Modeling Unsteady flow Effects in 3D Throughflow Calculations
The flow field in a transonic multistage compressor is compressible, three-dimensional and highly unsteady and can be predicted in principle by the exact time-accurate Navier-Stokes equations. The high Reynolds number encountered in multistage turbomachinery together with the wall-bounded nature of the flow environment however prevent the use of DNS to solve the exact N-S equations. Unsteady or Steady Reynolds-Averaged Navier-Stokes (URANS/RANS) equations, in which only the averaged impact of the turbulence quantities on the flow is accounted for, are solved instead by resorting to well calibrated turbulence models.
One of the the most widely used computational methods for analysis of turbomachinery flows today is the 3D RANS mixing-plane (MP) model, in which tangentially averaged flow properties are transferred between blade rows. When the MP method is used in a multistage axial compressor, all unsteady effects caused by blade row interactions are lacking, as compared to a URANS method. By writing the averaged-passage flow equations, it is seen that the so-called deterministic stress terms (DS) are missing in the MP case.
We have shown that the DS terms can be, to a reasonable accuracy, predicted by the linearized harmonic approach (LN-S). Results are compared with conventional RANS/URANS results and with measurements. Severe off-design conditions tend to give large unsteady effects and by including the DS terms a better prediction of the averaged flow is obtained. Equally important, the DS terms have been shown to have an effect on flow stability.
To summarize we can say that the main objectives of the project have been reached, i.e. we have found a robust way of computing and including medium scale unsteadiness in the steady-state mixing-plane method. In doing so, we have developed a new alternative method for solving the LN-S equations using a preconditioned GMRES algorithm, which has already been adapted by industry. Further development of the details in the MP and LN-S boundary conditions remains to be investigated before the method can be considered complete.
Deterministic stress terms