M. Nallasamy

Application of a Nonlinear Computational Aeroacoustics Code to the Gust-Airfoil Problem

A time-domain solution of the gust-airfoil problem is obtained using a high-accuracy computational aeroacoustics code to solve the nonlinear Euler equations. For computational efficiency, the equations are cast in chain-rule curvilinear form, and a structured multiblock solver is used on a distributed-memory parallel computer cluster. To fully investigate the performance of this solver, a test matrix of benchmark problems is computed (two airfoil geometries and four gust-reduced frequencies). These results are compared to benchmark solutions both on the airfoil surface and in the flow domain.

A Computational Aeroacoustic Prediction of Discrete-Frequency Rotor-Stator Interaction Noise - a Linear Theory Analysis

The discrete-frequency noise generated by a rotor-stator interaction is computed by solving the fully nonlinear Euler equations in the time domain in two-dimensions. The acoustic response of the stator is determined simultaneously for the first three harmonics of the convected vertical gust of the rotor. The spatial mode generation, propagation and decay characteristics are predicted by assuming the acoustic field away from the stator can be represented as a uniform flow with small harmonic perturbations superimposed. The computed field is then decomposed using a joint temporal-spatial transform to determine the wave amplitudes as a function of rotor harmonic and spatial mode order. The frequency and spatial mode order of computed acoustic field was consistent with linear theory. Further, the propagation of the generated modes was also correctly predicted. The upstream going waves propagated from the domain without reflection from the inflow boundary. However, reflections from the outflow boundary were noticed. The amplitude of the reflected wave was approximately 5% of the incident wave.

Comparison of Numerical Schemes for a Realistic Computational Aeroacoustics Benchmark Problem

In this work, a nonlinear block-structured CAA solver, the NASA Glenn Research Center BASS code, is tested on a realistic CAA benchmark problem in order to ascertain what effect the high-accuracy solution methods used in CAA have on a realistic test problem. In this test, the nonlinear 2-D compressible Euler equations are solved on a fully curvilinear grid from a commercial grid generator. The solutions are obtained using several finite-difference methods on an identical grid to determine the relative performance of these spatial differencing schemes on this benchmark problem.

Prediction of Noise from Realistic Rotor-Wake/Stator-Row Interaction Using Computational Aeroacoustics

Progress towards the computational prediction of the turbulent flow and broadband noise generated due to the interaction of rotor wakes and stator blades is presented. An inflow boundary treatment is developed which allows arbitrary incoming unsteady flow disturbances to be imposed while preserving the desired mean flow and generating minimal reflections. The boundary condition was implemented in a nonlinear Euler CAA code and validated on a 2D CAA benchmark problem. Preliminary results are shown for a loaded 2D cascade with realistic stator wakes specified from experimental data.

A Method for the Implementation of Boundary Conditions in High-Accuracy Finite-Difference Schemes

This work is concerned with the implementation strategy for boundary conditions in a high-accuracy finite-difference code. In such codes, the effect of a boundary condition on the local flow can be instantaneously propagated many mesh points into the computational domain, affecting the evolution of the flow solution away from the boundary. With such a large stencil footprint, the numerical implementation of the boundary condition has a large effect on code stability and accuracy.

Unsteady Validation of a Mean Flow Boundary Condition for Computational Aeroacoustics

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.

Mean Flow Boundary Conditions for Computational Aeroacoustics

In this work, a new type of boundary condition for time-accurate Computational Aeroacoustics solvers is described. This boundary condition is designed to complement the existing nonreflective boundary conditions while ensuring that the correct mean flow conditions are maintained throughout the flow calculation. Results are shown for a loaded 2D cascade, started with various initial conditions.

Validation of a Computational Aeroacoustics Code for Nonlinear Flow about Complex Geometries Using Ringleb's Flow

This work is concerned with the validation of a high-accuracy Computational Aeroacoustics (CAA) code designed for use in the prediction of unsteady compressible flows about complex geometries, using Ringlebs analytic solution of the compressible steady Euler equations. The flow itself is nonlinear, in some cases transitioning from subsonic to supersoni c and back to subsonic without a shock. Using such an analytic solution of the compressible Euler equations results in a strong validation case for testing the wall boundary conditions used in the code. In such codes, the effect of the boundary conditions on the local flow can be instantaneously propagated many mesh points into the computational domain, affecting the evolution of the flow solution away from the boundary. With such a large stencil footprint, the treatment of the boundary condition has a large effect on code stability and accuracy. A matrix of test cases was run to investigate the effect for different wall geometries, which were defined by the streamlines of the analytical solution. In all the cases Tam and Webb’s optimized explicit fourth-order Dispersion-Relation-Preserving (DRP) central differencing scheme was used. The CAA code gave accurate results for complex geometries when this scheme was used. When the explicit second-order central differencing scheme was used non-physical shocks we re observed for the case involving transonic flow.

COMPUTED LINEAR/NONLINEAR ACOUSTIC RESPONSE OF A CASCADE FOR SINGLE/MULTI FREQUENCY EXCITATION

This paper examines mode generation and propagation characteristics of a 2-D cascade due to incident vortical disturbances using a time domain approach. Full nonlinear Euler equations are solved employing high order accurate spatial differencing and time marching techniques. The solutions show the generation and propagation of mode orders that are expected from theory. Single frequency excitations show linear response over a wide range of amplitudes. The response for multi-frequency excitations tend to become nonlinear due to interaction between frequencies and self interaction. HE gust-cascade interaction problem has been studied extensively using semi-analytical and numerical approaches. These techniques mostly employ a frequency domain approach, examining one frequency at a time. With the availability of parallel processing algorithms, time domain approach has become feasible for gust-cascade interaction study. A time domain approach has the advantage that all harmonics of interest can be extracted from one solution and thus, may be able to mimic the real flow more closely. Also, linear/nonlinear regimes, self interaction, and multi-frequency interaction may be explored. In the nonlinear range, energy transfer between different frequencies (harmonics) occur, and such energy transfers are easily handled in a time domain approach. The 2-D cascade considered here is an unrolled section at a radial station of a modern high speed turbofan stator (Fig. 1), for which flow and noise data are available. The incident gust is the periodic mean wake impinging on the stator vanes. The measured wake is represented using a Fourier series which includes only three harmonics of the blade passing frequency (BPF). The acoustic response of the cascade for this specified gust is studied employing a time domain approach. The full nonlinear Euler equations are solved employing high order accurate spatial differencing schemes, time marching schemes, and boundary conditions. In an earlier study (Ref. 1), the acoustic response of the above 2-D cascade was examined for single and two frequency excitations. It was found that the acoustic response is linear for single frequency excitations. In the case of two frequency excitations (BPF+2BPF), the response was linear only when the BPF amplitude was small. For higher amplitudes of BPF, the response was nonlinear due to self interaction. The results also showed that the response was linear for equal excitation amplitudes of the two harmonics. When the amplitudes of the two harmonics are unequal and BPF amplitude is high, the self interaction of BPF (which is cutoff for the geometry) influences the amplitude of the propagating 2BPF mode in a significant way, both in the inflow and outflow regions.

Simulating Nonlinear Stator Noise for Active Control

This paper outlines an idea to achieve this type of active control with on-blade actuators. First, a simple analytical example demonstrates how a simple actuator could be used to nonlinearly control sound. Second, results from a realistic geometry demonstrate high amplitude vortical gusts that produce nonlinear harmonics which can destructively interfere with otherwise unattenuating (propagating) acoustical modes. We focus on the 2BPF acoustic response here to simplify the presentation and to show that nonlinear cancellation is effective on realistic blade rows, but similar simulations for higher frequencies have also been successfully completed.