Ray Hixon

Evaluation of Boundary Conditions for Computational Aeroacoustics

The performance of three acoustic boundary condition formulations is investigated by computing a test problem with a known analytic solution. By using a fixed grid and time step, all variations in the solution are due solely to the boundary condition. The effect of implementation differences on the performance of a given boundary condition is also studied. Details of all implementations are given. Results are shown for the acoustic field of a monopole in a uniform freestream.

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.

Use of linearized Euler equations for supersonic jet noise prediction

The use of linearized Euler equations for direct prediction of supersonic jet noise is explored. It is shown that a high-order numerical scheme coupled with proper boundary treatment can produce a stable solution nearly free from reflections. Results are verified against analytical results for sound radiated by instability waves. Applicability of this approach to real jets is explored by taking the inflow disturbances to be random in time and comparing the computed sound field to the experimentally measured one. Nomenclature D = jet exit nozzle diameter e = total energy per unit volume Me = jet exit Mach number p = pressure Ue = jet exit velocity u = axial velocity v = radial velocity w = azimuthal velocity p = density pe = jet exit density

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.

Evaluation of Boundary Conditions for the Gust-Cascade Problem

Using a high-order accuracy finite-difference time-domain algorithm, the acoustic scattering from a flat-plate cascade is computed. Keeping the grid and time step fixed, the effect of four different boundary conditions on the accuracy and stability of the computed solution is compared.

Multidimensional optimization of finite difference schemes for Computational Aeroacoustics

Because of the long propagation distances, Computational Aeroacoustics schemes must propagate the waves at the correct wave speeds and lower the isotropy error as much as possible. The spatial differencing schemes are most frequently analyzed and optimized for one-dimensional test cases. Therefore, in multidimensional problems such optimized schemes may not have isotropic behavior. In this work, optimized finite difference schemes for multidimensional Computational Aeroacoustics are derived which are designed to have improved isotropy compared to existing schemes. The derivation is performed based on both Taylor series expansion and Fourier analysis. Various explicit centered finite difference schemes and the associated boundary stencils have been derived and analyzed. The isotropy corrector factor, a parameter of the schemes, can be determined by minimizing the integrated error between the phase or group velocities on different spatial directions. The order of accuracy of the optimized schemes is the same as that of the classical schemes, the advantage being in reducing the isotropy error. The present schemes are restricted to equally-spaced Cartesian grids, so the generalized curvilinear transformation method and Cartesian grid methods are good candidates. The optimized schemes are tested by solving various multidimensional problems of Aeroacoustics.

Space-Time Mapping Analysis of Airfoil Nonlinear Interaction With Unsteady Inviscid Flow

A new computational method of space-time mapping analysis is applied to nonlinear, inviscid computation of unsteady airfoil response to an upstream flow with a finite amplitude of a time-harmonic vortical perturbation. The unique feature of the method is that it solves the unsteady problem as a steady-state one, by treating the time coordinate identically to space directions. The periodic nature of the flow is used to design the mesh covering one period of the vortical gust in the time direction, with a periodic boundary condition applied at the time-inflow and time-outflow boundaries. The computed solution is, thus, driven directly to the final long-time periodic solution using a pseudotime marching with a high-order discretization scheme. Computed unsteady aerodynamic and aeroacoustic airfoil responses are compared against available numerical solutions. Results obtained for a high-amplitude impinging gust identify zones in the computational domain where nonlinear response effects appear most significant.

Direct Computation of Jet Noise Produced by Large-Scale Axisymmetric Structures

A methodology is presented for directly calculating the noise emission associated with large-scale structures in a supersonic jet. The nonlinear governing equations are solved in a computational domain that encompasses both the jet e ow and the acoustic near e eld. A high-order discretization scheme is used along with careful boundary treatment to capture the disturbance e eld accurately. Nonlinear interactions among the various frequency modes of the e ow structure were found to alter the development of each mode and, hence, ine uence its radiation pattern. Comparingthecalculatedradiationpatterntoexperimentalobservationsindicatesthattheaxisymmetricstructure contributes preferentially in the forward direction, whereas the azimuthal structure is associated with a higher emission angle and with a stronger effect on jet spreading. Sensitivity of the radiated sound e eld to the type of incoming disturbances is studied.

Radiation and Wall Boundary Conditions for Computational Aeroacoustics: A Review

A review of unsteady computational boundary conditions for computational aeroacoustics (CAA) problems is presented. This review is meant to serve as a general overview of previous work on solid wall, radiation and outflow boundary conditions that have been proposed and used in CAA calculations. Both the physical nature of the boundary condition problem as well as the numerical considerations affecting their implementation are discussed.

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.