## 6.5. Time Transformation

The main advantage of the `Time Transformation` method is that conventional periodicity boundary conditions can be applied directly, resulting in relatively fast convergence.

The Time Transformation method:

- Is valid only for compressible flows

- Is valid only when the pitch ratio between the modeled components does not deviate much from unity

- Requires that the pitch ratio fall within a certain range, as described by the inequality:

  where is the Mach number associated with the rotor rotational speed (or signal speed in the case of an inlet disturbance problem), is the Mach number associated with the circumferential velocity, and the ratio of to is the pitch ratio between the stationary component and the rotating component.

  These limits are not strict, but approaching them can cause solution instability. The CFX-Solver calculates these limits at the start of a simulation and reports them in the output file at the beginning of a run.

For most compressible turbomachinery applications (for example, gas compressors and turbines), is in the range of 0.3 - 0.6, enabling pitch ratios in the range of 0.6 - 1.5 (Giles [217]). If necessary, you can make the pitch ratio fall within the permissible range by strategically choosing the number of passages per component for each of the components.

Note: See Time Transformation in the CFX-Solver Theory Guide for more theoretical information about the Time Transformation method.

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