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Using MacCormack-type methods, a new class of highly accurate compact MacCormack-type schemes is derived which does not require a tridiagonal matrix inversion to obtain the spatial derivatives. Two examples are shown, and results of these schemes for three linear and nonlinear CAA Benchmark Problems are presented.
Evaluation of the sound sources in a high Reynolds number turbulent flow requires time-accurate resolution of an extremely large number of scales of motion. Direct numerical simulations will therefore remain infeasible for the forseeable future: although current large eddy simulation methods can resolve the largest scales of motion accurately the, they must leave some scales of motion unresolved. A priori studies show that acoustic power can be underestimated significantly if the contribution of these unresolved scales is simply neglected. In this paper, the problem of evaluating the sound radiation properties of the unresolved, subgrid-scale motions is approached in the spirit of the simplest subgrid stress models: the unresolved velocity field is treated as isotropic turbulence with statistical descriptors, evaluated from the resolved field. The theory of isotropic turbulence is applied to derive formulas for the total power and the power spectral density of the sound radiated by a filtered velocity field. These quantities are compared with the corresponding quantities for the unfiltered field for a range of filter widths and Reynolds numbers.
The space-time conservation element and solution element(CE/SE) method is used to study the sound-shock interaction problem. The order of accuracy of numerical schemes is investigated. The linear model problem.govemed by the 1-D scalar convection equation, sound-shock interaction problem governed by the 1-D Euler equations, and the 1-D shock-tube problem which involves moving shock waves and contact surfaces are solved to investigate the order of accuracy of numerical schemes. It is concluded that the accuracy of the CE/SE numerical scheme with designed 2nd-order accuracy becomes 1st order when a moving shock wave exists. However, the absolute error in the CE/SE solution downstream of the shock wave is on the same order as that obtained using a fourth-order accurate essentially nonoscillatory (ENO) scheme. No special techniques are used for either high-frequency low-amplitude waves or shock waves.
In this paper, the space-time conservation element solution element (CE/SE) method is tested in the classical axisymmetric jet instability problem, rendering good agreement with the linear theory. The CE/SE method is then applied to numerical simulations of several nearly fully expanded axisymmetric jet flows and their noise fields and qualitative agreement with available experimental and theoretical results is demonstrated.
The Internal Propagation problems, Fan Noise problem, and Turbomachinery Noise problems are solved using the space-time conservation element and solution element (CE/SE) method. The problems in internal propagation problems address the propagation of sound waves through a nozzle. Both the nonlinear and linear quasi 1D Euler equations are solved. Numerical solutions are presented and compared with the analytical solution. The fan noise problem concerns the effect of the sweep angle on the acoustic field generated by the interaction of a convected gust with a cascade of 3D flat plates. A parallel version of the 3D CE/SE Euler solver is developed and employed to obtain numerical solutions for a family of swept flat plates. Numerical solutions for sweep angles of 0, 5, 10, and 15 deg are presented. The turbomachinery problems describe the interaction of a 2D vortical gust with a cascade of flat-plate airfoils with/without a downstream moving grid. The 2D nonlinear Euler Equations are solved and the converged numerical solutions are presented and compared with the corresponding analytical solution. All the comparisons demonstrate that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple and efficient manner. Furthermore, the simple non-reflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well in 1D, 2D and 3D problems.
An acoustic analysis based on the Ffowcs Williams and Hawkings equation was performed for a high-lift system. As input, the acoustic analysis used un- steady flow data obtained from a highly resolved, time-dependent, Reynolds-averaged Navier-Stokes calculation. The analysis strongly suggests that vor- tex shedding from the trailing edge of the slat results in a high-amplitude, high-frequency acoustic signal, similar to that which was observed in a correspond- ing experimental study of the high-lift system.
In this work, a previously developed mean flow boundary condition will be validated for unsteady flows. The test cases will be several reference benchmark flows consisting of vortical gusts convecting in a uniform mean flow, as well as the more realistic case of a vortical gust impinging on a loaded 2D cascade. The results will verify that the mean flow boundary condition both imposes the desired mean flow as well as having little or no effect on the instantaneous unsteady solution.
In this paper we show by means of numerical experiments that the error introduced in a numerical domain because of a Perfectly Matched Layer or Damping Layer boundary treatment can be controlled. These experimental demonstrations are for acoustic propagation with the Linearized Euler Equations with both uniform and steady jet flows. The propagating signal is driven by a time harmonic pressure source. Combinations of Perfectly Matched and Damping Layers are used with different damping profiles. These layer and profile combinations allow the relative error introduced by a layer to be kept as small as desired, in principle. Tradeoffs between error and cost are explored.
In this paper, numerical predictions of acoustic transmission through a 3D stator obtained using the NASA BASS code are compared with experimentally measured data. The influence of vane count and stagger as well as frequency and mode order on the transmission loss is investigated. The data-theory comparisons indicate that BASS can predict all the important trends observed in the experimental data.
In this paper, numerical predictions of acoustic transmission through a 3D stator obtained using the NASA BASS code are compared with experimentally measured data. The influence of vane count and stagger as well as frequency and mode order on the transmission loss is investigated. The data-theory comparisons indicate that BASS can predict all the important trends observed in the experimental data.
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Computational results are presented for a 15%-scale, full-span, generic low-boom concept aircraft model simulated as installed in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel and in free-air conditions. The simulations were conducted with the lattice Boltzmann solver PowerFLOW® to capture the time-accurate characteristics of the flow. The aerodynamic behavior of the aircraft was investigated with various combinations of flap and landing gear deployments. To replicate the flow speed used during tests of the model, a Mach number of approximately 0.20 was chosen while varying the angle of attack through a limited range. Analyses were performed on local flow quantities, global forces, as well as flow distributions between configurations. Aerodynamic quantities were shown to be sensitive to mesh resolution levels, especially with flap and landing gear systems retracted. When comparing wind tunnel to free-air simulations, the aerodynamic quantities sampled were found to be in good agreement, suggesting that tunnel blockage and model support effects did not adversely impact the aerodynamic behavior of the model during the wind tunnel test. The results of this study improve our understanding of the highly complex, vortical flow generated by configurations with swept, low aspect-ratio wings at speeds encountered during landing operations.
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Wind tunnel test data were used to validate the predicted aerodynamic behavior of a 15%-scale version of a generic, low-boom aircraft. The test was conducted in the NASA Langley 14- by 22-Foot Subsonic Tunnel to determine the low-speed aerodynamic characteristics of the model. Measured steady surface pressures and global forces were used to validate predicted aerodynamic results obtained from high-fidelity simulations of the model as installed in the tunnel. Very good agreement between predicted and measured aerodynamic trends was demonstrated, providing the impetus to proceed with companion airframe noise simulations that were conducted in a free-air setting. Computed near-field flow variables acquired on a permeable data surface were used to generate synthetic pressure records for two 800-element phased microphone arrays positioned overhead and to the side of the model. The array data were beamformed to generate noise source localization maps for the clean model and several landing configurations. Primary and secondary airframe sources were identified and their relative strengths were determined. Far-field integrated noise spectra for the full aircraft, as well as individual components, were obtained from the source maps via integration of tailored regions. The analysis showed that noise produced by the landing gear was the dominant contributor to the far-field acoustic signature of the model, followed by flap noise. The effects of permeable data surface end caps, spatial resolution, array orientation, angle of attack, component interaction, velocity scaling, and numerical precision on synthetic far-field spectra were also evaluated.
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