## Samenvatting

Computational Aeroacoustics (CAA) is a research field that focuses on the simulation of

sound. This is achieved by numerically solving the governing equations of sound. In its

most general form, these equations are the Navier-Stokes equations. However, for the

simulation of the propagation of sound from a known source, a simplified form can be

used without significant loss of accuracy. The linearized Euler equations are often used

for this purpose. During the present study a code for solving the linearized 2D Euler

equations was developed, as well as a code for calculating rotor noise. The calculation of

the rotor noise is done by solving a set of linearized 3D Euler equations that have been

reduced to 2D.

The discretization used is the Finite Volume method, with a fourth-order accurate compact

scheme [1] for the calculation of the fluxes through the cell faces. The time integration

is achieved with a fourth-order accurate low storage Runge Kutta algorithm.

In CAA the boundary conditions are very important, because the generation of nonphysical

reflections at the boundaries of the computational domain must be minimized.

Two different sets of non-reflecting boundary conditions were implemented and tested

during this study. The first is a set of radiation and outflow boundary conditions that

are based on an asymptotic solution [2]. The second set of boundary conditions is based

on the characteristic solutions of the linearized Euler equations. Although these sets of

boundary conditions produce fairly good results, some high-frequent reflections are generated

by them nonetheless. To dissipate these reflections Artificial Selective Damping [2]

is implemented in the code.

The code for solving the linearized Euler equations was tested by means of two numerical

experiments from the second workshop on benchmark problems for CAA [3]. Furthermore,

the sound radiation from a dipole and a quadrupole source [5] was calculated using

this code as well. Good results were achieved, especially with the boundary conditions

based on an asymptotic solution.

Finally, a benchmark problem from the third workshop on benchmark problems for CAA

[4] was solved on a non-uniform cartesian mesh using the code for the calculation of rotor

noise. For a rotor with subsonic as well as supersonic tip speed results were found that

showed a good match with the exact solution.

References

[1] C. Lacor, S. Smirnov, M. Baelmans, A finite volume formulation of compact central

schemes on arbitrary structured grids, J. Comput. Phys. 198 (2004) 535-566.

[2] C. K. W. Tam, Numerical Methods in Computational Aeroacoustics, AIAA Short

Course Computational Aeroacoustics: Methods and Applications, Lahaina, Hawaii,

10-11 June 2000.

[3] Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

(1996), NASA Conference Publication 3352, Eds. J.C. Hardin, J.R. Ristorcelli and

C.K.W. Tam, J.C. See also NASA CP 3300.

[4] Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

(2000), NASA CP 2000-209790.

[5] C. Bailly and D. Juv´e, Numerical Solution of Acoustic Propagation Problems Using

Linearized Euler Equations, AIAA Journal, Vol. 38, No. 1, 2000, pp. 22-29.

sound. This is achieved by numerically solving the governing equations of sound. In its

most general form, these equations are the Navier-Stokes equations. However, for the

simulation of the propagation of sound from a known source, a simplified form can be

used without significant loss of accuracy. The linearized Euler equations are often used

for this purpose. During the present study a code for solving the linearized 2D Euler

equations was developed, as well as a code for calculating rotor noise. The calculation of

the rotor noise is done by solving a set of linearized 3D Euler equations that have been

reduced to 2D.

The discretization used is the Finite Volume method, with a fourth-order accurate compact

scheme [1] for the calculation of the fluxes through the cell faces. The time integration

is achieved with a fourth-order accurate low storage Runge Kutta algorithm.

In CAA the boundary conditions are very important, because the generation of nonphysical

reflections at the boundaries of the computational domain must be minimized.

Two different sets of non-reflecting boundary conditions were implemented and tested

during this study. The first is a set of radiation and outflow boundary conditions that

are based on an asymptotic solution [2]. The second set of boundary conditions is based

on the characteristic solutions of the linearized Euler equations. Although these sets of

boundary conditions produce fairly good results, some high-frequent reflections are generated

by them nonetheless. To dissipate these reflections Artificial Selective Damping [2]

is implemented in the code.

The code for solving the linearized Euler equations was tested by means of two numerical

experiments from the second workshop on benchmark problems for CAA [3]. Furthermore,

the sound radiation from a dipole and a quadrupole source [5] was calculated using

this code as well. Good results were achieved, especially with the boundary conditions

based on an asymptotic solution.

Finally, a benchmark problem from the third workshop on benchmark problems for CAA

[4] was solved on a non-uniform cartesian mesh using the code for the calculation of rotor

noise. For a rotor with subsonic as well as supersonic tip speed results were found that

showed a good match with the exact solution.

References

[1] C. Lacor, S. Smirnov, M. Baelmans, A finite volume formulation of compact central

schemes on arbitrary structured grids, J. Comput. Phys. 198 (2004) 535-566.

[2] C. K. W. Tam, Numerical Methods in Computational Aeroacoustics, AIAA Short

Course Computational Aeroacoustics: Methods and Applications, Lahaina, Hawaii,

10-11 June 2000.

[3] Second Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

(1996), NASA Conference Publication 3352, Eds. J.C. Hardin, J.R. Ristorcelli and

C.K.W. Tam, J.C. See also NASA CP 3300.

[4] Third Computational Aeroacoustics (CAA) Workshop on Benchmark Problems

(2000), NASA CP 2000-209790.

[5] C. Bailly and D. Juv´e, Numerical Solution of Acoustic Propagation Problems Using

Linearized Euler Equations, AIAA Journal, Vol. 38, No. 1, 2000, pp. 22-29.

Originele taal-2 | English |
---|---|

Titel | Proceedings International Conference for Computational Fluid Dynamics (ICCFD) |

Status | Published - 12 jul 2006 |

Evenement | Unknown - Stockholm, Sweden Duur: 21 sep 2009 → 25 sep 2009 |

### Conference

Conference | Unknown |
---|---|

Land/Regio | Sweden |

Stad | Stockholm |

Periode | 21/09/09 → 25/09/09 |