### 6.8.4. Case 4: Harmonic Forced Response

The harmonic forced response analysis requires two inputs from the CFD analysis. They are the forcing function due to the unsteady pressure, and the contributions to the aerodynamic damping matrix. In both cases, the information is required in the form of the first harmonic of the surface pressure field on the blade being analyzed. For details, see Harmonic Analysis in the Mechanical APDL Theory Reference.

The forcing function in the harmonic forced response analysis is obtained from transient blade row interactions, while the contributions to the aerodynamic damping matrix is obtained from the blade flutter analysis. You can use either a full-wheel model or a reduced geometry using the Time-Transformation or Fourier-Transformation methods as a pitch-change model. These unsteady pressure values will be exported in the complex form obtained from their Fourier representation. In order for the solver to complete these calculations, you must specify the excitation frequency. The excitation frequency can be specified as an engine order or obtained from the blade vibration frequency. For details, see [Export Surface Name]: Excitation Frequency in the CFX-Pre User's Guide.

The engine order represents the number of disturbances (or pulses) per revolution. Therefore, the excitation frequency can be computed as , where is the excitation frequency, is the engine order, and is the angular velocity of the machine.

For blade flutter cases that have the Periodic Displacement mesh motion option, the CFX-Solver writes the passage number to the field data of the exported data.

- If the periodic mesh displacement input vector components are specified using `Cartesian Components`, then the CFX-Solver will export a profile file that contains both the nodal diameter and mode multiplier, where the value of the mode multiplier is the same as `Scaling`.

- If the periodic mesh displacement input vector components are specified using `Normalised Cartesian Components`, then:

  - In a new case, the CFX-Solver will export a profile file that contains both the nodal diameter and mode multiplier, where mode multiplier is defined as `Amplitude`/`Maximum Displacement`.

  - In an existing case that was made from a release earlier than Release 18.0, the CFX-Solver will export a profile file that does not contain the mode multiplier. However, an existing case can be upgraded as follows:

    1. With the case loaded in CFX-Pre, edit the boundary that has periodic mesh displacement (so that its details view appears).

    2. If the existing case was made from a release earlier than Release 17.2, select the Use Profile Data option (and, if there is more than one profile, select the applicable profile).

    3. Click Apply.

       This updates the case in CFX-Pre by adding the required CCL.

    4. Save the case file (and/or write the solver input file).

       Note that if the above procedure is not followed, the maximum displacement will not be in the solver input file, and the exported profile file will not contain the mode multiplier.

Note: When exporting complex pressures on a boundary with mesh motion (for example, a Fourier Transformation blade flutter case), the results will be exported using the initial mesh coordinates from the CFX-Solver run.

Note: CFX and Mechanical use different representations for harmonic pressure loads, , where pressure is a function of time .

CFX represents harmonic pressure loads using real-number Fourier coefficients as:

| (6–3)

where represents the index of the mode, represents the total number of modes, and represent the real-number Fourier coefficients, and represents the base frequency.

In contrast, Mechanical represents harmonic pressure loads using imaginary and real pressure components as:

| (6–4)

where and represent the real and imaginary pressure components, respectively, of the contribution for mode , and represents the real, time averaged, value.

By comparing Equation 6–3 and Equation 6–4, it can be seen that is analogous to , while is analogous to .

When exporting to Mechanical, CFX exports and .

For more details, see Harmonic Analysis in the Mechanical APDL Theory Reference.

Release 18.2 - © ANSYS, Inc. All rights reserved.