filtering approach is presented in Section 2. Influence of aliasing on signal distortion and selection and characteristics of the low-pass filter are also detailed. Application to analytical signals and to realistic problems are then performed in Sections 3 and 4, respectively. Finally, conclusions are given in Section 5. In the following, all represented power spectral densities (PSDs) are obtained using the method of averaged periodograms. The initial signal is decomposed into nr distinct signals without overlapping. Each signal is periodised using the Hanning window before being Fourier transformed; levels amplitudes are then averaged over the nr realisations to ensure the statistical convergence of the spectra.

A filtering method is proposed for an efficient post-processing of simulated aerodynamic data. Currently, people performing exploitation of computed data usually store investigated fields for subsequent exploitation. This storage can lead to unmanageable amounts of data, especially when considering volume fields and long wall-clock time simulations. A solution is to limit the post-processing to the low frequency range containing most of the energy, which encourages people to increase the time step of the storage by keeping only 1 every n iterations of the aerodynamic simulation. This operation nevertheless distorts the signal, either by aliasing or attenuation and phase shift, depending on the use or not of a low-pass filter. The method proposed in the article permits the decimation and storage of a limited amount of data without significant signal distortion and is composed of two phases. In a first step, a low-pass filter is applied to the aerodynamic fields before the storage to limit aliasing. Once the storage is done, a corrective filter is applied in a second step to cancel the attenuation and phase shift caused by the first filter. This method has been tested on different test cases, from the decimation of a single signal to that of a full set of data used for a sound radiation problem. Results were found to be successful for all tested configurations, spectra and time histories presenting very good comparisons with expected theoretical results. It demonstrates the interest of applying the filtering procedure whenever a data storage is performed with decimation, to ensure reliable time histories for the considered data.