Scott Sawyer

High-accuracy large-step explicit Runge-Kutta (HALE-RK) schemes for computational aeroacoustics

In many realistic calculations, the computational grid spacing required to resolve the mean flow gradients is much smaller than the grid spacing required to resolve the unsteady propagating waves of interest. Because of this, the high temporal resolution provided by existing optimized time marching schemes can be excessive due to the small time step required for stability in regions of clustered grid. In this work, explicit fourth-order accurate Runge-Kutta time marching schemes are optimized to increase the inviscid stability limit rather than the accuracy at large time steps. Single and multiple-step optimized schemes are developed and analyzed. The resulting schemes are validated on several realistic benchmark problems.

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.

Mean Stator Loading Effect on the Acoustic Response of a Rotating Cascade

Discrete-frequency tones generated by unsteady blade row interactions are of particular concern in the design of advanced turbine engines. With a rotor ‐ stator mounted in a duct, only certain specie c spatial modes are generated by the rotor ‐ stator interaction, where the generated modes are a function of the number of rotor blades and stator vanes. In addition, only some of these modes propagate to the far e eld, with the rest decaying before reaching the far e eld. Thus, it is only those spatial modes that propagate to the far e eld that represent the discrete-frequency noise received by an observer. This paper’ s aim is to determine the ine uence of steady stator loading on the acoustic response of an annular cascade. To accomplish this, the existence of the propagating modes generated by a rotor ‐ stator interaction must e rst be verie ed. Microphones placed in an axial plane in the outer annulus of the inlet of the Purdue Annular Cascade Research Facility are sampled simultaneously over one rotor revolution, and an ensemble-averaged data set is acquired. With the microphone signals treated as a function of time and space, dual Fourier transforms are utilized to determine the magnitude of the spatial modes at multiples of blade pass frequency. The wave equation is used to predict the propagation characteristics of these modes in the inlet duct. The two predicted propagating modes were found to have signie cantly higher amplitudes than modes that were predicted to decay, or were not to be generated by the rotor ‐ stator interaction, and steady stator loading had a profound ine uence on acoustic response of the cascade. The acoustic response at blade pass and twice blade pass frequency increased by more than 20 dB for angles of attack ranging from 220 to 25 deg.

Flutter Stability of a Detuned Cascade in Subsonic Compressible Flow

A mathematical model is developed to predict the unsteady aerodynamics of a detuned two-dimensional flat plate cascade in subsonic compressible flow. Aerodynamic detuning is introduced by nonuniform circumferential spacing and chordwise offset. Combined aerodynamic-structural detuning is accomplished by replacing alternate airfoils with splitter blades. A torsion mode stability analysis that considers aerodynamic and combined aerodynamic-structural detuning is developed by combining the unsteady aerodynamic model with a single degreeof-freedom structural model. The effect of these detuning techniques on flutter stability is then demonstrated by applying this model to a baseline unstable 12-bladed rotor and detuned variations of this rotor. This study demonstrates that detuning is a viable passive flutter control technique. Nomenclature A = cascade A airfoil index a — freestream speed of sound B - cascade B airfoil index CL = lift coefficient CM - moment coefficient C, = ratio of chord length of cascade B to cascade A CA = chord length of cascade A CB = chord length of cascade B ea = elastic axis location k - reduced frequency a>c/W n = airfoil index os - chordwise offset of cascade B relative to cascade A