Numerical simulation of multistage turbine sound generation and propagation

Frequency-domain method for multistage turbomachine tone noise calculation

“…This approach reduces computational domain to a single blade passage for each row. The boundary condition on the periodic boundaries of the first blade passage (for example, the boundary between the first and the second blade passage in the n-th stator) for the q-th harmonic fragment can be written according to equations (5) in the form…”

“…Let the solution in a row is characterized by the set of harmonic fragments, in which for any harmonic the maximum number of harmonic fragments is less or equal to H s(rm) . Then, in order to preserve the number of variables, fields of harmonic fragments at each step can be transformed using equation (5) initially to the fields of harmonics in H s(rm) blade passages of the row (in general arbitrary chosen) and after that in the time domain (including data in ghost cells on the periodic boundaries, obtained using equation (6)). After the calculation of fluxes, the results should be transformed back to the fields of fluxes of harmonic fragments.…”

“…where coefficients S n sj s fqg can be derived from equations (5) and depend only on the number of harmonic and the specified set of harmonic fragments.…”

“…The application of such methods for calculation of tone noise of multistage turbine can be found in literature. 1,5,6 Also the method of multistage interaction calculation, formulated in Vilmin et al, 7 should be referred here, though it takes into account some nonlinear effects. In the previous works of the author, 8,9 the method based on the kinematic relations featuring dependence of flow fields in a turbomachine on time and circumferential angle was proposed and was used for calculation of tone noise of the first booster stage of a fan model.…”