### 11.6.6. Transient versus Harmonic Solution Method

As mentioned in the theory guide, the turbomachinery flow is usually transient and periodic. Therefore, the harmonic solution method can be applied to converge the flow solution to a steady-periodic state faster than marching the solution in time until a steady-periodic state is reached.

True transient analyses differ from harmonic analyses:

- The flow solution obtained via a time-marching method typically has large frequency content and captures most of the flow characteristics, particularly when not using any pitch-change approximation. The amount of frequency content and flow details captured by transient flow are controlled by the true time-step size or the number of time steps per period.

- For a harmonic analysis, the solution contains only the frequency associated with targeted fundamental frequencies and retained harmonics (see Harmonic Analysis in the CFX-Solver Theory Guide). The targeted fundamental frequency, such as the blade passing frequency, is usually known in advance. Frequencies that are not associated with the blade passing frequency are not known before obtaining the HA solution and therefore will not be captured; they will be filtered out and not be part of the solution.

Additional factors that affect the accuracy and efficiency of the harmonic solution method:

- Number of harmonics retained (M): The more complex the flow features in the transient flow (for example, sharp discontinuities), the greater the number of harmonics that must be retained in order to resolve the flow features. Typically, if the flow contains no discontinuity or translating sharp wakes then a single harmonic is sufficient to resolve the flow. Flow that contains moving discontinuities and/or wakes requires three to five harmonics to be retained. Of course, the more harmonics that are retained, the more expensive the harmonic analysis becomes, reducing efficiency with respect to a true transient simulation.

- Number of pseudo time steps per period: In order to obtain a harmonic solution quickly, the number of pseudo-time steps should be minimized. This can be done by increasing the pseudo-time step size or by lowering the number of pseudo-time steps per period, within limits: an excessively large pseudo-time step and/or small number of pseudo-time steps per period can adversely affect solution stability. The number of pseudo-time steps per period should normally be in the range of 15 to 30.

Note: To properly measure the accuracy and efficiency of the harmonic solution method with respect to the transient time-marching solution method, it is of paramount importance that you run the time-marching solution with a sufficient number of time steps per period (to achieve a time-step-independent solution) and a sufficient number of blade passings or cycles to reach a fully converged steady-periodic state.

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