We have developed a computer simulation code for three-dimensional viscous flow in turbomachinery based on the time-averaged compressible Navier–Stokes equations and a low-Reynolds-number k–ε turbulence model. It is described in detail in this paper. The code is used to compute the flow fields for two types of rotor (a transonic fan NASA Rotor 67 and a transonic axial compressor NASA rotor 37), and numerical results are compared to experimental data based on aerodynamic probe and laser anemometer measurements. In the case of Rotor 67, calculated and experimental results are compared under the design speed to validate the code. The calculated results show good agreement with the experimental data, such as the rotor performance map and the spanwise distribution of total pressure, total temperature, and flow angle downstream of the rotor. In the case of Rotor 37, detailed comparisons between the numerical results and the experimental data are made under the design speed condition to assess the overall quality of the numerical solution. Furthermore, comparisons under the part-speed condition are used to investigate a flow field without passage shock. The results are well predicted qualitatively. However, considerable quantitative discrepancies remain in predicting the flow near the tip. In order to assess the predictive capabilities of the developed code, computed flow structures are presented with the experimental data for each rotor and the cause of the discrepancies is discussed.
A two-layer k-ε/algebraic Reynolds stress model (ARSM) has been adopted to the three-dimensional, Reynolds-averaged, Navier-Stokes code to include explicitly the Reynolds stress anisotropy. The code has been used to study the complex flow fields of a transonic axial compressor rotor (i.e., NASA Rotor 37) and a subsonic centrifugal compressor impeller (i.e., the backswept impeller of Krain, first reported in 1988). The computed results have been compared with those from a Baldwin-Lomax model, a low-Reynolds number k-ε turbulence model and actual experimental data. Calculated results for the axial compressor are compared with data reported by Suder in 1994. The suitability of the turbulence model to predict accurately the overall performance of the rotor, spanwise distributions of aerodynamic characteristics, and the wake flow profiles is assessed. Calculations for the centrifugal compressor impeller are compared with the experimental data reported by Hah and Krain in 1989. The usefulness of the turbulence models to predict accurately the overall performance of the impeller, the impeller-exit-velocity profile, and the meridional velocity and flow angle profiles at the cross-channel planes (via L2F measurements) has also been investigated. For modeling the turbulence of both the rotor and the impeller, reasonably good predictions have been obtained with the ARSM and the low-Reynolds number k-ε models, but have not been attainable using the Baldwin-Lomax model. The solutions obtained with the ARSM show better agreement with experimental data than those obtained with the other models. However, in some cases, the predicted differences between the ARSM and the low-Reynolds number k-ε models are not significant. The computed secondary flow and the relative helicity have also been used to investigate the effect of wall curvature and frame rotation on the flow field inside the centrifugal impeller for three operating conditions (i.e., design point, choke, and near surge) and the results are discussed.
A three-dimensional, Reynolds-averaged, compressible Navier-Stokes analysis (using a multi-block grid with the grid embedded in the tip-clearance space) has been developed to study the tip-clearance flow of an axial compressor rotor. A low-Reynolds number k-ε model have been used to reproduce the effects of turbulence. In order to assess the effect of the tip-clearance-grid treatment on prediction for the tip-clearance flow, calculations using a single-block grid (pinched grid topology) and multi-block grid (embedded grid topology) have been performed to calculate the flow field of NASA Rotor 37. The results are compared with experimental data. It has been found that both the single-block and multi-block approaches give a good agreement with the experimental data regarding the overall performance map of the rotor. For the prediction of the spanwise distributions of averaged aerodynamic properties downstream of the rotor, however, the orderly grid over the blade tip associated with the embedded grid has produced accurate predictions particularly from 40% to 80% span. In order to investigate the tip-clearance flow for different operating conditions, calculations have been performed for conditions at 100% (transonic inflow condition) and 60% (subsonic inflow condition) of the design point speed. Computed limiting streamlines at the blade tip surface and particle traces released from the tip-clearance have been used to study the tip-clearance flow. At the 100% speed, both separation and reattachment lines have been observed and a separation bubble occurs. At the 60% speed, the separation line shifts to the blade pressure side and the reattachment line can be partly observed near the leading edge of the blade tip surface. In order to investigate the interaction of the leakage vortex from the tip clearance with the main flow, the computed secondary flows on the cross-flow sections have been analyzed at the 100% and the 60% speeds. At the 100% speed, the vortex core apparently increases in size, as it moves downstream. At 60% speed, the second vortex, first reported by Suder and Celestina in 1994, is barely observable. Furthermore, the trajectory of vortex core identified using a semi-analytical method has also been used to study the vortex motion in the flow field near the blade tip.
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