A nonintrusive Reduced Basis Method applied to aeroacoustic simulations

The Reduced Basis Method can be exploited in an efficient way only if the so-called affine dependence assumption on the operator and right-hand side of the considered problem with respect to the parameters is satisfied. When it is not, the Empirical Interpolation Method is usually used to recover this assumption approximately. In both cases, the Reduced Basis Method requires to access and modify the assembly routines of the corresponding computational code, leading to an intrusive procedure. In this work, we derive variants of the EIM algorithm and explain how they can be used to turn the Reduced Basis Method into a nonintrusive procedure. We present examples of aeroacoustic problems solved by integral equations and show how our algorithms can benefit from the linear algebra tools available in the considered code.Comment: 28 pages, 7 figure

Nonintrusive approximation of parametrized limits of matrix power algorithms -- application to matrix inverses and log-determinants

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones

Variants of the Empirical Interpolation Method: symmetric formulation, choice of norms and rectangular extension

The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.Comment: 7 page

Data-driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response

Rapid prediction of the aeroacoustic response is a key component in the design of aircraft and turbomachinery. While it is possible to achieve accurate predictions using direct solution of the compressible Navier-Stokes equations, applications of such solvers is not feasible in design optimization due to the high cost of resolving wave phenomena in an Eulerian setting. In this work, we propose a technique for highly accelerated predictions of aeroacoustic response using a data-driven model reduction approach based on the eigensystem realization algorithm (ERA), as a non-intrusive balanced truncation method. Specifically, we create and compare ERA ROMs based on the training data generated by solving the linearized and nonlinear Euler equations with Gaussian pulse inputs, and use them for prediction of the aeroacoustic response of an airfoil subject to different types of gust loading. The results show that both ROMs are in good agreement with the full-order model (FOM) solution in a purely predictive setting, while achieving orders of magnitude reduction in the online computation time. Using ERA for prediction of the acoustic response requires activating each input channel separately in the FOM for training ROMs, and operating on a large Hankel matrix, that can become computationally infeasible. We address this bottleneck in two steps: first, we propose a multi-fidelity gappy POD method to identify the most impactful input channels based on a coarser grid. Therefore, we reduce the computation cost on the FOM and ROM levels as we build the Markov sequence by querying the high-resolution FOM only for the input channels identified by gappy POD. Second, we use tangential interpolation at the ROM level to reduce the size of the Hankel matrix. The proposed methods enable application of ERA for highly accurate online acoustic response prediction and reduce the offline computation cost of ROMs

Influence of blade aerodynamic model on prediction of helicopter rotor aeroacoustic signatures

Brown’s vorticity transport model has been used to investigate how the local blade aerodynamic model influences the quality of the prediction of the high-frequency airloads associated with blade–vortex interactions, and thus the accuracy with which the acoustic signature of a helicopter rotor can be predicted. The vorticity transport model can accurately resolve the structure of the wake of the rotor and allows significant flexibility in the way that the blade loading can be represented. The Second Higher-Harmonic Control Aeroacoustics Rotor Test was initiated to provide experimental insight into the acoustic signature of a rotor in cases of strong blade–vortex interaction. Predictions of two models for the local blade aerodynamics are compared with the test data. A marked improvement in accuracy of the predicted high-frequency airloads and acoustic signature is obtained when a lifting-chord model for the blade aerodynamics is used instead of a lifting-line-type approach. Errors in the amplitude and phase of the acoustic peaks are reduced, and the quality of the prediction is affected to a lesser extent by the computational resolution of the wake, with the lifting-chord model producing the best representation of the distribution of sound pressure below the rotor

Prediction of Turbulent Temperature Fluctuations in Hot Jets

Large-eddy simulations were used to investigate turbulent temperature fluctuations and turbulent heat flux in hot jets. A high-resolution finite-difference Navier-Stokes solver, WRLES, was used to compute the flow from a 2-inch round nozzle. Several different flow conditions, consisting of different jet Mach numbers and temperature ratios, were examined. Predictions of mean and fluctuating velocities were compared to previously obtained particle image velocimetry data. Predictions of mean and fluctuating temperature were compared to new data obtained using Raman spectroscopy. Based on the good agreement with experimental data for the individual quantities, the combined quantity turbulent heat flux was examined

Aeronautical engineering: A continuing bibliography with indexes (supplement 322)

This bibliography lists 719 reports, articles, and other documents introduced into the NASA scientific and technical information system in Oct. 1995. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics