A Model of Inlet Circumferential Fluctuation in Compressor Cascades

To figure out the flow field inside a turbomachine, numerically solving the fully three-dimensional Navier-Stokes equations will be an option. However, this will consume a large amount of calculation resource. Besides, during the design and optimization processes, iterative calculation is required. Thus, complete Navier-Stokes equations cannot be used for rapid analysis or to shorten developing period, while through-flow method is capable of these. Due to fast calculation and correctability through empirical formulas, through-flow method is still extensively used by designers.

Circumferentially-averaging method is one of the through-flow methods. Based on Navier-Stokes equations in cylindrical coordinates, the governing equations of circumferentially-averaging method are obtained. During the circumferentially averaging process, some extra terms will be produced, such as inviscid blade force term, viscous blade force term and circumferential fluctuation source term (CFST). In 1966, Smith believed that CFST is negligible when the blades are under low load. In 1976, Hirsch mentioned in his study that CFST did influence flow field, but model of CFST was not established yet. In 2007, by through-flow model, Simon discovered that considering some components of CFST or not could make a moderate difference to the calculation result. Recent study showed more attention to CFST. An accurate model of CFST can help circumferentially averaging through-flow method predict flow field more accurate, especially when the blades possess apparent three-dimensional features such as sweep and lean. However, models of CFST so far are rather few or too simplified to use. This paper presents an Algebraic statistical model of CFST with relative high accuracy and good value in engineering practice.

Firstly, this paper set dozens of three-dimensional numerical examples of linear cascade considering cambers, sweep angles, inlet Mach numbers and incidences as independent variables. Secondly, a circumferentially averaging post-processing program was employed to get CFST and circumferentially averaged flow field. Thirdly, by analyzing the trend of CFST, comparing those four independent variables and their interactions, a model of CFST was established. Lastly, several numerical examples were provided for accuracy verification of this model.

The analysis result showed that before the blade leading edge, there is no inviscid blade force or viscous blade force, but circumferential fluctuation already exists. This indicates that CFST plays an important role in this area and requires an accurate model to be predicted. Generally, among all three components of CFST, axial component is the largest, reaching 90 percent of the norm of CFST, while the radial and circumferential component are relatively small. However, when sweep angle increases up to 10 degree or above, radial component increases to the same order of magnitude as axial component. All those three components increase with inlet Mach number. Axial and radial components also increase when the absolute value of incidence increases, while the correlation between circumferential component and incidence is rather complex. Verification of this model suggests that within the common scope of use of aerospace compressor designing, this model shows a good accuracy, with a maximum error below ten percent.