# On Multistage Analysis of Transonic Compressors: From Axisymmetric Throughflow Time-Marching to Unsteady Three-Dimensional Methods

[Doktorsavhandling]

A throughflow time-marching finite-volume solver, capable of computing viscous transonic multistage compressor flows with embedded shocks, is presented. The behavior of the blade model, based on the blade mean surface flow tangency condition, was investigated for transonic flows. The captured passage shock was found to be treated as a normal blade passage shock by the blade model. The choke mass flow prediction was improved by introducing an alternative blade blockage based on a streamtube approach. Two techniques for solving the numerical problems associated with the leading edge singularity in case of incidence are described. Effects due to deviation, secondary losses, endwall skin friction and spanwise mixing are also modeled. The various models, once calibrated on two single stage transonic compressor test cases, were validated on a three-stage transonic model fan. The calculated speed-line performance agreed well with the measured data.

To assess the three-dimensional flow departure from the axisymmetry assumption, the tangential spatial perturbation stress terms were derived from the circumferential average of 3D computations of the Nasa 67 transonic rotor. A meridional picture of each of the averaged stresses is given for two flow conditions, near-stall and near-peak efficiency. With the source terms derived from the near-peak efficiency 3D solution, several throughflow computations were carried out to study the influence on the meridional flow of the averaged viscous stresses and of each spatial perturbation stress. The spatial stresses were found to be the main contributors to the blade passage losses and the spanwise mixing phenomenon in comparison with the viscous stresses. The relative importance study of each perturbation term showed that a few of them exert a significant influence on flow angles and losses in the tip region.

In order to compare the throughflow multistage calculations with their 3D counterparts, a multistage 3D computation of the three-stage fan speed-line was performed using a mixing plane approach. The tangential average of the near-peak efficiency fan 3D solution was compared with a throughflow computation regarding entropy increase and flow angles. The throughflow solution was found to yield an overprediction of shock losses in the first rotor because of a leading edge singularity related problem. Two alternatives to the original blade model were studied. The first is based on a prescribed blade loading distribution which yields a meridional flow similar to the tangentially averaged 3D flow but requires additional shock loss correlations. The second is based on applying the usual blade model for most of the blade chord, except for the first 20 % where a distributed blade loading is applied. This model proved to alleviate the leading edge singularity problem and still enables one to capture shocks and compute choked-flow conditions.

An unsteady calculation of the IGV and first stage of the transonic model fan was carried out in order to assess the reliability of the steady 3D multistage computational method. The steady and time-averaged flows were compared and the differences found were interpreted in terms of the so-called deterministic stresses. An evaluation of the spatial and temporal correlations, in accordance with the deterministic stress tensor decomposition of Adamczyk, was carried out for the rotor flow.

**Nyckelord: **transonic, fan, axisymmetric, throughflow, modelling, finite-volume, time-marching, body force, shock, singularity, viscous, 3D, perturbation, multistage, mixing-plane, unsteady, average-passage, deterministic, stress

Denna post skapades 2006-08-25. Senast ändrad 2013-09-25.

CPL Pubid: 791