Goldstein analogy

Error

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Description

This treatment predicts in-duct acoustic fluctuations and in-duct acoustic power for a rotor-stator configuration using Goldstein’s analogy.

The sources that are propagated are the fluctuations of static pressure over rotor blades or stator vanes. They can be obtained by performing a Discrete Fourier Transform (DFT) treatment. Once the DFT is done, the harmonics are stored in the instants of the base. In this treatment, it is assumed that the numbering of the harmonics is the one obtained after performing the DFT over a complete rotation (i.e. the harmonic H01 is the rotation harmonic). If the rotor has 22 blades, the BPF harmonic should therefore be numbered H22.

The DFT used for the sources must respect the convention described below (the one used in Antares DFT treatment). If \(W_n\) (\(n = 0 ... N-1\) with \(N\) the number of instants) denotes the time series of the variable of interest, then the harmonic \(\hat{W_k}\) is given by:

• \(\hat{W_k} = \frac{2}{N} \sum_{n=0}^{k=N-1} W_n \exp(-i 2\pi k n / N)\) if k > 0,

• \(\hat{W_k} = \frac{1}{N} \sum_{n=0}^{k=N-1} W_n \exp(-i 2\pi k n / N)\) if k = 0.

Parameters

• base: Base, default= None

  The base that contains the acoustic sources that will be propagated using Goldstein’s analogy. It should correspond to the field of the DFT of acoustic pressure over rotor blades or stator vanes. It can contain multiple zones and the harmonics should be stored in the different instants of the base. It is assumed that the numbering of the harmonics is done with 2 digits (e.g. H01 for the first harmonic) and after performing the DFT over a complete rotation. For example, if the rotor has 22 blades, the BPF harmonic is the harmonic H22. If ‘dtype_in’ is ‘mod/phi’, then the corresponding instant names should be ‘H22_mod’ and ‘H22_phi’. If it is ‘im/re’, then they should be ‘H22_re’ and ‘H22_im’. To compute the noise from stator sources at \(n^{th}\) BPF harmonic, the sources at \(n^{th}\) BPF harmonic must be given. For example, for 22 rotor blades, H22 and H44 must be given if one wants to compute the noise at the first two BPF harmonics. However, to compute the noise from rotor sources at \(n^{th}\) BPF harmonic, the sources at all rotation harmonics, including the \(0^{th}\) i.e. the mean part (instant named ‘mean’), must be given. This is due to frequency shifts caused by the rotation of the rotor. The harmonics that are not given are assumed to be zero.

• dtype_in: str, default: ‘im/re’

  The decomposition type of the input pressure data (which must result from a DFT): ‘mod/phi’ for modulus/phase decomposition or ‘im/re’ for imaginery/real part decomposition. If given, the phase must be expressed in degrees.

• pressure_variable: str, default: ‘psta’

  Name of the pressure variable.

• rotation_velocity: float, default: 0.0

  Rotation speed of the rotor expressed in radians per second.

• density: float, default: 1.18

  Density of the mean flow.

• mach: float, default: 0.0

  Mach number of the mean flow.

• speed_of_sound: float, default: 346.0

  Speed of sound of the mean flow.

• nb_blades: list(int), default: None

  List of two integers defining the number of rotor blades and the number of stator vanes.

• duct_radius: list(float), default: None

  List of two floats defining the hub radius and the tip radius.

• source_type: str: default: None

  The type of source (‘rotor’ or ‘stator’).

• homogeneous_source: bool, default: True

  True if the sources are given for one blade/vane and need to be duplicated considering an ideal phaselag.

• nb_harmonics: int, default: 1

  Number of BPF harmonics to compute.

• mode_max: list(int), default: None

  List defining the maximum azimuthal mode order and the maximum radial mode order to consider.

• export_field: bool, default: True

  True if the 3D acoustic field needs to be exported.

• dtype_out: str, default: ‘im/re’

  The decomposition type used for the exported 3D acoustic field: ‘mod/phi’ for modulus/phase decomposition or ‘im/re’ for imaginery/real part decomposition. If given, the phase is expressed in degrees. Useful only when export_field is set to True.

• evanescent_mode: bool, default: False

  True if the evanescent modes are included in the exported 3D acoustic field. Useful only when export_field is set to True.

• x_duct: list(int), default: [0, 1]

  List defining the inlet and the outlet axial coordinate. Useful when export_field is set to True.

• field_discretization: list(int), default: [100, 25, 180]

  List defining the number of points in the axial, radial and azimuthal directions of the grid describing the 3D acoustic field. Useful when export_field is set to True.

Postconditions

The treatment returns one base (if export_field is False) or two bases (if export_field is True).

The first base contains the acoustic power results. It has one zone and nb_harmonics instants (one per computed BPF harmonic, named ‘Hxx’ where xx is the number of the harmonic). In each instant, the upstream and downstream acoustic power of the corresponding harmonic is stored in the attrs ‘P_up’ and ‘P_dn’ respectively. Each instant also contains the upstream and downstream acoustic power of each mode. Four variables are then written: ‘m’ the azimuthal mode order, ‘j’ the radial mode order, ‘Pmj_up’ the upstream acoustic power of the mode (m, j) and ‘Pmj_dn’ the downstream acoustic power of the mode (m, j).

The second base (exported only if export_field is True) contains the acoustic field resulting from the given sources. It has one zone and 2* nb_harmonics instants (two per computed BPF harmonic: ‘Hxx_mod’ and ‘Hxx_phi’ if dtype_out is ‘mod/phi’ or ‘Hxx_re’ and ‘Hxx_im’ if dtype_out is ‘im/re’). Each instant contains the coordinates of the reconstructed grid (‘x’, ‘y’, ‘z’) and both the acoustic pressure ‘p’ and the acoustic axial velocity ‘u’ at the corresponding harmonic.