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NASA NTRS1994

Aeroacoustic computation of gust-blade interaction

To better understand and address the challenges faced in computing the acoustics of flow fields, test problems must be considered. In the present study, the sound radiated by the interaction of a flat plate with an oncoming gust containing a two component, mean velocity is computed. The gust has a uniform mean flow in x with Mach number M(infinity) equal to 0.5. The gust's mean velocity in y is of smaller amplitude and is given by: v = 0.1 sin(pi/8(x/M(sub infinity) - t)). This problem has been posed for an upcoming ICASE/LaRC workshop on benchmark problems in computational aeroacoustics. A plate with a length of 30 units in x is used. The plate is assumed to be infinitesimally thin and is centered at the origin. All variables are made dimensionless using the scales specified. Acoustic quantities are obtained by numerically integrating the linearized Euler equations. Integration is performed on the computational domain -100.0 less than or equal to x less than or equal to 100.0, -100.0 less than or equal to y less than or equal to 100.0, using unit length grid spacing in x and in y. An integration scheme is sought which will provide accurate solution to the small quantities of interest at a minimal computational expense. Results indicate that with the given discretization a scheme of minimal fourth order accuracy might be adequate to approximate the waves within the given flow. Thus, a variation of the MacCormack scheme with fourth order accuracy in space and second order accuracy in time was chosen. A scheme with sixth order accuracy in space has also been implemented and results compared with those of the fourth order accurate scheme. To ensure no mass flux, zero normal velocity is assigned at the plate. This condition will induce a discontinuity in the pressure across the plate location. Values for the perturbation pressure p' along the surface of the plate are obtained using a one-sided, third order Taylor expansion, such that p'(sub y) = O. In accordance with the Kutta condition, perturbation pressure at the trailing edge is assigned to zero. In the far field, radiation boundary conditions have been implemented. The effectiveness of the far field conditions are validated by computing in a larger computational domain and comparing the results. Early in time, sound waves begin to radiate from the plate. A Doppler effect is observed. After the initial transients disappear, the strongest waves leave the trailing edge at an approximate 45 degree angle. The intensity pattern of pressure fluctuations shows five lobes (of increasing magnitude with increasing downstream direction) emerging from the plate. Undesirable short wave contaminants are observed in the computed pressure distribution along the plate surface. For a more accurate solution at small scales, a more refined discretization will be required.

Martin, James E.↗
NASA NTRS2000

A Very High Order, Adaptable MESA Implementation for Aeroacoustic Computations

Since computational efficiency and wave resolution scale with accuracy, the ideal would be infinitely high accuracy for problems with widely varying wavelength scales. Currently, many of the computational aeroacoustics methods are limited to 4th order accurate Runge-Kutta methods in time which limits their resolution and efficiency. However, a new procedure for implementing the Modified Expansion Solution Approximation (MESA) schemes, based upon Hermitian divided differences, is presented which extends the effective accuracy of the MESA schemes to 57th order in space and time when using 128 bit floating point precision. This new approach has the advantages of reducing round-off error, being easy to program. and is more computationally efficient when compared to previous approaches. Its accuracy is limited only by the floating point hardware. The advantages of this new approach are demonstrated by solving the linearized Euler equations in an open bi-periodic domain. A 500th order MESA scheme can now be created in seconds, making these schemes ideally suited for the next generation of high performance 256-bit (double quadruple) or higher precision computers. This ease of creation makes it possible to adapt the algorithm to the mesh in time instead of its converse: this is ideal for resolving varying wavelength scales which occur in noise generation simulations. And finally, the sources of round-off error which effect the very high order methods are examined and remedies provided that effectively increase the accuracy of the MESA schemes while using current computer technology.

Dydson, Roger W.↗
NASA NTRS1983

Aeroacoustic computation of cylinder wake flow

Sound generation by uniform flow over a cylinder at the Reynolds number of 200 is calculated. The incompressible, time dependent flow field is first computed by standard computational fluid dynamics techniques using a stream function/vorticity formulation. The sound radiation is then obtained by integrating over the flow field with the Coriolis acceleration as the source term and a low frequency Green's function technique. Time histories, spectra, and directivity of the radiated sound are obtained. Comparisons with experimental data, where possible, indicate the feasibility of this computational aeroacoustics approach.

Hardin, J. C.↗
NASA NTRS2000

An Automated Approach to Very High Order Aeroacoustic Computations in Complex Geometries

Computational aeroacoustics requires efficient, high-resolution simulation tools. And for smooth problems, this is best accomplished with very high order in space and time methods on small stencils. But the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewslci recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that are located near wall boundaries. These procedures are used to automatically develop and implement very high order methods (>15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗
NASA NTRS2001

Automated Approach to Very High-Order Aeroacoustic Computations

Computational aeroacoustics requires efficient, high-resolution simulation tools. For smooth problems, this is best accomplished with very high-order in space and time methods on small stencils. However, the complexity of highly accurate numerical methods can inhibit their practical application, especially in irregular geometries. This complexity is reduced by using a special form of Hermite divided-difference spatial interpolation on Cartesian grids, and a Cauchy-Kowalewski recursion procedure for time advancement. In addition, a stencil constraint tree reduces the complexity of interpolating grid points that am located near wall boundaries. These procedures are used to develop automatically and to implement very high-order methods (> 15) for solving the linearized Euler equations that can achieve less than one grid point per wavelength resolution away from boundaries by including spatial derivatives of the primitive variables at each grid point. The accuracy of stable surface treatments is currently limited to 11th order for grid aligned boundaries and to 2nd order for irregular boundaries.

Dyson, Rodger W.↗
NASA NTRS2003

Nonlinear Aeroacoustics Computations by the Space-Time CE/SE Method

The Space-Time Conservation Element and Solution Element Method, or CE/SE Method for short, is a recently developed numerical method for conservation laws. Despite its second order accuracy in space and time, it possesses low dispersion errors and low dissipation. The method is robust enough to cover a wide range of compressible flows: from weak linear acoustic waves to strong discontinuous waves (shocks). An outstanding feature of the CE/SE scheme is its truly multi-dimensional, simple but effective non-reflecting boundary condition (NRBC), which is particularly valuable for computational aeroacoustics (CAA). In nature, the method may be categorized as a finite volume method, where the conservation element (CE) is equivalent to a finite control volume (or cell) and the solution element (SE) can be understood as the cell interface. However, due to its careful treatment of the surface fluxes and geometry, it is different from the existing schemes. Currently, the CE/SE scheme has been developed to a matured stage that a 3-D unstructured CE/SE Navier-Stokes solver is already available. However, in the present review paper, as a general introduction to the CE/SE method, only the 2-D unstructured Euler CE/SE solver is chosen and sketched in section 2. Then applications of the 2-D and 3-D CE/SE schemes to linear, and in particular, nonlinear aeroacoustics are depicted in sections 3, 4, and 5 to demonstrate its robustness and capability.

Loh, Ching Y.↗
NASA NTRS1997

Advances in Numerical Boundary Conditions for Computational Aeroacoustics

Advances in Computational Aeroacoustics (CAA) depend critically on the availability of accurate, nondispersive, least dissipative computation algorithm as well as high quality numerical boundary treatments. This paper focuses on the recent developments of numerical boundary conditions. In a typical CAA problem, one often encounters two types of boundaries. Because a finite computation domain is used, there are external boundaries. On the external boundaries, boundary conditions simulating the solution outside the computation domain are to be imposed. Inside the computation domain, there may be internal boundaries. On these internal boundaries, boundary conditions simulating the presence of an object or surface with specific acoustic characteristics are to be applied. Numerical boundary conditions, both external or internal, developed for simple model problems are reviewed and examined. Numerical boundary conditions for real aeroacoustic problems are also discussed through specific examples. The paper concludes with a description of some much needed research in numerical boundary conditions for CAA.

Tam, Christopher K. W.↗
NASA NTRS1992

Report on the final panel discussion on computational aeroacoustics

Some important conclusions about future prospects for aeroacoustics in general, and for computational aeroacoustics in particular, that were reached in the course of the Final Panel Discussion of the Workshop on Computational Aeroacoustics held from 6 to 9 April 1992 by ICASE and NASA Langley Research Center are summarized by the panel chairman. Aeroacoustics must now be involved in interactions with computational fluid dynamics (as applied not only to deterministic flows but also to the statistical characteristics of turbulence), while additionally incorporating rigorous comparisons with experiment. The new Computational Aeroacoustics will press forward in two parallel ways. In one of them, CFD will be used to determine aeroacoustic source strengths, the associated radiation being derived by the Acoustic Analogy approach in one of its forms. In the other, a direct Computational Aeroacoustics will apply CFD techniques over a region extending beyond the flow field so as to include at least the beginnings of the acoustic far field. There are some particularly important areas of study, including rotor noise, boundary-layer noise, and the noise of supersonic jets, where it is strongly recommended that use of both methods is continued. On the other hand, important problems of the diffraction of radiation from aeroacoustic sources around complicated aircraft shapes will require the use of comprehensively Computational Aeroacoustics, while Acoustic Analogy methods seem better suited to estimating subsonic jet noise. The study of model problems to allow comparisons with experiment will be valuable in both lines of attack.

Lighthill, James↗
NASA NTRS1995

Computational aeroacoustics on massively parallel computers

A computational fluid dynamics (CFD) technique is employed to solve aeroacoustics problems on massively parallel computers. The algorithm is based on a 4th order accurate central finite difference and 4th order accurate 4-stage Runge-Kutta time integration method that solves the 3-D full Navier-Stokes/Euler equations on a curvilinear coordinate system. The code has been developed to predict noise radiation from ducted fans. A specific application of this code is made here to the oscillating circular piston problem (Workshop Category 4, Problem 2) by solving the full Euler equations with nonreflecting boundary conditions in the axisymmetric mode. The features of the code that apply to this particular problem are described in this paper.

Oezyoeruek, Yusuf↗
NASA NTRS2001

An Overview of Computational Aeroacoustic Modeling at NASA Langley

The use of computational techniques in the area of acoustics is known as computational aeroacoustics and has shown great promise in recent years. Although an ultimate goal is to use computational simulations as a virtual wind tunnel, the problem is so complex that blind applications of traditional algorithms are typically unable to produce acceptable results. The phenomena of interest are inherently unsteady and cover a wide range of frequencies and amplitudes. Nonetheless, with appropriate simplifications and special care to resolve specific phenomena, currently available methods can be used to solve important acoustic problems. These simulations can be used to complement experiments, and often give much more detailed information than can be obtained in a wind tunnel. The use of acoustic analogy methods to inexpensively determine far-field acoustics from near-field unsteadiness has greatly reduced the computational requirements. A few examples of current applications of computational aeroacoustics at NASA Langley are given. There remains a large class of problems that require more accurate and efficient methods. Research to develop more advanced methods that are able to handle the geometric complexity of realistic problems using block-structured and unstructured grids are highlighted.

Lockard, David P.↗
NASA NTRS2005

Benchmark Problems Used to Assess Computational Aeroacoustics Codes

The field of computational aeroacoustics (CAA) encompasses numerical techniques for calculating all aspects of sound generation and propagation in air directly from fundamental governing equations. Aeroacoustic problems typically involve flow-generated noise, with and without the presence of a solid surface, and the propagation of the sound to a receiver far away from the noise source. It is a challenge to obtain accurate numerical solutions to these problems. The NASA Glenn Research Center has been at the forefront in developing and promoting the development of CAA techniques and methodologies for computing the noise generated by aircraft propulsion systems. To assess the technological advancement of CAA, Glenn, in cooperation with the Ohio Aerospace Institute and the AeroAcoustics Research Consortium, organized and hosted the Fourth CAA Workshop on Benchmark Problems. Participants from industry and academia from both the United States and abroad joined to present and discuss solutions to benchmark problems. These demonstrated technical progress ranging from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The results are documented in the proceedings of the workshop. Problems were solved in five categories. In three of the five categories, exact solutions were available for comparison with CAA results. A fourth category of problems representing sound generation from either a single airfoil or a blade row interacting with a gust (i.e., problems relevant to fan noise) had approximate analytical or completely numerical solutions. The fifth category of problems involved sound generation in a viscous flow. In this case, the CAA results were compared with experimental data.

Dahl, Milo D.↗
NASA NTRS1995

ICASE/LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA)

The proceedings of the Benchmark Problems in Computational Aeroacoustics Workshop held at NASA Langley Research Center are the subject of this report. The purpose of the Workshop was to assess the utility of a number of numerical schemes in the context of the unusual requirements of aeroacoustical calculations. The schemes were assessed from the viewpoint of dispersion and dissipation -- issues important to long time integration and long distance propagation in aeroacoustics. Also investigated were the effect of implementation of different boundary conditions. The Workshop included a forum in which practical engineering problems related to computational aeroacoustics were discussed. This discussion took the form of a dialogue between an industrial panel and the workshop participants and was an effort to suggest the direction of evolution of this field in the context of current engineering needs.

Hardin, Jay C.↗
NASA NTRS2000

Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

The proceedings of the Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems cosponsored by the Ohio Aerospace Institute and the NASA Glenn Research Center are the subject of this report. Fan noise was the chosen theme for this workshop with representative problems encompassing four of the six benchmark problem categories. The other two categories were related to jet noise and cavity noise. For the first time in this series of workshops, the computational results for the cavity noise problem were compared to experimental data. All the other problems had exact solutions, which are included in this report. The Workshop included a panel discussion by representatives of industry. The participants gave their views on the status of applying computational aeroacoustics to solve practical industry related problems and what issues need to be addressed to make CAA a robust design tool.

Dahl, Milo D.↗
NASA NTRS1999

Automated Development of Accurate Algorithms and Efficient Codes for Computational Aeroacoustics

The simulation of sound generation and propagation in three space dimensions with realistic aircraft components is a very large time dependent computation with fine details. Simulations in open domains with embedded objects require accurate and robust algorithms for propagation, for artificial inflow and outflow boundaries, and for the definition of geometrically complex objects. The development, implementation, and validation of methods for solving these demanding problems is being done to support the NASA pillar goals for reducing aircraft noise levels. Our goal is to provide algorithms which are sufficiently accurate and efficient to produce usable results rapidly enough to allow design engineers to study the effects on sound levels of design changes in propulsion systems, and in the integration of propulsion systems with airframes. There is a lack of design tools for these purposes at this time. Our technical approach to this problem combines the development of new, algorithms with the use of Mathematica and Unix utilities to automate the algorithm development, code implementation, and validation. We use explicit methods to ensure effective implementation by domain decomposition for SPMD parallel computing. There are several orders of magnitude difference in the computational efficiencies of the algorithms which we have considered. We currently have new artificial inflow and outflow boundary conditions that are stable, accurate, and unobtrusive, with implementations that match the accuracy and efficiency of the propagation methods. The artificial numerical boundary treatments have been proven to have solutions which converge to the full open domain problems, so that the error from the boundary treatments can be driven as low as is required. The purpose of this paper is to briefly present a method for developing highly accurate algorithms for computational aeroacoustics, the use of computer automation in this process, and a brief survey of the algorithms that have resulted from this work. A review of computational aeroacoustics has recently been given by Lele.

Goodrich, John W.↗
NASA NTRS1995

The use of staggered scheme and an absorbing buffer zone for computational aeroacoustics

Various problems from those proposed for the Computational Aeroacoustics (CAA) workshop were studied using second and fourth order staggered spatial discretizations in conjunction with fourth order Runge-Kutta time integration. In addition, an absorbing buffer zone was used at the outflow boundaries. Promising results were obtained and provide a basis for application of these techniques to a wider variety of problems.

Nark, Douglas M.↗
NASA NTRS2003

Computational Aeroacoustics: An Overview

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.

Tam, Christopher K. W.↗
NASA NTRS1995

Wave propagation and scattering in computational aeroacoustics

This paper describes predictions of model problems in computational aeroacoustics. Two problem classes are considered: The first (Workshop Category 3, Problem 1 and 2) considers two-dimensional wave propagation and non-reflecting boundary conditions in the presence of a mean flow. The second (Workshop Category 4, Problem 1) examines wall boundary conditions. For the last problem we introduce the Impedance Mismatch Method (IMM) to treat the solid wall boundaries. In this method the solid wall is simulated using a wall region in which the characteristic impedance is set to a different value to that in the fluid region. This method has advantages over traditional solid wall boundary conditions including simplicity of coding, speed of computations, and the ability to treat curved boundaries efficiently. Several numerical examples are given in addition to the Workshop Problems. The discretization of the Euler equations is performed in all cases with a Dispersion-Relation-Preserving (DRP) algorithm. The numerical results are compared with either analytical solutions or solutions obtained using traditional solid wall boundary conditions.

Chung, Cathy↗
NASA NTRS1986

Computational aeroacoustics - Present status and future promise

The field of computational aeroacoustics (CAA), in which sound generation by unsteady flows is calculated from first principles, has recently emerged as a viable discipline. This paper describes one CAA technique which has been validated for low Mach number, low Reynolds number, two-dimensional flows. Results of its application to geometries producing both dipole and quadrupole type sound sources are presented along with theoretical and experimental comparisons. In addition, the future promise of this and other CAA techniques in removing the present limitations is evaluated.

Hardin, J. C.↗