Specific chorochronic boundary condition

In order to reduce the size of the unsteady harmonic response computations, a specific time-space periodicity boundary condition is used for the turboma­chinery numerical simulations. The cascade is supposed to be made of N ge­ometrically and structurally identical blades. Therefore, using this boundary condition, only a single channel needs to be meshed and computed for various inter-blade phase angles, in order to obtain the values of the unsteady aerody­namic forces for the complete cascade.

The chorochronic boundary condition is applied between the upper and lower boundaries of the channel. This condition reads:

2n

F(x, R,d, t) = F(x, R,d + j — ,t + jo)

where F is any function, 9 the azimuthal angle and a the inter-blade phase angle, a is defined by n 2тг – у where 0 < n < N — 1

In order to reduce the storage, the fbw field at the chorochronic boundaries is simply stored at a reduced number of time steps during the cycle. The field at inner time steps is then rebuilt using a specific time interpolation technique.